Polymer-solvent interaction parameter determination methods

Experimental methods for determining the solubility parameter of a polymer are usually based on determining the Flory-Huggins polymer-solvent interaction parameter, X = Xh + Xs> and/or its enthalpic part Xh- The underlying theories will not be discussed here and the reader is referred to the books by Barton [ 1990B AR1, 1991BAR1],... 

METHODS FOR THE DETERMINATION OF POLYMER-SOLVENT INTERACTION PARAMETERS... 

Tseng et al. [164] suecessfully used UNIFAC to optimize polymer-solvent interactions in three-solvent systems, determining polymer activity as a function of the solvent eomposition. The composition yielding the minimum in polymer aetivity was taken as the eriterion for optimum interaetion, and it eompared well with experimental measurements of dissolution rate and solution clarity. Better agreement was obtained using UNIFAC than using solubility parameter methods. 

Vapour pressure depression and membrane osmometry are the most common methods to determine the polyer-solvent interaction parameter. The latter method will be described briefly. In a membrane osmometer a dilute polymer solution has been separated from pure solvent by means of a membrane. The membrane is penneable for solvent molecules but not for polymer molecules. Due to a chemical potential difference solvent molecules will diffuse from the diluted phase to the concentrated phase and this results in a pressure increase which is called the osmotic pressure ti (see also section VI - 2 for a more detaUed description of osmosis). The osmotic pressure is given by... 

Another possible variable for the characterization of the goodness of solvents is the interaction parameter x values, expressing the measure of deviations of actual solutions from ideal ones. This value can be determined by several methods, which are, mostly experimentally demanding and time-consuming, x is dependent on both the polymer concentration and molecular weight and information provided about the specific interactions in the solution is of no particular interest [11,30,31], Solvents, obviously different in quality, yield quite close values and thus the resolving capability is low. Comparison of results obtained by various methods and/or experimenters is thus fairly difficult [30,32-34],... 

The number-average molecular weight (MJ of polymers can be easily determined from methods based on colligative properties, which are dependent on the number of molecules in the solution [28]. Thus, the addition of a number of solute molecules to a solvent produces a change in the chemical potential (A/Ui) of the solvent from which the molecular and interactional parameters can be deduced. 

A.A. Tager [110] determined the change of AG k by producing thermodynamic cycles using static sorption of solvent vapors on the polymeric specimens. However, in solution the polymer compatibihty is influenced by the difference of the thermodynamic interaction parameters of the common solvent with each indvidual polymer. Additionally, compatibility in solution does not always correspond to that in the solid state (without a solvent). These shortcomings limit the applicability of the AG ix estimation method that Tager developed. 

Since the introduction in analysis of macromolecular coil stmcture, characterized by its fractal dimension Df, is the key moment of polycondensation process fractal physics, then the value Df determination methods are necessary for practical application of polycondensation fractal analysis for solutions. This parameter for macromolecular coil in solution is defined by two groups of interactions interactions polymer-solvent and interactions of coil elements among them [6]. At... 

Vapor sorption of PS/poly(a-methylstyrene) gave X23 = 0.504, varying with T and polymer concentration, indicating that this system is immiscible with UCST > 100 °C (Saeki et al. 1981). Light-scattering measurements of ternary systems, polymer(l)/polymer(2)/solvent(3), were also successfully used to determine polymer/polymer interaction parameters, Zi2(0)- The method is particularly easy to use either if one of the two polymers is iso-refractive with the solvent or if the polymers have equal contrast (Pinder 1997). The method was successfully used to measure X12 for PS/PMMA blends of different M ,. 

A necessary preliminary to obtaining reliable values of the interaction parameter a from swelling measurements is the determination of the degree of crosshnking of the network, that is, the crosslinked polymer must be calibrated before use. A method used is to determine the volume fraction of polymer present in the swollen gel when a sample of the crosslinked polymer has swelled to equilibrium in an excess of a solvent in which the a value is known for the polymer. The relation between the ratio of initial to nal weight and the volume fraction is given by... 

The solvent-polymer interaction parameters were calculated from vapor pressure data of aqueous homopolymer solutions [25], using the Flory-Huggins expression [26] x//=6 ln/)//) —ln(l — 0) —(1 — l/N)0, where p is the vapor pressure and 6 is the polymer volume fraction. The chain length N was determined using 13/3 (EO) or 30/9 (PO) monomers per bead. This gives for the interaction parameters X s=l-4, Xi>s=l-7 (here S denotes solvent). For the EO-PO interaction parameter from group contribution methods [27] we estimated xep = 3.0. 

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