Simplified Onsager theory for isotropic-nematic phase equilibria of length polydisperse hard rods
Simplified Onsager theory for isotropic-nematic phase equilibria of length polydisperse hard rods
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DOI：
10.1063/1.1499718
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发表时间：
2002-09-15
影响因子：
4.4
通讯作者：
Sollich, P
中科院分区：
文献类型：
--
作者：
Speranza, A;Sollich, P
多分散性被认为对棒状颗粒悬浮液中液晶相的形成具有重要影响。为了理解这种影响，我们分析了长度多分散性的薄硬棒的相行为。我们的治疗是基于一个简化的Onsager理论，通过截断排除体积的角度依赖性的级数展开。我们描述的模型，并给出了完整的相平衡方程，然后用矩自由能方法，减少了一个问题，从一个具有无限数量的保守密度的一个有限数量的有效密度的时刻的全密度分布数值求解。该方法准确地产生的发病率的顺序。除此之外，结果是近似的，但我们表明，它们可以通过添加自适应选择的额外时刻，同时仍然避免了直接解决全相平衡条件的数值复杂性基本上任意精确。我们详细研究了具有三种不同长度分布的系统的相行为：（单峰）Schulz分布，双分散分布，和双峰混合物的两个Schulz分布之间的插值这两种情况。一个三相各向同性，双分散的长度分布，如果长和短杆长度的比例是足够大的，但不是为单峰的长度分布的双相各向同性共存区域。我们系统地探讨了拓扑结构的相图作为一个功能的长度分布的宽度和杆的长度比在双分散和双峰的情况下。(C)2002年美国物理学会。
Polydispersity is believed to have important effects on the formation of liquid crystal phases in suspensions of rodlike particles. To understand such effects, we analyze the phase behavior of thin hard rods with length polydispersity. Our treatment is based on a simplified Onsager theory, obtained by truncating the series expansion of the angular dependence of the excluded volume. We describe the model and give the full phase equilibrium equations; these are then solved numerically using the moment free energy method which reduces the problem from one with an infinite number of conserved densities to one with a finite number of effective densities that are moments of the full density distribution. The method yields exactly the onset of nematic ordering. Beyond this, results are approximate but we show that they can be made essentially arbitrarily precise by adding adaptively chosen extra moments, while still avoiding the numerical complications of a direct solution of the full phase equilibrium conditions. We investigate in detail the phase behavior of systems with three different length distributions: a (unimodal) Schulz distribution, a bidisperse distribution, and a bimodal mixture of two Schulz distributions which interpolates between these two cases. A three-phase isotropic-nematic-nematic coexistence region is shown to exist for the bimodal and bidisperse length distributions if the ratio of long and short rod lengths is sufficiently large, but not for the unimodal one. We systematically explore the topology of the phase diagram as a function of the width of the length distribution and of the rod length ratio in the bidisperse and bimodal cases. (C) 2002 American Institute of Physics.