Determination of solubility parameter

Since a knowledge of a solubility parameter of polymers and liquids is of value in assessing solubility and solvent power it is important that this may be easily assessed. A number of methods have been reviewed by Burrell and of these two are of particular use. 

From heat of vaporisation data It has already been stated that 

Where 8 is the solubility parameter A the energy of vaporisation V the molar volume AN the latent heat of vaporisation R the gas constant T the temperature M the molecular weight D the density. 

Unfortunately values of AH at such low temperatures are not readily available and they have to be computed by means of the Clausius-Clapeyron equation or from the equation given by Hildebrand and Scott  

Some molar attraction constants compiled by Small are given in Table 5.8. 

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An alternate approach makes use of a group contribution analysis (7.9j approach. The group contribution analysis method has proved useful for the determination of solubility parameters (12.13L and has provided an approach for a host of other chemical properties (14). In a group contribution analysis, each moiety in the chemical or polymer contributes additively to the property in question. 

Terada, M. and Marchessault, R.H. (1999) Determination of solubility parameters for poly(3-hydroxyalkanaotes). International Journal of Biological Macromolecules, 25, 207-215. 

Litz LM. (1985, Nov) A novel gas-liquid stirred reactor. Chem. Eng. Prog., 81(ll) 36-39. Malpani V, Ganeshpure PA, Munshi P. (2011) Determination of solubility parameters for the p-xylene oxidation products. Ind. Eng. Chem. Res., 50 2467-2472. 

Predictive models for drug-polymer miscibility have been introduced, and they are largely derived from solution thermodynamics. Lattice-based solution models, such as the F-H theory, can be used to assess miscibility in drug-polymer blends, for which the F-H interaction parameter can be considered as a measure of miscibility. In addition, solubility parameter models can be used for this purpose. The methods used to estimate interaction parameters include melting point depression and the determination of solubility parameters using group contribution theory. 

Steven Abbott, University of Leeds, U K). Any parameter in the equation can be calculated using the information in this table. References Koenhen DM, Smolders CA (1975) The determination of solubility parameters of solvents and polymers by means of correlations with other physical quantities. J Appl Polym Sci 19 1163-1179 Abbott S, Hansen CM (2008) Hansen solubility parameters in practice, complete with software, data, and examples, 1st edn.( 2008), 2nd edn. (2009), 3rd edn. (2010). ISBN 9780955122026. 

Turbidity measurements use the onset of two-phase separation when adding a non-solvent to a dilute polymer solution in a good solvent. Two different non-solvents have to be used one having a solubility parameter above that of the (good) solvent, and another having a solubility parameter below that of the solvent. A series of experiments has to be done to find the solvent-polymer pair with 62 = di. Liquid-liquid equilibrium (LLE) curves of binary polymer solutions ean also be applied for the determination of solubility parameters of polymers. An appropriate thermodynamic model relating cloud-point or coexistence data with Xh is necessary, however. 

We will discuss the determination of solubility parameters to predict and to explain polymer-plasticizer/drugs miscibility. It is very important— both from a theoretical as well as from an experimental point of view—to ensure that two components are able to build a stable, homogenous mixture. 

Siemann (27) recently determined the solubility parameters and densities of a group of biodegradable polyesters. Solubility parameters... 

Polarographic studies of organic compounds are very complicated. Many of the compounds behave as surfactants, most of them exhibit multiple-electron charge transfer, and very few are soluble in water. The measurement of the capacitance of the double layer, the cell resistance, and the impedance at the electrode/solution interface presents many difficulties. To examine the versatility of the FR polarographic technique, a few simple water-soluble compounds have been chosen for the study. The results obtained are somewhat exciting because the FR polarographic studies not only help in the elucidation of the mechanism of the reaction in different stages but also enable the determination of kinetic parameters for each step of reduction. 

Another important use of solubility parameters is in interpreting the effects of different solvents on the rates of reactions. In a chemical reaction, it is the concentration of the transition state that determines the rate of the reaction. Depending on the characteristics of the transition state, the solvent used can either facilitate or hinder its formation. For example, a transition state that is large and has little charge separation is hindered in its formation by using a solvent that has a high value of S. The volume of activation is usually positive for forming such a transition state which requires expansion of the solvent. A reaction of this type is the esterification of acetic anhydride with ethyl alcohol ... 

