Poly theta temperature

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... 

Fig. 16. lAygTj at constant temperature versus logq>2Z for solutions of poly (vinyl acetate) in diethyl phthalate, O, and cetyl alcohol, —O, at the theta temperature for dilute cetyl alcohol solutions. The straight lines have slopes 1.0 and 3.4. The independence of from may be noted... 

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. 

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). 

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. 

Figure 6-18. Determination of the theta temperature of poly(styrene) in cyclohexane from the critical temperature dependence on the degree of polymerization (after A. R. Schultz).

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 0 for polystyrene in cyclohexane, and 14°C for poly isobutylene in benzene. 

Theta-temperatures of the poly-oxides as a function of the ratio of oxygen to carbon (63 and 0])... 

The data in Fig. 4 refer to linear polyethylene samples with less broad distributions since they were obtained by fractionation of a commercial Marlex 50 type polyethylene into 10 fractions. The shape of the curves indicates that some of them would intersect, if extrapolated. This points to considerable residual poly-molecularity in the fractions so that identification of minima with critical points is not permitted. Nakajima et al. [35, 36] nevertheless analyzed the data assuming the identification to be allowed and, using the Shultz-Flory method [45], derived values for the critical temperatures for solutions of polyethylene of infinite molar mass in -alkanes. This specific temperature is known as the theta temperature, . Nakajima et al. s values, listed in Table 4, agree within 5 K with those... 

TABLE 4 Theta Temperatures (°C) for Linear Poly(ethylene)... 

As will be discussed in Chapter 6, which deals with the physical properties of the poly(alkylene oxide)s, only poly(ethylene oxide) is generally considered to be water-soluble however, ethylene oxide polymers are water-soluble only within a specific temperature range. There are, in theory, upper and lower consolute temperatures, and for poly(ethylene oxide) in water, the "Flory" or "theta" temperature is 108°C. There are, also theoretically, consolute temperatures for other lower poly(alkylene oxide)s in water, though these temperatures may be outside the range of normally liquid water. As a result, a hydrophobe can be achieved by forming a random copolymer of ethylene oxide with another epoxide within a temperature and composition range, this copolymer block can serve as the hydrophobic block. Such a unit is sometimes termed a heteric block, and the block copolymer may consist of blocks of the heteric block and of poly(ethylene oxide). 

Amu (17) critically reviewed the effect of salts on the solubility of poly(ethylene oxide) in water together with intrinsic viscosity measurements and Flory theta conditions. From this work, Amu estimated the theta temperature of poly(ethylene oxide) in water to be 108.5°C. Amu presented data in terms of the Stockmayer-Fixman equation (18),... 

Poly( -butyl methacrylate) Isopropanol 21.5 Theta temperature sp 1 211... 

Poly( -hexyl methacrylate) Isopropanol 32.6 Theta temperature Vsp[Pg.1760]

Poly(n-octyl methaciylate) n-Butanol 16.8 Theta temperature Isp[Pg.1760]

Experimentally, good solvent conditions have been observed [22,23,27,28, 34,35]. On the other hand, none has been reported for the prediction of the theta condition, y = 101, whereas the prediction of poor solvent conditions giving rise to y > 3 has been reported. These all have y < 20 except for two they are poly(methyl acrylate) at lower temperatures [34] and poly(dimethyl siloxane) [24]. Others have failed to reproduce them since. A caveat needs to be raised with these results. Since the semi-dilute regime is so narrow in r before the collapse state sets in whereby the power exponent is commonly deduced for a r range less than one full decade hence, the r scaling is at best qualitative in the static characterization. 

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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