Critical composition/point/transition

Many different types of interaction can induce reversible phase transitions. For instance, weak flocculation has been observed in emulsions stabilized by nonionic surfactants by increasing the temperature. It is well known that many nonionic surfactants dissolved in water undergo aphase separation above a critical temperature, an initially homogeneous surfactant solution separates into two micellar phases of different composition. This demixtion is generally termed as cloud point transition. Identically, oil droplets covered by the same surfactants molecules become attractive within the same temperature range and undergo a reversible fluid-solid phase separation [9]. 

An application has been found in which a system that exhibits an upper, or lower, critical consolute point, UCST or LCST, respectively, is utilized. At a temperature above or below this point, the system is one homogeneous liquid phase and below or above it, at suitable compositions, it splits into two immiscible liquids, between which a solute may distribute. Such a system is, for instance, the propylene carbonate - water one at 25°C the aqueous phase contains a mole fraction of 0.036 propylene carbonate and the organic phase a mole fraction of 0.34 of water. The UCST of the system is 73 °C (Murata, Yokoyama and Ikeda 1972), and above this temperature the system coalesces into a single liquid. Temperature cycling can be used in order to affect the distribution of the solutes e.g. alkaline earth metal salts or transition metal chelates with 2-thenoyl trifluoroacetone (Murata, Yokayama and Ikeda 1972). 

Percolation theory applied to the two-phase system It is a well known fact that the transition of modulus takes place in the two-phase system from a rubbery state to a glassy state at the critical region (not a point) as a function of the composition. Morphologically the transition is understood as the reverse of phases. Recently by introducing the concept of percolation concept, the transition composition is defined by the elastic percolation threshold. The scaling rule proposed by de Gennes [9] is applied to such a variation of modulus, using the critical composition at the elastic percolation threshold. 

Fig. 17, we see that AS/R is equal to 0.417 when jc =l which is the Maier-Saupe prediction for monomers [63]. Then as the mole fraction of bent conformers increases the transitional entropy is also predicted to increase which is paradoxical because for a pure system of biaxial particles AS/R is predicted to decrease with increasing molecular biaxiality [65]. We shall return to this important point shortly but for the moment we note that for x of 0.5 AS/R has increased to 1.3 which is over three times the value found for monomers and so is analogous to the behavior of even liquid crystal dimers. As xf continues to decrease so AS/R increases until for a mole fraction of the linear conformer of less than 0.03 the transitional entropy falls catastrophically to a value of less than 0.03. This behavior is reminiscent of odd dimers although AS/R is somewhat less than the values usually found, as is the critical composition forx . In the limit thatx° vanishes so too does the transitional entropy, in... 

Despite the importance of initiators, synthesis conditions, and diluents on the properties of a gel, composition is, of course, the most important variable. When growing polymeric chains are first initiated, they tend to grow independently. As the reaction proceeds, different chains become connected through cross-links. At a critical conversion threshold, called the gel point or the sol-gel transition, enough growing chains become interconnected to form a macroscopic network. In other words, the solution gels. The reaction is typically far... 

The thermodynamic aspects of hydride formation from gaseous hydrogen are described by means of pressure-composition isotherms in equilibrium (AG = 0). While the solid solution and hydride phase coexist, the isotherms show a flat plateau, the length of which determines the amount of H2 stored. In the pure P-phase, the H2 pressure rises steeply vfith increase in concentration. The two-phase region ends in a critical point T, above which the transition from the a- to the P-phase is continuous. The equilibrium pressure peq as a function of temperature is related to the changes AH° and AS° of enthalpy and entropy ... 

Yamada et al. [9,10] demonstrated that the copolymers were ferroelectric over a wide range of molar composition and that, at room temperature, they could be poled with an electric field much more readily than the PVF2 homopolymer. The main points highlighting the ferroelectric character of these materials can be summarized as follows (a) At a certain temperature, that depends on the copolymer composition, they present a solid-solid crystal phase transition. The crystalline lattice spacings change steeply near the transition point, (b) The relationship between the electric susceptibility e and temperature fits well the Curie-Weiss equation, (c) The remanent polarization of the poled samples reduces to zero at the transition temperature (Curie temperature, Tc). (d) The volume fraction of ferroelectric crystals is directly proportional to the remanent polarization, (e) The critical behavior for the dielectric relaxation is observed at Tc. 

In spite of the constant density of the gel, the friction of the poly(N-isopropylacrylamide) gel reversibly decreases by three orders of magnitude and appears to diminish as the gel approaches a certain temperature. This phenomenon should be universal and may be observed in any gel under optimal experimental conditions of the solvent composition and the temperature because the unique parameter describing the friction is the correlation length which tends to diverge in the vicinity of the volume phase transition point of gels. The exponent v for the correlation length obtained from the frictional experiment is far from the theoretical value. It will, therefore, be important to study a poly(N-isopropylacrylamide) gel prepared at the critical isochore where the frictional property of gel may be governed by the critical density fluctuations of the gel. 

In summary, the measured rate constants (based on bulk concentrations) increase as the pressure is decreased near the critical point. This cannot be explained solely on the basis of the pressure effect on the rate constant predicted from transition state theory or cage effects. As a result, we believe that local composition increases near the critical point play an important role in the rate increase. 

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