mesoscopic nonequilibrium thermoydnamics
DESCRIPTION
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 . - PowerPoint PPT PresentationTRANSCRIPT
Mesoscopic nonequilibrium thermoydnamics
Application to interfacial phenomena
Dynamics of Complex Fluid-Fluid Interfaces Leiden, 2011
Miguel Rubi
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
000
fff
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
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 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
Unstable substance
Final product
Naked-eye: Sudden jump
Progressive molecular changes
Activation
DiffusionWatching closely
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
Protein folding
Intermediate configurations, same as for chemical reactions
Molecular motors
Energy transduction,Molecular motors
( ) 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
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
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)
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
Meso-scale entropy production
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
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
Physisorbed Chemisorbed
( ) 1 2
1 0 2
MNET of adsorption
Langmuir equation
I. Pagonabarraga, J.M. Rubi, Physica A, 188, 553 (1992)
Evaporation and condensationD. Bedeaux, S. Kjelstrup, J.M. Rubi, J. Chem. Phys., 119, 9163 (2003)
Condensation coefficient
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
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….