## Nonequilibrium diffusion at the liquid-liquid interface

By: Carlos Braga

From: Imperial College

At: Instituto de Investigação Interdisciplinar, B2-01

[2014-11-20]

(Note that exceptionally, this seminar will take place in room B2-01)

The liquid-liquid (LL) interface between two partially miscible liquids is an example of an inhomogeneous system which plays a fundamental role in understanding many surface phenomena occurring in physics, chemistry and biology [1, 2]. The presence of an interface renders its equilibrium statistical mechanical description necessarily position dependent. Configurational properties, e.g., density and energy, will be a function of the system coordinates and necessary care is needed to evaluate properties with tensorial character (pressure being the best known example) [3-5]. Vis-a-vis, dynamical properties will be affected, most notably the self-diffusion coefficient, where the movement of the particles, coupled with the thermal fluctuation of the interface, can make the evaluation of the transport properties in a given region of the LL system particularly challenging [6, 7].

Starting with the work of Evans et al. [8], a set of key statistical mechanical theorems have been derived [9-11] which provided important breakthroughs in our understanding of how irreversibility emerges at the microscopic scale from reversible dynamics. These theorems take into account distributions of work and dissipation along thermodynamically non equilibrium paths. For systems that are close to equilibrium, the Evans-Searles Fluctuation Theorem [9] can be used to derive Green-Kubo relations for linear transport coefficients [12] for a system in non equilibrium steady state. When valid, these expressions are consistent with those resulting from linear response theory and are valid in the linear regime.

We explore the use of the Evans-Searles Fluctuation Theorem to obtain the dynamical information on molecules at different points in the LL system and how their response properties are affected by the presence of one or more interfaces. This information will provide valuable insight into the understanding of dynamics of interphase mass transfer.

[1] J. S. Rowlinson and B. Widom, Molecular Theory of Capillarity, Dover books on chemistry, Dover Publications, 2002.

[2] I. Benjamin, Annual Review of Physical Chemistry 48, 407 (1997).

[3] P. P. J. Daivis, K. P. K. Travis, and B. D. B. Todd, The Journal of chemical physics 104, 9651 (1996).

[4] D. M. Heyes, E. R. Smith, D. Dini, and T. a. Zaki, The Journal of chemical physics 135, 024512 (2011).

[5] B. Todd, D. Evans, and P. Daivis, Physical Review E 52, 1627 (1995).

[6] M. Hayoun, M. Meyer, and P. Turq, The Journal of Physical Chemistry 98, 6626 (1994).

[7] D. Duque, P. Tarazona, and E. Chacon, The Journal of chemical physics 128, 134704 (2008).

[8] D. Evans, E. Cohen, and G. Morriss, Physical Review Letters 71, 2401 (1993).

[9] D. Evans and D. Searles, Physical Review E 52, 5839 (1995).

[10] G. Crooks, Physical Review E 61, 2361 (2000).

[11] D. Evans and D. Searles, Advances in Physics 51, 37 (2002).

[12] D. J. Searles and D. J. Evans, The Journal of Chemical Physics 112, 9727 (2000).

**Project**UIDB/00618/2020