Isotropic-Nematic Transition: Landau-de Gennes vs Molecular Theory
Isotropic-Nematic Transition: Landau-de Gennes vs Molecular Theory
复制标题
各向同性向列相转变：Landau-de Gennes 与分子理论
DOI：
10.1080/00268948208072135
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发表时间：
1982
影响因子：
0.7
通讯作者：
C. Woo
中科院分区：
文献类型：
--
作者：
L. Senbetu;C. Woo
摘要比较了Landau-de Gennes和分子平均场对各向同性向列相转变的描述。我们用两种方法计算了序参数关联函数，证明了朗道展开中三次项和四次项的修正是不可忽略的。在第一种方法中，我们应用最低阶图摄动理论，同时使用三次项和四次项作为摄动。第二种方法基本上将三次项处理为所有阶数，将四次项处理为前导阶数。将结果与实验进行比较，结果只显示了定性的一致性。研究还发现，过冷温度T*不同于关联长度发散的温度Tζ。由于修正的幅度不小，而且两种不同方法得到的结果也不一致，这一事实使人们对目前形式的朗道-德·根尼方法的定量有效性产生了严重的怀疑。我们提出了一种数值方法来建立平均值之间的联系。
Abstract Landau-de Gennes and molecular mean-field descriptions of the isotropic-nematic transition are compared. We use two methods to calculate the order parameter correlation function and show that corrections due to cubic and quartic terms in the Landau expansion are non-negligible. In the first method we apply lowest order diagrammatic perturbation theory using as perturbation both cubic and quartic terms. The second method essentially treats the cubic term to all orders and the quartic term to leading order. A comparison of the results with experiment indicates only qualitative agreement. It is also found that the supercooling temperature T* is different from Tζ, the temperature at which the correlation length diverges. The fact that the corrections are not small and that the results obtained by the two different methods are inconsistent cast grave doubt on the quantitative validity of the Landau-de Gennes approach in its present form. We propose a numerical way to establish contact between the mean...