Abstract In this work, the interphase in polymer nanocomposites is modeled as a multilayered part in which the Young’s modulus of each layer E k continuously changes from nanoparticle surface ( x k = 0) to polymer matrix ( x k = t ). The dependency of E k on x k is analyzed by linear, exponential and power functions. The average interphase modulus is determined by the Ji model for several samples and the accurate dependency of E k on x is derived. The linear and exponential relations display a relatively similar trend for E k , but they cannot suggest an accurate E k assuming the predicted interphase modulus by the Ji model. The equation which relates E k on x k Y can present acceptable values for E k , where the value of Y determines the Young’s modulus E k . This approach can be applied to evaluate the magnitude of interphase in polymer nanocomposites.

中文翻译：

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聚合物纳米复合材料中间相层杨氏模量的建模方法

摘要 在这项工作中，聚合物纳米复合材料中的界面被建模为多层部分，其中每一层的杨氏模量 E k 从纳米颗粒表面 (xk = 0) 到聚合物基质 (xk = t) 连续变化。E k 对xk 的依赖性通过线性、指数和幂函数进行分析。平均相间模量由几个样本的 Ji 模型确定，并推导出 E k 对 x 的准确依赖性。线性和指数关系对 E k 显示出相对相似的趋势，但它们不能提出准确的 E k 假设假设由 Ji 模型预测的相间模量。将 E k 与 xk Y 相关联的方程可以提供可接受的 E k 值，其中 Y 的值决定了杨氏模量 E k 。