分子任意取向体系中Weiss分子场理论的相变特征研究

Study on the Phase Transitions of Weiss' s Molecular Field Theory of Arbitrary Orientation Molecule Systems

Weiss分子场理论(Weiss’s molecular field theory,WMFT)对晶体中二级相变的定量描述是相当成功的.由于是平均场理论,可作为初步分析如液体等结构无序和复杂组分体系相变行为的理论依据,而结构无序等体系中分子更具有任意取向的特征.但是,迄今为止仍没有对分子任意取向体系中WMFT相变特征的研究.本文对该问题进行了研究,严格推导出了有外场E时该体系的自发极化P(T,E)s、内能u(T,E)、比热c(T,E)和静态极化率(T,E)s随温度T和外场E变化的表达式.结果表明,E=0时该体系中在一定温度c T发生了二级顺电-铁电相变;外电场的存在,使得体系的二级相变转化为弥散相变.另外,与分子仅有两个取向的体系相比,分子任意取向体系中P(T,E)s、u(T,E)、c(T,E)和(T,E)s的数学形式明显不同,相应的结果也有明显区别,具体为:分子任意取向体系的c T较低;P(T,0)s随c T/T减小的上升趋势较慢;c T以下的c(T,0)较大,特别是在较低温度出现一个弱依赖与E的"台阶"式下降;E对P(T,E)s的影响扩展到更低的温区,对相变温区c(T,E)峰的压低则更为明显.本文研究对完善WMFT以及该理论在结构无序等体系中的应用无疑是有益的.

The descriptions of Weiss＇s molecular field theory （WMFT） to the second order phase transitions （PTs） of crystals are quite successful. Because the WMFT is a mean-field theory, it is also a theoretical basis to initially analyze the PTs of structural disorder and complex compositional systems, such as liquids etc. in which the molecules usually have arbitrary orientation characters. However, there is not any study on the PTs of arbitrary orientation molecule systems according to the WMFT. In this paper, this question is studied, and specifically, the exact solutions of spontaneous polarization Ps（T,E）, internal energy u（Y,E）, specific heat c（T,E） and polarizability ^（T,E） of the systems vs temperature T and external electric field E are calculated. The results indicate that the systems have a second order PT at a definite temperature To for E-0, but the PT transforms to diffusive one for E ≠ 0. Moreover, compared with systems in which the molecules only have two orientation states, the mathematic forms of Ps（T,E）, u（T,E）, c（T,E） and ）χs（T,E） of arbitrary orientation molecule systems, as well as the corresponding results have clear differences. And specifically, the Tc shifts to much lower T; the increase tendency of Ps（T,0） with decreasing temperature is slower; c（T,0） below To is larger, and especially there appears step-like drop of c（T,E） at low T region that is weak dependent of E; the influence of E to Ps（T,E） is extended to lower temperatures, but the suppression to c（T,E） peak is more clear. The present researches would no doubt benefit to the consummation of WMFT and its applications to structural disorder systems.