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Register a new userGraphoepitaxy for translational and orientational ordering of monolayers of rectangular nanoparticles
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The combinations of particle aspect ratio and enthalpic-barrier templates that lead to translational and orientational ordering of monolayers of rectangular particles are determined using Monte Carlo simulations and density functional theory. For sufficiently high enthalpic barriers, we find that only specific combinations of particle sizes and template spacings lead to ordered arrays. The pattern multiplication factor provided by the template extends to approximately ten times the smallest dimension of the particle.
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Using scaled-particle theory for binary mixtures of two-dimensional hard particles with rotational freedom, we analyse the stability of nematic phases and the demixing phase behaviour of a variety of mixtures, focussing on cases where at least one of the components consists of hard rectangles or hard squares. A pure fluid of hard rectangles may exhibit, aside from the usual uniaxial nematic phase, an additional (tetratic) oriented phase, possessing two directors, which is the analogue of the biaxial or cubatic phases in three- dimensional fluids. There is computer simulation evidence that the tetratic phase might be stable with respect to phases with spatial order for rectangles with low aspect ratios. As hard rectangles are mixed with other particles not possessing stable tetratic order by themselves, the tetratic phase is destabilised, via a first- or second-order phase transition, to uniaxial nematic or isotropic phases; for hard rectangles of low aspect ratio tetratic order persists in a relatively large range of volume fractions. The order of these transitions depends on the particle geometry, dimensions and thermodynamic conditions of the mixture. The second component of the mixture has been chosen to be hard discs or disco-rectangles, the geometry of which is different from that of rectangles, leading to packing frustration and demixing behaviour, or simply rectangles of different aspect ratio. These mixtures may be good candidates for observing thermodynamically stable tetratic phases in monolayers of hard particles. Finally, demixing between fluid (isotropic--tetratic or tetratic--tetratic) phases is seen to occur in mixtures of hard squares of different sizes when the size ratio is sufficiently large.
We compute the free energy minimizing structures of particle monolayers in the presence of enthalpic barriers of a finite height b{eta}Vext using classical density functional theory and Monte Carlo simulations. We show that a periodic square template with dimensions up to at least ten times the particle diameter disrupts the formation of the entropically favored hexagonally close-packed 2D lattice in favor of a square lattice. The results illustrate how graphoepitaxy can successfully order nanoparticulate films into desired patterns many times smaller than those of the prepatterned template.
The concept of symmetry breaking has been a propelling force in understanding phases of matter. While rotational symmetry breaking is one of the most prevalent examples, the rich landscape of orientational orders breaking the rotational symmetries of isotropic space, i.e. $O(3)$, to a three-dimensional point group remain largely unexplored, apart from simple examples such as ferromagnetic or uniaxial nematic ordering. Here we provide an explicit construction, utilizing a recently introduced gauge theoretical framework, to address the three-dimensional point-group-symmetric orientational orders on a general footing. This unified approach allows us to enlist order parameter tensors for all three dimensional point groups. By construction, these tensor order parameters are the minimal set of simplest tensors allowed by the symmetries that uniquely characterize the orientational order. We explicitly give these for the point groups ${C_n, D_n, T, O, I} subset SO(3)$ and ${C_{nv}, S_n, C_{nh}, D_{nh}, D_{nd}, T_h, T_d, O_h, I_h}subset O(3)$ for $n={1,2,3,4,6, infty}$. This central result may be perceived as a roadmap for identifying exotic orientational orders that may become more and more in reach in view of rapid experimental progress in e.g. nano-colloidal systems and novel magnets.
Dense assemblies of self propelled particles, also known as active or living glasses are abundantaround us, covering different length and time scales: from the cytoplasm to tissues, from bacterialbio-films to vehicular traffic jams, from Janus colloids to animal herds. Being structurally disorderedas well as strongly out of equilibrium, these systems show fascinating dynamical and mechanicalproperties. Using extensive molecular dynamics simulation and a number of different dynamicaland mechanical order parameters we differentiate three dynamical steady states in a sheared modelactive glassy system: (a) a disordered phase, (b) a propulsion-induced ordered phase, and (c) ashear-induced ordered phase. We supplement these observations with an analytical theory based onan effective single particle Fokker-Planck description to rationalise the existence of the novel shear-induced orientational ordering behaviour in our model active glassy system that has no explicitaligning interactions,e.g.of Vicsek-type. This ordering phenomenon occurs in the large persistencetime limit and is made possible only by the applied steady shear. Using a Fokker-Planck descriptionwe make testable predictions without any fit parameters for the joint distribution of single particleposition and orientation. These predictions match well with the joint distribution measured fromdirect numerical simulation. Our results are of relevance for experiments exploring the rheologicalresponse of dense active colloids and jammed active granular matter systems.
We report on atomistic simulations of DPPC lipid monolayers using the CHARMM36 lipid force field and four-point OPC water model. The entire two-phase region where domains of the `liquid-condensed (LC) phase coexist with domains of the `liquid-expanded (LE) phase has been explored. The simulations are long enough that the complete phase-transition stage, with two domains coexisting in the monolayer, is reached in all cases. Also, system sizes used are larger than in previous works. As expected, domains of the minority phase are elongated, emphasizing the importance of anisotropic van der Waals and/or electrostatic dipolar interactions in the monolayer plane. The molecular structure is quantified in terms of distribution functions for the hydrocarbon chains and the PN dipoles. In contrast to previous work, where average distributions are calculated, distributions are here extracted for each of the coexisting phases by first identifying lipid molecules that belong to either LC or LE regions. The three-dimensional distributions show that the average tilt angle of the chains with respect to the normal outward direction is $(39.0pm 0.1)^{circ}$ in the LC phase. % and $(48.1pm 0.5)^{circ}$ in the LC phase. In the case of the PN dipoles the distributions indicate a tilt angle of $(110.8pm 0.5)^{circ}$ in the LC phase and $(112.5pm 0.5)^{circ}$ in the LE phase. These results are quantitatively different from previous works, which indicated a smaller normal component of the PN dipole. Also, the distributions of the monolayer-projected chains and PN dipoles have been calculated. Chain distributions peak along a particular direction in the LC domains, while they are uniform in the LE phase. Long-range ordering associated with the projected PN dipoles is absent in both phases.
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