Theta temperature solution viscosity

It is well established that the excluded volume effect vanishes under a special condition of temperature or solvent, which is usually known as the Flory theta temperature or solvent. Thus, light scattering measurements performed on solutions under theta conditions can furnish direct knowledge of the unperturbed dimensions [see, for example, Outer, Carr and Zimm (207) Shultz (233) and Notley and Debye (207)]. Viscosity measurements, though less directly, can also furnish similar knowledge with the aid of the Flory-Fox equation (103,109), which may be written... 

The viscosity method makes use of the fact that the exponent, a, in the Mark-Houwink equation (see Frictional Properties of Polymer Molecules in Dilute Solution), rj = KM° , is equal to 0.5 for a random coil in a theta-solvent. A series of polymers of the same type with widely different known molecular weights is used to determine intrinsic viscosities [t ] at different temperatures and hence a at different temperatures. The theta-temperature can thus be determined either by direct experiment or, if it is not in the measurable range, by calculation. 

Viscosity measurements were made on solutions of fractionated cis-1,4-polybutadiene samples in toluene at 30°C and in n-heptane at —1°C (theta temperature), yielding the following values of intrinsic viscosities (in dL/g) ... 

One of the main features of nonionic water-soluble cellulose derivatives is that they exhibit, like some other polyethers, an inverse solubility-temperature behavior, i.e. there is phase separation on heating above the so-called lower critical solution temperature (LCST). The temperature at which a polymer-rich phase separates is normally referred to as the cloud point (CP). For ideal solutions, this temperature corresponds to the theta-temperature. Actually, for some derivatives, the cloud point may be preceded, if the concentration is not too low, by a sol-gel transformation with an increase in viscosity and possibly formation of liquid crystals (see Sect. 3.5). As it will be seen later, this reversible thermotropic behavior may be detrimental to the performance of the derivatives or can be advantageneously utilized to develop applications. 

We first consider the behavior of the dynamic storage modulus and the dynamic loss modulus. Colby, et a/. (15) report an extremely extensive series of measurements of the storage and loss moduli of a 925 kDa (M ) polybutadiene having a narrow molecular weight distribution (M /Mn < 1.1 M /Mw < 1-1). Solutions were made in the Theta solvent dioctylphthalate (DOP) at 12°C above the Theta temperature, and the good solvent phenyloctane (PO). Viscosities were reported at 15 volume fractions extending from extreme dilution 0.001) up to the melt full... 

The intrinsic viscosity in any solvent is therefore predicted to vary as at the theta point (T = 0f). Comparing Equations 7.42 and 7.44 indicates that a = 0.5 for all polymer solutions at the theta temperature. Under good solvent conditions, a and a = 0.8. 

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. 

Equations (19) and (20) are valid in theta solvent. The more compact structure and the lack of chain ends result in different chemical and physical properties of cyclic polymers, including lower translational friction coefficients, higher glass transition temperatures [167], faster crystallization [168], higher refractive index [169], higher density [170], higher critical solution temperature [167], and lower intrinsic viscosity [167, 171, 172]. 

The change in viscosity of these solutions is due to changes in the dimensions of the coils of polymer molecules in solution. Depending on the type of solvent, the polymer molecules will either seek more contact with the solvent molecules (the coil will swell) or with itself (coils become more compact). Under certain, the so-called theta, conditions, the coil has undisturbed, ideal dimensions. A solvent in which at room temperature a polymer forms such undisturbed coils is named a theta solvent for this polymer. In principle such a solvent has exactly the same solubility parameters as the polymer in question. 

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