Melting point depression, theory

The effect of different types of comonomers on varies. VDC—MA copolymers mote closely obey Flory s melting-point depression theory than do copolymers with VC or AN. Studies have shown that, for the copolymers of VDC with MA, Flory s theory needs modification to include both lamella thickness and surface free energy (69). The VDC—VC and VDC—AN copolymers typically have severe composition drift, therefore most of the comonomer units do not belong to crystallizing chains. Hence, they neither enter the crystal as defects nor cause lamellar thickness to decrease, so the depression of the melting temperature is less than expected. 

Floras melting-point depression theory, 25 700 Flotation... 

When Flory s theory (1953) of melting point depression is applied to starch gelatinization (or phase transition) in the presence of water, the situation can be described as follows. Af equilibrium state, the chemical potentials between amorphous (pu) and crystalline repeating units (p of fwo phases are equal ... 

Application of the Flory-Huggins theory to the melting point depression gives the relationship1... 

Using Flory-Huggins theory it is possible to account for the equilibrium thermodynamic properties of polymer solutions, particularly the fact that polymer solutions show major deviations from ideal solution behavior, as for example, the vapor pressure of solvent above a polymer solution invariably is very much lower than predicted from Raoult s law. The theory also accounts for the phase separation and fractionation behavior of polymer solutions, melting point depressions in crystalline polymers, and swelling of polymer networks. However, the theory is only able to predict general trends and fails to achieve precise agreement with experimental data. 

According to the Flory-Huggins theory, the equilibrium melting point depression can be related to the polymer-polymer interaction parameter, Xi2> by (46,47) ... 

The gel melting data were analyzed using the Flory theory for the melting point depression of a polymer by a diluent [181] so that the fundamental thermodynamic parameters referred to earlier could be evaluated. This theory predicts the following dependence of melting point on the volume fraction of the diluent, which in this case is the solvent ... 

The melting point depression of solid polymers (with no liquid diluent) may be derived from classical solution theory considerations. For ideal solutions of low molecular weight molecules, the equation analogous to equation 3.100 is... 

Equation (9.9), however, only approximately describes the internal dilution of a liquid crystalline copolymer [64]. Here internal means that the diluent is part of the chain and not a second independent component. Nishi and Wang [67] have derived equation (9.10) which describes polymers diluted by polymers. Their extension of the Flory-Huggins-Staverman theory gives the melting point depression ... 

NMR cryoporometry method was developed (Overloop and Van Gerven 1993, Strange et al. 1993, Akporiaye et al. 1994) on the basis of the thermodynamic theory of the phase transition in materials in confined space pioneered by J.W. Gibbs, J. Thomson, and W. Thomson. According to Gibbs-Thomson equation for the melting point depression, A7j , for a small isolated spherical crystal of diameter x in its own liquid can be written as (Jackson and McKenna 1990)... 

The theory of melting point depressions applied to such polymer-diluent systems was first developed by Flory. For polymer blends discussion is now usually based on the subsequent work of Nishi and Wang [40] who derived the expression... 

Predictive models for drug-polymer miscibility have been introduced, and they are largely derived from solution thermodynamics. Lattice-based solution models, such as the F-H theory, can be used to assess miscibility in drug-polymer blends, for which the F-H interaction parameter can be considered as a measure of miscibility. In addition, solubility parameter models can be used for this purpose. The methods used to estimate interaction parameters include melting point depression and the determination of solubility parameters using group contribution theory. 

An alternative method which avoids these problems is to apply the Flory theory of melting point depression of polymer solutions. A crystalline polymer may be in equilibrium with a solution of the same polymer at a temperature Ts, lower than the melting point of the pure polymer Tm. At equilibrium the chemical potentials of the polymer in the two phases must be equal, i. e. ( 2)- This can be expressed as... 

In the course of analyzing experimental results of melting point depressions, recourse will be made to the different expressions that have been developed. It can be expected, however, that with the many expressions available, and the possibility of adding additional terms to the ideal Flory theory, it will be difficult to differentiate whether or not the crystalline phase is pure based solely on melting temperature-composition relations. Except in a few special cases recourse will have to be made to direct physical measurements to determine the composition of the crystalline phase. 

An attempt to quantitatively examine these observations in terms of theory is given in Fig. 7.5. The solid line in this plot is computed from Eq. (7.18) with x i = 0 and neglect of the elastic contribution. For the low values of v, where neither the thermodynamic interaction term nor the elastic term make an appreciable contribution to the melting point depression, the data follows the simplest theoretical expectation. As the polymer concentration in the mixed phase decreases, a contribution to the melting point depression of the omitted terms is expected. Small deviations from the simplified theory are observed. A small positive value of xi believed to be appropriate for this system, brings the observed and calculated values very close... 

The theory of the melting-point depression of crystalline polymers with defects was developed by Flory (/05) and has been applied to copolymers 106,107). According to the theory, the relationship between the equUibrium melting point of a copolymer and that of the corresponding homopolymer is ... 

Experimental tests of the theory have shown that in some cases the correlation between theory and experiment is good 110), but sometimes deviations from dependence occur, and these can be both positive 110) and negative 107,111) the latter may be attributed to the non equilibrium conditions of the crystallization of loi blocks 107) and to the difference between the d/f values for copolymers and homopolymers 111). At any rate, the data on melting point depression make it eaqr to differentiate between random and block copolyn rs erf the same composition 111). 

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