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Mesoscopic nonequilibrium thermoydnamics Application to interfacial phenomena Dynamics of Complex Fluid-Fluid Interfaces Leiden, 2011 Miguel Rubi
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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
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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
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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
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Chemical reactions Law of mass action Conclusion: NET only accounts for the linear regime. linearization
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Unstable substance Final product Naked-eye: Sudden jump Progressive molecular changes Activation Diffusion Watching closely
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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
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Protein folding Intermediate configurations, same as for chemical reactions
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Molecular motors Energy transduction, Molecular motors
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Activated process viewed as a diffusion process along a reaction coordinate From local to global:
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What can we learn from kinetic theory? J. Ross, P. Mazur, JCP (1961) Boltzmann equation LMA Chapman-Enskog
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Probability conservation: Entropy production: Fokker-Planck Thermodynamics and stochasticity J.M. Vilar, J.M. Rubi, PNAS (2001)
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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
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Meso-scale entropy production
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Relaxation equations hydrodynamic Fick Maxwell-Cattaneo Burnett J.M. Rubi, A. Perez, Physica A 264 (1999) 492
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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)
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Adsorption Physisorbed Chemisorbed ( ) 1 2 10 2
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MNET of adsorption
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Langmuir equation I. Pagonabarraga, J.M. Rubi, Physica A, 188, 553 (1992)
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Evaporation and condensation D. Bedeaux, S. Kjelstrup, J.M. Rubi, J. Chem. Phys., 119, 9163 (2003)
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Condensation coefficient
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stickslip shear Stick-slip transition C. Cheikh, G. Koper, PRL, 2003
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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….
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