Solvents polarity-dispersion Hansen

A three-dimensional model is used to plot polymer solubilities by giving the coordinates of the centre of a solubility sphere based on dispersion force components, hydrogen bonding and polar components, and by plotting a radius of interaction of around 2 SI units. A sphere of solution is plotted from the coordinates and radius. Liquids whose parameters lie within the sphere for a particular polymer are likely to be suitable solvents for it (Hansen, 1971). While extensive data has been published for liquids, the number of Hansen solubility parameters for polymers is more limited (Barton, 1983). From tbe selected solubility parameters for liquids and polymers in Table 4.1, it is clear tbat the high value for water excludes it as a solvent for polymers and that polystyrene and poly (methyl methacrylate) should be soluble in acetone. 

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. 

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... 

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 ... 

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. 

The nature of polymer-solvent interactions plays an important role in deciding the influence of chemical and solvent effects on blends. The Hildebrand s solubility parameter, has been extended to systems that have dispersive (subscript d), polar (subscript p) and hydrogen bonding (subscript h) interactions, i.e., 5, 5p, and 5j, respectively [Hildebrand and Scott, 1949 Burrel and Hansen, 1975]. 

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 separation of the cohesion energy into contributions of various forces implies fliat it is possible to substitute energy for parameter and sum contributions proportional to the second power of a difference of corresponding components. Hansen s treatment permits evaluation of the dispersion and polar contribution to cohesive energy. The fitting parameter of the approach (the solubility sphere radius) reflects on the supermolecular structure of polymer-solvent system. Its values should be higher for amorphous polymers and lower for glass or crystalline polymers. 

Hansen firstly determined d for a solvent using the homomorph concept. The energy of vaporisation of a hydrocarbon molecule of the same size and shape as the solvent molecule in question at the same reduced temperature (absolute temperature divided by the critical temperature) is assumed to be that due to dispersion forces existing in the solvent. The difference between the energy of vaporisation of the solvent, AE, and that calculated as the contribution due to dispersion forces, A d, is taken as that due to both polar and hydrogen bonding forces, i.e. ... 

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. 

Charles Hansen introduced the concept of 3D solubility parameters, which offers an extension of the regular solution theory to polar and hydrogen bonding systems. Hansen observed that when the solubility parameter increments of the solvents and polymers are plotted in 3D plots, then the good solvents lie approximately within a sphere of radius R (with the polymer being in the center). This can be mathematically expressed as shown in Equation 3.2. The quantity under the square root is the distance between the solvent and the polymer. Hansen found empirically that a universal value 4 should be added as a factor in the dispersion term to approximately attain the shape of a sphere. This universal factor has been confirmed by many experiments. Hansen in his book provides a review of the method together with extensive tables of parameters. 

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. 

Where 8, 8 and 8, are the solubility parameters corresponding to the non-poiar (dispersion) contribution, polar contribution and hydrogen bond contribution respectively. Values of the Hansen solubility parameter 8 for some common solvents as well as their 8, 8 and 8j vaiues are shown in Table 4.1. In the Hansen system, solvents are represented as a single spot in the three dimensional model, while polymers are represented by a volume. Solvents that have their spot within this volume dissolve the polymer, while solvents lying outside the volume will not. For mixed solvents, a weighted average of the three partial solubility parameters can be calculated. 

Cl, Cj acceptor parameters of solvent and solute, respectively For certain polymers Rider has drawn solubility maps. Thus the area of solubility was represented by a pair of symmetric quarters of a plane lying in coordinates b.C. Values of parameters were defined fi om data for enthalpies of hydrogen bonds available from the earlier works. The model is a logical development of the Hansen method. A shortcoming of this model is in neglecting all other factors influencing solubility, namely dispersion and polar interactions, change of entropy, molecular mass of polymer and its phase condition. The model was developed as a three-dimensional dualistic model (see Section 4.1.5). 4.1.4 HANSEN S SOLUBILITY... 

The solubility parameter may be thought of as a vector in a three-dimensional d-p-h space. The above equation provides the magnitude of this vector. Each solvent and each polymer can be characterized by the three solubility parameter increments , 8, 8p, 8f, due to dispersion, polar and hydrogen bonding forces, respectively. These are often called Hansen solubUity parameters (HSPs). 

Panayiotou s method is based on the so-called PSPs (partial solvation parameters) which he has recently developed and applied in numerous cases (polymer-polymer miscibility, polymer-solvent interactions, solubility parameters, pharmaceuticals, phase equih-biia, etc.) (see Panayiotou, 2012b,c,d, 2013). The PSPs bear similarities with the Hansen solubility parameters presented in Section 3.4.2 but there are four distinct contributions due to dispersion, polarity, acid and base contributions ea, trca, < Gb and, moreover, there are predictive methods for their estimation. 

The Hildebrandt parameter St can be calculated with the three Hansen solubility parameters in consideration of the dispersive Sj, polar 5p, and hydrogen S bonding components. Thus, the interaction between the fatty acids (FA) used as pure substances and bonded onto the magnetite surface (FA Fe304) could be characterized [15, 22]. The calculated values are presented in Table 1 and the following correlation applies The smaller the value, the more soluble is the surfactant in the solvent. 

---