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SURFACE TENSION 2 SPS Lectures January 2006

SURFACE TENSION 2 SPS Lectures January 2006. Wayne Lawton Department of Mathematics National University of Singapore http://math.nus.edu.sg/~matwml matwml@nus.edu.sg.

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SURFACE TENSION 2 SPS Lectures January 2006

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  1. SURFACE TENSION 2SPS Lectures January 2006 Wayne Lawton Department of Mathematics National University of Singapore http://math.nus.edu.sg/~matwml matwml@nus.edu.sg

  2. 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. ABSTRACT • 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

  3. Thermodynamics ENTROPY 1st Law 2st Law Statistical Mechanics Boltzmann’s tombstone

  4. Entropy of a System With Two Subsystems EQUIPARTITION 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

  5. We consider a constant volume system whose entropy S = S(E) that is in thermal equilibrium with an infinite reservoir that has temperature T A = HELMHOLTZ FREE ENERGY 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  for every value of therefore Remark

  6. ENDOTHERMIC REACTIONS We consider a system consisting of molecules that can be in states 1 or 2 having respective energies 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

  7. SURFACE TENSION THERMODYNAMICS 2nd Law&surf. ten. Enthalpy Guggenheim-Hill [1] incorporate into hence into Gibbs Free Energy Systems in therm. equil. minimize G

  8. TUTORIAL PROBLEMS 1. Boltzmann’s 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/wiki/Chemical_equilibrium

  9. RESEARCH PROJECTS • Carry out experiments described in • http://www.iit.edu/~smile/ch8623.html 2. Carry out experiments described in [3]

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

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