Theta temperature determination

Theta temperature (Flory temperature or ideal temperature) is the temperature at which, for a given polymer-solvent pair, the polymer exists in its unperturbed dimensions. The theta temperature, , can be determined by colligative property measurements, by determining the second virial coefficient. At theta temperature the second virial coefficient becomes zero. More rapid methods use turbidity and cloud point temperature measurements. In this method, the linearity of the reciprocal cloud point temperature (l/Tcp) against the logarithm of the polymer volume fraction (( )) is observed. Extrapolation to log ( ) = 0 gives the reciprocal theta temperature (Guner and Kara 1998). 

Theta temperature is one of the most important thermodynamic parameters of polymer solutions. At theta temperature, the long-range interactions vanish, segmental interactions become more effective and the polymer chains assume their unperturbed dimensions. It can be determined by light scattering and osmotic pressure measurements. These techniques are based on the fact that the second virial coefficient, A2, becomes zero at the theta conditions. 

This stipulation of the interaction parameter to be equal to 0.5 at the theta temperature is found to hold with values of Xh and Xs equal to 0.5 - x < 2.7 x lO-s, and this value tends to decrease with increasing temperature. The values of = 308.6 K were found from the temperature dependence of the interaction parameter for gelatin B. Naturally, determination of the correct theta temperature of a chosen polymer/solvent system has a great physic-chemical importance for polymer solutions thermodynamically. It is quite well known that the second viiial coefficient can also be evaluated from osmometry and light scattering measurements which consequently exhibits temperature dependence, finally yielding the theta temperature for the system under study. However, the evaluation of second virial... 

Guner, A., Kibarer, G. 2001. The important role of thermodynamic interaction parameter in the determination of theta temperature, dextran/water system. European Polymer Journal, 37, 619-622. 

Table 8. Concentration dependent parameters p, and p2 in the y parameter, Flory s theta temperature 9, and the entropy parameter J/ of cellulose diacetate, determined by different methods611... 

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 critical temperature %) at which the solutions of cis-1,4-polybutadiene in n-heptane underwent separation into two phases were measured for three carefully fractionated polymer samples having different molecular weights (M). From the data, given below, determine the theta temperature (0) for the polymer in n-heptane. 

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. 

The method for determining the theta temperature based on Equation (6-100) requires several samples of known degree of polymerization and is... 

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).

Only a few sterns are available which meet these conditions. The first degradation studies investigating the interrelation of thermodynamics and chain scission were done using polystyrene (PS) in various solvents The system studied most extensively so far is given by trons-decalin/PS (TD/PS) It exhibits upper critical solution temperature and a theta temperature of 21 °C Figure 5 shows the corresponding cloud point curves determined for narrowly distributed PS samples. 

The same behavior as that described for the second osmotic virial coefficients has been reported for the radii of gyration determined by static light scattering. At the theta temperature of the system PMAC dissolved in toluene, Kuhn s law (< Kg A4) was verified [13, 15, 20]. 

The method for determining the theta temperature based on equation (6-100) requires several samples of known degree of polymerization and is very time consuming. The theta temperature for a single sample of unknown molecular weight can be determined by another process. The method was first evolved for the determination of theta mixtures and was later used to determine the theta temperatures of binary and quasibinary systems. 

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... 

Theoretical approaches to determine solution structures of neutral polymers act on the assumption of the pseudo ideal state. Here the solvation forces from the solvent and the aggregation forces of the chain segments are in an equilibrium where the coil appears to be unaffected by forces. This pseudo ideal state is called the theta state. Theta conditions exist when the exponent a of the [q]-M-relationship has the value a=0.5 and at the same time the value of the second virial coefficient is A2=0 (see the chapter "The [q]-M-relationship in this monograph). Accordingly, a pseudo ideal solvent is called theta solvent and the corresponding temperature is called theta temperature. As Flory showed in his Nobel price lecture [1], the theta state can be described mathematically exactly from the chemical structure of the chain. 

Solvents where a Q has the value one are so-called theta -solvents with the coil in its unperturbed dimensions. In general, all solvents for a certain polymer can behave as a theta-solvent at theta -temperature, since the solvent polymer interactions depend on the temperature. Theta-temperatures are listed for several polymer-solvent systems [13,45]. The values for C ,listed in the polymer handbook are determined for theta-systems. Only for these systems, a calculation of the radius of gyration according to Eq. (8.15) is acceptable. The parameter a is experimentally not accessible and therefore not tabulated. Since a also depends on the molar mass M, the radius of gyration for non-theta systems is generally determined directly from the molar mass via an i Q-M-relationship. 

Methods to Determine Theta Solvents Solvents in which, at a given temperature a polymer molecule is in the so-called theta-state, are called theta (6) solvents. The temperature is known as the theta-temperature or the Flory temperature (as P. J. Hory was the rst to show the importance... 

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