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Nonlinear potentials

The figures below show theoretical curves when (a) a 4-6 potential
U(x)=-B/4(x-x0)^4+C/6(x-x0)^6
and (b) a 1-6 potential
U(x)=-A/(x-x0)+A'/6(x-x0)^6
is added. The following page shows simulations in which the theoretical predictions are confirmed.

Predicted histograms of piston coordinate at equilibrium
images/theory4-6
Adding in a 4-6 potential to emulate dipole binding massively increases work done during the expansion: without 4-6 potential - about 4kT; with 4-6 potential - about 16kT illustrated here. [Probability densities are not accurately normalized.]

images/onesixtheory

Adding a 1-6 potential. The red curve shows the total free energy G(x) = U(x) - TS(x).
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Site last modified Tue Jul 5 12:32:01 BST 2005