Parameter solubility

Solubility parameters are determined by Hansen s iteration method from the 3D solubility parameters of the solvents in which the polymer is miscible [9,10]. In this method, solubility of the polymer in various solvents is initially examined. The plots of the 3D solubility parameters of the solvents (available in the literature [8]) give a 3D spherical space, called Hansen s space . If the distance between any two points is measured by a computation method, then the straight line connecting the two points situated at the longest distance will represent the diameter of the sphere, and the center of the sphere will represent the 3D solubility parameter of the polymer. 

Solubility parameter. Pass and Huglin (92) have measured the solubility parameter of PTHF in several way s. The results for a PTHF prepared with PF5 are given in Table 16. 

Cross-linked PTHF swollen in aliphatic esters 8.6 

The study of the crystallization behavior of PTHF is just beginning. It is now well established from x-ray and other studies that PTHF is a 

The interaction between a polymer and a solvent is often expressed by a solubility parameter. The solubility parameter 5, of substance i is defined as 

Equation 2.42 illustrates that the polymer and the solvent mix when their solubility parameters are close and do not when they differ a lot. However, this is not always the case. For instance, polyethylene and 1,4-dioxane have similar solubility parameters but do not mix partly because of crystallinity of polyethylene. Poly(methyl methacrylate) dissolves well in tetrahydrofuran, although the solubility parameters are greatly different. Furthermore, Eq. 2.42 is always positive. It fails to describe specific interactions that may make x negative such as the hydrogen bonding. We should regard Eq. 2.42 as one of the possible ways to describe x for some polymer-solvent systems. 

Problem 2.17 We apply Flory s method (Section 1.4) to find how much a small deviation from the theta condition changes the end-to-end distance. For this purpose, we express the fiee energy per chain that has an end-to-end distance R by 

Solvents used to cement plastics should be chosen with approximately the same solubility parameter ( ) as the plashc to be bonded. The solubility parameter is the square root cohesive energy density (CED) of the liquid solvent or polymer. It is defined as follows  

A non-polar molecule, such as methane, evaporates readily and is a gas at ordinary temperatures. It has a low CED, hence a low d ( 6). By contrast, a highly polar, associated (hydrogen-bonded) molecule of the same size, such as water, requires high heat input to evaporate it, and consequenhy has a very high 6 of 23.4. Literature sources provide data for s of a number of plashes and resins. A great deal of the data is shown in Tables 9.1 and 9.2. The solubility parameters help explain why polystyrene ( = 9.1) 

Standard Hildebrand values from Hansenl SI Hildebrand values from Hansenl Values in parenthesis from Crowley et all  

When the adherend is an organic compound and is not too polar, the solubility parameter is useful in selecting an adhesive, allowing one to prescreen adhesives 

Material Solubility Parameter, ft (hildebrands) Critical Surface Tension, -j, (dyn cm ) 

For polar substances, the types of interactions, as well as their strength, becomes significant, and selection of a proper adhesive by solubility parameter alone does not always work well. A more general, simple rule for selection of adhesives is like sticks to like. In other word, the greater the chemical similarity between two materials, the larger will be the intermolecular forces between them. 

6) the absolute value of is the most important factor in determining the sign of AG . It is possible to obtain an estimate of the value for AH by using the relation proposed by Hildebrand and Scott [2,6,9,13], assuming AV = 0, 

As polymers are nonvolatile, their solubility parameters cannot be calculated from their physical constants. The 8 for a given polymer may, however, be estimated as the midpoint of known 8 values for solvents that solubilize or swell the polymer [13,14]. As shown schematically in Fig. 1.1, the 8 value range is larger for linear or branched polymers than for cross-linked polymers. 

Some 8 values for well-known polymers are given in Table 1.1 [14,15], and more extensive tables are published elsewhere [6,13,16-18]. Experience shows that a polymer is soluble in a solvent when the difference between 8 values of solvent and polymer is not larger than 25% of polymer 8 value [15]. When mixed solvents are used, their average 8 values are of prime importance in determining their ability to dissolve a given polymer. Thus there is a series of mixed solvents that solubilize certain polymers and that are made of nonsolvents for the same polymers some typical examples are given in Table 1.2 [2]. 

