Solubility parameter theory , polymer

Values of 6 for many liquids have been reported, and these have been recorded in extensive Tables [27, 28, 32, 34, 56-59]. The availability of these data provide an easy means of estimating 8. The solubility parameter theory also has serious shortcomings, however, which limits further the reliability of thermodynamic properties computed by the combination of both theories. Nevertheless it does provide useful qualitative, if not quantitative, descriptions of polymer-solvent systems. 

Guillet and coworkers (8-10) have determined the solubility parameter of polymers from the probe-polymer interaction coefficients. They separated the interaction parameter into entropic and enthalpic contributions, such that Xi2=X h+Xs to yield, in combination with Hildebrand s solution theory, the following expression ... 

When this theory was used to predict the solubility of polymers in a variety of solvents, it was only partially successful. It was apparent that other intermolecular forces were at work which could not be calculated by this simple procedure. Hydrogen bonding, probably the strongest type of intermolecular force in a nonelectrolyte, was the clue for making solubility parameter theory work. 

Ideally, Xi is a measure of the heat of mixing of the sorbed molecules with the polymer the less endothermic this process is, the greater the extent of sorption will be. For nonpolar components, the interaction parameter can be estimated by using solubility parameter theory... 

Complications such as these extend also to the case of polytetra-fluoroethylene. The large difference in estimated solid-vacuum tensions between this polymer and polyethylene is not imexpected, since a proportionately large difference exists for the liquid surface tensions of hydrocarbons and fluorocarbons having five to eight carbon atoms [58]. The underlying cause of this difference is, however, more obscure. The inter molecular forces for fluorocarbons apparently have features wuich lead to anomalous behavior, at least from the point of view of solubility parameter theory [59]. Thus, theoretical calculations of the surface tension for the bare solid in the case of polytetrafluoroethylene would face a number of difficulties not encountered with paraffin crystals. 

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,... 

When Gjj / e < 1 then 8j < 82 and hence dX, / dP < Oin the solubility parameters theory and in the eorresponding states theory. When ej, / 22 is greater than unity 8j > 82 and the solvent becomes less compressible than the polymer. Then pressure ean inerease the (5j - 82) value, giving / dP > 0. 

It is not possible to determine solubility parameters of polymers by direct measurement of evaporation enthalpy. For this reason, all methods are indirect. The underlining principles of these methods are based on the theory of regular solutions that assumes that the best mutual dissolution of substances is observed at the equal values of solubility parameters (see Chapter 4). 

Evaluation of solubility parameters of polymers by direct methods is not possible. All the methods of evaluation of polymers solubility parameters are indirect. The assumption of the solutions theory in which the best mutual dissolution of substances is observed when solubility parameters are equal serves as the basis for indirect methods (see 6.2.1). 

A basic assumption of solubility parameter theory is that a correlation exists between the CED of pure substances and their mutual solubility. Therefore, Eq.(6) predicts that = 0 if 6p = 6 hence, two substances with equal solubUity parameters should be mutually soluble. This is in accordance with the general rule that chemical and structural similarities favor solubility. Therefore, the relative affinity of a polymer and solvent can be assessed using solubUity parameters. 

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. 

A special feature in this book is the inclusion of the Hansen solubility parameter theory that can be used to classify solvents in terms of their nonpolar, polar and hydrogen bonding characteristics. Use of the Hansen solubility parameter theory will allow the worker to systematically search for a solvent substitute or determine the solubility of a resin/polymer in a certain solvent or solvent blend. The files necessary to construct computer spreadsheets that can utilize the Hansen solubility parameter theory are included with this book. The useful spreadsheet files on a computer disk are included in a plastic pocket on the back inside cover of the book. These files can be used on an IBM-compatible computer with Lotus 123 (or Excel) software. These computer spreadsheets were developed in the Lotus 123. WKl file format. The data files can be used with the Lotus 123 Version 5.0 for Windows, the Microsoft Excel Version 5.0 for Windows or any earlier version of the spreadsheet software. The files can also be translated into the Macintosh Excel format if the correct version of Excel is available. The coating industry will find the information on solvent substitution using the Hansen solubility parameter theory of particular interest. The use of computer spreadsheets to compare the solubility envelope of the polymer with likely solvent candidates has been very helpful to the author in past work and others in the coating in selecting substitute solvents or solvent blends. The Hansen solubility parameter values for 166 resins and polymers and 289 solvents are listed. 

