Wypych Handbook of Solvents

This approach has become a constituent of the Hansen approach and has not received a separate development.

Polar interactions can themselves be divided into two types:

•Polar interactions where molecules having permanent dipole moments interact in solution with the dipole orientation in a symmetrical manner. It follows that the geometric mean rule is obeyed for orientation interactions and the contribution of dipole orientations to the cohesive energy and dispersion interactions.

•Polar interactions accompanied by the dipole induction. These interactions are

asymmetrical.

Thus for a pure polar liquid without hydrogen bonds:10

where:

A more traditional approach of contribution of the induction interaction was published elsewhere;11 however, it was used only for the estimation of the common value of the δparameter rather than for evaluation of solubility:

The first method taking into account the hydrogen bonding was proposed by Beerbower et al.,12 who expressed hydrogen bonding energy through the hydrogen bonding number Δν. The data for various solvents were plotted into a diagram with the solubility parameter along the horizontal axis and the hydrogen bonding number Δν along the vertical axis. Data were obtained for a given polymer for suitable solvents. All solvents in which a given polymer was soluble got a certain regions. Lieberman also plotted two-dimensional graphs of solubility parameters versus hydrogen-bonding capabilities.13

On the base of work by Gordy and Stanford, the spectroscopic criterion, related to the extent of the shift to lower frequencies of the OD infrared absorption of deuterated methanol, was selected. It provides a measure of the hydrogen-bonding acceptor power of a solvent.14,15 The spectrum of a deuterated methanol solution in the test solution was compared with that of a solution in benzene and the hydrogen-bonding parameter was defined as

where:

Crowley et al.16 used an extension of this method by including the dipole moment of the solvents. One of the axis represented solubility parameter, the second the dipole moment, and the third hydrogen bonding expressed by spectroscopic parameter γ. Because this method involved an empirical comparison of a number of solvents it was impractical. Nelson et al.17 utilized this approach to hydrogen bond solubility parameters. Hansen (see the next section) developed this method.

Chen introduced a quantity χH 18

where:

δtotal solubility parameter

δd, δp, δh components of the solubility parameter determined by the corresponding contributions to the cohesive energy.

Hansen gave a visual interpretation of his method by means of three-dimensional spheres of solubility, where the center of the sphere has coordinates corresponding to the values of components of solubility parameter of polymer. The sphere can be coupled with a radius to characterize a polymer. All good solvents for particular polymer (each solvent has been represented as a point in a three-dimensional space with coordinates) should be inside the sphere, whereas all non-solvents should be outside the solubility sphere. An example is given in Section 4.1.7.

In the original work these parameters were evaluated by experimental observations of solubility. It was assumed that if each of the solubility parameter components of one liquid is close to the corresponding values of another liquid, then the process of their mixing should readily occur with a more negative free energy. The solubility volume has dimensions δd, δp, 2δh. The factor 2 was proposed to account for the spherical form of solubility volumes and had no physical sense. However, it is necessary to notice that, for example, Lee and Lee31 have evaluated spherical solubility volume of polyimide with good results without using the factor 2. Because of its simplicity, the method has become very popular.

Using the Hansen approach, the solubility of any polymer in solvents (with known Hansen’s parameters of polymer and solvents) can be predicted. The determination of polymer parameters requires evaluation of solubility in a great number of solvents with known values of Hansen parameters. Arbitrary criteria of determination are used because Hansen made no attempts of precise calculations of thermodynamic parameters.

The separation of the cohesion energy into contributions of various forces implies that 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.

The weak point of the approach is the incorrect assignment of the hydrogen bond contribution in the energy exchange that does not permit its use for polymers forming strong hydrogen bonds.

