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## Complex dynamics of fluids in disordered and crowded environments

#### Centre Blaise Pascal, ENS-Lyon, France

#### Organisers

Over the past two decades, the dynamics of fluids under nanoscale confinement has attracted much attention [1,2,3]. A great variety of molecular systems under different types of confinement, disordered in most cases, has been investigated using a broad spectrum of experimental techniques.At the same time, quite a few studies of simple model systems using molecular dynamics simulations were undertaken.

Motivation for the rapidly increasing interest in this topic is based on both practical and fundamental reasons. On the practical and rather applied side, the study of many problems in several scientific fields, such as polymer and colloidal sciences, rheology, geology, or biophysics, would undoubtedly benefit from a more profound understanding of the dynamical behaviour of confined fluids [4]. Furthermore, effects similar to those observed in confinement are expected in fluids whose constituents have strong size or mass asymmetry, hence widely different mobilities, and in biological systems where crowding and obstruction phenomena in the cytosol are responsible for clear separations of time scales for macromolecular transport in the cell [5].

In fundamental research, the main interest lies in the complex interplay between confinement and structural relaxation, which is responsible for the emergence of new phenomena in the dynamics of the system: in confinement, geometric constraints associated with the pore shape are imposed to the adsorbed fluids and new, additional characteristic length scales, like the pore size, come into play. Theory and simulations have predicted new and surprising dynamic features, such as the occurrence of subdiffusive laws, which result from the trapping due to the geometric and topological constraints and/or quenched disorder [6,7,8], the presence of both continuous and discontinuous glass transitions, diffusion-localization transitions, and a re-entrant glass transition scenario for particular system parameter combinations [9,10,11]. While there is evidence that confinement might be considered as a potential tool to investigate the concept of cooperativity in the glass transition phenomenon [12,13,14], we are still far from a deep and thorough understanding of these phenomena: effects predicted in theory and/or simulation have to be compared and assessed in a critical way, new and more detailed studies are required to obtain insight into the underlying processes.

The first, pioneering investigations of the dynamic properties of fluids confined in disordered matrices [15,16] were prohibitively expensive and thus had to be restricted to isolated state points. Meanwhile, the situation has considerably improved, mainly due to the remarkable increase in available computational power. Simulations based on ensembles of a few thousand particles and averaging over 10 to 20 different, but equivalent realizations of disordered confinement are nowadays realizable [17]. Being extended over several orders of magnitude in (intrinsic) time-units, the simulations offer the possibility to study the long-time behaviour of single and collective time correlation functions as well as of the mean-square displacement within high numerical accuracy; this makes, for instance, the identification of different types of dynamical slowing down possible. In addition, efficient visualisation techniques offer ideal tools to "observe" the motions of the particles along their trajectories in phase space.

From the conceptual point of view, a comprehensive description of the physical situation within a theoretical framework is very delicate and represents a formidable challenge to scientists: on one side, the framework should take into account the porosity and the randomness of the confinement; on the other side, it should provide reliable information on the complexity of the dynamic properties of the confined fluid, a task that already for the nonconfined fluid is highly non-trivial. Such a framework has been put forward by one of us [9,10,11], combining the replica Ornstein-Zernike (ROZ) approach for the so-called quenched-annealed (QA) systems with mode coupling theory (MCT). In the QA description, the disordered confinement is viewed as a quenched fluid which is then brought into contact with the annealed component, the fluid. The ROZ approach, pioneered by Madden and Glandt [18] and later by Given and Stell [19], provides information about the static correlators of the fluid confined in the disordered matrix. The static correlators, in turn, are required as an input by MCT [20], a highly intricate theory, which is generally accepted as one of the successful approaches to study slow dynamic properties of fluids, in particular of the glass transition.

As specified below, the QA model establishes, from the theoretical point of view, a link to closely related systems, which will also be addressed in this workshop. From the experimental point of view, a QA system could be realized in colloidal suspensions by fixing particles in appropriate positions with the help of optical tweezers or by designing appropriate matrix templates using soft lithography.

The QA model with its either quenched or arbitrarily pinned particle positions is closely related to the following models, which have attracted considerable interest in several theoretical studies:

* The classical random Lorentz gas is actually a QA mixture in the limit of a vanishing density of the annealed component. In fact, early theoretical work on the classical Lorentz gas [21,22,23] can be viewed as a precursor of the theoretical framework outlined above.

* QA systems can be viewed as limiting cases of systems with large dynamic disparity, induced, for instance, by a large mass- or size-disparity [24,25,26]. Similar features are also observed in star polymer mixtures [27]. Quite a few surprising effects have been identified in these investigations.

* Analogies exist between the dynamics in QA systems and that in exotic crystalline phases with highly mobile constituents, like binary colloidal crystals with large size asymmetry [28] or cluster crystals made of ultrasoft particles [29].

## References

**Austria**

Gerhard Kahl ( Institut für Theoretische Physik, TU Wien ) - Organiser

**France**

Daniele Coslovich ( Université de Montpellier ) - Organiser

Vincent Krakoviack ( Ecole normale supérieure de Lyon ) - Organiser