Temperature theta

In polymer solutions with LCST, the critical temperature is higher than T, (Fig. 2.23b). The sign of A2 changes from positive to negative as the temperature exceeds T.  

The theta temperature is different for each combination of polymer and solvent. Table 2.6 lists for some polymer solutions. Each system has its own theta temperature, although it may not be reached in the liquid phase of the solvent or below the decomposition temperature of the polymer. 

There is a slight molecular weight dependence of the temperature that renders A2 = 0 when the molecular weight is not sufficiently high. The dependence is much 

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Table 8.3 Theta Temperatures for a Few Polymer-Solvent Systems...

Polymers in Solution. Polyacrylamide is soluble in water at all concentrations, temperatures, and pH values. An extrapolated theta temperature in water is approximately —40° C (17). Insoluble gel fractions are sometimes obtained owing to cross-link formation between chains or to the formation of imide groups along the polymer chains (18). In very dilute solution, polyacrylamide exists as unassociated coils which can have an eUipsoidal or beanlike stmcture (19). Large aggregates of polymer chains have been observed in hydrolyzed polyacrylamides (20) and in copolymers containing a small amount of hydrophobic groups (21). 

Although the properties of specific polymer/wall systems are no longer accessible, the various phase transitions of polymers in confined geometries can be treated (Fig. 1). For semi-infinite systems two distinct phase transitions occur for volume fraction 0 = 0 and chain length N oo, namely collapse in the bulk (at the theta-temperature 6 [26,27]) and adsorp-... 

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. 1999. Unperturbed dimensions and theta temperature of dextran in aqueous solutions. Journal of Applied Polymer Science 72, 871-876. 

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. 

For the first non electrostatic term, such a dependence can be calculated from the classical Flory theory and the value of the theta temperature of unhydrolyzed polyacrylamide ( 0 = 265°K (22))... 

Fig. 12. Inverse of the reduced theta temperature for which the second virial coefficient vanishes from MC calculations on a cubic lattice for linear chains (squares) and f=6 stars (cir-clelike) broken lines (no symbols) stars with f=4 and 5. Reprinted with permission from [144]. Copyright (1991) American Chemical Society...

The slope of the lines in Figure 3.10, i.e., the virial constant B, is related to the CED. The value for B would be zero at the theta temperature. Since this slope increases with solvency, it is advantageous to use a dilute solution consisting of a polymer and a poor solvent to minimize extrapolation errors. 

However, if the original temperature is below the theta temperature, the viscosity will increase when the mixture of polymer and solvent is heated to a temperature slightly above the theta temperature. 

Flory and Huggins developed an interaction parameter that may be used as a measure of the solvent power of solvents for amorphous polymers. Flory and Krigbaum introduced the idea of a theta temperature, which is the temperature at which an infinitely long polymer chain exists as a statistical coil in a solvent. 

What is the value of the Gibbs free energy change at the theta temperature ... 

At which temperature will the polymer coil be larger in a poor solvent (a) at the theta temperature (b) below the theta temperature or (c) above the theta temperature ... 

The interactions between solvent and polymer depend not only on the nature of the polymer and type of solvent but also on the temperature. Increasing temperature usually favors solvation of the macromolecule by the solvent (the coil expands further and a becomes larger), while with decreasing temperature the association of like species, i.e., between segments of the polymer chains and between solvent molecules, is preferred. In principle, for a given polymer there is a temperature for every solvent at which the two sets of forces (solvation and association) are equally strong this is designated the theta temperature. At this temperature the dissolved polymer exists in solution in the form of a nonexpanded coil, i.e., the exponent a has the value 0.5. This situation is found for numerous polymers e.g., the theta temperature is 34 °C for polystyrene in cyclohexane, and 14 °C for polyisobutylene in benzene. 

Flory has defined the theta temperature as that temperature at which the pointer exists in a advent in an unperturbed conformation. The polymer chain ft[pt nh as the temperature is increased and contracts m the temperature to decreased below the theta temperature. 

Interactions between different distant parts of the molecule tend to expand it, so that in the absence of other effects a would be greater than unity, but in solution in poor solvents interactions with the solvent tend to contract it. According to Flory s theory (18) these two tendencies will just balance so that a — 1 at a particular temperature T—0 (the theta temperature ), and at this temperature A2 =0 and further this temperature is the limit as Mn- go of the upper critical solution temperature for the polymer-solvent system in question. Quantities relating to T=0 will be denoted by subscript 0. Flory s theory implies that ... 

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. 

We discuss this more fully below, but one thing to note immediately is that T = 9 describes the same state as described by x = 1/2, namely, the condition of B = 0. It is apparent that 9 is a temperature —variously known as the theta temperature or the Flory temperature. Introducing this parameter indicates why the B = 0 situation is called the 9 condition. In order to justify the equivalence of the two sides of Equation (81), consider the following steps ... 

The ratio of A// to AS has kelvin units this quantity is called the theta temperature. 

EXAMPLE 3.4 Theta Temperature of A Polymer Solution from Second Virial Coefficient Data. Values of the second virial coefficient along with some pertinent volumes are tabulated below for the polystyrene-cyclohexane system at three temperatures. 

Solution The theta temperature is that value of T at which B = 0. It is apparent that B changes sign (i.e., passes through zero) about midway between 303 and 313K. Equations (80) and (81) can be combined to give... 

What is theta temperature (or, the Flory temperature) What are the relative magnitudes of the excluded-volume interactions and the energetic interactions in a dilute polymer solution at its theta temperature ... 

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