Depletion effects in smectic phases of hard-rod-hard-sphere mixtures
Depletion effects in smectic phases of hard-rod-hard-sphere mixtures
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DOI：
10.1140/epje/i2006-10058-4
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发表时间：
2006-10-01
影响因子：
1.8
通讯作者：
Mederos, L.
中科院分区：
文献类型：
--
作者：
Martinez-Raton, Y.;Cinacchi, G.;Mederos, L.
众所周知，在纯硬棒体系中加入硬球，可大大提高近晶相的稳定性，这种效应可以用耗竭力来解释。在本文中，我们首先研究了在这种特殊的双星系统中，取向顺序对耗尽力的影响，并将我们的结果与采用考虑杆平行且取向冻结的通常近似得到的结果进行了比较。我们考虑不同长径比的棒材和不同直径的球体的混合物，我们用Onsager理论来处理它们。我们的研究结果表明，与基于冻结取向近似的相应数据相比，由于近晶相的取向紊乱，耗竭效应和近晶稳定性显著降低。这些结果讨论了tau参数，这已被提出作为一个方便的测量损耗强度。我们提出了tau的封闭表达式，并表明它与耗竭势密切相关。然后，我们通过比较不同形状的平行棒系统（球柱体、圆柱体和平行六面体）的结果来分析粒子几何的影响。最后，我们给出了基于兹万齐格近似的基测度密度泛函理论在不同尺寸的平行六面体和立方体混合物中的应用结果。在这种情况下，我们证明了tau参数在硬杆长径比大值的极限下表现出线性渐近的行为，符合Onsager理论，以及在杆宽与立方体边长之比d大值的极限下表现出线性渐近的行为，这与Onsager近似相反，后者预测的tau与d(3)相似。基于这一结果和硬球二元混合物在相同无限不对称极限下的直接相关函数的percusi - yevick近似，我们推测，对于球柱体和球，当d趋于无穷时，τ参数应该是一个阶单位。
It is known that when hard spheres are added to a pure system of hard rods the stability of the smectic phase may be greatly enhanced, and that this effect can be rationalised in terms of depletion forces. In the present paper we first study the effect of orientational order on depletion forces in this particular binary system, comparing our results with those obtained adopting the usual approximation of considering the rods parallel and their orientations frozen. We consider mixtures with rods of different aspect ratios and spheres of different diameters, and we treat them within Onsager theory. Our results indicate that depletion effects, and consequently smectic stability, decrease significantly as a result of orientational disorder in the smectic phase when compared with corresponding data based on the frozen-orientation approximation. These results are discussed in terms of the tau parameter, which has been proposed as a convenient measure of depletion strength. We present closed expressions for tau, and show that it is intimately connected with the depletion potential. We then analyse the effect of particle geometry by comparing results pertaining to systems of parallel rods of different shapes (spherocylinders, cylinders and parallelepipeds). We finally provide results based on the Zwanzig approximation of a fundamental-measure density-functional theory applied to mixtures of parallelepipeds and cubes of different sizes. In this case, we show that the tau parameter exhibits a linear asymptotic behaviour in the limit of large values of the hard-rod aspect ratio, in conformity with Onsager theory, as well as in the limit of large values of the ratio of rod breadth to cube side length, d, in contrast to Onsager approximation, which predicts tau similar to d(3). Based on both this result and the Percus-Yevick approximation for the direct correlation function for a hard-sphere binary mixture in the same limit of infinite asymmetry, we speculate that, for spherocylinders and spheres, the tau parameter should be of order unity as d tends to infinity.