Solubility parameter estimation

What is the difference in the solubility parameter estimate of a copolymer with alternating sequence distribution and random sequence distribution with the same composition ... 

What is the effect of the glass transition temperature on the Hildebrandt solubility parameter estimate of the polymer ... 

Solubility parameter estimation and differential scanning calorimetry (DSC) help assess the drugipolymer miscibility and determine drug loading. 

Recently [57], our previous approach to solubility parameter estimation [120,121] was extended, in an effort to account for all three components of the solubility parameter. This was done by adopting the NRHB EoS framework, modified in order to explicitly account for dipole-dipole interactions and, thus, explicitly calculate the polar component, 5. In what follows, we summarize these developments and show some representative applications. 

Zeller (13 1) reviewed graphical three-dimensional solubility parameter estimation methods (12,14,49,55,172,173) as applied to solvent swelling of crosslinked elastomers. In general, the graphical method (Eqs. B22 and B23) does not account for the known influence of molar volume and crosslink density of solubility, and incorrectly assumes a linear relationship between the solubility parameter difference and solubility. An improved method used the Flory-Rehner equation to modify the interaction parameter for the effects of crosslink density (132). 

To illustrate the criterion for parameter estimation, let 1, 2, and 3 represent the three components in a mixture. Components 1 and 2 are only partially miscible components 1 and 3, as well as components 2 and 3 are totally miscible. The two binary parameters for the 1-2 binary are determined from mutual-solubility data and remain fixed. Initial estimates of the four binary parameters for the two completely miscible binaries, 1-3 and 2-3, are determined from sets of binary vapor-liquid equilibrium (VLE) data. The final values of these parameters are then obtained by fitting both sets of binary vapor-liquid equilibrium data simultaneously with the limited ternary tie-line data. 

Thus, a list of 1 5 descriptors was calculated for these purposes, as described below. The partition coefficient log P (calculated by a method based on the Gho.sc/Crip-pen approach [11]) (see also Chapter X, Section 1.1 in the Handbook) was calculated because it affects the solubility dramatically [17, 18]. All the other descriptors were calculated with the program PETRA (Parameter Estimation for the Treatment of Reactivity Applications) [28. ... 

Solubility Parameter. CompatibiHty between hydrocarbon resins and other components in an appHcation can be estimated by the Hildebrand solubiHty parameter (2). In order for materials to be mutually soluble, the free energy of mixing must be negative (3). The solubiHty of a hydrocarbon resin with other polymers or components in a system can be approximated by the similarities in the solubiHty parameters of the resin and the other materials. Tme solubiHty parameters are only available for simple compounds and solvents. However, parameters for more complex materials can be approximated by relative solubiHty comparisons with substances of known solubiHty parameter. 

The Hildebrand Solubility Parameter. This parameter, 4 can be estimated (10) based on data for a set of additive constants, E, for the more common groups ia organic molecules to account for the observed magnitude of the solubiHty parameter d = EE/V where Erepresents molar volume. SolubiHty parameters can be used to classify plasticizers of a given family ia terms of their compatibihty with PVC, but they are of limited use for comparing plasticizers of differeat families, eg, phthalates with adipates. 

The solubihty coefficients are more difficult to predict. Although advances are being made, the best method is probably to use a few known solubility coefficients in the polymer to predict others with a simple plot of S vs ( poiy perm Y where and are the solubility parameters of the polymer and permeant respectively. When insufficient data are available, S at 25°C can be estimated with equation 19 where k = 1 and the resulting units of cal/cm are converted to kj /mol by dividing by the polymer density and multiplying by the molecular mass of the permeant and by 4.184 (16). 

Plasticizers reduce hardness, enhance tack and reduce cost in rubber base adhesive formulations. A plasticizer must be easily miscible and highly compatible with other ingredients in the formulations and with the surfaces to which the adhesive is applied. The compatibility and miscibility of plasticizers can be estimated from the solubility parameter values. Most of plasticizers have solubility parameters ranging between 8.5 and 10.5 hildebrands. However, the high miscibility and compatibility also lead to easier diffusion of the plasticizer to the surface, decreasing the adhesion properties. Therefore, plasticizers should be carefully selected and generally combinations of two or more of them are used. 

