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arXiv 1004.1471cond-mat.stat-mech
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受限流体动力学相关性的动力学伊辛模型研究:快时间尺度和慢时间尺度的出现

A kinetic Ising model study of dynamical correlations in confined fluids: Emergence of both fast and slow time scales

Rajib Biswas, Biman Bagchi

摘要:

实验和计算机模拟研究揭示了在受限体系中分子取向弛豫存在丰富的动力学过程,如反胶束、环糊精空腔和纳米管中的水。在这里,我们介绍了一种新的有限长度的一维伊辛模型调查的传播和有限系统中的动力学相关性的湮灭,并了解有趣的缩短取向弛豫时间,已报告的小尺寸的反胶束。在我们的有限尺寸模型中,两个末端单元的两个自旋方向相反,以模拟真实系统中将水方向固定在相反方向上的表面效应。这会产生相反的偏振,从表面向内部传播,并在中心产生块状条件。这个模型可以解析地解决短链。对于长链,我们用Glauber自旋翻转动力学(以及Metropolis单自旋翻转Monte Carlo算法)数值求解模型。我们表明,该模型很好地再现了实验中观察到的许多功能。由于从表面传播到核心的相关性之间的相消干涉,其中一个旋转弛豫时间分量比体块衰减得更快。一般来说,由于各种相互作用之间的相互作用,自旋的弛豫是非指数的。在自旋之间强耦合的极限或低温的极限中,自旋弛豫的性质随着均匀动力学的出现而发生质的变化,其中衰变主要是指数的,再次与实验一致。

英文摘要:

Experiments and computer simulation studies have revealed existence of rich dynamics in the orientational relaxation of molecules in confined systems such as water in reverse micelles, cyclodextrin cavities and nano-tubes. Here we introduce a novel finite length one dimensional Ising model to investigate the propagation and the annihilation of dynamical correlations in finite systems and to understand the intriguing shortening of the orientational relaxation time that has been reported for small sized reverse micelles. In our finite sized model, the two spins at the two end cells are oriented in the opposite directions, to mimic the effects of surface that in real system fixes water orientation in the opposite directions. This produces opposite polarizations to propagate inside from the surface and to produce bulk-like condition at the centre. This model can be solved analytically for short chains. For long chains we solve the model numerically with Glauber spin flip dynamics (and also with Metropolis single-spin flip Monte Carlo algorithm). We show that model nicely reproduces many of the features observed in experiments. Due to the destructive interference among correlations that propagate from the surface to the core, one of the rotational relaxation time components decays faster than the bulk. In general, the relaxation of spins is non-exponential due to the interplay between various interactions. In the limit of strong coupling between the spins or in the limit of low temperature, the nature of relaxation of the spins undergoes a qualitative change with the emergence of a homogeneous dynamics where decay is predominantly exponential, again in agreement with experiments.

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