0000000000255783
AUTHOR
Hans-peter Deutsch
The mean field to Ising crossover in the critical behavior of polymer mixtures : a finite size scaling analysis of Monte Carlo simulations
Monte Carlo simulations of the bond fluctuation model of symmetrical polymer mixtures (chain lengths N A =N B =N) are analyzed near the critical temperature T c (N) of their unmixing transition. Two choices of interaction range are studied, using a square-well potential with effective coordination number z eff ≃ 14 or z eff ≃ 5, respectively, at a volume fraction O= 0.5 of occupied lattice sites, and chain lengths in the range 8≤ N≤ 512. A linear relation between N and T c (N) is established, T c (N)= AN+B, where the correction term B is positive for z eff = 14 but negative for z eff = 5. The critical behavior of the models is analyzed via finite size scaling techniques, paying attention to…
Optimized analysis of the critical behavior in polymer mixtures from Monte Carlo simulations
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 nearT c 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 scali…
Monte carlo studies of phase transitions in polymer blends and block copolymer melts
The unmixing transition of both symmetrical polymer blends AB (i.e. chain lengthsNA=NB=N) and asymmetrical ones (NB/NA=2,3) is studied by large-scale Monte Carlo simulations of the bond fluctuation model. Combination of semi-grand-canonical simulation techniques, «histogram reweighting» and finitesize scaling allows an accurate location of the coexistence curve in the critical region. The variation of the critical temperature with chain length (N) is studied and compared to theoretical predictions. For the symmetrical case, use of chain lengths up toN=512 allows a rough estimation of crossover scaling functions for the crossover from Ising to mean-field exponents. The order-disorder transit…
MONTE CARLO METHODS FOR FIRST ORDER PHASE TRANSITIONS: SOME RECENT PROGRESS
This brief review discusses methods to locate and characterize first order phase transitions, paying particular attention to finite size effects. In the first part, the order parameter probability distribution and its fourth-order cumulant is discussed for thermally driven first-order transitions (the 3-state Potts model in d=3 dimensions is treated as an example). First-order transitions are characterized by a minimum of the cumulant, which gets very deep for large enough systems. In the second part, we discuss how to locate first order phase boundaries ending in a critical point in a large parameter space. As an example, the study of the unmixing transition of asymmetric polymer mixtures…
Simulation of first- and second-order transitions in asymmetric polymer mixtures
The critical properties of dense asymmetric binary polymer mixtures are studied by grand canonical simulations within the framework of the 3-dimensional bond fluctuation lattice model. The monomers interact with each other via a potential ranging over the entire first peak of the pair distribution. An asymmetry is realized by giving the ratio of interactions λ = ∈AA/∈BB between monomers of the A-species and of the B-species a value different from 1. Using multiple histogram extrapolation techniques for the data analysis, the two phase region, which is a line of first-order transitions driven by the chemical potential difference, and the critical point are determined for a mixture of chains …
Phase transitions in polymeric systems: A challenge for Monte Carlo simulation
Polymers are more difficult to simulate than small molecule systems, due to the large size of random polymer coils (and their slow relaxation, that is observed when dynamic simulation algorithms are used). However, variation of the chain length N of a flexible polymer chain provides a very useful additional control parameter, allowing stringent tests of theories, and new physical phenomena may emerge. As an example of these concepts, critical phenomena in polymer mixtures are described. It is shown that unmixing of symmetrical mixtures ( N A = N B = N ) is described by an equation for the critical temperature T c ( N ) = aN + b rather than T c ∝ N as claimed by some theories. While for fini…
Monte Carlo studies of polymer interdiffusion and spinodal decomposition: A review
Abstract Putting a layer of polymer A on top of a layer of polymer B, the broadening of the interfacial profile is observed in the framework of a lattice model (‘bond fluctuation method’). The interdiffusion constant is studied as a function of chain length, vacancy concentration, and interaction energy between unlike monomers, and a comparison with pertinent theoretical predictions is made. A lattice model where polymers are represented as self-avoiding walks on a simple cubic lattice is used to model ‘spinodal decomposition’, i.e. phase separation by ‘uphill diffusion’ in the unstable part of the phase diagram of a polymer mixture. For chain lengths N ≤ 32, the linearized Cahn-like theory…