Monte Carlo simulations are presented for binary (AB) symmetric polymer mixtures (chain lengths NANBN) for the case that an attractive interaction ϵ exists between monomers of the same kind, and the limiting case that one species (B) is very diluted. It is shown that with increasing interaction strength ϵ/(kB · T), T being the absolute temperature, the minority chains collapse to a very dense configuration, while the majority chains stay nearly Gaussian. Both chain radii, structure factors and numbers of nearest neighbour contacts are discussed.

Phase separation of symmetric polymer mixtures in a common good solvent in the semidilute concentration regime

Monte Carlo simulations of lattice models of binary (AB) symmetric polymer mixtures (chain lengthsN A=N B=N) in a common good solvent are carried out and the phase diagrams and critical properties of the unmixing transitions are estimated and interpreted in terms of recent theories. Polymers are modeled by self-avoiding walks of lengthN=16, 32 and 64 on the simple cubic lattice. Data for vacancy concentrations of φV=0.6, 0.8 and 0.85 are analyzed. It is shown that forN=16, φV=0.85 no phase separation occurs, down to the lowest temperature, while forN=32, φV=0.85 still phase separation occurs but no longer is complete. Our results are compatible with a scaling theory based on a “renormalizat…

Scattering from concentration fluctuations in polymer blends: A monte carlo investigation

The collective scattering function Scoll( $$\vec q$$ ), which describes light (neutron-, x-ray) scattering under wavevector $$\vec q$$ , is obtained from Monte Carlo simulations for a symmetrical polymer mixture. The polymers are modelled by self-avoiding walks ofN A=NB=N steps on a simple cubic lattice, where a fractionφ V of sites is left vacant, and an attractive energye occurs if two neighboring sites are taken by the same kind of monomer. Spinodal curves are estimated from linear extrapolation of S coll −1 (0) vs.e/k B T, whereT is the temperature. Also the single chain structure factor is obtained and the de Gennes random phase approximation (RPA) can thus be tested. Unexpectedly, str…

Critical phenomena in polymer mixtures: Monte Carlo simulation of a lattice model

A lattice model of a symmetrical binary (AB) polymer mixture is studied, modelling the polymer chains by self-avoiding walks withN A =N B =N steps on a simple cubic lattice. If a pair of nearest neighbour sites is taken by different monomersAB orBA, an energye ab is won; if the pair of sites is taken by anAA or aBB pair, an energye is won, while the energy is reduced to zero if at least one of the sites of the pair is vacant. To allow enough chain mobility, 20% of the lattice sites are vacancies. In addition to local motions of the chain segments we use a novel “grand-canonical” simulation technique:A chains are transformed intoB chains and vice versa, keeping the chemical potential differe…

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…

Monte Carlo simulation of a lattice model for ternary polymer mixtures

Monte Carlo studies of symmetrical polymer mixturesAB, modelled by selfavoiding walks withNA=NB=N steps on a simple cubic lattice, are presented for arbitrary concentrations of vacanciesφv in the range fromφv=0.2 toφv=0.8 and chain lengthsN≤64. We obtained the phase diagrams and the equation of state for three choices of the ratio ∈ / ∈AB (∈ being the energy between monomers of the same kind, ∈AB being the energy between different monomers). Flory-Huggins theory provides only a qualitative understanding of these results. If the equation of state is “fitted” with an effective Flory-Huggins parameterχeff, the latter turns out to be strongly dependent on both concentration and temperature.