Exact Calculations of Membrane Areas with Simple Models

Details Exact Calculations of Membrane Areas with Simple Models Exact Calculations of Membrane Areas with Simple Models

2008-07-29

arxiv.org/abs/0807.4593v1

Physics

Condensed Matter

Soft Condensed Matter

17 pages, 5 Figures

Scientific paper

The distinction between the true total area and the projected area is elucidated with soluble models which represent the membrane as a self-avoiding string on a plane. Constraining the total area to a predetermined value changes the averages very significantly. The latter are calculated exactly from the generating functions of self-avoiding walks and are shown as functions of activities $q$ and $r$ related to temperature $T=\pm 1/\log (q)$ and lateral force $f=-\log (r)$. The constraint makes the partition functions and averages valid for all $q,r >0$ and reduces the ratio of $A_{tot}$ to the projected area $L$. High temperature divergences are supressed. Possible applications to simulated bilayers/membranes are discussed.

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