Volume change, discontinuous

In addition to the thermodynamic models, Khokhlov et al proposed a model for the hydrophobic interaction of an ionic surface active agent and electrolyte gel where the volume changes discontinuously in a gel due to the micelle formation [45]. For actual descriptions, the readers are referred to the original monograph. 

The formation of discontinuities, particularly the grosser forms of pores and cracks, in an oxide layer is often attributable to the mass flows and volume changes occasioned by oxidation. As can be seen from Table 1.27 it is usual... 

The parameters which characterize the thermodynamic equilibrium of the gel, viz. the swelling degree, swelling pressure, as well as other characteristics of the gel like the elastic modulus, can be substantially changed due to changes in external conditions, i.e., temperature, composition of the solution, pressure and some other factors. The changes in the state of the gel which are visually observed as volume changes can be both continuous and discontinuous [96], In principle, the latter is a transition between the phases of different concentration of the network polymer one of which corresponds to the swollen gel and the other to the collapsed one. 

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. 

MnAs exhibits this behavior. It has the NiAs structure at temperatures exceeding 125 °C. When cooled, a second-order phase transition takes place at 125 °C, resulting in the MnP type (cf. Fig. 18.4, p. 218). This is a normal behavior, as shown by many other substances. Unusual, however, is the reappearance of the higher symmetrical NiAs structure at lower temperatures after a second phase transition has taken place at 45 °C. This second transformation is of first order, with a discontinuous volume change AV and with enthalpy of transformation AH. In addition, a reorientation of the electronic spins occurs from a low-spin to a high-spin state. The high-spin structure (< 45°C) is ferromagnetic,... 

Kirk et al (1972) show that at 6.5 kbar there is a discontinuous change in the reflectivity of SmS, suggesting a metal-insulator transition, which was later observed by Bader et al (1973) with an 8% volume change (see also Chapter 4 below and Jayaraman et al 1970a, b, Maple and Wohlleben 1971). 

The present author (Mott 1949,1956,1961) first proposed that a crystalline array of one-electron atoms at the absolute zero of temperature should show a sharp transition from metallic to non-metallic behaviour as the distance between the atoms was varied. The method used, described in the Introduction, is now only of historical interest. Nearer to present ideas was the prediction (Knox 1963) that when a conduction and valence band in a semiconductor are caused to overlap by a change in composition or specific volume, a discontinuous change in the number of current carriers is to be expected a very small number of free electrons and holes is not possible, because they would form exdtons. 

The second example used visible light absorption that increased the temperature locally within the thermosensitive gel [39]. The gel consisted of a covalently cross-linked copolymer network of N-isopropylacrylamide and chloro-phyllin, a combination of a thermo-sensitive gel and a chromophore. In the absence of light, the gel volume changed sharply but continuously as the temperature was varied. Upon illumination the transition temperature was lowered, and beyond a certain irradiation threshold the volume transition became discontinuous. The phase transition was presumably induced by local heating of polymer chains due to the absorption and subsequent thermal dissipation of light energy by the chromophore. The details will be discussed in a later section. 

Fig. 31. Temperature dependence for equilibrated volumes of NIPA gel including the Con A-DDS complex (DSS-gel, open circles), MP (MP-gel, filled circles), and free of both DSS and MP squares). The latter was prepared as a control sample. Hysteresis was observed in the volume changes of DSS-gel and the free-Con A gel on heating and cooling, indicating a discontinuous phase transition. The diameter of each gel in the collapsed state, determined at 50 °C, was do = 0.074 mm the volume of this gel is denoted by V0. The concentration of dry matter in the collapsed state was estimated from the preparation recipe to be 90wt%.

The swelling behavior of poly(N-isopropylacrylamide) has been studied extensively [18,19]. It has been shown that this gel has a lower critical point due to the hydrophobic interaction. Such a swelling curve is schematically illustrated in Fig. 9. The gel is swollen at a lower temperature and collapses at a higher temperature if the sample gel is allowed to swell freely in water. The volume of the gel changes discontinuously at 33.6°C. The swelling curves obtained in this way correspond to the isobar at zero osmotic pressure. On the other hand, the friction coefficient is measured along the isochore, which is given in Fig. 9,... 

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