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26 pages, 5179 KiB  
Article
Thermally Induced Phenomena in Amorphous Nifedipine: The Correlation Between the Structural Relaxation and Crystal Growth Kinetics
by Roman Svoboda
Molecules 2025, 30(1), 175; https://doi.org/10.3390/molecules30010175 - 4 Jan 2025
Viewed by 563
Abstract
The particle size-dependent processes of structural relaxation and crystal growth in amorphous nifedipine were studied by means of non-isothermal differential scanning calorimetry (DSC) and Raman microscopy. The enthalpy relaxation was described in terms of the Tool–Narayanaswamy–Moynihan model, with the relaxation motions exhibiting the [...] Read more.
The particle size-dependent processes of structural relaxation and crystal growth in amorphous nifedipine were studied by means of non-isothermal differential scanning calorimetry (DSC) and Raman microscopy. The enthalpy relaxation was described in terms of the Tool–Narayanaswamy–Moynihan model, with the relaxation motions exhibiting the activation energy of 279 kJ·mol−1 for the temperature shift, but with a significantly higher value of ~500 kJ·mol−1 being obtained for the rapid transition from the glassy to the undercooled liquid state (the latter is in agreement with the activation energy of the viscous flow). This may suggest different types of relaxation kinetics manifesting during slow and rapid heating, with only a certain portion of the relaxation motions occurring that are dependent on the parameters of a given temperature range and time frame. The DSC-recorded crystallization was found to be complex, consisting of four sub-processes: primary crystal growth of αp and βp polymorphs, enantiotropic βp → βp′ transformation, and βpp′ → αp recrystallization. Overall, nifedipine was found to be prone to the rapid glass-crystal growth that occurs below the glass transition temperature; a tendency of low-temperature degradation of the amorphous phase markedly increased with decreasing particle size (the main reason being the increased number of surface and bulk micro-cracks and mechanically induced defects). The activation energies of the DSC-monitored crystallization processes varied in the 100–125 kJ·mol−1 range, which is in agreement with the microscopically measured activation energies of crystal growth. Considering the potential correlations between the structural relaxation and crystal growth processes interpreted within the Transition Zone Theory, a certain threshold in the complexity and magnitude of the cooperating regions (as determined from the structural relaxation) may exist, which can lead to a slow-down of the crystal growth if exceeded. Full article
(This article belongs to the Special Issue Exclusive Feature Papers in Physical Chemistry, 2nd Edition)
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Figure 1

Figure 1
<p>(<b>A</b>–<b>F</b>) DSC curves obtained for differently sized NIF powders at heating rates <span class="html-italic">q<sup>+</sup></span> = 0.5–20 °C·min<sup>−1</sup>. Exothermic effects evolve in the upwards direction. The DSC curves were shifted along the Y axis to enhance the clarity.</p>
Full article ">Figure 2
<p>(<b>A</b>–<b>D</b>) DSC curves obtained for the 50–125 μm and 500–1000 μm NIF powders at heating rates <span class="html-italic">q<sup>+</sup></span> = 0.5–20 °C·min<sup>−1</sup>. Graphs (<b>B</b>,<b>D</b>) are zoomed in on the crystallization peaks measured at the lowest <span class="html-italic">q<sup>+</sup></span>. Exothermic effects evolve in the upwards direction. The DSC curves were shifted along the Y axis to enhance the clarity.</p>
Full article ">Figure 3
<p>(<b>A</b>) DSC curves obtained for different NIF powders at <span class="html-italic">q<sup>+</sup></span> = 0.5 °C·min<sup>−1</sup>—the graph is zoomed in on the glass transition region. The purple curves show the original measurements, during which nucleation and crystal growth occurred already during the idle period in the DSC autosampler. (<b>B</b>–<b>D</b>) Kissinger plots constructed for the <span class="html-italic">T<sub>g</sub></span>, <span class="html-italic">T<sub>p</sub></span><sub>1</sub>, and <span class="html-italic">T<sub>p</sub></span><sub>2</sub> quantities. (<b>E</b>,<b>F</b>) Crystallization and melting enthalpies obtained for the NIF powders in dependence on <span class="html-italic">q<sup>+</sup></span> and <span class="html-italic">d<sub>aver</sub></span>.</p>
Full article ">Figure 4
<p>(<b>A</b>) A set of CR cycles obtained for the re-melted NIF powder. The exothermic effects evolve in the upward direction. The arrows and symbols <span class="html-italic">q<sup>−</sup></span> and <span class="html-italic">q<sup>+</sup></span> denote the parts of the DSC data in which the cooling and heating steps of the CR cycles are shown, respectively. Absolute magnitudes of <span class="html-italic">q<sup>−</sup></span> and <span class="html-italic">q<sup>+</sup></span> being applied in the corresponding steps of the cyclic program increase in the directions of the given arrows. (<b>B</b>) DSC data for the CR cycles zoomed in on the heating steps performed at low <span class="html-italic">q<sup>+</sup></span>. (<b>C</b>) A set of CHR cycles obtained for the re-melted NIF powder; only the data corresponding to the already normalized heating curves are shown. The arrows denote the increase in |<span class="html-italic">q<sup>−</sup></span>| in the cooling step preceding to the depicted heating step.</p>
Full article ">Figure 5
<p>(<b>A</b>) DSC curve measured for the amorphous 180–250 μm NIF powder at 1 °C·min<sup>−1</sup> (red data; top and right axes), where the letters A–F denote specific positions (defined by the corresponding temperatures) on the DSC curve. The Raman spectra then correspond to these characteristic events (as denoted by the arrows and letters) on the DSC curve (black data; bottom and left axes). (<b>B</b>,<b>C</b>) Optical micrographs of NIF crystals grown at high <span class="html-italic">q</span><sup>+</sup>.</p>
Full article ">Figure 6
<p>(<b>A</b>) Evaluation of Δ<span class="html-italic">h<sup>*</sup></span> from the CR cycles – points represent experimental data and line is their linear fit. (<b>B</b>) Evaluation of Δ<span class="html-italic">h<sup>*</sup></span> from the CHR cycles – points represent experimental data and lines are their linear fits in two different temperature regions (see text for details). (<b>C</b>) The application of the simulation-comparative method to the CHR relaxation measurements of the amorphous NIF. Points correspond to the experimental data. Black solid lines refer to simulated data for the various combinations of the TNM parameters <span class="html-italic">β</span> and <span class="html-italic">x</span> (both parameters changing with the 0.1 step). Colored line refers to the simulated <span class="html-italic">β</span> + <span class="html-italic">x</span> combination best fitting the experimental data.</p>
Full article ">Figure 7
<p>(<b>A</b>) Activation energies calculated for the three characteristic temperatures based on the Kissinger plots (<a href="#molecules-30-00175-f003" class="html-fig">Figure 3</a>B–D). (<b>B</b>) An example of the NIF crystallization DSC curve (125–180 μm at 10 °C·min<sup>−1</sup>) deconvoluted by means of the sc-MKA method. (<b>C</b>) Crystallization enthalpies obtained via sc-MKA method for the NIF powders (the data are averaged over all <span class="html-italic">q<sup>+</sup></span>). (<b>D</b>) AC kinetic parameters obtained via sc-MKA method for the DSC crystallization data of the NIF powders (the data are averaged over all <span class="html-italic">q<sup>+</sup></span>). The lines (scaled according to the top axis) indicate the fingerprint <span class="html-italic">M</span> + <span class="html-italic">N</span> combinations attributed to the various values of the kinetic exponent of the JMA model.</p>
Full article ">Figure 8
<p>(<b>A</b>) Temperature dependences of different crystal growth modes (taken from [<a href="#B70-molecules-30-00175" class="html-bibr">70</a>]). Points represent experimental data, lines indicate second-order polynomial fits. (<b>B</b>) Temperature dependences of dynamic viscosity (black data and left Y axis) and dielectric relaxation time (red data and right Y axis) taken from [<a href="#B42-molecules-30-00175" class="html-bibr">42</a>,<a href="#B71-molecules-30-00175" class="html-bibr">71</a>]. Points represent experimental data, lines indicate second-order polynomial fits. (<b>C</b>) Comparison of temperature dependences of activation energies determined for different processes occurring in amorphous NIF.</p>
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22 pages, 4619 KiB  
Article
Contribution of Protonation to the Dielectric Relaxation Arising from Bacteriopheophytin Reductions in the Photosynthetic Reaction Centers of Rhodobacter sphaeroides
by Gábor Sipka and Péter Maróti
Biomolecules 2024, 14(11), 1367; https://doi.org/10.3390/biom14111367 - 27 Oct 2024
Viewed by 860
Abstract
The pH dependence of the free energy level of the flash-induced primary charge pair P+IA was determined by a combination of the results from the indirect charge recombination of P+QA and from the delayed fluorescence [...] Read more.
The pH dependence of the free energy level of the flash-induced primary charge pair P+IA was determined by a combination of the results from the indirect charge recombination of P+QA and from the delayed fluorescence of the excited dimer (P*) in the reaction center of the photosynthetic bacterium Rhodobacter sphaeroides, where the native ubiquinone at the primary quinone binding site QA was replaced by low-potential anthraquinone (AQ) derivatives. The following observations were made: (1) The free energy state of P+IA was pH independent below pH 10 (–370 ± 10 meV relative to that of the excited dimer P*) and showed a remarkable decrease (about 20 meV/pH unit) above pH 10. A part of the dielectric relaxation of the P+IA charge pair that is not insignificant (about 120 meV) should come from protonation-related changes. (2) The single exponential decay character of the kinetics proves that the protonated/unprotonated P+IA and P+QA states are in equilibria and the rate constants of protonation konH +koffH are much larger than those of the charge back reaction kback ~103 s−1. (3) Highly similar pH profiles were measured to determine the free energy states of P+QA and P+IA, indicating that the same acidic cluster at around QB should respond to both anionic species. This was supported by model calculations based on anticooperative proton distribution in the cluster with key residues of GluL212, AspL213, AspM17, and GluH173, and the effect of the polarization of the aqueous phase on electrostatic interactions. The larger distance of IA from the cluster (25.2 Å) compared to that of QA (14.5 Å) is compensated by a smaller effective dielectric constant (6.5 ± 0.5 and 10.0 ± 0.5, respectively). (4) The P* → P+QA and IAQA → IAQA electron transfers are enthalpy-driven reactions with the exemption of very large (>60%) or negligible entropic contributions in cases of substitution by 2,3-dimethyl-AQ or 1-chloro-AQ, respectively. The possible structural consequences are discussed. Full article
(This article belongs to the Special Issue New Insights into the Membranes of Anoxygenic Phototrophic Bacteria)
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<p>Structural view of the hydrophobic belt of the isolated RC from anoxygenic photosynthetic bacterium <span class="html-italic">Rhodobacter sphaeroides</span> sandwiched by aqueous phases (water molecules) at the cytoplasmic and periplasmic sides. The pairs of cofactors BChl dimer (P), monomeric BChls (B), bacteriopheophytins (I), and quinones (Q)) are arranged in active (A) and passive (B) branches. The protonation of the acidic cluster around Q<sub>B</sub> plays a crucial role in the stabilization of light-induced anions in the RC. The distances of I<sub>A</sub> and Q<sub>A</sub> from the key residue in the cluster GluL212 are indicated. ChimeraX was used to visualize the RC of the model organism <span class="html-italic">Rb. sphaeroides</span> (PDB ID: 3I4D) [<a href="#B6-biomolecules-14-01367" class="html-bibr">6</a>].</p>
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<p>The standard free energy levels of ground (PI<sub>A</sub>Q<sub>A</sub>) and charge-separated (P<sup>+</sup>I<sub>A</sub><sup>−</sup> and P<sup>+</sup>Q<sub>A</sub><sup>−</sup>) states, referring to that of the photoexcited singlet BChl dimer (P*), and the possible transitions between different states in the RC from purple photosynthetic bacterium <span class="html-italic">Rba.</span> <span class="html-italic">sphaeroides</span>. The native ubiquinone (UQ<sub>10</sub>) at the primary quinone binding site is substituted by a series of low-potential quinones whose chemical structures and in situ midpoint electrochemical potentials (<span class="html-italic">E</span><sub>m</sub>) at pH 8.0 are demonstrated. The dimer P is photoexcited (wavy arrow) and the main path of P* decay is electron transfer (<span class="html-italic">k</span><sub>et</sub>) to Q<sub>A</sub> via a transient reduction in I<sub>A</sub>. The charge pair can be stabilized by conformational heterogeneity (closely spaced thick lines), protein relaxation (shaded area), and proton uptake. The separated charges of the P<sup>+</sup>I<sub>A</sub>Q<sub>A</sub><sup>−</sup> state can be either recombined through direct or indirect pathways or can repopulate P*, which can decay through fluorescence emissions with the intrinsic rate constant <span class="html-italic">k</span><sub>f</sub> (delayed fluorescence).</p>
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<p>Models and demonstration of the drop in the effective dielectric constant between interactive groups (Q<sub>A</sub> (1), I<sub>A</sub> (2) and the acidic cluster (3)) in the RC upon an increase in the characteristic distance (<span class="html-italic">x</span>) from the aqueous phase. The dielectric (water) interface is represented either by a single planar boundary (<b>A</b>) or by a sandwich-type double parallel sheet (<b>C</b>). Panels (<b>B</b>,<b>D</b>) show the calculated results of models A and C, respectively. The variable <span class="html-italic">x</span> denotes either the distance of Q<sub>A</sub> and the cluster from the dielectric (water) interface (model A) or the width of the RC between the parallel boundaries (model C). Numerical values: <span class="html-italic">R</span><sub>13</sub> = 14.5 Å (distance between Q<sub>A</sub> and GluL212, PDB ID: 3I4D) and <span class="html-italic">R</span><sub>23</sub> = 25.2 Å (distance between I<sub>A</sub> and GluL212, PDB ID: 3I4D), and the dielectric constants of water (<span class="html-italic">D</span><sub>w</sub>) and the RC protein (<span class="html-italic">D</span><sub>RC</sub>) are 80 and 2, respectively.</p>
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<p>Kinetics of flash-induced absorption change (at 430 nm, <b>top</b>) and delayed fluorescence (at 910 nm, <b>bottom</b>) of RC (concentration 1.5 μM) where the native ubiquinone at Q<sub>A</sub> is replaced by 1-chloro-AQ.</p>
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<p>The pH dependence of the rate constant of the P<sup>+</sup>Q<sub>A</sub><sup>−</sup> → PQ<sub>A</sub> charge recombination of RCs with native quinone (ubiquinone) (<b>bottom</b>) and anthraquinone (<b>top</b>) at the Q<sub>A</sub> binding site. Conditions are the same as in <a href="#biomolecules-14-01367-f004" class="html-fig">Figure 4</a>, except for the varying pH and buffers given in M&amp;M.</p>
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<p>pH-dependence of the free energy states of P<sup>+</sup>IQ<sub>A</sub><sup>−</sup> relative to that of P<sup>+</sup>I<sub>A</sub><sup>−</sup>Q<sub>A</sub> determined from the rate constants of the temperature-dependent P<sup>+</sup>I<sub>A</sub>Q<sub>A</sub><sup>−</sup> → PQ<sub>A</sub> indirect charge recombination kinetics via P<sup>+</sup>I<sub>A</sub><sup>−</sup>Q<sub>A</sub>. The native UQ<sub>10</sub> at Q<sub>A</sub> was replaced by derivatives of the low-potential AQ: <span style="color:#00FF00">■</span> 2,3-dimethyl-AQ; <span style="color:#FF00FF">■</span> 1-amino-AQ; <span style="color:#3333FF">■</span> 2-methyl-AQ; <span style="color:#66FFFF">■</span> 2-ethyl-AQ; <span style="color:#FF0000">■</span> AQ; <span style="color:#000000">■</span> 1-chloro-AQ; Conditions: 1 μM RC, 0.4 mM buffer (Mes, Tris, Caps, Ches, Mops), 0.03% LDAO, and 100 mM NaCl.</p>
Full article ">Figure 7
<p>pH dependence of the free energy states of P<sup>+</sup>Q<sub>A</sub><sup>−</sup> relative to that of P*Q<sub>A</sub> determined from the measurement of the delayed fluorescence of the BChl dimer (set of lower traces) and the pH dependence of the free energy states of P<sup>+</sup>I<sub>A</sub><sup>−</sup> relative to that of P*I<sub>A</sub> determined from the difference in the lower traces and data in <a href="#biomolecules-14-01367-f003" class="html-fig">Figure 3</a>: Δ<span class="html-italic">G</span><sup>o</sup>(P*I<sub>A</sub> → P<sup>+</sup>I<sub>A</sub><sup>−</sup>) = Δ<span class="html-italic">G</span><sup>o</sup>(P*Q<sub>A</sub> → P<sup>+</sup>Q<sub>A</sub><sup>−</sup>) − Δ<span class="html-italic">G</span><sup>o</sup>(P<sup>+</sup>I<sub>A</sub><sup>−</sup>Q<sub>A</sub> → P<sup>+</sup>I<sub>A</sub>Q<sub>A</sub><sup>−</sup>) (set of upper traces) in the RCs of substituted different AQ derivatives at the Q<sub>A</sub> binding site. <span style="color:#00FF00">■</span> 2,3-dimethyl-AQ; <span style="color:#FF00FF">■</span> 1-amino-AQ; <span style="color:#3333FF">■</span> 2-methyl-AQ; <span style="color:#66FFFF">■</span> 2-ethyl-AQ; <span style="color:#FF0000">■</span> AQ; <span style="color:#000000">■</span> 1-chloro-AQ; Conditions are the same as in <a href="#biomolecules-14-01367-f003" class="html-fig">Figure 3</a>.</p>
Full article ">Figure 8
<p>Temperature dependence of the delayed fluorescence of the BChl dimer (van’t Hoff plot) in RCs where the native UQ<sub>10</sub> at the Q<sub>A</sub> binding site is replaced by different low-potential forms of AQ: <span style="color:#3333FF">■</span> 2-methyl-AQ; <span style="color:#000000">■</span> 1-chloro-AQ; <span style="color:#FF00FF">■</span> 1-amino-AQ; <span style="color:#FF0000">■</span> AQ; <span style="color:#66FFFF">■</span> 2-ethyl-AQ; <span style="color:#00FF00">■</span> 2,3-dimethyl-AQ.</p>
Full article ">Figure 9
<p>High pH dependence of the measured (data points from <a href="#biomolecules-14-01367-f007" class="html-fig">Figure 7</a>) and calculated (solid lines, M&amp;M) free energies of Q<sub>A</sub>/Q<sub>A</sub><sup>−</sup> and I<sub>A</sub>/I<sub>A</sub><sup>−</sup>, referring to those at pH 8 when Q<sub>A</sub> is the native UQ (black) or is substituted by 1-amino-AQ (blue for Q<sub>A</sub>/Q<sub>A</sub><sup>−</sup> and green for I<sub>A</sub>/I<sub>A</sub><sup>−</sup>). The parameters of the calculated curves are given in <a href="#biomolecules-14-01367-t002" class="html-table">Table 2</a>.</p>
Full article ">Figure 10
<p>Surface exposure of I<sub>A</sub> and its connection to the Q<sub>A</sub> pocket. The solvent-accessible cavities of the RC of <span class="html-italic">Rba. sphaeroides</span> (PDB ID: 3I4D) were visualized with ChimeraX [<a href="#B6-biomolecules-14-01367" class="html-bibr">6</a>]. For clarity, the pythol tail of the I<sub>A</sub> and the isoprenyl subunits of the Q<sub>A</sub> are not shown.</p>
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13 pages, 5074 KiB  
Article
Docking, MD Simulations, and DFT Calculations: Assessing W254’s Function and Sartan Binding in Furin
by Nikitas Georgiou, Thomas Mavromoustakos and Demeter Tzeli
Curr. Issues Mol. Biol. 2024, 46(8), 8226-8238; https://doi.org/10.3390/cimb46080486 - 30 Jul 2024
Viewed by 916
Abstract
Furins are serine endoproteases that are involved in many biological processes, where they play important roles in normal metabolism, in the activation of various pathogens, while they are a target for therapeutic intervention. Dichlorophenyl-pyridine “BOS” compounds are well known drugs that are used [...] Read more.
