Flory-Huggins theory polymer solubility

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. 

According to the Flory-Huggins theory of polymer solutions, if the mixing process were driven only by an entropic gradient (nonpolar solvent) the solubility coefficient... 

According to Flory-Huggins theory, in the limit of x the critical x parameter is 0.5.(H) Below this value the polymer and solvent will be miscible in all proportions. Above this value, the solvent will not dissolve the polymer, but will act only as a swelling solvent. Thus, the pure solvent may not dissolve the polymer even though it is not crosslinked. If x is not , the critical value of x is larger, but the same qualitative arguments regarding mutual solubility of the solvent and polymer hold. Thus, the application of Equation 1 does not require that the pure solvent be able to completely dissolve the polymer, only that the solvent dissolve into the polymer by an amount that can be measured. 

The Flory-Huggins theory of polymer solutions has been documented elsewhere [26, 27]. The basic parameters necessary to predict polymer miscibility are the solubility parameter 6, the interaction parameter %, and the critical interaction parameter ( ) . 

To calculate AWm (the enthalpy of mixing) the polymer solution is approximated by a mixture of solvent molecules and polymer segments, and AW is estimated from the number of 1,2 contacts, as in Section 12.2.1. The terminology is somewhat different in the Flory-Huggins theory, however. A site in the liquid lattice is assumed to have z nearest neighbors and a line of reasoning similar to that developed above for the solubility parameter model leads to the expression... 

The Flory-Huggins theory has been modified and improved and other models for polymer solution behavior have been presented. Many of these theories are more satisfying intellectually than the solubility parameter model but the latter is still the simplest model for predictive uses. The following discussion will therefore focus mainly on solubility parameter concepts. 

Also, the original Hildebrand approach has been refined to take into account the contribution of polar groups and hydrogen bsolubility parameters. These mndifications of the Flory-Huggins theory and of the solubility parameter concept have made these methods an even more useful tool in the description of solutions, especially of mixtures containing polymer compounds. A comprehensive treatment of these extensions of Flory-Huggins and Hildebrand s theories, as well as the new equation of state approach of Flory (1965), bns re ntly been published (Shinoda, 1978 Olahisi et al 1979). 

The solubility of hydrocarbons in rubbery polymers can be described in more detail by several theories of solutions using various criteria of thermodynamic affinity [7,25-28], of which the Flory-Huggins theory is the most popular one. It takes into account the volume content of the penetrant dissolved in the polymer and the change in the length of the polymer s thermodynamic segment as a result of dissolution [7]. However, it should be pointed out that to describe dissolution, a rehned dual-mode sorption model can be used, e.g., the model by Pace and Datyner [7,29,30]. 

A polymer-like model based on Flory-Huggins theory including different sizes of ions was applied in order to study the effect of ionic size on the solubility. It was found that the size effect can be characterized by introducing effective volumes and that with larger effective volume better solvent power is achieved as expressed by Henry s law constant [153],... 

The solution properties of copolymers are much more compHcated. This is due mainly to the fact that the two copolymer components A and B behave differently in different solvents, and only when the two components are soluble in the same solvent will they exhibit similar solution properties. This is the case, for example for a nonpolar copolymer in a nonpolar solvent. It should also be emphasised that the Flory-Huggins theory was developed for ideal Hnear polymers. Indeed, with branched polymers with a high monomer density (e.g. star-branched polymers), the 0-temperature will depend on the length of the arms, and is in general lower than that of a linear polymer with the same molecular weight. 

This brings us to the question about the applicability of the Flory-Huggins theory for food polymers. For polyelectrolytes, the theory is invalid, unless ionic strength is very high. In Section 7.3 the solubility of proteins will be discussed. Very few polysaccharides are simple homo-... 

FIGURE 6.17 Solubility of a homopolymer according to the Flory-Huggins theory. Variables are the excluded volume parameter ft (or the polymer-solvent interaction parameter y), the net volume fraction of polymer q>, and the polymer-to-solvent molecular volume ratio q. Solid lines denote binodal, the broken line spinodal decomposition. Critical points for decomposition (phase separation) are denoted by . See text. 