The basic idea behind the use of 5 in identifying the optimum surfactant for stabilizing a particular colloidal system is best illustrated by the following 

Aldehydes and Ketones Methoxy benzene 19.5 T riphenyl phosphate 17.6 

The 8 data for some representative materials are collected in Table 2.3 [15]. The hydrophilicity of compounds increases with increasing 8. The 8 and HLB data for some simple surfactants are summarized in Table 2.4 [15]. What if the 8 data for some materials are not available in the literature Just like the HLB approach, the equation based on the group contribution method for calculating 8 at 25 °C is shown below [16]. 

Considering the emulsification of oil in water, the strategy is to match the hydrophobic and hydrophilic groups of surfactant, respectively, with the oily and continuous aqueous phases. This can be achieved by manipulating the molecular structure of surfactant or by adjusting the composition of one or both phases. When the choice of surfactant is limited, one can adopt the concept of solubility parameter to effectively modify the recipe. As a first approximation, the solubility parameter of a mixture (finux) can be estimated by the following equation  

This section and the next do not fit very logically here, but they fit as well here as any other place in the book and do not deserve a chapter of their own. So far this book has treated equilibrium as an experimental science, in which we use thermodynamics to help us correlate, interpolate, and extrapolate experimental data, without much effort to explain 

Scatchard and Hildebrand suggested that the measure of this force of attraction is 

This is an intuitively satisfying idea. Liquids that have a high latent heat of vaporization require a large energy input to overcome the strong intermolecular attractions to change to a vapor. A more dense liquid (one with a lower value of Vzj must have a higher intermolecular attractive force per unit mass than one with a lower density. They then defined 

They chose this form because in the regular solution theory [9], which they devised to go with the solubUity parameter. 

The internal energy change of vaporization and the liquid volume may be expressed per mol or per gram the molecular weight cancels. The traditional unit of the solubility parameter (sometimes called the Hildebrand parameter) 

---

Taken together, these solvent-solute interactions make up the solvent polarity, which is represented well by Hildebrand s solubility parameter (1950). 

The solubility parameters calculated at 25°C have been tabulated for numerous hydrocarbons in the API technical data book. They can also by calculated by the relationship ... 

The values of common hydrocarbon solubility parameters vary between 300 and 600 (kJ/m3) /2 Several tables are available where the solubility parameters are shown as (cal/cm ) / Jq convert these values, it is necessary to multiply by 64.69. Thus a solubility parameter value of 10 (cal/cm ) / jg equal to 646.9 (kJ/m ) / ... 

Soave m coefficient Solubility parameter at 25°C 0iJ/m ) /2 Temperature n °c Interfacial tension at mN/m Lee Kesier acentric factor... 

The solubility parameter is not calculated directly. It is calculated as the square root of the cohesive energy density. There are a number of group additivity techniques for computing cohesive energy. None of these techniques is best for all polymers. 

Table 8.2 Values of the Cohesive Energy Density (CED) for Some Common Solvents and the Solubility Parameter 6 for These Solvents and Some Common Polymers...

Solubility, aqueous Solubility coefficient Solubility coefficients Solubility diagrams Solubility parameter Solubility parameters Solubility products... 

Table 3. Solubility Parameters of Acrylic Homopolymers Calculated by Small s Method ...

A. F. M. Martin, Handbook of Solubility Parameters and Other Cohesion Parameters, CRC Press, Inc., Boca Raton, Fla., 1983. 

The isolation and/or identification of nonpolymerics has been described, including analyses for residual monomers (90,102,103) and additives (90,104—106). The deterrnination of localized concentrations of additives within the phases of ABS has been reported the partitioning of various additives between the elastomeric and thermoplastic phases of ABS has been shown to correlate with solubility parameter values (41). 

Solubility Parameter. CompatibiHty between hydrocarbon resins and other components in an appHcation can be estimated by the Hildebrand solubiHty parameter (2). In order for materials to be mutually soluble, the free energy of mixing must be negative (3). The solubiHty of a hydrocarbon resin with other polymers or components in a system can be approximated by the similarities in the solubiHty parameters of the resin and the other materials. Tme solubiHty parameters are only available for simple compounds and solvents. However, parameters for more complex materials can be approximated by relative solubiHty comparisons with substances of known solubiHty parameter. 

The Hildebrand Solubility Parameter. This parameter, 4 can be estimated (10) based on data for a set of additive constants, E, for the more common groups ia organic molecules to account for the observed magnitude of the solubiHty parameter d = EE/V where Erepresents molar volume. SolubiHty parameters can be used to classify plasticizers of a given family ia terms of their compatibihty with PVC, but they are of limited use for comparing plasticizers of differeat families, eg, phthalates with adipates. 