Furins are serine endoproteases that are involved in many biological processes, where they play important roles in normal metabolism, in the activation of various pathogens, while they are a target for therapeutic intervention. Dichlorophenyl-pyridine “BOS” compounds are well known drugs that are used as inhibitors of human furin by an induced-fit mechanism, in which tryptophan W254 in the furin catalytic cleft acts as a molecular transition energy gate. The binding of “BOS” drug into the active center of furin has been computationally studied using the density functional theory (DFT) and ONIOM multiscaling methodologies. The binding enthalpies of the W254 with the furin-BOS is −32.8 kcal/mol (“open”) and −18.8 kcal/mol (“closed”), while the calculated torsion barrier was found at 30 kcal/mol. It is significantly smaller than the value of previous MD calculations due to the relaxation of the environment, i.e., nearby groups of the W254, leading to the reduction of the energy demands. The significant lower barrier explains the experimental finding that the dihedral barrier of W254 is overcome. Furthermore, sartans were studied to evaluate their potential as furin inhibitors. Sartans are AT1 antagonists, and they effectively inhibit the hypertensive effects induced by the peptide hormone Angiotensin II. Here, they have been docked into the cavity to evaluate their effect on the BOS ligand via docking and molecular dynamics simulations. A consistent binding of sartans within the cavity during the simulation was found, suggesting that they could act as furin inhibitors. Finally, sartans interact with the same amino acids as W254, leading to a competitive binding that may influence the pharmacological efficacy and potential drug interactions of sartans. Full article
(This article belongs to the Special Issue Synthesis and Theoretical Study of Bioactive Molecules)
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<p>Chemical structures of (<b>a</b>) sartans, (<b>b</b>) furin enzyme, (<b>c</b>) BOS-318 ligand, and (<b>d</b>) tryptophan amino acid. (C atoms: grey balls, H: white, O: red, N: blue, F: cyan, Cl: green).</p>
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<p>Optimized conformations of furin–BOS complex with “open” and “closed” conformation of W254 amino acids via ONIOM(M06-2X/6-311+G(d,p):PM6) method.</p>
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<p>Interactions of losartan with 7LCU in (<b>a</b>) 2D and (<b>b</b>) 3D presentation.</p>
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<p>Interactions of Benzimidazole bis-N,N′-biphenyltetrazole with 7LCU in (<b>a</b>) 2D and (<b>b</b>) 3D presentation.</p>
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<p>Interactions of BV6 with 7LCU in (<b>a</b>) 2D and (<b>b</b>) 3D presentation.</p>
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<p>Interactions of candesartan with 7LCU in (<b>a</b>) 2D and (<b>b</b>) 3D presentation.</p>
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<p>Interactions of losartan carboxylic acid with 7LCU in (<b>a</b>) 2D and (<b>b</b>) 3D presentation.</p>
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<p>Interactions of nirmitrevil with 7LCU in (<b>a</b>) 2D and (<b>b</b>) 3D presentation.</p>
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<p>Interactions of telmisartan with 7LCU in (<b>a</b>) 2D and (<b>b</b>) 3D presentation.</p>
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<p>Interactions of benzimidazole-N-biphenyltetrazole with 7LCU in (<b>a</b>) 2D and (<b>b</b>) 3D presentation.</p>
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<p>Protein’s Ca atoms display a RMSD value &lt;8.0 Å. Blue line for the protein and red line for the ligand.</p>
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24 pages, 28885 KiB  
Article
Dimerization of the β-Hairpin Membrane-Active Cationic Antimicrobial Peptide Capitellacin from Marine Polychaeta: An NMR Structural and Thermodynamic Study
by Pavel A. Mironov, Alexander S. Paramonov, Olesya V. Reznikova, Victoria N. Safronova, Pavel V. Panteleev, Ilia A. Bolosov, Tatiana V. Ovchinnikova and Zakhar O. Shenkarev
Biomolecules 2024, 14(3), 332; https://doi.org/10.3390/biom14030332 - 11 Mar 2024
Cited by 3 | Viewed by 1892
Abstract
Capitellacin is the β-hairpin membrane-active cationic antimicrobial peptide from the marine polychaeta Capitella teleta. Capitellacin exhibits antibacterial activity, including against drug-resistant strains. To gain insight into the mechanism of capitellacin action, we investigated the structure of the peptide in the membrane-mimicking environment [...] Read more.
Capitellacin is the β-hairpin membrane-active cationic antimicrobial peptide from the marine polychaeta Capitella teleta. Capitellacin exhibits antibacterial activity, including against drug-resistant strains. To gain insight into the mechanism of capitellacin action, we investigated the structure of the peptide in the membrane-mimicking environment of dodecylphosphocholine (DPC) micelles using high-resolution NMR spectroscopy. In DPC solution, two structural forms of capitellacin were observed: a monomeric β-hairpin was in equilibrium with a dimer formed by the antiparallel association of the N-terminal β-strands and stabilized by intermonomer hydrogen bonds and Van der Waals interactions. The thermodynamics of the enthalpy-driven dimerization process was studied by varying the temperature and molar ratios of the peptide to detergent. Cooling the peptide/detergent system promoted capitellacin dimerization. Paramagnetic relaxation enhancement induced by lipid-soluble 12-doxylstearate showed that monomeric and dimeric capitellacin interacted with the surface of the micelle and did not penetrate into the micelle interior, which is consistent with the “carpet” mode of membrane activity. An analysis of the known structures of β-hairpin AMP dimers showed that their dimerization in a membrane-like environment occurs through the association of polar or weakly hydrophobic surfaces. A comparative analysis of the physicochemical properties of β-hairpin AMPs revealed that dimer stability and hemolytic activity are positively correlated with surface hydrophobicity. An additional positive correlation was observed between hemolytic activity and AMP charge. The data obtained allowed for the provision of a more accurate description of the mechanism of the oligomerization of β-structural peptides in biological membranes. Full article
(This article belongs to the Special Issue Marine Natural Compounds with Biomedical Potential: 2nd Edition)
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Figure 1
<p>Secondary structures of capitellacin and other β-hairpin antimicrobial peptides in membrane-mimicking environments. (<b>A</b>,<b>B</b>) Monomer and antiparallel (symmetric) dimers of capitellacin observed in DPC micelles (present work). (<b>C</b>) Parallel (asymmetric) dimer of arenicin-2 observed in DPC micelles [<a href="#B15-biomolecules-14-00332" class="html-bibr">15</a>]. (<b>D</b>) Monomer of tachyplesin I observed in DPC micelles [<a href="#B18-biomolecules-14-00332" class="html-bibr">18</a>]. (<b>E</b>) Parallel (asymmetric) dimer of protegrin-1 observed in POPC and POPE/POPG (3:1) bilayers [<a href="#B11-biomolecules-14-00332" class="html-bibr">11</a>,<a href="#B14-biomolecules-14-00332" class="html-bibr">14</a>]. (<b>F</b>) Antiparallel (symmetric) dimer of protegrin-3 observed in DPC micelles [<a href="#B13-biomolecules-14-00332" class="html-bibr">13</a>]. (<b>G</b>) Antiparallel (symmetric) non-covalent dimer of the antiparallel disulfide-linked homodimers of cathelicidin-1 (ChDode, tetramer) observed in DPC micelles [<a href="#B16-biomolecules-14-00332" class="html-bibr">16</a>]. (<b>H</b>) Antiparallel (symmetric) dimer of thanatin observed in lipopolysaccharide (LPS) micelles [<a href="#B17-biomolecules-14-00332" class="html-bibr">17</a>]. Aromatic, hydrophobic, polar, positively charged, and Cys residues are shown as green, pink, magenta, blue, and grey circles, respectively. Asterisks indicate <span class="html-italic">C</span>-terminal amides. Disulfide bonds and H-bonds are shown as bars and gray dotted lines, respectively. Residues with sidechains directed up from the picture plane (toward readers) are marked with black labels; the residues with sidechains facing down from the picture plane are marked with white labels. The green arrows on panel (<b>B</b>) show intermonomer NOE contacts observed for the capitellacin dimer.</p>
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<p>NMR data on capitellacin dimerization in DPC micelles. (<b>A</b>,<b>B</b>) 2D sensitivity-enhanced <sup>15</sup>N-HSQC spectra of <sup>15</sup>N-labeled capitellacin at D:P of 50:1 (<b>A</b>) and 200:1 (<b>B</b>) (0.07 mM, pH 5.4, 45 °C). Resonance assignments for monomer (M) and dimer (<b>D</b>) are shown in blue and red colors, respectively. The Val8 and Gly20 signal sets, probably arising from the <span class="html-italic">cis–trans</span> isomerization of the Ser1–Pro2 peptide bond in the monomer and dimer of capitellacin, are highlighted by blue and red circles. The H<sup>ε1</sup> signals of the Trp19 sidechains in the monomer and dimer are highlighted by cyan circles. (<b>C</b>) Temperature gradients of amide protons (∆δ<sup>1</sup>H<sup>N</sup>/∆T) for monomer (blue columns) and dimer (red columns) measured at D:P of 200:1 and 50:1, respectively. The values &gt; −4.5 ppb/K (dashed line) indicate the possible participation of the HN group in hydrogen bond formation. The H<sup>N</sup> signals of Arg3, Val4, and Asn11 in the dimer (marked by crosses) were not observed at temperatures below 40 °C due to line broadening. Asterisks indicate HN groups that did not form H-bonds in the monomer but formed H-bonds in the dimer. (<b>D</b>) The fragment of a 2D NOESY spectrum of capitellacin at a D:P of 100:1 (0.07 mM, pH 5.4, 45 °C). The intermonomer Arg3:HN–Arg10:HA NOE-contact is indicated by green dot. The corresponding contacts are shown by arrows in <a href="#biomolecules-14-00332-f001" class="html-fig">Figure 1</a>B.</p>
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<p>(<b>A</b>–<b>C</b>) Representative conformers of the capitellacin monomer and dimer in DPC micelles (present work, PDB ID: 8B4R and 8B4S, respectively) and capitellacin monomer in water (PDB ID 7ALD [<a href="#B23-biomolecules-14-00332" class="html-bibr">23</a>]). Residues from each monomer of the dimer are marked by “1” or “2”. Positively charged, aliphatic (including Cys), aromatic, and polar residues are colored blue, yellow, green, and magenta, respectively. (<b>D</b>,<b>E</b>) Two-sided view of electrostatic potential on the molecular surface of the capitellacin monomer and dimer in DPC micelles. Red and blue denote negative and positive regions, respectively.</p>
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<p>Two-sided views of molecular hydrophobicity potential (<span class="html-italic">MHP</span>) [<a href="#B27-biomolecules-14-00332" class="html-bibr">27</a>] on the molecular surface of the (<b>A</b>) capitellacin monomer (PDB ID 8B4R, present work), (<b>B</b>) capitellacin symmetric dimer (PDB ID 8B4S, present work), (<b>C</b>) asymmetric dimer of arenicin-2 (PDB ID 2L8X [<a href="#B15-biomolecules-14-00332" class="html-bibr">15</a>]), (<b>D</b>) symmetric tetramer of cathelicidin-1 ChDode (PDB ID 7ACB [<a href="#B16-biomolecules-14-00332" class="html-bibr">16</a>]), (<b>E</b>) symmetric dimer of protegrin-3 (PDB ID 2MZ6 [<a href="#B13-biomolecules-14-00332" class="html-bibr">13</a>]), (<b>F</b>) asymmetric dimer of protegrin-1 (PDB ID 1ZY6 [<a href="#B14-biomolecules-14-00332" class="html-bibr">14</a>]), and (<b>G</b>) symmetric dimer of thanatin (PDB ID 5XO9 [<a href="#B17-biomolecules-14-00332" class="html-bibr">17</a>]). Different molecules in the dimers and tetramer are denoted by numbers (‘1’, ‘2’, ‘3’, and ‘4’). Green and yellow denote polar and hydrophobic regions, respectively. Please note that two sides of symmetric dimers are different and contain different sidechains, while two sides of asymmetric dimers contain the same sidechains, and are similar, but not identical.</p>
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<p>(<b>A</b>) Attenuation of the HN cross-peaks in the 2D <sup>15</sup>N-HSQC spectrum of the capitellacin monomer (red) and dimer (blue) through a lipid-soluble paramagnetic probe 12-doxylstearate. Values for the H<sup>ε1</sup> signal of Trp19 are shown as red and blue triangles. The 0.3 threshold line separates the residues in contact with the hydrophobic region of the micelle (below the threshold). (<b>B</b>) A model of the capitellacin dimer/micelle complex. The regions of the peptide affected by 12-DSA are shown in blue. Residues Arg10 and Asn11 are colored magenta. Different molecules in the dimer are denoted by numbers (‘1’, ‘2’). The dashed line represents the micelle surface with radius 21 Å. (<b>C</b>) Proposed model of the capitellacin dimer/DPC micelle complex. The peptide molecular surface is colored by the distribution of the molecular hydrophobicity potential. Green represents the polar surface area, and hydrophobic regions are colored white. The structure of a micelle containing 60 detergent molecules was generated in CHARMM-GUI [<a href="#B51-biomolecules-14-00332" class="html-bibr">51</a>]. The positively charged choline groups and negatively charged phosphate groups of the DPC molecules are colored blue and red, respectively. (<b>D</b>) Hypothetical model of the interaction of the capitellacin monomer and dimer with a bilayer.</p>
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<p>Thermodynamics of capitellacin dimerization in DPC micelles. (<b>A</b>,<b>B</b>) Titration of a 0.14 mM unlabeled capitellacin sample with DPC (pH 5.4, 30 °C). The peptide in water and in DPC micelles demonstrates additional conformational heterogeneity due to the <span class="html-italic">cis-trans</span> isomerization of the Ser1–Pro2 peptide bond. W, D, and M are the signals of the peptide monomer in water, as well as the capitellacin dimer and monomer in DPC micelles with the <span class="html-italic">trans</span>-configuration of the Ser1–Pro2 peptide bond. cis–W, cis–M, and cis–D are the signals of minor forms with a <span class="html-italic">cis</span>–Ser1–Pro2 bond. The D:P ratios shown in panel A were not adjusted for the presence of non-micellar detergent in the sample (the critical micelle concentration of DPC is 1.5 mM). The data in panel <b>B</b> were fitted using the ‘micellar solvent’ model [<a href="#B43-biomolecules-14-00332" class="html-bibr">43</a>]. See the fitting parameters in <a href="#sec3dot4-biomolecules-14-00332" class="html-sec">Section 3.4</a> of the manuscript. (<b>C</b>,<b>D</b>) Temperature dependence of the capitellacin NMR spectrum and linear approximation of the temperature dependence of the free energy (ΔG<sup>D</sup>) of capitellacin dimerization in DPC micelles (0.14 mM, D:P = 400:1, pH 5.4). The ΔG<sup>D</sup> values were calculated from the measured concentrations of the monomeric and dimeric capitellacin using the ‘micellar solvent’ model with fitted parameters. The obtained values of ΔH<sup>D</sup> and ΔS<sup>D</sup> are provided in <a href="#sec3dot4-biomolecules-14-00332" class="html-sec">Section 3.4</a> of the manuscript.</p>
