Solubility three dimensional

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

Fig. 23. The compatibility sphere delined by the three-dimensional solubility parameters . +, the solubility parameter coordinates of a given polymer , coordinates of solvents showing a high degree of compatibility (e.g., full mi.scibility) with the polymer U, solvents showing a lower degree of compatibility.

Extensive use of the three-dimensional solubility parameters for predicting adhesion seems not to have been made, although its additional flexibility should make it successful over a wider range of conditions than the single-parameter approach. Some recent studies involving dental adhesion employed the method with success. Asmussen and Uno fl40 successfully correlated the shear bond strength of various dental adhesive resins, characterized in terms of their three-... 

There have been many attempts to divide the overall solubility parameter into components corresponding to the several intermolecular forces. For example, a so-called three-dimensional solubility parameter concept is built on the assumption that the ced is an additive function of contributions from dispersion (d), polar (p), and H-bonding (h) forces. It follows that... 

We have limited our treatment to solubility of one polymer in multiple solvent system. Three dimensional solubility parameter... 

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

While the solubility parameter can be used to conduct solubility studies, it is more informative, in dealing with charged polymers such as SPSF, to employ the three dimensional solubility parameter (A7,A8). The solubility parameter of a liquid is related to the total cohesive energy (E) by the equation 6 = (E/V) 2, where V is the molar volume. The total cohesive energy can be broken down into three additive components E = E j + Ep + Ejj, where the three components represent the contributions to E due to dispersion or London forces, permanent dipole-dipole or polar forces, and hydrogen bonding forces, respectively. This relationship is used... 

The three-dimensional solubility parameters are substituted for the solubility parameters in Equation 2.40 to arrive at an expression describing the activity coefLcient in these solutions ... 

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. 

To improve further on this equation, three-dimensional solubility parameters were proposed [45-47] to account for more speciLc interactions that can occur, such as hydrogen bonding. The solubility parameter was divided into three components ... 

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... 

Here 6d, <5p, and <5h are the contributions to the solubility parameter from dispersive forces, dipole-dipole forces, and hydrogen bonding forces, respectively. Since the three forces can occur to varying degrees in different components and can be represented on a three dimensional diagram, this theory is termed the three-dimensional solubility parameter. Barton (1983, 1990) tabulates the contributions to the three dimensional solubility parameter for a variety of solvents and polymers. 

Regular solution theory, the solubility parameter, and the three-dimensional solubility parameters are commonly used in the paints and coatings industry to predict the miscibility of pigments and solvents in polymers. In some applications quantitative predictions have been obtained. Generally, however, the results are only qualitative since entropic effects are not considered, and it is clear that entropic effects are extremely important in polymer solutions. Because of their limited usefulness, a method using solubility parameters is not given in this Handbook. Nevertheless, this approach is still of some use since solubility parameters are reported for a number of groups that are not treated by the more sophisticated models. 

The three-dimensional solubility parameler concept defines the limits of compatibility as a sphere. Values of these parameters for some of the solvents listed earlier in Table 12-3 are given in Table 12-4. More complete lists are available in handbooks and technological encyclopedias. The recommended procedure in conducting a solubility parameter study is to try to dissolve the polymeric solute in a limited number of solvents that are chosen to encompass the range of subsolubility parameters. A three-dimensional plot of solubility then reveals a solubility volume for the particular polymer in 5d, 5p, space. 

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 ... 

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. 

Crowley, J. D. "Some Applications of Three-Dimensional Solubility Parameter Theories," presented at Kent State University, 1972, short course on "Solubility Parameters—Their Origin and Use."... 

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 ... 

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