  The scaled particle theory (SPT) approximation is applied for the study of
the influence of a porous medium on the isotropic-nematic transition in a hard
spherocylinder fluid. Two new approaches are developed in order to improve the
description in the case of small lengths of spherocylinders. In one of them,
the so-called SPT-CS-PL approach, the Carnahan-Starling (CS) correction is
introduced to improve the description of thermodynamic properties of the fluid,
while the Parsons-Lee (PL) correction is introduced to improve the
orientational ordering. The second approach, the so-called SPT-PL approach, is
connected with generalization of the PL theory to anisotropic fluids in
disordered porous media. The phase diagram is obtained from the bifurcation
analysis of a nonlinear integral equation for the singlet distribution function
and from the thermodynamic equilibrium conditions. The results obtained are
compared with computer simulation data. Both ways and both approaches
considerably improve the description in the case of spherocylinder fluids with
smaller spherocylinder lengths. We did not find any significant differences
between the results of the two developed approaches. We found that the
bifurcation analysis slightly overestimates and the thermodynamical analysis
underestimates the predictions of the computer simulation data. A porous medium
shifts the phase diagram to smaller densities of the fluid and does not change
the type of the transition.