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<p>Correlations of the physicochemical properties of the β-hairpin and helical AMPs with their tendency to form dimers and hemolytic activity. (<b>A</b>) Relationship between the relative surface area of the hydrophobic regions (<span class="html-italic">S<sub>lip</sub></span>/<span class="html-italic">S<sub>tot</sub></span>) and the combination of the AMP hydrophobicity on the Kyte and Doolittle scale [<a href="#B28-biomolecules-14-00332" class="html-bibr">28</a>] (<span class="html-italic">GRAVY</span>) with the aromatic content (<span class="html-italic">AROM</span>). (<b>B</b>) Relationship between the combination of <span class="html-italic">GRAVY</span> and <span class="html-italic">AROM</span> parameters with the total charge of AMP (<span class="html-italic">CHARGE</span>) and its minimal hemolytic concentration (<span class="html-italic">MHC</span>). (<b>C</b>) Relationship between the combination of the average <span class="html-italic">MHP</span> value on the peptide surface (<span class="html-italic">MHP<sub>mean</sub></span>) with the total charge and the <span class="html-italic">MHC</span> value. Abbreviations: Protegrin-3 (P3), Protegrin-2 (P2), Protegrin-1 (P1), Arenicin-2 (A2), ChDode (CD), Capitellacin (CT), Thanatin (TT), Tachyplesin I (TP), Arenicin-1 [V8R] (AR), PcDode (PD), Alvinellacin (AL), Polyphemusin I (PM), PV5 (PV), Arenicin-3 (A3), Gomesin (GM), Fowlicidin-1 (FL), Melittin (MT), Magainin-2 (M2), and MSI-594 (MS). To calculate the parameters of monomeric peptides, structures in DPC micelles were used. If they were not available, then the structures of peptides in water were used.</p>
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10 pages, 4021 KiB  
Article
Measurement of Reverse-Light-Induced Excited Spin State Trapping in Spin Crossover Systems: A Study Case with Zn1−xFex(6-mepy)3tren(PF6)2·CH3CN; x = 0.5%
by Teresa Delgado and Anne-Laure Pelé
Crystals 2024, 14(3), 210; https://doi.org/10.3390/cryst14030210 - 23 Feb 2024
Viewed by 1118
Abstract
In an attempt to better understand the physics governing the apparition of reverse-light-induced excited spin state trapping (LIESST) phenomena in spin crossover (SCO) compounds, we have studied the LIESST effect and the possibility of a reverse-LIESST effect in the SCO complex Zn1−x [...] Read more.
In an attempt to better understand the physics governing the apparition of reverse-light-induced excited spin state trapping (LIESST) phenomena in spin crossover (SCO) compounds, we have studied the LIESST effect and the possibility of a reverse-LIESST effect in the SCO complex Zn1−xFex(6-mepy)3tren(PF6)2·CH3CN, x = 0.5%. ((6-mepy)3tren = tris{4-[(6-methyl)-2-pyridyl]-3-aza-butenyl}amine)). This complex was chosen as a good candidate to show reverse-LIESST by comparison with its unsolvated analogue, since the introduction of acetonitrile in the structure leads to the stabilisation of the high-spin state and both exhibit a very abrupt thermal spin transition. Indeed, the steep thermal spin transitions of two differently polarised crystals of Zn1−xFex(6-mepy)3tren(PF6)2·CH3CN, x = 0.5% have been characterised in detail in a first step using absorption spectroscopy and no influence of the polarisation was found. These were then fitted within the mean field model to obtain the variation in the enthalpy and entropy and the critical temperatures associated with the process, which are significantly lower with respect to the unsolvated compound due to the incorporation of acetonitrile. In a second step, the light-induced low-spin-to-high-spin transition at low temperatures based on LIESST and its subsequent high-spin-to-low-spin relaxation at different temperatures were characterised by time-resolved absorption spectroscopy, with exponential behaviour in both cases. The stabilisation of the high-spin state due to the presence of acetonitrile was evidenced. Finally, light-induced high-spin-to-low-spin state transition at low temperature based on reverse-LIESST was attempted by time-resolved absorption spectroscopy but the Fe(II) concentration was too low to observe the effect. Full article
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Figure 1
<p>Schematic view of the HS-to-LS relaxation. In the initial moments, the HS centres are located in a 100% HS lattice and the internal pressure is low. Once the relaxation takes place, the density of the lattice increases as well as the pressure. In other words, at the beginning, the activation energy is much higher, and it starts to decrease as the relaxation proceeds, increasing the speed of the process [<a href="#B23-crystals-14-00210" class="html-bibr">23</a>].</p>
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<p>Zn<sub>1−x</sub>Fe<sub>x</sub>(6-mepy)<sub>3</sub>tren(PF<sub>6</sub>)<sub>2</sub>·CH<sub>3</sub>CN structure. Legend: C (grey), H (white), F (green), Fe (dark blue), N (blue), and P (pink). Empirical formula C<sub>29</sub>H<sub>36</sub>F<sub>12</sub>FeN<sub>8</sub>P<sub>2</sub>.</p>
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<p>(<b>a</b>) Temperature evolution of the HS fraction (heating/cooling at 5 K/min) of a single crystal of Zn<sub>1−x</sub>Fe<sub>x</sub>(6-mepy)<sub>3</sub>tren(PF<sub>6</sub>)<sub>2</sub>·CH<sub>3</sub>CN, x = 0.5% and temperature-dependent absorption spectra under polarised light for (<b>b</b>) n<sub>0</sub>||P and (<b>c</b>) n<sub>e</sub>||P.</p>
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<p>(<b>a</b>) Absorption spectra of a single crystal of Zn<sub>1−x</sub>Fe<sub>x</sub>(6-mepy)<sub>3</sub>tren(PF<sub>6</sub>)<sub>2</sub>·CH<sub>3</sub>CN, x = 0.5% (thickness = 390 µm) and (<b>b</b>) corresponding γ<sub>HS</sub> evolution with time during the irradiation at 10 K with a W-halogen lamp at 8.3 A.</p>
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<p>(<b>a</b>) Absorption spectra evolution during LIESST at 10 K and subsequent HS→LS relaxation at 30 K. Inset: Time γ<sub>HS</sub> evolution during the HS→LS relaxation at 30 K after LIESST (<b>b</b>) Time γ<sub>HS</sub> evolution during the HS→LS relaxation between 10 and 60 K after LIESST. (<b>c</b>) Arrhenius plot of <span class="html-italic">k</span><sub>HL</sub> vs. <span class="html-italic">1/T</span> from T = 10 K to T = 175 K and comparison with the data obtained for the unsolvated compound.</p>
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<p>Reverse-LIESST on a mixed-crystal Zn<sub>1−x</sub>Fe<sub>x</sub>(6-mepy)<sub>3</sub>tren(PF<sub>6</sub>)<sub>2</sub>·CH<sub>3</sub>CN, x = 0.5% (390 µm) at 10 K after irradiation during 5 min at 532 nm and 830 nm.</p>
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<p>Energy level diagram of the excited and ground HS and LS states involved in the LIESST and reverse-LIESST effects. The red, green, and purple arrows represent the excitation of the sample in the IR (830 nm), visible (532 nm), and UV region of the spectra (the latter was not performed in this experiment). The t<sub>2g</sub> and e<sub>g</sub> orbitals are, respectively, the lower energy triply degenerate set and higher energy doubly degenerate set in which the d orbitals of Fe are split in the presence of an octahedral crystal field [<a href="#B30-crystals-14-00210" class="html-bibr">30</a>].</p>
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14 pages, 5408 KiB  
Article
Exploring the Impact of Intermolecular Interactions on the Glassy Phase Formation of Twist-Bend Liquid Crystal Dimers: Insights from Dielectric Studies
by Antoni Kocot, Małgorzata Czarnecka, Yuki Arakawa and Katarzyna Merkel
Molecules 2023, 28(21), 7441; https://doi.org/10.3390/molecules28217441 - 6 Nov 2023
Cited by 1 | Viewed by 1346
Abstract
The formation of the nematic to twist-bend nematic (NTB) phase has emerged as a fascinating phenomenon in the field of supramolecular chemistry, based on complex intermolecular interactions. Through a careful analysis of molecular structures and dynamics, we elucidate how these intermolecular [...] Read more.
The formation of the nematic to twist-bend nematic (NTB) phase has emerged as a fascinating phenomenon in the field of supramolecular chemistry, based on complex intermolecular interactions. Through a careful analysis of molecular structures and dynamics, we elucidate how these intermolecular interactions drive the complex twist-bend modulation observed in the NTB. The study employs broadband dielectric spectroscopy spanning frequencies from 10 to 2 × 109 Hz to investigate the molecular orientational dynamics within the glass-forming thioether-linked cyanobiphenyl liquid crystal dimers, namely, CBSC7SCB and CBSC7OCB. The experimental findings align with theoretical expectations, revealing the presence of two distinct relaxation processes contributing to the dielectric permittivity of these dimers. The low-frequency relaxation mode is attributed to an “end-over-end rotation” of the dipolar groups parallel to the director. The high-frequency relaxation mode is associated with precessional motions of the dipolar groups about the director. Various models are employed to describe the temperature-dependent behavior of the relaxation times for both modes. Particularly, the critical-like description via the dynamic scaling model seems to give not only quite good numerical fittings, but also provides a consistent physical picture of the orientational dynamics in accordance with findings from infrared (IR) spectroscopy. Here, as the longitudinal correlations of dipoles intensify, the m1 mode experiences a sudden upsurge in enthalpy, while the m2 mode undergoes continuous changes, displaying critical mode coupling behavior. Interestingly, both types of molecular motion exhibit a strong cooperative interplay within the lower temperature range of the NTB phase, evolving in tandem as the material’s temperature approaches the glass transition point. Consequently, both molecular motions converge to determine the glassy dynamics, characterized by a shared glass transition temperature, Tg. Full article
(This article belongs to the Special Issue Liquid Crystals II)
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Graphical abstract

Graphical abstract
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<p>Plots of relaxation times for modes <b>m</b><sub>1</sub> and <b>m</b><sub>2</sub> (5 μm planar cell): (<b>a</b>) symmetric dimer (CBSC7SCB), (<b>b</b>) asymmetric dimer (CBSC7OCB). Symbols: red circles (<b><span style="color:red">○</span></b>)—<b>m</b><sub>1</sub> mode, dark blue squares (<b><span style="color:#3333CC">□</span></b>)—<b>m</b><sub>2</sub> mode, rotational diffusion model fitting: black solid line—<b>m</b><sub>1</sub> mode, dash blue line—<span class="html-italic">τ</span><sub>D</sub> relaxation time, solid blue line—VFT model [<a href="#B30-molecules-28-07441" class="html-bibr">30</a>], solid red line—fitting of experimental data by Equation (2), purple/burgundy triangles (<b><span style="color:#9900FF">∇</span></b>, <b><span style="color:#660033">∇</span></b>)—order parameter, S (as an insert).</p>
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<p>Plots show a linear dependence <math display="inline"> <semantics> <mrow> <msup> <mrow> <mfenced close="]" open="["> <mrow> <msub> <mi>H</mi> <mi>A</mi> </msub> <mfenced> <mi>T</mi> </mfenced> <mo>/</mo> <mi>R</mi> <mo> </mo> </mrow> </mfenced> </mrow> <mrow> <mo>−</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics> </math> on the inverse temperature in N<sub>TB</sub> phase. (<b>a</b>)—CBSC7SCB dimer, (<b>b</b>)—CBSC7OCB. The red arrows show the jump of the <span class="html-italic">H<sub>A</sub></span> that omits the critical fluctuation at the N-N<sub>TB</sub> transition, where <span class="html-italic">H</span><sub>A</sub> is denoted as the apparent enthalpy of the activation. Symbols: red circles (<b><span style="color:red">○</span></b>)—<b>m</b><sub>1</sub> mode, dark blue squares (<b><span style="color:#3333CC">□</span></b>)—<b>m</b><sub>2</sub> mode, solid line: model fitting according to Equation (9). The fitting parameters are listed in <a href="#molecules-28-07441-t002" class="html-table">Table 2</a>.</p>
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<p>Results of the temperature-derivative analysis (Equation (10)) in N<sub>TB</sub> phase applied to both <b>m</b><sub>1</sub> and <b>m</b><sub>2</sub> modes in which linear dependences indicate domains of validity of the critical-like description; (<b>a</b>) symmetric dimer (CBSC7SCB), (<b>b</b>) asymmetric dimer (CBSC7OCB). Symbols: red circles (<b><span style="color:red">○</span></b>)—<b>m</b><sub>1</sub> mode, dark blue squares (<b><span style="color:#3333CC">□</span></b>)—<b>m</b><sub>2</sub> mode, solid lines: model fitting according to Equation (10). The fitting parameters are listed in <a href="#molecules-28-07441-t003" class="html-table">Table 3</a>.</p>
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<p>Results of the temperature-derivative analysis (Equation (11)) in N<sub>TB</sub> phase applied to both <b>m</b><sub>1</sub> and <b>m</b><sub>2</sub> modes of (<b>a</b>) CBSC7SCB and (<b>b</b>) CBSC7OCB. Dashed lines (red and black) indicate dynamic domains of validity of the critical-like description. Symbols: red circles (<b><span style="color:red">○</span></b>)—<b>m</b><sub>1</sub> mode, black squares (<b>□</b>)—<b>m</b><sub>2</sub> mode.</p>
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<p>(<b>a</b>) Molecular structure of symmetric (CBSCnSCB) and asymmetric (CBSCnOCB) dimers. (<b>b</b>) POM textures of the 5 μm planar cell for the CBSC7OCB sample in the N phase (375 K) and the N<sub>TB</sub> phase (355 K) (cooling rate of 5 °C/min). The scale bar equals 50 μm.</p>
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<p>Laboratory and molecular frame of reference. Planar (top) and homeotropic cell (bottom) (<b>a</b>) in the N phase, (<b>b</b>) in the N<sub>TB</sub> phase, where k is the helical axis, (<b>c</b>) molecular frame of reference.</p>
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<p>Fitting of the derivative of permittivity vs. ln(f) showing the deconvolution of the molecular modes: <b>m</b><sub>1</sub> and <b>m</b><sub>2</sub>.</p>
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1112 KiB  
Proceeding Paper
First-Principle Calculation Analysis on Electronic Structures and Molecular Dynamics of Gadolinium-Doped FAPbI3
by Atsushi Suzuki and Takeo Oku
Eng. Proc. 2023, 56(1), 33; https://doi.org/10.3390/ASEC2023-15332 - 26 Oct 2023
Viewed by 672
Abstract
First-principle calculation analysis on electronic structures and molecular dynamics was performed to investigate the addition of gadolinium ion into a formamidinium lead iodine (FAPbI3) perovskite crystal for use in the application of photovoltaic devices with stability of performance. Band dispersion, density [...] Read more.
