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20 pages, 3095 KiB  
Article
Scaling Relationships of the Structural and Rheological Behavior of Tadpole Polymer Chains in Dilute Solution Systems Using Brownian Dynamics Simulations
by Chaehyun Cho and Jun Mo Kim
Polymers 2024, 16(20), 2871; https://doi.org/10.3390/polym16202871 - 11 Oct 2024
Viewed by 907
Abstract
Tadpole polymers, also known as lasso polymers, feature molecular structures that combine a single ring with a single linear side branch, leading to distinct conformational, dynamical, and rheological characteristics compared to their corresponding counterparts, particularly pure linear and pure ring polymers. To elucidate [...] Read more.
Tadpole polymers, also known as lasso polymers, feature molecular structures that combine a single ring with a single linear side branch, leading to distinct conformational, dynamical, and rheological characteristics compared to their corresponding counterparts, particularly pure linear and pure ring polymers. To elucidate the mechanisms underlying these distinctive behaviors, comprehensive mesoscopic Brownian dynamics (BD) simulations of dilute solution systems of tadpole polymers were conducted using a bead–rod chain model under both equilibrium and flow conditions. Three types of tadpole polymer chains were prepared by varying the ring-to-linear ratio within the tadpole chain and comparing them with the corresponding linear and ring chains. Depending on this ratio, tadpole polymer chains exhibit entirely different structural properties and rotational dynamics, both in equilibrium and under shear flow. As the linear proportion within the tadpole chain increased, the structural, dynamic, and rheological properties of the tadpole polymer chains became more similar to those of pure linear polymers. Conversely, with an increasing ring proportion, these properties began to resemble those of pure ring polymers. Based on these observed tendencies, a simple general scaling expression is proposed for tadpole polymer properties that integrates scaling expressions for both pure linear and pure ring polymers. Our results indicate that the conformational, dynamic, and rheological properties of tadpole polymers, as predicted by these simple scaling expressions, are in good agreement with the simulated values, a result we consider statistically significant. Full article
(This article belongs to the Special Issue Rheological Properties of Polymers and Polymer Composites)
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Figure 1

Figure 1
<p>Schematic representation of three types of tadpole chain polymers designed with different ring-to-linear ratios within the chain. Note that <span class="html-italic">N<sub>R</sub></span> and <span class="html-italic">N<sub>L</sub></span> represent the number of beads in the ring and linear side branches, respectively. (<b>a</b>) T_R33L33 chain, with 33 beads in the ring and 33 beads in the linear side branch. (<b>b</b>) T_R33L66 chain, with 33 beads in the ring and 66 beads in the linear side branch. (<b>c</b>) T_R66L33 chain, with 66 beads in the ring and 33 beads in the linear side branch.</p>
Full article ">Figure 2
<p>Comparison of (<b>a</b>) snapshots of a randomly selected individual chain in pure linear, pure ring, and tadpole polymer systems in equilibrium, and (<b>b</b>) time autocorrelation function (TACF) of chain unit end-to-end vector, <b><span class="html-italic">u</span></b>. For tadpole polymers, the chain unit end-to-end vector <b><span class="html-italic">u</span></b> is defined as the sum of the chain ring diameter vector, <b>R</b><sub>d</sub>, and the unit end-to-end vector of the linear side branch, <b>R</b><sub>L</sub>.</p>
Full article ">Figure 3
<p>The mean-square radius of gyration, <math display="inline"><semantics> <mrow> <mfenced close="&#x232A;" open="&#x2329;"> <mrow> <msubsup> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">g</mi> <mn>2</mn> </msubsup> </mrow> </mfenced> </mrow> </semantics></math>, of (<b>a</b>) the entire tadpole chain, (<b>b</b>) the ring part within the tadpole polymer chain, and (<b>c</b>) the linear side branch within the tadpole polymer chain as a function of <span class="html-italic">Wi</span>. The statistical uncertainties are represented by standard errors, which were calculated according to [<a href="#B95-polymers-16-02871" class="html-bibr">95</a>], for all simulation results. The error bars are smaller than the symbol sizes unless otherwise specified. The mean-square radius of gyration, <math display="inline"><semantics> <mrow> <mfenced close="&#x232A;" open="&#x2329;"> <mrow> <msubsup> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">g</mi> <mn>2</mn> </msubsup> </mrow> </mfenced> </mrow> </semantics></math>, of all tadpole chain systems, as well as corresponding pure linear and ring chain systems, can be found in <a href="#app1-polymers-16-02871" class="html-app">Figure S1 of the Supplementary Material</a>.</p>
Full article ">Figure 4
<p>Probability distribution function (PDF) of <math display="inline"><semantics> <mrow> <mfenced close="|" open="|"> <mrow> <msub> <mi mathvariant="bold">R</mi> <mi>g</mi> </msub> </mrow> </mfenced> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi mathvariant="normal">P</mi> <mfenced> <mrow> <mfenced close="|" open="|"> <mrow> <msub> <mi mathvariant="bold">R</mi> <mi>g</mi> </msub> </mrow> </mfenced> </mrow> </mfenced> </mrow> </semantics></math>, for the chain in shear flow. The <math display="inline"><semantics> <mrow> <mi mathvariant="normal">P</mi> <mfenced> <mrow> <mfenced close="|" open="|"> <mrow> <msub> <mi mathvariant="bold">R</mi> <mi>g</mi> </msub> </mrow> </mfenced> </mrow> </mfenced> </mrow> </semantics></math> for the entire tadpole chains in both (<b>a</b>) the weak shear flow regime (<span class="html-italic">Wi</span> = 0.1) and (<b>b</b>) the strong shear flow regime (<span class="html-italic">Wi</span> = 100) is presented. Additionally, the <math display="inline"><semantics> <mrow> <mi mathvariant="normal">P</mi> <mfenced> <mrow> <mfenced close="|" open="|"> <mrow> <msub> <mi mathvariant="bold">R</mi> <mi>g</mi> </msub> </mrow> </mfenced> </mrow> </mfenced> </mrow> </semantics></math> is provided for (<b>c</b>) the ring part and (<b>d</b>) thelinear side branch part of the tadpole polymer chain in the strong flow regime (<span class="html-italic">Wi</span> = 100).</p>
Full article ">Figure 5
<p>Schematic illustration of chain rotation and tumbling motions for (<b>a</b>) T_R33L33 chain, (<b>b</b>) T_R33L66 chain, and (<b>c</b>) T_R66L33 chain during a tumbling cycle under shear flow. The ring and linear side branches of the tadpole polymer chain are colored in blue and orange, respectively. The green and yellow dots serve to illustrate the complex chain rotation and tumbling behavior of the tadpole polymer chains.</p>
Full article ">Figure 6
<p>(<b>a</b>) Time autocorrelation function (TACF) of the chain unit end-to-end vector, <b><span class="html-italic">u</span></b>, for the selected tadpole polymer chain system at <span class="html-italic">Wi</span> = 100. (<b>b</b>) Rotational time for the selected tadpole polymer chain system as a function of <span class="html-italic">Wi</span>. The rotational times for all tadpole chain systems and corresponding pure linear and ring chain systems can be found in <a href="#app1-polymers-16-02871" class="html-app">Figure S2 of the Supplementary Material</a>.</p>
Full article ">Figure 7
<p>Macroscopic rheological properties of tadpole polymer chains. (<b>a</b>) Shear viscosity, <math display="inline"><semantics> <mi>η</mi> </semantics></math>, and (<b>b</b>) first normal stress coefficient, <math display="inline"><semantics> <mrow> <msub> <mo>Ψ</mo> <mn>1</mn> </msub> </mrow> </semantics></math>, as a function of <span class="html-italic">Wi</span>. The shear viscosity, <math display="inline"><semantics> <mi>η</mi> </semantics></math>, and first normal stress coefficient, <math display="inline"><semantics> <mrow> <msub> <mo>Ψ</mo> <mn>1</mn> </msub> </mrow> </semantics></math>, for all tadpole chain and corresponding pure linear and ring chain systems can be found in <a href="#app1-polymers-16-02871" class="html-app">Figures S3 and S4 in the Supplementary Material</a>.</p>
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17 pages, 5385 KiB  
Article
Mechanistic Insight into the Enantioselective Degradation of Esterase QeH to (R)/(S)–Quizalofop–Ethyl with Molecular Dynamics Simulation Using a Residue-Specific Force Field
by Yu-Meng Zhu, Gui Yao, Song Shao, Xin-Yu Liu, Jun Xu, Chun Chen, Xing-Wang Zhang, Zhuo-Ran Huang, Cheng-Zhen Xu, Long Zhang and Xiao-Min Wu
Int. J. Mol. Sci. 2024, 25(18), 9964; https://doi.org/10.3390/ijms25189964 - 15 Sep 2024
Viewed by 1299
Abstract
The enantioselective mechanism of the esterase QeH against the two enantiomers of quizalofop–ethyl (QE) has been primitively studied using computational and experimental approaches. However, it is still unclear how the esterase QeH adjusts its conformation to adapt to substrate binding and promote enzym [...] Read more.
