Mass transport by diffusion within composite materials may depend not only on internal microstructural geometry, but also on the chemical interactions between the transported substance and the material of the microstructure. Retrospectively, there is a gap in methods and theory to connect material microstructure properties with macroscale continuum diffusion characteristics. Here we present a new hierarchical multiscale model for diffusion within composite materials that couples material microstructural geometry and interactions between diffusing particles and the material matrix. This model, which bridges molecular dynamics (MD) and the finite element (FE) method, is employed to construct a continuum diffusion model based on a novel numerical homogenization procedure. The procedure is general and robust for evaluating constitutive material parameters of the continuum model. These parameters include the traditional bulk diffusion coefficients and, additionally, the distances from the solid surface accounting for surface interaction effects. We implemented our models to glucose diffusion through the following two geometrical/material configurations: tightly packed silica nanospheres, and a complex fibrous structure surrounding nanospheres. Then, rhodamine 6G diffusion analysis through an aga-rose gel network was performed, followed by a model validation using our experimental results. The microstructural model, numerical homogenization and continuum model offer a new platform for modeling and predicting mass diffusion through complex biological environment and within composite materials that are used in a wide range of applications, like drug delivery and nanoporous catalysts.

中文翻译：

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基于数值均化程序的具有内表面相互作用的复合介质中扩散的多尺度 MD-FE 模型

复合材料内通过扩散进行的质量传输不仅取决于内部微观结构的几何形状，还取决于被传输物质与微观结构材料之间的化学相互作用。回顾过去，将材料微观结构特性与宏观连续扩散特性联系起来的方法和理论存在差距。在这里，我们提出了一种新的分层多尺度模型，用于复合材料内的扩散，该模型将材料微观结构几何形状以及扩散粒子与材料基质之间的相互作用耦合起来。该模型连接了分子动力学 (MD) 和有限元 (FE) 方法，用于构建基于新的数值均匀化程序的连续扩散模型。该过程对于评估连续模型的本构材料参数是通用且稳健的。这些参数包括传统的体扩散系数，此外，考虑到表面相互作用效应的固体表面的距离。我们通过以下两种几何/材料配置实现了我们的葡萄糖扩散模型：紧密堆积的二氧化硅纳米球和围绕纳米球的复杂纤维结构。然后，通过琼脂玫瑰凝胶网络进行罗丹明 6G 扩散分析，然后使用我们的实验结果进行模型验证。微观结构模型，