Theta temperature intrinsic viscosity

Ratio of a dimensional characteristic of a macromolecule in a given solvent at a given temperature to the same dimensional characteristic in the theta state at the same temperature. The most frequently used expansion factors are expansion factor of the mean-square end-to-end distance, Ur = (/o) expansion factor of the radius oj gyration, as = (/0) relative viscosity, = ([ /]/[ /]o), where [ ] and [ /]o are the intrinsic viscosity in a given solvent and in the theta state at the same temperature, respectively. 

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. 

In principle, intrinsic viscosities used for estimating branching should be measured under conditions where the expansion factor a is unity, but as indicated in Section 6, it is not easy to identify such conditions. Some authors, e.g. Moore and Millns (40) have measured [tf at the theta-temperature of the corresponding linear polymer, but it is doubtful whether a is unity at that temperature for either linear or branched polymer, if the theories of Casassa or of Candau et al. are valid. If a were the same for both linear and branched polymers under the same conditions g would be unaffected and g could be measured at any convenient temperature some authors have presented data suggesting that g is nearly the same in good and poor solvents, e.g. Hama (42) and Graessley (477), but other authors, e.g. Berry (43) have found g to vary. The best that can be done at present would appear to be to measure g at the theta-temperature on the assumption that this ratio will be less temperature-sensitive than either intrinsic viscosity, and that even if this temperature is not the correct one it will be near it. Errors in estimates of branching due to this effect are likely to be much less serious than those due to the use of an incorrect relation between g and g0. 

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. 

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. 

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. 

Problem 3.25 For a fractionated sample of cis-1,4-polybutadiene of molecular weight 123x10 intrinsic viscosities were measured [30] in three different solvents at respective theta temperatures. From the results given below determine the variation of the unperturbed dimensions of the polymer molecule with temperature. 

The intrinsic viscosities of polyisobutylene of molecular weight 5.58x10 in cyclohexane at 30°C and in benzene at 24°C (theta temperature) are 2.48 dI7g and 0.799 dL/g, respectively. Calculate (a) unperturbed end-to-end chain length of the polymer, (b) end-to-end chain length of the polymer in cyclohexane at 30°C, and (c) volume expansion factor in cyclohexane at 30°C. Take = 2.5xl0 . 

Polyisobutylene fraction of molecular weight 540,000 was used for viscosity measurements in cyclohexane and benzene. The intrinsic viscosity values obtained were 2.48 dL/g in cyclohexane at 30°C and 0.80 dL/g in benzene at the theta temperature (24°C). The observed relation between molecular weight and unperturbed end-to-end distance is given by... 

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) ... 

From Equation 12.71, the intrinsic viscosity depends on the molecular weight as a result of the factor and also through the dependence of the expansion factor on molecular weight. By choosing a theta-solvent or 0 temperature, the influence of the molecular expansion due to intramolecular interactions can be eliminated. Under these conditions, a = 1, and the intrinsic viscosity depends only on the molecular weight. Thus Equation 12.71 is reduced to ... 

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]. 

At the theta temperature, the intrinsic viscosity [17] is related to the unperturbed dimension of the polymer and its molecular weight [1] by... 

The determination of the theta temperature by several techniques, such as intrinsic viscosity, phase equilibria, osmometry, light scattering, sedimentation equilibrium, and cloud point titration has been discussed comprehensively in a number of sources [1,14—16]. The influence of... 

The Hory-Fox eqnation predicts that the intrinsic viscosity wonld depend on (i) the stiffness of the polymer chain (throngh the term (r )olM), (ii) the molecnlar weight of the polymer (through and (iii) the solvent-polymer-temperature combination (throngh a ). Under theta conditions, a,j is unity and Eq. (3.149) predicts a dependence of [q] on the sqnare root of the molecular weight. This behavior has been con rmed experimentally for several polymer-solvent systems. The exponent 0.5 can be considered as a lower limit since much poorer solvents will not dissolve the polymer. On the other hand, in very good solvents, where there is large expansion of polymer coil, is proportional to (see Problem 3.12). Hence the intrinsic viscosity will vary as i.e., as This is an upper limit. For other solvents and non-theta... 

Universal Calibration Curve in SEC In the Zimm model (theta and good solvents), the intrinsic viscosity is essentially the ratio of the volume of the polymer chain, R/, to the mass of each polymer chain, M/Np. The solvent viscosity and the temperature do not show up explicitly in the final expression. Thus we can define hydrodynamic volume VMby... 

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),... 

In mixed solvents, these effeets may be enhaneed by a possible distribution of solvent components, depending on the polarities of the polymer 2 and liquids 1 and 3 1 is a solvent and liquid 3 usually a non-solvent (precipitant). It seems that in the absence of large variations of theta temperatures, the unperturbed dimension of a given apolar polymer is approximately the same in various apolar solvents. However, unperturbed dimensions (as determined from intrinsic viscosities) m vary widely for polar polymers in various polar theta mixtures (3 1,95,154). For a review of various methods for the determination of unperturbed dimensions in mixed solvents see (526). 

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