Polymeric materials containing fibrils with a phase transition. Part IV. Comparison of model predictions with behavior of wool fibers

In previous papers in this series [l-3] and elsewhere [4,5], we have proposed theoretical models for the mechanical behavior of a polymer system consisting of a matrix containing fibrils, which are able to undergo a phase transition with increase of length. These models are particularly relevant to the study of wool fibers, in which the bulk of the material consists of parallel crystalline microfibrils, about 70 Å in diameter and spaced 100 Å apart, embedded in a crosslinked matrix. General features of the tensile behavior of wool fibers were discussed in the first article [l]; in the present article the detailed predictions of the various models are examined and compared with experimental results, and other complexities of behavior of wool fibers are discussed. It must be remembered that, although there are specific differences, the models are all similar in concept and will give generally similar results.     

On a phase transition for semitransparent materials in terms of the Stefan problem

The paper deals with justification of the formula for the latent heat of phase transition of the first kind, taking into account superheating and subcooling of the formed two-phase system, in application to the solution of Stefan problem in semitransparent materials.     

On the layering transition of an SOS surface interacting with a wall. II. The Glauber dynamics

We continue our study of the statistical mechanics of a 2D surface above a fixed wall and attracted towards it by means of a very weak positive magnetic fieldh in the solid on solid (SOS) approximation, when the inverse temperature is very large. In particular we consider a Glauber dynamics for the above model and study the rate of approach to equilibrium in a large cube with arbitrary boundary conditions. Using the results proved in the first paper of this series we show that for allh(h _k+1 ^* ,h _k ^* ) ({h _k ^* } being the critical values of the magnetic field found in the previous paper) the gap in the spectrum of the generator of the dynamics is bounded away from zero uniformly in the size of the box and in the boundary conditions. On the contrary, forh=h _k ^* and free boundary conditions, we show that the gap in a cube of sideL is bounded from above and from below by a negative exponential ofL. Our results provide a strong indication that, contrary to what happens in two dimensions, for the three dimensional dynamical Ising model in a finite cube at low temperature and very small positive external field, with boundary conditions that are opposite to the field on one face of the cube and are absent (free) on the remaining faces, the rate of exponential convergence to equilibrium, which is positive in infinite volume, may go to zero exponentially fast in the side of the cube.Work partially supported by grant SC1-CT91-0695 of the Commission of European Communities.     

On the influence of phase transformations in a metal matrix of composite materials upon mechanical alloying during the disintegration of agglomerates of nanodiamond reinforcing particles

The disintegration of agglomerates of nanodiamond reinforcing particles in a metal matrix upon mechanical alloying is studied. This process is shown to be influenced by phase transformations in the matrix. A hypothesis is suggested that the disintegration is a result of additional microstresses and microstrains arising in local domains due to variations in the density and molar (gram-atom) volumes of phases and parameters of the metal lattice upon phase transformations.     

On aC*-algebra approach to phase transition in the two-dimensional Ising model. II

We investigate the statesφ _β on theC*-algebra of Pauli spins on a one-dimensional lattice (infinitely extended in both directions) which give rise to the thermodynamic limit of the Gibbs ensemble in the two-dimensional Ising model (with nearest neighbour interaction) at inverse temperature β. We show that if β _c is the known inverse critical temperature, then there exists a family {v _β :β≠β _c } of automorphisms of the Pauli algebra such that $$\phi _\beta = \left\{ {_{\phi _\infty \circ v_\beta ,}^{\phi _0 \circ v_\beta ,} } \right. _{\beta > \beta _c .}^{0 \leqslant \beta< \beta _c } $$ .     

The Hermitian intensity matrix of a multipole transition

TheL-pole transition is described by a Hermitian (2L+1)×(2L+1) matrix. The incoherent absorption process of the nuclei in a crystal allows to sum up the matrices of all transitions at the same energy. The result is an intensity matrix of the crystal. The evaluation of the polarisation state of dipole transitions dependent on the -direction can be done by very simple tensor equations.     

The role of CDW gap on the magnetic phase transition in CMR materials

We propose a model to study the magnetic phase transition in the Colossal-Magneto-Resistance (CMR) material of general type R_1−x A _x MnO₃ (R = La, Sm, Nd; A = Ca, Sr, Ba). The model Hamiltonian consists of a Charge Density Wave (CDW) gap in the e _g -band and the strong magnetic field due to the spin ordering in the localized t _g core electrons. The Hamiltonian is solved by using Zubarev’s Green’s function technique to calculate CDW gap (Δ) and magnetization (M ^d ) in t _2g band. Both of them are solved self-consistently. Their combined effect on the temperature dependent magnetization (M ^c ) due to the e _g band electrons is investigated. Both the magnitude and the transition temperature of (M ^c ) are strongly influenced by both Δ and M ^d . Hence the hopping of the band electrons are strongly controlled by these two long range interactions. The results are discussed by varying the model parameters of the manganite system.      

On the quantum phase transition of a quantum Hall liquid

It is shown that, in the absence of disorder, a quantum Hall liquid undergoes a second-order quantum phase transition as function of the applied magnetic field. The analysis is carried out in the framework of the Chem-Simons-Ginzburg-Landau theory which is shown to exhibit a nontrivial infrared stable fixed point. The corresponding critical exponents are found to be gaussian, and thus universal and independent of the filling fraction.     

