Phase transitions in systems of hard rectangles with non-integer aspect ratio

We investigate, using Monte Carlo simulations, the phase diagram of a system of hard rectangles of size $m\times mk$ on a square lattice when the aspect ratio $k$ is a non-integer. The existence of a disordered isotropic phase, a nematic with only orientational order, a columnar phase with orientational and partial translational order, and a high density phase with no orientational order is shown. The high density phase is a solid-like sublattice phase only if the length and width of the rectangles are not mutually prime, else, it is an isotropic phase. The minimum value of $k$ beyond which the nematic and columnar phases exist are determined for $m=2$ and $3$. The nature of the transitions between different phases is determined, and the critical exponents are numerically obtained for the continuous transitions.Comment: 6 pages, 6 figure

Bypassing sluggishness: SWAP algorithm and glassiness in high dimensions

The recent implementation of a swap Monte Carlo algorithm (SWAP) for polydisperse mixtures fully bypasses computational sluggishness and closes the gap between experimental and simulation timescales in physical dimensions $d=2$ and $3$. Here, we consider suitably optimized systems in $d=2, 3,\dots, 8$, to obtain insights into the performance and underlying physics of SWAP. We show that the speedup obtained decays rapidly with increasing the dimension. SWAP nonetheless delays systematically the onset of the activated dynamics by an amount that remains finite in the limit $d \to \infty$. This shows that the glassy dynamics in high dimensions $d>3$ is now computationally accessible using SWAP, thus opening the door for the systematic consideration of finite-dimensional deviations from the mean-field description

Phase diagram of a bidispersed hard rod lattice gas in two dimensions

We obtain, using extensive Monte Carlo simulations, virial expansion and a high-density perturbation expansion about the fully packed monodispersed phase, the phase diagram of a system of bidispersed hard rods on a square lattice. We show numerically that when the length of the longer rods is $7$, two continuous transitions may exist as the density of the longer rods in increased, keeping the density of shorter rods fixed: first from a low-density isotropic phase to a nematic phase, and second from the nematic to a high-density isotropic phase. The difference between the critical densities of the two transitions decreases to zero at a critical density of the shorter rods such that the fully packed phase is disordered for any composition. When both the rod lengths are larger than $6$, we observe the existence of two transitions along the fully packed line as the composition is varied. Low-density virial expansion, truncated at second virial coefficient, reproduces features of the first transition. By developing a high-density perturbation expansion, we show that when one of the rods is long enough, there will be at least two isotropic-nematic transitions along the fully packed line as the composition is varied.Comment: 7 pages, 4 figure

Selective gas capture via kinetic trapping

Conventional approaches to the capture of CO_2 by metal-organic frameworks focus on equilibrium conditions, and frameworks that contain little CO_2 in equilibrium are often rejected as carbon-capture materials. Here we use a statistical mechanical model, parameterized by quantum mechanical data, to suggest that metal-organic frameworks can be used to separate CO_2 from a typical flue gas mixture when used under {\em nonequilibrium} conditions. The origin of this selectivity is an emergent gas-separation mechanism that results from the acquisition by different gas types of different mobilities within a crowded framework. The resulting distribution of gas types within the framework is in general spatially and dynamically heterogeneous. Our results suggest that relaxing the requirement of equilibrium can substantially increase the parameter space of conditions and materials for which selective gas capture can be effected.Comment: 12 pages, 10 figure

Cooperative gas adsorption without a phase transition in metal-organic frameworks

Cooperative adsorption of gases by porous frameworks permits more efficient uptake and removal than does the more usual non-cooperative (Langmuir-type) adsorption. Cooperativity, signaled by a step-like isotherm, is usually attributed to a phase transition of the framework. However, the class of metal-organic frameworks mmen-M$_2$(dobpdc) exhibit cooperative adsorption of CO2 but show no evidence of a phase transition. Here we show how cooperativity emerges in these frameworks in the absence of a phase transition. We use a combination of quantum and statistical mechanics to show that cooperativity results from a sharp but finite increase, with pressure, of the mean length of chains of CO2 molecules that polymerize within the framework. Our study provides microscopic understanding of the emergent features of cooperative binding, including the position, slope and height of the isotherm step, and indicates how to optimize gas storage and separation in these materials.Comment: 18 pages, 11 figure

Hysteresis curves reveal the microscopic origin of cooperative CO2_2 adsorption in diamine-appended metal{organic frameworks

Diamine-appended metal{organic frameworks (MOFs) of the form Mg2(dobpdc)(diamine)2 adsorb CO2 in a cooperative fashion, exhibiting an abrupt change in CO2 occupancy with pressure or temperature. This change is accompanied by hysteresis. While hysteresis is suggestive of a firstorder phase transition, we show that hysteretic temperature-occupancy curves associated with this material are qualitatively unlike the curves seen in the presence of a phase transition; they are instead consistent with CO2 chain polymerization, within one-dimensional channels in the MOF, in the absence of a phase transition. Our simulations of a microscopic model reproduce this dynamics, and point the way toward rational control, in and out of equilibrium, of cooperative adsorption in this industrially important class of materials