Intermolecular forces solubility parameters

As already mentioned molecules cohere because of the presence of one or more of four types of forces, namely dispersion, dipole, induction and hydrogen bonding forces. In the case of aliphatic hydrocarbons the dispersion forces predominate. Many polymers and solvents, however, are said to be polar because they contain dipoles and these can enhance the total intermolecular attraction. It is generally considered that for solubility in such cases both the solubility parameter and the degree of polarity should match. This latter quality is usually expressed in terms of partial polarity which expresses the fraction of total forces due to the dipole bonds. Some figures for partial polarities of solvents are given in Table 5.5 but there is a serious lack of quantitative data on polymer partial polarities. At the present time a comparison of polarities has to be made on a commonsense rather than a quantitative approach. 

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... 

In a fundamental sense, the miscibility, adhesion, interfacial energies, and morphology developed are all thermodynamically interrelated in a complex way to the interaction forces between the polymers. Miscibility of a polymer blend containing two polymers depends on the mutual solubility of the polymeric components. The blend is termed compatible when the solubility parameter of the two components are close to each other and show a single-phase transition temperature. However, most polymer pairs tend to be immiscible due to differences in their viscoelastic properties, surface-tensions, and intermolecular interactions. According to the terminology, the polymer pairs are incompatible and show separate glass transitions. For many purposes, miscibility in polymer blends is neither required nor de-... 

The Composition of T, All of the T parameters represent a difference in intermolecular forces (imf). This difference results from a transfer of some substrate from one phase p to another. For partition the change is from (aq) to (nonaq). For solubility it is from CP(s) to jP(sqln), while for chromatographle quan titles it is from p (mobile) to (P(fixed). Thus,... 

Plasticizers are compounds which increase the flexibility and process -bility of polymers. It has been postulated that the added plasticizer reduces the intermolecular forces in PVC and increases the free volume. Effective plasticizers, like effective solvents, have solubility parameters within 1.8 H (Hildebrand units) of that of the polymer. 

PVC and CPVC are resistant to nonoxidizing adds, alkalis, and salts. They are also more resistant than hope or PS to weak oxidizing adds, such as 10% nitric add at room temperature. PVC has a solubility parameter of 9.5 H. Because of its moderate degree of crystallinity and relatively strong intermolecular forces it is difficult to dissolve. It is soluble in cydohexanone... 

Dispersive Interactions. For pairs of nonpolar polymers, the intermolecular forces are primarily of the dispersive type, and in such cases the energy of interaction between unlike segments is expected to be closely approximated by the geometric mean of the energies of interaction between the two like pairs (98). In this case, the Flory-Huggins interaction eneigy between this polymer pair can be expressed in terms of the solubility parameters 6 of the pure components. 

Actual values of solubility parameters show the same trends for both solvents and polymers. Non-polar molecules and repeat units have weak intermolecular forces, small energies of vaporization, and therefore small solubility parameters. As might be expected, increased polarity increases the solubility parameter, and hydrogen bonding gives the largest values of all. 

When changing force field parameters of a compound, overall exactness of the model is determined by the parameterization criteria. As this work was parameterized to reproduce the solubility, which is related to the thermodynamic quantity of free energy, this raises the question of solvent structure, as the structure-energy relationship is evident even in the gas phase interactions. One way to test the solvent structure is to check the density of the aqueous solution as a rough estimate of the ability of the model to reproduce the correct intermolecular interaction between the solute and the solvent. For this purpose, additional MC simulations were carried out on the developed models to test their ability to reproduce the experimental density of solution, at the specified concentration. The density was calculated using the experimentally derived density equations for carbon dioxide in aqueous solution from Teng et al., which is calculated from the fyj, of the C02(aq) and the density of the pure solvent [36, 37]. 

A solubility parameter based on dispersion forces (SD) can be calculated as the summation of the intermolecular attraction forces (F) for all functional groups as ... 

Intermolecular forces in the presence of water include the dispersion forces as well as the dipole-dipole forces and the hydrogen-bonding forces. The hydrogenbonding component to the solubility parameter ( SH ) can be estimated as ... 

To illustrate the use and interpretation of solubility parameters, let us examine three cases. First, the alkyl germanes, which are nonpolar and are not associated in the liquid phase, show a regular, slight increase in 8 as the molecular masses, and hence the London forces, increase (see Table 3.11). This series represents one where all of the molecules interact by the same type of force with no tendency to dimerize. Second, the 8 values for ethanol and acetone, both of which have empirical formulas C2H60, are 26.6 and 20.0 J1/2 cm 3/2, respectively. The high value for the ethanol reflects intermolecular hydrogen bonding, whereas acetone molecules interact only by weaker dipole-dipole and London forces. 

Although the use of solubility parameters is extensive for organic compounds, this approach to understanding and interpreting intermolecular forces has received almost no attention in inorganic chemistry. 

The square route of the cohesive pressure is termed Hildebrand s solubility parameter (5). Hildebrand observed that two liquids are miscible if the difference in 5 is less than 3.4 units, and this is a useful rule of thumb. However, it is worth mentioning that the inverse of this statement is not always correct, and that some solvents with differences larger than 3.4 are miscible. For example, water and ethanol have values for 5 of 47.9 and 26.0 MPa°-, respectively, but are miscible in all proportions. The values in the table are measured at 25 °C. In general, liquids become more miscible with one another as temperature increases, because the intermolecular forces are disrupted by vibrational motion, reducing the strength of the solvent-solvent interactions. Some solvents that are immiscible at room temperature may become miscible at higher temperature, a phenomenon used advantageously in multiphasic reactions. 