The Flory-Huggins theory of polymer solubility suggests that if a polymer is growing in a poor solvent, when it reaches a critical molecular weight, a phase separation will occur in which a polymer-rich or gel phase... 

For the description of such interactions as well as of polymer swelling, models based on the Flory-Huggins Theory (Flory, 1953 Mulder, 1991) and UNIQUAC are often applied for mixtures in general and, for binary mixtures, also the Solubility Parameter Theory if the feed components are hydrophobic (Hildebrand and Scott,... 

Prior to Harwood s work, the existence of a Bootstrap effect in copolymerization was considered but rejected after the failure of efforts to correlate polymer-solvent interaction parameters with observed solvent effects. Kamachi, for instance, estimated the interaction between polymer and solvent by calculating the difference between their solubility parameters. He found that while there was some correlation between polymer-solvent interaction parameters and observed solvent effects for methyl methacrylate, for vinyl acetate there was none. However, it should be noted that evidence for radical-solvent complexes in vinyl acetate systems is fairly strong (see Section 3), so a rejection of a generalized Bootstrap model on the basis of evidence from vinyl acetate polymerization is perhaps unwise. Kratochvil et al." investigated the possible influence of preferential solvation in copolymerizations and concluded that, for systems with weak non-specific interactions, such as STY-MMA, the effect of preferential solvation on kinetics was probably comparable to the experimental error in determining the rate of polymerization ( 5%). Later, Maxwell et al." also concluded that the origin of the Bootstrap effect was not likely to be bulk monomer-polymer thermodynamics since, for a variety of monomers, Flory-Huggins theory predicts that the monomer ratios in the monomer-polymer phase would be equal to that in the bulk phase. 

On polymerization of a dissolved monomer to a soluble polymer, the interactions with the solvent have also to be considered. With the Flory-Huggins theory, the Gibbs polymerization energy is given as ... 

Also a thermodynamic model based on the coupled Equation of State model and Flory-Huggins theory for polymer solutions was developed. The model parameters such as solubility-parameter of asphaltenes, molecular weight of asphaltenes, and molar volume of asphaltenes were obtained by fitting the model to experimental data. 

Let us try to substantiate the solubility equation 55 in terms of Flory-Huggins theory for binary systems. It is reasonable to consider just binary systems as Equation 55 is obtained on polymer fractions. 

The Flory—Huggins theory, which is based upon statistical thermodynamic models, has been used to assess the miscibility of polymer blends and was developed by Flory (1941, 1942) and Huggins (1941,1942) in the 1940s. Unlike the Hildebrand solubility parameter, it provides a fundamental understanding backed with classical thermodynamic theories. 

In this section the basic principles of membrane formation by phase inversion will be described in greater detail. All phase inversion processes are based on the same thermodynamic principles, since the starting point in all cases is a thermodynamically stable solution which is subjected to demixing. Special attention will be paid to the immersion precipitation process with the basic charaaeristic that at least three components are used a polymer, a solvent and a nonsolvent where the solvent and nonsolvent must be miscible with each other. In fact, most of the commercial phase inversion membranes are prepared from multi-component mixtures, but in order to understand the basic principles only three component systems will be considered. An introduction to the thermodynamics of. polymer solutions is first given, a qualitatively useful approach for describing polymer solubility or polymer-penetrant interaction is the solubility parameter theory. A more quantitative description is provided by the Flory-Huggins theory. Other more sophisticated theories have been developed but they will not be considered here. 

In real systems, nonrandom mixing effects, potentially caused by local polymer architecture and interchain forces, can have profound consequences on how intermolecular attractive potentials influence miscibility. Such nonideal effects can lead to large corrections, of both excess entropic and enthalpic origin, to the mean-field Flory-Huggins theory. As discussed in Section IV, for flexible chain blends of prime experimental interest the excess entropic contribution seems very small. Thus, attractive interactions, or enthalpy of mixing effects, are expected to often play a dominant role in determining blend miscibility. In this section we examine these enthalpic effects within the context of thermodynamic pertubation theory for atomistic, semiflexible, and Gaussian thread models. In addition, the validity of a Hildebrand-like molecular solubility parameter approach based on pure component properties is examined. 

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