Polystyrene theta solvents

A theoretical expression for the concentration dependence of the polymer diffusion coefficient is derived. The final result is shown to describe experimental results for polystyrene at theta conditions within experimental errors without adjustable parameters. The basic theoretical expression is applied to theta solvents and good solvents and to polymer gels and polyelectrolytes. 

Fig. 5.1. Intrinsic moduli for narrow distribution polystyrene (M = 860000) in two theta solvents (114). This comparison with theory is equivalent to that of reduced moduli described in the text. [Reproduced from Polymer J. 1,747 (1970).]...

Fig, 5.3. Viscosity at various concentrations and molecular weights in the low to moderate concentration range. Polystyrene-decalin and polymethyl methacrylate-xylene are theta or near-theta systems the remainder are good solvent systems (121,177). Note that the c[i/] reduction is somewhat better in theta solvents, and that the Martin equation [Eq. (5.9)], which would give a straight line in the figure, is a somewhat better representation for... 

Gebhard and Killmann69 reported an ellipsometric study of the adsorption of polystyrene onto various metal surfaces from theta solvents, M ranging from 76 x 103 to 340 x 103. A proportionality between t,ms and M1/2 was also observed, and the adsorb-ance was found to increase with rising M. 

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. 

Riseman (139) or Kuhn and Kuhn (153 , 153"). For the sake of comparison, Fig. 12 also shows the theta-solvent intrinsic viscosities of polystyrene in cyclohexane [experimental valuesofKRiGBAUMandFuoRY (149), small black points theoretical values, broken line] and the theoretical intrinsic viscosities of rigid ellipsoids with axial ratios p = M/500 (chain curve). As a matter of course, the chain curve reduces to the Einstein value of [rf in the range of M below500 [see, for example, Petehlin (16) ]z. 

Figure 3.13 Linear viscoelastic data (symbols) for polystyrene in two theta solvents, decalin and diocty Iphthalate, compared to the predictions (lines) of the Zimm theory with dominant hydrodynamic interaction, h = oo. The reduced storage and loss moduli and G are defined by = [G ]M/NAksT and G s [G"]M/A /cbT, where the brackets denote intrinsic values extrapolated to zero concentration, [G jj] = limc o(G /c) and [G j ] = limc +o[(G" — cor)s]/c), and c is the mass of polymer per unit volume of solution. The characteristic relaxation time to is given by to = [rj]oMrjs/NAkBT. For frequencies ro

Both the scaling with co and the proportionality constant, V3, are confirmed by experimental data (see Fig. 3-13). The lines in Fig. 3-13 are proportional to G and G" — computed in the nondraining limit. The agreement with data for a polystyrene of high molecular weight (M = 860,000) in theta solvents is excellent. In addition to its agreement with experimental data, the predictions of Zimm theory are supported by molecular dynamics simulations (Pierleoni and Ryckaert 1991 DUnweg and Kremer 1991). 

Similar phase separation was observed in theta solvents containing polymers with pendant photochromic chromophores. In a theta solvent, the interaction between the polymer and the solvent is in balance with intra- and iftter-polymer interactions. The isomerization of the pendant diromophores alters this balance. The system studied was a cyclohexane solution of polystyrene with pendant azobenzene groups [64]. 

Cyclohexane becomes a theta solvent for polystyrene at 35 °C. Moderate molecular weight polystyrene (M = 5 x 10 ) with pendant azobenzene groups is soluble in... 

In addition, the data shown in Fig. 16 reveal that rj is in this case independent of the solvent, even though in dilute solution cetyl alcohol is a theta-solvent at the temperature for which r] was measured (0 = 396° C), and diethyl phthalate presumably is a good solvent. This provides direct evidence of an instance in which thermodynamic ejects on the coil dimensions in dilute solution appear to be suppressed in concentrated solution, as was suggested by the data on some polystyrene-diluent systems described above. 

Problem 2.11 Assuming that the RMS end-to-end distance is an approximation to the diameter of the spherical, coiled polymer in dilute solution, calculate the volume occupied by one molecule of polystyrene (molecular weight 10 ) in a theta solvent at 25°C. (carbon-carbon bond length = 1.54x10 cm tetrahedral bond angle 109.5°)... 

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 )... 

FIGURE 1.7 Plots of viscomelric branching parameter, g, versus branch functionahty, p, for star chains on a simple cubic lattice (unfilled circles), together with experimental data for star polymers in theta solvents , polystyrene in cyclohexane , polyisoprene in dioxane. Solid and dashed lines represent calculated values via Eqs. (1.70) and (1.71), respectively. (Adapted... 

Eigures 2.5 and 2.6 compare DR results for three narrow-molecular-weight (MW)-distribution polystyrenes in toluene, a good solvent, and in a theta solvent, respectively. In each case, at fixed polymer concentration, increased MW leads to greater drag reduction. Also, at fixed MW, increased polymer concentration leads to increased DR. Moreover, at fixed MW and polymer concentration, the magnitude of DR appears... 

Fig. 7. Flow curves for solutious of a narrowly distributed polystyrene sample at equal concentration in tra/is-decalin (TD, theta solvent) and in toluene (TL, good solvent)...

Fig. 8. Comparison of entanglement part of the shear viscosity (cf. Eq. 14)) measured for solutions of polystyrene in the theta solvent (rans-decaline (TD) with the Graessley mastercurve Eqs. (14), (106) and (17) for the concentrations indicated in the graph...

Fig. 10. Ratio of the shift factor Xo determined experimentally (cf. Eq. (15)) and the Rouse relaxation time Tk as a function of temperature for polystyrene in the good solvent toluene (TL) and in the theta solvent trnnr-decaline (TD)...

IMR lime, A. and van Hook, W.A., Continuity of solvent quality in polymer solutions. Poor-solvent to theta-solvent continuity in some polystyrene solutions, J. Polym. Sci. Part B Polym. Phys., 35, 1251, 1997. 

Figure 5.19. The dependence of the amount adsorbed on the relative molecular mass for polystyrene adsorbing onto silica from theta solvents (o, cyclohexane and A, decalin) and a good solvent (+ and X, carbon tetrachloride). Adapted from Fleer et...

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