Numerous attempts have been made lo improve the predictive ability of the solubility parameter method without making its use very much more cumbersome. These generally proceed on the recognition that intermolecular forces can involve dispersion, dipole-dipole, dipole-induced dipole, or acid-base interactions, and a simple S value is too crude an overall measurement of these specific interactions. 

For the purpose of estimating the solubility of a solute it is necessary to have some measure of the polarity of a solute or a solvent. Based on Eqs. (1) and (2), a useful polarity index should be a measure of a material s intermolecular forces, Cn and C22-Table 1 contains a list of solvents that are typically used in liquid pharmaceutical formulations and three measures of solvent polarity. Each measure of solvent polarity, or polarity index, is based upon a different measure of a material s property. For example, dielectric constant is a measure of the electrical insulating properties of a solvent, solubility parameter is determined from the molar energy of vaporization, and... 

The use of the ADR method may not always provide accurate vehicle compositions for a given solute since intermolecular forces are dependent on structural characteristics of the solvent and solute that are not expressed by It is possible, and perhaps desirable, to substitute other measures of cosolvent polarity, such as solubility parameter, surface or interfacial tension, etc., for e when blending solvents, although inaccuracies in vehicle predictions will generally continue to exist. 

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,... 

The solubility parameter, 6, derived from the cohesive energy density, 62, used as a measure of intermolecular forces may be defined [19] as... 

One possible explanation lies in the nature of the intermol-ecular forces involved. Amongst the most popular extensions to the basic solubility parameter theory is that due to Hansen [38] which considers contributions from three types of intermolecular forces ... 

Dispersive Forces. In the absence of permanent or induced dipoles, London dispersive forces (17) become important. Random fluctuations in the electron cloud produce a time-varying, temperature-independent intermolecular force of attraction termed the dispersive force. The magnitude of these dispersive forces (typically 0.1 to 2 kcal/mole) can be represented by a variety of cohesive parameters Including the dispersive component of the Hansen solubility parameter (16). 

Fortunately, most organic solvents are nonpolar and therefore their intermolecular forces are weak London or dispersion forces. Hildebrand used the term "regular solutions" to describe solutions of nonelectrolytes and their nonpolar solvents. Additional theories on the solubility of polymers were developed by Flory ( ) and Huggins O). Probably the most important publications leading to the practical use of solubility theories by polymer scientists were those published by Burrell in 1955 ( ) and 1966 ( ). Modifications in the Hildebrand solubility parameter concept for regular solutions to account for larger intermolecular forces were made by Liebermann ( ), Crowley (.7), Hansen and Beerbower ( ) and Nelson et al. (9). 

Considering Table 1.16, only the first polymer, polyethylene, has non-polar contributions alone the next three have also polar components and the last, nylon-6,6, has contributions from all three forces. The largest solubility parameter for this polymer also corresponds to the highest melting point and stiffness, reflecting the importance of cohesive energy density as a measure of intermolecular forces. 

The solubility parameter concept has been used to correlate many physical phenomena. Miscibility of solvents with polymers, diffusion of solvents within polymers, effects of intermolecular forces on the glass transition temperature and interfacial interactions within copolymer materials would be included, just to mention a few examples. In many cases, meaningful interpretation of results was facilitated with the use of the solubility parameter. 

When this theory was used to predict the solubility of polymers in a variety of solvents, it was only partially successful. It was apparent that other intermolecular forces were at work which could not be calculated by this simple procedure. Hydrogen bonding, probably the strongest type of intermolecular force in a nonelectrolyte, was the clue for making solubility parameter theory work. 

Solubility maps usually show the soluble area of a resin in a variety of solvents and are usually based on the physical chemical constants of the solvents. We recognize the various solution parameters such as solubility parameter, internal pressure, dipole moment, fractional polarity, or the various measures of hydrogen bonding, but we have chosen solubility parameter (8), (the measure of all the intermolecular forces present in... 

In this chapter we describe the methods used to calculate solubility isotherms as well as the entire phase diagram for binary and ternary solute-SCF mixtures. The objective of the first part of the chapter is to discuss the relevant physical properties of the solute and solvent pair that are needed to describe the intermolecular forces in operation between molecules in a mixture that ultimately fix solubility levels. A brief description is provided on the application of solubility parameters to supercritical fluids. 

Let s progress now to the situation with supercritical ethane. There are dangers to blindly employing solubility parameters with any gas-liquid pair. We can illustrate them by investigating supercritical ethane at 400 bar and 37°C. What does it do with the five liquids listed in table 5.2 The solubility parameter of ethane is about 6.0H. Ethane is miscible with hexane we previously related that fact in chapter 3, and we would predict that ethane and hexane would be miscible based upon solubility parameter considerations. Hildebrand solubility parameters can in fact be employed here because only dispersive intermolecular forces are in play and ethane has a liquid-like... 

A measure of the intermolecular attraction forces in a material is provided by the cohesive energy. Approximately, this equals the heat of vaporization (for liquids) or sublimation (for solids) per mol. The cohesive energy density in the liquid state is thus AEyfV, in which AE-o is the molar energy of vaporization and V is the molar volume of the liquid. The square root of this cohesive energy density is known as the solubility parameter (d), that is,... 

As stated before, the solubility parameter concept was developed for non-polar, low molecular weight liquids at room temperamre. For polar molecules the method did not provide consistent information. To avoid trouble, initially all liquids were divided into three categories for poorly, moderately and strongly interacting systems. Another route was taken by Hansen [1967], who postulated that all the intermolecular forces ... 

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