Kim Sang-Un, Kim Joo-Yong
Department of Smart Wearable Engineering, Soongsil University, Seoul 06978, Republic of Korea.
Department of Materials Science and Engineering, Soongsil University, Seoul 06978, Republic of Korea.
Materials (Basel). 2025 Jun 30;18(13):3097. doi: 10.3390/ma18133097.
Conductive polymer composites (CPCs) are widely used in flexible electronics due to their tunable electrical properties and mechanical deformability. However, accurately predicting the evolution of conductive networks, particularly under compressive strain, remains a significant challenge. In this study, we developed a statistical mechanics model and an extended dynamic statistical mechanics model to quantitatively describe percolation behavior in CPCs. The static model incorporates filler geometry, aspect ratio (AR), and surface-to-volume ratio, and was validated using Monte Carlo simulations. Results show that the percolation threshold for spherical fillers was 0.11965, while significantly lower values of 0.00669 and 0.00203 were observed for plate- and rod-shaped fillers, respectively, confirming the enhanced connectivity of anisotropic particles. To capture strain-dependent behavior, a dynamic model was constructed using a Smoluchowski-type gain-loss framework. This model separates conductive network formation (gain) from network disconnection (loss) caused by filler alignment and Poisson-induced expansion. At high Poisson's ratios (0.3 and 0.5), the model accurately predicted the reduction in connectivity, particularly for anisotropic fillers. Across all tested conditions, the model exhibited strong agreement with simulation data, with RMSE values ranging from 0.0004 to 0.0449. The results confirm that high AR fillers enhance conductivity under compression, while large Poisson's ratios suppress network formation. These findings provide a reliable, physically grounded modeling framework for designing strain-sensitive devices such as flexible pressure sensors.
导电聚合物复合材料（CPCs）因其可调的电学性能和机械可变形性而广泛应用于柔性电子器件中。然而，准确预测导电网络的演变，尤其是在压缩应变下的演变，仍然是一项重大挑战。在本研究中，我们开发了一个统计力学模型和一个扩展的动态统计力学模型，以定量描述CPCs中的渗流行为。静态模型纳入了填料几何形状、纵横比（AR）和表面积与体积比，并通过蒙特卡罗模拟进行了验证。结果表明，球形填料的渗流阈值为0.11965，而对于板状和棒状填料，分别观察到显著更低的值0.00669和0.00203，证实了各向异性颗粒连通性的增强。为了捕捉应变相关行为，使用Smoluchowski型增益-损失框架构建了一个动态模型。该模型将由填料排列和泊松诱导膨胀引起的导电网络形成（增益）与网络断开（损失）分开。在高泊松比（0.3和0.5）下，该模型准确预测了连通性的降低，特别是对于各向异性填料。在所有测试条件下，该模型与模拟数据表现出高度一致性，均方根误差（RMSE）值范围为0.0004至0.0449。结果证实，高纵横比填料在压缩下可提高导电性，而大泊松比会抑制网络形成。这些发现为设计应变敏感器件（如柔性压力传感器）提供了一个可靠的、基于物理的建模框架。
