(647b) Modeling Solvent Diffusion in Highly Cross-Linked Polymer Resins

Highly cross-linked polymers play a key role in protecting sensitive electronic components in medical devices by serving as encapsulation materials that shield the interior against liquids or steam during sterilization. However, these resins are also capable of absorbing liquids, which can cause short circuits in the electronics. Modeling solvent uptake can optimize polymer thickness and extend the lifespan of electronics.

We are currently investigating the swelling behavior of epoxy and phenolic resins, as well as silicon, in water, heptane, and isopropanol.^[1] To measure the change in weight during swelling, we are conducting experiments in liquids or steam. The diffusion behavior over time is captured by repeatedly measuring the weight using a Sartorius Secura 26-1CEU microbalance.

Additionally, we are modelling the swelling behavior by combining the PC-SAFT equation of state^[2] with the Maxwell-Stefan diffusion equation. PC-SAFT considers the stretching of polymer chains due to liquid uptake and the repelling forces that this causes against further uptake. This elastic contribution is described by the network term of Miao et al.^[3] The model parameters are fitted to the total liquid uptake and polymer density.^[4] Thus, the diffusion with multiple solvents is described using only one parameter set for the polymer. Diffusion is modeled using the Maxwell-Stefan equation, where the driving force is the chemical potential, which is calculated using PC-SAFT. For linear diffusion behavior, we supplement the Maxwell-Stefan model with the viscoelastic Kelvin-Voigt model^[5], which combines a viscous damper and elastic spring in parallel.

At this conference, we are presenting and discussing our latest experimental and modelling results, including a comparison of predicted and experimental total solvent uptake. We are also comparing the measured time-dependent solvent uptake with simulation results in 1D, 2D, and 3D space to examine the diffusion behavior. Our approach introduces a method for predicting diffusion behavior within electronic encapsulation.

[1] Krenn, P.; Zimmermann, P.; Fischlschweiger, M.; Zeiner, T. SAFT-Based Maxwell-Stefan Approach to Model the Diffusion through Epoxy Resins, J. Chem. Eng. Data 2020, 65 (12), 5677–5687.

[2] Gross, J.; Sadowski, G. Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 2001, 40 (4), 1244−1260.

[3] Miao, B.; Vilgis, T. A.; Poggendorf, S.; Sadowski, G. Effect of Finite Extensibility on the Equilibrium Chain Size. Macromol. Theory Simul. 2010, 19 (7), 414−420.

[4] Krenn, P.; Zimmermann, P.; Fischlschweiger, M.; Zeiner, T. Modeling Highly Cross-Linked Epoxy Resins in Solvents of Different Polarities with PC-SAFT. Ind. Eng. Chem. Res. 2020, 59, 5133−5141.

[5] Cohen, D. S.; White, A. B., Jr. Sharp Fronts Due to Diffusion and Viscoelastic Relaxation in Polymers. SIAM J. Appl. Math. 1991, 51 (2), 472−483.