Department of Mechanical and Aerospace Engineering, UCLA, Los Angeles, CA 90095, USA.
Acta Biomater. 2011 May;7(5):2109-18. doi: 10.1016/j.actbio.2010.12.025. Epub 2010 Dec 25.
This paper explores the effects of filament length polydispersity on the mechanical properties of semiflexible crosslinked polymer networks. Extending previous studies on monodisperse networks, we compute numerically the response of crosslinked networks of elastic filaments of bimodal and exponential length distributions. These polydisperse networks are subject to the same affine to nonaffine (A/NA) transition observed previously for monodisperse networks, wherein the decreases in either crosslink density or bending stiffness lead to a shift from affine, stretching-dominated deformations to nonaffine, bending-dominated deformations. We find that the onset of this transition is generally more sensitive to changes in the density of longer filaments than shorter filaments, meaning that longer filaments have greater mechanical efficiency. Moreover, in polydisperse networks, mixtures of long and short filaments interact cooperatively to generally produce a nonaffine mechanical response closer to the affine prediction than comparable monodisperse networks of either long or short filaments. Accordingly, the mechanical affinity of polydisperse networks is dependent on the filament length composition. Overall, length polydispersity has the effect of sharpening and shifting the A/NA transition to lower network densities. We discuss the implications of these results on experimental observation of the A/NA transition, and on the design of advanced materials.
本文探讨了长丝长度多分散性对半刚交联聚合物网络力学性能的影响。在对单分散网络进行研究的基础上，我们通过数值计算研究了双模态和指数长度分布弹性长丝交联网络的响应。与单分散网络中观察到的相同，这些多分散网络经历了同样的从仿射到非仿射（A/NA）转变，其中交联密度或弯曲刚度的降低导致从仿射、拉伸主导变形到非仿射、弯曲主导变形的转变。我们发现，这种转变的开始通常对较长长丝密度的变化比对较短长丝更敏感，这意味着较长的长丝具有更高的机械效率。此外，在多分散网络中，长丝和短丝的混合物相互协作，通常会产生更接近仿射预测的非仿射力学响应，而不是具有相同长丝或短丝的单分散网络。因此，多分散网络的机械亲和性取决于长丝长度组成。总的来说，长度多分散性的作用是使 A/NA 转变更加尖锐，并将其转移到较低的网络密度。我们讨论了这些结果对 A/NA 转变实验观察以及先进材料设计的影响。
