Solubility and Interaction Parameters

In an alternate thermodynamic treatment of polymer blends Flory (1942) had developed an expression for regular solutions of nonelectrolytes. A regular solution is one in which the change in volume on mixing is zero while the 

Assuming that dissolution requires replacing similar molecules with dissimilar ones, they derived a relationship, between A H and the square root of the energy of vaporization, the solubility parameter S, 

In a further refinement Hansen (1967a,b) and Hansen and Beerbower (1971) have further elaborated the concept and have shown that S can be described in terms of three components Sd the contribution from dispersion interaction, Sp the contribution from polarity, and Sh the contribution from hydrogen bonding, and the total solubility parameter 8t is the root mean square of the three components  

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This discussion refers to external plasticization only. Several theories, varying in detail and complexity, have been proposed in order to explain plasticizer action. Some theories involve detailed analysis of polarity, solubility, and interaction parameters and the thermodynamics of polymer behavior, whereas others treat plasticization as a simple lubrication of chains of polymer from each other, analogous to the lubrication of metal parts by oil. Although each theory is not exhaustive, an understanding of the plasticization process can be gained by combining ideas from each theory, and an overall theory of plasticization must include all these aspects. 

Standard Methods of Evaluation of Miscibility, Solubility, and Interaction Parameter... 

Application of pollutant chemodynamic models, which neglect the DHS phase, may result in inaccurate estimations of apparent solubility and transport parameters. The impact of a DHS solubility enhancement is most pronounced for the least water-soluble solutes. The affinity of a solute for a DHS is a function of the same properties, which drive a complex organic mixture(s) to sorb onto the stationary solid phase, namely bonding interactions and hydrophobicity. 

D solubility parameter and interaction parameter values used to explain behavior (selectivity and flux). Copolymers of AN showed good selectivity with reasonable flux... 

In the second step, with the hydrolysis constants and the specific interaction parameter for ZrOH" and for Zr3(OH) fixed to the values optimised as detailed above, the equilibrium constants and interaction parameter for all other species in the overall hydrolysis model were obtained by a global fit of the potentiometric, solubility, solvent extraction and ion exchange data mentioned above. The fit was extended to the determination of equilibrium constants for heterogeneous reactions ion exchange constants, solubility constants and liquid/liquid distribution coefficients. The fit was based on a preselection of the stoichiometries of dominant species which included invariably the species Zr(OH)4(aq), Zr ) ), Zr (OH)Jj and Zr4(OH)i6(aq) and various other mono-, di-, tri- and tetravalent species to improve the fit. The potential formation of chloride complexes of Zr was considered for chloride containing solutions, using the stability constants determined in Section V-4. If all fitted results were found insensitive to the equilibrium constants of a given species, the respective species was removed from the list of species. 

Solubility parameter (5) and interaction parameter (y) at infinite dilution ... 

The convenience of use of solubility parameters has become the reason for easy integration with compatibility concepts. Any numerical description of interactions in polymer solutions requires the use of thermodynamic theories and interactions parameters. 

The Hansen approach provides extensive information on the nature of solubility and interactions of solvents and polymers. " But it has its own set of difficulties related to estimating the correct values of the parameters and generating graphical interpretation of results. " ... 

Following equilibrium constant and interaction parameters (ej, are recommend for solubility of nitrogen in iron-carbon melts [1999Svy] ... 

Zup] evolved statistical thermodynamics of C in ternary austenite using the C-Fe-V system as an example. A review of thermodynamic properties of C in alloyed austenite, including C-Fe-V system, was performed by [1968Chi]. [1970Sch] analyzed the literature data on the effect of V, Ga and In on the solubility of C in molten iron and tried to establish a relationship between the solubility or interaction parameters and the structure of the periodic table. The activity of C in (aFe) and (yFe) solid solutions was studied by [1981Bra]. 

Table 3.2 Solubility Parameter and Interaction Parameter x between PLA and Plasticizers (Pilin et al., 2006)...

Pilin et al. (2006) extended the study on the effect of food grade plasticizer in PLA, as listed in Table 3.2. The solubility parameter 6 and interaction parameter x were used to evaluate the extent of compatibility of the PLA and the plasticizer. When the 6 of the components are close to each other or blend with X < 0-5, it can be considered that the mixture is miscible and no phase separation is expected. The differential scanning calorimetry results as shown in Table 3.3 indicate that the... 

The presence of charge serves as structural motifs underpinning various functionalities. Firstly, it increases the solubility of the molecules in aqueous solution. Even though not much is known about the environment that molecules experience inside a cell, many biological processes are assumed to occur in aqueous environment as thus, the many components should be water soluble and interact in a controllable fashion. Polyelectrolyte complexes adopt structures with extent of order depending on the type of molecules involved and their molecular parameters. The structures of PEC have conceptually been described to span Irom the formation... 

Most properties of linear polymers are controlled by two different factors. The chemical constitution of tire monomers detennines tire interaction strengtli between tire chains, tire interactions of tire polymer witli host molecules or witli interfaces. The monomer stmcture also detennines tire possible local confonnations of tire polymer chain. This relationship between the molecular stmcture and any interaction witli surrounding molecules is similar to tliat found for low-molecular-weight compounds. The second important parameter tliat controls polymer properties is tire molecular weight. Contrary to tire situation for low-molecular-weight compounds, it plays a fimdamental role in polymer behaviour. It detennines tire slow-mode dynamics and tire viscosity of polymers in solutions and in tire melt. These properties are of utmost importance in polymer rheology and condition tlieir processability. The mechanical properties, solubility and miscibility of different polymers also depend on tlieir molecular weights. 

A. F. M. Barton, Handbook of Polymer—Eiquid Interaction Parameters and Solubility Parameters, CRC Press, Boca Raton, Fla., 1990. 

Polyisobutylene is readily soluble in nonpolar Hquids. The polymer—solvent interaction parameter Xis a. good indication of solubiHty. Values of 0.5 or less for a polymer—solvent system indicate good solubiHty values above 0.5 indicate poor solubiHty. Values of X foi several solvents are shown in Table 2 (78). The solution properties of polyisobutylene, butyl mbber, and halogenated butyl mbber are very similar. Cyclohexane is an exceUent solvent, benzene a moderate solvent, and dioxane a nonsolvent for polyisobutylene polymers. 

Figure 5.7 Comparison of four-parameter fy-maxi mum, v-minimum. IC50, and h) and two-parameter (IC50 and h) fits of non-ideal concentration-response data. In panels A and B the data indicate a nonzero plateau at low inhibitor concentration that might reflect a low-amplitude, high-affinity second binding interaction. In panels C and D the data indicate a plateau at high inhibitor concentration that does not achieve full inhibition of the enzyme. There could be multiple causes of behavior such as that seen in panels C and D. One common cause is low compound solubility at the higher concentrations used to construct the concentration-response plot. Note that the discordance between the experimental data and the expected behavior is most immediately apparent in the plots that are fitted by the two-parameter equation.

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... 

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