First-principle calculation analysis on electronic structures and molecular dynamics was performed to investigate the addition of gadolinium ion into a formamidinium lead iodine (FAPbI3) perovskite crystal for use in the application of photovoltaic devices with stability of performance. Band dispersion, density of state, enthalpy, and kinetic energy were predicted during the relaxation process. The Gd2+-doped FAPbI3 perovskite crystal had an effective mass ratio of 0.02 in narrow band dispersion, consisting of 5d and 4f orbitals of gadolinium ion, a 6p orbital of lead ion, and a 5p orbital of iodine ion, supporting the charge transfer and carrier diffusion related to carrier mobility as a photovoltaic parameter. The molecular dynamics of the Gd2+-doped perovskite crystal indicate dynamic stability while suppressing decomposition, with separation between nitrogen and hydrogen ions on FA in the crystal. The first-principle calculation predicts that it is advantageous to apply the Gd2+-doped FAPbI3 perovskite crystal to the perovskite solar cell, providing stability of photovoltaic performance. Full article
(This article belongs to the Proceedings of The 4th International Electronic Conference on Applied Sciences)
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<p>(<b>a</b>) Electron density distribution; (<b>b</b>) band dispersion; and (<b>c</b>) DOS of spin up (black and blue lines) and spin down (red and green lines) for the Gd<sup>2+</sup>-doped FAPbI<sub>3</sub> perovskite crystal.</p>
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<p>(<b>a</b>) Enthalpy, kinetic energy, and (<b>b</b>) distance of N-H in FA of (<b>b</b>) Gd<sup>2+</sup>-doped FAPbI<sub>3</sub> crystal.</p>
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14 pages, 2494 KiB  
Article
Physical Ageing of Amorphous Poly(lactic acid)-Indapamide System Studied by Differential Scanning Calorimetry
by Marcin Skotnicki, Agata Drogoń, Janina Lulek and Marek Pyda
Pharmaceutics 2023, 15(9), 2341; https://doi.org/10.3390/pharmaceutics15092341 - 19 Sep 2023
Viewed by 1192
Abstract
The process of isothermal and non-isothermal physical ageing of amorphous polylactide (PLA) with the active pharmaceutical ingredient, indapamide (IND), was investigated. A PLA–IND system with a 50/50 weight ratio was obtained and characterized using differential scanning calorimetry (DSC). In the 50/50 (w [...] Read more.
The process of isothermal and non-isothermal physical ageing of amorphous polylactide (PLA) with the active pharmaceutical ingredient, indapamide (IND), was investigated. A PLA–IND system with a 50/50 weight ratio was obtained and characterized using differential scanning calorimetry (DSC). In the 50/50 (w/w) mixture, two glass transitions were observed: the first at 64.1 ± 0.3 °C corresponding to the glass transition temperature (Tg) of PLA, and the second at 102.6 ± 1.1 °C corresponding to the Tg of IND, indicating a lack of molecular mixing between the two ingredients. The PLA–IND system was subjected to the isothermal physical ageing process at different ageing temperatures (Ta) for 2 h. It was observed that the highest effect of physical ageing (enthalpy relaxation change) on IND in the PLA–IND system occurred at Ta = 85 °C. Furthermore, the system was annealed for various ageing times at 85 °C. The relaxation enthalpies were estimated for each experiment and fitted to the Kohlrausch–Williams–Watts (KWW) equation. The KWW equation allowed for the estimation of the relaxation time and the parameter describing the distribution of relaxation times of the isothermal physical ageing process of IND in the PLA–IND system. The physical ageing of the PLA–IND mixture (50/50) was also discussed in the context of heat capacity. Moreover, the activation energy and fragility parameters were determined for the PLA–IND (50/50) system. Full article
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<p>Scheme for determination of enthalpy relaxation from DSC plot of heat capacity vs. temperature.</p>
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<p>Chemical structure of (<b>a</b>) polylactide and (<b>b</b>) indapamide.</p>
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<p>Heat-flow rate as a function of temperature for polylactide (PLA; blue curve), indapamide (IND; red curve) and the PLA–IND 50/50 (<span class="html-italic">w</span>/<span class="html-italic">w</span>) system (purple curve). Two glass transitions (<span class="html-italic">T</span><sub>g</sub>) are observed for the PLA–IND system, indicating the immiscibility of the components.</p>
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<p>Heat-flow rate vs. temperature for the isothermal physical ageing showing enthalpy relaxation changes of the PLA–IND 50/50 (<span class="html-italic">w</span>/<span class="html-italic">w</span>) system after annealing for 2 h at different ageing temperatures, <span class="html-italic">T</span><sub>a</sub> = (30, 40, 50, 60, 70, 80, 85, 90) °C. The curve for the sample aged at 30 °C was shifted for clarity—no significant changes in enthalpy relaxation occurred.</p>
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<p>Heat-flow rate as a function of the temperature of the PLA–IND (50/50) system after annealing at 85 °C for various ageing times.</p>
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<p>Experimental enthalpy relaxation for IND in the PLA–IND (50/50) system (dots) and for pure IND (squares) aged at 85 °C as a function of ageing time. The solid lines present the calculated enthalpy relaxation from the best fit of the experimental data to the KWW equation.</p>
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<p>The recovery parameter, <math display="inline"><semantics> <mi>φ</mi> </semantics></math>, values for IND in the PLA–IND (50/50) system (dots) and for pure IND (squares) aged at 85 °C as a function of ageing time. Solid lines represent the fit of the calculated data to Equation (9).</p>
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<p>Arrhenius plots of temperature dependence on the cooling rates of the IND in the PLA–IND (50/50) system and of pure IND.</p>
Full article ">Figure 9
<p>Heat capacity of the PLA–IND (50/50) system studied by DSC, where <span class="html-italic">c</span><sub>p</sub>(aged-1200 min) and <span class="html-italic">c</span><sub>p</sub>(unaged) represent the experimental heat capacity of the aged and unaged sample, <span class="html-italic">c<sub>p</sub></span>(vibration) represents the vibrational heat capacity of the PLA–IND (50/50) system and <span class="html-italic">c<sub>p</sub></span>(liquid) represents the heat capacity of the liquid state of PLA–IND (50/50).</p>
Full article ">
54 pages, 10229 KiB  
Review
pH Effects on the Conformations of Galacturonan in Solution: Conformational Transition and Loosening, Extension and Stiffness
by Sergio Paoletti and Ivan Donati
Polysaccharides 2023, 4(3), 271-324; https://doi.org/10.3390/polysaccharides4030018 - 8 Sep 2023
Cited by 1 | Viewed by 1633
Abstract
Calorimetric (from both isothermal micro-calorimetry and DSC), chiro-optical, viscometric and rheological data on aqueous solutions of pectic acid and low-methoxyl pectin (LMP), published over decades from different laboratories, have been comparatively revisited. The aim was to arrive at a consistent and detailed description [...] Read more.
Calorimetric (from both isothermal micro-calorimetry and DSC), chiro-optical, viscometric and rheological data on aqueous solutions of pectic acid and low-methoxyl pectin (LMP), published over decades from different laboratories, have been comparatively revisited. The aim was to arrive at a consistent and detailed description of the behavior of galacturonan as a function of pH, i.e., of the degree of charging (as degree of dissociation, α) of the polyanion. The previously hypothesized pH-induced transition from a 31 to a 21 helix was definitely confirmed, but it has been shown, for the first time, that the transition is always coupled with loosening/tightening effects brought about by an increase in charge. The latter property has a twofold effect: the former effect is a purely physical one (polyelectrolytic), which is always a loosening one. However, in the very low range of pH and before the beginning of the transition, an increase in charge tightens the 31 helix by strengthening an intramolecular—but inter-residue—hydrogen bond. The value of the enthalpy change of 31 → 21 transition—+0.59 kcal·mol−1—is bracketed by those provided by theoretical modeling, namely +0.3 and +0.8 kcal·mol−1; the corresponding entropy value is also positive: +1.84 cal·mole r.u.−1·K−1. The enthalpic and the entropic changes in chain loosening amount only to about 23% of the corresponding 31 → 21 changes, respectively. Much like poly(galacturonic acid), the 31 conformation of LMP also stiffens on passing from pH = 2.5 to 3.0, to then start loosening and transforming into the 21 one on passing to pH = 4.0. Lowering the pH of a salt-free aqueous solution of LMP down to 1.6 brings about a substantial chain–chain association, which is at the root of the interchain junctions stabilizing the acid pH gels, in full agreement with the rheological results. A comparison of the enthalpic data reveals that, at 85 °C, LMP in acidic pH conditions has lost its initial order by about 2.3 times more than pectic acid brought from low charging to full neutralization (at α = 1.0) at 25 °C. A proper combination of experiments (enthalpic measurements) and theory (counterion condensation polyelectrolyte theory) succeeded in demonstrating, for the first time ever, a lyotropic/Hofmeister effect of the anion perchlorate in stabilizing the more disordered form of the 21 helix of galacturonan. The viscometric results in water showed that the 31 helix is capable of forming longer rheologically cooperative units compared with the 21 helix. Extrapolation to infinite ionic strength confirmed that, once all electrostatic interactions are cancelled, the elongation of the two helical forms is practically the same. At the same time, however, they indicated that the flexibility of the two-fold helix is more than fifteen times larger than that of the three-fold one. The result is nicely corroborated by a critical revisiting of 23Na relaxation experiments. Full article
Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>(<b>a</b>) Dependence of the reduced specific viscosity, η<sub>red</sub>, on the degree of dissociation, α, for pectic acid in water (blue symbols) and in aqueous NaClO<sub>4</sub> 0.05 M (red symbols); (<b>b</b>) dependence of the apparent pK<sub>a</sub>, (pK<sub>a</sub>)<span class="html-italic"><sup>app</sup>.</span>, on α for pectic acid in water (blue symbols) and in aqueous NaClO<sub>4</sub> 0.05 M (red symbols); the dotted line connecting the data points in the initial and in the final range has been used for the calculation of the (pKa)<span class="html-italic"><sup>excess</sup></span> values reported in the following <a href="#polysaccharides-04-00018-f020" class="html-fig">Figure 20</a>a. α<sub>1</sub>, α<sub>2</sub>, and α<sub>3</sub> correspond to the values of α of (initial) self-dissociation of the polyacid and of the start and end of the conformational transition, respectively. Roman numerals identify the three regions defined in the text.</p>
Full article ">Figure 2
<p>(<b>a</b>) Dependence on α of the molar enthalpy change in dissociation, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>diss</mi> </mrow> </msub> </mrow> </semantics></math>, of pectic acid in aqueous NaClO<sub>4</sub> 0.05 M (black symbols), and of the (integral) curve of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi mathvariant="italic">tr</mi> </mrow> <mrow> <mi mathvariant="italic">excess</mi> </mrow> </msubsup> </mrow> </semantics></math> (red symbols, scale on the right); (<b>b</b>) Dependence on α of the molar entropy change in dissociation, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mrow> <mover> <mi mathvariant="normal">S</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>diss</mi> </mrow> </msub> </mrow> </semantics></math>, of pectic acid in aqueous NaClO<sub>4</sub> 0.05 M (black symbols), and of the (integral) curve of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">S</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi mathvariant="italic">tr</mi> </mrow> <mrow> <mi mathvariant="italic">excess</mi> </mrow> </msubsup> </mrow> </semantics></math> (red symbols, scale on the right).</p>
Full article ">Figure 3
<p>(<b>a</b>) Dependence on α of the molar enthalpy change in dissociation, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>diss</mi> </mrow> </msub> </mrow> </semantics></math>, of pectic acid in salt-free aqueous solution (black symbols), and of the (integral) curve of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>t</mi> <mi>r</mi> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>c</mi> <mi>e</mi> <mi>s</mi> <mi>s</mi> </mrow> </msubsup> </mrow> </semantics></math> (red symbols, scale on the right); (<b>b</b>) Dependence on α of the molar entropy change in dissociation, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mrow> <mover> <mi mathvariant="normal">S</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>diss</mi> </mrow> </msub> </mrow> </semantics></math>, of pectic acid in salt-free aqueous solution (black symbols), and of the (integral) curve of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">S</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>t</mi> <mi>r</mi> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>c</mi> <mi>e</mi> <mi>s</mi> <mi>s</mi> </mrow> </msubsup> </mrow> </semantics></math> (red symbols, scale on the right).</p>
Full article ">Figure 4
<p>(<b>a</b>) Dependence on α of the enthalpy of dilution of pectic acid (concentration halving; initial value of C<sub>p</sub>: 1.94·10<sup>−2</sup> mole r.u.⋅L<sup>−1</sup>) (black symbols, l.h.s.) and of the enthalpy of dissociation, (red symbols, data from <a href="#polysaccharides-04-00018-f003" class="html-fig">Figure 3</a>a, at 25 °C in water; inset, dependence on α, in the interval from α = α<sub>3</sub> to α = 1.0, of the enthalpy of dilution (red symbols; data from main panel) and of molar ellipticity (blue symbols; data from the following <a href="#polysaccharides-04-00018-f006" class="html-fig">Figure 6</a>b) of pectic acid at 25 °C in water; (<b>b</b>) dependence on the negative logarithm of the polymer concentration of the enthalpy of dilution from the initial concentration, (C<sub>p</sub>)<sub>i</sub>, of pectic acid in water at 25 °C: blue symbols: α = 0.34, (C<sub>p</sub>)<sub>i</sub> = 2.04·10<sup>−2</sup> mole r.u.⋅L<sup>−1</sup>; red symbols: α = 0.96, (C<sub>p</sub>)<sub>i</sub> = 3.42·10<sup>−2</sup> mole r.u.⋅L<sup>−1</sup>. The broken lines represent the corresponding theoretical curves calculated according to the CC theory of polyelectrolytes.</p>
Full article ">Figure 5