Table 4.1.2. Solubility parameters and their components for solvents (after refs 37,40)

A large number of data were accumulated for different solvents and polymers (see Tables 4.1.1, 4.1.2). A variation of the Hansen method is the approach of Teas.33 He showed for some polymer-solvent systems that it was possible to use fractional cohesive energy densities plotted on a triangular chart to represent solubility limits:

where δ20 = δ2d + δ2p + δ2h

This representation was completely empirical without any theoretical justification. Some correlations between components of solubility parameters and physical parame-

ters of liquids (surface tension, dipole moment, the refraction index) were generalized elsewhere.11

Koenhan and Smolder proposed the following equation applicable to the majority of solvents, except cyclic compounds, acetonitrile, carboxylic acids, and multi-functional alcohols.34

They also proposed a correlation between polar contribution to the solubility parameter and refractive index:

where:

Kpacking parameter

Iionization potential

αmolecular polarizability

Nnumber of molecules in the volume unit

For the estimation of nonpolar component of δ Brown et al.36 proposed the homomorph concept. The homomorph of a polar molecule is the nonpolar molecule most closely resembling it in the size and the structure (e.g., n-butane is the homomorph of n-butyl alcohol). The nonpolar component of the cohesion energy of a polar solvent is taken as the experimentally determined total vaporization energy of the corresponding homomorph at the same reduced temperature (the actual temperature divided by the critical temperature in Kelvin’s scale). For this comparison the molar volumes must also be equal. Blanks and Prausnitz proposed plots of dependencies of dispersion energy density on a molar volume for straight-chain, alicyclic and aromatic hydrocarbons. If the vaporization energies of appropriate hydrocarbons are not known they can be calculated by one of the methods of group contributions (See Chapter 5).

Hansen and Scaarup28 calculated the polar component of solubility parameter using Bottcher’s relation to estimating the contribution of the permanent dipoles to the cohesion energy:

where:

εdielectric constant,

µdipole moment

116 Valery Yu. Senichev, Vasiliy V. Tereshatov

Nnumber of hydroxyl groups in molecule

It should be noted that in Hansen’s approach these contributions are cumulative:

For the calculation of hydrogen-bonding component, δh, Hansen and Scaarup28 proposed an empirical expression based on OH-O bond energy (5000 cal/mol) applicable to alcohols only:

In Subchapter 5.3, the values of all the components of a solubility parameter are calculated using group contributions.

4.1.5 THREE-DIMENSIONAL DUALISTIC MODEL

The heat of mixing of two liquids is expressed by the classical theory of regular polymer solutions using Eq. [4.1.10]. This expression is not adequate for systems with specific interactions. Such interactions are expressed as a product of the donor parameter and the acceptor parameter. The contribution of H-bonding to the enthalpy of mixing can be written in terms of volume units as follows:21

Hence enthalpy of mixing of two liquids per volume unit can be expressed by:32

This equation is used for the calculation of the enthalpy contribution to the Huggins parameter (see Subchapter 4.2) for a polymer-solvent system:

Results of calculations using Eq. [4.1.44] of three-dimension dualistic model coincide with the experimental values of χH and the χH values calculated by other methods.37 Values A, D, and δ′ can been obtained from IR-spectroscopy evaluations and Hansen’s parameters.24,25 Values of the TDM parameters are presented in Tables 4.1.3, 4.1.4. It should be noted that Hansen parameters are used for estimation of values of TDM parameters from

Table 4.1.3. TDM parameters of some solvents. [Adapted, by permission, from V.Yu. Senichev, V.V. Tereshatov , Vysokomol . Soed ., B31 , 216 (1989).]

Table 4.1.4. TDM parameters of some polymers, (MJ/m3)1/2. [Adapted, by permission, from V.Yu. Senichev, V.V. Tereshatov , Vysokomol . Soed ., B31 , 216 (1989)]

δh can be separated into donor and acceptor components using values of enthalpies of the hydrogen bond formation between proton-donors and proton-acceptors. In the absence of such data it is possible to evaluate TDM parameters by means of analysis of parameters of compounds similar in the chemical structure. For example, propyl acetate parameters can been calculated by the interpolation of corresponding parameters of butyl acetate and ethyl acetate,24 parameters of benzene can be calculated by decomposition of δh into acceptor and donor components in the way used for toluene elsewhere.25

The solubility prediction can be made using the relationship between solubility and the χ1 parameter (see Subchapter 4.2). The total value of the χ1 parameter can be evaluated by adding the entropy contribution:

where:

The value of the parameter is inversely proportional to coordination number that is number of molecules of a solvent interacting with a segment of polymer. The value of the entropy contribution to the parameter should be included in solubility calculations. The value χ S = 0.34 is then used in approximate calculations.