Blavats'ka V, von Ferber C, Holovatch Yu
Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Sep;74(3 Pt 1):031801. doi: 10.1103/PhysRevE.74.031801. Epub 2006 Sep 11.
We present a quantitative picture of the separation of star polymers in a solution where part of the volume is influenced by a porous medium. To this end, we study the impact of long-range-correlated quenched disorder on the entropy and scaling properties of f-arm star polymers in a good solvent. We assume that the disorder is correlated on the polymer length scale with a power-law decay of the pair correlation function g(r) approximately r-a. Applying the field-theoretical renormalization group approach we show in a double expansion in epsilon=4-d and delta=4-a that there is a range of correlation strengths delta for which the disorder changes the scaling behavior of star polymers. In a second approach we calculate for fixed space dimension d=3 and different values of the correlation parameter a the corresponding scaling exponents gammaf that govern entropic effects. We find that gammaf-1, the deviation of gammaf from its mean field value is amplified by the disorder once we increase delta beyond a threshold. The consequences for a solution of diluted chain and star polymers of equal molecular weight inside a porous medium are that star polymers exert a higher osmotic pressure than chain polymers and in general higher branched star polymers are expelled more strongly from the correlated porous medium. Surprisingly, polymer chains will prefer a stronger correlated medium to a less or uncorrelated medium of the same density while the opposite is the case for star polymers.
我们展示了在部分体积受多孔介质影响的溶液中星形聚合物分离的定量图景。为此，我们研究了长程相关的淬火无序对良溶剂中f臂星形聚合物的熵和标度性质的影响。我们假设无序在聚合物长度尺度上相关，对关联函数g(r) 以约r-a的幂律衰减。应用场论重整化群方法，我们在ε = 4 - d和δ = 4 - a的双重展开中表明，存在一系列关联强度δ，对于这些δ，无序会改变星形聚合物的标度行为。在第二种方法中，我们针对固定的空间维度d = 3和不同的关联参数a值计算了控制熵效应的相应标度指数γf。我们发现，一旦我们将δ增加到超过一个阈值，γf与其平均场值的偏差γf - 1会因无序而放大。对于在多孔介质中具有相同分子量的稀释链状聚合物和星形聚合物溶液而言，其结果是星形聚合物比链状聚合物施加更高的渗透压，并且一般来说，更高支化的星形聚合物从相关多孔介质中被排出得更强。令人惊讶的是，聚合物链会更喜欢密度相同但相关性更强的介质，而不是相关性较弱或不相关的介质，而星形聚合物的情况则相反。