C. M. Hansen, The Three-Dimensional Solubility Parameter and Solvent Diffusion Coefficient, Danish Technical Press, Copenhagen, Denmark, 1967. 

Table 1. Solubility Parameter Ranges for Some Commercial PVF and PVB Resins ...

When more than routine water resistance is required, a copolymer vinyl acetate emulsion can be used. The plasticizing comonomer in the polymer particles increases their intrinsic coalescing ability thus, they can coalesce more readily than homopolymer particles to a film that has a higher resistance to water. This resistance to water does not extend to the organic solvents, however, which are better resisted by homopolymer films. The soft copolymers have lower solubility parameters than homopolymers and are more readily attacked by solvents of low polarity, eg, hydrocarbons. 

The solubihty coefficients are more difficult to predict. Although advances are being made, the best method is probably to use a few known solubility coefficients in the polymer to predict others with a simple plot of S vs ( poiy perm Y where and are the solubility parameters of the polymer and permeant respectively. When insufficient data are available, S at 25°C can be estimated with equation 19 where k = 1 and the resulting units of cal/cm are converted to kj /mol by dividing by the polymer density and multiplying by the molecular mass of the permeant and by 4.184 (16). 

When viscometric measurements of ECH homopolymer fractions were obtained in benzene, the nonperturbed dimensions and the steric hindrance parameter were calculated (24). Erom experimental data collected on polymer solubiUty in 39 solvents and intrinsic viscosity measurements in 19 solvents, Hansen (30) model parameters, 5 and 5 could be deterrnined (24). The notation 5 symbolizes the dispersion forces or nonpolar interactions 5 a representation of the sum of 8 (polar interactions) and 8 (hydrogen bonding interactions). The homopolymer is soluble in solvents that have solubility parameters 6 > 7.9, 6 > 5.5, and 0.2 < <5.0 (31). SolubiUty was also determined using a method (32) in which 8 represents the solubiUty parameter... 

Solid-Fluid Equilibria The phase diagrams of binai y mixtures in which the heavier component (tne solute) is normally a solid at the critical temperature of the light component (the solvent) include solid-liquid-vapor (SLV) cui ves which may or may not intersect the LV critical cui ve. The solubility of the solid is vei y sensitive to pressure and temperature in compressible regions where the solvent s density and solubility parameter are highly variable. In contrast, plots of the log of the solubility versus density at constant temperature exhibit fairly simple linear behavior. 

The solubility parameter is thus an experimentally determinable property although special methods are necessary with polymers, which cannot normally be vaporised without decomposition. Such methods are discussed in Section 5.3.3. 

It is the aim of this part of the chapter to show how certain predictions may be made about the solubility of a given material such as a polymer in any given solvent. We have seen that the solubility parameter has given us a measure of and Fbb but the magnitude of F b will have to be considered separately for the following systems ... 

Tables 5.4 and 5.5 predict that unvulcanised natural rubber (8 = 16.5) will be dissolved in toluene (8 = 18.2) and in carbon tetrachloride (8 = 17.5) but not in ethanol (8 = 26.0), all values being in units ofMPa. This is found to be true. Similarly it is found that there is a wide range of solvents for polystyrene in the solubility parameter range 17.2-19.7 MPa. ...

Table 5.5 Solubility parameters and partial polarities (P) of some common solvents...

A comprehensive list of solubility parameters is given in reference 7. 

There are thus no solvents at room temperature for polyethylene, polypropylene, poly-4 methylpent-l-ene, polyacetals and polytetrafluoroethylene. However, as the temperature is raised and approaches F , the FAS term becomes greater than AH and appropriate solvents become effective. Swelling will, however, occur in the amorphous zones of the polymer in the presence of solvents of similar solubility parameter, even at temperatures well below T. ... 

As already mentioned molecules cohere because of the presence of one or more of four types of forces, namely dispersion, dipole, induction and hydrogen bonding forces. In the case of aliphatic hydrocarbons the dispersion forces predominate. Many polymers and solvents, however, are said to be polar because they contain dipoles and these can enhance the total intermolecular attraction. It is generally considered that for solubility in such cases both the solubility parameter and the degree of polarity should match. This latter quality is usually expressed in terms of partial polarity which expresses the fraction of total forces due to the dipole bonds. Some figures for partial polarities of solvents are given in Table 5.5 but there is a serious lack of quantitative data on polymer partial polarities. At the present time a comparison of polarities has to be made on a commonsense rather than a quantitative approach. 

---