The enantioselective mechanism of the esterase QeH against the two enantiomers of quizalofop–ethyl (QE) has been primitively studied using computational and experimental approaches. However, it is still unclear how the esterase QeH adjusts its conformation to adapt to substrate binding and promote enzyme–substrate interactions in the catalytic kinetics. The equilibrium processes of enzyme–substrate interactions and catalytic dynamics were reproduced by performing independent molecular dynamics (MD) runs on the QeH-(R)/(S)-QE complexes with a newly developed residue-specific force field (RSFF2C). Our results indicated that the benzene ring of the (R)-QE structure can simultaneously form anion–π and cation–π interactions with the side-chain group of Glu328 and Arg384 in the binding cavity of the QeH-(R)-QE complex, resulting in (R)-QE being closer to its catalytic triplet system (Ser78-Lys81-Tyr189) with the distances measured for the hydroxyl oxygen atom of the catalytic Ser78 of QeH and the carbonyl carbon atom of (R)-QE of 7.39 Å, compared to the 8.87 Å for (S)-QE, whereas the (S)-QE structure can only form an anion–π interaction with the side chain of Glu328 in the QeH-(S)-QE complex, being less close to its catalytic site. The computational alanine scanning mutation (CAS) calculations further demonstrated that the π–π stacking interaction between the indole ring of Trp351 and the benzene ring of (R)/(S)-QE contributed a lot to the binding stability of the enzyme–substrate (QeH-(R)/(S)-QE). These results facilitate the understanding of their catalytic processes and provide new theoretical guidance for the directional design of other key enzymes for the initial degradation of aryloxyphenoxypropionate (AOPP) herbicides with higher catalytic efficiencies. Full article
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<p>The proposed catabolic pathway of (<span class="html-italic">R</span>)–quizalofop–ethyl and (<span class="html-italic">S</span>)–quizalofop–ethyl by the esterase QeH.</p>
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<p>Ramachandran plot (<b>A</b>) and verify 3D score (<b>B</b>) for the QeH model. The red regions indicated the most favored areas, the yellow regions represented the generously allowed areas, and the blank regions was the disallowed areas. The yellow line in the VERIFY plot (<b>B</b>) represented a threshold for the averaged 3D-1D score, specifically at Y = 0.1. This line was used to indicate areas or scores that meet or exceed this threshold value.</p>
Full article ">Figure 3
<p>Molecular dynamics simulations of the QeH-(<span class="html-italic">R</span>)-QE and QeH-(<span class="html-italic">S</span>)-QE complexed systems. The root-mean-square deviation (RMSD) and root-mean-square fluctuation (RMSF) curves of the QeH-(<span class="html-italic">R</span>)-QE (<b>A</b>,<b>C</b>) and QeH-(<span class="html-italic">S</span>)-QE (<b>B</b>,<b>D</b>) complexed systems as functions of simulation time during the MD runs.</p>
Full article ">Figure 4
<p>The ten representative snapshots of (<span class="html-italic">R</span>)-QE (<b>A</b>) and (<span class="html-italic">S</span>)-QE (<b>B</b>) superposed at their respective QeH active sites inside the interior of hydrophobic pocket during their MD runs. Key residues of QeH and two ligands were represented by stick models, and the residues (Tyr331, Tyr350, Trp351, Gly352 and Arg384 for the QeH-(<span class="html-italic">R</span>)-QE complex; Tyr189, Phe326, Glu328, Tyr350, Trp351 and Val354 for the QeH-(<span class="html-italic">S</span>)-QE complex) with their respective binding affinities over −1.0 kcal·mol<sup>−1</sup> were marked by black labels.</p>
Full article ">Figure 5
<p>The total binding free energy (∆<span class="html-italic">G<sub>bind</sub></span>) contributions of the QeH-(<span class="html-italic">R</span>)-QE (<b>A</b>) and QeH-(<span class="html-italic">S</span>)-QE (<b>B</b>) complexes. Each residue for the QeH-(<span class="html-italic">R</span>)-QE and QeH-(<span class="html-italic">S</span>)-QE complexes calculated from the equilibrated conformations during independent MD runs. The residues contribution exceeding −1.00 kcal·mol<sup>−1</sup> to the binding free energy were marked with red dashed lines.</p>
Full article ">Figure 6
<p>The key interactions at the active sites of the representative conformations of the QeH-(<span class="html-italic">R</span>)-QE and QeH-(<span class="html-italic">S</span>)-QE complexes with equilibrium stabilization. The interactions derived from the representative conformation of the QeH-(<span class="html-italic">R</span>)-QE (<b>A</b>,<b>B</b>) and QeH-(<span class="html-italic">S</span>)-QE (<b>C</b>,<b>D</b>) complexes generated by the MD simulations were represented by dotted lines in different colors, and the unit of interaction distances was Å.</p>
Full article ">Figure 7
<p>Time-dependent distances between the hydroxyl oxygen atom of the catalytic Ser78 of QeH and the carbonyl carbon atom of (<span class="html-italic">R</span>)/(<span class="html-italic">S</span>)-QE (<b>A</b>), and the representation of the catalytic triad of QeH and the substrate (<span class="html-italic">R</span>)/(<span class="html-italic">S</span>)-QE (<b>B</b>,<b>C</b>). The catalytic triad (Ser78, Lys81, and Tyr189) of QeH was in blue and green, whereas the (<span class="html-italic">R</span>)/(<span class="html-italic">S</span>)-QE was salmon.</p>
Full article ">Figure 8
<p>Schematic illustration of the ester bond hydrolysis process of (<span class="html-italic">R</span>)-QE catalyzed by esterase QeH. The purple arrows displayed the transfer reaction of hydrogen atoms, and the dotted green lines showed the formation of hydrogen bonds between hydroxyl hydrogen atoms and nitrogen atoms on amino groups.</p>
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19 pages, 2237 KiB  
Article
The Application of Osmodehydrated Tomato and Spinach in Ready-to-Eat Mixed Salad Products: Design, Development, and Shelf Life Study
by Alexandros Katsimichas, George Dimopoulos, Efimia Dermesonlouoglou and Petros Taoukis
Appl. Sci. 2024, 14(13), 5863; https://doi.org/10.3390/app14135863 - 4 Jul 2024
Viewed by 771
Abstract
Osmotically dehydrated cherry tomatoes and spinach leaves were incorporated into Greek salad-type (including OD-treated and air-dried feta cheese trimmings and air-dried olive rings) and green salad-type (including OD-treated and air-dried feta cheese trimmings and roasted ground peanuts) ready-to-eat (RTE) product prototypes, respectively. The [...] Read more.
Osmotically dehydrated cherry tomatoes and spinach leaves were incorporated into Greek salad-type (including OD-treated and air-dried feta cheese trimmings and air-dried olive rings) and green salad-type (including OD-treated and air-dried feta cheese trimmings and roasted ground peanuts) ready-to-eat (RTE) product prototypes, respectively. The osmotic dehydration of cherry tomatoes and spinach leaves was conducted in a pilot scale setting (100 L) in a 60% glycerol-based solution at 35 °C and 25 °C for 180 min and 60 min, respectively. To quantify the moisture transfer between the three ingredients of different moisture content (and water activity), the moisture equilibrium curves for each ingredient of the RTE product were determined. The equilibrium water activity of RTE products was 0.86 and 0.76, respectively. The quality of the RTE products (more specifically, tomato and spinach color and texture, instrumentally measured and sensorially perceived, sensory characteristics) was evaluated. The shelf life of the prototypes (from 4 °C to 20 °C) was kinetically modeled based on sensory deterioration and microbial growth, using the zero-order kinetic model and the Gompertz model, respectively. In the case of the tomato-based product, a shelf life of 54 days (based on sensory deterioration) was achieved at 4 °C, a shelf-life extension of 40 days compared to untreated, fresh-cut tomato. The shelf life of the spinach-based product (based on sensory deterioration) was 36 days at 4 °C, 30 days longer when compared to untreated spinach. Our results indicate that osmotic dehydration was successful in significantly extending the shelf life of such products, contributing to the increased temperature resilience of their keeping quality and allowing for their distribution and storage in a variable cold chain. Full article
(This article belongs to the Special Issue Innovative Technologies for Food Preservation and Processing)
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<p>OD-treated (<b>a</b>) tomato- and (<b>b</b>) spinach-based ready-to-eat (RTE) salad product prototypes.</p>
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<p>Apparent moisture equilibrium curves at 25 °C for (<b>a</b>) OD-treated tomatoes, (<b>b</b>) dehydrated olives and (<b>c</b>) OD-treated and air-dried cheese. The dashed lines represent the fitting of the GAB model (Equation (1)) to the experimental data.</p>
Full article ">Figure 3
<p>Apparent moisture equilibrium curves at 25 °C for (<b>a</b>) OD-treated spinach, (<b>b</b>) peanuts and (<b>c</b>) OD-treated and air-dried cheese. The dashed lines represent the fitting of the GAB model to the experimental data.</p>
Full article ">Figure 4
<p>Evolution of microbial load of the tomato-based composite product with storage time for all storage temperatures studied (4, 8, 12, 20 °C): (<b>a</b>) total viable counts, (<b>b</b>) total molds (<b>c</b>) yeasts and molds. Dashed lines represent the fitting of the Gompertz model to the experimental data.</p>
Full article ">Figure 5
<p>Evolution of sensory liking of the (<b>a</b>) OD-treated tomato and (<b>b</b>) OD-treated spinach-based RTE product with storage time for storage temperatures 4, 8, 12, 20 °C. Dashed lines represent fitting of the zero-order kinetic model to the experimental data, where applicable.</p>
Full article ">Figure 6
<p>Evolution of (<b>a</b>) the total color difference Δ<span class="html-italic">Ε</span> and (<b>b</b>) the relative firmness (<span class="html-italic">F</span>/<span class="html-italic">F</span><sub>0</sub>) of tomatoes in the tomato-based RTE product with storage time at storage temperatures 4, 8, 12, 20 °C.</p>
Full article ">Figure 7
<p>Evolution of (<b>a</b>) the total color difference (Δ<span class="html-italic">Ε</span>) and (<b>b</b>) the relative burst strength of OD-treated spinach samples with storage time at storage temperatures 4, 8, 12, and 20 °C.</p>
Full article ">Figure 8
<p>Shelf-life (SL) curves of the developed (<b>a</b>) tomato- (based on microbial growth and sensory criteria) and (<b>b</b>) spinach- (based on sensory criteria) based RTE products at storage temperatures 4–20 °C. Lines represent the prediction of the shelf life based on the overall mathematical models developed. The continuous red line represents the expected shelf life of the product if untreated tomatoes had been used in the formulation.</p>
Full article ">
14 pages, 5780 KiB  
Article
Exploring the Odd–Even Effect, Current Stabilization, and Negative Differential Resistance in Carbon-Chain-Based Molecular Devices
by Lijun Wang, Liping Zhou, Xuefeng Wang and Wenlong You
Electronics 2024, 13(9), 1764; https://doi.org/10.3390/electronics13091764 - 2 May 2024
Cited by 1 | Viewed by 1187
Abstract
The transport properties of molecular devices based on carbon chains are systematically investigated using a combination of non-equilibrium Green’s function (NEGF) and density functional theory (DFT) first-principle methods. In single-carbon-chain molecular devices, a distinct even–odd behavior of the current emerges, primarily influenced by [...] Read more.