<p>Excess enthalpy of dilution of Na<sup>+</sup> pectate in water at 25 °C. Data from <a href="#polysaccharides-04-00018-f004" class="html-fig">Figure 4</a>b. (<b>a</b>) Data fit with the general hyperbola equation: <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>=</mo> <mi>a</mi> <mo>−</mo> <mfrac> <mi>b</mi> <mrow> <msup> <mrow> <mfenced> <mrow> <mn>1</mn> <mo>+</mo> <mi>c</mi> <mo>·</mo> <mi>x</mi> </mrow> </mfenced> </mrow> <mrow> <mfrac bevelled="true"> <mn>1</mn> <mi>d</mi> </mfrac> </mrow> </msup> </mrow> </mfrac> </mrow> </semantics></math>; (<b>b</b>) data fit with the Hill equation: <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>=</mo> <mi>A</mi> <mo>+</mo> <mfenced> <mrow> <mi>B</mi> <mo>−</mo> <mi>A</mi> </mrow> </mfenced> <mo>·</mo> <mfrac bevelled="true"> <mrow> <msup> <mi>x</mi> <mi>n</mi> </msup> </mrow> <mrow> <mfenced> <mrow> <msup> <mi>k</mi> <mi>n</mi> </msup> <mo>+</mo> <msup> <mi>x</mi> <mi>n</mi> </msup> </mrow> </mfenced> </mrow> </mfrac> </mrow> </semantics></math>, with <math display="inline"><semantics> <mrow> <mi>x</mi> <mo>=</mo> <mfrac bevelled="true"> <mn>1</mn> <mrow> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">p</mi> </msub> </mrow> </mfrac> </mrow> </semantics></math>. The numerical values of the parameters are given in the footnote to <a href="#polysaccharides-04-00018-t003" class="html-table">Table 3</a>. In both cases, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <msub> <mrow> <mfenced> <mrow> <msub> <mn>2</mn> <mn>1</mn> </msub> </mrow> </mfenced> </mrow> <mrow> <msub> <mi mathvariant="normal">C</mi> <mrow> <mi mathvariant="normal">p</mi> <mo>→</mo> <mo>∞</mo> </mrow> </msub> <mo> </mo> </mrow> </msub> <mo>→</mo> <mo> </mo> <msub> <mrow> <mfenced> <mrow> <msub> <mn>2</mn> <mn>1</mn> </msub> </mrow> </mfenced> </mrow> <mrow> <msub> <mi mathvariant="normal">C</mi> <mrow> <mi mathvariant="normal">p</mi> <mo>→</mo> <mn>0</mn> </mrow> </msub> <mo> </mo> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msubsup> <mrow> <mfenced> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>l</mi> <mi>o</mi> <mi>o</mi> <mi>s</mi> <mi>e</mi> <mi>n</mi> <mo>.</mo> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>c</mi> <mi>e</mi> <mi>s</mi> <mi>s</mi> </mrow> </msubsup> </mrow> </mfenced> </mrow> <mrow> <mi mathvariant="sans-serif">α</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">p</mi> </msub> <mo>→</mo> <mo>∞</mo> </mrow> <mrow> <mi mathvariant="sans-serif">α</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">p</mi> </msub> <mo>→</mo> <mn>0</mn> </mrow> </msubsup> <mo>=</mo> <msub> <mrow> <mfenced> <mrow> <mo>Δ</mo> <msup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>c</mi> <mi>e</mi> <mi>s</mi> <mi>s</mi> </mrow> </msup> </mrow> </mfenced> </mrow> <mrow> <mi>dil</mi> <mo>.</mo> <mo>,</mo> <msub> <mi mathvariant="normal">C</mi> <mrow> <mi mathvariant="normal">p</mi> <mo>→</mo> <mn>0</mn> </mrow> </msub> <mo> </mo> </mrow> </msub> <mo>−</mo> <msub> <mrow> <mfenced> <mrow> <mo>Δ</mo> <msup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>c</mi> <mi>e</mi> <mi>s</mi> <mi>s</mi> </mrow> </msup> </mrow> </mfenced> </mrow> <mrow> <mi>dil</mi> <mo>.</mo> <mo>,</mo> <msub> <mi mathvariant="normal">C</mi> <mrow> <mi mathvariant="normal">p</mi> <mo>→</mo> <mo>∞</mo> </mrow> </msub> <mo> </mo> </mrow> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 6
<p>Dependence on α of the chiro-optical properties of pectic acid in water at 25 °C: (<b>a</b>) molar optical activity at λ = 365 nm; (<b>b</b>) molar ellipticity at λ = 215 nm.</p>
Full article ">Figure 7
<p>(<b>a</b>) Dependence of the chiro-optical properties of poly(galacturonic acid) in water at 25 °C on α (purple symbols): molar ellipticity at λ = 215 nm (open circles, blue inner scale on r.h.s.) [<a href="#B29-polysaccharides-04-00018" class="html-bibr">29</a>]; molar optical activity at λ = 365 nm (crossed-lozenges, purple outer scale on r.h.s.) [<a href="#B29-polysaccharides-04-00018" class="html-bibr">29</a>]; ellipticity(arbitrary units) at λ = 208 nm (half-filled circles, red scale on l.h.s. and α as abscissa); ellipticity (arbitrary units) at λ = 208 nm (half-filled circles with magenta small full circle in the core, red scale on l.h.s. and α’ as abscissa) [<a href="#B7-polysaccharides-04-00018" class="html-bibr">7</a>]; I, II, III are the three regions defined in <a href="#sec2dot1-polysaccharides-04-00018" class="html-sec">Section 2.1</a>; (<b>b</b>) dependence on pH of the optical activity in salt-free aqueous solution: full symbols and connecting curves of different colors at the indicated temperatures for LMP at polymer concentration 0.4 wt% and λ = 436 nm [<a href="#B32-polysaccharides-04-00018" class="html-bibr">32</a>]; red open lozenges and dash-dotted connecting curve for poly(galacturonic acid) at 25 °C, polymer concentration 0.47% and λ = 365 nm [<a href="#B29-polysaccharides-04-00018" class="html-bibr">29</a>].</p>
Full article ">Figure 8
<p>(<b>a</b>) Dependence on α of the molar ellipticity at λ = 215 nm of pectic acid in water at 25 °C. The blue dash-dotted curve and the red one are the parabolic and the hyperbolic best-fit curves calculated for the data in region I and in region III, respectively; the purple dash-dotted curves has been drawn to guide the eye. The short-dotted lines represent the tangents to the dash-dotted curves at the beginning of their respective range; the black short-dashed rectangle is the blow-up area reported in <a href="#polysaccharides-04-00018-f009" class="html-fig">Figure 9</a>b; (<b>b</b>) dependence on α of the difference, δ[ϑ]<sub>215</sub>, between the best-fit curves of the molar ellipticity data at λ = 215 nm (dash-dotted) and the corresponding tangent curves in panel (<b>a</b>): red curve, 2<sub>1</sub> helix, blue curve 3<sub>1</sub> helix. Inset: “A typical snapshot taken from the MD simulation of a galacturonic acid dimer in explicit water solvent showing the relevant direct [r.h.s.] and water-mediated [l.h.s.] intramolecular H-bonds” [<a href="#B31-polysaccharides-04-00018" class="html-bibr">31</a>]; it is figure 1 of reference [<a href="#B31-polysaccharides-04-00018" class="html-bibr">31</a>], reproduced with permission.</p>
Full article ">Figure 9
<p>(<b>a</b>) Blow-up of the black short-dashed rectangle of <a href="#polysaccharides-04-00018-f008" class="html-fig">Figure 8</a>a (see for details). The two opposite effects of the increase in charge density on the conformation of the 3<sub>1</sub> helix have been indicated with A and B; (<b>b</b>) dependence on α of the mole fractions of 3<sub>1</sub> (blue full circles) and 2<sub>1</sub> (red full circles) helical conformations calculated from the experimental data of panel (<b>a</b>); magenta open circles; <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>l</mi> <mi>o</mi> <mi>o</mi> <mi>s</mi> <mi>e</mi> <mi>n</mi> <mo>.</mo> </mrow> </msub> </mrow> </semantics></math>, fraction of repeating units of galacturonan in the “loose” conformation, calculated from calorimetric data (see the discussion in <a href="#sec5dot1-polysaccharides-04-00018" class="html-sec">Section 5.1</a>).</p>
Full article ">Figure 10
<p>Dependence on pH of the thermal properties of LMP solutions (3 wt%) as determined by DSC experiments from 10 °C to 85 °C. Data replotted from [<a href="#B32-polysaccharides-04-00018" class="html-bibr">32</a>]. (<b>a</b>) melting temperatures, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">T</mi> <mi mathvariant="normal">m</mi> </msub> </mrow> </semantics></math>; (<b>b</b>) experimental <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mo>.</mo> </mrow> <mrow> <mi>DSC</mi> </mrow> </msubsup> </mrow> </semantics></math> (blue open circles) and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">S</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mo>.</mo> </mrow> <mrow> <mi>DSC</mi> <mo>,</mo> <msub> <mi mathvariant="normal">T</mi> <mi mathvariant="normal">m</mi> </msub> </mrow> </msubsup> </mrow> </semantics></math> values; the latter calculated as <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">S</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mo>.</mo> </mrow> <mrow> <mi>DSC</mi> <mo>,</mo> <msub> <mi mathvariant="normal">T</mi> <mi mathvariant="normal">m</mi> </msub> </mrow> </msubsup> <mfenced> <mrow> <mi>pH</mi> </mrow> </mfenced> <mo>=</mo> <mfrac bevelled="true"> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mo>.</mo> </mrow> <mrow> <mi>DSC</mi> </mrow> </msubsup> <mfenced> <mrow> <mi>pH</mi> </mrow> </mfenced> </mrow> <mrow> <msub> <mi mathvariant="normal">T</mi> <mi mathvariant="normal">m</mi> </msub> <mfenced> <mrow> <mi>pH</mi> </mrow> </mfenced> </mrow> </mfrac> </mrow> </semantics></math> (red full circles). The dashed rectangles identify two ranges of pH which in the <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">T</mi> <mi mathvariant="normal">m</mi> </msub> </mrow> </semantics></math> vs. pH data trends are separated by an abrupt upraise: magenta, pH ≤ 2.0, black, pH ≥ 2.5.</p>
Full article ">Figure 11
<p>(<b>a</b>) Dependence of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mo>.</mo> </mrow> <mrow> <mi>DSC</mi> </mrow> </msubsup> </mrow> </semantics></math> on <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">S</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mo>.</mo> </mrow> <mrow> <mi>DSC</mi> <mo>,</mo> <msub> <mi mathvariant="normal">T</mi> <mi mathvariant="normal">m</mi> </msub> </mrow> </msubsup> </mrow> </semantics></math> for LMP at different pH values (data from <a href="#polysaccharides-04-00018-f011" class="html-fig">Figure 11</a>b). Blue open circles and dash-dotted line: data in the pH range from 2.5 to 4.0; magenta open circles and dash-dotted line: data at pH 1.65 and 2.0; the black dash-dotted line is the linear best-fit through all data points; (<b>b</b>) dependence on polymer concentration of the DSC calorimetric results replotted from figure 10a of reference [<a href="#B32-polysaccharides-04-00018" class="html-bibr">32</a>], black symbols and r.h.s scale: full circles, experimental data points; dash-dotted curve, polynomial best fit of experimental data; dotted line, first derivative of the polynomial curve at [Pectin] = 0.0 (wt%) to highlight the polynomial trend. Red open circles and dash-dotted line: <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mo>.</mo> </mrow> <mrow> <mi>DSC</mi> </mrow> </msubsup> </mrow> </semantics></math> values as a function of LMP concentration from the polynomial fitting of the black full circles data and transformation to the cal·mole r.u.<sup>−1</sup> scale. Horizontal red dashed line: average value of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mo>.</mo> </mrow> <mrow> <mi>DSC</mi> </mrow> </msubsup> </mrow> </semantics></math> from figure 8b of [<a href="#B32-polysaccharides-04-00018" class="html-bibr">32</a>]. Inset: reproduction of figure 10b of reference [<a href="#B32-polysaccharides-04-00018" class="html-bibr">32</a>]: pectin concentration dependence of the temperature of maximum heat flow (T<sub>max</sub>) or the mid-point temperature (T<sub>m</sub>), with permission.</p>
Full article ">Figure 12
<p>Dependence on pH of (<b>a</b>) experimental enthalpy change in transition by DSC from [<a href="#B32-polysaccharides-04-00018" class="html-bibr">32</a>]<math display="inline"><semantics> <mrow> <mo>,</mo> <mo> </mo> <mo>Δ</mo> <msubsup> <mi mathvariant="normal">H</mi> <mrow> <mi>e</mi> <mi>x</mi> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mo>.</mo> </mrow> <mrow> <mi>DSC</mi> </mrow> </msubsup> </mrow> </semantics></math> (black squares); calculated values—as described in <a href="#app1-polysaccharides-04-00018" class="html-app">Supplementary paragraph 3.4</a>—of the enthalpy changes of separation, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>s</mi> <mi>e</mi> <mi>p</mi> <mi>a</mi> <mi>r</mi> <mo>.</mo> </mrow> <mrow> <mi>DSC</mi> </mrow> </msubsup> </mrow> </semantics></math> (magenta open circles), of 3<sub>1</sub> → 2<sub>1</sub> transition, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mi mathvariant="normal">H</mi> <mrow> <msub> <mn>3</mn> <mn>1</mn> </msub> <mo>→</mo> <msub> <mn>2</mn> <mn>1</mn> </msub> </mrow> <mrow> <mi>DSC</mi> </mrow> </msubsup> </mrow> </semantics></math>(red open circles) and of loosening, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>l</mi> <mi>o</mi> <mi>o</mi> <mi>s</mi> <mi>e</mi> <mi>n</mi> <mo>.</mo> </mrow> <mrow> <mi>DSC</mi> </mrow> </msubsup> </mrow> </semantics></math> (purple open circles). The superscript “DSC” has been omitted in the figure for simplicity; (<b>b</b>) fraction of repeating units in the 3<sub>1</sub> conformation (open circles, l.h.s. scale) or in the 2<sub>1</sub> conformation (full lozenges, r.h.s. scale) at T = 10 °C (blue color) and at T = 85 °C (red color); fraction of repeating units (relative to the corresponding maximum value of enthalpy change) in the “associated” form (magenta open circles, l.h.s. scale) and in the “ordered” (tightened) conformation (purple open circles, r.h.s. scale); purple stars represent the fractions (relative to maximum) in the ordered conformation as calculated from the optical activity data of [<a href="#B32-polysaccharides-04-00018" class="html-bibr">32</a>]. All curves have been drawn to help the eye only.</p>
Full article ">Figure 13
<p>(<b>a</b>) Dependence on the degree of dissociation, α (full circles), or on the degree of neutralization, α’ (open circles), of the wavelength of maximum ellipticity, λ<sub>max</sub>, (blue symbols, l.h.s. scale) and of the ellipticity, Δε<sub>208</sub>, (red symbols, r.h.s. scale) of poly(galacturonic acid) in water at λ = 208 nm; data replotted from [<a href="#B7-polysaccharides-04-00018" class="html-bibr">7</a>]; (<b>b</b>) dependence on pH (full circles, lower x scale) and on α (open circles, upper x scale) of the enthalpy changes of transition by DSC, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mo>.</mo> </mrow> <mrow> <mi>DSC</mi> </mrow> </msubsup> </mrow> </semantics></math>, (purple symbols, l.h.s. scale), data replotted from [<a href="#B32-polysaccharides-04-00018" class="html-bibr">32</a>]; and dependence on the degree of dissociation, α (full circles), or on the degree of neutralization, α’ (open circles), of the ellipticity at λ = 208 nm of LMP in water (red symbols, r.h.s.); data replotted from [<a href="#B7-polysaccharides-04-00018" class="html-bibr">7</a>].</p>
Full article ">Figure 14
<p>Dependence on pH of the modulus of rigidity, G′, of 3.0 wt% LMP after 100 min at 5 °C (black full circles, data replotted from figure 3a of [<a href="#B32-polysaccharides-04-00018" class="html-bibr">32</a>], l.h.s. scale), of the fraction of maximum association (purple open circles, data replotted from <a href="#polysaccharides-04-00018-sch004" class="html-scheme">Scheme 4</a>, r.h.s. scale) and of the logarithm of tan δ (tan δ = G′′/G′; red open circles and dash-dotted curve, outer l.h.s. scale). The magenta and black dotted rectangles correspond to the dotted rectangles in <a href="#polysaccharides-04-00018-f010" class="html-fig">Figure 10</a>. The transition range of the sigmoid is indicated with a light grey rectangle; the three regimes corresponding to the viscoelastic solution, to the weak gel and to the strong gel have been indicated with dashed rectangles: light blue, magenta and purple, respectively. Inset: reproduction of the data on the dependence of the logarithm of &lt;M&gt;<sub>w</sub> on pH of different LMPs and poly(galacturonic acid) from figure 3 of reference [<a href="#B38-polysaccharides-04-00018" class="html-bibr">38</a>], with permission.</p>
Full article ">Figure 15
<p>Dependence on pH of the negative value of the average slope of log η* vs. log ω (−slope) across the frequency range studied of 3.0 wt% LMP after 100 min at 5 °C (black open circles, data replotted from figure 3a of [<a href="#B32-polysaccharides-04-00018" class="html-bibr">32</a>], l.h.s. scale), and of log tan δ (full grey circles: same data as in <a href="#polysaccharides-04-00018-f013" class="html-fig">Figure 13</a>, r.h.s. scale). The red dashed curve is the parabolic fitting (R<sup>2</sup> = 0.9985) of all data points except that at pH = 1.6; the red open circle is the calculated intercept of the fitting parabola with the line at (−slope) = 1.0; the magenta dotted curve is the parabolic extrapolation to minimum of the (−slope) function and the magenta full circle is the calculated point at minimum. The blue dashed line is the linear best fit of the (−slope) data at pH = 1.6 and 2.0; the blue open circle is the calculated intercept of the fitting line with the line at (−slope) = 1.0. A purple arrow indicates the value of pH corresponding to the maximum tightening and expansion of the 3<sub>1</sub> helical conformation; a red dotted circle represents the close matching of the conditions of the lower pH limit of the conformational transition region, of maximum tightness of the 3<sub>1</sub> helix and of incipient (weak) gel formation: log tan δ = 0.</p>
Full article ">Figure 16