Selection of a suitable solvent or blend for an industrial process or for determination of a resin or polymer solubility characteristics can make use of the Hansen solubility parameter theory. The solvent selection rules are applied by calculating the solubility parameters of the solvent or solvent blend to be replaced and then selecting new solvents that have similar solubility parameters. The concept is that the total solubility parameter value can be represented as a dispersion (nonpolar) 6, a polar 6, and a hydrogen-bonding 6 component. The total solubility parameter can be mathematically expressed as the square root of the sum of the squares of the nonpolar, polar, and hydrogen-bonding components as shown in Equation 1.1. 

Other uses of the solubility parameter theory include pigment-solvent interactions in terms of suspension behavior, the compatibility of plasticizers and polymers, the critical strain behavior of commercial plastics in the presence of solvents, the effects of solvents on other mechanical properties of the polymers and the affinities of organic solvents in biological systems. Equation 1.3, which uses the three partial Hansen solubility parameters, can be used to estimate the surface tension of a liquid. 

A separate list of resin and polymer solubility parameters are available from another Barton publication [5] and are discussed in Chapter 5. Archer [6] discussed the use of the Hansen solubility parameter theory to reformulate a solvent-based coating. The following example demonstrates the usefulness of the Hansen method. Neither xylene nor methanol are good solvents for a D.E.N. epoxy novolac 438 resin. However, calculations suggested that a 50 50 (by volume) solvent blend should be able to dissolve the epoxy resin. Using the Hansen parameters for xylene and methanol from Table 4.1 the solubility parameters for the 50 50 blend were calculated as follows ... 

Coating and paint formulations, adhesives, polymer-plasticizer compatibility and solvent effects on plastic surfaces are only a few of the areas that can benefit from the Hansen solubility parameter theory. Hansen [1] extended the solubility concepts discussed in Chapter 4 to include resin and polymeric materials. The total solubility parameter of a polymer is the point in three-dimensional space where the three partial solubility parameter vectors meet as the center point of the idealized spherical envelope. The distance in space between the two sets of parameters (solvent and polymer) can be represented by the term, radius of interaction or R. The radius of interaction term is used to express the degree of mutual solubility. All of these solubility comparisons can be made by using computer spreadsheets that are described in Chapters 4, 19, and this chapter. 

The Hansen solubility parameter theory can be used to classify solvents in terms of their nonpolar, polar and hydrogen bonding characteristics. Use of the theory allows one to systematically search for a solvent substitute or to determine the solubility of a resin/polymer in a certain solvent or solvent blend. For example, the theory can be applied to identifying a suitable solvent substitute whereby a more environmentally friendly or less toxic solvent may be substituted for in a particular application. 

Originally the solubility parameter theory was established to study the heats of mixing for nonpolar liquids (30,31) later on it was also employed to polymer solutions. The improjjer assumption that the Floiy-Huggins interaction parameter is exclusively of enthalpic origin yields the following simple expression... 

Of particular interest is the fact that two plasticisers of similar molecular weight and solubility parameter can, when blended with polymers, lead to compounds of greatly differing properties. Many explanations have been offered of which the most widely quoted are the polar theory and the hydrogen bonding theory. 

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. 

Molecularly motivated empiricisms, such as the solubility parameter concept, have been valuable in dealing with mixtures of weakly interacting small molecules where surface forces are small. However, they are completely inadequate for mixtures that involve macromolecules, associating entities like surfactants, and rod-like or plate-like species that can form ordered phases. New theories and models are needed to describe and understand these systems. This is an active research area where advances could lead to better understanding of the dynamics of polymers and colloids in solution, the rheological and mechanical properties of these solutions, and, more generally, the fluid mechaiucs of non-Newtonian liquids. 

Various models of SFE have been published, which aim at understanding the kinetics of the processes. For many dynamic extractions of compounds from solid matrices, e.g. for additives in polymers, the analytes are present in small amounts in the matrix and during extraction their concentration in the SCF is well below the solubility limit. The rate of extraction is then not determined principally by solubility, but by the rate of mass transfer out of the matrix. Supercritical gas extraction usually falls very clearly into the class of purely diffusional operations. Gere et al. [285] have reported the physico-chemical principles that are the foundation of theory and practice of SCF analytical techniques. The authors stress in particular the use of intrinsic solubility parameters (such as the Hildebrand solubility parameter 5), in relation to the solubility of analytes in SCFs and optimisation of SFE conditions. 

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