Flory Diluent Theory

The FH free energy of liquid-liquid demixing of a crystalline polymer blend (or with polymeric solvent) may be written as [54—58]  

Here (])i = (]) and [ 2 = (1 — 4 ) volume fractions of the crystalline component and amorphous component, respectively r and ri represent the numbers of statistical segments of the polymer chain of crystalline and amorphous constituents, respectively, with Xaa = Xfh = A+B/T, where the FH interaction parameter represents the amorphous-amorphous interaction and A and B are constants. Let us consider a situation where a crystalline polymer is mixed with an amorphous polymer, that is, polymeric solvent. The chemical potential of the liquid phase can be calculated from the Flory-Huggins theory of liquid-liquid mixing for polymer blends as follows  

The complete free energy of the system is expressed as fmix=f + An alternative approach of determining the Gibb s coexistence points is to equate the chemical potentials of each phase simultaneously to their common tangent, which renders the following equation  

Assuming that the solid crystal is pure, that is, (t) =l, then Eq. (4.19) can be reduced to determine an analytical expression of the liquidus line  

From Eqs. (4.17) and (4.18), one obtains the following equation, called the melting 

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The formation mechanism of structure of the crosslinked copolymer in the presence of solvents described on the basis of the Flory-Huggins theory of polymer solutions has been considered by Dusek [1,2]. In accordance with the proposed thermodynamic model [3], the main factors affecting phase separation in the course of heterophase crosslinking polymerization are the thermodynamic quality of the solvent determined by Huggins constant x for the polymer-solvent system and the quantity of the crosslinking agent introduced (polyvinyl comonomers). The theory makes it possible to determine the critical degree of copolymerization at which phase separation takes place. The study of this phenomenon is complex also because the comonomers act as diluents. 

The polymer solubility can be estimated using solubility parameters (11) and the value of the critical oligomer molecular weight can be estimated from the Flory-Huggins theory of polymer solutions (12), but the optimum diluent is still usually chosen empirically. 

In deriving this equation, the chemical potentials in the melt of the two components are given by the Flory-Huggins theory [22]. In Eq. (11.6), Vu and Vi are the molar volumes of the chain repeating unit and diluent, respectively V2 is the volume fraction of polymer in the mixture and Xi is the Flory-Huggins interaction parameter [22]. The implicit assumption is made in deriving Eq. (11.6) that tree is independent of composition. The similarity of Eq. (11.6) to the... 

The melting mechanism of such systems is described by the Flory-Huggins theory of polymer-diluent interaction, which correlates the melting temperature of the dilute polymer (Tm) to that of the undiluted polymer T°ni as a function of the volume... 

Using DSC, Giannotti and Valvassori [96] studied the melting enthalpy of SPS crystals in the presence of diluents by a melting-temperature depression approach. A A// value of 82.4 J/g was obtained, based on Flory s theory of polymer solutions. In contrast, a relatively low value A// = 53.2J/g was... 

Flory, P. J. (1949). Thermodynamics of crystallization in high polymers. IV. A theory of crystalline states and fusion in polymers, copolymers, and their mixtures with diluents. 

Figure 10. Dependence of the reduced equilibrium modulus of POP triol - MDI networks prepared in the presence of diluent. POP triol Mu= 708 stress-strain measurements in the presence of diluent (o) and after evaporation of the diluent ( ). Flory theory for the values of the front factor A indicated, theoretical dependence including trapped interchain constraints Numbers at curves Indicate the value of ry.

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 ... 

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 ... 

So far, the role of phase separation in gelation has been limited to polymers which are regarded as flexible in solution. Thermoreversible gels can be formed from solutions of many rod-like polymers. " Miller et have reviewed the phase separation and networks formed by some rod-like polymers. The nature of the restoring force in such networks of rods must clearly be different from that of a rubber-like, flexible polymer network. However, that network formation occurs via a phase separation remains a possibility. Flory has developed a detailed theory for the liquid crystal-isotropic phase behaviour of rod-like particles in a diluent. 

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... 

The phase separation in the presence of an inert medium occurring during the crosslinked formation was studied using Flory s thermodynamic theory (Dusek and Duskova-Smrckova 2000). Because the monomers themselves act as diluents, phase separation will be strongly influenced by the polymerization time, the phase equilibrium being described by the conversion function. 

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