Matrix phase transitions

For the analysis heat and mass transfer in concrete samples at high temperatures, the numerical model has been developed. It describes concrete, as a porous multiphase system which at local level is in thermodynamic balance with body interstice, filled by liquid water and gas phase. The model allows researching the dynamic characteristics of diffusion in view of concrete matrix phase transitions, which was usually described by means of experiments. 

However, we also need to discuss how the attractive interactions between species can be included in the theory of partly quenched systems. These interactions comprise an intrinsic feature of realistic models for partially quenched fluid systems. In particular, the model for adsorption of methane in xerosilica gel of Kaminsky and Monson [41] is characterized by very strong attraction between matrix obstacles and fluid species. Besides, the fluid particles attract each other via the Lennard-Lones potential. Both types of attraction (the fluid-matrix and fluid-fluid) must be included to gain profound insight into the phase transitions in partly quenched media. The approach of Ford and Glandt to obtain the chemical potential utilizing... 

However, a substantial improvement in impact energies of PP-NBR blends with GMA or IPO functionalized PPs is observed. The PP-NBR blends went through a brittle-ductile transition as the concentration of the functionalized PPs in the matrix phase reached a leveling off at 13 wt% in the case of IPO functionalized PP and 25 wt% in the case of GMA functionalized PP. Up to a ten-fold improvement in impact energy was observed when the brittle-ductile transition was reached. 

The boundary layers, or interphases as they are also called, form the mesophase with properties different from those of the bulk matrix and result from the long-range effects of the solid phase on the ambient matrix regions. Even for low-molecular liquids the effects of this kind spread to liquid layers as thick as tens or hundreds or Angstrom [57, 58], As a result the liquid layers at interphases acquire properties different from properties in the bulk, e.g., higher shear strength, modified thermophysical characteristics, etc. [58, 59], The transition from the properties prevalent in the boundary layers to those in the bulk may be sharp enough and very similar in a way to the first-order phase transition [59]. 

Wood Hill (1991b) induced phase-separation in the clear glasses by heating them at temperatures above their transition temperatures. They found evidence for amorphous phase-separation (APS) prior to the formation of crystallites. Below the first exotherm, APS appeared to take place by spinodal decomposition so that the glass had an intercoimected structure (Cahn, 1961). At higher temperatures the microstructure consisted of distinct droplets in a matrix phase. 

During a phase transition or a reaction in the solid state which results in one or more products of lower symmetry, very often the higher symmetry of the starting material is indirectly preserved by the orientation of domains formed within the crystalline matrix. 

Among the methods discussed in this book, FEP is the most commonly used to carry out alchemical transformations described in Sect. 2.8 of Chap. 2. Probability distribution and TI methods, in conjunction with MD, are favored if there is an order parameter in the system, defined as a dynamical variable. Among these methods, ABF, derived in Chap. 4, appears to be nearly optimal. Its accuracy, however, has not been tested critically for systems that relax slowly along the degrees of freedom perpendicular to the order parameter. Adaptive histogram approaches, primarily used in Monte Carlo simulations - e.g., multicanonical, WL and, in particular, the transition matrix method - yield superior results in applications to phase transitions,... 

Fig. 68 Comparison of temperature-dependent intensity of first-order Bragg peak for bare matrix copolymer (A) containing 0.5 wt% nanocomposites with plate-like (V), spherical (o) and rod-like ( ) geometry. Data are vertically shifted for clarity. Inset dependence of ODT temperature on dimensionality of fillers (spherical 0, rod-like 1, plate-like 2). Vertical bars width of phase transition region. Pure block copolymer is denoted matrix . From [215]. Copyright 2003 American Chemical Society...

From the modelling results for bilayers composed of unsaturated lipids one can begin to speculate about the various roles unsaturated lipids play in biomembranes. One very well-known effect is that unsaturated bonds suppress the gel-to-liquid phase transition temperature. Unsaturated lipids also modulate the lateral mobility of molecules in the membrane matrix. The results discussed above suggest that in biomembranes the average interpenetration depth of lipid tails into opposite monolayers can be tuned by using unsaturated lipids. Rabinovich and co-workers have shown that the end-to-end distance of multiple unsaturated acyl chains was significantly less sensitive to the temperature than that of saturated acyls. They suggested from this that unsaturated... 

In order to characterize the interaction between different clusters, it is necessary to consider the mechanism of cluster identification during the process of the DA algorithm. As the temperature (Tk) is reduced after every iteration, the system undergoes a series of phase transitions (see (18) for details). In this annealing process, at high temperatures that are above a pre-computable critical value, all the lead compounds are located at the centroid of the entire descriptor space, thereby there is only one distinct location for the lead compounds. As the temperature is decreased, a critical temperature value is reached where a phase transition occurs, which results in a greater number of distinct locations for lead compounds and consequently finer clusters are formed. This provides us with a tool to control the number of clusters we want in our final selection. It is shown (18) for a square Euclidean distance d(xi,rj) = x, — rj that a cluster Rj splits at a critical temperature Tc when twice the maximum eigenvalue of the posterior covariance matrix, defined by Cx rj =... 

When a split occurs (phase transition), identify individual clusters and use the weights (p(rj x)) to construct the transition matrix. 

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