Journal of Statistical Physics, Vol. 67, Nos. 5/6, 1992. p. 1039-1082.
A complete outline is given for how to determine the critical properties of polymer mixtures with extrapolation methods similar to the Ferrenberg-Swendsen techniques recently devised for spin systems. By measuring not only
averages but the whole distribution of the quantities of interest, it is possible to extrapolate the data obtained in only a few simulations near T,. over the entire critical region, thereby saving at least 90% of the computer time normally needed to locate susceptibility peaks or cumulant intersections and still getting more precise results. A complete picture of the critical properties of polymer mixtures in the thermodynamic limit is then obtained with finite-size scaling functions. Since the amount of information extracted from a simulation in this way is drastically increased as compared to conventional methods, the investigation of mixtures with long chains or built-in asymmetries is now possible. As an example, the critical points, exponents, and amplitudes of dense, symmetric polymer mixtures with chain lengths ranging from N = 16 up to N = 256 are determined within the framework of the 3D bond fluctuation model using grand canonical simulation techniques. As an example for an asymmetry, the generalization of the method to asymmetric monomer potentials is briefly discussed.