Determine Theta Solvents

Methods to Determine Theta Solvents Solvents in which, at a given temperature, a polymer molecule is in the so-called theta-state, are called theta 6) solvents. The temperature is known as the theta-femperature or the Flory temperature (as P. J. Hory was the first to show the importance of the theta-state for a better understanding of molecular and technological properties of polymers). In the theta-state, the polymer solution behaves as thermodynamically ideal at low concentrations. 

Several methods can be used to determine theta solvents. These include phase equilibria studies (see Phase Equilibria in Poor Solvents), determination of second virial coefficient (see Problem 3.7), viscosity-molecular weight relationship, and cloud point titration. 

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Comparison of the limiting viscosity numbers determined in deionized water with those determined in 1 molar sodium nitrate shows a 20 per cent decrease in copolymer intrinsic viscosity in the saline solution. These results are consistent with previous studies using aqueous saline solutions as theta solvents for 2-propenamide polymers(47) Degree of hydrolysis controls the value of limiting viscosity number for the hydrolyzed copolymers in distilled water. 

An alternative approach for determining the molecular weight of a polymer in theta solvents includes the determination of the polymer s concentration at the meniscus (c ,) and at the bottom ic, ) (or alternatively at two other positions Xi and X2) in the cell. These two outstanding positions have a distance of x ix ) and Xh(x2), respectively, from the center of rotation. Then, one obtains the weight-average molecular weight of a polydisperse polymer sample via the equation ... 

The thermodynamic properties of the diluent appear to be unimportant in determining (Me)sojn.. Polyvinyl acetate in diethyl phthalate and in cetyl alcohol conform to Eq.(5.17), although the former is a good solvent and the latter a theta solvent at the temperature of measurement (157). 

To determine the conformation of adsorbed sodium polyacrylate, we first assume a loop-train conformation. Then, t at the theta point can be evaluated by Eq. (B-108). Since 1.5N NaBr at 15 °C is the theta solvent for sodium polyacrylate120, this calculation... 

Direct experimental data providing the temperature dependence of are not available in the literature. However, as discussed earlier, the dependence of 0 on the quality of the solvent (change in the values of the polymer-solvent interaction parameter) is expected to suggest the trend with temperature also. The experimental determination of

silica particles having polystyrene as the free polymer, indicated [5] that the amount of polymer required to produce phase separation decreased by a factor of three when the theta solvent cyclohexane (x = 0.5) is replaced by the good solvent toluene (x < 0.5). This implies that increased temperatures (reduced values for x) should lead to lower values of the amounts of polymer required for phase separation. It can be safely concluded that the available experimental and theoretical information thus far, exhibits the trend of smaller values of the limiting polymer concentration at higher temperatures. 

The value of M determined by MO in tetrachloroethane (TCE) decreases with increasing temperature, approaching M as determined by MO in THF, as shown in Fig. 18 40). The CDA molecules have a considerable tendency to form aggregates in poor solvents, as is TCE below 70 °C. Ikeda and Kawaguchi52), who overlooked this phenomenon for CDA in TCE, claimed that TCE at 56.5 °C acts as a Flory theta solvent for CDA, for which the second virial coefficient A2 vanishes. 

The viscosity method makes use of the fact that the exponent, a, in the Mark-Houwink equation (see Frictional Properties of Polymer Molecules in Dilute Solution), rj = KM° , is equal to 0.5 for a random coil in a theta-solvent. A series of polymers of the same type with widely different known molecular weights is used to determine intrinsic viscosities [t ] at different temperatures and hence a at different temperatures. The theta-temperature can thus be determined either by direct experiment or, if it is not in the measurable range, by calculation. 

Problem 3.24 The intrinsic viscosity of polystyrene of molecular weight 3.2x10 in toluene at 30°C was determined to be 0.846 dlVg. In a theta solvent (cyclohexane at 34°C) the same polymer had an intrinsic viscosity of 0.464 dL/g. Calculate (a) unperturbed end-to-end distance of the polymer molecule, (b) end-to-end distance of the polymer in toluene solution at 30°C, and (c) volume expansion factor in toluene solution. (3> = 2.5x10 mol )... 

The molecular weight of a polymer determined by an osmotic pressure measurement in a theta solvent is 20,000. What osmotic pressure (atm) would be expected at a concentration of 1.20 g/dL and 30°C. Would there be a difference in molecular weight if the osmotic measurement were made in a good solvent ... 

There are two basic ways in which measurements of the unperturbed dimensions are obtained (1) determination of unperturbed dimensions directly, by measurements in theta solvents and (2) determination of the perturbed dimensions in a good solvent and extrapolation of the values to the unperturbed state using one of the existing theories. Both methods have been widely used as will be shown. 

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