Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India.
J Chem Phys. 2013 Jun 28;138(24):244904. doi: 10.1063/1.4811332.
The confinement of a polymer to volumes whose characteristic linear dimensions are comparable to or smaller than its bulk radius of gyration R(G,bulk) can produce significant changes in its static and dynamic properties, with important implications for the understanding of single-molecule processes in biology and chemistry. In this paper, we present calculations of the effects of a narrow rectangular slit of thickness d on the scaling behavior of the diffusivity D and relaxation time τr of a Gaussian chain of polymerization index N and persistence length l0. The calculations are based on the Rouse-Zimm model of chain dynamics, with the pre-averaged hydrodynamic interaction being obtained from the solutions to Stokes equations for an incompressible fluid in a parallel plate geometry in the limit of small d. They go beyond de Gennes' purely phenomenological analysis of the problem based on blobs, which has so far been the only analytical route to the determination of chain scaling behavior for this particular geometry. The present model predicts that D ∼ dN(-1)ln (N∕d(2)) and τr ∼ N(2)d(-1)ln (N∕d(2)) in the regime of moderate confinement, where l0 ≪ d < R(G,bulk). The corresponding results for the blob model have exactly the same power law behavior, but contain no logarithmic corrections; the difference suggests that segments within a blob may actually be partially draining and not non-draining as generally assumed.
聚合物被限制在其特征线性尺寸与本体回旋半径 R(G,bulk) 相当或更小的体积中，会导致其静态和动态性质发生显著变化，这对理解生物学和化学中的单分子过程具有重要意义。在本文中，我们提出了一种计算方法，用于研究厚度为 d 的狭窄矩形狭缝对扩散系数 D 和弛豫时间 τr 的影响，这些参数与聚合指数 N 和持久长度 l0 的高斯链有关。计算基于链动力学的 Rouse-Zimm 模型，其中预平均的流体动力学相互作用是通过求解不可压缩流体在平行板几何形状中的 Stokes 方程得到的，其限制条件是 d 很小。这些计算方法超越了 de Gennes 基于液滴的纯唯象分析，这是迄今为止确定这种特殊几何形状下链缩放行为的唯一分析途径。本模型预测，在中等限制条件下，即 l0 ≪ d < R(G,bulk) 时，D∼dN(-1)ln(N∕d(2))和 τr∼N(2)d(-1)ln(N∕d(2))。而液滴模型的相应结果具有完全相同的幂律行为，但不包含对数修正；这种差异表明，液滴内的链段实际上可能部分排出，而不是通常假设的非排出。
