The adsorption of long, straight rigid rods of length k (k-mers) on 2D lattices is described by using a new theoretical approach based on a generalization of the classical Guggenheim-DiMarzio approximation. In this scheme, the Helmholtz free energy and its derivatives are written in terms of the order parameter δ, which characterizes the nematic phase occurring in the system at intermediate densities. Then, using the principle of minimum free energy with δ as a parameter, the main adsorption properties are calculated. Comparisons with Monte Carlo simulations are performed in order to test the validity of the theoretical model. The obtained results indicate that the new thermodynamic description is significantly better than the existing theoretical models developed to treat the polymer adsorption problem.