Hansens Three-Dimensional Solubility Parameter

According to Hansen [4—7], the total change in internal energy on vaporization, AE, may be considered as the sum of three individual contributions one due to hydrogen bonds, AE/, another due to permanent dipole interactions, AEp, and a third from dispersion (van der Waals or London) forces, AE  

the solubility parameter 8 may be thought of as a vector in a three-dimensional d, p, and h space. Equation 7.8 gives the magnitude of the vector in terms of its components. A solvent, therefore, with given values of 8pi, Sdi, and Shi is represented as a point in space, with 8 being the vector from the origin to this point. 

A polymer (being denoted as component 2) is then characterized by 8p2, Sd2, and 8h2-Furthermore, it has been found on a purely empirical basis that if 8d is plotted on a scale twice the size as that used for 8 and 8, then all solvents that dissolve that polymer fall within a sphere of radius R surrounding the point (8 2, and 8 2)- 

The three-dimensional equivalent of Equation 7.4 is obtained by calculating the magnitude of the vector from the center of the sphere surrounding the solubility parameters for the polymer (8 2, and 8 2) to the point representing the solvent (8pi,8di, and 8hi). If this is less than R, the polymer is deemed soluble  

The range of 8Js spanned by typical polymers and solvents is rather small. In practice, therefore, the three-dimensional scheme is often reduced to two dimensions, with polymers and solvents represented on 8f,—8p coordinates with a polymer solubility circle of radius R. 

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C.M. Hansen, Three Dimensional Solubility Parameters and Solvent Diffusion Coefficient, Danish Technical Press, Cc ienhagen, 1967. 

Hildebrand solubility parameter Hansen three-dimensional solubility parameter Hydrogen bonding in polymer blends Association model Combinatorial entropy Chemical and physical forces Equilibrium rate constant... 

Hansen CM (1967) The Three Dimensional Solubility Parameter - Key to Paint Component Affinities I. J Paint Technol 39 104... 

In addition, the theoretical equations in the Hildebrand and Hansen approaches can be effectively applied to predicting the solubility of a new compound by employing the experimental solubility data of a structurally related compound. The predicted values for the new compound would be based on the experimental one- or three-dimensional solubility parameter of the structurally related compound, and the group additivity principles would be applied to estimate the respective solubility parameter of the second compound. Solubility parameters associated with the Hildebrand and Hansen approaches have proved useful in the selection of not only solvents, but also of other excipients found in formulations (Belmares et al., 2004). 

Hansen, C. M. 1967. The three dimensional solubility parameter. Key to paint component af nities I. Solvents, plasticizers, polymers, and resiials.PaintTechnol39 104-117. 

The solvating strength of a plasticiser for PVC is a measure of the interactive forces between these two materials. Hansen s three-dimensional solubility parameters provide a quantitative measure of these... 

Hansen CM. The three-dimensional solubility parameter— key to paint component affinities. J. Paint Tech. 1967 39(505) 104—117. Rogers CE. Permeation of gases and vapors in Polymers. In Comyn J. ed.. Polymer Permeability. New York Elsevier Applied... 

Modifications to the Hildebrand solubility parameter model have been advanced in attempts to achieve better degrees of solubility prediction (Taft et al., 1969 Rohrschneider, 1973). Among these, the three-dimensional solubility parameter introduced by Hansen and Beerbower (1971) showed the most practical application. These workers calculated the total solubility parameter (5totai) using three partial parameters, 3d, 3p, and 3h ... 

Hansen, C. M. "The Three Dimensional Solubility Parameter and Solvent Diffusion Coefficient. Their Importance in Surface Coating Formulation" Danish Technical Press Copenhagen 1967. 

BurreU, H., Solubility parameters for film formers, Off. Dig., 27(369), 726-758, 1972 BurreU, H., A solvent formulating chart. Off. Dig., 29(394), 1159-1173, 1957 Burrell, H., The use of the solubility parameter concept in the United States, VI Federation d Associations de Techniciens des Industries des Peintures, Vemis, Emawc et Encres d Imprimerie de VEurope Continentale, Congress Book, 1962, 21-30. Hansen, C.M., The three dimensional solubility parameter-key to paint component affinities 1, J. Paint TechnoL, 39(505), 104-117, 1967. 

Hansen, C.M., The three dimensional solubility parameter — key to paint component affinities II, J. Paint TechnoL, 39(511), 505-510, 1967. 

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... 

Summaries of three-dimensional solubility parameters are given by Hansen and Beerbower (21) and by Hoy (22). A problem that now arises, however, and that is of real significance, is the fact that the three-dimensional parameters tabulated by Hansen and Beerbower and by Hoy do not always agree. This disagreement is illustrated in Table I for three common solvents, chosen at random from the source tables. An additional problem, noted by Hansen, is that the homomorph concept for estimating 6j fails in cases of solvents containing chlorine or sulfur atoms, and, in addition, homomorphs for cyclic compounds are hard to find. 

The quantities Cjj and C221 by this interpretation, thus become directly measurable experimentally through the Internal pressures of the pure components at total system pressures not too far removed from atmospheric. Furthermore, from this interpretation, a two-dimensional solubility parameter concept emerges. One of these, 6y, is a solubility parameter evaluated from and includes the volume dependent terms in the total liquid state energy expression the second is termed a residual solubility parameter, 6j-, evaluated as the difference between for a component and AE. Both 6y and 61-are thus directly measured on the pure components (25) and are related to Hansen s three-dimensional solubility parameters by Equations 15 and 16. 

Hildebrand applied the solubility parameter approach to mixing of two polymers, to estimate the enthalpy of mixing per unit volume [Hildebrand and Scott, 1964]. The concept was extended to incorporate the polar and hydrogen bonding interactions [Hansen, 1967, 1969 Nelson et al., 1970]. Thus, the three-dimensional solubility parameter was expressed as ... 

Hansen CM. The three dimensional solubility parameter and solvent diffusion coefficient. Their importance in surface coating formulation [PhD thesis]. Technical University of Denmark Copenhagen 1967. 

Miscible blends are most commonly formed from elastomers with similar three-dimensional (Hansen, 1967a,b Hansen and Beerbower, 1971) solubility parameters. An example of this is blends from copolymer elastomers (e.g., ethylene-propylene or styrene-butadiene copolymers) of slightly different composition, or microstructure. When the forces between the components of the polymer blend are mostly dispersive, miscibility is only achieved in neat polymers with a very close match in Hansen s three-dimensional solubility parameter (Hansen, 1967a,b Hansen and Beerbower, 1971), such that small combinatorial entropy for high molecular weight elastomers can drive miscibility. 

Hansen CM. 1967. The three-dimensional solubility parameter—Key to paint component affinities. J. Paint Technol 39(505) 104-117. 

Where such a program is available, in principle the following steps have to be taken. For the design of a completely new solvent system, the solubility sphere within a three-dimensional solubility parameter system should either be known or has to be constructed for the solute in question. As a simplification, a solubility map described in the chapter on solvent power (Figure 2.10) may be used [10]. For many polymeric materials these data already exist for the Nelson, Hemwall and Edwards or the Hansen solubility parameter concepts. Alternatively as described in section 2.2 a sphere or map can be constructed. Once the area of solubility is known, suitable solvent blends can be designed with solubility parameters falling within this area. When one has to choose one of the above concepts it should be noted that the idea of a sphere of... 

For more general solution systems containing polar molecules, Hansen proposed the concept of three-dimensional solubility parameter, as given by... 

Hansen CM (1967) Three dimensional solubility parameters and solvent diffusion coefficients. Danish Technology Press, Copenhagen... 

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