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arXiv 1010.4680cond-mat.soft
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非均匀混合物的介观理论

Mesoscopic theory for inhomogeneous mixtures

A. Ciach

摘要:

从细观理论出发,通过系统的粗粒化过程,发展了以介观体积分数表示的球形颗粒非均匀混合物的介观密度泛函理论。在介观长度尺度上,得到了弱有序下的关联函数和巨势的近似表达式。无序相的稳定性分析进行平均场近似(MF)和超越。MF表明在体积分数温度相图上存在旋节线或$λ$ -表面。分离成均匀相或形成不均匀分布的颗粒分别发生在前者或后者表面的低温侧,这取决于相互作用势和不同物种的颗粒之间的尺寸比。超过MF的旋节面移动,和不稳定性的$λ$ -表面被抑制的波动。我们解释的$λ$ -表面之间的边界线均匀和不均匀(包含集群或其他聚集体)结构的无序相。对于两个组件系统的显式表达式的MF旋节线和$λ$ -表面推导。简单形式的相互作用势的例子进行了详细的分析,以确定导致不均匀结构的条件。

英文摘要:

Mesoscopic density functional theory for inhomogeneous mixtures of sperical particles is developed in terms of mesoscopic volume fractions by a systematic coarse-graining procedure starting form microscopic theory. Approximate expressions for the correlation functions and for the grand potential are obtained for weak ordering on mesoscopic length scales. Stability analysis of the disordered phase is performed in mean-field approximation (MF) and beyond. MF shows existence of either a spinodal or a $λ$-surface on the volume-fractions - temperature phase diagram. Separation into homogeneous phases or formation of inhomogeneous distribution of particles occurs on the low-temperature side of the former or the latter surface respectively, depending on both the interaction potentials and the size ratios between particles of different species. Beyond MF the spinodal surface is shifted, and the instability at the $λ$-surface is suppressed by fluctuations. We interpret the $λ$-surface as a borderline between homogeneous and inhomogeneous (containing clusters or other aggregates) structure of the disordered phase. For two-component systems explicit expressions for the MF spinodal and $λ$-surfaces are derived. Examples of interaction potentials of simple form are analyzed in some detail, in order to identify conditions leading to inhomogeneous structures.

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