Journal of Statistical Physics, Vol. 110, Nos. 1/2, January 2003. p. 419-429.
The equation of state of a quasi one-dimensional model lipid monolayer is obtained in analytic form. The method used is the Laplace transform approach leading to a homogeneous Fredholm integral equation. Two cases are studied. The first considers a purely short range repulsive potential, when we recover the results previously obtained by Gianotti et al. (J. Phys. A.: Math. Gen. 25:2889 (1992)). The second incorporates the long range attractive Kac potential, and,the equation of state is calculated in the van der Waals limit. This extends the
approach originally developed by Kac et al. (J. Math. Phys. 4:216 (1963)).