van Westen Thijs, Vlugt Thijs J H, Gross Joachim
Process and Energy Laboratory, Delft University of Technology, Leeghwaterstraat 44, 2628 CA Delft, The Netherlands.
Institut für Thermodynamik und Thermische Verfahrenstechnik, Universität Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany.
J Chem Phys. 2014 Jan 21;140(3):034504. doi: 10.1063/1.4860980.
An analytical equation of state (EoS) is derived to describe the isotropic (I) and nematic (N) phase of linear- and partially flexible tangent hard-sphere chain fluids and their mixtures. The EoS is based on an extension of Onsager's second virial theory that was developed in our previous work [T. van Westen, B. Oyarzún, T. J. H. Vlugt, and J. Gross, J. Chem. Phys. 139, 034505 (2013)]. Higher virial coefficients are calculated using a Vega-Lago rescaling procedure, which is hereby generalized to mixtures. The EoS is used to study (1) the effect of length bidispersity on the I-N and N-N phase behavior of binary linear tangent hard-sphere chain fluid mixtures, (2) the effect of partial molecular flexibility on the binary phase diagram, and (3) the solubility of hard-sphere solutes in I- and N tangent hard-sphere chain fluids. By changing the length bidispersity, two types of phase diagrams were found. The first type is characterized by an I-N region at low pressure and a N-N demixed region at higher pressure that starts from an I-N-N triphase equilibrium. The second type does not show the I-N-N equilibrium. Instead, the N-N region starts from a lower critical point at a pressure above the I-N region. The results for the I-N region are in excellent agreement with the results from molecular simulations. It is shown that the N-N demixing is driven both by orientational and configurational/excluded volume entropy. By making the chains partially flexible, it is shown that the driving force resulting from the configurational entropy is reduced (due to a less anisotropic pair-excluded volume), resulting in a shift of the N-N demixed region to higher pressure. Compared to linear chains, no topological differences in the phase diagram were found. We show that the solubility of hard-sphere solutes decreases across the I-N phase transition. Furthermore, it is shown that by using a liquid crystal mixture as the solvent, the solubility difference can by maximized by tuning the composition. Theoretical results for the Henry's law constant of the hard-sphere solute are in good agreement with the results from molecular simulation.
推导了一个解析状态方程（EoS），用于描述线性和部分柔性切向硬球链流体及其混合物的各向同性（I）相和向列（N）相。该EoS基于在我们之前的工作中发展的昂萨格第二维里理论的扩展 [T. van Westen, B. Oyarzún, T. J. H. Vlugt, and J. Gross, J. Chem. Phys. 139, 034505 (2013)]。使用Vega-Lago重标度程序计算更高阶的维里系数，在此将其推广到混合物。该EoS用于研究：（1）长度双分散性对二元线性切向硬球链流体混合物的I-N和N-N相行为的影响；（2）部分分子柔性对二元相图的影响；（3）硬球溶质在I相和N相切向硬球链流体中的溶解度。通过改变长度双分散性，发现了两种类型的相图。第一种类型的特征是在低压下有一个I-N区域，在较高压力下有一个从I-N-N三相平衡开始的N-N混合区域。第二种类型没有显示出I-N-N平衡。相反，N-N区域从I-N区域上方的一个较低临界点开始。I-N区域的结果与分子模拟结果非常吻合。结果表明，N-N混合是由取向熵和构型/排斥体积熵共同驱动的。通过使链部分柔性化，结果表明构型熵产生的驱动力减小（由于各向异性的对排斥体积减小），导致N-N混合区域向更高压力移动。与线性链相比，在相图中未发现拓扑差异。我们表明，硬球溶质的溶解度在I-N相变过程中降低。此外，结果表明，通过使用液晶混合物作为溶剂，可以通过调节组成使溶解度差异最大化。硬球溶质亨利定律常数的理论结果与分子模拟结果吻合良好。
