Monte Carlo simulation of binary mixtures of hard colloidal cuboids

Abstract

We perform extensive Monte Carlo simulations to investigate the phase behaviour of colloidal suspensions of hard board-like particles (HBPs). While theories restricting particle orientation or ignoring higher ordered phases suggest the existence of a stable biaxial nematic phase, our recent simulation results on monodisperse systems indicate that this is not necessarily the case, even for particle shapes exactly in between prolate and oblate geometries, usually referred to as self-dual shape. Motivated by the potentially striking impact of incorporating biaxial ordering into display applications, we extend our investigation to bidisperse mixtures of short and long HBPs and analyse whether size dispersity can further enrich the phase behaviour of HBPs, eventually destabilise positionally ordered phases and thus favour the formation of the biaxial nematic phase. Not only do our results indicate that bidisperse mixtures of self-dual shaped HBPs cannot self-assemble into biaxial nematic phases, but they also show that these particles are not able to form uniaxial nematic phases either. This surprising behaviour is also observed in monodisperse systems. Additionally, bidisperse HBPs tend to phase separate in coexisting isotropic and smectic phases or, at relatively large pressures, in a smectic phase of mostly short HBPs and a smectic phase of mostly long HBPs. We conclude that limiting the particle orientational degrees of freedom or neglecting the presence of positionally ordered (smectic, columnar and crystal) phases can dramatically alter the phase behaviour of HBPs and unrealistically enlarge the region of stability of the biaxial nematic phase. Molecular Simulation paper˙V2colloidal particles with precise symmetry and directional interactions sparked the discovery of a collective behaviour, key for the synthesis of photonic crystals [2] and macroporous solids [3], that is not observed in atomic and molecular systems. Recognising this breakthrough has conferred to colloids a position in materials science in their own right [4]. Although current LC display technology is entirely based on molecular LCs, the appealing scenario of employing materials with high thermal stability, enhanced susceptibility to external fields and more accessible production costs, makes colloidal LCs excellent candidates for displays [5][6][7]. Additionally, and perhaps more interestingly, colloidal suspensions of board-like particles can form biaxial nematic (N B ) phases [8], whose existence, theoretically predicted by Freiser almost 50 years ago [9], is still an open question at the molecular scale. The intriguing prospect of manufacturing biaxial LCDs has been enfeebled by the difficulty of obtaining a stable molecular N B phase, especially at convenient temperatures for display applications. The experimental findings by Vroege and coworkers, who observed a remarkably stable N B phase in systems of polydisperse goethite particles, have provided renewed expectations and perhaps an indication on how, at the molecular scale, the stability...

Biaxial nematics of hard cuboids in an external field

“…To explain the origin of these experimental results, the same authors formulated a mean-field theory to calculate the phase diagram of HBPs in the presence of a magnetic field. Despite the good qualitative agreement between theory and experiments, the former neglects the effect of size polydispersity, being crucial to stabilise the N B phase [8], and is limited by the strong approximations imposed by the Zwanzig model, which was shown to be not especially accurate to describe the phase behavior of HBPs [2,5].In this work, we perform Monte Carlo (MC) simulations of freely-rotating monodisperse HBPs in the presence of an external field that promotes a phase transition from the isotropic (I) or uniaxial nematic (N U ) phase to the N B phase. Because our main interest is gaining an insight into the energetics associated to this process, the field strength is a simulation parameter that assumes values between * f ≡ f β = 0.1 and 3, with β the inverse temperature.…”

“…In the arXiv:1811.03677v1 [cond-mat.soft] 8 Nov 2018 following, we discuss the main aspects of the model and simulation methodology applied. The interested reader is referred to our previous works for additional details [2,5].…”

Engineering self-assembly

“…The contributions to this issue reflect, first of all, the diversity of self-assembly applications described above. For example, Patti and Cuetos [1] explore the phase behaviour of colloidal suspensions of cuboidal particles with potential relevance for liquid crystal displays, whereas Rozhkov et al [2] present a detailed study of magnetic colloids that can be used to develop new responsive soft materials. The interactions between nanoparticles and surfactant micelles, and their effect on the rheology of suspensions, is the focus of the paper by Sambasivam et al [3].…”

“…Here, with one exception [9], all papers apply some form of coarse-graining in their simulations. It is common to represent colloids [1,2] and nanoparticles [3,4] as single interaction sites instead of describing them in atomistic detail, whereas surfactants [5,8] and biomolecules [7] are usually modelled as a collection of beads, thus preserving some of their structure and flexibility. Although this reduction of the number of interaction sites may sometimes appear quite drastic, it is often a direct consequence of the need to sample large time and length scales in order to probe the self-assembly mechanism.…”

Self-assembly of freely-rotating polydisperse cuboids: unveiling the boundaries of the biaxial nematic phase

“…6 The stability of this N B phase was ascribed to the particles' quasi self-dual shape, a geometry in between oblate and prolate, and to their significant size dispersity, which hinders the formation of the Sm phase. This key work has reignited recent interest, sparking numerous theoretical, experimental and computer simulation studies on hard board-like particles (HBPs) [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] and other biaxial geometries. 24,[28][29][30][31][32] Theoretical and computational studies on monodisperse systems have suggested that self-dual-shaped particles exhibit a higher tendency to form biaxial nematics.…”