Cavallo A, Müller M, Binder K
Institut für Physik, WA 331, Johannes Gutenberg Universität, D-55099 Mainz, Germany.
J Phys Chem B. 2005 Apr 14;109(14):6544-52. doi: 10.1021/jp0458506.
The interplay between chain conformations and phase separation in binary symmetric polymer mixtures confined into thin films by "neutral" hard walls (i.e., walls that do not preferentially attract or repel one of the two components of the mixture) is studied by Monte Carlo simulations. Using the bond fluctuation model on a simple cubic lattice in the semi grand canonical ensemble, we locate the critical temperature of demixing via finite size scaling methods for a wide range of chain lengths (16 </= N </= 256 effective monomers per chain) and film thicknesses (2 </= D </= 19 lattice spacings). Simultaneously, we investigate the geometrical structure of the chains, showing that despite using melt densities there are pronounced "correlation hole effects", in particular for the smaller values of D. Also the components of the radius of gyration and end-to-end distance parallel and perpendicular to the confining walls are analyzed and their scaling behavior is studied. Evidence is presented that for strictly two-dimensional polymers (as occur for D = 2) the average number of intermolecular contacts scales with chain length N as z(c) proportional, variant N(-3/8) and therefore the critical temperature scales as T(c) proportional, variant N(5/8), whereas for values of D that exceed the excluded volume screening length, z(c) remains nonzero for N --> infinity, and hence T(c) proportional, variant N. However, strong deviations from the Flory-Huggins theory occur as long as the unperturbed chain dimension exceeds D, and the critical behavior falls in the universality class of the two-dimensional Ising model for any finite value of D.
通过蒙特卡罗模拟研究了二元对称聚合物混合物在由“中性”硬壁（即不优先吸引或排斥混合物两种组分之一的壁）限制在薄膜中的链构象与相分离之间的相互作用。在半巨正则系综的简单立方晶格上使用键涨落模型，我们通过有限尺寸标度方法确定了广泛链长范围（每条链16≤N≤256个有效单体）和薄膜厚度范围（2≤D≤19个晶格间距）下的相分离临界温度。同时，我们研究了链的几何结构，表明尽管使用了熔体密度，但仍存在明显的“相关空穴效应”，特别是对于较小的D值。还分析了与限制壁平行和垂直的回转半径和端到端距离的分量，并研究了它们的标度行为。有证据表明，对于严格二维聚合物（如D = 2时出现的情况），分子间接触的平均数量与链长N的标度关系为zc∝N^(-3/8)，因此临界温度的标度关系为Tc∝N^(5/8)，而对于超过排除体积屏蔽长度的D值，当N→∞时zc仍不为零，因此Tc∝N。然而，只要未扰动的链尺寸超过D，就会出现与弗洛里 - 哈金斯理论的强烈偏差，并且对于任何有限的D值，临界行为都属于二维伊辛模型的普适类。
