Crystallinity liquid-solid equilibria

The pressure difference between the liquid-solid equilibrium curves for pure and impure materials corresponds to the freezing temperature depression caused by the presence of an impurity. The pressure increase accompanying the increase in pure crystalline material deposited is related to the concentration of impurities in the liquid. With this information, therefore, the mother liquor composition at any stage can be estimated from the system pressure. Consequently, a highly pure solid phase can be obtained by separating the liquid phase from the solid phase while maintaining an appropriate pressure corresponding to the desired solid fraction or mother liquor composition. 

It will be useful now to review some elementary facts regarding the structure of liquids at equilibrium. When a crystalline solid melts to form a liquid, the long range order of the crystal is destroyed. However, a residue of local order persists in the liquid state with a range of several molecular diameters. The local order characteristic of the liquid state is described in terms of a pair correlation function, g-i(R)> defined as the ratio of the average molecular density, p(R), at a distance R from an arbitrary molecule to the mean bulk density, p, of the liquid... 

A number of studies have examined the segregation of an impurity between a liquid phase and crystalline phase at equilibrium (Ratner 1933 Hall 1953 Thurmond and Struthers 1953 Burton, J.A., et al. 1953 Weiser 1958 Rosenberger and Riveros 1974 Sloan and McGhie 1988 Woensdregt et al. 1993 Sangwal et al. 2000 Thomas et al. 2000). The simplest case to consider theoretically is that of a dilute binary mixture of S in a nearly pure component A. If both liquid phase and solid phases are assumed ideal, then at equilibrium at temperature T the distribution across both phases is given by... 

Liquid-Vapor Equilibrium The Boiling Process Water-An "Unusual" Compound The Solid State Types of Crystalline Solids Energy and Change of State Energy and Change of Temperature Specific Heat Change in Temperature Plus Change of State... 

For a substance to dissolve in a liquid, it must be capable of disrupting the solvent structure and permit the bonding of solvent molecules to the solute or its component ions. The forces binding the ions, atoms or molecules in the lattice oppose the tendency of a crystalline solid to enter solution. The solubility of a solid is thus determined by the resultant of these opposing effects. The solubility of a solute in a given solvent is defined as the concentration of that solute in its saturated solution. A saturated solution is one that is in equilibrium with excess solute present. The solution is still referred to as saturated, even... 

Polymerization thermodynamics has been reviewed by Allen and Patrick,323 lvin,JM [vin and Busfield,325 Sawada326 and Busfield/27 In most radical polymerizations, the propagation steps are facile (kp typically > 102 M 1 s l -Section 4.5.2) and highly exothermic. Heats of polymerization (A//,) for addition polymerizations may be measured by analyzing the equilibrium between monomer and polymer or from calorimetric data using standard thermochemical techniques. Data for polymerization of some common monomers are collected in Table 4.10. Entropy of polymerization ( SP) data are more scarce. The scatter in experimental numbers for AHp obtained by different methods appears quite large and direct comparisons are often complicated by effects of the physical state of the monomei-and polymers (i.e whether for solid, liquid or solution, degree of crystallinity of the polymer). 

This equation is called the Clapeyron equation and can be applied to any two phases in equilibrium, e.g., solid and liquid, liquid and vapor, solid and vapor or two crystalline forms of the same solid. Thus for the equilibrium... 

The crystallization process of flexible long-chain molecules is rarely if ever complete. The transition from the entangled liquid-like state where individual chains adopt the random coil conformation, to the crystalline or ordered state, is mainly driven by kinetic rather than thermodynamic factors. During the course of this transition the molecules are unable to fully disentangle, and in the final state liquid-like regions coexist with well-ordered crystalline ones. The fact that solid- (crystalline) and liquid-like (amorphous) regions coexist at temperatures below equilibrium is a violation of Gibb s phase rule. Consequently, a metastable polycrystalline, partially ordered system is the one that actually develops. Semicrystalline polymers are crystalline systems well removed from equilibrium. 

Unlike supercooling of liquids, superheating of crystalline solids is difficult due to nucleation of the liquid at surfaces. However, by suppressing surface melting, superheating to temperatures well above the equilibrium melting temperature has... 

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