Melting-point depression, Flory

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. 

A very recent application of the two-dimensional model has been to the crystallization of a random copolymer [171]. The units trying to attach to the growth face are either crystallizable A s or non-crystallizable B s with a Poisson probability based on the comonomer concentration in the melt. This means that the on rate becomes thickness dependent with the effect of a depletion of crystallizable material with increasing thickness. This leads to a maximum lamellar thickness and further to a melting point depression much larger than that obtained by the Flory [172] equilibrium treatment. 

In this study, melting point depression was used to obtain the parameter X12, known as the Flory-Huggins interaction parameter [40] ... 

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 ... 

The heat of fusion, AHu, and the entropy of fusion, ASu can be determined from the crystalline melting point depression caused by solvents, using the equations given by Flory (5) ... 

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

This assumption is based on the fact that the polymer-solvent interaction parameter [see Eq. (8)] of the tributyrin-cellulose tributyrate system, as evaluated from melting-point depressions, is nearly zero at about 100° C [Mandelkern and Flory (160)]. It does not follow, however, that the system is athermal, for the parameter generally involves an entropy contribution. Furthermore, the heat and entropy parts of this parameter vary with the concentration in a complicated way, especially in polar systems [see, for example, Takenaka (243) Zimm (22) Kurata (154)]. Thus it is extremely hazardous to predict dilute solution properties from concentrated solution properties such as the melting-point depression, at least on a highly quantitative level as in the present problem. 

The depression of the melting point of a polymer by the presence of small amounts of comonomer is described by Flory and Eby Flory suggested that the comonomer is relegated to the amorphous regions of the polymer, its presence thus reducing the extension of the crystalline regions. Flory s equation for the melting point depression caused by comonomer B in polymer A reads ... 

Blend Melting Behavior. The melting point depression shown by a miscible, high molecular weight, crystallizable blend component in a high molecular weight diluent can be analyzed by the Flory-Huggins equation... 

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. 

The melting temperature depends on water content, as depicted in Figure 6.24b. This phenomenon is comparable to the melting point depression commonly observed for impure solid materials (e.g., imperfect crystals). Flory has derived an equation for the melting temperature Tm as a function of the volume fraction of polymer q> in concentrated polymer-... 

The DSC results for HyPPS03Na materials demonstrate the existence of low-melting crystals that form when these polymers are maintained at room temperature. The volume fraction of such crystals increases as the degree of sulfonation is increased, but the melting temperature is unaffected by the level of sulfonation. The higher-melting crystallites qualitatively obey the Flory equation for melting-point depression in random copolymers. 

The melting point depression resulting from thermodynamic effects can be described by the following equation [Flory, 1953 Nishi and Wang, 1975] ... 

Melting point depression data are often used to determine the Huggins-Flory interaction parameter, X12 Table 3.11), that is a measure for the miscibility of the blend, i.e., X12 is negative for a miscible blend. A lack of melting point depression means that is zero. Eq 3.39 is only valid for systems in which the crystalline morphology is not affected by the composition. 

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 principles of polymer fractionation by solubility or crystallization in solution have been extensively reviewed on the basis of Hory-Huggins statistical thermodynamic treatment [58,59], which accounts for melting point depression by the presence of solvents. For random copolymers the classical Flory equation [60] applies ... 

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 ... 

A linearizing plot of the melting point depression vs. (I) theoretically starts at the origin. The Flory-Huggins-Staverman interaction parameter X, which depends principally on the temperature and the composition, can be obtained from the slope of equation (9.10). 

In 1949, Flory derived the equation for melting-point depression due to presence or addition of diluents (with the volume fraction 4>i) (Hory 1949), as given by... 

SgConf jjig eonformational entropy per molar struetural unit at Tg h, is also given by rewriting the modified Flory s equation, which expresses the melting point depression as a function of the mole fraction of major component, X, for binary random copolymers " ... 

Miscible CTystaUine/amorphous polymer blends such as PLA/PVC blends have been widely investigated, and oriented crystallization has also been applied to some miscible ciystalline/amorphous polymer blends. For miscible blends containing semicrystaUine polymers, analysis of the melting point depression is widely used to estimate the Flory-Huggins interaction parameter (x). 

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... 

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