弹性Maier-Saupe-Zwanzig模型与弹性体的某些性质

nematic liquid crystals中铁电纳米粒子的Maier-Saupe型理论

Maier-Saupe-type theory of ferroelectric nanoparticles in nematic liquid crystals

几个实验已经报道了铁电纳米颗粒对双折射液晶具有显著的影响--将各向同性-双折射转变温度提高约5 K，并且极大地提高了对所施加的电场的灵敏度。在最近的一篇论文[L。M. Lopatina和J.V. Selinger，Phys. Rev. Lett. 102，197802（2009）]，我们基于液晶和纳米颗粒的耦合取向序参量通过Landau理论对这些效应进行建模。这个模型有一个重要的局限性：像所有的朗道理论一样，它涉及到自由能的序参量幂的展开，因此它高估了低温阶段出现的序参量。因此，我们现在开发一个新的Maier-Saupe型模型，它明确地显示了序参量的低温饱和。该模型在高温或弱耦合的极限下近似于朗道理论，但在相反的极限下表现出不同的行为。我们比较这些计算与实验结果的铁电纳米粒子在液晶。

Probability distribution function for reorientations in Maier-Saupe potential

Exact analytic solution for the probability distribution function of the non-inertial rotational diffusion equation, i.e., of the Smoluchowski one, in a symmetric Maier-Saupe uniaxial potential of mean torque is obtained via the confluent Heun's function. Both the ordinary Maier-Saupe potential and the double-well one with variable barrier width are considered. Thus, the present article substantially extends the scope of the potentials amenable to the treatment by reducing Smoluchowski equation to the confluent Heun's one. The solution is uniformly valid for any barrier height. We use it for t…

Maier-Saupe向列相理论在Tsalis热统计学中的推广

Generalization of the Maier-Saupe theory of the nematics within Tsa llis Thermostatistics

在这项研究中，平均场论在向列，Maier-Saupe理论（MST），推广内Tsallis热统计（TT）。研究了对偶氮苯甲醚（PAA）的序参量随温度的变化规律，并与实验数据进行了比较。到目前为止，我们认为这是TT在液晶中应用的第一次尝试。众所周知，MST不能解释某些向列相的实验数据，其中之一是PAA。然而，广义MST（GMST）是能够解释的实验数据的温度范围很长。此外，在这项研究中，nonextensivity的效果示出了各种值的熵指数。

液晶高分子Doi模型中矩方程的生成

Generating moment equations in the Doi model of liquid-crystalline polymers

我们提出了一个自洽的方法推导矩方程的动力学模型的聚合物动力学。Doi模型[M.作者声明：J.科学，Polym. Phys. Ed. 19，229（1981）]中描述的具有Onsager排除体积势的液晶聚合物作为一个例子。在最低阶，这种方法相当于一个简单的有效势不同于Maier-Saupe形式。分析结果表明，这种有效的潜力提供了一个更好的近似Onsager潜力比Maier-Saupe潜力。得到了有效势的修正。

Exact solution of Smoluchowski's equation for reorientational motion in Maier-Saupe potential

The analytic treatment of the non-inertial rotational diffusion equation, i.e., of the Smoluchowski's one (SE), in a symmetric genuinely double-well Maier-Saupe uniaxial potential of mean torque is considered. Such potential may find applications to reorientations of the fragments of structure in polymers and proteins. We obtain the exact solution of SE via the confluent Heun's function. The solution is uniformly valid for any barrier height. We apply the obtained solution to the calculation of the mean first passage time and the longitudinal correlation time and obtain their precise dependenc…

Theory of inhomogeneous rod-like Coulomb fluids

A field theoretic representation of the classical partition function is derived for a system composed of a mixture of anisotropic and isotropic mobile charges that interact {\sl via} long range Coulomb and short range nematic interactions. The field theory is then solved on a saddle-point approximation level, leading to a coupled system of Poisson-Boltzmann and Maier-Saupe equations. Explicit solutions are finally obtained for a rod-like counterion-only system in proximity of a charged planar wall, generalizing the standard Gouy-Chapman results. The nematic order parameter profile, the counter…

A Molecular Field Approach to Pressure Induced Phase Transitions in Liquid Crystals : Smectic-Nematic transition

Since a rigorous microscopic treatment of a nematic fluid system based on a pairwise interaction potential is immensely complex we had introduced a simple mean field potential which was a modification of the Maier-Saupe potential in a previous paper. Building up on that here we have modified that potential to take into account the various aspects of a smectic A-nematic phase transition. In particular we have studied the dependence of the phase transition on the coupling coefficient between the nematic and smectic order parameters which in turn depends on the length of alkyl chain, existence of…

Phase behavior of a lattice-gas model for biaxial nematics

We employ a lattice-gas extension of the Maier--Saupe model with discrete orientation states to study the phase behavior of a statistical model for biaxial nematogenic units in mean-field theory. The phase behavior of the system is investigated in terms of the strength of isotropic interaction between anisotropic objects, as well as the degree of biaxiality and the concentration of those units. We obtain phase diagrams with isotropic phases and stable biaxial and uniaxial nematic structures, various phase coexistences, many types of critical and multicritical behaviors, such as ordinary vapor-…

耦合非线性系统格点模型的高阶和全局phase diagram

Enhancement of nematic order and global phase diagram of a lattice model for coupled nematic systems

我们使用一个无限程Maier-Saupe模型，两套本地四极变量和限制方向，研究两个耦合子系统的全局相图。用统计力学的标准方法精确地计算了自由能和状态方程。系统A的向列相-各向同性转变温度随系统B的介晶间相互作用能和两子系统间耦合$J$的增大而增大。在相互作用参数和温度$T$方面的全局相图中表现出这种增强的α相。我们提出了一些意见，这些结果与实验结果的稀释铁电纳米粒子嵌入在一个液晶环境中的系统的连接。

Bethe格点上双组分分子混合物模型的Phase diagram

Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice

我们调查的Maier-Saupe模型的离散版本的相图，包括额外的自由度，以模仿棒状和盘状分子的分布。在Bethe格上这个问题的解来自于对一组非线性递归关系的不动点的分析。除了与各向同性和单轴双折射结构相关联的不动点之外，还存在与双轴双折射结构相关联的不动点。由于存在大的重叠的稳定区域，我们采取了一个计划来计算这些结构的自由能深处的一个大凯莱树的内部。热力学和动力学稳定性分析排除了双轴相的存在下，在定性协议与以前的平均场结果。

Mean-field limit and phase transitions for nematic liquid crystals in the continuum

We discuss thermotropic nematic liquid crystals in the mean-field regime. In the first part of this article, we rigorously carry out the mean-field limit of a system of $N$ rod-like particles as $N\to\infty$, which yields an effective `one-body' free energy functional. In the second part, we focus on spatially homogeneous systems, for which we study the associated Euler-Lagrange equation, with a focus on phase transitions for general axisymmetric potentials. We prove that the system is isotropic at high temperature, while anisotropic distributions appear through a transcritical bifurcation as …