Confinement of Equilibrium Polymers: A Field-Theoretic Model and Mean-Field Solution
Confinement of Equilibrium Polymers: A Field-Theoretic Model and Mean-Field Solution
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平衡聚合物的约束：场论模型和平均场解
DOI：
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发表时间：
2006
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通讯作者：
G. Fredrickson
中科院分区：
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作者：
Edward H. Feng;G. Fredrickson
本文建立了一个适用于良溶剂中平衡聚合物的场论模型。本文利用高斯链模型，导出了巨正则系综的一个推导式，其中参数为单体化学势μM，排斥体积参数u 0和成键能量减少2 h。只有与u 0 e-2 h成比例的量Γ在确定平均场解时起作用。对于块体系统，均匀平均场解给出了指数聚合物长度分布，其特征长度随r的增加而减小。此外，在平均场近似下，半稀溶液中聚合物重叠的程度随着密度的增加而减小。本文用数值自洽场论研究了两平行排斥板间平衡聚合物的非均匀性质。聚合物长度分布对于所有L（板之间的无量纲距离）都是指数分布。对于小L，特征聚合物长度的…
We develop a field-theoretic model for equilibrium polymers in good solvent. Using the Gaussian chain model, we present a derivation in the grand canonical ensemble in which the parameters are the monomer chemical potential μM, the excluded volume parameter u0, and the energy decrease for forming a bond 2h. Only the quantity Γ, which is proportional to u0e-2h, matters in determining the mean-field solution. For a bulk system, the homogeneous mean-field solution gives an exponential polymer length distribution with a characteristic length that decreases with increasing Γ. Moreover, the extent of polymer overlap in a semi-dilute solution decreases with increasing density in the mean-field approximation. We study the inhomogeneous properties of equilibrium polymers confined between two parallel repulsive plates with numerical self-consistent field theory. The polymer length distribution is exponential for all L, the dimensionless distance between the plates. For small L, the characteristic polymer length of ...