The transport properties of molecular devices based on carbon chains are systematically investigated using a combination of non-equilibrium Green’s function (NEGF) and density functional theory (DFT) first-principle methods. In single-carbon-chain molecular devices, a distinct even–odd behavior of the current emerges, primarily influenced by the density of states (DOS) within the chain channel. Additionally, linear, monotonic currents exhibit Ohmic contact characteristics. In ladder-shaped carbon-chain molecular devices, a notable current stabilization behavior is observed, suggesting their potential utility as current stabilizers within circuits. We provide a comprehensive analysis of the transport properties of molecular devices featuring ladder-shaped carbon chains connecting benzene-ring molecules. The occurrence of negative differential resistance (NDR) in the low-bias voltage region is noted, with the possibility of manipulation by adjusting the position of the benzene-ring molecule. These findings offer a novel perspective on the potential applications of atom chains. Full article
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Figure 1
<p>(<b>a</b>) Atomic structure of the single-carbon-chain devices. The blue rectangle areas indicate the left and right electrodes, between which is the central scattering region. (<b>b</b>) I–V curves of C4–C9. The inset is the zero-bias transmission spectra of C4–C9.</p>
Full article ">Figure 2
<p>(<b>a</b>) The atomic structure of device C9 is shown as an example to indicate the three projected component parts, which are L, R, and the chain. (<b>b</b>) The total density of states of devices C4–C9. Projected density of states of devices C4–C9, (<b>c</b>) part L, and (<b>d</b>) part R.</p>
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<p>The PDOSchain of devices (<b>a</b>) C4, (<b>b</b>) C5, (<b>c</b>) C6, (<b>d</b>) C7, (<b>e</b>) C8, and (<b>f</b>) C9.</p>
Full article ">Figure 4
<p>(<b>a</b>) Atomic structure of the ladder-shaped carbon-chain devices. The blue rectangle areas indicate the left and right electrodes, between which is the central scattering region. (<b>b</b>) I–V curves of all the ladder-shaped carbon-chain devices. The inset shows the zero-bias transmission spectra of L4 and L8.</p>
Full article ">Figure 5
<p>Transmission spectra for (<b>a</b>) device L4 and (<b>b</b>) device L8 under various bias voltages. The red dotted area is the bias window.</p>
Full article ">Figure 6
<p>(<b>a</b>) Total density of states of devices L4 and L8. Projected density of states of devices L4 and L8, (<b>b</b>) the chain, (<b>c</b>) part L, and (<b>d</b>) part R.</p>
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<p>Top view of devices D1–D5. The electron transport is along the z-axis. The blue rectangle areas indicate the left and right electrodes, between which is the central scattering region.</p>
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<p>Zero-bias transmission spectra of D1–D5.</p>
Full article ">Figure 9
<p>Conductance spectra of devices D1, D2, and D3 are plotted in (<b>a</b>,<b>c</b>,<b>e</b>), respectively. The molecular-energy spectra for the central molecule corresponding to each device are indicated with several red straight lines. The energy bands of the virtual bulks corresponding to devices D1, D2, and D3 are presented in (<b>b</b>,<b>d</b>,<b>f</b>), respectively. In devices D2 and D3, some bands corresponding to the bands of device D1 are marked with the same numbers as device D1.</p>
Full article ">Figure 9 Cont.
<p>Conductance spectra of devices D1, D2, and D3 are plotted in (<b>a</b>,<b>c</b>,<b>e</b>), respectively. The molecular-energy spectra for the central molecule corresponding to each device are indicated with several red straight lines. The energy bands of the virtual bulks corresponding to devices D1, D2, and D3 are presented in (<b>b</b>,<b>d</b>,<b>f</b>), respectively. In devices D2 and D3, some bands corresponding to the bands of device D1 are marked with the same numbers as device D1.</p>
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<p>The wave function for <span class="html-italic">k</span> = 0 states in each and every band of the virtual bulk corresponding to device D1.</p>
Full article ">Figure 11
<p>(<b>a</b>) Energy bands of a 6-ZGNR bulk calculated with unit cell of four primitive cells. (<b>b</b>) The wave function of the four bands. (<b>c</b>) The wave functions of LUMO, HOMO, HOMO-1, and HOMO-2 of the central molecule of device D1.</p>
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<p>I–V curves of D1–D5.</p>
Full article ">
12 pages, 511 KiB  
Article
Richard Kerner’s Path Integral Approach Aims to Understand the Self-Organized Matter Agglomeration and Its Translation into the Energy Landscape Kinetics Paradigm
by Gerardo G. Naumis
Axioms 2024, 13(1), 8; https://doi.org/10.3390/axioms13010008 - 22 Dec 2023
Viewed by 1414
Abstract
Matter grows and self-assembles to produce complex structures such as virus capsids, carbon fullerenes, proteins, glasses, etc. Due to its complexity, performing pen-and-paper calculations to explain and describe such assemblies is cumbersome. Many years ago, Richard Kerner presented a pen-and-paper path integral approach [...] Read more.
Matter grows and self-assembles to produce complex structures such as virus capsids, carbon fullerenes, proteins, glasses, etc. Due to its complexity, performing pen-and-paper calculations to explain and describe such assemblies is cumbersome. Many years ago, Richard Kerner presented a pen-and-paper path integral approach to understanding self-organized matter. Although this approach successfully addressed many important problems, including the yield of fullerene formation, the glass transition temperature of doped chalcogenide glasses, the fraction of boroxol rings in B2O3 glasses, the first theoretical explanation for the empirical recipe of window and Pyrex glass and the understanding of virus capsid self-assembly, it still is not the primary choice when tackling similar problems. The reason lies in the fact that it diverges from mainstream approaches based on the energy landscape paradigm and non-equilibrium thermodynamics. In this context, a critical review is presented, demonstrating that the Richard Kerner method is, in fact, a clever way to identify relevant configurations. Its equations are simplified common physical sense versions of those found in the energy landscape kinetic equations. Subsequently, the utilization of equilibrium Boltzmann factors in the transition Markov chain probabilities is analyzed within the context of local two-level energy landscape models kinetics. This analysis demonstrates that their use remains valid when the local energy barrier between reaction coordinate states is small compared to the thermal energy. This finding places the Richard Kerner model on par with other more sophisticated methods and, hopefully, will promote its adoption as an initial and useful choice for describing the self-agglomeration of matter. Full article
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Figure 1
<p>Agglomeration model of Se<math display="inline"><semantics> <msub> <mrow/> <mrow> <mn>1</mn> <mo>−</mo> <mi>x</mi> </mrow> </msub> </semantics></math>As<math display="inline"><semantics> <msub> <mrow/> <mi>x</mi> </msub> </semantics></math> glass. A cluster made of Se atoms, with coordination <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>S</mi> <mi>e</mi> </mrow> </msub> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> and As atoms, with coordination <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>A</mi> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> as indicated by the curve. The unsatisfied bonds at the rim of the cluster are indicated by dotted edges bonds. The three kinds of surface sites <span class="html-italic">u</span>, <span class="html-italic">v</span>, <span class="html-italic">w</span> are indicated. Free atoms in the melt are indicated with arrows that indicate the velocity vector.</p>
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<p>A funnel energy landscape <span class="html-italic">E</span> as a function of the reaction coordinate <span class="html-italic">q</span>. The circle indicates that in a certain energy range, locally, the system can be seen as the two-level model depicted below the landscape. In this reduced two-level model, we indicate the barrier height <span class="html-italic">V</span> and the energy <math display="inline"><semantics> <msub> <mi>E</mi> <mn>1</mn> </msub> </semantics></math> of the high-energy states and <math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> of the local ground state.</p>
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17 pages, 8769 KiB  
Article
Size- and Voltage-Dependent Electron Transport of C2N-Rings-Based Molecular Chains
by Dian Song, Jie Li, Kun Liu, Junnan Guo, Hui Li and Artem Okulov
Molecules 2023, 28(24), 7994; https://doi.org/10.3390/molecules28247994 - 7 Dec 2023
Cited by 2 | Viewed by 1407
Abstract
C2N-ring-based molecular chains were designed at the molecular level and theoretically demonstrated to show distinctive and valuable electron transport properties that were superior to the parent carbonaceous system and other similar nanoribbon-based molecular chains. This new -type molecular chain presented an [...] Read more.
C2N-ring-based molecular chains were designed at the molecular level and theoretically demonstrated to show distinctive and valuable electron transport properties that were superior to the parent carbonaceous system and other similar nanoribbon-based molecular chains. This new -type molecular chain presented an exponential attenuation of the conductance and electron transmission with the length. Essentially, the molecular chain retained the electron-resonant tunneling within 7 nm and the dominant transport orbital was the LUMO. Shorter molecular chains with stronger conductance anomalously possessed a larger tunnel barrier energy, attributing to the compensation of a much smaller HOMO–LUMO gap, and these two internal factors codetermined the transport capacity. Some influencing factors were also studied. In contrast to the common O impurity with a tiny effect on electron transmission of the C2N rings chain, the common H impurity clearly improved it. When the temperature was less than 400 K, the electron transmission varied with temperature within a narrow range, and the structural disorder deriving from proper heating did not greatly modify the transmission possibility and the exponentially decreasing tendency with the length. In a non-equilibrium condition, the current increased overall with the bias but the growth rate varied with size. A valuable negative differential resistance (NDR) effect appeared in longer molecular chains with an even number of big carbon–nitrogen rings and strengthened with size. The emergence of such an effect originated from the reduction in transmission peaks. The conductance of longer molecular chains was enhanced with the voltage but the two shortest ones presented completely different trends. Applying the bias was demonstrated to be an effective way for C2N-ring-based molecular chains to slow down the conductance decay constant and affect the transport regime. C2N-ring-based molecular chains show a perfect application in tunneling diodes and controllable molecular devices. Full article
(This article belongs to the Special Issue Advances in Molecular Modeling in Chemistry)
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<p>(<b>a</b>) Geometry of C<sub>2</sub>N monolayer.The unit cell is indicated by the red dashed circle and the corresponding. Molecular electrostatic potential is shown in <a href="#app1-molecules-28-07994" class="html-app">Figure S1 of Supporting Information (SI)</a> [<a href="#B17-molecules-28-07994" class="html-bibr">17</a>]. (<b>b</b>–<b>d</b>) Structure schematic of C<sub>2</sub>N-ring-chain-based devices, 2D-C<sub>2</sub>N-based device and GNR-based device, respectively.</p>
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<p>(<b>a</b>) Equilibrium quantum conductance—number of C<sub>2</sub>N rings curve with an exponential fit and conductance of 2D-C<sub>2</sub>N-based device. (<b>b</b>) lnG as a function of length with a linear fit. (<b>c</b>) Changes in the conductance decay constant within the length range of [2.85, 7] nm. (<b>d1</b>,<b>d2</b>) LUMOs and HOMOs for representative device C<sub>2</sub>N rings 1, 2, 3, 4, 7 and 8, respectively.</p>
