The correlation functions of hard-sphere chains: Monodisperse chains as a complete association limit

Abstract

The mixture of associating hard spheres with two random association sites is considered to model freely jointed tangent hard-sphere chains of fixed length. In the case of the complete association limit with infinite association strength, the associating fluid becomes the hard-sphere chain fluid. The multidensity Ornstein–Zernike equation is applied to this limiting case, and an analytical solution is obtained within the polymer Percus–Yevick (PPY) approximation. In doing so, we imposed connectivity constraints between bonded segments in order to avoid numerically inconvenient forms. Explicit expressions for the contact values of the correlation functions are obtained, and the correlation functions for the region beyond the hard core are calculated from a set of integral equations involving only finite quantities. Predictions of the theory for 4- and 8-mer fluid are compared to computer simulation results. For overall correlation functions accurate predictions are obtained over the whole density range. For the inter- and intramolecular correlation functions, a significant improvement is found at low density compared to our previous theory with the PPY ideal-chain approximation. As chain length increases, the theory overestimates the intermolecular correlation functions, and underestimates the intramolecular correlation functions. It is concluded that the good accuracy for the overall correlation functions is due to the cancellation of errors between the inter- and intramolecular correlation functions.