<p>Enthalpy changes upon mixing Na<sup>+</sup> pectate with NaClO<sub>4</sub> in aqueous solution at 25 °C. (<b>a</b>) Blue full circles: salt-free condition (“water”), the abscissa is R<sub>i</sub>, the molar ratio of added NaClO<sub>4</sub> over the polymer concentration (moles r.u.); (<b>b</b>) red full circles; concentration of supporting 1:1 electrolyte: [NaClO<sub>4</sub>] = 0.05 M, the abscissa is δR<sub>i</sub>, the molar ratio of added NaClO<sub>4</sub> over the polymer concentration (moles r.u.). Magenta dashed curves in both panels: theoretical values of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>m</mi> <mi>i</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> for a polyelectrolyte with a linear charge density, ξ, equal to that of Na<sup>+</sup> pectate at α = 1.0 (ξ = <span class="html-italic">l</span><sub>B</sub>/b<sub>0</sub> = 7.13<sub>5</sub>/4.35 = 1.64, where <span class="html-italic">l</span><sub>B</sub> is the Bjerrum length and b<sub>0</sub> was defined in <a href="#sec1dot1-polysaccharides-04-00018" class="html-sec">Section 1.1</a>). Inset in panel (<b>b</b>): enthalpy change upon mixing Na<sup>+</sup> mannuronate with NaClO<sub>4</sub> in aqueous [NaClO<sub>4</sub>] = 0.05 M at 25 °C; purple lozenges, experimental data points, purple dashed curve, theoretical values of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>m</mi> <mi>i</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> for a polyelectrolyte with a linear charge density, ξ, equal to that of Na<sup>+</sup> mannuronate at α = 1.0 (ξ = <span class="html-italic">l</span><sub>B</sub>/b<sub>0</sub> = 7.13<sub>5</sub>/5.17 = 1.38) [<a href="#B76-polysaccharides-04-00018" class="html-bibr">76</a>].</p>
Full article ">Figure 17
<p>Dependence of the difference, <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mrow> <mo>Δ</mo> <mo> </mo> <mi mathvariant="normal">H</mi> <mo> </mo> <mo>¯</mo> </mrow> </mrow> <mrow> <mi>m</mi> <mi>i</mi> <mi>x</mi> </mrow> <mrow> <mi>excess</mi> </mrow> </msubsup> </mrow> </semantics></math>, between the experimental and the theoretical values of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>m</mi> <mi>i</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math>, δR<sub>i</sub> and <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mrow> <mo>Δ</mo> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> </mrow> <mrow> <mi>m</mi> <mi>i</mi> <mi>x</mi> </mrow> <mrow> <mi>theor</mi> </mrow> </msubsup> </mrow> </semantics></math>, respectively, as a function of: (<b>a</b>) δR<sub>i</sub>, i.e., the incremental value of the NaClO<sub>4</sub>/pectate molar ratio R<sub>i</sub>, for the “salt” case (red curve) and the “water” case (blue curve; in this case δR<sub>i</sub> coincides with R<sub>i</sub>). The limit values of <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mrow> <mo>Δ</mo> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> </mrow> <mrow> <mi>m</mi> <mi>i</mi> <mi>x</mi> </mrow> <mrow> <mi>excess</mi> </mrow> </msubsup> </mrow> </semantics></math> at δR<sub>i</sub> → ∞ from <a href="#polysaccharides-04-00018-f015" class="html-fig">Figure 15</a> have been indicated as a red full circle (“salt” case) and a blue full square (“water” case) with the corresponding probable errors. Numbers from (1) to (3) identify the corresponding regions of the two cases as defined in the text (red: “salt”, blue: “water”); (<b>b</b>) the (absolute) value of the molar concentration of NaClO<sub>4</sub> (the added salt, C<sub>s</sub>), for the cases in “salt” (red dashed curve) and in “water” (blue dashed curve). The values of <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mrow> <mo>Δ</mo> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> </mrow> <mrow> <mi>m</mi> <mi>i</mi> <mi>x</mi> </mrow> <mrow> <mi>excess</mi> </mrow> </msubsup> </mrow> </semantics></math> and C<sub>s</sub> at maximum have been indicated in the figure (red: “salt”, blue: “water”). The two asterisks mark the transition from positive to negative values of the corresponding <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mrow> <mo>Δ</mo> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> </mrow> <mrow> <mi>m</mi> <mi>i</mi> <mi>x</mi> </mrow> <mrow> <mi>excess</mi> </mrow> </msubsup> </mrow> </semantics></math> functions: their C<sub>s</sub> values are 0.67 M and to 0.015 M for the “salt” and the “water” case, respectively.</p>
Full article ">Figure 18
<p>Dependence on α (α is the degree of dissociation) of the enthalpy change in loosening, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>l</mi> <mi>o</mi> <mi>o</mi> <mi>s</mi> <mi>e</mi> <mi>n</mi> <mo>.</mo> </mrow> </msub> </mrow> </semantics></math>, as blue symbols, and dependence on β (β is the fraction of unscreened charge; for definition, see text) of the excess enthalpy change in mixing, <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mrow> <mo>Δ</mo> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> </mrow> <mrow> <mi>m</mi> <mi>i</mi> <mi>x</mi> </mrow> <mrow> <mi>excess</mi> </mrow> </msubsup> </mrow> </semantics></math>, red symbols, of pectic acid at 25 °C. The maximum variation of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>l</mi> <mi>o</mi> <mi>o</mi> <mi>s</mi> <mi>e</mi> <mi>n</mi> <mo>.</mo> </mrow> </msub> </mrow> </semantics></math>, of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>t</mi> <mi>i</mi> <mi>g</mi> <mi>h</mi> <mi>t</mi> <mi>e</mi> <mi>n</mi> <mo>.</mo> </mrow> </msub> </mrow> </semantics></math> and of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>l</mi> <mi>y</mi> <mi>o</mi> <mi>t</mi> <mi>r</mi> <mi>o</mi> <mi>p</mi> <mo>.</mo> </mrow> </msub> </mrow> </semantics></math> have been indicated in purple, magenta and deep blue colors, respectively. (<b>a</b>) the “water” case, (<b>b</b>) the “salt” case. β<sub>θ</sub> is the value of β at which the electrostatic and the lyotropic terms are equal; the subscript “θ” has been used to highlight the condition of equality of the opposing interactions, a (kind of) θ-condition of the polyelectrolyte.</p>
Full article ">Figure 19
<p>(<b>a</b>) Dependence on α of the reduced specific viscosity, η<sub>red</sub>, of pectic acid solutions at 25 °C: blue open lozenges and dash-dotted curve, system in “water” (“w”), red open circles and dash-dotted curve, system in “salt” (“s”). The dashed segments are the best linear fit of the data points in the initial range of α (data replotted from <a href="#polysaccharides-04-00018-f001" class="html-fig">Figure 1</a>a); (<b>b</b>) dependence on α of the difference between the experimental values of η<sub>red</sub> and the corresponding values of the linear baseline indicated in panel (<b>a</b>), δ η<sub>red</sub>: blue open lozenges and dash-dotted curve, system in “water” (“w”), red open circles and dash-dotted curve, system in “salt” (“s”). The values of α<sub>1</sub>, α<sub>2</sub>, α<sub>3</sub> for the two cases have also been indicated, together with α<sub>c</sub>, the critical value of α.</p>
Full article ">Figure 20
<p>(<b>a</b>) Dependence on α of δ η<sub>red</sub> of pectic acid in “water” (blue open circles and dash-dotted curve, data from <a href="#polysaccharides-04-00018-f018" class="html-fig">Figure 18</a>b; l.h.s. scale), and of (pKa)<span class="html-italic"><sup>excess</sup></span> (magenta (peak 1) and purple (peak 2) dot-centered lozenges and dashed-dotted curves calculated with the Origin<sup>®</sup> Multiple Peak Fit routine, data calculated as the difference between the experimental (pK<sub>a</sub>)<span class="html-italic"><sup>app.</sup></span>(α) data points of <a href="#polysaccharides-04-00018-f001" class="html-fig">Figure 1</a>b and the dotted line—baseline—there indicated; magenta and purple r.h.s. scale); segments A–D described in the text. I, II, III are the three regions defined in <a href="#sec2dot1-polysaccharides-04-00018" class="html-sec">Section 2.1</a>; (<b>b</b>) dependence on α of the δ η<sub>red</sub> values (blue open circles and dash-dotted curve, l.h.s. scale), of the derivative with respect to α of the integral enthalpy change in transition, d<math display="inline"><semantics> <mrow> <mo>Δ</mo> <msubsup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>t</mi> <mi>r</mi> </mrow> <mrow> <mi>e</mi> <mi>x</mi> <mi>c</mi> <mi>e</mi> <mi>s</mi> <mi>s</mi> </mrow> </msubsup> </mrow> </semantics></math>/dα, from <a href="#polysaccharides-04-00018-f003" class="html-fig">Figure 3</a>a (magenta open circles and dash-dotted curve, inner r.h.s. scale), of the derivative with respect to α of the molar ellipticity at λ = 215 nm, d[<span class="html-italic">ϑ</span>]<sub>215</sub>/dα, from <a href="#polysaccharides-04-00018-f006" class="html-fig">Figure 6</a>b (purple open circles and dash-dotted curve, outer r.h.s. scale; the abscissa has been translated to account for the difference in α stemming from the difference in polymer concentration).</p>
Full article ">Figure 21
<p>(<b>a</b>) Dependence on α of the calculated values of the reduced viscosity, η<sub>red</sub>, in the limit of infinite ionic strength (<span class="html-italic">I</span> → ∞) of pectic acid at 25 °C. Data replotted from figure 2 of reference [<a href="#B31-polysaccharides-04-00018" class="html-bibr">31</a>]. Blue and red full circles represent the limit values of the 3<sub>1</sub> and of the 2<sub>1</sub> conformations at α = 0.0 and 1.0, respectively. Indications of the two conformations and of the conformational transition are given on the plots; (<b>b</b>) dependence on α of the data of panel (<b>a</b>) (magenta open circles and dash-dotted curve, r.h.s. scale), of the experimental values of the reduced viscosity, η<sub>red</sub>, in “water” for comparison (blue dash-dotted curve, r.h.s scale, together with the indication of the two conformational transition ranges) and the relative values (to the value at α = 1.0) of the derivative of η<sub>red</sub> with respect to <span class="html-italic">I</span> <sup>−0.5</sup> (red full circles and dash-dotted curve, l.h.s. scale). Comments are given on the plots.</p>
Full article ">Figure 22
<p>(<b>a</b>) Transversal <sup>23</sup>Na NMR relaxation rates, <math display="inline"><semantics> <mrow> <mi>π</mi> <mo>·</mo> <msub> <mi>ν</mi> <mrow> <mfrac bevelled="true"> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msub> </mrow> </semantics></math>, for sodium poly(galacturonate) solutions at the concentration of 0.08 wt% as a function of the degree of neutralization, α’, at 24 °C and 26.4 MHz. The blue dashed line has been drawn through the two initial points; the red dashed curve is the best fit polynomial in the range of counterion condensation (for α &gt; 0.61); (<b>b</b>) difference between the line through the two initial points and the experimental data of panel (<b>a</b>), δ Δν<sub>1/2</sub>, as a function of the degree of neutralization, α’. Magenta symbols and area represent the range of counterion condensation; the two orange dashed segments have been drawn to guide the eye in the two ranges of the conformational transition.</p>
Full article ">Scheme 1
<p>Schematic representation of the coupling of the “tightness”/“looseness” (or order/disorder) effect—vertical axis—with the conformational equilibrium (between one element of the set of the 3<sub>1</sub> conformations and one element of the set of the 2<sub>1</sub> conformations)—horizontal axis. Top view along the helix axis of the two conformations taken from [<a href="#B41-polysaccharides-04-00018" class="html-bibr">41</a>], with permission, and adapted.</p>
Full article ">Scheme 2
<p>(<b>a</b>). Schematic representation of the enthalpy (internal energy) profile of the two wells of the conformational energy minimum of galacturonan. Narrow horizontal segments represent the range of states visited in each helical conformation, with the corresponding entropy difference; (<b>b</b>) schematic representation of the enthalpy (internal energy) profile of the “tightened” (red) and the “loosened” (purple) forms of the 2<sub>1</sub> helix, with the wider range of accessible states (for both cases indicated by the arrows) and the ensuing variations of both enthalpy and entropy.</p>
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<p>Schematic representation of the hypothetical exothermic contribution to the <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>s</mi> </mrow> </msup> </mrow> </semantics></math> curve of pectic acid in water from the tightening of the 3<sub>1</sub> helical conformation; it masks an endothermic fraction of equal value. This enthalpic process is paralleled by an increase in order, as shown by the parallel increase in [ϑ]<sub>215</sub> (red symbols; from <a href="#polysaccharides-04-00018-f006" class="html-fig">Figure 6</a>b). The “missing” endothermic fraction of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msup> <mrow> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> </mrow> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>s</mi> </mrow> </msup> </mrow> </semantics></math> is sketched as a skewed parabolic segment (light blue); the range of development of the two experimental properties accompanying chain tightening is indicated by the two dotted light blue rectangles. The inset on the r.h.s. sketches the effect of an increase in α on the conformational energy map of galacturonan; the increase in H-boding (ΔE &lt; 0, A) would progressively narrow the accessible area of the map (horizontal blue dotted segments) whereas the electrostatic loosening (ΔE &gt; 0, B) would counteract by widening it. The overall result is a net decrease in accessible states which, however, increasingly loses momentum.</p>
Full article ">Scheme 4
<p>Dependence on pH of association, conformations and ordering of 3 wt% LMP in water at 10 °C. Vertical bars pertain to % of maximum association (grey) to % transformation to the 3<sub>1</sub> (blue) and to the 2<sub>1</sub> (yellow) conformations, respectively. Orange vertical bars pertain to % of maximum ordering resulting from the calorimetric evaluation (see <a href="#polysaccharides-04-00018-sch004" class="html-scheme">Scheme 4</a> and the related discussion); the brown stars pertain to % of maximum ordering resulting from the analysis of the optical activity data of figure 11 of [<a href="#B32-polysaccharides-04-00018" class="html-bibr">32</a>] (the value at pH = 2.5 has been obtained by linear interpolation of those data at pH = 2.0 and 3.0).</p>
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<p>Images of helices (modified after reproduction from [<a href="#B41-polysaccharides-04-00018" class="html-bibr">41</a>], with permission) as viewed along the helical axis represent from left to right: two chains—in the (partially loose) 3<sub>1</sub> conformation—associated through hydrophobic interactions involving facing COOCH<sub>3</sub> groups (as grey circles—pH 1.6 and 2.0); isolated (partially loose) helix in the 3<sub>1</sub> conformation (pH 2.5); isolated—tightened—helix in the 3<sub>1</sub> conformation (pH 3.0); conformational equilibrium <math display="inline"><semantics> <mrow> <msub> <mn>3</mn> <mn>1</mn> </msub> <mo>⇌</mo> <msub> <mn>2</mn> <mn>1</mn> </msub> </mrow> </semantics></math> (pH &gt; 3.0); isolated (partially loose) helix in the 2<sub>1</sub> conformation (pH &gt; 4.0). For a detailed explanation, see text.</p>
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<p>Schematic representation of the proposed variation of the hydrodynamic behavior of pectic acid as a function of α. (1)–(5): significant steps in the considered range; A to D intervals of prevailing behavior; blue color: 3<sub>1</sub> conformation; red color: 2<sub>1</sub> conformation; the size of the rectangles is proportional to the cooperativity, the number of connected rectangles is inversely proportional to it; the style of the border of rectangles reflects loosening: full line—tightened (at α<sub>c</sub>); dashed—slightly loosened (at α<sub>1</sub> and α<sub>1/2</sub>); short dashed—moderately loosened (at α<sub>3</sub>); dotted—very loosened (for α<sub>3</sub> &lt; α &lt; α =1.0). Purple color: tightening; violet color, loosening. Fractions of repeating units in the 3<sub>1</sub> conformation, in the 2<sub>1</sub> conformation and in the loosened form are given in the corresponding colors. Side views of the 3<sub>1</sub> helical conformation and of the 2<sub>1</sub> conformation taken from [<a href="#B41-polysaccharides-04-00018" class="html-bibr">41</a>], with permission, and adapted.</p>
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18 pages, 4473 KiB  
Article
A Phenomenological Model for Enthalpy Recovery in Polystyrene Using Dynamic Mechanical Spectra
by Koh-hei Nitta, Kota Ito and Asae Ito
Polymers 2023, 15(17), 3590; https://doi.org/10.3390/polym15173590 - 29 Aug 2023
Cited by 3 | Viewed by 1672
Abstract
This paper studies the effects of annealing time on the specific heat enthalpy of polystyrene above the glass transition temperature. We extend the Tool–Narayanaswamy–Moynihan (TNM) model to describe the endothermic overshoot peaks through the dynamic mechanical spectra. In this work, we accept the [...] Read more.
