1. Mesoscopic nonequilibrium thermoydnamics Application to interfacial phenomena Dynamics of Complex Fluid-Fluid Interfaces Leiden, 2011 Miguel Rubi

2. Interfaces The interface is a thermodynamic system; excess properties; Local equilibrium holds. Transport and activated processes take place The state of the surface can be described by means of an internal coordinate boundfree shear

4. stickslip shear Activation Examples: Chemical reactions, adsorption, evaporation, condensation, thermionic emmision, fuel cells…. Activation: to proceed the system has to surmount a potential barrier; nonlinear NET: provides linear relationships between fluxes and forces

6. Nonequilibrium thermodynamics Global description of nonequilibrium processes (k  0; ω  0) Shorter scales: memory kernels (Ex. generalyzed hydrodynamics, non-Markovian) Description in terms of average values; absence of fluctuations Fluctuations can be incorporated through random fluxes (fluctuating hydrodynamics) Linear domain of fluxes and thermodynamic forces

7. Chemical reactions Law of mass action Conclusion: NET only accounts for the linear regime. linearization

8. Unstable substance Final product Naked-eye: Sudden jump Progressive molecular changes Activation Diffusion Watching closely

9. Translocation of ions (through a protein channel) short time scale: local equilibrium along the coordinate biological pumps, chemical and biochemical reactions Arrhenius, Butler-Volmer, Law of mass action Local, linear  Global, non-linear Biological membrane

10. Protein folding Intermediate configurations, same as for chemical reactions

11. Molecular motors Energy transduction, Molecular motors

12. Activated process viewed as a diffusion process along a reaction coordinate From local to global:

13. What can we learn from kinetic theory? J. Ross, P. Mazur, JCP (1961) Boltzmann equation LMA Chapman-Enskog

14. Probability conservation: Entropy production: Fokker-Planck Thermodynamics and stochasticity J.M. Vilar, J.M. Rubi, PNAS (2001)

15. Molecular changes: diffusion through a mesoscopic coordinate Second law D. Reguera, J.M. Rubi and J.M. Vilar, J. Phys. Chem. B (2005); Feature Article

16. Meso-scale entropy production

17. Relaxation equations hydrodynamic Fick Maxwell-Cattaneo Burnett J.M. Rubi, A. Perez, Physica A 264 (1999) 492

18. References A. Perez, J.M. Rubi, P. Mazur, Physica A (1994) J.M. Vilar and J.M. Rubi, PNAS (2001) D. Reguera, J.M. Rubi and J.M. Vilar, J. Phys. Chem. B (2005); Feature Article J.M. Rubi, Scientific American, November, 40 (2008)

19. Adsorption Physisorbed Chemisorbed  ( ) 1 2 10 2

20. MNET of adsorption

21. Langmuir equation I. Pagonabarraga, J.M. Rubi, Physica A, 188, 553 (1992)

22. Evaporation and condensation D. Bedeaux, S. Kjelstrup, J.M. Rubi, J. Chem. Phys., 119, 9163 (2003)

23. Condensation coefficient

24. stickslip shear Stick-slip transition C. Cheikh, G. Koper, PRL, 2003

25. Conclusions MNET offers a unified and systematic scheme to analyze dissipative interfacial phenomena. The different states of the surface are characterized by a reaction coordinate. Chemical reactions, adsorption, evaporation, condensation, thermionic emmision, fuel cells….