Solute depression, melting temperature

The melting temperature depression or enhancement may now be expressed in terms of the melting temperature and the entropy of fusion of component A, the activity coefficients of impurity B in the liquid and solid solutions at infinite dilution, and the total concentration of the impurity B, xb [12] ... 

As occurs with other crystalline substances, the melting temperature of polymers decreases in the presence of solvents (melting point depression). Thermodynamic arguments lead to expressions that relate the depression of the melting point to the solution concentration. The equation that gives the melting temperature of a polymer solution as a function of the concentration (17) can be written as... 

The addition of small concentrations of solutes to water depresses the equilibrium melting point (a colligative property) and appears in all cases studied to depress the temperature at which nucleation is observed as well. This is discussed in particular by Oguni and Angell with respect to alcohols and related solutes that form hydrogen bonds with the water. They discuss the possibility, based on extrapolations from other solutes, that T may increase slightly with the addition of neopentane, but the proposal is speculative and has not been tested experimentally. 

The enthalpy of melting can be readily determined by non-calorimetric methods. One method involves the determination of the cryoscopic constant of the solvent from the temperature depression observed by the addition of a non-associating solute. The second method, using the Clapeyron equation, involves measuring the volume change on melting for the solvent and the pressure dependence of the melting temperature of the solvent. ... 

Following Eq. (8.12) the freezing point depression is proportional to the cryoscopic constant and the concentration of the solute (m2 (mol/kg)) in the molality scale. Since the cryoscopic constant K ry of the solvent depends on the molar mass, the melting temperature T and the enthalpy of fusion, the various liquids show different values. From Eq. (8.12) it can be seen that the measurement of the freezing point depression allows the determination of the molar mass of unknown compounds, if the melting temperature and the enthalpy of fusion is known. 

Figure 13.5 shows the variation of melting and crystallization temperatures corresponding to each semicrystalline block within PLLA-6-PCL diblock copolymers as a function of composition [34]. For comparison purposes, solution blends of PCL and PLLA homopoljuners of equivalent molecular weights to those of the diblock copolymers were prepared and their characteristic transition temperatures were also reported in Fig. 13.5. This figure shows that the prepared PLLA and PCL blends are immiscible for the compositions examined as can be gathered by the invariance of the melting points associated with each homopolymer. Instead, the diblock copolymers exhibit signs of miscibility. In particular, the melting temperature of the PLLA block decreases as the content of PCL increases, and in the case of the L32C68 sample, the melting point depression of the PLLA block reaches 11°C.

If the steric structures of both comonomer imits in random copolymers are similar, the melting temperature depression equation will be the same as Eq. 1, with the interaction parameter calculated with Eq. 4. For a given copolymer, the crystallizabilities of copolymer chains in dilute solution strongly depend on the chain composition. From thermodynanuc considerations, this can be explained from the fact that changes in copolymer composition alter the value of the interaction parameter de ed by Eq. 4. For copolymers with two chemically similar comonomers, xia will be very dose to xiB, ind Xab will approach zero, hi this system, one can simply use Eq. 1 with Xl = XiA Xib-... 

Let us mention here only one of the earliest applications of DTA/DSC the rapid determination of the impurity (of mostly organic compounds) without the requirement for using a reference material [650,651,662,663], The procedure for quantitative evaluation of purity is based on the thermodynamic relationship for the depression of the melting point by the presence of usually unknown contamination. For the derivation of this procedure, it is assumed that (i) the solute forms an ideal solution upon melting, (ii) the solvent and solute are immisible in the solid phase, (iii) the concentration of impurities can be expressed as a mole fraction of solute and (iv) the enthalpy of fusion of the sample is unchanging over the range of temperatures investigated. 

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