Specific volume, phase transitions

The goal of this research is to develop a new class of bioresponsive materials that undergo rapid, large-magnitude, volume-phase transitions in response to specific biological stimuli. Our approach to these materials is based on two fundamental aspects of hydrogels (1) hydrogel solvation/desolvation thermodynamics can be perturbed... and... 

Several attempts have been made to construct stimuli-responsive polymer solution and gel systems which undergo isothermal phase transitions by external stimulation, such as photons or chemicals. Aqueous solutions of poly(A -isopropylacrylamide) having photoisomerizable chromophores or host molecules in the pendant groups showed reversible phase separations by photoirradiation or by the addition of specific metal or ammonium ions. The gels made of the polymers also underwent photostimulated or chemical-induced volume phase transitions. 

From the discussion of swelling equilibrium follows that a volume phase transition of a gel needs further contributions to free energy, resulting, for example, in specific polymer-solvent interactions. The high-temperature collapse of a nonionic single chain and gels in water has been described by using the concentration-dependent interaction parameters x"-... 

Although there have been few data collected, postshock temperatures are very sensitive to the models which specify y and its volume dependence, in the case of the Gruneisen equation of state (Boslough, 1988 Raikes and Ahrens, 1979a Raikes and Ahrens, 1979b). In contrast, the absolute values of shock temperatures are sensitive to the phase transition energy Ejp of Eq. (4.55), whereas the slope of the versus pressure curve is sensitive to the specific heat (see, e.g.. Fig. 4.28). 

The transition from a ferromagnetic to a paramagnetic state is normally considered to be a classic second-order phase transition that is, there are no discontinuous changes in volume V or entropy S, but there are discontinuous changes in the volumetric thermal expansion compressibility k, and specific heat Cp. The relation among the variables changing at the transition is given by the Ehrenfest relations. 

Although the properties of specific polymer/wall systems are no longer accessible, the various phase transitions of polymers in confined geometries can be treated (Fig. 1). For semi-infinite systems two distinct phase transitions occur for volume fraction 0 = 0 and chain length N oo, namely collapse in the bulk (at the theta-temperature 6 [26,27]) and adsorp-... 

Glass transition temperature (Tg), measured by means of dynamic mechanical analysis (DMA) of E-plastomers has been measured in binary blends of iPP and E-plastomer. These studies indicate some depression in the Tg in the binary, but incompatible, blends compared to the Tg of the corresponding neat E-plastomer. This is attributed to thermally induced internal stress resulting from differential volume contraction of the two phases during cooling from the melt. The temperature dependence of the specific volume of the blend components was determined by PVT measurement of temperatures between 30°C and 270°C and extrapolated to the elastomer Tg at —50°C. 

Generally, a phase transition is triggered by an external stress which most commonly is a change in temperature or pressure. Properties that can change discontinuously include volume, density, specific heat, elasticity, compressibility, viscosity, color, electric conductivity, magnetism and solubility. As a rule, albeit not always, phase transitions involve structural changes. Therefore, a phase transition in the solid state normally involves a change from one to another modification. 

Cp is the specific heat at constant pressure, k is the compressibility at constant temperature. The conversion process of a second-order phase transition can extend over a certain temperature range. If it is linked with a change of the structure (which usually is the case), this is a continuous structural change. There is no hysteresis and no metastable phases occur. A transformation that almost proceeds in a second-order manner (very small discontinuity of volume or entropy) is sometimes called weakly first order . 

A very simple model that predicts lyotropic phase transitions is the hard-rod model proposed by Onsager (Friberg, 1976). This theory considers the volume excluded from the center-of-mass of one idealized cylinder as it approaches another. Specifically, if the cylinders are oriented parallel to one another, there is very little volume that is excluded from the center-of-mass of the approaching cylinder (it can come quite close to the other cylinder). If, however, the cylinders are at some angle to one another, then there is a large volume surrounding the cylinder where the... 

When the free energies F of the two crystal structures are identical, the system is at a critical point. The identity of F does not imply identical fimctions (otherwise the two phases would be indistinguishable). Therefore, at the critical point first derivatives of F might differ and therefore enthalpy, volume, and entropy of the two phases would be different. These transformations are first-order phase transitions, according to Ehrenfest [105]. A discontinuous enthalpy imphes heat exchange at the transition temperature, which can easily be measured with DSC experiments. A discontinuous volume is evident under the microscope or, more precisely, with diffraction experiments on single crystals or powders. Some phase transitions are however characterized by continuous first derivatives of the free energy, whereas the second derivatives (specific heat, compressibility, or thermal expansivity, etc.) are discontinuous. These transformations are second-order transitions and are clearly softer. 

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