The virial coefficients of the pearl-necklace model

We consider the virial coefficients of an idealized model polymer under goo d solvent conditions, the so-called pearl-necklace model, consisting of a f ully flexible chain of m tangent hard spheres. We employ an efficient algor ithm recently proposed to determine the second, third, and fourth virial co efficients of chains of up to 100 monomers. We also include some preliminar y results for chains of up to 200 monomers. These results, which include th e first off-lattice calculations of third and fourth virial coefficients of polymer models, are compared with predictions obtained from Wertheim's equ ation of state. It is shown that, despite the good agreement of Wertheim's equation of state for the compressibility factor, the predictions for the i ndividual virial coefficients are far from satisfactory. It it shown that f or the values of m considered in this work, the truncated virial expansion correctly describes the equation of state up to packing fractions of 0.25. A new equation of state which describes the low and high density regimes of the pearl-necklace model is proposed. (C) 2000 American Institute of Physi cs. [S0021-9606(00)50946-5].