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<p>(<b>a</b>) Equilibrium electron transmission for E<sub>F</sub> number of C<sub>2</sub>N rings curve with an exponential fit and the transmission of a 2D-C<sub>2</sub>N-based device. (<b>b</b>) Tunnel barrier energy as a function of number of C<sub>2</sub>N rings in [1, 8], and the inset shows the corresponding changes in a narrower range of [3, 8]. (<b>c1</b>–<b>c4</b>) Transmission pathways of representative device C<sub>2</sub>N rings 1, 2, 3 and 8, respectively. (<b>d</b>) HOMO–LUMO gap as a function of number of C<sub>2</sub>N rings. (<b>e</b>) Conductance as a function of HOMO–LUMO gap of C<sub>2</sub>N rings.</p>
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<p>(<b>a</b>) Conductance at E<sub>F</sub> as a function of number of rings (1–8) for GNR-based devices. The inset shows the number range [3, 8]. (<b>b</b>) lnG as a function of length for GNR-based devices. (<b>c</b>) Comparison of conductance between C<sub>2</sub>N-ring-chain-based devices and GNR-based devices changing with the length. (<b>d</b>) Electron transmission at E<sub>F</sub> as a function of number of rings (1–8) for GNR-based devices. The inset shows the number range [3, 8]. (<b>e</b>) Comparison of electron transmission at E<sub>F</sub> between C<sub>2</sub>N-ring-chain-based devices and GNR-based devices changing with the length. (<b>f</b>–<b>h</b>) Transmission spectrum around E<sub>F</sub> of GNR-based devices in transmission ranges [0, 0.2], [0, 1.38 × 10<sup>−3</sup>] and [0, 2 × 10<sup>−4</sup>], respectively.</p>
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<p>(<b>a</b>) Electron transmission at E<sub>F</sub> of the C<sub>2</sub>N ring chains with O and H impurities, changing with the number of C<sub>2</sub>N rings. The insets show the positions of two such impurities. (<b>b</b>) Comparison of electron transmission at E<sub>F</sub> of the C<sub>2</sub>N ring chains with no defect and O and H impurities, changing with the length of the chains. (<b>c</b>) Electron transmission spectrum around E<sub>F</sub> of device C<sub>2</sub>N ring 1 with no defect and O and H impurities. (<b>d</b>) Electron transmission at E<sub>F</sub> as a function of the number of C<sub>2</sub>N rings at 300 K. The insets show the corresponding 5 structures of the C<sub>2</sub>N ring chains at 300 K. (<b>e</b>) Comparison of electron transmission at E<sub>F</sub> of C<sub>2</sub>N rings at 0 K and 300 K changing with the number of C<sub>2</sub>N rings and the length (shown in the inset), respectively. (<b>f</b>) Electron transmission at E<sub>F</sub> of device C<sub>2</sub>N rings 1 and 2 as a function of the temperature T. (<b>g</b>,<b>h</b>) Electron transmission at E<sub>F</sub> as a function of the number of C<sub>2</sub>N rings for the C<sub>2</sub>N-ring-chain-based devices with 2D graphene electrodes and 3D Au electrodes, respectively. The insets show the device structures. (<b>i</b>) Comparison of electron transmission at E<sub>F</sub> of C<sub>2</sub>N ring chains based on 3 different electrodes changing with the length of the chains. For clarity, all comparisons are shown on a logarithmic scale.</p>
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<p>(<b>a</b>–<b>c</b>) I–V curves of representative device C<sub>2</sub>N rings 1, 4 and 7, respectively. Each inset shows the first derivative of corresponding I–V curve. (<b>d</b>,<b>e</b>) I–V curves of device C<sub>2</sub>N rings 6 and 7, respectively. I–V curves within the specific bias interval are exhibited in the insets. (<b>f</b>) I–V curve of the device 2D-C<sub>2</sub>N.</p>
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<p>(<b>a</b>–<b>d</b>) Transmission spectrum within narrower energy ranges at 0 V, 0.1 V, 0.2 V, 0.3 V and 0.4 V of representative device C<sub>2</sub>N rings 1, 3, 6 and 8, respectively. (<b>e</b>) Transmission spectrum at 0.3 V and 0.325 V of device C<sub>2</sub>N ring 6. (<b>f</b>) Transmission spectrum at 0.19 V and 0.235 V of device C<sub>2</sub>N ring 8. (<b>g</b>,<b>h</b>) Transmission spectrum in (<b>e</b>,<b>f</b>) within narrower energy ranges.</p>
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<p>(<b>a</b>–<b>c</b>) Conductance–voltage functions of device 2D-C<sub>2</sub>N, device C<sub>2</sub>N ring 1 and device C<sub>2</sub>N ring 2, respectively. (<b>d</b>,<b>e</b>) Comparison of the conductance changing with bias for device C<sub>2</sub>N rings 3, 4, 5, 6, 7 and 8 on linear and log scales, respectively. (<b>f</b>,<b>g</b>) Conductance as a function of number of C<sub>2</sub>N rings with an exponential fit at 0.1 V and 0.4 V, respectively. Each inset exhibits the corresponding lnG as a function of length with a linear fit. (<b>h</b>) Changing trend of the conductance decay constant with voltage.</p>
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<p>The comparison of electron transmission spectrum calculated with GGA and HSE06 functionals.</p>
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17 pages, 2266 KiB  
Article
Conformational Parameters and Hydrodynamic Behavior of Poly(2-Methyl-2-Oxazoline) in a Broad Molar Mass Range
by Alexander S. Gubarev, Alexey A. Lezov, Anna N. Podsevalnikova, Nina G. Mikusheva, Petr A. Fetin, Ivan M. Zorin, Vladimir O. Aseyev, Ondrej Sedlacek, Richard Hoogenboom and Nikolai V. Tsvetkov
Polymers 2023, 15(3), 623; https://doi.org/10.3390/polym15030623 - 25 Jan 2023
Cited by 7 | Viewed by 2838
Abstract
In this work, we report our results on the hydrodynamic behavior of poly(2-methyl-2-oxazoline) (PMeOx). PMeOx is gaining significant attention for use as hydrophilic polymer in pharmaceutical carriers as an alternative for the commonly used poly(ethylene glycol) (PEG), for which antibodies are found in [...] Read more.
In this work, we report our results on the hydrodynamic behavior of poly(2-methyl-2-oxazoline) (PMeOx). PMeOx is gaining significant attention for use as hydrophilic polymer in pharmaceutical carriers as an alternative for the commonly used poly(ethylene glycol) (PEG), for which antibodies are found in a significant fraction of the human population. The main focus of the current study is to determine the hydrodynamic characteristics of PMeOx under physiological conditions, which serves as basis for better understanding of the use of PMeOx in pharmaceutical applications. This goal was achieved by studying PMeOx solutions in phosphate-buffered saline (PBS) as a solvent at 37 °C. This study was performed based on two series of PMeOx samples; one series is synthesized by conventional living cationic ring-opening polymerization, which is limited by the maximum chain length that can be achieved, and a second series is obtained by an alternative synthesis strategy based on acetylation of well-defined linear poly(ethylene imine) (PEI) prepared by controlled side-chain hydrolysis of a defined high molar mass of poly(2-ethyl-2-oxazoline). The combination of these two series of PMeOx allowed the determination of the Kuhn–Mark–Houwink–Sakurada equations in a broad molar mass range. For intrinsic viscosity, sedimentation and diffusion coefficients, the following expressions were obtained: η=0.015M0.77, s0=0.019M0.42 and D0=2600M0.58, respectively. As a result, it can be concluded that the phosphate-buffered saline buffer at 37 °C represents a thermodynamically good solvent for PMeOx, based on the scaling indices of the equations. The conformational parameters for PMeOx chains were also determined, revealing an equilibrium rigidity or Kuhn segment length, (A) of 1.7 nm and a polymer chain diameter (d) of 0.4 nm. The obtained value for the equilibrium rigidity is very similar to the reported values for other hydrophilic polymers, such as PEG, poly(vinylpyrrolidone) and poly(2-ethyl-2-oxazoline), making PMeOx a relevant alternative to PEG. Full article
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Figure 1
<p>The distributions are obtained with SEC: (<b>a</b>)—the PMeOx samples are eluted with DMA/LiCl and (<b>b</b>)—DMF/LiBr. The numbers next to the distributions correspond to the sample numbering.</p>
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<p>(<b>a</b>): The normalized specific viscosity <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mrow> <mi>s</mi> <mi>p</mi> </mrow> </msub> <mo>/</mo> <mi>c</mi> </mrow> </semantics></math> (open symbols) and natural logarithm of relative viscosity <math display="inline"><semantics> <mrow> <mi>ln</mi> <msub> <mi>η</mi> <mi>r</mi> </msub> <mo>/</mo> <mi>c</mi> </mrow> </semantics></math> (filled symbols) vs. concentration <math display="inline"><semantics> <mi>c</mi> </semantics></math> in PBS at 37 °C; (<b>b</b>): the dependence of <math display="inline"><semantics> <mrow> <mfenced> <mrow> <mi>ρ</mi> <mo>−</mo> <msub> <mi>ρ</mi> <mn>0</mn> </msub> </mrow> </mfenced> </mrow> </semantics></math> vs. concentration <math display="inline"><semantics> <mi>c</mi> </semantics></math> in H<sub>2</sub>O at 37 °C, obtained for the studied PMeOx samples. The numbers next to the data points correspond to sample numbering.</p>
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<p>(<b>a</b>): The normalized <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>norm</mi> </mrow> </msub> <mfenced> <mi>s</mi> </mfenced> </mrow> </semantics></math> distributions vs. sedimentation coefficients <math display="inline"><semantics> <mi>s</mi> </semantics></math> resolved with Sedfit at the lowest studied concentrations <math display="inline"><semantics> <mrow> <mi>c</mi> <mo>≈</mo> <mn>0.025</mn> </mrow> </semantics></math> g/dL and (<b>b</b>): the normalized distributions of weight–component concentration <math display="inline"><semantics> <mrow> <mi>w</mi> <mo>/</mo> <msub> <mi>w</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> over hydrodynamic radii <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>h</mi> </msub> </mrow> </semantics></math>. Both <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mrow> <mi>norm</mi> </mrow> </msub> <mfenced> <mi>s</mi> </mfenced> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>w</mi> <mo>/</mo> <msub> <mi>w</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> are obtained for PMeOx solutions in PBS at 37 °C. The numbers next to the distributions correspond to the sample numbering.</p>
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<p>(<b>a</b>): The double logarithmic plot of KMHS relationships, for intrinsic viscosity (1), sedimentation coefficients (2) and diffusion coefficients (3) obtained for PMeOx samples in PBS solutions at 37 °C, (4) represents the combined analysis of the viscometry data obtained herein and in earlier studies (ref. [<a href="#B41-polymers-15-00623" class="html-bibr">41</a>]) for PMeOx in H<sub>2</sub>O solutions at 20 °C. The equation parameters are presented in <a href="#polymers-15-00623-t004" class="html-table">Table 4</a>. (<b>b</b>): The specific hydrodynamic volume plot, representing data for relevant water soluble polymers: PVP in 0.1 M sodium acetate at 25 °C [<a href="#B66-polymers-15-00623" class="html-bibr">66</a>]; PEG disregarding end-groups in H<sub>2</sub>O at 20 °C [<a href="#B67-polymers-15-00623" class="html-bibr">67</a>] and 25 °C [<a href="#B68-polymers-15-00623" class="html-bibr">68</a>,<a href="#B69-polymers-15-00623" class="html-bibr">69</a>]; PEtOX in H<sub>2</sub>O at 20 °C [<a href="#B41-polymers-15-00623" class="html-bibr">41</a>] and PBS at 37 °C [<a href="#B45-polymers-15-00623" class="html-bibr">45</a>]; PMeOx in H<sub>2</sub>O at 20 °C, is combined data of the research herein [<a href="#B41-polymers-15-00623" class="html-bibr">41</a>], and PMeOx in PBS at 37 °C is from the data of the current study; lines (1) and (2) are the linear extrapolation of PVP and PEG data.</p>
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13 pages, 2082 KiB  
Article
Unsaturated Copolyesters from Macrolactone/Norbornene: Toward Reaction Kinetics of Metathesis Copolymerization Using Ruthenium Carbene Catalysts
by Araceli Martínez, Daniel Zárate-Saldaña, Joel Vargas and Arlette A. Santiago
Int. J. Mol. Sci. 2022, 23(9), 4521; https://doi.org/10.3390/ijms23094521 - 20 Apr 2022
Cited by 1 | Viewed by 2219
Abstract
Unsaturated copolyesters are of great interest in polymer science due to their broad potential applications and sustainability. Copolyesters were synthesized from the ring-opening metathesis copolymerization of ω-6-hexadecenlactone (HDL) and norbornene (NB) using ruthenium-alkylidene [Ru(Cl2)(=CHPh)(1,3-bis(2,4,6-trimethylphenyl)-2-imidazolidinylidene)(PCy3)] (Ru1 [...] Read more.
