Solubility molar attraction constants

It is possible to calculate the solubility parameter and the solubility parameter components of almost all molecules and polymers by a group contribution method (Van Krevelen, 1990 Bicerano, 1996). For this purpose, as explained by Van Krevelen (1990) it is useful to introduce the molar attraction constant simply defined as ... 

A direct measure of nonpolar character of a hydrocarbon molecule is given either by its molar solubility in water or by its molar attraction constant (Small s number) as given by Small... 

Because the heat of vaporization of a polymer is not readily obtained. Small determined values for various components of a polymer chain to calculate the solubility parameter. These values are called molar attraction constants and are additive and have been used for estimation of the solubility parameter for nonpolar polymers. In this approach 8 = D%G/M, where D is density, G are the Small molar attraction constants, and M is the molecular weight of the particular repeat unit. As expected, the more polar units have greater G values while the less polar units have smaller G values. 

Earlier, Small (1953) had demonstrated that the combination (Ecoh/V(298))1/2 = F, the molar attraction constant, is a useful additive quantity for low-molecular as well as for high-molecular substances. His set of values is very frequently applied. Accordingly, the corresponding solubility parameter is < smaii = F/V. Later Hoy (1970) proposed group contributions to F, slightly different from those of Small. 

The solubility parameter of a given material can be calculated either from the cohesive energy, or from the molar attraction constant F, as <5 = F/V... 

This means that for the prediction of <5d the same type of formula is used as Small proposed for the prediction of the total solubility parameter 8. The group contributions Fdi to the dispersion component Fd of the molar attraction constant can simply be added. 

Fig. 12-1. Calculation of solubility parameters from molar attraction constants.

Other molecular properties have been also proposed to model the hydrophobic interactions. The parachor, which is related to the surface tension of a compound (139, 140) represents mainly the intermolecular interactions in a liquid. The Hildebrand-Scott solubility parameter, 6, (141) is related to intermolecular van der Waals forces and the closely related molar attraction constant, F, is obtained by multiplying 6 by the molar volume (142). The partition coefficient between two solvents can be obtained from the solubility parameters and the molar volumes of the solute and the solvents (193). This relationship is based on regular solution theory (194) and the assumption that the partial molar volumes of the solute is not different from its molar volume. Recently this has been criticized and a new derivation was proposed (195) in which the partial molar volumes are taken into account. The molar refractivity, MR, is related to dispersion forces and can be obtained as a sum of the partial molar refractivi-ties assigned to atoms and bonds (140, 143). These parameters have been compared (144) to establish their relative applicability to correlations with biological activity. The conclusion was that logP and molecular refractivity were the best parameters. Parameters obtained from high pressure liquid chromatography (144,... 

Solubility parameters may also be calculated by a molar-additivity approach if the chemical composition is known. Tables of group molar attraction constants, G, obtained from molar heats of vaporization (Sperling, 2001) may be used. The solubility parameter, S, is then given by summing these for all species Q G) in the monomer repeat unit of molar mass M and density p ... 

Small considered that the F quantity of Equation 16.9 shows better additive characteristics than the cohesive energy. The total molar attraction constant is calculated from Equation 16.1 and the solubility parameter is calculated from the equation ... 

Solubility parameters of solvents can be correlated with the structure, molecular weight, and density of the solvent molecule. According to the additive method of Small [15], the solubility parameter is calculated from a set of additive constants, F, called molar attraction constants, by the relationship. ... 

While the solubility parameter of a homopolymer can be calculated from the molar attraction constants as illustrated in Problem 3.19, the solubility parameter of random copolymers. Sc, may be calculated from... 

Problem 3.20 Calculate the solubility parameter for a methyl methacrylate-butadiene copolymer containing 25 mol % methyl methacrylate. The solubility parameter values for poly(methyl methacrylate) (PMMA) and polybutadiene (PB) homopolymers, calculated from molar attraction constants, are, respectively, 9.3 and 8.4 (cal cm ). ... 

Rheineck (12) has proposed a modification of Small s Molar Attraction Constants in which he gives corrections for molar volumes. These values are useful for calculating approximate solubility parameters when only the structural formula of a compound is known. 

By the method of Small (14). a procedure was developed to predict compatibility without determining the energy of vaporization. Small developed "molar attraction constants" for the more common atom groupings in solvents and in macroraolecules. By adding these constants for the resin and doing the same for the plasticizer and then dividing these totals by their respective molar volumes, one can obtain solubility parameters (11, 15). When these are used in Hildebrand s comparison, compatibility on the order of the 90% confidence limit can be predicted. 

In addition, the solubility parameter can be estimated from the molar attraction constants, E, using the structural formula of the compound and its density (Table 12.2). For a polymer ... 

