Search results for "CRITICAL PHENOMENA"
showing 10 items of 91 documents
Critical phenomena at surfaces
1990
Abstract The presence of free surfaces adds a rich and interesting complexity to critical phenomena associated with phase transitions occurring in bulk materials. We shall review Monte Carlo computer simulation studies of surface critical behavior in simple cubic Ising- and XY-models with nearest-neighbor interactions J in the bulk and Js at the surface. These studies allow the identification of various critical exponents and critical amplitude ratios involving both the critical behavior of local quantities and of surface excess corrections to the bulk. We consider both the “ordinary” transition (surface criticality controlled by the bulk) and the “special transition” (a multicritical point…
Thermodynamic potentials for the infinite range Ising model with strong coupling
2003
Abstract The specific Gibbs free energy has been calculated for the infinite range Ising model with fixed and finite interaction strength. The model shows a temperature driven first-order phase transition that differs from the infinite ranged Ising model with weak coupling. In the temperature-field phase diagram the strong coupling model shows a line of first-order phase transitions that does not end in a critical point.
Monte Carlo investigations of phase transitions: status and perspectives
2000
Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies of Ising models are discussed, as well as the extension to models of polymer mixtures and solutions. It is shown that using appropriate cluster algorithms, even the scaling functions describing the crossover from the Ising universality class to the mean-field behavior with increasing interaction range can be described. Additionally, the issue of finite-size scaling in Ising models above the marginal dimension (d*=4) is discussed.
Surface-directed spinodal decomposition: modelling and numerical simulations
1997
We critically review the modelling and simulations of surface-directed spinodal decomposition, namely, the dynamics of phase separation of a critical or near-critical binary mixture in the presence of a surface with a preferential attraction for one of the components of the mixture.
PHASE TRANSITIONS AT INTERFACES
1989
The interface between two phases may exhibit significant structural changes if one of them comes close to a phase transition in its bulk. Surface critical phenomena, critical adsorption, and wetting phenomena, like e.g. surface melting or surface induced disorder, can occur. The grazing incidence of X rays and neutrons is particularly well suited in order to obtain precise informations about these kind of critical phenomena which link the space dimensions two and three.
Phase separation of symmetric polymer mixtures in a common good solvent in the semidilute concentration regime
1994
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…
Simulation studies of fluid critical behaviour
1997
We review and discuss recent advances in the simulation of bulk critical phenomena in model fluids. In particular we emphasise the extensions to finite-size scaling theory needed to cope with the lack of symmetry between coexisting fluid phases. The consequences of this asymmetry for simulation measurements of quantities such as the particle density and the heat capacity are pointed out and the relationship to experiment is discussed. A general simulation strategy based on the finite-size scaling theory is described and its utility illustrated via Monte-Carlo studies of the Lennard-Jones fluid and a two-dimensional spin fluid model. Recent applications to critical polymer blends and solutio…
Growing range of correlated motion in a polymer melt on cooling towards the glass transition
1999
Many liquids cooled to low temperatures form glasses (amorphous solids) instead of crystals. As the glass transition is approached, molecules become localized and relaxation times increase by many orders of magnitude1. Many features of this ‘slowing down’ are reasonably well described2 by the mode-coupling theory of supercooled liquids3. The ideal form of this theory predicts a dynamical critical temperature T c at which the molecules become permanently trapped in the ‘cage’ formed by their neighbours, and vitrification occurs. Although there is no sharp transition, because molecules do eventually escape their cage, its signature can still be observed in real and simulated liquids. Unlike c…
Dynamics of phase separation and critical phenomena in polymer mixtures
1987
The phenomenological mean-field theory for statics and dynamics of polymer mixtures is described, generalizing the approaches of Flory-Huggins, Cahn-Hilliard and de Gennes. Predictions are made for critical behavior, spinodal decomposition and homogeneous nucleation. The validity of the mean-field approximations is discussed with Ginzburg criteria. The results of the theory are compared to computer simulations and recent experiments.
Phase transitions in polymeric systems: A challenge for Monte Carlo simulation
1995
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…