Solutions Theta temperature

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). 

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. 

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. 

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. 

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 ... 

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 ... 

Theta solvents. Selection of a poor solvent for a polymer is desirable when making solution property measurements because it permits the use of higher concentrations and minimizes the effects of nonideality. The most suitable choice is a theta solvent (73). Table 12 lists the theta solvents and the corresponding theta temperatures which have been found for PTHF. 

The sample was a solution of polystyrene (PS) dissolved in dioctyl phthalate (DOP). This system has a theta temperature of approximately 22°C [183] and has been the subject of most of the studies investigating flow-induced phase transitions in polymer solutions. The particular sample used here had a molecular weight for PS of 2 million, a poly-dispersity of MW/MN = 1.06, and a concentration of 6%. This results in a semidilute... 

J. O. Park and G. C. Berry, Moderately concentrated solutions of polystyrene. III. Viscoelastic properties at the Flory theta temperature , Macromolecules, 22, 3022 (1989). 

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 Flory-temperature or theta-temperature (0F) is defined as the temperature where the partial molar free energy due to polymer-solvent interactions is zero, i.e. when y = 0, so that the polymer-solvent systems show ideal solution behaviour. If T = 0F, the molecules can interpenetrate one another freely with no net interactions. For systems with an upper critical solution temperature (UCST) the polymer molecules attract one another at temperatures T < 0F. If the temperature is much below 0F precipitation occurs. On the other hand for systems with a lower critical solution temperature (LOST) the polymer molecules attract one another at temperatures T > F. If the temperature is much above 0F precipitation occurs. Aqueous polymer solutions show this behaviour. Systems with both UCST and LCST are also known (see, e.g. Napper, 1983). 

Fig. 6. Phase diagram for the solution of semi-flexible macromolecules. I isotropic phase, II anisotropic phase. III phase separation region. Dotted curves - phase diagram for the solution of rigid rods with the same p (see Fig. 2). T3 triple point temperature, 6 the theta temperature...

Krigbaum, W. R. Geymer, D. 0., "Thermodynamics of Polymer Solutions. The Polystyrene-Cyclohexane System Near the Flory Theta Temperature," J. Am. Chem. Soc., 81, 1859 (1959). 

Fujimatsu, H. Ogasawara, S. Kuroiwa, S., "Lower Critical Solution Temperature (LCST) and Theta Temperature of Aqueous Solutions of Nonionic Surface Active Agents of Various Polyoxyethylene Chain Lenghts," Coll. Polym. Sci., 266, 594 (1988). 

Nanoparticles of PS (M =1.0xl0 -3.0xl0 mol ) microlatexes (10-30 nm) have also been successfully prepared from their respective commercial PS for the first time [75]. The dilute PS solutions (cyclohexane, toluene/methanol or cyclohexane/toluene) were induced to form polymer particles at their respective theta temperatures. The cationic CTAB was used to stabihze th microlatexes. The characteristics of these as-formed PS latex particles were quite similar to those obtained from the microemulsion polymerization of styrene as reported in literature. These microlatexes could also be grown to about 50 nm by seeding the polymerization of styrene with a monodisperse size distribution of D /Djj=1.08. This new physical method for preparing polymer nano-sized latexes from commercial polymers may have some potential applications, and therefore warrants further study. 

Most polymers are more soluble in their solvents the higher the solution temperature. This is reflected in a reduction of the virial coefficient as the temperature is reduced. At a sufficiently low temperature, the second virial coeflicient may actually be zero. This is the Flory theta temperature, which is defined as that temperature at which a given polymer species of infinite molecular weight would be insoluble at great dilution in a particular solvent. A solvent, or mixture of solvents, for which such a temperature is experimentally attainable is a theta solvent for the particular polymer. 

At equilibrium, the distribution of conformations in a solvent at the theta temperature (see Section 2.3.1.2), or in a concentrated solution, is given by a set of random walks or, equivalently, by the conformations of a. freely jointed chain (see Section 2.2.3.2). If one end of the freely jointed chain with links, each of length bjc, lies at the origin, then-the probability, jrodR, that the other end lies at a position between R and R + dR is approximately a Gaussian function (Flory 1969 Larson 1988) ... 

Figure 5.13 Predicted phase diagrams for physical gels made from low-molecular-weight molecules with junctions of unrestricted functionality 4> is the total volume fraction of polymer, and Tr is here the reduced distance from the theta temperature, Tr = — Q/T. The parameter Aq controls the equilibrium constant among aggregates of various sizes. The outer solid lines are binodals, the inner solid lines are spinodals, and the dashed lines are gelation transitions. CP is a critical solution point, CEP is a critical end point, and TCP is a tricriti-cal point. (Reprinted with permission from Tanaka and Stockmayer, Macromolecules 27 3943. Copyright 1994 American Chemical Society.)...

Fig. 16. lAygTj at constant temperature versus logq>2Z for solutions of poly (vinyl acetate) in diethyl phthalate, O, and cetyl alcohol, —O, at the theta temperature for dilute cetyl alcohol solutions. The straight lines have slopes 1.0 and 3.4. The independence of from may be noted... 

The lower theta temperature corresponds to the minimum solution temperature extrapolated to infinite chain length. Polymer precipitation at low temperatures comes about because of a poor heat of mixing between polymer and solvent. In a sealed tube at high temperatures, solvent volume expands much more than that of the polymer. Entropic factors make mixing more difficult when there is a large free volume mismatch between solute and solvent. One believes that the polymer dimensions contract as the LCST is approached. Phase separation occurs when it is exceeded. 

Particularly evident is the lack of systematic reports on polymer-mixed solvents data (VLE or LLE) in the open hterature, especially in form of full-phase equilibrium measurements. Most experimental studies for mixed solvent systans have been reported by Chinese and Japanese investigators - and only a few by other investigators. Data are often reported simply as soluble/nonsoluble or as theta temperatures (critical solution temperature at infinite polymer molecular weight). Several reported polymer-mixed solvent data concern supercritical fluid applications (e.g., polypropylene/pen-tane/C02, and PEG/C02/cosolvent ) and bioseparations, especially for systems related to the partitioning of biomolecules in aqueons two-phase systems, which contain PEG and dextran. A recent review for data on solnbihty of gases in glassy polymers is also available. ... 

Schultz and Flory have developed, starting from the FH model and Equation 16.41, the following expression, which relates the critical solution temperature (CST), with the theta temperature and the polymer molecular weight ... 

Theta (6) solvents are solvents in which, at a given temperature, a polymer molecule is in the so-called theta-state. The temperature is known as the theta-temperature or the Flory temperature. (Since P. J. Flory was the first to show the importance of the theta-state for a better understanding of molecular and technological properties of polymers, theta temperatures are also called Flory temperatures. ) In the theta-state, as explained above, the solution behaves thermodynamically ideal at low concentrations. 

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. 

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