Unsaturated copolyesters are of great interest in polymer science due to their broad potential applications and sustainability. Copolyesters were synthesized from the ring-opening metathesis copolymerization of ω-6-hexadecenlactone (HDL) and norbornene (NB) using ruthenium-alkylidene [Ru(Cl2)(=CHPh)(1,3-bis(2,4,6-trimethylphenyl)-2-imidazolidinylidene)(PCy3)] (Ru1), [Ru(Cl)2(=CHPh)(PCy3)2] (Ru2), and ruthenium-vinylidene [RuCl2(=C=CH(p-C6H4CF3))(PCy3)2] (Ru3) catalysts, respectively, yielding HDL-NB copolymers with different ratios of the monomer HDL in the feed. The activity of N-heterocyclic-carbene (NHC) (Ru1) and phosphine (Ru2 and Ru3) ligands containing ruthenium-carbene catalysts were evaluated in the synthesis of copolymer HDL-NB. The catalysts Ru1 with an NHC ligand showed superior activity and stability over catalysts Ru2 and Ru3 bearing PCy3 ligands. The incorporation of the monomers in the copolymers determined by 1H-NMR spectroscopy was similar to that of the HDL-NB values in the feed. Experiments, at distinct monomer molar ratios, were carried out using the catalysts Ru1Ru3 to determine the copolymerization reactivity constants by applying the Mayo–Lewis and Fineman–Ross methods. The copolymer distribution under equilibrium conditions was studied by the 13C NMR spectra, indicating that the copolymer HDL-NB is a gradient copolymer. The main factor determining the decrease in melting temperature is the inclusion of norbornene units, indicating that the PNB units permeate trough the HDL chains. The copolymers with different molar ratios [HDL]/[NB] have good thermal stability up to 411 °C in comparison with the homopolymer PHDL (384 °C). Further, the stress–strain measurements in tension for these copolymers depicted the appreciable increment in stress values as the NB content increases. Full article
(This article belongs to the Collection Frontiers in Polymeric Materials)
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<p><sup>1</sup>H-NMR (400 MHz, CDCl<sub>3</sub>) spectrum of the copolymer HDL-NB (<a href="#ijms-23-04521-t001" class="html-table">Table 1</a>, <span class="html-italic">entry 12</span>).</p>
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<p><sup>13</sup>C-NMR (100 MHz, CDCl<sub>3</sub>) spectrum for the copolymer HDL-NB (<a href="#ijms-23-04521-t001" class="html-table">Table 1</a>, <span class="html-italic">entry 7</span>).</p>
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<p>(<b>A</b>) Second-heat thermograms of DSC and (<b>B</b>) X-ray diffraction pattern of PHD, PNB, and HDL-NB copolymers (from 10:1 to 1:10).</p>
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<p>Strain–stress curves of pure PNB, PHDL, and HDL-NB copolymers with several molar ratios [HDL]/[NB].</p>
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<p>HDL copolymers with NB <span class="html-italic">via</span> ROMP.</p>
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33 pages, 10111 KiB  
Article
Stability of Rhodamine Lactone Cycle in Solutions: Chain–Ring Tautomerism, Acid–Base Equilibria, Interaction with Lewis Acids, and Fluorescence
by Olena M. Obukhova, Nikolay O. Mchedlov-Petrossyan, Natalya A. Vodolazkaya, Leonid D. Patsenker and Andrey O. Doroshenko
Colorants 2022, 1(1), 58-90; https://doi.org/10.3390/colorants1010006 - 24 Feb 2022
Cited by 9 | Viewed by 4830
Abstract
The equilibrium between different tautomers that can be colored or colorless is an important feature for rhodamine dyes. Presently, this phenomenon is mostly discussed for rhodamine B. Herein, we studied the tautomerism and acid–base dissociation (HR+ ⇄ R + H+) [...] Read more.
The equilibrium between different tautomers that can be colored or colorless is an important feature for rhodamine dyes. Presently, this phenomenon is mostly discussed for rhodamine B. Herein, we studied the tautomerism and acid–base dissociation (HR+ ⇄ R + H+) of a set of rhodamines in organic media. Form R is an equilibrium mixture of the colored zwitterion R± and colorless lactone R0. Absorption spectra in 90 mass% aqueous acetone reflects the correlation between the dyes structure and the equilibrium constant, KT = [R0]/[R±]. Increase in the pKa value on transferring from water to organic solvents confirms the highly polar character of the R± tautomer. To reveal the role of the solvent nature, the tautomerism of an asymmetrical rhodamine, 2-(12-(diethyliminio)-2,3,5,6,7,12-hexahydro-1H-chromeno[2,3-f]pyrido[3,2,1-ij]quinolin-9-yl)benzoate, was examined in 14 media. This chain–ring tautomerism is an intramolecular acid–base reaction; the central carbon atom acts as a Lewis acid. The interaction with other Lewis acids, Li+, Ca2+, Mg2+, and La3+, results in rupture of lactone cycle. In polar solvents, lactones undergo photocleavage resulting in formation of highly fluorescent R±, whereas the blue fluorescence and abnormally high Stokes shift in low-polar media may be explained either by another photoreaction or by spiroconjugation and charge transfer in the exited state. Full article
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Figure 1
<p>Absorption spectra of HR<sup>+</sup> and R species of substance <b>5</b> in <span class="html-italic">n</span>-butanol (<b>a</b>), 2-methyl-propane-2-ol (<span class="html-italic">tert</span>-butanol) (<b>b</b>), acetonitrile (<b>c</b>), and DMSO (<b>d</b>). Dye concentrations were around 1 × 10<sup>−5</sup> M except the spectra of the form R in acetonitrile and DMSO, where the concentration was 7 × 10<sup>−5</sup> M.</p>
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<p>Infrared spectra of compound <b>5</b> (0.03 M) in DMSO in cationic form HR<sup>+</sup> and neutral form, mainly as lactonic tautomer R<sup>0</sup>.</p>
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<p>Correlations between the experimental <sup>13</sup>C NMR spectra of lactone (inclusion of both aromatic and aliphatic atoms were needed for identification of C-9) and zwitterion (only aromatic atoms are included) tautomers of compound <b>5</b> and corresponding calculated magnetic shielding.</p>
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<p>Absorption of the cationic and neutral forms of rhodamine dyes in 90 mass% aqueous acetone. The HR<sup>+</sup> and R spectra are obtained in 0.01 M HCl and 0.001 M NaOH, respectively. Dye concentrations are around 10<sup>−5</sup> M.</p>
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<p>Absorption of the cationic and neutral forms of rhodamine dyes in 90 mass% aqueous acetone. The HR<sup>+</sup> and R spectra are obtained in 0.01 M HCl and 0.001 M NaOH, respectively. Dye concentrations are around 10<sup>−5</sup> M.</p>
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<p>Dependence of the sum of absorbances of dye <b>5</b> at 550, 555, 560, and 565 nm on pH in aqueous solutions (1) and <math display="inline"><semantics> <mrow> <mi mathvariant="normal">p</mi> <msubsup> <mi>a</mi> <mrow> <msup> <mi mathvariant="normal">H</mi> <mo>+</mo> </msup> </mrow> <mo>∗</mo> </msubsup> </mrow> </semantics></math> in 90 mass % aqueous acetone (2).</p>
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<p>Dependence of the logarithm of tautomerization constant of dye <b>5</b> in different solvents on the (<math display="inline"><semantics> <mrow> <mi mathvariant="normal">p</mi> <msubsup> <mi>K</mi> <mrow> <mrow> <mi mathvariant="normal">a</mi> <mo>,</mo> </mrow> <mi>HBenz</mi> </mrow> <mi mathvariant="normal">s</mi> </msubsup> <mo>−</mo> <mi mathvariant="normal">p</mi> <msubsup> <mi>K</mi> <mrow> <mrow> <mi mathvariant="normal">a</mi> <mo>,</mo> </mrow> <mi>HBenz</mi> </mrow> <mi mathvariant="normal">w</mi> </msubsup> <mo>−</mo> <mi>log</mi> <msub> <mi>γ</mi> <mrow> <msup> <mi mathvariant="normal">H</mi> <mo>+</mo> </msup> </mrow> </msub> </mrow> </semantics></math>) values.</p>
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<p>Absorption spectrum of the neutral form, R, of rhodamine <b>5</b> (1.0 × 10<sup>−5</sup> M) in acetonitrile with 0.2 M Mg(ClO<sub>4</sub>)<sub>2</sub>·3H<sub>2</sub>O (1) and without this salt (2).</p>
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<p>Rhodamine <b>5</b> (1.0 × 10<sup>−5</sup> M) in CH<sub>3</sub>CN; (<b>a</b>): 0.001 and 0.003 M DBU (1, 2); 5 × 10<sup>−4</sup> and 0.001 M <span class="html-italic">p</span>-toluenesulfonic acid (3, 4); 2 × 10<sup>−3</sup>, 5 × 10<sup>−3</sup>, 0.01, 0.02, and 0.04 M LiClO<sub>4</sub> (5, 6, 7, 8, and 9); (<b>b</b>): 2 × 10<sup>−3</sup>, 5 × 10<sup>−3</sup>, and 0.01 M Ca(ClO<sub>4</sub>)<sub>2</sub> (5, 6, and 7).</p>
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<p>Rhodamine <b>5</b> (1.0 × 10<sup>−5</sup> M) in CH<sub>3</sub>CN at varying of LiClO<sub>4</sub> concentrations.</p>
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<p>Emission spectra of compound <b>5</b> in acetone: neutral (lactonic, colorless) form, <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>excit</mi> </mrow> </msub> </mrow> </semantics></math> = 330 nm, and cationic form, <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>excit</mi> </mrow> </msub> </mrow> </semantics></math> = 565 nm. The conversion of the dye in the cationic form is reached by addition of sulfuric acid traces.</p>
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<p>The ground (<b>left</b>) and the excited state (<b>right</b>) optimized molecular geometry of rhodamine B <b>1</b> lactone in vacuo.</p>
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<p>Molecular structure of rhodamine B lactone, optimized in its excited S1 state, which wave function was analyzed with application of the elements of AIM theory [<a href="#B112-colorants-01-00006" class="html-bibr">112</a>,<a href="#B113-colorants-01-00006" class="html-bibr">113</a>,<a href="#B114-colorants-01-00006" class="html-bibr">114</a>]. Unconventional H-bond with its bond path and critical point of (3,-1) type is marked by a circle.</p>
