采用自洽平均场理论并结合蒙特卡洛方法考查不同溶剂中高分子单链回转半径与聚合度的标度关系。计算结果表明，在Θ溶剂中标度指数ν≈0.495，说明此时高分子链遵循理想链的行为；另一方面，在良溶剂中标度指数ν并非普适常数，而是随着溶剂性质的变化而改变，并且总是明显低于经典理论预测值0.6。分析指出，有限链长效应是造成这一偏差的重要原因。
We employ the self-consistent field theory (SCFT) with the help of Monte Carlo technique to study the scaling behavior of the radius of gyration Rg of a single polymer chain with respect to the chain length N. The numerical results indicate the scaling exponent ν≈0.495 for Θ-solvent, which is a typical ideal chain behavior. However, for good solvent cases, the ν value displays explicit dependence on the solvent quality and is always lower than the classical prediction of 0.6. We argue that such a discrepancy is mainly attributed to the finite chain length effect.
[1] Rubinstein M, Colby R H. Polymer physics[M]. Oxford, UK:Oxford University Press, 2003:102-104.
[2] Flory P J. Principles of polymer chemistry[M]. Ithaca, New York:Cornell University Press, 1953:29-66.
[3] Fetters L J, Hadjichristidis N, Lindner J S, et al. Molecular weight dependence of hydrodynamic and thermodynamic properties for well-defined linear polymers in solution[J]. J Phys Chem Ref Data, 1994, 23(4):619-640.
[4] Grest G S, Murat M. Structure of grafted polymeric brushes in solvents of varying quality:a molecular dynamics study[J]. Macromolecules, 1993, 26(12):3108-3117.
[5] Elliott I G, Kuhl T L, Faller R. Molecular simulation study of the structure of high density polymer brushes in good solvent[J]. Macromolecules, 2010, 43(21):9131-9138.
[6] Suo T, Whitmore M D. Self-consistent field theory of tethered polymers:one dimensional, three dimensional, strong stretching theories and the effects of excluded-volume-only interactions[J]. J Chem Phys, 2014, 141(20):204903.
[7] Edwards S F. The statistical mechanics of polymers with excluded volume[J]. Proc Phys Soc, 1965, 85:613-624.
[8] Suo T, Yan D. Theoretical study on tethered polymers with explicit grafting points in Θ-solvent[J]. J Chem Phys, 2011, 134(5):054901.
[9] Matsen M W. Self-consistent field theory and its applications[C]//Gompper G, Schick M. Soft Matter. Weinheim:Wiley-VCH Verlag GmbH & Co. KGaA, 2007:7-11.
[10] Tang J, Zhang X, Yan D. Compression induced phase transition of nematic brush:a mean-field theory study[J]. J Chem Phys, 2015, 143(20):204903.
[11] Fu J, Zhang X, Miao B, et al. Light-responsive expansion-contraction of spherical nanoparticle grafted with azopolymers[J]. J Chem Phys, 2017, 146(16):164901.
[12] Xu G, Huang Z, Chen P, et al. Optimal reactivity and improved self-healing capability of structurally-dynamic polymers grafted on janus nanoparticles governed by chain stiffness and spatial organization[J]. Small, 2017, 13(13):1603155.