The polymer solubility can be estimated using solubility parameters (11) and the value of the critical oligomer molecular weight can be estimated from the Flory-Huggins theory of polymer solutions (12), but the optimum diluent is still usually chosen empirically. 

Absorption rates of carbon dioxide were measured in organic solutions of glycidyl methacrylate at 101.3 kPa to obtain the reaction kinetics between carbon dioxide and glycidyl methacrylate using tricaprylylmethylammonium chloride(Aliquat 336) as catalysts. The reaction rate constants were estimated by the mass transfer mechanism accompanied by the pseudo-first-order fast reaction. An empirical correlation between the reaction rate constants and the solubility parameters of solvents, such as toluene, A-methyl-2-pirrolidinone, and dimethyl sulfoxide was presented. 

The polymer-solvent interaction parameter can be estimated by using the solubility parameters for the polymer and solvent. An approximate relationship between these parameters is... 

It is helpful in lc to have a quantitative measure of polarity, so that, for example, the relative polarity of a solvent or a mixture of solvents can be expressed as a number. There are several ways in which this has been done none of them are entirely satisfactory, but they do allow us to arrange solvents in order of polarity and to make rough estimates of the polarity of solvent mixtures. One such way is to use as a measure of polarity a quantity called the solubility parameter, 6, defined by ... 

Although being qualitatively in agreement with experimental results, disagreements between experiment and theory remain. Besides the composition, /a, and the total degree of polymerization, N, all theoretical works refer to the segmental interaction parameter x This parameter can be estimated from a relationship to the solubility parameters. The ODT as a thermodynamic measure of the incompatibility was used to compare a set of symmetrically composed diblock copolymers from different hydrocarbons, polydimethyl-siloxane and poly(ethylene oxide) (PEO) [33]. While the behaviour of hydrocarbon diblock copolymers was successfully described by a consistent set of solubility parameters, this procedure failed for systems containing PEO. The... 

Kamlet, M. J., Doherty, R. M., Carr, P. W., Mackay, D., Abraham, M. H., Taft, R. W. (1988) Linear solvation energy relationships. 44. Parameter estimation rules that allow accurate prediction of octanol/water partition coefficients and other solubility and toxicity properties of polychlorinated biphenyls and polycyclic aromatic hydrocarbons. Environ. Sci. Technol. 22, 503-509. 

The solvent should have high solubility for the solute being crystallized. The capacity of the solvent to solvate can be quantitatively assessed through its solubility parameter value. Under the like dissolves like paradigm, anon-polar solute is generally more soluble in a non-polar solvent. Hence a solvent with solubility parameter value close to that of the solute can be assumed to have high solubility for the solute. The following empirical equation can be used to estimate the solubility parameter... 

Figure 7.2 The relationship between the solubility parameter (8), and the relative rates for the reaction shown in Scheme 7.4. (Note that 8 for trifluoroethanol did not appear in the original publication [10] and was estimated by correlating it for other alcohols)...

They generally exhibit a UCST, To, = bf,B(T)/2R. It must be remembered that only pairs of liquids that mix at least partly behave as regular mixtures and that Eqs. (2.5) and (2.6) cannot be used for the general case of any two liquids, except as a very rough approximation. The value of bA iT) can be estimated from the properties of the individual liquids to be mixed, by invoking their solubility parameters [Eq. (2.1)]. The expression is ... 

If Z9b(ai) can be equated with P calculated from the entries in Table 2.5, then Z9b(a2) in any other solvent Ab can be estimated from Eq. (2.62). Equation (2.62) is actually a combination of four expressions of the form of Eq. (2.8) (see section 2.2.2), two for water and solvent Ai and two for water and solvent A2, presuming them to be immiscible pairs of liquids. It employs concentrations on the mole fraction scale, and assumes that the systems behave as regular solutions (which they hardly do). This eliminates the use of the solubility parameter 8 of water, which is a troublesome quantity (see Table 2.1). Solvent Ai need not, of course, be 1-octanol for Eq. (2.62) to be employed, and it suggests the general trends encountered if different solvents are used in solvent extraction. 

Thus from solubility parameters, which are specific for the various solutes and solvents, and molar volumes, values for can be estimated, or deviations from regularity can be assessed. These deviations can be estimated quantitatively and, in individual systems, can be ascribed to specific reactions in either of the phases, e.g., hydration, solvation, adduct formation, etc. 

---