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<p>The ground (<b>left</b>) and the excited state <b>(right</b>) optimized molecular geometry of rhodamine B <b>18</b> lactone in vacuo.</p>
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<p>Rhodamine B (<b>1</b>) cation HR<sup>+</sup> and the tautomers of the neutral R form: R<sup>±</sup> and R<sup>0</sup>.</p>
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<p>Molecular structures of rhodamine dyes studied in the present work. Dye <b>7</b> is also named as rhodamine 101. <b>1</b> (X<sup>1</sup> = Et; X<sup>2</sup> = 6-NEt<sub>2</sub>; Y = CH), <b>2</b> (X<sup>1</sup> = Et; X<sup>2</sup> = 6-NMe<sub>2</sub>; Y = CH), <b>3</b> (X<sup>1</sup> = Me; X<sup>2</sup> = 6-NMe<sub>2</sub>; Y = CH), <b>4</b> (X<sup>1</sup> = Et; X<sup>2</sup> = 6-NH<sub>2</sub>; Y = CH), <b>9</b> (X<sup>1</sup> = Et; X<sup>2</sup> = 7.8-benzo; Y = CH), <b>10</b> (X<sup>1</sup> = Et; X<sup>2</sup> = 7-NH<sub>2</sub>; Y = CH), <b>11</b> (X<sup>1</sup> = Et; X<sup>2</sup> = 6-Cl; Y = CH), <b>12</b> (X<sup>1</sup> = Et; X<sup>2</sup> = 6-NMe<sub>2,</sub> 8-OH; Y = CH), <b>13</b> (X<sup>1</sup> = Me; X<sup>2</sup> = 6-NMe<sub>2</sub>; Y = N), <b>14</b> (X<sup>1</sup> = Et; X<sup>2</sup> = 6-NEt<sub>2</sub>; Y = N), <b>5</b> (X = Et; Y = CH), <b>6</b> (X = Me; Y = CH), <b>7</b> (Y = CH), <b>8</b> (X = Et). <b>15</b> (Y = N).</p>
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<p>Acidic dissociation and tautomerism of rhodamine <b>5</b> {HR<sup>+</sup> ⇄ (R<sup>±</sup> ⇄ R<sup>0</sup>) + H<sup>+</sup>}.</p>
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<p>Atom numbering in compound <b>5</b> (shown as cation).</p>
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<p>Zwitterions as two kinds of intramolecular ionic pairs; left-hand side: solvent-separated (solvent-shared, externally solvated, long); right-hand side: contact (intimate, short).</p>
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<p>Associate of the zwitterionic tautomer R<sup>±</sup> with Li<sup>+</sup>.</p>
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<p>Lactones of rhodamines 110 (<b>16</b>), 19 (<b>17</b>), and succinyl rhodamine (<b>18</b>).</p>
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<p>Carbinols of pyronine G (<b>19</b>) and rhodamine 6G (<b>20</b>).</p>
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<p>Alternative explanation of the blue fluorescence of rhodamine lactones.</p>
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14 pages, 4483 KiB  
Article
Autogenous Oxidation/Reduction of Polyaniline in Aqueous Sulfuric Acid
by Amrita Singh, Ravindra Kale, Arindam Sarkar, Vinay Juvekar and Asfiya Contractor
Processes 2022, 10(3), 443; https://doi.org/10.3390/pr10030443 - 22 Feb 2022
Cited by 2 | Viewed by 2362
Abstract
In this work, we have shown through open circuit potential experiments that in aqueous sulfuric acid solutions, a thick polyaniline film undergoes autogenous oxidation when reduced below a threshold potential and autogenous reduction when oxidized above the threshold potential. This phenomenon is associated [...] Read more.
In this work, we have shown through open circuit potential experiments that in aqueous sulfuric acid solutions, a thick polyaniline film undergoes autogenous oxidation when reduced below a threshold potential and autogenous reduction when oxidized above the threshold potential. This phenomenon is associated with the high resonance stability of polarons in long polyaniline chains present in thicker films. We have determined the rates of these reactions using a linear sweep chronopotentiometry technique. We propose that the oxidation reaction of polyaniline produces polarons with a concomitant reduction of hydrogen ions to hydrogen radicals, which further combine with each other to produce the hydrogen molecule in the absence of dissolved oxygen. On the other hand, at high potentials polarons are reduced with the concomitant oxidation of water to hydroxyl radicals. Both the radicals are stabilized due to the interaction of their unpaired electrons with pi-electrons of the aromatic rings of the polymer backbone. At the equilibrium value of the open circuit potential, both the hydrogen radicals and hydroxyl radicals are generated at equal rates and react with each other to form water. Full article
(This article belongs to the Special Issue Novel Electrode Materials for Electrochemical Applications)
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Graphical abstract

Graphical abstract
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<p>Cyclic voltammograms: (<b>a</b>) and cyclic coulogram plots; (<b>b</b>) of polyaniline films of different surface mass densities. Concentration of H<sub>2</sub>SO<sub>4</sub> = 0.5 M, concentration of aniline = 0.1 M and temperature = 25 °C. Scan rate = 50 mV s<sup>−1</sup>. All potentials are reported with respect to SCE.</p>
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<p>Rising open circuit potential of polyaniline film with initial potential of −0.2V. Concentration of H<sub>2</sub>SO<sub>4</sub> = 0.5 M, surface mass density of the film = 24.4 g m<sup>−2</sup>, temperature = 25 °C. All potentials are reported with respect to SCE.</p>
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<p>Equilibrium potential of polyaniline film versus surface mass density of polyaniline. Concentration of H<sub>2</sub>SO<sub>4</sub> = 0.5 M, temperature = 25 °C. All potentials are reported with respect to SCE.</p>
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<p>Chronopotentiograms for reduction of polyaniline films. (<b>a</b>) Black line: from equilibrium potential to −0.2 V at current density of −2.25 A m<sup>−2</sup>; surface mass density of the film = 24.4 g m<sup>−2</sup>; (<b>b</b>) Red line: constant current of −8.75 × 10<sup>−4</sup> A m<sup>−2</sup>; surface mass density of the film = 13.91 g m<sup>−2</sup>. Concentration of H<sub>2</sub>SO<sub>4</sub> = 0.5 M, temperature = 25 °C. All potentials are reported with respect to SCE.</p>
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<p>Open circuit potential of polyaniline with and without nitrogen bubbling (<b>a</b>) OCP curve with surface aeration; (<b>b</b>) OCP curve with nitrogen bubbling through the solution. Concentration of H<sub>2</sub>SO<sub>4</sub> = 0.5 M, surface mass density of the film = 16.3 g m<sup>−2</sup>, temperature = 25 °C. All potentials are reported with respect to SCE.</p>
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<p>Linear current sweep chronopotentiogram performed on a polyaniline film. Concentration of H<sub>2</sub>SO<sub>4</sub> = 0.5 M, surface mass density of the film = 16.41 g m<sup>−2</sup>, temperature = 25 °C; initial current= −0.25 mA, current scan rate: 10<sup>−4</sup> mA s<sup>−1</sup>, turning time = 1521 s. All potentials are reported with respect to SCE.</p>
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<p>Polyaniline oxidation current density vs. potential plot. Concentration of H<sub>2</sub>SO<sub>4</sub> = 0.5M, Temperature = 25 °C. All potentials are with respect to SCE. Surface mass densities of polyaniline are-curve a: 0. 645 g m<sup>−2</sup>; curve b: 6.92 g m<sup>−2</sup>; curve c: 16.4 g m<sup>−2</sup>.</p>
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<p>Open circuit potential curve of a polyaniline film which is pre-oxidized to a potential much greater than the equilibrium potential (0.39 V<sub>SCE</sub>). (<b>a</b>) Without nitrogen bubbling; (<b>b</b>) with nitrogen bubbling. Concentration of H<sub>2</sub>SO<sub>4</sub> = 0.5 M, surface mass density of the film = 16.3g m<sup>−2</sup> and temperature = 25 °C. All potentials are reported with respect to SCE. Inset shows the OCP in the region around the turning point marked on curve a.</p>
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<p>Anodic chronopotentiogram of polyaniline film at constant current density of 2.50 A m<sup>−2</sup>. Surface aerated system, concentration of H<sub>2</sub>SO<sub>4</sub> = 0.5 M, surface mass density of the film = 16.3 g m<sup>−2</sup> and temperature = 25 °C. All potentials are reported with respect to SCE. The inset shows the chronopotentiogram for the same film at the current density of 7.5 A m<sup>−2</sup> under otherwise identical conditions.</p>
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<p>Linear current sweep chronopotentiogram of a polyaniline film. Surface aerated system, concentration of H<sub>2</sub>SO<sub>4</sub> = 0.5 M, surface mass density of the film = 16.41 g m<sup>−2</sup>, temperature = 25 °C. Initial current = +0.8 mA, current scan rate: 5 × 10<sup>−3</sup> mA s<sup>−1</sup>, turning time = 52 s. All potentials are reported with respect to SCE.</p>
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<p>Variation of the oxidation and reduction current density in polyaniline film. Surface aerated system, concentration of H<sub>2</sub>SO<sub>4</sub> = 0.5 M, surface mass density of the film = 16.4 g m<sup>−2</sup> and temperature = 25 °C. All potentials are reported with respect to SCE.</p>
Full article ">Scheme 1
<p>Schematic representation of the turning potential method for determination of autogenous oxidation current.</p>
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13 pages, 2702 KiB  
Article
Magnetic Poly(glycidyl methacrylate) Microspheres with Grafted Polypyrrole Chains for the High-Capacity Adsorption of Congo Red Dye from Aqueous Solutions
by Ying Yu, Jielong Su, Jia Liu and Wensong Li
Coatings 2022, 12(2), 168; https://doi.org/10.3390/coatings12020168 - 28 Jan 2022
Cited by 9 | Viewed by 2740
Abstract
In this study, novel magnetic poly(glycidyl methacrylate) (PGMA) microspheres with grafted polypyrrole chains (magnetic PGMA-g-PPy) were developed for the high-capacity adsorption of Congo red (CR) from aqueous solutions. The magnetic PGMA-g-PPy was synthesized by the typical dispersion polymerization method and the ring-opening reaction [...] Read more.
