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Diffusion coefficients of water and leachables in methacrylate-based crosslinked polymers using absorption experiments

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Abstract

The diffusion of water into dentin adhesive polymers and leaching of unpolymerized monomer from the adhesive are linked to their mechanical softening and hydrolytic degradation. Therefore, diffusion coefficient data are critical for the mechanical design of these polymeric adhesives. In this study, diffusion coefficients of water and leachables were obtained for sixteen methacrylate-based crosslinked polymers using absorption experiments. The experimental mass change data was interpreted using numerical solution of the two-dimensional diffusion equations. The calculated diffusion coefficients varied from 1.05 × 10−8 cm2/sec (co-monomer TMTMA) to 3.15 × 10−8 cm2/sec (co-monomer T4EGDMA). Correlation of the diffusion coefficients with crosslink density and hydrophilicity showed an inverse trend (R 2 = 0.41). The correlation of diffusion coefficient with crosslink density and hydrophilicity are closer for molecules differing by simple repeat units (R 2 = 0.95). These differences in the trends reveal mechanisms of interaction of the diffusing water with the polymer structure.

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Acknowledgment

This investigation was supported by Research Grants: R01DE14392 (PI: Spencer) and 3R01DE14392-08S109 (PI: Spencer) from the National Institute of Dental and Craniofacial Research, National Institutes of Health, Bethesda, MD 20892.

Author information

Authors and Affiliations

  1. Bioengineering Research Center, University of Kansas, Lawrence, KS, USA

    Ranganathan Parthasarathy, Jonggu Park, Qiang Ye & Paulette Spencer

  2. Civil, Environmental and Architectural Engineering Department, The University of Kansas, Learned Hall, 1530 W. 15th Street, Lawrence, KS, 66045-7609, USA

    Anil Misra

  3. Department of Mechanical Engineering, University of Kansas, Lawrence, KS, USA

    Paulette Spencer

  4. Bioengineering Graduate Program, University of Kansas, Lawrence, KS, USA

    Ranganathan Parthasarathy & Anil Misra

Authors
  1. Ranganathan Parthasarathy
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  2. Anil Misra
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  3. Jonggu Park
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  4. Qiang Ye
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  5. Paulette Spencer
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Corresponding author

Correspondence to Anil Misra.

Appendix

Appendix

The diffusion of leachables is explained in a similar way to water diffusion. The governing equations for leaching are given in terms of the local flux \( (\vec{j}) \), the diffusion coefficient \( (E) \) and the concentration of leachable \( \nu \) as follows:

$$ \overrightarrow {j} = - D_{\text{L}} \overrightarrow {\nabla } v $$
(21)
$$ \frac{\partial v}{\partial t} + \overrightarrow {\nabla } .\overrightarrow {j} = 0 $$
(22)
$$ \nabla^{2} v \approx \frac{{v_{i + 1,j}^{t + 1} - 2v_{i,j}^{t + 1} + v_{i - 1,j}^{t + 1} }}{{\left( {\Updelta x} \right)^{2} }} + \frac{{v_{i,j + 1}^{t + 1} - 2v_{i,j}^{t + 1} + v_{i,j - 1}^{t + 1} }}{{\left( {\Updelta x} \right)^{2} }} $$
(23)
$$ \frac{\partial v}{\partial t} \approx \frac{{v_{i,j}^{t + 1} - v_{i,j}^{t} }}{\Updelta t} $$
(24)
$$ - \beta_{x} \left[ {v_{i - 1,j}^{t + 1} + v_{i + 1,j}^{t + 1} } \right] + \left[ {1 + 2\beta_{x} + 2\beta_{y} } \right]v_{{_{i,j} }}^{t + 1} - \beta_{y} \left[ {v_{i,j - 1}^{t + 1} + v_{i,j}^{t + 1} } \right] = v_{i,j}^{t} $$
(25)
$$ \beta_{x} = \frac{{D_{\text{L}} \Updelta t}}{{\left( {\Updelta x} \right)^{2} }} $$
(26)
$$ \beta_{y} = \frac{{D_{\text{L}} \Updelta t}}{{\left( {\Updelta y} \right)^{2} }} $$
(27)

Assembling the system of discretized equations gives the form shown below.

$$ KD_{{{\text{L}}_{ij} }} v_{j}^{t + 1} = v_{j}^{t} $$
(28)

KDLij are the diffusion (leachable) multipliers obtained from Eq. 25.

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Parthasarathy, R., Misra, A., Park, J. et al. Diffusion coefficients of water and leachables in methacrylate-based crosslinked polymers using absorption experiments. J Mater Sci: Mater Med 23, 1157–1172 (2012). https://doi.org/10.1007/s10856-012-4595-5

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