Theta temperature Polyisobutylene

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. 

The intrinsic viscosities of polyisobutylene of molecular weight 5.58x10 in cyclohexane at 30°C and in benzene at 24°C (theta temperature) are 2.48 dI7g and 0.799 dL/g, respectively. Calculate (a) unperturbed end-to-end chain length of the polymer, (b) end-to-end chain length of the polymer in cyclohexane at 30°C, and (c) volume expansion factor in cyclohexane at 30°C. Take = 2.5xl0 . 

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... 

Although (ro/M) is a function of temperature and solvent character, in many cases it is not very sensitive to either variable at temperatures near the theta temperature. The ratio of [q] to [q]0f therefore provides a good estimate of a, no matter what solvent was used to measure [q]0f. Taking values of K and a from Table 7.6, we find for polyisobutylene in cyclohexane at 30° (see Table 7.7) ... 

The system polyisobutylene-benzene has a theta temperature of 24°C. Describe how each of the quantities mentioned below would change for a given sample as the temperature is increased to 40°C from 24°C (increase, decrease, or no change). Explain why. 

According to the statistical-mechanical theory of rubber elasticity, it is possible to obtain the temperature coefficient of the unperturbed dimensions, d InsjdT, from measurements of elastic moduli as a function of temperature for lightly cross-linked amorphous networks [Volken-stein and Ptitsyn (258 ) Flory, Hoeve and Ciferri (103a)]. This possibility, which rests on the reasonable assumption that the chains in undiluted amorphous polymer have essentially their unperturbed mean dimensions [see Flory (5)j, has been realized experimentally for polyethylene, polyisobutylene, natural rubber and poly(dimethylsiloxane) [Ciferri, Hoeve and Flory (66") and Ciferri (66 )] and the results have been confirmed by observations of intrinsic viscosities in athermal (but not theta ) solvents for polyethylene and poly(dimethylsiloxane). In all these cases, the derivative d In sjdT is no greater than about 10-3 per degree, and is actually positive for natural rubber and for the siloxane polymer. 

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