Fluids confined in random porous media: A hard sponge model
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Zusammenfassung
The morphology of many porous materials is sponge-like. Despite
the abundance of such materials 1,2, simple models which
allow for a theoretical description of such materials are still
lacking. Here, we propose a hard sponge model which is made by
digging percolated spherical cavities in a solid continuum (see
Fig.1). The interaction potential of fluid particles with such
a porous medium can be modelled by the following expression,
equation
U_10 = \sum_i=1^N_1 u_10(\mathbf
r_i; q^N_0 ). eq1
equation
with
equation
u_10(r_i; q^N_0 ) = - k_B T
ln 1 - e^-\sum_j=1^N_0 \phi^HS(łeft| \mathbf
r_i - q_j \right|). eq2
equation
where $k_B$ and $T$ are respectively Boltzmann constant and the
temperature and $\phi^HS$ is the hard sphere potential with
a diameter of $\sigma$ which is the diameter of the spherical
cavity in our model. The interaction potential described by
eqs.(1) and (2) is clearly not pair additive. Despite of this
non additive form of
fluid-matrix interaction, we show that the diagrammatic
expansions can be still obtained for various distribution
function. We derived also the Ornstein-Zernike equations for
a fluid confined in such a hard sponge model. We show also
how the replica method 3,4 can be extended to treat this
model.
1) P.M. Adler, Porous Media, Butterworth-Heinemann,
Boston, 1992.\\
2) P. Spanne, J.F. Thovert, C.J. Jacquin, W.B. Lindquist, K.W.
Jones and P.M. Adler, Phys. Rev. Lett. 73, 2001, (1994).\\
3) J.A. Given, Phys. Rev. A, 45, 816, (1992).\\
4) J.A. Given and G.R. Stell, Physica A, 209, (1994).