Mesoscopic nonequilibrium thermoydnamics Application to interfacial phenomena Miguel Rubi Dynamics of Complex Fluid-Fluid Interfaces Leiden, 2011 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 shear bound free f 0 f 0 f 0 Activation shear F 0 stick F 0 Examples: Chemical reactions, adsorption, evaporation, condensation, thermionic emmision, fuel cells…. slip Activation: to proceed the system has to surmount a potential barrier; nonlinear NET: provides linear relationships between fluxes and forces Nonequilibrium thermodynamics • Global description of nonequilibrium processes (k0; ω0) 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 Chemical reactions 1 JA T L L J A ( 2 1 ) T T Law of mass action linearization 2 1 A kT L kT kT J D e e D(1 e ) A T Conclusion: NET only accounts for the linear regime. Activation Unstable substance Final product Naked-eye: Sudden jump Watching closely Progressive molecular changes Diffusion Translocation of ions (through a protein channel) Biological membrane short time scale: local equilibrium along the coordinate biological pumps, chemical and biochemical reactions Local, linear Global, non-linear Arrhenius, Butler-Volmer, Law of mass action Protein folding Intermediate configurations, same as for chemical reactions Molecular motors Energy transduction, Molecular motors Activated process viewed as a diffusion process along a reaction coordinate L kL kT kT ( ) J e e De kT e kT T P From local to global: 2 1 d Je kT kT D d e 1 2 d ... 2 1 kT J D e e kT D( z2 z1 ) What can we learn from kinetic theory? Boltzmann equation f A E AS RA t S A B CD Chapman-Enskog 2 (2) f A f A(0) 1 (1) A .. A LMA J. Ross, P. Mazur, JCP (1961) 1 JA T Thermodynamics and stochasticity J.M. Vilar, J.M. Rubi, PNAS (2001) Probability conservation: J x J v P t x v Entropy production: Jx Jv 0 x v Fokker-Planck P v D vP 2 P t x v v Molecular changes: diffusion through a mesoscopic coordinate :mesoscopiccoordinate P( , t ) : probability Second law D. Reguera, J.M. Rubi and J.M. Vilar, J. Phys. Chem. B (2005); Feature Article Meso-scale entropy production Relaxation equations J.M. Rubi, A. Perez, Physica A 264 (1999) 492 v Pudu hydrodynamic i) t 1 ii) t 1 P p1 kT 1 dv P v dt Fick Maxwell-Cattaneo J D 1 dJ dt D(k )k 2 t D(k ) D(1 D 1k 2 ) Burnett 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) Adsorption ( ) 1 1 Physisorbed 2 0 2 Chemisorbed MNET of adsorption Langmuir equation I. Pagonabarraga, J.M. Rubi, Physica A, 188, 553 (1992) Evaporation and condensation D. Bedeaux, S. Kjelstrup, J.M. Rubi, J. Chem. Phys., 119, 9163 (2003) Condensation coefficient Stick-slip transition shear F 0 stick F 0 f b J l ( e kT e kT ) slip f kT ln c f 0 b kT ln cb 0 C. Cheikh, G. Koper, PRL, 2003 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….