Theta temperature Polystyrenes

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. 

Fig. 5.9. Comparison of extinction angle curves of high molecular weight fractions of polystyrene and cellulose tricarbanilate, using linear scales and reduced shear rate For data on polystyrene Taps. No. 5 and solvents see Table 3.2. (n) Taps. No. 5 in methyl (4-bromo-phenyl carbinol) at 18° C (theta-temperature), (V) the same at 50° C, (o) Taps. No. 5 in monobromo benzene at 25° C, ( ) cellulose tricarbanilate M = 720,000 in benzophenone at 55° C (jy = 4.70 cps) and (a) at...

Detailed analysis of the results published by Casper and Schulz 2) and measurements with the new chromatograph mentioned above 3) have shown that irrevesible thermodynamics, including two different kinetic effects, has to be applied to explain the resolution of the PDC-column 4 5 9) and to obtain the MWD of narrowly distributed polystyrene samples 6 8). In this way, not only the MWD is obtained, but also kinetic constants and thermodynamic functions of the polymer transfer between sol and gel, as well as hydrodynamic and kinetic spreading parameters of the system investigated, can be calculated from PDC-measurements performed at different constant column temperatures, with the same sample injected. The usual static quantities (such as the exponent of the partition function, ratio of the gel/sol volumes, etc.) proposed by Casper and Schulz can then be obtained by extrapolating the results to the theta temperature of the system. In addition, spreading phenomena alone can directly be... 

Fig. 22a and b. Dependence of the measured elution volume V = VD (in cm3, Fig. a), and of the standard deviation ctd (in cm3), skewness yD, and kurtosis 5D (Fig. b) on the weight-average of the polymerization degree Pw of very narrowly distributed polystyrene samples (BW-middle fractions of the anionic polystyrene standards), injected into the PDC-column 3) at 28 °C where the resolution of the column can be neglected in the Pw-range as indicated (polystyrene/cyclohexane, theta temperature 34 °C)... 

The sample was a solution of polystyrene (PS) dissolved in dioctyl phthalate (DOP). This system has a theta temperature of approximately 22°C [183] and has been the subject of most of the studies investigating flow-induced phase transitions in polymer solutions. The particular sample used here had a molecular weight for PS of 2 million, a poly-dispersity of MW/MN = 1.06, and a concentration of 6%. This results in a semidilute... 

J. O. Park and G. C. Berry, Moderately concentrated solutions of polystyrene. III. Viscoelastic properties at the Flory theta temperature , Macromolecules, 22, 3022 (1989). 

Krigbaum, W. R. Geymer, D. 0., "Thermodynamics of Polymer Solutions. The Polystyrene-Cyclohexane System Near the Flory Theta Temperature," J. Am. Chem. Soc., 81, 1859 (1959). 

Figure 5.12 Phase diagram of atactic polystyrene in nitro-propane. The theta temperature is 0 — 200 K. (Reprinted with permission from Tan et al.. Macromolecules 16 28. Copyright 1983 American Chemical Society.)...

For polystyrene in cyclopentane, one predicts that there should be two theta-temperatures, at 22 and 150 respectively. In the intermediate temperature range, cyclopentane should be a good solvent for PS. 

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. 

Saeki et al. (1973) measured a set of upper and lower critical solution temperatures for the polystyrene/methyleyelohexane system at various molecular weights. Demonstrate that the data listed as follows for both UCST and LCST behavior follow the expeeted trend with moleeular wdghL (Note that r should be taken as the ratio of the molar volumes of the polyma-and the solvent, and it can be assumed to be independent of the temperature.) What is the difference between the theta temperature for UCST and LCST ... 

From these data determine the second virial coefficient and the theta temperature of poly(a-methyl styrene) in cyclohexane, knowing that K = K hl AhlAcf, where K = 18.17 mol cm , the refractive index increment (d /dc) is 0.199 ml gr, and the temperature dependence of the refractive index is expressed by = -0.0005327 x T (°C) + 1.446. Static light-scattering measurements were carried out by Zimm (1948b) on polystyrene in butanone at 340 K at two concentrations. 

Only a few sterns are available which meet these conditions. The first degradation studies investigating the interrelation of thermodynamics and chain scission were done using polystyrene (PS) in various solvents The system studied most extensively so far is given by trons-decalin/PS (TD/PS) It exhibits upper critical solution temperature and a theta temperature of 21 °C Figure 5 shows the corresponding cloud point curves determined for narrowly distributed PS samples. 

SIP Siporska, A., Szydlowski, J., and Rebelo, L.P.N., Solvent H/D isotope effects on miscibility and theta-temperature in the polystyrene-cyclohexane system, Phys. Chem. Chem. Phys., 5, 2996, 2003. 

Figure 5. of [top to bottom] 262, 657, and 861 kDa polystyrenes in cyclopentane near the theta temperature, as obtained with FRS by Deschamps and Leger [79], and fits to stretched exponentials. 

The collapse of a polymer brush as the temperature is dropped through theta conditions is nicely illustrated by a neutron reflection study of end-grafted polystyrene in cyclohexane (Karim et al. 1994). The results are shown in figure 6.9 note that the brush height varies in a smooth way through the theta temperature, with no sign of a sharp transition. 

Figure 6.9. Volume fraction profiles of an end-grafted polystyrene brush, of relative molecular mass 105 000, imder various solvent conditions (O, toluene at 21 C and cyclohexane at A, 53.4 °C , 31.5 °C o, 21.4 °C and A, 14.6 "C), deduced from neutron reflectivity measurements (all the solvents are deuterated). Toluene at 21 °C is a good solvent and the solid line is the classical parabolic profile. The theta temperature for d-cyclohexane is 34 °C and the dashed line is the elliptical profile predicted by analytical self-consistent field theory for theta conditions. After Karim et al. (1994).

Figure 2,24. Second virial coefficient A2 for polystyrene in cyclohexane at different temperatures near the theta temperature. (From Ref. 16.)...

Figure 2.25. Radius of gyration of polystyrene in cyclohexane at the theta temperature (35.4°C), plotted as filled circles as a function of molecnlar weight. Open symbols indicate Rg of polystyrene in toluene and benzene (good solvents) and are the same as those in Figure 1.37. A slope of 1/2 is indicated in the figure. (From Ref. 2.)...

For typical ro = 0.2nm and n =l0, the radius of gyration is about 20nm and Tolman s length at ATI 10 " reaches the absolute value of about 100 nm, while the thickness of the interface is about a micron. More remarkably, in the polymer regime, even not very close to the tricritical phase separation (e.g., about 3 K away from the theta temperature, Ar = 10 ), Tolman s length for the polystyrene-cyclohexane solution is already mesoscopic, being about 50 nm, following the width of the interface of about 100 nm. In these conditions, as follows from eq 7.91, for a polymer-rich droplet with the radius 500 nm, the... 

SLA Slagowski, E., Tsai, B., and McIntyre, D., The dimensions of polystyrene near and below the theta temperature. Macromolecules, 9, 687, 1976. 

Fig. 7.38. Semidilute solutions of polystyrene in cyclohexane. The condition ( ) = Rg Ts)/ 3 may be used to locate the theta temperature. (Reproduced with permission from [235]. Copyright 1997 American Physical Society.)...

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