Numerical test of the generalized Flory and generalized Flory dimer theories

We report results of a numerical test of the generalized Flory and generalized Flory dimer theories. Using continuous space Rosenbluth sampling, we have tested the basic assumptions of these theories. We find that the discrepancy between the predictions of the generalized Flory theory and simulation data is caused by the use of the Carnahan-Starling equation of state to estimate the incremental chemical potential of a chain molecule. Although the assumptions made in deriving the generalized Flory dimer theory are similarly flawed, the predictions of the latter theory are in excellent agreement with simulation results. This is explained by the occurrence of a cancellation of errors. Therefore, it is not to be expected a priori that increasingly higher order extensions of these theories will be improvements. In particular, the disappointing performance of the recently developed generalized Flory trimer theory may be due to the fact that this theory lacks the cancellation of errors that is present in the generalized Flory dimer theory.