In this study, novel magnetic poly(glycidyl methacrylate) (PGMA) microspheres with grafted polypyrrole chains (magnetic PGMA-g-PPy) were developed for the high-capacity adsorption of Congo red (CR) from aqueous solutions. The magnetic PGMA-g-PPy was synthesized by the typical dispersion polymerization method and the ring-opening reaction of epoxy groups, producing abundant hydroxyls for the grafting polymerization of pyrrole in the presence of FeCl3 as an oxidizing agent on the surface of the microspheres. The characterization results showed that magnetic PGMA-g-PPy was successfully fabricated. The adsorption equilibrium data of the adsorbents could be well fitted by the Langmuir isotherm model, showing a high maximum adsorption capacity of 502.5 mg/g for CR. The adsorption followed pseudo-second-order kinetics with a fast speed. The adsorbents had no leaching of Fe in the solution at pH 1.0–11.0 for 24 h. The adsorption process was strongly pH-dependent and weakly ionic-strength-dependent. Furthermore, the magnetic microspheres could be easily regenerated, rapidly separated from the solution, and reused for wastewater treatment. The results suggest that magnetic PGMA-g-PPy microspheres are a promising efficient adsorbent for the removal of CR from wastewater. Full article
(This article belongs to the Special Issue Surface Chemical Modification II)
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<p>SEM image of magnetic PGMA-g-PPy microspheres.</p>
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<p>FT-IR spectrum of Fe<sub>3</sub>O<sub>4</sub> (<b>A</b>), magnetic PGMA (<b>B</b>), and magnetic PGMA-g-PPy (<b>C</b>).</p>
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<p>XRD patterns of magnetic PGMA (<b>A</b>) and magnetic PGMA-g-PPy (<b>B</b>).</p>
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<p>Magnetization curves of magnetic PGMA-g-PPy microspheres.</p>
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<p>Adsorption isotherms of CR onto magnetic PGMA-g-PPy at room temperature. (Adsorbent dose, 28.5 mg; volume, 10 mL; pH, 2.0; contact time, 2 h.)</p>
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<p>Adsorption kinetics of CR in aqueous solution on the magnetic PGMA-g-PPy. (Adsorbent dose, 237 mg; volume, 50 mL; initial concentration, 500 mg/L; pH, 7.0.)</p>
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<p>Effect of pH on the removal of CR by PGMA-g-PPy. (Adsorbent dose, 15 mg; volume, 6 mL; initial concentration, 500 mg/L; contact time, 1 h.)</p>
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<p>Effect of ionic strength on the removal of CR by PGMA-g-PPy. (Adsorbent dose, 28.5 mg; volume, 6 mL; initial concentration, 500 mg/L; pH, 7.0; contact time, 1 h.)</p>
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<p>The adsorption capacity of CR on magnetic PGMA-g-PPy in five successive cycles of desorption–adsorption.</p>
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<p>Preparation route of magnetic PGMA-g-PPy microspheres.</p>
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19 pages, 391 KiB  
Article
On Nash Equilibria in Non-Cooperative All-Optical Networks
by Vittorio Bilò, Michele Flammini and Luca Moscardelli
Algorithms 2021, 14(1), 15; https://doi.org/10.3390/a14010015 - 9 Jan 2021
Cited by 1 | Viewed by 2242
Abstract
We consider the problem of determining a routing in all-optical networks, in which some couples of nodes want to communicate. In particular, we study this problem from the point of view of a network provider that has to design suitable payment functions for [...] Read more.
We consider the problem of determining a routing in all-optical networks, in which some couples of nodes want to communicate. In particular, we study this problem from the point of view of a network provider that has to design suitable payment functions for non-cooperative agents, corresponding to the couples of nodes wishing to communicate. The network provider aims at inducing stable routings (i.e., routings corresponding to Nash equilibria) using a low number of wavelengths. We consider three different kinds of local knowledge that agents may exploit to compute their payments, leading to three corresponding information levels. Under complete information, the network provider can design a payment function, inducing the agents to reach a Nash equilibrium mirroring any desired routing. If the price to an agent is computed only as a function of the wavelengths used along connecting paths (minimal level) or edges (intermediate level), the most reasonable functions either do not admit Nash equilibria or admit very inefficient ones, i.e., with the largest possible price of anarchy. However, by suitably restricting the network topology, a constant price of anarchy for chains and rings and a logarithmic one for trees can be obtained under the minimal and intermediate levels, respectively. Full article
(This article belongs to the Special Issue Algorithmic Game Theory 2020)
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Figure 1
<p>In this graph, nodes <span class="html-italic">a</span> and <span class="html-italic">b</span> are connected through a single edge and <span class="html-italic">n</span> chains of <span class="html-italic">k</span> edges.</p>
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<p>In this graph, there exists a path consisting of <span class="html-italic">h</span> edges between the nodes <span class="html-italic">a</span> and <span class="html-italic">d</span>, and there exist two paths, one consisting of a single edge and the other consisting of <span class="html-italic">k</span> edges between the nodes <span class="html-italic">b</span> and <span class="html-italic">c</span>.</p>
Full article ">Figure A1
<p>The graph not yielding a Nash equilibrium for the payment function <math display="inline"><semantics> <mrow> <mi>s</mi> <mi>u</mi> <mi>m</mi> <mo>−</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </semantics></math>.</p>
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<p>In this graph, there exist two edges between any pair of nodes <span class="html-italic">b</span> and <math display="inline"><semantics> <msub> <mi>c</mi> <mi>i</mi> </msub> </semantics></math>.</p>
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19 pages, 4294 KiB  
Article
Creation of a PDMS Polymer Brush on SiO2-Based Nanoparticles by Surface-Initiated Ring-Opening Polymerization
by Karin Koch, Sven Geller, Kubilay Acar, Patricia Bach, Ekaterina Tsarenko and Annette Schmidt
Polymers 2020, 12(4), 787; https://doi.org/10.3390/polym12040787 - 2 Apr 2020
Cited by 3 | Viewed by 4140
Abstract
The incorporation of nanoparticles into soft matrices opens a broad spectrum of novel property combinations. However, one of the major challenges for these systems remains the compatibilization of particles with the surrounding matrix by proper surface functionalization. For silicon-based systems or liquid crystalline [...] Read more.
The incorporation of nanoparticles into soft matrices opens a broad spectrum of novel property combinations. However, one of the major challenges for these systems remains the compatibilization of particles with the surrounding matrix by proper surface functionalization. For silicon-based systems or liquid crystalline phases, polydimethylsiloxane (PDMS) brushes at the surface of particles increase the stability against particle agglomeration in such systems. Here, we report a novel approach for the functionalization of particles with a polysiloxane brush by surface-initiated ring-opening polymerization of a cyclosiloxane. For this purpose, surface hydroxy groups of silica and silica-coated hematite particles are used as initiators in combination with phosphazene bases as catalysts. The ring–chain equilibrium of a model-based solution polymerization is investigated in detail to find the appropriate reaction parameters. The corresponding molar masses are determined and compared by 1H-NMR and SEC measurements to confirm the underlying mechanism. In the resulting hybrid nanostructures, a covalently bound PDMS fraction is achieved up to 47 mass %. Full article
(This article belongs to the Special Issue Nanoparticle Functionalization by Polymers: Methods and Applications)
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Figure 1
<p>(<b>a</b>) Yield <span class="html-italic">Φ</span> as a function of the reciprocal monomer concentration for the ROP of M<sub>4</sub> in toluene with NeOH as initiator and P<sub>4</sub>-<span class="html-italic">t</span>-Bu as catalyst for different monomer concentrations ([M<sub>4</sub>]<sub>0</sub> and constant monomer-to-initiator ratio n<span class="html-italic"><sub>M</sub></span>/n<span class="html-italic"><sub>I</sub></span> = 25. (<b>b</b>) Double logarithmic plot of the ring concentration [M<sub>x</sub>]<sub>eq</sub> over the extent of active groups <math display="inline"><semantics> <mi>p</mi> </semantics></math> with linear fit function (red line) for the ROP of M<sub>4</sub> in toluene ([M<sub>4</sub>]<sub>0</sub> = 0.96 mol∙L<sup>−1</sup>), NeOH as initiator and P<sub>4</sub>-<span class="html-italic">t</span>-Bu as catalyst. (<b>c</b>) Molar mass <span class="html-italic">M</span><sub>n</sub> (obtained by SEC and <sup>1</sup>H-NMR) as a function of <span class="html-italic">M</span><sub>n,theo</sub> for the ROP of M<sub>4</sub> in toluene ([M<sub>4</sub>]<sub>0</sub> = 0.96 mol∙L<sup>−1</sup>) with NeOH as initiator and two different catalysts (B: P<sub>4</sub>-<span class="html-italic">t</span>-Bu and B’: P<sub>2</sub>-<span class="html-italic">t</span>-Bu).</p>
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<p>TEM image of (<b>a</b>) SiO<sub>2</sub> particles and (<b>b</b>) SiO<sub>2</sub>@α-Fe<sub>2</sub>O<sub>3</sub> particles.</p>
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<p>(<b>a</b>) ATR–IR spectrum and (<b>b</b>) TGA of pure silica particles and PDMS@SiO<sub>2</sub> exemplary shown for the SI–ROP of M<sub>4</sub> with [M<sub>4</sub>]<sub>0</sub> = 1.49 mol∙L<sup>−1</sup> and [B] = 1.49 × 10<sup>−2</sup> mol∙L<sup>−1</sup>.</p>
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<p>Yields of surface-attached PDMS and free PDMS as a function of monomer concentration for the SI–ROP of M<sub>4</sub> on SiO<sub>2</sub> and on SiO<sub>2</sub>@α-Fe<sub>2</sub>O<sub>3</sub> obtained in Series 3 to 6.</p>
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<p>(<b>a</b>) Yield <span class="html-italic">Φ</span> as a function of the reciprocal monomer concentration and (<b>b</b>) polymer concentration from SI–ROP of M<sub>4</sub> with SiO<sub>2</sub> particles as a function of <math display="inline"><semantics> <mrow> <msub> <mrow> <mrow> <mo>[</mo> <mrow> <msub> <mi mathvariant="normal">M</mi> <mn>4</mn> </msub> </mrow> <mo>]</mo> </mrow> </mrow> <mn>0</mn> </msub> </mrow> </semantics></math> for Series 3 and 5.</p>
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<p>Surface-attached polymer fraction <span class="html-italic">µ</span><sub>PDMS,p</sub> as a function of reaction time (Series 7).</p>
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<p>TGA for (<b>a</b>) PDMS@SiO<sub>2</sub> and (<b>b</b>) PDMS@SiO<sub>2</sub>@Fe<sub>2</sub>O<sub>3</sub> synthesized with different injection methods.</p>
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<p>Mechanism of the ring-opening (ROP) of M<sub>4</sub> initiated by NeOH and phosphazene base.</p>
Full article ">Scheme 2
<p>Ring–chain equilibrium in the anionic ring-opening polymerization of cyclosiloxanes. One monomeric unit M represents one -SiO(CH<sub>3</sub>)<sub>2</sub>- unit, while <span class="html-italic">n</span> and <span class="html-italic">x</span> give the numbers of repeating units in linear chains and ring molecules.</p>
Full article ">Scheme 3
<p>Base catalyzed surface-initiated (SI)–ROP of M<sub>4</sub> initiated by SiO<sub>2</sub> surface of NP.</p>
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<p>Proposed equilibria in the SI–ROP of M<sub>4</sub>.</p>
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15 pages, 3369 KiB  
Article
Thermomechanical and Morphological Properties of Poly(ethylene terephthalate)/Anhydrous Calcium Terephthalate Nanocomposites
by Franco Dominici, Fabrizio Sarasini, Francesca Luzi, Luigi Torre and Debora Puglia
Polymers 2020, 12(2), 276; https://doi.org/10.3390/polym12020276 - 30 Jan 2020
Cited by 16 | Viewed by 4303
Abstract
Calcium terephthalate anhydrous salts (CATAS), synthetized by reaction of terephthalic acid with metal (Ca) oxide were incorporated at different weight contents (0–30 wt. %) in recycled Poly(ethylene terephthalate) (rPET) by melt processing. Their structure, morphology, thermal and mechanical properties (tensile and flexural behavior) [...] Read more.
