Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911 Leganés, Madrid, Spain.
J Chem Phys. 2011 Mar 28;134(12):124904. doi: 10.1063/1.3570964.
We theoretically discuss, using density-functional theory, the phase stability of nematic and smectic ordering in a suspension of platelets of the same thickness but with a high polydispersity in diameter, and study the influence of polydispersity on this stability. The platelets are assumed to interact like hard objects, but additional soft attractive and repulsive interactions, meant to represent the effect of depletion interactions due to the addition of nonabsorbing polymer, or of screened Coulomb interactions between charged platelets in an aqueous solvent, respectively, are also considered. The aspect (diameter-to-thickness) ratio is taken to be very high, in order to model solutions of mineral platelets recently explored experimentally. In this regime a high degree of orientational ordering occurs; therefore, the model platelets can be taken as completely parallel and are amenable to analysis via a fundamental-measure theory. Our focus is on the nematic versus smectic phase interplay, since a high degree of polydispersity in diameter suppresses the formation of the columnar phase. When interactions are purely hard, the theory predicts a continuous nematic-to-smectic transition, regardless of the degree of diameter polydispersity. However, polydispersity enhances the stability of the smectic phase against the nematic phase. Predictions for the case where an additional soft interaction is added are obtained using mean-field perturbation theory. In the case of the one-component fluid, the transition remains continuous for repulsive forces, and the smectic phase becomes more stable as the range of the interaction is decreased. The opposite behavior with respect to the range is observed for attractive forces, and in fact the transition becomes of first order below a tricritical point. Also, for attractive interactions, nematic demixing appears, with an associated critical point. When platelet polydispersity is introduced the tricritical temperature shifts to very high values.
我们使用密度泛函理论从理论上讨论了相同厚度但直径高度分散的盘状颗粒悬浮液中向列相和近晶相有序的相稳定性，并研究了分散性对这种稳定性的影响。假设盘状颗粒相互作用类似于硬物体，但也考虑了附加的软吸引和排斥相互作用，分别代表由于添加非吸收性聚合物或在水溶剂中带电荷的盘状颗粒之间的屏蔽库仑相互作用而导致的耗尽相互作用的影响。取纵横比非常高，以便模拟最近实验探索的矿物盘状颗粒溶液。在该区域中会发生高度的取向有序，因此，模型盘状颗粒可以被视为完全平行的，并且可以通过基本测量理论进行分析。我们的重点是向列相与近晶相的相互作用，因为直径的高度分散性会抑制柱状相的形成。当相互作用纯粹是硬相互作用时，理论预测无论直径分散度如何，都会发生连续的向列相到近晶相转变。然而，分散性增强了近晶相相对于向列相的稳定性。使用平均场微扰理论获得了添加附加软相互作用的情况的预测。对于单组分流体，排斥力的转变仍然是连续的，随着相互作用范围的减小，近晶相变得更加稳定。对于吸引力，观察到相反的行为，实际上，在三临界点以下，转变变为一级。此外，对于吸引力相互作用，会出现向列相的混合，并有相关的临界点。当引入盘状颗粒的分散性时，三临界点会转移到非常高的值。