The effective stiffness of an embedded graphene in a polymeric matrix

Modeling the real sizes of an embedded graphene and the surrounding polymer of a representative volume element in a molecular dynamics simulation is a tedious task. The less computational limitations made the continuum-based method a good candidate for modeling of nanocomposites. However, having a good knowledge of mechanical properties of the embedded graphene in a polymeric matrix is a challenge for employing a continuum-based method. Since the applied stress on the graphene/epoxy nanocomposites has not been directly transferred to the embedded graphene, it brings the following question to mind. Is the stiffness of the embedded graphene different from that of the isolated one? To answer to this question, a model was developed by combining the molecular dynamic simulation and the finite element method to calculate the stiffness of an embedded graphene in a polymeric matrix. The results show that the longitudinal stiffness of the embedded graphene is different from that of the isolated graphene and is a function of its length. The use of this relationship in the micromechanical method leads to consider the nanosize effect in macroscale. The results were compared with some available experimental data to validate the model.     

Dynamics of interaction of a high-current electron beam with polymeric materials

The fracture dynamics of transparent polymeric materials under the impact of shockwaves induced by the energy release due to a high-power electron beam has been studied in polymethyl methacrylate (plexiglas), polystyrene, and epoxy samples by high frame-rate imaging. A qualitatively different character of fracture has been observed in polystyrene as compared to plexiglas and epoxy. The causes of the difference are discussed.     

The dispersion of polymeric materials with the use of supercritical fluids

The dispersion of polyisobutylene was studied on a Thar RESS-100-2 test bench over the temperature and pressure ranges 45–120°C and 100–350 bar; 30–1000 nm particles were obtained. Particle size could be controlled by varying process parameters. A procedure for modifying polymer particles during rapid expansion of supercritical solutions was suggested. Modification suppressed agglomeration and caused particle coating with a modifier (NaCl). The use of supercritical fluid antisolvents was shown to be promising for the dispersion of polymers to nanosized particles. An experimental bench for performing such processes was described. A procedure for trapping nanoparticles prepared using antisolvents was suggested. Particles with sizes of 10 to 150 nm were obtained in the dispersion of polystyrene in the toluene-polystyrene-supercritical carbon dioxide system at 40–150 bar and temperatures of 40 and 100°C.     

Localisation and phase transition of acoustic waves in a soft medium containing air bubbles

We study via numerical experiments the localisation property of an acoustic wave in a viscoelastic soft medium containing randomly-distributed air bubbles. The behaviours of the oscillation phases of bubbles are particularly investigated in various cases for distinguishing efficiently the acoustic localisation from the effects of acoustic absorption caused by the viscosity of medium. The numerical results reveal the phenomenon of `phase transition' characterized by an unusual collective oscillation of bubbles, which is an effective criterion to unambiguously identify the acoustic localisation in the presence of viscosity. Within the localisation region, the phenomenon of phase transition persists, and a remarkable decrease in the fluctuation of the oscillation phases of bubbles is observed. The localisation phenomenon will be impaired by the enhancement of the viscosity factors, and the extent to which the acoustic wave is localised may be determined by appropriately analyzing the values of the oscillation phases or the amount of reduction of the phase fluctuation. The results are particularly significant for the practical experiments in an attempt to observe the acoustic localisation in such a medium, which is in general subjected to the interference of the great ambiguity resulting from the effect of acoustic absorption.     

On electrostatic models of a metal-insulator phase transition in crystalline semiconductors with hydrogen-like impurities

Two well-known models for calculating the critical density N _C of a metal-insulator transition, as a function of the Bohr radius a _H of an isolated impurity as temperature T→0 K, are refined by making allowance for the screening of ions by electrons hopping along impurities. In one model, the transition at N _C1 is explained by the appearance of delocalized electrons as the impurity band is displaced into the allowed-energy band as a result of a decrease in the electron (hole) affinity of ionized impurities. In the other model the transition is explained by an unbounded increase in the static permittivity of the crystal as the density of impurity atoms increases to N _C2. The obtained approximations N _C1 ^1/3 a _H≈0.24 and N _C2 ^1/3 a _H≈0.20 for the degree of compensation K=0.01 describe existing experimental data for 1<a _H<10 nm. Fiz. Tverd. Tela (St. Petersburg) 40, 147–151 (January 1998)     

On the nature of a new phase transition in α-MnS

Magnetic-susceptibility and X-ray-diffraction data of polycrystalline and oriented single crystal α-MnS reveal a new phase transition at T_tr = 131 K below the Néel temperature T_N = 148 K. The phase transition is characterized by an abrupt inversion of the rhombohedral distortion of the f.c.c. lattice along [111]. At T_tr there is a discontinuous change in the susceptibility of single crystals.     

On phase ordering behind the propagating front of a second-order transition

In a real system the heating is nonuniform, and a second-order phase transition to a broken-symmetry phase occurs by propagation of a temperature front. Two parameters, the cooling rate τ _Q and the transition front velocity ν _T determine the nucleation of topological defects. Depending on the relation of these parameters, two regimes are found: in the regime of fast propagation defects are created according to the Zurek scenario for the homogeneous case, while in the slow-propagation regime vortex formation is suppressed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 96–101 (10 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.