Calcium terephthalate anhydrous salts (CATAS), synthetized by reaction of terephthalic acid with metal (Ca) oxide were incorporated at different weight contents (0–30 wt. %) in recycled Poly(ethylene terephthalate) (rPET) by melt processing. Their structure, morphology, thermal and mechanical properties (tensile and flexural behavior) were investigated. Results of tensile strength of the different formulations showed that when the CATAS content increased from 0.1 to 0.4 wt. %, tangible changes were observed (variation of tensile strength from 65.5 to 69.4 MPa, increasing value for E from 2887 up to 3131 MPa, respectively for neat rPET and rPET_0.4CATAS). A threshold weight amount (0.4 wt. %) of CATAS was also found, by formation at low loading, of a rigid amorphous fraction at the rPET/CATAS interface, due to the aromatic interactions (π−π conjugation) between the matrix and the filler. Above the threshold, a restriction of rPET/CATAS molecular chains mobility was detected, due to the formation of hybrid mechanical percolation networks. Additionally, enhanced thermal stability of CATAS filled rPET was registered at high content (Tmax shift from 426 to 441 °C, respectively, for rPET and rPET_30CATAS), essentially due to chemical compatibility between terephthalate salts and polymer molecules, rich in stable aromatic rings. The singularity of a cold crystallization event, identified at the same loading level, confirmed the presence of an equilibrium state between nucleation and blocking effect of amorphous phase, basically related to the characteristic common terephthalate structure of synthetized Ca–Metal Organic Framework and the rPET matrix. Full article
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Figure 1
<p>Chemical structure of calcium terephthalate salts (<b>a</b>) and FESEM morphology in their hydrated (<b>b</b>) and anhydrous state (<b>c</b>).</p>
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<p>XRD profile for CATAS (<b>a</b>); TG/DTG curves for CATS (<b>b</b>); and CATAS nanofillers (<b>c</b>); thickness distribution for CATAS (<b>d</b>).</p>
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<p>G’ (<b>a</b>) and tan δ curve (<b>b</b>) from DMTA tests for rPET and rPET/CATAS nanocomposites.</p>
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<p>Stress-strain curves from flexural (<b>a</b>) and tensile tests (<b>b</b>), variation of tensile modulus and strain at break (<b>c</b>), variation of flexural stress and strain (<b>d</b>) for rPET_CATAS nanocomposites at the different loading levels.</p>
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<p>XRD diffraction curves for rPET and rPET/CATAS nanocomposites at low and high loadings.</p>
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<p>FESEM images of fractured surfaces for rPET and rPET/CATAS nanocomposites.</p>
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<p>TG curve (<b>a</b>) and DTG curve (<b>b</b>) for rPET and rPET/CATAS nanocomposites at 3 and 30 wt. % of CATAS.</p>
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<p>DSC heating scan for rPET and rPET/CATAS nanocomposites at low (<b>a</b>) and high (<b>b</b>) loading levels.</p>
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<p>Evolution of different phase fractions for rPET and rPET_CATAS content.</p>
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15 pages, 4098 KiB  
Article
Lignin-Only Polymeric Materials Based on Unmethylated Unfractionated Kraft and Ball-Milled Lignins Surpass Polyethylene and Polystyrene in Tensile Strength
by Yi-ru Chen, Simo Sarkanen and Yun-Yan Wang
Molecules 2019, 24(24), 4611; https://doi.org/10.3390/molecules24244611 - 17 Dec 2019
Cited by 8 | Viewed by 3220
Abstract
Functional polymeric materials composed solely of lignin preparations appeared only very recently. A gradual paradigm shift spanning 56 years has revealed how lignin–lignin blends can upgrade the performance of 100 wt% lignin-based plastics. The view, first espoused in 1960, that lignin macromolecules are [...] Read more.
Functional polymeric materials composed solely of lignin preparations appeared only very recently. A gradual paradigm shift spanning 56 years has revealed how lignin–lignin blends can upgrade the performance of 100 wt% lignin-based plastics. The view, first espoused in 1960, that lignin macromolecules are crosslinked reduces the plausibility of creating functional polymeric materials that are composed only of lignin preparations. Lignin-based materials would be much weaker mechanically if interstices remain in significant numbers between adjoining macromolecular structures that consist of rigid crosslinked chains. In 1982, random-coil features in the hydrodynamic character of kraft lignin (KL) components were evident from ultracentrifugal sedimentation equilibrium studies of their SEC behavior. In 1997, it was recognized that the macromolecular species in plastics with 85 wt% levels of KL are associated complexes rather than individual components. Finally, in 2016, the first polymeric material composed entirely of ball-milled softwood lignin (BML) was found to support a tensile strength above polyethylene. Except in its molecular weight, the BML was similar in structure to the native biopolymer. It was composed of associated lignin complexes, each with aromatic rings arranged in two domains. The inner domain maintains structural integrity largely through noncovalent interactions between cofacially-offset aromatic rings; the peripheral domain contains a higher proportion of edge-on aromatic-ring arrangements. Interdigitation between peripheral domains in adjoining complexes creates material continuity during casting. By interacting at low concentrations with the peripheral domains, non-lignin blend components can improve the tensile strengths of BML-based plastics to values well beyond those seen in polystyrene. The KL-based plastics are weaker because the peripheral domains of adjoining complexes are less capable of interdigitation than those of BML. Blending with 5 wt% 1,8-dinitroanthraquinone results in a tensile strength above that of polyethylene. Analogous effects can be achieved with 10 wt% maple γ-valerolactone (GVL) lignin which, with a structure close to the native biopolymer, imparts some native character to the peripheral domains of the KL complexes. Comparable enhancements in the behavior of BML complexes upon blending with 10 wt% ball-milled corn-stover lignin (BMCSL) result in lignin-only polymeric materials with tensile strengths well beyond polystyrene. Full article
(This article belongs to the Special Issue Lignin—Chemistry and Materials: Past, Present and Future)
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Figure 1

Figure 1
<p>Adaptation of the macromolecular “microgel” structure proposed in 1960 [<a href="#B8-molecules-24-04611" class="html-bibr">8</a>] to describe a ligninsulfonate crosslinked polymer chain (sulfonate groups omitted).</p>
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<p>Effect of softwood kraft lignin content on the tensile strength (σ<sub>max</sub>) of (<b>A</b>) hydroxypropyl kraft lignin–hexamethylene diisocyanate polyurethanes [<a href="#B10-molecules-24-04611" class="html-bibr">10</a>] and (<b>B</b>) kraft lignin–polyether triol–polymeric MDI polyurethanes (0.9 overall NCO/OH reactant ratio) from four kraft lignin fractions [<a href="#B11-molecules-24-04611" class="html-bibr">11</a>].</p>
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<p>Sephadex G100/aqueous 0.10 M NaOH size-exclusion chromatographic absolute molecular-weight calibration curves determined by sedimentation equilibrium studies of paucidisperse kraft lignin fractions: aspen kraft lignin analyzed by Beckman XLA ultracentrifuge [<a href="#B13-molecules-24-04611" class="html-bibr">13</a>] and Douglas fir kraft lignin analyzed by Beckman model E instrument [<a href="#B14-molecules-24-04611" class="html-bibr">14</a>] compared with the elution behavior of poly(styrenesulfonate) standards.</p>
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<p>Tensile behavior of polymeric materials composed solely of unmethylated (BML) and methylated (MBML) softwood ball-milled lignin [<a href="#B3-molecules-24-04611" class="html-bibr">3</a>].</p>
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<p>X-ray powder diffraction patterns of uncast and cast polymeric materials based on unmethylated and methylated ball-milled softwood lignins. (<b>A</b>) uncast and (<b>B</b>) cast unmethylated ball-milled lignins (BMLs); (<b>C</b>) uncast and (<b>D</b>) cast ball-milled lignin successively methylated with dimethyl sulfate and diazomethane (MBML) [<a href="#B3-molecules-24-04611" class="html-bibr">3</a>].</p>
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<p>AFM height image of associated lignin complexes on 100 wt% methylated ball-milled lignin-based plastic surface [<a href="#B17-molecules-24-04611" class="html-bibr">17</a>].</p>
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<p>Apparent molecular weight distributions representing a homologous series of kraft lignin samples secured by desalting after association and dissociation in aqueous alkaline solutions [<a href="#B21-molecules-24-04611" class="html-bibr">21</a>] for (<b>1</b>) 300 h, (<b>2</b>) 144 h, and (<b>3</b>) 48 h at 170 gL<sup>−1</sup> in 1.0 M ionic strength aqueous 0.40 M NaOH; (<b>4</b>) 0 h, (<b>5</b>) 144 h, and (<b>6</b>) 644 h at 0.50 gL<sup>−1</sup> in aqueous 0.10 M NaOH. Sephadex G100/aqueous 0.10 M NaOH elution profiles monitored at 320 nm.</p>
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<p>Relationship between <span class="html-italic">M<sub>w</sub></span> and <span class="html-italic">M<sub>n</sub></span> during associative/dissociative processes in aqueous alkaline solutions between molecular kraft lignin species leading to a series of samples with different degrees of association [<a href="#B21-molecules-24-04611" class="html-bibr">21</a>] in <a href="#molecules-24-04611-f007" class="html-fig">Figure 7</a>, desalted through Sephadex LH20/aqueous 35% dioxane.</p>
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<p>Tensile behavior to fracture of thermoplastics containing 85 wt% kraft lignin preparations that differ only in degree of intermolecular association [<a href="#B24-molecules-24-04611" class="html-bibr">24</a>] in biphasic blends with 12.6% poly(vinyl acetate), 1.6% diethyleneglycol dibenzoate, and 0.8% indene.</p>
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<p>Tensile behavior of polymeric materials composed of industrial softwood kraft lignin alone and with 95–98 wt% kraft-lignin contents.</p>
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<p>Tensile behavior of plastics based on softwood kraft lignin alone and in blends with 1,8-dinitroanthraquinone and maple GVL lignin, compared with plastics containing maple GVL lignin alone.</p>
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<p>Tensile behavior of polymeric materials composed of ball-milled lignin alone and in blends with polycaprolactone (PCL), poly(ethylene oxide-<span class="html-italic">b</span>-1,2-butadiene-<span class="html-italic">b</span>-ethylene oxide) (EBE), poly(trimethylene glutarate) (PTMG), and tetrabromobisphenol A (TBBP-A).</p>
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<p>Tensile behavior of plastics based on ball-milled softwood lignin alone and in blends with ball-milled corn-stover lignin (BMCSL), poly(ethylene oxide-<span class="html-italic">b</span>-1,2-butadiene-<span class="html-italic">b</span>-ethylene oxide) (EBE), and tetrabromobisphenol A (TBBP-A).</p>
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