The solvent may serve only as the medium for the reaction, or it may in addition be a reactant, as in a solvolysis reaction. It is possible that the reaction mechanism may be changed by a change in solvent (e.g., from SnI to Sn2) or that the rate-determining step of a complex reaction may be altered. All of these phenomena can be studied by examining the solvent dependence. One goal of research on medium effects is to achieve a level of understanding that will allow us to make mechanistic interpretations from such data. Handbooks of solubility parameters are valuable (Barton, 1983). 

The following components of solubility parameters for PPO have been obtained (177) Sd = 16.3 1, Sp = 4.7 0.5, 6h = 7.4 0.5, and So = 18.5 1.2 with units (J/mL)"/2. The determination was based on the use of three mixtures of solvents. For each mixture, the point of maximum interaction between the mixture and the polyol was obtained from the maximum value of the intrinsic viscosity. The parameter 8d measures dispersion 8p, polar bonding 5h, hydrogen bonding and 5q is the Hildebrand solubility parameter which is the radius vector of the other orthogonal solubility parameters. Water solubility of PPO has been determined using turbidimetric titration (178) (Table 7). 

As we shall see, the solution conductivity depends on the ion concentration and the characteristic mobility of the ions present. Therefore, conductivity measurements of simple, one-solute solutions can be interpreted to indicate the concentration of ions (as in the determination of solubility or the degree of dissociation) or the mobility of ions (as in the investigations of the degree of solvation, complexation, or association of ions). In multiple-solute solutions, the contribution of a single ionic solute to the total solution conductivity cannot be determined by conductance measurements alone. This lack of specificity or selectivity of the conductance parameter combined with the degree of tedium usually associated with electrolytic conductivity measurements has, in the past, discouraged the development of conductometry as a widespread electroanalyti-cal technique. Today, there is a substantial reawakening of interest in the practical applications of conductometry. Recent electronic developments have resulted in automated precision conductometric instrumentation and applications... 

It is also common to measure by voltammetry the thermodynamic properties of purely chemical reactions that are in some way coupled to the electron transfer step. Examples include the determination of solubility products, acid dissociation constants, and metal-ligand complex formation constants for cases in which precipitation, proton transfer, and complexation reactions affect the measured formal potential. Also in these instances, studies at variable temperature will afford the thermodynamic parameters of these coupled chemical reactions. 

It is relatively easy to determine the solubility parameter of a solvent. The molar volume can be obtained from pycnometry, or a value can possibly be found in the literature. Also, since most solvents of interest have significant volatility, their heats of vaporization can be determined calorimetrically. The experimentally determined heat of vaporization can be converted into the desired energy of vaporization through a conversion term that is simply the change in pressure-volume product for the process. Specifically, AH = AE + A(pV). At constant pressure this is pAV and, to the adequate approximation that the vapor is an ideal gas, the conversion term is thus simply RT (where R is the usual gas constant). 

Figure 2.24 Solubility bar graph for determining the solubility parameter for a polymer. Reprinted with permission from J. E. Mark, Physical Chemistry of Polymers, ACS Audio Course C-89, American Chemical Society, Washington, DC, 1986. Copyright 1986, American Chemical Society.

Polymers degrade before they vaporize, so indirect methods must be used to determine their solubility parameters. The simplest of these methods is a two-valued bar graph, as is illustrated in Figure 2.24. A series of solvents of known solubility parameter are used. Each is tested to determine if it is a solvent for the polymer. The yes or no answers are then plotted at different heights along the <5, abscissa. The value of corresponding to the midpoint of the yes bar is taken to be the solubility parameter S2 of the polymer. This is a reverse application of equation (24). The argument is now that solvents that are found to dissolve the polymer must have solubility parameters close to the unknown solubility parameter of the polymer. 

