Neves D E, Scott R A
Macromolecules. 1975 May-Jun;8(3):267-71. doi: 10.1021/ma60045a005.
A Monte Carlo study of the distribution functions for the end-to-end distance and radius of gyration for hard-sphere models of poly(glycine) and poly(L-alanine) random coils has been conducted in the chain-length range n = 3 to 100 monomer units for both unperturbed chains and chains perturbed by long-range interactions (excluded volume effects). The distribution functions for the radius of gyration in all cases have been very precisely calculated, those for the perturbed end-to-end distance less precisely, and those for the unperturbed end-to-end distance least precisely. Empirical distribution functions of the form W(p) = ap-b exp(-cp-d) for the reduced end-to-end distance p = r/"r-2"-one-half and a similar form for the reduced radius of gyration could be least-squares fit to the Monte Carlo data. The expansion factors alpha-r and alpha-s were calculated vs. chain length and were used to test various versions of the two-parameter theory of the excluded volume effect. To be consistent with the chain-length dependence of alpha-r and alpha-s as determined by the Monte Carlo calculations, each of these theories required two different binary cluster integrals, a beta-r based on alpha-r and a beta-s based on alpha-s, both of which were strongly chain-length dependent. Both of these results suggest that the two-parameter theory is not applicable to the models used in this study. It was also found that, except for very short chain lengths, plots of ln alphs-r vs. ln n were linear, and thus that alpha-r could be estimated for long chain lengths. Comparison of these estimates with the experimental data on four polypeptide chains in one-earth solvents that the hard-sphere models used in this study yield expansion factors that do not seriously overestimate the magnitude of the excluded volume effect.
针对聚甘氨酸和聚L-丙氨酸无规线团硬球模型，在链长范围n = 3至100个单体单元内，对无扰链以及受长程相互作用（排除体积效应）扰动的链的端到端距离和回转半径的分布函数进行了蒙特卡罗研究。在所有情况下，回转半径的分布函数都得到了非常精确的计算，受扰端到端距离的分布函数计算精度稍低，无扰端到端距离的分布函数计算精度最低。对于折合端到端距离p = r/〈r²〉½，可将形式为W(p) = ap^-b exp(-cp^-d)的经验分布函数以及类似形式的折合回转半径的经验分布函数进行最小二乘拟合到蒙特卡罗数据。计算了膨胀因子αr和αs随链长的变化，并用于检验排除体积效应两参数理论的各种版本。为了与蒙特卡罗计算确定的αr和αs的链长依赖性相一致，这些理论中的每一个都需要两个不同的二元簇积分，一个基于αr的βr和一个基于αs的βs，两者都强烈依赖于链长。这两个结果都表明两参数理论不适用于本研究中使用的模型。还发现，除了非常短的链长外，lnαr对ln n的图是线性的，因此可以估计长链长的αr。将这些估计值与在一种地球溶剂中四条多肽链的实验数据进行比较，结果表明本研究中使用的硬球模型产生的膨胀因子不会严重高估排除体积效应的大小。
