Molecular solubility parameter theory

In spite of widespread applications, the exact mechanism of retention in reversed-phase chromatography is still controversial. Various theoretical models of retention for RPC were suggested, such as the model using the Hildebrand solubility parameter theory [32,51-53], or the model supported by the concept of molecular connectivity [54], models based on the solvophobic theory [55,56) or on the molecular statistical theory [57j. Unfortunately, sophisticated models introduce a number of physicochemical constants, which are often not known or are difficult and time-consuming to determine, so that such models are not very suitable for rapid prediction of retention data. 

The retention times of analytes are controlled by the concentration(s) of the organic solvent(s) in the mobile phase. If a relatively small entropic contribution to the retention is neglected, theoretical considerations based either on the model of interaction indices [58], on the solubility parameter theory [51,52] or on the molecular statistical theory [57], lead to the derivation of a quadratic equation for the dependence of the logarithm of the retention factor of a solute. A, on the concentration of organic solvent. aqueous-organic mobile phase ... 

Complications such as these extend also to the case of polytetra-fluoroethylene. The large difference in estimated solid-vacuum tensions between this polymer and polyethylene is not imexpected, since a proportionately large difference exists for the liquid surface tensions of hydrocarbons and fluorocarbons having five to eight carbon atoms [58]. The underlying cause of this difference is, however, more obscure. The inter molecular forces for fluorocarbons apparently have features wuich lead to anomalous behavior, at least from the point of view of solubility parameter theory [59]. Thus, theoretical calculations of the surface tension for the bare solid in the case of polytetrafluoroethylene would face a number of difficulties not encountered with paraffin crystals. 

Of presently available methods for the prediction of solvent physical properties, the solubility parameter theory by Hildebrand may still supply one of the most accurate and eompre-hensive results. However, the solubility parameter used there has no purely molecular character. Many other methods are more or less of empirical character. 

In real systems, nonrandom mixing effects, potentially caused by local polymer architecture and interchain forces, can have profound consequences on how intermolecular attractive potentials influence miscibility. Such nonideal effects can lead to large corrections, of both excess entropic and enthalpic origin, to the mean-field Flory-Huggins theory. As discussed in Section IV, for flexible chain blends of prime experimental interest the excess entropic contribution seems very small. Thus, attractive interactions, or enthalpy of mixing effects, are expected to often play a dominant role in determining blend miscibility. In this section we examine these enthalpic effects within the context of thermodynamic pertubation theory for atomistic, semiflexible, and Gaussian thread models. In addition, the validity of a Hildebrand-like molecular solubility parameter approach based on pure component properties is examined. 

Of particular interest is the fact that two plasticisers of similar molecular weight and solubility parameter can, when blended with polymers, lead to compounds of greatly differing properties. Many explanations have been offered of which the most widely quoted are the polar theory and the hydrogen bonding theory. 

Strictly speaking Eq. (8-51) should be applied only to reacting systems whose molecular properties are consistent with the assumptions of regular solution theory. This essentially restricts the approach to the reactions of nonpolar species in nonpolar solvents. Even in these systems, which we recall do not exhibit a marked solvent dependence, correlations with tend to be poor. - pp Nevertheless, the solubility parameter and its partitioning into dispersion, polar, and H-bonding components provide some insight into solvent behavior that is different from the information given by other properties such as those in Tables 8-2 and 8-3. 

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. 

Molecularly motivated empiricisms, such as the solubility parameter concept, have been valuable in dealing with mixtures of weakly interacting small molecules where surface forces are small. However, they are completely inadequate for mixtures that involve macromolecules, associating entities like surfactants, and rod-like or plate-like species that can form ordered phases. New theories and models are needed to describe and understand these systems. This is an active research area where advances could lead to better understanding of the dynamics of polymers and colloids in solution, the rheological and mechanical properties of these solutions, and, more generally, the fluid mechaiucs of non-Newtonian liquids. 

More fundamental treatments of polymer solubility go back to the lattice theory developed independently and almost simultaneously by Flory (13) and Huggins (14) in 1942. By imagining the solvent molecules and polymer chain segments to be distributed on a lattice, they statistically evaluated the entropy of solution. The enthalpy of solution was characterized by %, the Flory-Huggins interaction parameter, which is related to solubility parameters by equation 5. For high molecular weight polymers in monomeric solvents, the Flory-Huggins solubility criterion is x A 0.5. 

Based on the pioneering work of Molau [64], it is evident that phase separation can occur in blends of two or more copolymers produced from the same monomers when the composition difference between the blend components exceeds some critical value. The mean field theory for random copolymer-copolymers blends has been applied to ES-ES blends differing in styrene content to determine the miscibility behavior of blends [65,66]. On the basis of the solubility parameter difference between PS and PE, it was predicted that the critical comonomer difference in styrene content at which phase separation occurs is about 10 wt% S for ESI with molecular weight around 105. DMS plots for ES73 and ES66 copolymers and their 1 1 blend are presented in Figure 26.8. 

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,... 

Also a thermodynamic model based on the coupled Equation of State model and Flory-Huggins theory for polymer solutions was developed. The model parameters such as solubility-parameter of asphaltenes, molecular weight of asphaltenes, and molar volume of asphaltenes were obtained by fitting the model to experimental data. 

A thermodynamic model based on Flory-Huggins polymer-solution theory was developed and coupled with Equation of State model to predict the amount of asphaltene precipitation. The model prediction shows close agreement with the experimental data after regression of asphaltene properties such as molar volume, solubility parameter and molecular weight. The model, however, fails to account for the effect of large changes in the solubility parameters of the oil-solvent mixtures. 

Solubility parameters can also be estimated from intrinsic viscosity. Flory [101] related intrinsic viscosity to polymer molecular weight and the chain-expansion factor. The chain-expansion factor can, in turn, be related to the polymer-solvent interaction parameter using the Flory-Hug-gins theory. A variety of models can be used to relate the interaction parameter to solubility parameters [87,102,103] these equations have the form... 

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