立足于连续介质力学理论,建立了一套描述聚合物中Case Ⅱ扩散与材料溶胀变形耦合行为的理论模型,其控制方程包括力-化学平衡状态方程、溶剂扩散方程和分子数守恒方程,以及反映聚合物力学行为时间依赖性的粘-超弹本构方程.将该理论方法用于分析两种材料体系的瞬态自由溶胀过程,探讨无约束情况下柱状和板状聚合物试样中发生单向Case Ⅱ扩散的行为特征.结合适当的边界条件和初始条件,直接求解单向扩散的浓度场和应力/变形场函数,并将其分布、演变规律与实测结果进行对比,较充分验证了本文建立的聚合物溶胀耦合分析框架的有效性和适应性.这些结果丰富了 Case Ⅱ扩散相关的表征理论,可望为后续的薄膜设计、药物输送等实际应用场景提供重要支撑.
Modeling and Analysis on Case Ⅱ Diffusion Coupled with Swelling Deformation Behavior in Polymers
For some polymers below or near their glass transition temperature,a particular type of non-Fickian solvent diffusion,known as Case Ⅱ diffusion,is typically observed.To describe the coupling effect of Case Ⅱ diffusion and swelling deformation in polymers,theoretical models are established based on continuum mechanics.Here,governing equations for solvent penetration into polymer are derived and specialized in the reference configuration,including the mechanical-chemical equilibrium state equation,the concentration-dependent diffusion equation,and the molecular number conservation equation.Additional-ly,a visco-hyperelastic constitutive equation taking into account the time-dependent deformation character-istics of the material is integrated to reflect the competition mechanism between relaxation rate of the poly-meric network and migration of solvent in Case Ⅱ diffusion.This modeling approach is used to analyze the transient free swelling process for two material systems,so as to investigate the behavior of unidirectional Case Ⅱ diffusion in columnar and tabular polymer specimens without constraint.By applying appropriate boundary and initial conditions,the concentration,stress,and deformation field variables during the unidi-rectional diffusion are directly obtained.The distribution and evolution of these calculation results are com-pared with experimental observations,moderately validating the effectiveness and adaptability of the pro-posed coupling analysis method regarding polymer swelling.This developed theory may provide important guidance for practical applications such as membrane designing or drug delivery systems,where Case Ⅱ diffusion commonly occurs.It also aids in enhancing understanding of the combination of different poly-mer-solvent diffusion scenarios,from Fickian to non-Fickian circumstances.
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