Transitions between phases

Most solid materials produce isotropic liquids directly upon melting. However, in some cases one or more intermediate phases are formed (called mesophases), where the material retains some ordered structure but already shows the mobility characteristic of a liquid. These materials are liquid crystal (LCs)(or mesogens) of the thermotropic type, and can display several transitions between phases at different temperatures crystal-crystal transition (between solid phases), melting point (solid to first mesophase transition), mesophase-mesophase transition (when several mesophases exist), and clearing point (last mesophase to isotropic liquid transition) [1]. Often the transitions are observed both upon heating and on cooling (enantiotropic transitions), but sometimes they appear only upon cooling (monotropic transitions). 

This chapter describes some of the properties of solids that affect transport across phases and membranes, with an emphasis on biological membranes. Four aspects are addressed. They include a comparison of crystalline and amorphous forms of the drug, transitions between phases, polymorphism, and hydration. With respect to transport, the major effect of each of these properties is on the apparent solubility, which then affects dissolution and consequently transport. There is often an opposite effect on the stability of the material. Generally, highly crystalline substances are more stable but have lower free energy, solubility, and dissolution characteristics than less crystalline substances. In some situations, this lower solubility and consequent dissolution rate will result in reduced bioavailability. 

Some substances undergo transitions between phases even though the outward appearance does not change. Certain solids have multiple phases consisting of different molecular arrangements a transition between these two phases results in considerable internal rearrangement, though the material remains a solid. 

The transitions between phases discussed in Section 10.1 are classed as first-order transitions. Ehrenfest [25] pointed out the possibility of higher-order transitions, so that second-order transitions would be those transitions for which both the Gibbs energy and its first partial derivatives would be continuous at a transition point, but the second partial derivatives would be discontinuous. Under such conditions the entropy and volume would be continuous. However, the heat capacity at constant pressure, the coefficient of expansion, and the coefficient of compressibility would be discontinuous. If we consider two systems, on either side of the transition point but infinitesimally close to it, then the molar entropies of the two systems must be equal. Also, the change of the molar entropies must be the same for a change of temperature or pressure. If we designate the two systems by a prime and a double prime, we have... 

The six possible transitions between phases. What phase changes can occur between solids and liquids ... 

Transitions between phases inclnde evaporation and condensation (liquid to gas and reverse), melting and freezing (liquid to solid and reverse) and sublimation and condensation (solid to gas and reverse). 

Figure 13-18 Some interpretations of phase diagrams, (a) The phase diagram of water. Phase relationships at various points in this diagram are described in the text, (b) Two paths by which a gas can be liquefied. (1) Below the critical temperature. Compressing the sample at constant temperature is represented by the vertical line WZ. Where this line crosses the vapor pressure curve AC, the gas liquefies at that set of conditions, two distinct phases, gas and liquid, are present in equilibrium with each other. These two phases have different properties, for example, different densities. Raising the pressure further results in a completely liquid sample at point Z. (2) Above the critical temperature. Suppose that we instead first warm the gas at constant pressure from W to X, a temperature above its critical temperamre. Then, holding the temperamre constant, we increase the pressure to point Y. Along this path, the sample increases smoothly in density, with no sharp transition between phases. From Y, we then decrease the temperature to reach final point Z, where the sample is clearly a liquid.

N2O4known at ambient pressure [87, 88]. Figure 10 summarizes the pressure-induced transitions between phases with different molecular geometries. 

Predictions of phase diagrams, i.e., calculations of equilibria between solid-solid and solid-liquid phases as functions of temperature and pressure and the development of microscopic (atomic-level) mechanisms for the transitions between phases. 

The transition between phases I and II of CF4 has been studied, using far-i.r. spectroscopic techniques."" As a result, the published X-ray diffraction data for phase II have been reinterpreted in terms of a unit cell with space group C2/c (Z = 4) to give a structure which is consistent with the far-i.r. spectra. A theoretical consideration " of the crystal growth and orientational disorder in CHBr, has also been undertaken. 

Sometimes the transition between phases is very sharp. In other cases there is a considerable rounding off, and one sometimes refers to intermediate phases, i.e., an acceleration phase between the lag and the exponential phases, and a deceleration phase between the exponential phase and the stationary phase. 

Transitions between a solid and a mesophase, or between two mesophases, or between a mesophase and an isotropic liquid, are thermodynamic events and are classified as either first or second order. In liquid crystals, transitions between phases are usually thought of as being weakly first order, although second-order transitions are not uncommon the melting transition is, however, first order. 

Typical enthalpy changes between successive liquid-crystal phases or between a liquid-crystal phase and an isotropic liquid are usually small at around 1 kj mol , while transitions between a crystal and a liquid-crystal phase are strongly first order and often in the range of 30-50 kJ mol . Transitions between phases of the same symmetry are always first order and, while all liquid crystal transitions can be first order, the SmC-SmA and SmA-N transitions... 

Imagine a series of transitions between phases of different symmetry, as shown in Fig. 6.2, for instance, with decreasing temperature. Our task is to select one of these transitions, find the temperature behaviour of the order parameter and other thermodynamic functions close to the phase transition [2]. To this effect, we should make the following steps. 

Figure 4.15 Alternative representations of data from an expression test comprising filtration and consolidation phases the correct transition between phases is represented by the dashed vertical line on each plot.

Figure 5. Response of polar dielectrics (containing local permanent dipoles) to an applied electric field from top to bottom paraelectric, ferroelectric, ferrielectric, antiferroelectric, and helielectric (helical anti-ferroelectric). A pyroelectric in the strict sense hardly responds to a field at all. A paraelectric, antiferro-electric, or helieletric phase shows normal, i.e., linear dielectric behavior and has only one stable, i.e., equilibrium, state for E=0. A ferroelectric as well as a ferrielectric (a subclass of ferroelectric) phase shows the peculiarity of two stable states. These states are polarized in opposite directions ( P) in the absence of an applied field ( =0). The property in a material of having two stable states is called bistability. A single substance may exhibit several of these phases, and temperature changes will provoke observable phase transitions between phases with different polar characteristics.

---