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arXiv 0810.5389cond-mat.soft
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polymer熔体中局部关联的链长依赖性和对称polymer共混体系的微扰理论

On the chain length dependence of local correlations in polymer melts and a perturbation theory of symmetric polymer blends

David C. Morse, Jun Kyung Chung

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submitted to J. Chem. Phys
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摘要：

稠密高分子液体的自洽场（SCF）理论假设短程关联几乎与单体如何连接成聚合物无关。在结构相同的聚合物物质A和B的混合物的微扰理论的背景下，探讨了这种想法的一些限制，其中AB对相互作用与AA和BB相互作用略有不同，并且差异由参数α控制。将自由能扩展到O（α）产生形式为α $z(N)ϕ_{A}ϕ_{B}$的过量自由能，在晶格和连续模型中，其中z（N）是单组分液体中每个单体的分子间近邻的数量的量度。这个数量随着N的增加而略有下降，因为来自相同链的单体的自浓度对于较长的链略高，从而对于较长的链产生更深的相关性空穴。我们分析了由此产生的$N$依赖性，并预测$z(N) = z^{\infty}[1 + β\bar{N}^{-1/2}]$，其中$\bar{N}$是不变的聚合度，和$β=(6/π)^{3/2}$ .通过与模拟的比较，证实了这一预测和其他预测。我们还提出了一种方法来估计有效的相互作用参数适当的模拟数据的比较SCF理论和粗粒度的理论修正SCF理论，这是基于外推的系数在这个微扰理论的限制$N \to \infty$。我们表明，重整化的单圈理论包含一个定量的正确描述的$N$依赖的本地结构研究。

英文摘要：

The self-consistent field (SCF) theory of dense polymer liquids assumes that short-range correlations are almost independent of how monomers are connected into polymers. Some limits of this idea are explored in the context of a perturbation theory for mixtures of structurally identical polymer species, A and B, in which the AB pair interaction differs slightly from the AA and BB interaction, and the difference is controlled by a parameter alpha Expanding the free energy to O(α) yields an excess free energy of the form alpha $z(N)ϕ_{A}ϕ_{B}$, in both lattice and continuum models, where z(N) is a measure of the number of inter-molecular near neighbors of each monomer in a one-component liquid. This quantity decreases slightly with increasing N because the self-concentration of monomers from the same chain is slightly higher for longer chains, creating a deeper correlation hole for longer chains. We analyze the resulting $N$-dependence, and predict that $z(N) = z^{\infty}[1 + β\bar{N}^{-1/2}]$, where $\bar{N}$ is an invariant degree of polymerization, and $β=(6/π)^{3/2}$. This and other predictions are confirmed by comparison to simulations. We also propose a way to estimate the effective interaction parameter appropriate for comparisons of simulation data to SCF theory and to coarse-grained theories of corrections to SCF theory, which is based on an extrapolation of coefficients in this perturbation theory to the limit $N \to \infty$. We show that a renormalized one-loop theory contains a quantitatively correct description of the $N$-dependence of local structure studied here.

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