Search results for "Critical exponent"
showing 10 items of 141 documents
Thermodynamic properties of a liquid–vapor interface in a two-component system
2010
Abstract We report a complete set of thermodynamic properties of the interface layer between liquid and vapor two-component mixtures, using molecular dynamics. The mixtures consist of particles which have identical masses and diameters and interact with a long-range Lennard-Jones spline potential. The potential depths in dimensionless units for like interactions is 1 (for component 1) and 0.8 (for component 2). The surface excess entropy decreases when the temperature increases, so the surface has a negative excess heat capacity. This is a consequence of the fact that the surface tension decreases to zero at the critical point, proportional to ( T C , i − T ) 2 ν . The surface entropy decre…
On the critical behavior for time-fractional pseudo-parabolic type equations with combined nonlinearities
2022
AbstractWe are concerned with the existence and nonexistence of global weak solutions for a certain class of time-fractional inhomogeneous pseudo-parabolic-type equations involving a nonlinearity of the form $|u|^{p}+\iota |\nabla u|^{q}$ | u | p + ι | ∇ u | q , where $p,q>1$ p , q > 1 , and $\iota \geq 0$ ι ≥ 0 is a constant. The cases $\iota =0$ ι = 0 and $\iota >0$ ι > 0 are discussed separately. For each case, the critical exponent in the Fujita sense is obtained. We point out two interesting phenomena. First, the obtained critical exponents are independent of the fractional orders of the time derivative. Secondly, in the case $\iota >0$ ι > 0 , we show that the gradie…
Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture
1995
Abstract We have performed a molecular dynamics computer simulation study to investigate the dynamical behavior of a supercooled simple liquid for comparison with the predictions of mode-coupling theory (MCT). By scaling the intermediate scattering function by the α-relaxation time r we find that the correlators fall onto a master curve extending over several decades in time. Thus we find that the time temperature superposition principle holds. In the late β-relaxation regime this master curve can be fitted very well by a master curve predicted by the idealized version MCT. However, there is no evidence for the presence of the critical decay predicted by the theory for the early part of the…
Critical behavior of a colloid-polymer mixture confined between walls
2006
We investigate the influence of confinement on phase separation in colloid-polymer mixtures. To describe the particle interactions, the colloid-polymer model of Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)] is used. Grand canonical Monte Carlo simulations are then applied to this model confined between two parallel hard walls, separated by a distance D=5 colloid diameters. We focus on the critical regime of the phase separation and look for signs of crossover from three-dimensional (3D) Ising to two-dimensional (2D) Ising universality. To extract the critical behavior, finite size scaling techniques are used, including the recently proposed algorithm of Kim et al. [Phys. Rev. Lett. 91…
Concentration and energy fluctuations in a critical polymer mixture
1995
A semi-grand-canonical Monte Carlo algorithm is employed in conjunction with the bond fluctuation model to investigate the critical properties of an asymmetric binary (AB) polymer mixture. By applying the equal peak-weight criterion to the concentration distribution, the coexistence curve separating the A-rich and B-rich phases is identified as a function of temperature and chemical potential. To locate the critical point of the model, the cumulant intersection method is used. The accuracy of this approach for determining the critical parameters of fluids is assessed. Attention is then focused on the joint distribution function of the critical concentration and energy, which is analysed usi…
Phase separation of symmetrical polymer mixtures in thin-film geometry
1995
Monte Carlo simulations of the bond fluctuation model of symmetrical polymer blends confined between two “neutral” repulsive walls are presented for chain lengthNA=NB=32 and a wide range of film thicknessD (fromD=8 toD=48 in units of the lattice spacing). The critical temperaturesTc(D) of unmixing are located by finite-size scaling methods, and it is shown that\(T_c (\infty ) - T_c (D) \propto D^{ - {1 \mathord{\left/ {\vphantom {1 {v_3 }}} \right. \kern-\nulldelimiterspace} {v_3 }}} \), wherev3≈0.63 is the correlation length exponent of the three-dimensional Ising model universality class. Contrary to this result, it is argued that the critical behavior of the films is ruled by two-dimensi…
Self-assembly of bioelastomeric structures from solutions: Mean-field critical behavior and Flory-Huggins free energy of interactions
1993
Elastic and quasi-elastic light scattering studies were performed on aqueous solutions of poly (Val-Pro-Gly-Gly), a representative synthetic bioelastomer that differs from the previously studied poly (Val-Pro-Gly-Val-Gly) by the deletion of the hydrophobic Val in position four. When the spinodal line was approached from the region of thermodynamic stability, the intensity of light scattered by fluctuations, and the related lifetime and correlation length, were observed to diverge with mean-field critical exponents for both systems. Fitting of the experimental data allowed determining the spinodal and binodal (coexistence) lines that characterize the phase diagrams of the two systems, and it…
CLASSIFICATION THEORY FOR PHASE TRANSITIONS
1993
A refined classification theory for phase transitions in thermodynamics and statistical mechanics in terms of their orders is introduced and analyzed. The refined thermodynamic classification is based on two independent generalizations of Ehrenfests traditional classification scheme. The statistical mechanical classification theory is based on generalized limit theorems for sums of random variables from probability theory and the newly defined block ensemble limit. The block ensemble limit combines thermodynamic and scaling limits and is similar to the finite size scaling limit. The statistical classification scheme allows for the first time a derivation of finite size scaling without reno…
Phase diagram of polymer blends in confined geometry
2001
Within self-consistent field theory we study the phase behavior of a symmetrical binary AB polymer blend confined into a thin film. The film surfaces interact with the monomers via short range potentials. One surface attracts the A component and the corresponding smei-infinite system exhibits a first order wetting transition. The surface interaction of the opposite surface is varied as to study the crossover from capillary condensation for symmetric surfaces fields to the interface localization/delocalization transition for antisymmetric surface fields. In the former case the phase diagram has a single critical point close to the bulk critical point. In the latter case the phase diagram exh…
Rigidity transition in two-dimensional random fiber networks
2000
Rigidity percolation is analyzed in two-dimensional random fibrous networks. The model consists of central forces between the adjacent crossing points of the fibers. Two strategies are used to incorporate rigidity: adding extra constraints between second-nearest crossing points with a probability p(sn), and "welding" individual crossing points by adding there four additional constraints with a probability p(weld), and thus fixing the angles between the fibers. These additional constraints will make the model rigid at a critical probability p(sn)=p(sn)(c) and p(weld)=p(weld)(c), respectively. Accurate estimates are given for the transition thresholds and for some of the associated critical e…