Polarity-dispersion Hansen parameter

Figure 2. Polarity-dispersion Hansen parameter map (Reproduced with permission from reference 1. Copyright 2002 Elsevier.)...

The dispersive Hansen parameter treats the molar attraction constants as additive. The polar Hansen parameters also are additive, unless more than one polar group is present. Methods for treating additional polar groups are given in... 

In an attempt to improve on the Hildebrand parameter and take into account the range of intermolecular interactions present in the majority of real fluids, there have been a number of multi-contribution derivations of the Hildebrand parameter (4). Probably the best known of these are the Hansen parameters where the Hildebrand parameter is broken down into three intermolecular contributions - dispersion forces, polar forces and hydrogen bonding forces ... 

The many theories behind the various models developed to calculate the solubility of polymers, and to predict the ability of liquids to dissolve them, are described clearly and in high detail by Burke (Burke, 1984). All define a term known as solubility parameter for liquids and polymers using one or more of the intermolecular force components and represent the parameter in two or three dimensions. Calculating solubility parameters is a mathematically complex process which will not be discussed here. The most widely used method today for predicting whether a polymer is soluble in a liquid was developed by Charles M. Hansen in 1966. Hansen parameters ( ) for solvents and polymers are calculated from the dispersion force component ( d), polar component ((5p) and hydrogen bonding component ( h) for each using the formula ... 

The Hansen parameters are additive. The numerical values for the component solubility parameters are determined in a stepwise fashion. The homograph method can be used to obtain the dispersive component. The homomorph of a polar molecule is the nonpolar molecular closely resembling it in size and structure. The Hildebrandt value for the nonpolar homograph due to dispersive forces is assigned to the polar molecule as its dispersion component value. The square of the dispersion component is subtracted from the Hildebrandt value squared. The remainder represents the polar interaction between the molecules. By trial and error, and by use of numerous solvents and polymers, Hansen separated the polar value into polar and hydrogen bonding component parameters from the best fit of experimental data. Further, he derived polymer solubilities. The spherical volume of solubility was formed for each polymer by doubling the dispersion parameter axis. An interaction radius was defined. The solubility parameter values for some polymers are provided in Table 4.1. 

There are two PSP schemes, the s and the o-scheme. The two schemes have identical hydrogen bonding parameters but they differ in the way they partition the non-hydrogen-bonding interactions of the molecule. In the s-scheme this partitioning leads to the dispersion, and polar, Sp PSP, which are equivalent to the more familiar Hansen s dispersion solubility parameter, 5j, and polar solubility parameter, 5, respectively [25], In the o-scheme the partitioning leads to the van der Waals, o, and polarity/polarizability, o PSP. The van der Waals PSP is, simply, the weak van der Waals energy density ... 

The minimum in fractal dimension is mainly due to the polar contribution of the solubility Hildebrand parameter. This can be proved by the reproducibility of the minimum when the polar solubility parameter of Hansen is used, while no correlation between fractal dimension and the dispersive or hydrogen bond Hansen parameters can be found [69]. Moreover a similar tendency, but oppositely now showing a maximum, can hold for the glass transition temperature of the resulting membrane [67], as shown in Figure 5.9 with a very similar extremal Hildebrand parameter. The maximum glass transition temperature, or minimum fractal dimension, appears at a solvent Hildebrand parameter that very finely estimates that of the polymer. 

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... 

Paine et al. [85] extensively studied the effect of solvent in the dispersion polymerization of styrene in the polar media. In their study, the dispersion polymerization of styrene was carried out by changing the dispersion medium. They used hydroxypropyl cellulose (HPC) as the stabilizer and its concentration was fixed to 1.5% within a series of -alcohols tried as the dispersion media. The particle size increased from only 2.0 /itm in methanol to about 8.3 /itm in pentanol, and then decreased back to 1 ixm in octadecanol. The particle size values plotted against the Hansen solubility parameters... 

Hansen [28,29] expanded this theory by dividing the cohesive forces of liquids into three components—dispersive (d), polar (p) and hydrogen bonding (h) forces—and defined the three component solubihty parameter 3o as ... 

The nucleation mechanism of dispersion polymerization of low molecular weight monomers in the presence of classical stabilizers was investigated in detail by several groups [2,6,7]. It was, for example, reported that the particle size increased with increasing amount of water in the continuous phase (water/eth-anol), the final latex radius in their dispersion system being inversely proportional to the solubility parameter of the medium [8]. In contrast, Paine et al.[7] reported that the final particle diameter showed a maximum when Hansen polarity and the hydrogen-bonding term in the solubility parameter were close to those of steric stabilizer. 

The solubility parameter is valid only for regular solutions (where the excess entropy is equal to zero) and mainly for nonpolar classes of substances. Of the numerous suggested improvements that have been made, the one by Hansen is worth mentioning. Here the solubility parameter is the sum of three parts (Barton, 1983) corresponding to a nonpolar or pure dispersive (8,/), polar (8P) and hydrogen bonding (8/,) based interactions ... 

More commonly used descriptors of polymer solubility are the solubility parameters introduced by Hildebrand and Scott for dispersive interaction forces, and extended by Hansen " for dispersive (8 ), polar (8d), and hydrogen bonding contributions (8 ) to interaction energies. An equation sometimes used to estimate the solubility range of Polymer 2 in a solvent (subscript 1) is ... 

A number of methods based on regular solution theory also are available. Only pure-component parameters are needed to make estimates, so they may be applied when UNIFAC group-interaction parameters are not available. The Hansen solubility parameter model divides the Hildebrand solubility parameter into three parts to obtain parameters 8d, 5p, and 5 accounting for nonpolar (dispersion), polar, and hydrogenbonding effects [Hansen,/. Paint Technot, 39, pp. 104-117 (1967)]) An activity coefficient may be estimated by using an equation of the form... 

A variety of parameters used to describe the polar interactions, dispersive forces and hydrogen bonding of molecules have been introduced. All of these parameters represent forces of attraction and were originally derived for low molecular weight compounds. Because the interactions between two molecules can be the result of a combination of all or any of these three force types, it is most convenient to select one parameter or a set of related parameters capable of dealing with all three forces. The Hansen cohesive energy parameter or solubility parameter, 6, with... 

The most comprehensive approach to resin solubilities has been that of Hansen [19] in which the solubility parameter is divided into three components. The basis of this three-dimensional solubility parameter system is the assumption that the energy of evaporation, i.e., the total cohesive energy AjEJt which holds a liquid together, can be divided into contribution from dispersion (London) forces ABd, polar forces AEp, and hydrogenbonding forces AEh- Thus,... 

The polarity of the oil can be estimated from Hansen s three-dimensional solubility parameters. Hansen separated Hildebrand s solubility parameter into three independent components < d for the dispersion contribution, polar contribution, and 51, for the H-bonding contribution. As an estimation of the oil polarity, we define Dpi, as the square root of the square of the polar component plus the... 

Recently, Bagley (4, 5) confirmed Hansen s approach by measuring directly the internal pressure of several solvents. The solubility parameters Bagley obtained corresponded closely to the sum of the dispersion and polar forces that Hansen proposed,... 

Hansen (86) has modified the method of Nelson, et al. by incorporating solubility parameters for the three component forces in the solubility parameter, viz, dispersion, polar, and hydrogen bonding forces. The solvent selection procedure was designed for use by plant laboratories on a time sharing terminal. The enlistment of the computer in the selection of solvent blends has been a boon to the formulator, but the use of older methods is still very useful. 

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