论文标题
半灵性聚合物溶液的坦克弹性常数
Frank Elastic Constants of Semiflexible Polymer Solutions
论文作者
论文摘要
我们为半灵聚合物的列溶液提供了坦克弹性常数。我们将这些结果绘制为粗粒的maier-saupe四极强度和聚合物刚度的函数，从刚度到高度柔韧性。该派生使用随机相近似，并使用球形谐波基础结合了类似蠕虫的链的统计结果与聚合物场理论的确切结果。使用数值逆Laplace变换评估结果。我们以显微镜特征（例如发夹和聚合物结尾）介绍结果，因此可以独立于衍生趋势来理解趋势。关键发现是，对于刚性聚合物$ k_ {bend}> k_ {splay}> k_ {twist} $，而对于灵活的聚合物$ k_ {splay}> k_ {bend}> k_ {twist} $。对于刚性聚合物，坦克弹性常数随聚合物长度而生长。对于柔性聚合物，弹性常数随持久性长度而生长，这成为特征长度的比例，除了$ k_ {play} $以高对准强度的$ k_ {play} $，由于消除发夹的消除而随着聚合物长度而生长。
We derive the Frank elastic constants for nematic solutions of semiflexible polymers. We plot these results as a function of the coarse-grained Maier-Saupe quadrupole aligning strength and polymer stiffness ranging from rigid to highly flexible. The derivation uses the random phase approximation and combines the exact results for the statistics of a worm-like-chain with polymer field theory using a spherical harmonic basis. The results are evaluated using a numerical inverse Laplace transform. We present the results in terms of microscopic features such as hairpins and polymer ends so the trends can be understood independently from the derivation. Key findings are that for rigid polymers $K_{bend}>K_{splay}>K_{twist}$ while for flexible polymers $K_{splay}>K_{bend}>K_{twist}$. For rigid polymers, the Frank elastic constants grow with the polymer length. For flexible polymers the elastic constants grow with the persistence length, which becomes the characteristic length scale, with the exception of $K_{splay}$ at high alignment strengths which grows with polymer lengths due to the elimination of hairpins.