The fundamental idea is to determine the solubility parameter of the polymer, and then to use tabulated results to identify a number of solvents that have solubility parameters close to this value. The list of potential solvents is then narrowed to two or three candidates. Solvents that are too volatile, too toxic, too flammable, too expensive, and so on can be removed from the list. Other criteria would depend on the nature of the studies to be pursued. If the objective is to carry out light-scattering measurements, the need for maximizing the contrast factor would make the index of refraction of the solvent an additional important consideration. 

The interaction parameter / can also be estimated by the use of solubility parameters (8) / is proportional to (8M — 8TS)2. But this approach has a considerable error (A8 in the range of 0.4 MPa1/2), and considers only the excess free enthalpy. For these reasons it is better to determine the miscibility window experimentally. 

Equation (3.15) is used to determine the solubility parameters of the solute and the solvent ... 

The solubility of a liquid solute in octanol can be determined in terms of solubility parameters of the solute and octanol, as shown in Equation (3.20). However, the solubility parameters of liquid solutes (i.e., AHV) are generally unknown or are close to that of octanol and thus the liquid solutes are expected to be completely miscible with octanol. The critical solution temperature (Tc) of a nonideal solution of similar size solutes for complete miscibility is given by Hildebrand ... 

Critical surface tensions (yc) of a series of functional polymers were determined. These results are compared with those calculated on the basis of solubility parameter (8) according to the following equation ... 

Determination of the thermodynamic parameters for the transfer of non-polar organic compounds from aqueous to non-aqueous phases has been extensively used to estimate the free energy changes involved in hydrophobic interactions (Nemethy, 1967 Jencks, 1969). The experimental difficulties involved in the accurate determination of solubilities together with the approximations necessitated by limiting the measurements to simple organic compounds are the inherent disadvantages of this model. 

Because the term solubility parameter is too restrictive for this quantity, which can be used to correlate a wide range of physical an chemical properties (for instance, cf. Section 5.4.2), the term cohesion parameter has been proposed by Barton [99]. The term solubility parameter suggests a close relationship between the phenomenon solubihty or miscibility and that of cohesion or vapourization . This seems to be reasonable, considering what happens in a mixing process the like molecules of each component in a mixture are separated from one another to an infinite distance, comparable to what happens in the vapourization process. A comprehensive review on the determination and application of solubility parameters has been given by Barton [99],... 

The use of models and particularly those of a sophisticated nature is, however, seriously restricted by the limitations of the parameters involved in the model equations. It is actually the determination of certain parameters which becomes the crucial point in designing. The major uncertainties originate from two sources. Firstly, the process data, i.e. estimation of phase equilibria (solubilities), diffusivities and especially kinetic rate data,involves inaccuracies. The second major source of large uncertainties is the reliability of the nonadjustable hydrodynamic quantities. 

Three important properties which describe the behavior of a contaminant in aqueous systems are log Kow, water solubility, and vapor pressure [219]. Due to the complex composition of toxaphene and analytical uncertainty in the determination of these parameters (see Sect. 1.1), an exact evaluation of the congener-specific fate of toxaphene in water and air is presently not possible. However, Shoelb et al. identified B7-1001, B8-1413 (P-26), B8-806/B8-809 (P-42), B8-531 (P-39), B9-1679 (P-50), and further unknown toxaphene congeners in air from the north of Lake Ontario [68]. Interestingly, toxaphene levels in deep water (225 m) were significantly higher than in pelagic water (10 m) [220]. 

Interaction characteristics in polymer-related areas frequently make use of solubility parameters (16). While the usefulness of solubility parameters is undeniable, there exists the limitation that they need to be estimated either by calculation or from indirect experimental measurements. The thermodynamic basis of IGC serves a most useful purpose in this respect by making possible a direct experimental determination of the solubility parameter and its dependence on temperature and composition variables. Price (17) uses IGC for the measurement of accurate % values for macromolecule/vapor pairs, which are then used for the evaluation of solubility parameters for a series of non-volatile hydrocarbons, alkyl phthalates, and pyrrolidones. It may be argued that IGC is the only unequivocal, experimental route to polymer solubility parameters, and that its application in this regard may further enhance the practical value of that parameter. Guillet (9) also notes the value of IGC in this regard. 

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