Schweizer Kenneth S, Saltzman Erica J
Department of Materials Science & Engineering, University of Illinois, Urbana, Illinois 61801, USA.
J Chem Phys. 2004 Jul 22;121(4):1984-2000. doi: 10.1063/1.1756854.
A statistical mechanical theory of collective dynamic barriers, slow segmental relaxation, and the glass transition of polymer melts is developed by combining, and in some aspects extending, methods of mode coupling, density functional, and activated hopping transport theories. A coarse-grained description of polymer chains is adopted and the melt is treated as a liquid of segments. The theory is built on the idea that collective density fluctuations on length scales considerably longer than the local cage scale are of primary importance in the deeply supercooled regime. The barrier hopping or segmental relaxation time is predicted to be a function primarily of a single parameter that is chemical structure, temperature, and pressure dependent. This parameter depends on the material-specific dimensionless amplitude of thermal density fluctuations (compressibility) and a reduced segmental density determined by the packing length and backbone characteristic ratio. Analytic results are derived for a crossover temperature T(c), collective barrier, and glass transition temperature T(g). The relation of these quantities to structural and thermodynamic properties of the polymer melt is established. A universal power-law scaling behavior of the relaxation time below T(c) is predicted based on identification of a reduced temperature variable that quantifies the breadth of the supercooled regime. Connections between the ratio T(c)/T(g), two measures of dynamic fragility, and the magnitude of the local relaxation time at T(g) logically follow. Excellent agreement with experiment is found for these generic aspects, and the crucial importance of the experimentally observed near universality of the dynamic crossover time is established. Extensions of the theory to treat the full chain dynamics, heterogeneity, barrier fluctuations, and nonpolymeric thermal glass forming liquids are briefly discussed.
通过结合并在某些方面扩展模式耦合、密度泛函和活化跳跃传输理论的方法，发展了一种关于聚合物熔体的集体动态势垒、慢链段弛豫和玻璃化转变的统计力学理论。采用了聚合物链的粗粒化描述，并将熔体视为链段的液体。该理论基于这样一种观点，即在深度过冷状态下，长度尺度远大于局部笼尺度的集体密度涨落至关重要。势垒跳跃或链段弛豫时间预计主要是一个单一参数的函数，该参数取决于化学结构、温度和压力。这个参数取决于材料特定的热密度涨落（压缩性）的无量纲幅度以及由堆积长度和主链特征比确定的约化链段密度。推导了交叉温度T(c)、集体势垒和玻璃化转变温度T(g)的解析结果。建立了这些量与聚合物熔体的结构和热力学性质之间的关系。基于对量化过冷状态广度的约化温度变量的识别，预测了低于T(c)时弛豫时间的通用幂律标度行为。T(c)/T(g)的比值、两种动态脆性度量与T(g)处局部弛豫时间大小之间的联系也随之而来。在这些一般方面与实验结果达成了极好的一致，并确立了实验观察到的动态交叉时间近乎普遍性的关键重要性。简要讨论了该理论在处理全链动力学、非均匀性、势垒涨落和非聚合热玻璃形成液体方面的扩展。
