Mesoscopic nonequilibrium thermoydnamics
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Transcript of Mesoscopic nonequilibrium thermoydnamics
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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
bound free
shear
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000
fff
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0F 0F
stick slip
shear
Activation
Examples:
Chemical reactions, adsorption, evaporation, condensation, thermionic emmision, fuel cells….
Activation: to proceed the system has to surmount a potential barrier; nonlinearNET: provides linear relationships between fluxes and forces
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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
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Chemical reactions1 JAT
2 1( )L LJ AT T
Law of mass action
2 1
(1 )A
kT kT kT LJ D e e D e AT
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
DiffusionWatching closely
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Translocation of ions (through a protein channel)
short time scale: local equilibrium alongthe 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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( ) kT kT kT kTL kLJ e e De eT P
2 2
1 1kT kTd Je D d e
2 1
2 1( )kT kTJ D e e D z z
Activated process
viewed as a diffusion process along a reaction coordinate
From local to global: ...d
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What can we learn from kinetic theory?
J. Ross, P. Mazur, JCP (1961)
A B C D A
AS AS
f E Rt
(0) (1) 2 (2)1 ..A A A Af f
Boltzmann equation
LMA 1 JAT
Chapman-Enskog
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Probability conservation:
x vJ JPt x v
Entropy production:
0x vJ Jx v
2
P v DvP Pt x v v
Fokker-Planck
Thermodynamics and stochasticity
J.M. Vilar, J.M. Rubi, PNAS (2001)
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Molecular changes: diffusion through a mesoscopic coordinate
:( , ) :mesoscopic coordinate
P t probability
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
v Pudu
hydrodynamic
dv P vdt
1 1P p kT
1)i t Fick
1)ii t Maxwell-Cattaneo
1 dJJ Ddt
2( )D k kt
1 2( ) (1 )D k D D k
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
1 0 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 condensationD. Bedeaux, S. Kjelstrup, J.M. Rubi, J. Chem. Phys., 119, 9163 (2003)
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Condensation coefficient
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0F 0F
stick slip
shear
Stick-slip transition
0
0
( )
ln
ln
f bkT kT
f f
b b
J l e e
kT c
kT c
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….