Values of the solubility parameter for simple liquids can be readily calculated from the enthalpy of vaporization. The same method cannot be used for a polymer, and one must resort to comparative techniques. Usually, 8 for a polymer is established by finding the solvent that will produce maximum swelling of a network or the largest value of the limiting viscosity number, as both indicate maximum compatibility. The polymer is then assigned a similar value of 8 (see Table 8.2). Alternatively, Small and Hoy have tabulated a series of group molar attraction constants from which a good estimate of 8 for most polymers can be made. 

The suggested group contributions are shown in Table 8.3, and the solubility parameter for a polymer can be estimated from the sum of the various molar attraction constants F for the groups that make up the repeat unit i.e.. 

Correlations of solyent solubility parameters with molar attraction constants and with properties like surface tension, dipole moment, and index of refraction haye been explored. ... 

Thus, one can calculate the solubility parameter from a knowledge of the heat of vaporization, A//m, and the molar volume, Vm- This is straightforward for many solvents and values of 8 have been tabulated by Barton (6). For polymers this is not easy since the heat of vaporization is not known and other methods have to be applied to determine the solubility parameter of various polymers. Several experimental methods such as the measurement of polymer swelling or intrinsic viscosity may be applied. Alternatively, 5 may be calculated from a knowledge of the molar attraction constants, G, of the various functional groups in the polymer (7, 8). The values of G for the various groups are assumed to be additive ... 

The theory also assumes that the ideal entropy is possible for systems when AH . But the change of energy of interactions occurs in the course of dissolution that determines the inevitable change of entropy of molecules. It is assumed that the interactive forces are additive and that the interactions between a pair of molecules are not influenced by the presence of other molecules. Certainly, such an assumption is simplistic, but at the same time it has allowed us to estimate solubility parameters using group contributions or molar attractive constants (see Subchapter 5.3). 

Solubility parameters for pure NBR and PANI.DBSA were estimated by using the molar attraction constants values, F, as calculated by Hoy [3]. Chloroform has a solubility parameter of 19.0 (MJ.m )°- [1]. The calculated values of solubility parameter for both NBR 48 wt% ACN and PAni.DBSA were 20.7 and 20.8 (MJ.m )°-, respectively [1]. The pure NBR (48 wt% ACN) and PAni.DBSA were highly soluble in it. 

In short, the rules above can be summarized into one sentence, Like likes Uke . The solubility parameters of common solvents and polymers can be found from the conventional handbooks for physical chemistry or polymers. It is also possible to estimate the solubility parameter of polymers with the method of molar attractive constants according to... 

Solubility parameter can be expressed by Equation (39), where [F] is molar attraction constant and V molar volume. Small [45] has shown that [F] is an additive and constitutive property and has derived partial molar attraction constants for a range of substituent groups, from which molar attraction constants and solubility parameters of the parent molecules can be calculated. Small quotes partial molar attraction constants of 250 for Cl and 28 for CH, which yield a molar attraction constant of 778 for chloroform. In comparison, 745 is obtained from the product of molar volume and solubility parameter. 

Originally intended for application to substances whose cohesion arose from dispersion forces, the parameter seem to be of limited use with polymers, which generally decompose before vaporization enthalpies can be determined. The concept now has been greatly expanded. The overall 6 can be divided into dispersion and polar contributions. Often non-polar homomorphs of polar molecules can provide values of 5, and polar contributions, can then be obtained from differences between 6 and Further refinements due to Hansen " have introduced a three-component solubility parameter, which separates non-dispersive contributions into polar and hydrogen bond components. This has been applied to organic liquids, and to some polymers. Calculations of b for macromolecules also can be made from tabulated values of molar attraction constants, and extensive summaries of b and of other cohesion parameters are readily available to the potential user. Ultimately, however, the application of b to polymer systems is impeded for the following reasons ... 

For instance, polystyrene has p = 1.05gcm , m = 104gmol The molar attraction constant can be found from the table in Figure 2.16(a). The solubility parameter is... 

It is reasonably easy to use Eq. 26 to determine the solubility parameter of a solvent, but since the heat of vaporization of polymers is usually not known, other methods are needed to determine the solubility parameters of polymers. There are several experimental methods, based on polymer swelling measurements or on the determination of the intrinsic viscosity of polymer solutions. Alternatively, solubility parameters can be predicted from knowledge of the chemical structure of each component. The latter method is due to Small (72) and Hoy (73), who supplied values for molar attraction constants (G) of a large number of functional groups (Table 4). The constants G are additive. With these values it is possible to estimate the solubility parameter of any polymer using Eq. 28, where p represents the density and M the molecular weight of the polymer. 

Group contribution methods for the estimation of poljuner surface tension are cast in terms of these two factors. The strength of the interactions is represented by the dispersive solubility parameter 8, which can be calculated from tabulated values of dispersive molar attraction constants Fi according to (6)... 

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