This paper studies the effects of annealing time on the specific heat enthalpy of polystyrene above the glass transition temperature. We extend the Tool–Narayanaswamy–Moynihan (TNM) model to describe the endothermic overshoot peaks through the dynamic mechanical spectra. In this work, we accept the viewpoint that the enthalpy recovery behavior of glassy polystyrene (PS) has a common structural relaxation mode with linear viscoelastic behavior. As a consequence, the retardation spectrum evaluated from the dynamic mechanical spectra around the primary Tg peak is used as the recovery function of the endothermic overshoot of specific heat. In addition, the sub-Tg shoulder peak around the Tg peak is found to be related to the structural relaxation estimated from light scattering measurements. The enthalpy recovery of annealed PS is quantitatively described using retardation spectra of the primary Tg, as well as the kinetic process of the sub-Tg relaxation process. Full article
(This article belongs to the Special Issue Polymer Physics: From Theory to Experimental Applications)
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Graphical abstract

Graphical abstract
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<p>Schematic plots of enthalpy and heat capacity during cooling and subsequent heating at a fixed rate for a glassy polymer.</p>
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<p>Schematic illustration of temperature scanning in aging experiment.</p>
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<p>Annealing time dependence of fictive temperature and normalized heat capacity curves at an annealing temperature of 80 °C.</p>
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<p>Annealing time dependence of the normalized change of enthalpy relaxation.</p>
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<p>Annealing time dependence of dynamic mechanical spectra measured at 10 Hz for PS annealed at 80 °C.</p>
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<p>Curve fitting for dynamic mechanical spectra of loss modulus <span class="html-italic">E</span>″ around glass relaxation region at 1, 30, 100, and 200 Hz for PS annealed for 1 h at 80 °C.</p>
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<p>Annealing time dependence of the activation energies of <span class="html-italic">T<sub>g</sub></span> and sub-<span class="html-italic">T<sub>g</sub></span>.</p>
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<p>Frequency dependencies of (<b>a</b>) storage elastic modulus (<span class="html-italic">E</span>′) and loss elastic modulus (<span class="html-italic">E</span>″) and (<b>b</b>) their master curves at <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> °C.</p>
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<p>Scattering angle depends of <span class="html-italic">V<sub>V</sub></span> and <span class="html-italic">H<sub>V</sub></span> scattering intensities.</p>
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<p>Annealing time dependence of correlation length.</p>
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<p>Comparison of normalized heat capacity evaluated from DSC and DMA (primary <span class="html-italic">T<sub>g</sub></span>).</p>
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<p>(<b>a</b>) Comparison of (<b>a</b>) enthalpy loss evaluated from DSC and activation energy of sub-<span class="html-italic">T<sub>g</sub></span> and (<b>b</b>) enthalpy loss <math display="inline"><semantics> <mrow> <mo>∆</mo> <msub> <mrow> <mi>H</mi> </mrow> <mrow> <mi>DSC</mi> </mrow> </msub> </mrow> </semantics></math>/kJmol<sup>−1</sup> and normalized enthalpy loss <math display="inline"><semantics> <mrow> <mo>∆</mo> <msup> <mrow> <mi>H</mi> </mrow> <mrow> <mi>N</mi> </mrow> </msup> </mrow> </semantics></math>/K.</p>
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<p>Comparison of normalized heat capacity evaluated from DSC and DMA (both sub-<span class="html-italic">T<sub>g</sub></span> and primary <span class="html-italic">T<sub>g</sub></span>).</p>
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<p>Schematic illustration of sub-<span class="html-italic">T<sub>g</sub></span> relaxation process.</p>
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15 pages, 1785 KiB  
Article
Effect of Drug Encapsulation and Hydrothermal Exposure on the Structure and Molecular Dynamics of the Binary System Poly(3-hydroxybutyrate)-chitosan
by S. G. Karpova, A. A. Olkhov, I. A. Varyan, A. A. Popov and A. L. Iordanskii
Polymers 2023, 15(10), 2260; https://doi.org/10.3390/polym15102260 - 10 May 2023
Cited by 1 | Viewed by 1750
Abstract
In this work, film materials based on binary compositions of poly-(3-hydroxybutyrate) (PHB) and chitosan with different ratios of polymer components in the range from 0/100 to 100/0 wt. % were studied. Using a combination of thermal (DSC) and relaxation (EPR) measurements, the influence [...] Read more.
In this work, film materials based on binary compositions of poly-(3-hydroxybutyrate) (PHB) and chitosan with different ratios of polymer components in the range from 0/100 to 100/0 wt. % were studied. Using a combination of thermal (DSC) and relaxation (EPR) measurements, the influence of the encapsulation temperature of the drug substance (DS) of dipyridamole (DPD) and moderately hot water (at 70 °C) on the characteristics of the PHB crystal structure and the diffusion rotational mobility of the stable TEMPO radical in the amorphous regions of the PHB/chitosan compositions is shown. The low-temperature extended maximum on the DSC endotherms made it possible to obtain additional information about the state of the chitosan hydrogen bond network. This allowed us to determine the enthalpies of thermal destruction of these bonds. In addition, it is shown that when PHB and chitosan are mixed, significant changes are observed in the degree of crystallinity of PHB, degree of destruction of hydrogen bonds in chitosan, segmental mobility, sorption capacity of the radical, and the activation energy of rotational diffusion in the amorphous regions of the PHB/chitosan composition. The characteristic point of polymer compositions was found to correspond to the ratio of the components of the mixture 50/50%, for which the inversion transition of PHB from dispersed material to dispersion medium is assumed. Encapsulation of DPD in the composition leads to higher crystallinity and to a decrease in the enthalpy of hydrogen bond breaking, and it also slows down segmental mobility. Exposure to an aqueous medium at 70 °C is also accompanied by sharp changes in the concentration of hydrogen bonds in chitosan, the degree of PHB crystallinity, and molecular dynamics. The conducted research made it possible for the first time to conduct a comprehensive analysis of the mechanism of action of a number of aggressive external factors (such as temperature, water, and the introduced additive in the form of a drug) on the structural and dynamic characteristics of the PHB/chitosan film material at the molecular level. These film materials have the potential to serve as a therapeutic system for controlled drug delivery. Full article
(This article belongs to the Special Issue Natural Degradation: Management of Polymer Degradation)
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Figure 1

Figure 1
<p>Heating endotherms of 40/60% PHB/chitosan mixed compositions: (<b>a</b>) initial binary composition and (<b>b</b>) PHB/chitosan/DPD ternary composition.</p>
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<p>Dependence of the thermal characteristics on the composition of the PHB/chitosan composition: (<b>a</b>) the degree of crystallinity of PHB (χ), (<b>b</b>) the enthalpy of cleavage of hydrogen bonds of chitosan (ΔH), and (<b>c</b>) the maximum temperature of decomposition of hydrogen bonds of chitosan (T<sub>D</sub>). The numbers on the curves: 1—binary composition of PHB/chitosan; 2—the same, but with encapsulated DPD; 3—binary composition of PHB/chitosan after exposure in the aquatic environment at 70 °C; 4—the same, but with encapsulated DPD after exposure in the aquatic environment at 70 °C.</p>
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<p>ESR spectra of nitroxyl radical TEMPO for the blends of PHB-chitosan with the content of the polysaccharide: 1—0, 2—30, 3—50, 4—60, 5—70, 6—80, 7—100%.</p>
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<p>Concentration of TEMPO radical (<b>a</b>) and its time of correlation (<b>b</b>) in the PHB–chitosan blends. Binary system (1) and the same system with embedded DPD (2).</p>
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<p>Characteristic time correlation of TEMPO as the blend characterization of hydrothermal action at 70 °C. Time of sample contact with the aqueous medium. (<b>a</b>) Initial binary system; (<b>b</b>) the same system with encapsulated DPD. Time of exposure: 1—0, 2—30, 3—60, 4—120 min.</p>
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<p>Effect of the composition of the PHB/chitosan mixture on the effective activation energy of the rotational mobility of the TEMPO molecular probe. 1—binary system, PHB-chitosan; 2—the same system with encapsulated DPD.</p>
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15 pages, 3639 KiB  
Article
Thermal Behavior of Water in Sephadex® G25 Gels at Low Temperatures Studied by Adiabatic Calorimetry
by Noriko Onoda-Yamamuro, Hiroaki Minato, Eiji Nakayama and Norio Murase
Gels 2023, 9(2), 126; https://doi.org/10.3390/gels9020126 - 2 Feb 2023
Cited by 1 | Viewed by 1508
Abstract
Water in a crosslinked dextran gel, Sephadex® G25, is known to remain partially unfrozen during cooling and undergoes ice crystallization during rewarming. However, the mechanism of ice crystallization during rewarming is still unclear. To elucidate the frozen state of water in the [...] Read more.
Water in a crosslinked dextran gel, Sephadex® G25, is known to remain partially unfrozen during cooling and undergoes ice crystallization during rewarming. However, the mechanism of ice crystallization during rewarming is still unclear. To elucidate the frozen state of water in the gel, thermal behavior at low temperatures was investigated by using adiabatic calorimetry. Heat capacities and enthalpy-relaxation rates of the gel-containing water of mass ratio h (=g H2O/g dry G25) = 1.00 were measured between 80 and 300 K during rewarming, where the gel was intermittently heated at the rate of 50–100 mK min−1. Although an exotherm indicating ice crystallization during rewarming was confirmed with the gel precooled rapidly, at 5 K min−1, it disappeared when precooled slowly, at 20 mK min−1. During rewarming after the rapid cooling, two glass transitions were observed at ca. 175 K and 240–242 K. A higher-temperature glass transition due to the water trapped by the polymer network was not so clear, as it was overlapped with an endotherm due to the melting of small ice crystals, which indicates that the ice crystals formed have a broad size-distribution and that water in the gel is vitrified when ice crystals of even the smallest size cannot be formed. Full article
(This article belongs to the Special Issue Recent Advances in Crosslinked Gels)
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Figure 1
<p>DTA rewarming traces obtained with Sephadex<sup>®</sup> G25 gels (<span class="html-italic">h</span> = 0.29–1.50), where <span class="html-italic">h</span> = g H<sub>2</sub>O/g dry G25. Heating rate was 2 K min<sup>−1</sup> and precooling rate was 5 K min<sup>−1</sup>. The vertical scale was set arbitrarily in each thermogram. ↑: small endotherm, <span style="color:red">↓</span>: exotherm due to ice crystallization, <span style="color:#0070C0">↔</span>: temperature range of exotherm.</p>
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<p>Heat capacities of a Sephadex<sup>®</sup> G25 gel (<span class="html-italic">h</span> = 1.00) dependent on the rate of previous cooling. <span style="color:red">●</span>: rapidly precooled, ●: slowly precooled, <span style="color:#3B37FF">●</span>: annealed. Open circles represent the data obtained before reaching equilibrium. <span class="html-italic">T</span><sub>anneal</sub> indicates a temperature of annealing.</p>
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<p>Rates of the enthalpy change –(d<span class="html-italic">H</span>/d<span class="html-italic">t</span>) dependent on the rate of previous cooling –(d<span class="html-italic">H</span>/d<span class="html-italic">t</span>) &gt; 0: enthalpy release; –(d<span class="html-italic">H</span>/d<span class="html-italic">t</span>) &lt; 0: enthalpy absorption. <span style="color:red">●</span>: rapidly precooled, ●: slowly precooled, <span style="color:#3B37FF">●</span>: annealed. Data of the heat capacity shown in <a href="#gels-09-00126-f002" class="html-fig">Figure 2</a> are redisplayed in (<b>A</b>) for reference. A vertical enlargement of (<b>B</b>) is shown in (<b>C</b>). A lateral enlargement of the green dashed-line area in (<b>C</b>) is shown in (<b>D</b>). The vertical dashed line in blue represents the annealing temperature and the vertical dashed line in black the initiation temperature of ice melting.</p>
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<p>Schematic presentation of typical temperature dependence of the configurational enthalpy <span class="html-italic">H</span><sub>conf</sub> of the molecule near the glass-transition temperature (<b>A</b>) and the spontaneous enthalpy-relaxation rate –(d<span class="html-italic">H</span><sub>conf</sub>/d<span class="html-italic">t</span>) observed in the heat-capacity measurement (<b>B</b>) [<a href="#B10-gels-09-00126" class="html-bibr">10</a>]. The dashed line in (<b>A</b>) indicates the equilibrium enthalpy. The vertical dashed line indicates the glass-transition temperature <span class="html-italic">T</span><sub>g</sub>.</p>
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<p>Heat capacities of the water per mole within the Sephadex<sup>®</sup> G25 gel (<span class="html-italic">h</span> = 1.00) precooled slowly. A black dashed line indicates the heat capacity of the bulk H<sub>2</sub>O (water or ice) [<a href="#B18-gels-09-00126" class="html-bibr">18</a>]. The blue dashed line (1) represents the baseline for determining the configurational enthalpy, and the red dashed line (2) represents the baseline for determining the fusion enthalpy (see text for details).</p>
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<p>Temperature dependence of the configurational enthalpy of the water within the Sephadex<sup>®</sup> G25 gel (<span class="html-italic">h</span> = 1.00) precooled slowly.</p>
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<p>Fusion enthalpy of the water within the slowly precooled gel (●) and the crystallization enthalpy of the water during rewarming observed with the rapidly precooled gel (<span style="color:red">●</span>) and the annealed gel (<span style="color:#3B37FF">●</span>). A red two−directional arrow indicates the crystallization enthalpy in the low subzero-temperature region, and a blue two-directional arrow indicates the crystallization enthalpy in the high subzero-temperature region.</p>
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<p>Schematic diagram of the network structure of Sephadex<sup>®</sup> G25 gel (<span class="html-italic">h</span> = 1.00). Two types of molecular assemblies of water separated from each other are shown. Blue: compartmentalized by the network structure made of crosslinked dextran, pink: confined within the narrow spaces formed by the entangled dextran chains.</p>
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<p>Schematic diagram of the adiabatic calorimeter cryostat used in this study. A: sample cell, B: double adiabatic shields, C: vacuum jacket, D: Dewar vessel.</p>
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<p>Schematic diagram of the temperature change of the sample with time during the heat-capacity measurement by using an adiabatic calorimeter (upper) and an example of the data of the temperature measurement (lower). The measurements were performed by the intermittent-heating method, repetition of an equilibration period (A) and a heating period (B). In the equilibration period (A), the dashed and solid lines represent thermal equilibration time and temperature measuring time, respectively.</p>
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20 pages, 4687 KiB  
Article
Evidence of Self-Association and Conformational Change in Nisin Antimicrobial Polypeptide Solutions: A Combined Raman and Ultrasonic Relaxation Spectroscopic and Theoretical Study
by Afrodite Tryfon, Panagiota Siafarika, Constantine Kouderis, Spyridon Kaziannis, Soghomon Boghosian and Angelos G. Kalampounias
Antibiotics 2023, 12(2), 221; https://doi.org/10.3390/antibiotics12020221 - 20 Jan 2023
Cited by 6 | Viewed by 2269
Abstract
The polypeptide Nisin is characterized by antibacterial properties, making it a compound with many applications, mainly in the food industry. As a result, a deeper understanding of its behaviour, especially after its dissolution in water, is of the utmost importance. This could be [...] Read more.
