Dennison Matthew, Masters Andrew J
School of Chemical Engineering and Analytical Science, University of Manchester, Oxford Road, Manchester M13 9PL, UK.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Aug;84(2 Pt 1):021709. doi: 10.1103/PhysRevE.84.021709. Epub 2011 Aug 25.
We present a method for calculating high-order virial expansions of the isotropic-nematic phase transition which we apply here to hard spheroids. Studying a range of aspect ratios, for both oblate and prolate particles, we obtain equations of state, coexistence densities, and nematic order parameters, using expansions truncated at up to eighth virial level. For particles of large aspect ratios our results show rapid convergence, with truncation at sixth order sufficient to give excellent agreement with simulation data. For more spherical particles the convergence is less rapid, with results for up to eighth-order theory approaching but still not reaching simulation data. Our results indicate that high-order viral expansions are better suited to predicting equations of state than coexistence densities. We also test the validity of using the Onsager trial function to approximate the orientational distribution function, finding only small errors when making this approximation.
我们提出了一种计算各向同性-向列相转变高阶维里展开式的方法，在此将其应用于硬椭球体。通过研究一系列扁长和长扁比的粒子，我们获得了状态方程、共存密度和向列序参量，使用的展开式最高截断到第八维里水平。对于大长径比的粒子，我们的结果显示收敛迅速，截断到六阶就足以与模拟数据取得极好的一致性。对于更接近球形的粒子，收敛速度较慢，八阶理论的结果接近但仍未达到模拟数据。我们的结果表明，高阶维里展开式比共存密度更适合预测状态方程。我们还测试了使用昂萨格试函数近似取向分布函数的有效性，发现进行这种近似时只有很小的误差。
