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在模型线虫状液晶中寻找各向同性-向列相转变附近取向弛豫中的时间幂律。

In search of temporal power laws in the orientational relaxation near isotropic-nematic phase transition in model nematogens.

作者信息

Jose Prasanth P, Bagchi Biman

机构信息

Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India.

出版信息

J Chem Phys. 2004 Jun 15;120(23):11256-66. doi: 10.1063/1.1742942.

Abstract

Recent Kerr relaxation experiments by Gottke et al. have revealed the existence of a pronounced temporal power law decay in the orientational relaxation near the isotropic-nematic phase transition (INPT) of nematogens of rather small aspect ratio, kappa (kappa approximately 3-4). We have carried out very long (50 ns) molecular dynamics simulations of model (Gay-Berne) prolate ellipsoids with aspect ratio 3 in order to investigate the origin of this power law. The model chosen is known to undergo an isotropic to nematic phase transition for a range of density and temperature. The distance dependence of the calculated angular pair correlation function correctly shows the emergence of a long range correlation as the INPT is approached along the density axis. In the vicinity of INPT, the single particle second rank orientational time correlation function exhibits power law decay, (t(-alpha)) with exponent alpha approximately 2/3. More importantly, we find the sudden appearance of a pronounced power-law decay in the collective part of the second rank orientational time correlation function at short times when the density is very close to the transition density. The power law has an exponent close to unity, that is, the correlation function decays almost linearly with time. At long times, the decay is exponential-like, as predicted by Landau-de Gennes mean field theory. Since Kerr relaxation experiments measure the time derivative of the collective second rank orientational pair correlation function, the simulations recover the near independence of the signal on time observed in experiments. In order to capture the microscopic essence of the dynamics of pseudonematic domains inside the isotropic phase, we introduce and calculate a dynamic orientational pair correlation function (DOPCF) obtained from the coefficients in the expansion of the distinct part of orientational van Hove time correlation function in terms of spherical harmonics. The DOPCF exhibits power law relaxation when the pair separation length is below certain critical length. The orientational relaxation of a local director, defined in terms of the sum of unit vectors of all the ellipsoidal molecules, is also found to show slow power law relaxation over a long time scale. These results have been interpreted in terms of a newly developed mode coupling theory of orientational dynamics near the INPT. In the present case, the difference between the single particle and the collective orientational relaxation is huge which can be explained by the frequency dependence of the memory kernel, calculated from the mode coupling theory. The relationship of this power law with the one observed in a supercooled liquid near its glass transition temperature is explored.

摘要

戈特克等人最近进行的克尔弛豫实验揭示,在纵横比相当小(κ约为3 - 4)的向列型液晶的各向同性 - 向列相转变(INPT)附近的取向弛豫过程中,存在明显的时间幂律衰减。我们对纵横比为3的模型(盖伊 - 伯恩)长椭球体进行了非常长时间(50纳秒)的分子动力学模拟,以研究这种幂律的起源。所选用的模型在一定密度和温度范围内会经历从各向同性到向列相的转变。计算得到的角关联函数的距离依赖性正确地显示出,当沿着密度轴接近INPT时,长程关联的出现。在INPT附近,单粒子二阶取向时间关联函数呈现幂律衰减,即(t^(-α)),指数α约为2/3。更重要的是,我们发现在密度非常接近转变密度时,二阶取向时间关联函数的集体部分在短时间内突然出现明显的幂律衰减。该幂律的指数接近1,即关联函数几乎随时间线性衰减。在长时间时,衰减呈指数形式,正如朗道 - 德热纳平均场理论所预测的那样。由于克尔弛豫实验测量的是集体二阶取向关联函数的时间导数,因此模拟结果重现了实验中观察到的信号对时间的近似独立性。为了捕捉各向同性相内伪向列域动力学的微观本质,我们引入并计算了一个动态取向关联函数(DOPCF),它是从取向范霍夫时间关联函数的不同部分在球谐函数展开中的系数得到的。当对分离长度低于某个临界长度时,DOPCF呈现幂律弛豫。根据所有椭球形分子单位向量之和定义的局部指向矢的取向弛豫,在长时间尺度上也显示出缓慢的幂律弛豫。这些结果已根据新发展的INPT附近取向动力学的模式耦合理论进行了解释。在当前情况下,单粒子和集体取向弛豫之间的差异巨大,这可以通过从模式耦合理论计算得到的记忆核的频率依赖性来解释。本文还探讨了这种幂律与在过冷液体接近其玻璃化转变温度时观察到的幂律之间的关系。

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