Flory-Huggins solubility parameter

There are some who question the usefulness of the Flory-Huggins solubility parameter for problems related to the solubilization of polymers, although it is agreed that it is useful for study of the thermodynamics of dilute solutions. Barton (1975) has referred to literature that cites its shortcomings as a practical criterion of solubility. Some of these are ... 

In order to explain the experimental phase diagrams of water-soluble polymers, a number of semiempirical approaches that assume the concentrational dependence of the Flory-Huggins solubility parameter were developed. " " Hie two-state models, which involve equilibtium coexistence of two interconvertible (solvophilic and solvophobic) states of the monomer units, as well as the n-duster model, which assumes temperature-dependent inversion of the higher order virial coeffident, allow to rationalize the apparent concentrational dependence of the solubility parameter in aqueous solutions of water-soluble polymers. 

A completely new approach for the simulation of PE solutions was published by Katz and Leibler in 2009, not by using the Flory-Huggins solubility parameter of the polymer backbone, but instead using the one of the counterions [50]. The concept is logical and overdue, since the solubilization of a PE is caused by the release of the counterions and the resulting gain in entropy. Katz and Leibler were able to show all features observed up to now, such as phase separation, meso- and macro-phases and also the calculation of mixing ratio, depended on structure factors [50]. 

In addition to the solubility parameter model to treat SEC adsorption effects, an approach based on Flory-Huggins interaction parameters has also been proposed (24-27). For an excellent review of both mechanisms, see reference 28.- A general treatment of polymer adsorption onto chromatographic packings can be found in Belenkii and Vilenchik s recent book (29). 

More fundamental treatments of polymer solubility go back to the lattice theory developed independently and almost simultaneously by Flory (13) and Huggins (14) in 1942. By imagining the solvent molecules and polymer chain segments to be distributed on a lattice, they statistically evaluated the entropy of solution. The enthalpy of solution was characterized by %, the Flory-Huggins interaction parameter, which is related to solubility parameters by equation 5. For high molecular weight polymers in monomeric solvents, the Flory-Huggins solubility criterion is x A 0.5. 

We can also summarized a method for calculating the Flory - Huggins interaction parameter, x, for a given polymer and solvent using the solubility parameters 8. 

Section 2 reviewed the relevant contributions to the understanding of polymer swelling and permeation reported by earlier investigators. It also discusses the important parameters that have bearing on these phenomena, namely the Hildebrand Solubility Parameters, 8, the Flory-Huggins Interaction Parameters,... 

The Flory-Huggins interaction parameter (x) and the Wilson parameters (L13 and L31) are considered here adjustable parameters and are calculated from the experimental data regarding the solubility of drugs in aqueous mixed solvents. 

The Flory-Huggins interaction parameter x and the Hildebrand-Scatchard solubility parameter 0 for the polymer may also be calculated using previously described procedures (3). 

Determination of the Flory-Huggins interaction parameter (x) for solvent-polymer pairs again requires careful fractionation of the humic macromolecules. In the view of this author, much can be learned about the ways in which humic substances are associated through determination of Flory-Huggins and solubility parameters of carefully fractionated humic substances, and through applications of empirical equations such as those of Flory-Huggins [Equation (6)] and Hildebrand-Scatchard [Equation (7)]. 

Just a few years ago, the limitations of solubility parameter calculations and measurements discussed above were serious impediments to modeling the phasic and interfacial behaviors of polymeric systems. The coming of age of atomistic simulation methods over the last few years has improved this situation dramatically. As discussed in Section 5.A.3, whenever accuracy is important in calculating the phasic or the interfacial behavior of a system, it is nowadays strongly preferable to use atomistic simulations employing modem force fields of the highest available quality instead of solubility parameters in order to estimate the Flory-Huggins interaction parameters (%) between the system components as input for further calculations. 

The necessary for calculations experimental data (solubility parameters of polymers 6 and solvents Flory-Huggins interaction parameters Xi, the exponents in Mark-Kuhn-Houwink equation) were accepted according to the data of chapters [1, 14, 16,29, 32]. The experimental values of fractal dimension of a macromoleeular coil in diluted solution were determined according to the equation (4). 

If Rab lies below a certain threshold Ro, the substances are predicted to be miscible, i. e.the polymer is predicted to be soluble in the solvent. On the other hand, the solvent will neither dissolve nor swell the solute in case of Rab Ro- Furthermore, the Hansen solubility parameters can be used for estimating the Flory-Huggins interaction parameter of two polymers... 

Molecular weight between two crosslink points = Flory-Huggins interaction parameter = Solubility parameter of solvent... 

It is clear from Equation 14.18 that when the Flory-Huggins interaction parameter, % is <0.5, that is, the chains are in good solvent conditions, is positive, and the interaction is repulsive and increases very rapidly with decreasing h, when the latter is lower than 28. This explains why polymeric surfactants such as Hypermer CG6 (a graft copolymer of polymethylmethacrylate backbone and PEO side chains, produced by ICl) are ideal for stabilizing dispersions in aqueous media. For stabilization of dispersions in nonaqueous media, such as w/o emulsions, the stabilizing chains have to be soluble in the oil phase (normally a hydrocarbon). In this case, polyhydroxystearic acid (PHS) chains are ideal. A polymeric surfactant such as Aralcel P135 (an ABA block copolymer of PHS-PEO-PHS produced by ICl) is an ideal w/o emulsifier. 

Relationship between Flory—Huggins interaction parameter and solubility parameters... 

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