The polypeptide Nisin is characterized by antibacterial properties, making it a compound with many applications, mainly in the food industry. As a result, a deeper understanding of its behaviour, especially after its dissolution in water, is of the utmost importance. This could be possible through the study of aqueous solutions of Nisin by combining vibrational and acoustic spectroscopic techniques. The velocity and attenuation of ultrasonic waves propagating in aqueous solutions of the polypeptide Nisin were measured as a function of concentration and temperature. The computational investigation of the molecular docking between Nisin monomeric units revealed the formation of dimeric units. The main chemical changes occurring in Nisin structure in the aqueous environment were tracked using Raman spectroscopy, and special spectral markers were used to establish the underlying structural mechanism. Spectral changes evidenced the presence of the dimerization reaction between Nisin monomeric species. The UV/Vis absorption spectra were dominated by the presence of π → π* transitions in the peptide bonds attributed to secondary structural elements such as α-helix, β-sheets and random coils. The analysis of the acoustic spectra revealed that the processes primarily responsible for the observed chemical relaxations are probably the conformational change between possible conformers of Nisin and its self-aggregation mechanism, namely, the dimerization reaction. The activation enthalpy and the enthalpy difference between the two isomeric forms were estimated to be equal to ΔH1* = 0.354 ± 0.028 kcal/mol and ΔH10 = 3.008 ± 0.367 kcal/mol, respectively. The corresponding thermodynamic parameters of the self-aggregation mechanism were found to be ΔH2* = 0.261 ± 0.004 kcal/mol and ΔH20 = 3.340 ± 0.364 kcal/mol. The effect of frequency on the excess sound absorption of Nisin solutions enabled us to estimate the rate constants of the self-aggregation mechanism and evaluate the isentropic and isothermal volume changes associated with the relaxation processes occurring in this system. The results are discussed in relation to theoretical and experimental findings. Full article
(This article belongs to the Section Antimicrobial Peptides)
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Figure 1

Figure 1
<p>The molecular structure of polypeptide Nisin.</p>
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<p>(<b>a</b>) Self-association reaction as predicted by the molecular docking study. Red circles denote the binding sites between Nisin monomers. (<b>b</b>) Binding regions of the two monomers constituting the dimer. (<b>c</b>,<b>d</b>) The two parts of the dimer structure of Nisin that were used for the theoretical calculation of vibrational frequencies denoted by ellipses. The yellow dashed line corresponds to a hydrogen bond between atoms belonging to a different monomer chain.</p>
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<p>(<b>a</b>) Concentration dependence of the polarized (VV) Stokes-side Raman spectra of aqueous Nisin solutions in the dilute region corresponding to concentrations from 0 (solvent) to 5 mM with steps of 1 mM. The spectrum of Nisin in the solid state is also shown at the bottom. (<b>b</b>) Theoretically predicted Raman spectra corresponding to the binding regions of the two monomers constituting the dimer denoted by ellipses in <a href="#antibiotics-12-00221-f002" class="html-fig">Figure 2</a>b. See text for details. The experimental Raman spectra of pure Nisin in the solid state and in solution at the concentration of 5 mM are also shown for comparison.</p>
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<p>UV-Vis absorption spectra of Nisin as a function of concentration at 20 °C.</p>
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<p>Acoustic absorption as a function of frequency at 20 °C in Nisin solutions. Solid lines represent the total fitting curves as received from the fitting procedure described in the text.</p>
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<p>Representative fitting example of excess ultrasound absorption in a Nisin solution with C = 5 mM at 20 °C. The continuous red line represents the total relaxation curve, while the two individual dashed, and dot-dashed relaxation curves are assigned to distinct relaxation processes as described in the text. Circles correspond to the experimental data. Absorption coefficient α<span class="html-italic">/f</span><sup>2</sup> corresponding to the solvent was found to be frequency independent in the MHz range covered here and was subtracted from the absorption coefficient of the solution.</p>
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<p>Ultrasonic relaxation amplitude <span class="html-italic">A<sub>i</sub></span> (<b>a</b>,<b>c</b>) and relaxation frequency <span class="html-italic">f<sub>ri</sub></span> (<b>b</b>,<b>d</b>) as functions of Nisin concentration at 20 °C. The error of relaxation frequency <span class="html-italic">f<sub>r</sub></span> was estimated to be lower than ±2.5%, while the corresponding error for A and B was below ±5%. Subscripts 1 and 2 denote the acoustic parameters related to the conformational changes and self-aggregation of Nisin, respectively.</p>
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<p>Frequency-reduced ultrasonic absorption <span class="html-italic">α</span>/<span class="html-italic">f</span><sup>2</sup> for Nisin solution at concentration C = 3 mM. Continuous lines represent relaxation curves for each temperature after the fitting procedure. Reduction in the <span class="html-italic">α</span>/<span class="html-italic">f</span><sup>2</sup> ratio with the increase in frequency was observed for all temperatures, which is typical of an ultrasonic relaxation process.</p>
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<p>Ultrasonic relaxation amplitude <span class="html-italic">A<sub>i</sub></span> (<b>a</b>,<b>c</b>) and relaxation frequency <span class="html-italic">f<sub>ri</sub></span> (<b>b</b>,<b>d</b>) as functions of temperature for Nisin solution at concentration C = 3 mM. As in <a href="#antibiotics-12-00221-f007" class="html-fig">Figure 7</a>, subscripts 1 and 2 denote the acoustic parameters related to the conformational changes and self-aggregation of Nisin, respectively.</p>
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<p>Relaxation frequencies as functions of reciprocal temperature for conformational change (<b>a</b>) and aggregation mechanism (<b>c</b>). Graphs of ln(<span class="html-italic">Tμ<sub>max</sub>/u</span><sup>2</sup>) versus 1<span class="html-italic">/T</span> for conformational change (<b>b</b>) and aggregation mechanism (<b>d</b>).</p>
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<p>Isothermal and isentropic volume changes due to confirmational change (<b>a</b>) and self-aggregation (<b>b</b>) as functions of Nisin concentration. The enthalpy term contributes only slightly, and isothermal and isentropic volume changes are comparable in both relaxation processes.</p>
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<p>Intermolecular free length as a function of concentration at 20 °C (<b>a</b>) and temperature (<b>b</b>) at three selected solution concentrations.</p>
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13 pages, 2225 KiB  
Article
DMSO-Induced Unfolding of the Antifungal Disulfide Protein PAF and Its Inactive Variant: A Combined NMR and DSC Study
by András Czajlik, Ágnes Batta, Kinga Kerner, Ádám Fizil, Dorottya Hajdu, Mária Raics, Katalin E. Kövér and Gyula Batta
Int. J. Mol. Sci. 2023, 24(2), 1208; https://doi.org/10.3390/ijms24021208 - 7 Jan 2023
Cited by 3 | Viewed by 2135
Abstract
PAF and related antifungal proteins are promising antimicrobial agents. They have highly stable folds around room temperature due to the presence of 3–4 disulfide bonds. However, unfolded states persist and contribute to the thermal equilibrium in aqueous solution, and low-populated states might influence [...] Read more.
PAF and related antifungal proteins are promising antimicrobial agents. They have highly stable folds around room temperature due to the presence of 3–4 disulfide bonds. However, unfolded states persist and contribute to the thermal equilibrium in aqueous solution, and low-populated states might influence their biological impact. To explore such equilibria during dimethyl sulfoxide (DMSO)-induced chemical unfolding, we studied PAF and its inactive variant PAFD19S using nuclear magnetic resonance (NMR) and differential scanning calorimetry (DSC). According to the NMR monitoring at 310 K, the folded structures disappear above 80 v/v% DMSO concentration, while the unfolding is completely reversible. Evaluation of a few resolved peaks from viscosity-compensated 15N-1H HSQC spectra of PAF yielded ∆G = 23 ± 7 kJ/M as the average value for NMR unfolding enthalpy. The NMR-based structures of PAF and the mutant in 50 v/v% DMSO/H2O mixtures were more similar in the mixed solvents then they were in water. The 15N NMR relaxation dynamics in the same mixtures verified the rigid backbones of the NMR-visible fractions of the proteins; still, enhanced dynamics around the termini and some loops were observed. DSC monitoring of the Tm melting point showed parabolic dependence on the DMSO molar fraction and suggested that PAF is more stable than the inactive PAFD19S. The DSC experiments were irreversible due to the applied broad temperature range, but still suggestive of the endothermic unfolding of PAF. Full article
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Figure 1
<p>The assigned <sup>1</sup>H-<sup>15</sup>N HSQC spectrum of the PAF in the presence of 50% DMSO, added to an acetate buffer (pH 4.5), as measured with a NEO 700 MHz spectrometer (Bruker) at 310 K temperature. Residue specific NH peak assignments are labelled: see also BMRB 34655 deposition in case of overlap.</p>
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<p>Comparison of the solution backbone structures in water (blue) and in 50% DMSO (green). PAF (2MHV vs. 7PGD) (<b>A</b>) and PAF<sup>D19S</sup> (2NB0 vs. 7NXI) (<b>B</b>). Overlaid structures of PAF (blue) and PAF<sup>D19S</sup> (red) as measured in 50% DMSO (<b>C</b>). The mutation site is labelled with red (<b>A</b>,<b>B</b>) or yellow (<b>C</b>). (PyMOL visualization software was used).</p>
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<p>S<sup>2</sup> order parameters of the NH vectors in PAF ((<b>A</b>), 310 K, 70.96 MHz) and PAF<sup>D19S</sup>, ((<b>B</b>), 298 K, 50.68 MHz), as measured from <sup>15</sup>N relaxation experiments, and the Lipari–Szabo method was used for evaluation. Errors are shown on the top of the bars. A few data are not shown due to spectral overlap and from 29-Pro residue (see also <a href="#app1-ijms-24-01208" class="html-app">Supplementary Table S1B</a>).</p>
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<p>Reduced spectral density mapping as obtained in 50 <span class="html-italic">v</span>/<span class="html-italic">v</span>% DMSO from <sup>15</sup>N relaxation data for PAF ((<b>A</b>), 310 K) and PAF<sup>D19S</sup>, ((<b>B</b>), 298 K). The same input experimental data were used as for <a href="#ijms-24-01208-f003" class="html-fig">Figure 3</a> (see also <a href="#app1-ijms-24-01208" class="html-app">Supplementary Table S1</a>). The continuous curve represents the absence of internal motion. Spectral densities (i.e., the strength of radiofrequency (RF) fields from molecular motions) at the <sup>15</sup>N frequency JomN are shown as a function of RF fields close to zero frequency J0 (slow-motion regime). The units of both axes are 10<sup>−9</sup> (s rad<sup>−1</sup>).</p>
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<p>Thermodynamic stability of PAF (<b>A</b>) and PAF<sup>D19S</sup> (<b>B</b>) as a function of the DMSO concentration. Second-order polynomials fitted to the melting point temperatures (T<sub>m</sub>) are shown in both cases. T<sub>m</sub> values are shown in °C on the vertical scale.</p>
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<p>Titration of <sup>15</sup>N-PAF with gradually increasing the DMSO-d<sub>6</sub> concentration at 310 K temperature, as measured using a Bruker AVANCE-II 500 MHz spectrometer. The series of <sup>1</sup>H-<sup>15</sup>N HSQC spectra display the changes in the chemical shifts and intensity of the amide NH groups.</p>
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<p>The NMR unfolding enthalpies as derived for six well-separated peaks of PAF (C7, K9, C14, K15, G21, and T37) and for the average (<b>A</b>), as obtained from HSQC experiments measured at 310 K temperature. For the average of six peak volumes (<b>B</b>), we obtained ∆G<sub>F-U</sub> = 20.0 kJ/M, and the fit error was 3.1%, while the individual errors were in the 4–9% range (see also <a href="#app1-ijms-24-01208" class="html-app">Figure S3</a>).</p>
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16 pages, 3695 KiB  
Article
Numerical Study on Heat-Transfer Characteristics of Convection Melting in Metal Foam under Sinusoidal Temperature Boundary Conditions
by Xiang-Bo Feng, Shi-Fan Huo, Xiao-Tao Xu, Fei Liu and Qing Liu
Entropy 2022, 24(12), 1779; https://doi.org/10.3390/e24121779 - 5 Dec 2022
Cited by 1 | Viewed by 1557
Abstract
Convection melting in metal foam under sinusoidal temperature boundary conditions is numerically studied in the present study. A multiple-relaxation-time lattice Boltzmann method, in conjunction with the enthalpy approach, is constructed to model the melting process without iteration steps. The effects of the porosity, [...] Read more.
Convection melting in metal foam under sinusoidal temperature boundary conditions is numerically studied in the present study. A multiple-relaxation-time lattice Boltzmann method, in conjunction with the enthalpy approach, is constructed to model the melting process without iteration steps. The effects of the porosity, phase deviation, and periodicity parameter on the heat-transfer characteristics are investigated. For the cases considered in this work, it is found that the effects of the phase deviation and periodicity parameter on the melting rate are weak, but the melting front can be significantly affected by the sinusoidal temperature boundary conditions. Full article
(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics)
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<p>Physical model.</p>
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<p>The melting front (<math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mi>l</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>) at different <span class="html-italic">Fo</span>.</p>
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<p>Temperature profiles (<math display="inline"><semantics> <mrow> <mrow> <mi>y</mi> <mo>/</mo> <mi>L</mi> </mrow> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>) at different <span class="html-italic">Fo</span>.</p>
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<p>The total liquid fractions for different <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> with <span class="html-italic">Ra</span> = 10<sup>6</sup>, <span class="html-italic">φ</span> = π/4 and <span class="html-italic">k</span> = 0.</p>
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<p>The total liquid fractions for <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math> and 0.95 under non-uniform and uniform thermal boundary conditions.</p>
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<p>The total liquid fractions for different values of <math display="inline"><semantics> <mi>φ</mi> </semantics></math> under non-uniform thermal boundary conditions.</p>
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<p>The liquid-fraction fields for different values of <math display="inline"><semantics> <mi>φ</mi> </semantics></math> with <span class="html-italic">Φ</span> = 0.8 under non-uniform thermal boundary conditions (<span class="html-italic">Fo</span> = 0.0025, <span class="html-italic">Ra</span> = 10<sup>6</sup>, <span class="html-italic">k</span> = 0, <span class="html-italic">N<sub>x</sub></span> × <span class="html-italic">N<sub>y</sub></span> = 150 × 150).</p>
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<p>The liquid-fraction fields for different values of <math display="inline"><semantics> <mi>φ</mi> </semantics></math> with <span class="html-italic">Φ</span> = 0.95 under non-uniform thermal boundary conditions (<span class="html-italic">Fo</span> = 0.0065, <span class="html-italic">Ra</span> = 10<sup>6</sup>, <span class="html-italic">k</span> = 0, <span class="html-italic">N<sub>x</sub></span> × <span class="html-italic">N<sub>y</sub></span> = 150 × 150).</p>
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<p>The liquid-fraction fields for different values of <math display="inline"><semantics> <mi>φ</mi> </semantics></math> with <span class="html-italic">Φ</span> = 0.95 under non-uniform thermal boundary conditions (<span class="html-italic">Fo</span> = 0.0065, <span class="html-italic">Ra</span> = 10<sup>6</sup>, <span class="html-italic">k</span> = 0, <span class="html-italic">N<sub>x</sub></span> × <span class="html-italic">N<sub>y</sub></span> = 150 × 150).</p>
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<p>The total liquid fractions for different values of <math display="inline"><semantics> <mi>φ</mi> </semantics></math> under non-uniform thermal boundary conditions (<span class="html-italic">Ra</span> = 10<sup>6</sup>, <span class="html-italic">Φ</span> = 0.9 and <span class="html-italic">φ</span> = 0).</p>
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<p>The liquid-fraction fields for different values of <math display="inline"><semantics> <mi>k</mi> </semantics></math> under non-uniform thermal boundary conditions (<span class="html-italic">Fo</span> = 0.002, <span class="html-italic">Ra</span> = 10<sup>6</sup>, <span class="html-italic">Φ</span> = 0.9, <span class="html-italic">φ</span> = 0, <span class="html-italic">N<sub>x</sub></span>× <span class="html-italic">N<sub>y</sub></span> = 150 × 150).</p>
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