Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA.
Soft Matter. 2016 Aug 10;12(32):6757-70. doi: 10.1039/c6sm00851h.
We present a hybrid model for polymeric glasses under deformation that combines a minimal model of segmental dynamics with a beads-and-springs model of a polymer, solved by Brownian dynamics (BD) simulations, whose relaxation is coupled to the segmental dynamics through the drag coefficient of the beads. This coarse-grained model allows simulations that are much faster than molecular dynamics and successfully capture the entire range of mechanical response including yielding, plastic flow, strain-hardening, and incomplete strain recovery. The beads-and-springs model improves upon the dumbbell model for glassy polymers proposed by Fielding et al. (Phys. Rev. Lett., 2012, 108, 048301) by capturing the small elastic recoil seen experimentally without the use of ad hoc adjustments of parameters required in the model of Fielding et al. With appropriate choice of parameters, predictions of creep, recovery, and segmental relaxation are found to be in good agreement with poly(methylmethacrylate) (PMMA) data of Lee et al. (Science, 2009, 323, 231-234). Our model shows dramatic differences in behavior of the segmental relaxation time between extensional creep and steady extension, and between extension and shear. The non-monotonic response of the segmental relaxation time to extensional creep and the small elastic recovery after removal of stress are shown to arise from sub-chains that are trapped between folds, and that become highly oriented and stretched at strains of order unity, connecting the behavior of glassy polymers under creep to that of dilute polymer solutions under fast extensional flows. We are also able to predict the effects of polymer pre-orientation in the parallel or orthogonal direction on the subsequent response to extensional deformation.
我们提出了一种聚合物玻璃在变形下的混合模型，该模型将片段动力学的最小模型与聚合物的珠-弹簧模型相结合，通过布朗动力学（BD）模拟求解，其弛豫通过珠子的阻力系数与片段动力学耦合。这种粗粒模型允许比分子动力学快得多的模拟，并成功地捕捉到包括屈服、塑性流动、应变硬化和不完全应变恢复在内的整个力学响应范围。珠-弹簧模型改进了 Fielding 等人提出的用于玻璃态聚合物的哑铃模型（Phys. Rev. Lett.，2012，108，048301），通过捕捉到实验中观察到的小弹性回弹，而无需对 Fielding 等人模型中所需的参数进行特殊调整。通过适当选择参数，发现蠕变、恢复和片段松弛的预测与 Lee 等人的聚甲基丙烯酸甲酯（PMMA）数据（Science，2009，323，231-234）非常吻合。我们的模型显示了在拉伸蠕变和稳态拉伸之间以及在拉伸和剪切之间，片段松弛时间的行为有显著的差异。片段松弛时间对拉伸蠕变的非单调响应以及在去除应力后小的弹性恢复被证明是由于被困在褶皱之间的亚链引起的，这些亚链在应变达到单位量级时变得高度取向和拉伸，将玻璃态聚合物在蠕变下的行为与稀溶液聚合物在快速拉伸流动下的行为联系起来。我们还能够预测聚合物在平行或正交方向上的预取向对随后对拉伸变形的响应的影响。
