Theta solvent/temperature

Fig.9a-c. Scaled distribution function for the center-to-end distances of stars of f=3,10 and 50 arms (a is the repulsive distance range of the intramolecular potential) T=4 /kg corresponds to a good solvent T=3e/kg corresponds to a theta solvent T=2e/kg (lower temperatures correspond to the curves on the left). Solid curves Simulation data dashed lines Gaussian functions. Reprinted with permission from [131]. Copyright (1994) American Chemical Society... 

As demonstrated by numerous experiments, temperature does not well influence the exclusion processes (compare Equation 16.6) in eluents, which are thermodynamically good solvents for polymers. In this case, temperature dependence of intrinsic viscosity [ii] and, correspondingly, also of polymer hydrodynamic volume [p] M on temperature is not pronounced. The situation is changed in poor and even theta solvents (Section 16.2.2), where [p] extensively responds to temperature changes. 

Some relationship between viscosity crossover in theta solvents and polymer polarity is suggested by the results, supporting the idea of enhanced intermolecular association in poor solvents. However, from the data on hand, one could also infer a correlation with the glass transition temperature of undiluted polymer,... 

The thermodynamic properties of the diluent appear to be unimportant in determining (Me)sojn.. Polyvinyl acetate in diethyl phthalate and in cetyl alcohol conform to Eq.(5.17), although the former is a good solvent and the latter a theta solvent at the temperature of measurement (157). 

Theta solvents. Selection of a poor solvent for a polymer is desirable when making solution property measurements because it permits the use of higher concentrations and minimizes the effects of nonideality. The most suitable choice is a theta solvent (73). Table 12 lists the theta solvents and the corresponding theta temperatures which have been found for PTHF. 

The polymer assumes this average radius only if the individual links can move freely. This is the case if we neglect the excluded volume effect due to the other segments and if we assume an ideal solvent. In an ideal solvent, the interaction between subunits is equal to the interaction of a subunit with the solvent. In a real solvent the actual radius of gyration can be larger or smaller. In a good solvent a repulsive force acts between the monomers. The polymer swells and Rg increases. In a bad solvent the monomers attract each other, the polymer shrinks and Rg decreases. Often a bad solvent becomes a good solvent if the temperature is increased. The temperature, at which the polymer behaves ideally, is called the theta temperature, T0. The ideal solvent is called the theta solvent. 

For a series of homologous polymers A2 depends on M as well as T and the nature of the solvent. Experimental studies have repeatedly shown that for a given polymer there is a combination of poor solvent and temperature 0 for which A2 vanishes regardless of M. This spetial poor solvent at is called the theta solvent, and 0, the theta temperature. 

In between these cases we can define a so-called theta-solvent, which, as far as interactions are concerned, behaves, at a certain temperature, like the polymer. 

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. 

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. 

The method outlined above is now well established. Its application, however, is often limited by the difficulty of finding appropriate theta solvents. This limitation becomes especially serious for the investigation of crystalline polymers with high melting points, because for such polymers the theta condition can rarely be attained at ordinary temperatures. It is therefore highly desirable to develop a method for estimating the unperturbed dimensions without the aid of theta-solvent experiments. 

The Mandelkern-Flory viscosity data for cellulose tributyrate are plotted according to Eq. (58) in Fig. 18. It is seen that the line for the viscosities in the good solvent methyl ethyl ketone at 30° C passes without strain to the same intercept as the lines for the two high-temperature theta solvents. The intercept gives K = (9.7 1.5) 10-4 and a = 1.79 0.10, as listed in Table 9. Although, as discussed in the... 

Boldface letters and numbers indicate theta solvents and theta temperatures. ... 

Comprehensive Tables of Theta-solvents and Theta-temperatures have been published, e.g. by Elias (1999) and by Sundararajan (1996). 

The value of M determined by MO in tetrachloroethane (TCE) decreases with increasing temperature, approaching M as determined by MO in THF, as shown in Fig. 18 40). The CDA molecules have a considerable tendency to form aggregates in poor solvents, as is TCE below 70 °C. Ikeda and Kawaguchi52), who overlooked this phenomenon for CDA in TCE, claimed that TCE at 56.5 °C acts as a Flory theta solvent for CDA, for which the second virial coefficient A2 vanishes. 

It is well known that [r ] of most CD solutions decreases significantly with increasing temperature 80,82,83,86 90 103 109). Even in theta solvents, this effect has been observed for cellulose tricaprylate 104> and CTCp 86). This finding is in sharp contrast with what is known for vinyl polymers. 

Most polymers are more soluble in their solvents the higher the solution temperature. This is reflected in a reduction of the virial coefficient as the temperature is reduced. At a sufficiently low temperature, the second virial coeflicient may actually be zero. This is the Flory theta temperature, which is defined as that temperature at which a given polymer species of infinite molecular weight would be insoluble at great dilution in a particular solvent. A solvent, or mixture of solvents, for which such a temperature is experimentally attainable is a theta solvent for the particular polymer. 

The overlap concentration can be estimated as the concentration at which the number of coils per unit volume, v, times the volume pervaded by a single coil, R, is roughly unity, where Rg = R )q /Vb is the radius of gyration of the polymer coil. Now v = cNa/M, where c is the mass per unit volume of polymer in solution and Na is Avogadro s number. Therefore, in a theta solvent (a solvent at a temperature where polymer excluded-volume interactions are negligible see Section 2.3.1.2), the overlap concentration, c, is given by... 

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. 

Other factors affecting retention volume are the viscosity of the mobile phase, the sizes of gel pores, and the effective size of the solute molecules. Of these, the former two can be ignored, because they exhibit either no effect or only a small effect. The effective size of a solute molecule may also change with changing column temperature. The dependence of intrinsic viscosity on column temperature for PS in chloroform, tetrahydrofuran, and cyclohexane were tested [5]. The temperature dependence of intrinsic viscosity of PS solutions was observed over a range of temperatures. The intrinsic viscosity of PS in tetrahydrofuran is almost unchanged from 20°C up to 55°C, whereas the intrinsic viscosity in chloroform decreased from 30°C to 40°C. Cyclohexane is a theta solvent for PS at around 35°C and intrinsic viscosity in cyclohexane increased with increasing column temperature. 

C) Theta solvents. At some special temperature, called the -temperature. 

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