SURFACE TENSION 2 SPS Lectures January 2006 Wayne Lawton Department of Mathematics National University of Singapore

ABSTRACT The Journal of Chemical Physics -- September 1, Volume 113, Issue 9, pp Spatial and energetic-entropic decomposition of surface tension in lipid bilayers from molecular dynamics simulations Erik LindahlErik Lindahl and Olle EdholmOlle Edholm Theoretical Physics, Royal Institute of Technology, SE Stockholm, Sweden 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.

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

EQUIPARTITION Entropy of a System With Two Subsystems therefore EP Theorem Microstates have equal probability Hence 2 nd Law  Corollary Two subsystems in thermal equilibrium with constant total energy will maximize EP Theorem (Boltzmann) Each translational or rotational component of the random thermal motion of a molecule has an average kinetic energy

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 thereforefor every value of is maximized  Remark

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

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

TUTORIAL PROBLEMS 3. Study the role of entropy in the chemical equilibrium formula in 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

1.Carry out experiments described in RESEARCH PROJECTS 2.Carry out experiments described in [3]

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