Theta temperature values

Polymers in Solution. Polyacrylamide is soluble in water at all concentrations, temperatures, and pH values. An extrapolated theta temperature in water is approximately —40° C (17). Insoluble gel fractions are sometimes obtained owing to cross-link formation between chains or to the formation of imide groups along the polymer chains (18). In very dilute solution, polyacrylamide exists as unassociated coils which can have an eUipsoidal or beanlike stmcture (19). Large aggregates of polymer chains have been observed in hydrolyzed polyacrylamides (20) and in copolymers containing a small amount of hydrophobic groups (21). 

This stipulation of the interaction parameter to be equal to 0.5 at the theta temperature is found to hold with values of Xh and Xs equal to 0.5 - x < 2.7 x lO-s, and this value tends to decrease with increasing temperature. The values of = 308.6 K were found from the temperature dependence of the interaction parameter for gelatin B. Naturally, determination of the correct theta temperature of a chosen polymer/solvent system has a great physic-chemical importance for polymer solutions thermodynamically. It is quite well known that the second viiial coefficient can also be evaluated from osmometry and light scattering measurements which consequently exhibits temperature dependence, finally yielding the theta temperature for the system under study. However, the evaluation of second virial... 

For the first non electrostatic term, such a dependence can be calculated from the classical Flory theory and the value of the theta temperature of unhydrolyzed polyacrylamide ( 0 = 265°K (22))... 

The slope of the lines in Figure 3.10, i.e., the virial constant B, is related to the CED. The value for B would be zero at the theta temperature. Since this slope increases with solvency, it is advantageous to use a dilute solution consisting of a polymer and a poor solvent to minimize extrapolation errors. 

What is the value of the Gibbs free energy change at the theta temperature ... 

The interactions between solvent and polymer depend not only on the nature of the polymer and type of solvent but also on the temperature. Increasing temperature usually favors solvation of the macromolecule by the solvent (the coil expands further and a becomes larger), while with decreasing temperature the association of like species, i.e., between segments of the polymer chains and between solvent molecules, is preferred. In principle, for a given polymer there is a temperature for every solvent at which the two sets of forces (solvation and association) are equally strong this is designated the theta temperature. At this temperature the dissolved polymer exists in solution in the form of a nonexpanded coil, i.e., the exponent a has the value 0.5. This situation is found for numerous polymers e.g., the theta temperature is 34 °C for polystyrene in cyclohexane, and 14 °C for polyisobutylene in benzene. 

EXAMPLE 3.4 Theta Temperature of A Polymer Solution from Second Virial Coefficient Data. Values of the second virial coefficient along with some pertinent volumes are tabulated below for the polystyrene-cyclohexane system at three temperatures. 

Solution The theta temperature is that value of T at which B = 0. It is apparent that B changes sign (i.e., passes through zero) about midway between 303 and 313K. Equations (80) and (81) can be combined to give... 

Polyisobutylene fraction of molecular weight 540,000 was used for viscosity measurements in cyclohexane and benzene. The intrinsic viscosity values obtained were 2.48 dL/g in cyclohexane at 30°C and 0.80 dL/g in benzene at the theta temperature (24°C). The observed relation between molecular weight and unperturbed end-to-end distance is given by... 

Viscosity measurements were made on solutions of fractionated cis-1,4-polybutadiene samples in toluene at 30°C and in n-heptane at —1°C (theta temperature), yielding the following values of intrinsic viscosities (in dL/g) ... 

Equations 70 and 72 are numerically very similar using the value v = 2.5 for any particle with spherical symmetry and have been reported to accurately describe kf of PS and poly-a-methylstyrene in cyclohexane at the theta temperature (84) based on sedimentation data. However, recent translational diffusion measurements of polystyrene/ cyclohexane solutions under theta conditions using QLLS indicate experimental kf values which lie between the extremes represented by Equation 71 on one hand and Equations 70 and 72 on the other (34). For smaller molecular weights, the values are closer to the Pyun Fixman or Freed theory for high molecular weights, they are closer to the Yamakawa-Imai result. 

The temperature at which these conditions are obtained is the Hory or theta temperature 0, conveniently defined as 0 = TiCi/ti/,. This tells us that 0 will only have a meaningful value when /, and K, have the same sign. 

The theta temperature of a polymCT-solvent systen can be measured from phase separation studies. The value of at the critical concentration is related to the chain length of the polymer by Equation 8.39, and substitution in Equation 8.45 leads to... 

Remembering that = (MV2/V1), where M and V2 are the molar mass and partial specific volume of the polymer, respectively, and is the molar volume of the solvent, the equation states that the critical temperature is a function of M and the value of at infinite M is the theta temperature for the system. 

Note Values have been derived using Equation 8.47 0=theta temperature, / = entropy of dilution. 

Values of 0 and Xj/i, in Table 8.1, show that for systems 1 to 4 the entropy parameter is positive, as expected, but for poly(acrylic acid) in dioxan and polymethacrylonitrile in butanone, f is negative at the theta temperature. As /i = when T= 0, the enthalpy is also negative for these systems. This means that systems 5 and 6 exhibit an unusual decrease in solubility as temperature rises, and the cloud-point curve is now inverted as in area B. The corresponding critical temperature is located at the minimum of the miscibility curve and is known as the lower critical solution temperature (LCST). 

This means that the critical concentration is shifted to lower values with increasing segment number (molar mass) of the polymer and becomes zero for infinite molar mass. Equation [4.4.61] explains also why the x(T)-function becomes 0.5 for infinite molar mass. The critieal temperature of these conditions is then called theta-temperature. Solvent activities can be calculated from critical %(T)-function data via Equation [4.4.13]. However, results are in most cases of approximate quality only. 

The results of the few LS measurements show unusual dependence on temperature. The A values change with temperature only in thermodynamically bad solvents and remain almost constant in other cases [13, 15, 20]. A visible clouding of the solution on cooling has been observed by Ohm and others even before reaching the theta temperature. A value of = 16 + 1°C for the theta temperature of PMAC in toluene independent of the molar mass has been reported [13, 15, 20]. 

The number of skeletal vibrational modes used in the Tarasov equation with the theta temperatures of the previous two columns. Values of theta temperatures in parentheses are estimates based on data from polymers of similar backbone structure. The group vibration frequencies are usually tabulated in the listed references. 

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