In theta solvent

In particular it has been conjectured that the terminal relaxation of star polymers might be the most sensitive test of the dilution exponent P in Go theta solvents suggest a mean value of nearer 2.3 [32]. A physically reasonable scahng assumption for the density of topological entanglements in a melt of Gaussian chains leads to a value of 7/3 [31]. 

What is the value of the exponent a in the Mark-Houwink equation for polymers in theta solvents ... 

An alternative approach for determining the molecular weight of a polymer in theta solvents includes the determination of the polymer s concentration at the meniscus (c ,) and at the bottom ic, ) (or alternatively at two other positions Xi and X2) in the cell. These two outstanding positions have a distance of x ix ) and Xh(x2), respectively, from the center of rotation. Then, one obtains the weight-average molecular weight of a polydisperse polymer sample via the equation ... 

Experimentally k is essentially independent of molecular weight for long chains, with values of roughly 0.30-0.40 in good solvents and 0.50-0.80 in theta solvents. 

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,... 

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... 

The value of kA is large and positive for high molecular weight polymers in good solvents, where the term involving A2 dominates, while in theta solvents (A2 = 0), kd has a small negative value which reflects k, (Kent et al. 1994). 

The new factor ccrJctf is unity in theta solvents and 0.97 in the asymptotic limit of very good solvents. This indicates that the quantity / varies only from 2.7 10 to 2.6 10 with increasing solvent power. The molecular weight obtained by Eq. (72) is thus affected to only 5 or 6% by the variation of y5, and the effect may be safely ignored for most purposes. 

Fig. 27. Viscosity-molecular weight relation lor paiy-y-benzyl-L-glutamate. Solid curve, theory lor random coil in DCA, Eqs. (58) and (86). Chain curve, theory lor rigid ellipsoids in DMF. Dashed curve, random coils in theta solvent, K — 58 10". Dotted curve, hypothetical curve lor random coils (or interrupted helices)...

Obviously the value a is dependent on the nature of the polymer-solvent interaction in theta solvents a = 0.5, while in "good" solvents a 0.8. Therefore some relationship between a and the solubility parameter of the solvent, r)s, may be expected. 

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. 

In theta solvents, experimental results confirm the scaling predicted for [rjh in the limit of dominant hydrodynamic interaction. In good solvents, the measured exponent is generally slightly less than the value, 4/5, predicted for dominant hydrodynamic interaction. The scaling law, [jyJo = for a flexible polymer in a theta solvent is often used to... 

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). 

In theta solvents, excluded volume effects vanish and flexible molecular chains behave as phantom chains (1). The characteristic ratio Cn = where (r )o is the mean square end-to-end distance of a... 

In theta solvents v=l/2, and consequently A i/2 Therefore, Eqs (11.21) and (11.25) suggest that the scaling laws for the diffusion coefficient and the rotational relaxation time are... 

The current state of theory is quite crude state-of-the-art density functional theory calculations (e.g. PRISM ) have yielded scant clues about the renormalisation of isomeric state potentials due to density, and phenomenological theories have introduced an admittedly ad hoc coupling. Hence there is a clear need for theory which captures the minimal necessary molecular detail of orientation, conformation and packing. A possible route is simulation computational speed can almost handle the necessary melt simulations, while simulations of solution crystallisation have demonstrated how orientational correlations grow as crystallisation in theta solvent conditions. ... 

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]. 

There are two basic ways in which measurements of the unperturbed dimensions are obtained (1) determination of unperturbed dimensions directly, by measurements in theta solvents and (2) determination of the perturbed dimensions in a good solvent and extrapolation of the values to the unperturbed state using one of the existing theories. Both methods have been widely used as will be shown. 

Viscosity measurements on polymers dissolved in theta solvents have proved more useful. However, again measurements are subject to difficulties due to poor solubility near the theta point. At the theta temperature the Flory-Fox relationship31 reduces to ... 

The unperturbed dimensions for a number of stereoregular polymers have been studied by dilute solution viscometry in theta solvents. Given in Tables (1—8) are... 

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