Statistical mechanics of homogeneous partly pinned fluid systems

The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture. In this paper, their configurational properties are investigated. It is shown that a peculiar complementarity exists between the mobile and immobile phases, which originates from the fact that the solid is prepared in presence of and in equilibrium with the adsorbed fluid. Simple identities follow, which connect different types of configurational averages, either relative to the fluid-matrix system or to the bulk fluid from which it is prepared. Crucial simplifications result for the computation of important structural quantities, both in computer simulations and in theoretical approaches. Finally, possible applications of the model in the field of dynamics in confinement or in strongly asymmetric mixtures are suggested.Comment: 12 pages, 2 figure

Comment on: "Static correlations functions and domain walls in glass-forming liquids: The case of a sandwich geometry" [J. Chem. Phys. 138, 12A509 (2013)]

In this Comment, we argue that the behavior of the overlap functions reported in the commented paper can be fully understood in terms of the physics of simple liquids in contact with disordered substrates, without appealing to any particular glassy phenomenology. This suggestion is further supported by an analytic study of the one-dimensional Ising model provided as Supplementary Material.Comment: 2+2 pages, 1+3 figure

Mode-coupling theory predictions for the dynamical transitions of the partly pinned fluid systems

The predictions of the mode-coupling theory (MCT) for the dynamical arrest scenarios in a partly pinned (PP) fluid system are reported. The corresponding dynamical phase diagram is found to be very similar to that of a related quenched-annealed (QA) system. The only significant qualitative difference lies in the shape of the diffusion-localization lines at high matrix densities, with a re-entry phenomenon for the PP system but not for the QA model, in full agreement with recent computer simulation results. This finding clearly lends support to the predictive power of the MCT for fluid-matrix systems. Finally, the predictions of the MCT are shown to be in stark contrast with those of the random first-order transition theory. The PP systems are thus confirmed as very promising models for tests of theories of the glass transition.Comment: 5 pages, 2 figure

Mode-coupling theory of the glass transition for confined fluids

We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the walls, which implies that the density profile and the density-density correlation function depends explicitly on the distances to the walls. We discuss the residual symmetry properties in slab geometry and introduce a symmetry adapted complete set of two-point correlation functions. Since the currents naturally split into components parallel and perpendicular to the walls the mathematical structure of the theory differs from the established mode-coupling equations in bulk. We prove that the equations for the nonergodicity parameters still display a covariance property similar to bulk liquids.Comment: 16 pages; to be published in PR

Multi-scale coarse-graining of diblock copolymer self-assembly: from monomers to ordered micelles

Starting from a microscopic lattice model, we investigate clustering, micellization and micelle ordering in semi-dilute solutions of AB diblock copolymers in a selective solvent. To bridge the gap in length scales, from monomers to ordered micellar structures, we implement a two-step coarse graining strategy, whereby the AB copolymers are mapped onto ``ultrasoft'' dumbells with monomer-averaged effective interactions between the centres of mass of the blocks. Monte Carlo simulations of this coarse-grained model yield clear-cut evidence for self-assembly into micelles with a mean aggregation number n of roughly 100 beyond a critical concentration. At a slightly higher concentration the micelles spontaneously undergo a disorder-order transition to a cubic phase. We determine the effective potential between these micelles from first principles.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Lett

Simple physics of the partly pinned fluid systems

In this paper, we consider some aspects of the physics of the partly pinned (PP) systems obtained by freezing in place particles in equilibrium bulk fluid configurations in the normal (nonglassy) state. We first discuss the configurational overlap and the disconnected density correlation functions, both in the homogeneous and heterogeneous cases, using the tools of the theory of adsorption in disordered porous solids. The relevant Ornstein-Zernike equations are derived, and asymptotic results valid in the regime where the perturbation due to the pinning process is small are obtained. Second, we consider the homogeneous PP lattice gas as a means to make contact between pinning processes in particle and spin systems and show that it can be straightforwardly mapped onto a random field Ising model with a strongly asymmetric bimodal distribution of the field. Possible implications of these results for studies of the glass transition based on PP systems are also discussed.Comment: 13 pages, 4 figures; v2 to appear in J. Chem. Phy

Dynamics of glassforming liquids in confinement

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Tagged-particle dynamics in a fluid adsorbed in a disordered porous solid: Interplay between the diffusion-localization and liquid-glass transitions

http://arxiv.org/abs/0901.3649International audienceA mode-coupling theory for the slow single-particle dynamics in fluids adsorbed in disordered porous media is derived, which complements previous work on the collective dynamics [V. Krakoviack, Phys. Rev. E 75, 031503 (2007)]. Its equations, such as the previous ones, reflect the interplay between confinement-induced relaxation phenomena and glassy dynamics through the presence of two contributions in the slow part of the memory kernel, which are linear and quadratic in the density correlation functions, respectively. From numerical solutions for two simple models with pure hard-core interactions, it is shown that two different scenarios result for the diffusion-localization transition depending on the strength of the confinement. For weak confinement, this transition is discontinuous and coincides with the ideal glass transition, such as in one-component bulk systems, while, for strong confinement, it is continuous and occurs before the collective dynamics gets nonergodic. In the latter case, the glass transition manifests itself as a secondary transition, which can be either continuous or discontinuous, in the already arrested single-particle dynamics. The main features of the anomalous dynamics found in the vicinity of all these transitions are reviewed and illustrated with detailed computations

Structure and dynamics of a fluid in a quenched disordered potential

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