SURFACE TENSION 2 SPS Lectures January 2006

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SURFACE TENSION 2SPS Lectures January 2006

• Wayne Lawton
• Department of Mathematics National University of
  Singapore
• http//math.nus.edu.sg/matwml
• matwml_at_nus.edu.sg

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ABSTRACT
We explain molecular cause of surface tension
using thermodynamic concepts that explain the
role of both energy and entropy cutting edge
concepts in biochemistry and life sciences.
The Journal of Chemical Physics -- September 1,
2000 -- Volume 113, Issue 9, pp. 3882-3893
Spatial and energetic-entropic decomposition of
surface tension in lipid bilayers from molecular
dynamics simulations Erik Lindahl and Olle Edholm
Theoretical Physics, Royal Institute of
Technology, SE-100 44 Stockholm, Sweden
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ENTROPY
Thermodynamics
1st Law
2st Law
Statistical Mechanics
Boltzmanns tombstone
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EQUIPARTITION
Entropy of a System With Two Subsystems
EP Theorem Microstates have equal probability
Corollary Two subsystems in thermal equilibrium
with constant total energy will
maximize
therefore
Hence 2nd Law ?
EP Theorem (Boltzmann) Each translational or
rotational component of the random thermal motion
of a molecule has an average kinetic energy
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A HELMHOLTZ FREE ENERGY
We consider a constant volume system whose
entropy S S(E) that is in thermal equilibrium
with an infinite reservoir that has temperature T
Theorem Energy will flow into / out of the system
so as to minimize A(E) E TS(E)
Proof At thermal equilibrium the total entropy is
is maximized ?
therefore
for every value of
Remark
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We consider a system consisting of molecules that
can be in states 1 or 2 having respective energies
ENDOTHERMIC REACTIONS
Theorem The fraction p of molecules
in state 1 satisfies
Proof For a system of N molecules the binomial
theorem and Stirling approx ?
and the result follows since
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Enthalpy
SURFACE TENSION THERMODYNAMICS
2nd Lawsurf. ten.?
Guggenheim-Hill 1 incorporate
into
hence into
Gibbs Free Energy
Systems in therm. equil. minimize G?
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TUTORIAL PROBLEMS
1. Boltzmanns formula uses the natural log and
log W gives information in nats. How many bits of
information 1 nat ?
2. Derive A(p) endothermic in reactions
3. Study the role of entropy in the chemical
equilibrium formula in http//en.wikipedia.org/wi
ki/Chemical_equilibrium
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RESEARCH PROJECTS

• Carry out experiments described in
• http//www.iit.edu/smile/ch8623.html

2. Carry out experiments described in 3
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1 Chemistry of Interfaces, M. J. Jaycock and G.
D. Parfitt, Ellis Horwood, Chichester, 1986.
REFERENCES
2 Dynamics of Surface Phenomena, P. Joos,
Ridderprint, Utrecht, 1999.
3 Science with Soap Films, D. Lovett,
Institute of Physics Publishing, Bristol, 1994.