Dilute theta solutions

Er. Gulari, Es. Gulari, Y. Sunashima and B. Chu, Polymer diffusion in a dilute theta solution, 1, Polystyrene in cyclohexane, Polymer 20 (1979) 347-355. 

The pseudoideal or theta solution is an important special case of irregular solutions in macromolecular science. The enthalpy of mixing and the excess entropy of mixing exactly compensate each other at a certain temperature with the dilute theta solution. Theta solutions at this theta temperature thus behave like ideal solutions. In contrast to ideal solutions, however, the enthalpy of mixing is not zero and the entropy of mixing differs considerably from the ideal entropy of mixing. Thus, an ideal solution exhibits ideal behavior at all temperatures, the pseudoideal solution only behaves ideally at... 

Theta conditions in dilute polymer solutions are similar to tire state of van der Waals gases near tire Boyle temperature. At this temperature, excluded-volume effects and van der Waals attraction compensate each other, so tliat tire second virial coefficient of tire expansion of tire pressure as a function of tire concentration vanishes. On dealing witli solutions, tire quantity of interest becomes tire osmotic pressure IT ratlier tlian tire pressure. Its virial expansion may be written as... 

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 ... 

Figure 14 Potential distribution at the surface of the A1 matrix near a theta phase precipitate assuming a nonpolarizable cathode site (Al2Cu precipitate), polarizable passive A1 matrix, and a dilute acidic solution. The effect of precipitate size is shown. (From Ref. 26.)...

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. 

When X = 2 th e two effects compensate each other, (/ii — / l) = 0 and the dilute polymer solution behaves ideally, i.e., as if Hrmx — 0 and the polymer chain segments were not connected. Flory used the term theta conditions to describe this ideal state of dilute polymer solutions and developed the concept further by defining the excess partial molar enthalpy,, and entropy, AS, of mixing as... 

Mixing is promoted by a negative value of (/ii — which according to Eq. (3.98) corresponds to x < 2 according to Eq. (3.107) corresponds to T > 0 for positive ip and T < 6 for negative ip. These equations also show that under theta conditions x = 2 T = 6 and the dilute polymer solution then behaves as an ideal solution. Values of 6 and -ip for a number of polymer-solvent systems [5] are given in Table 3.1. 

Adam, M., and Delsanti, M., Viscosity and longest relaxation time of semi-dilute polymer solutions n. Theta solvent, J. Phys. (Paris), 45, 1513-1521 (1984). 

The process uses very dilute solutions, normally in the concentration range of 2 between 10" and 10. In what is called the cloud-point titration method, dilute polymer solutions are titrated with nonsolvent at constant temperature to the first cloud point. The volume fraction 3 of nonsolvent to give the first cloud point is plotted against the logarithm of the volume fraction 2 of the polymer at the cloud point. The extrapolated straight line obtained for a hoinologous series at a point on the 2 = 1 axis was found experimentally and theoretically to be equivalent to (3)0 (Figure 6-19). (3)e corresponds to the solvent-precipitant theta mixture for the polymer at this temperature. 

Flory s analysis focuses on the thermodynamic interactions between polymers, and defines the theta point at the critical polymer concentration for phase separation (equal to the critical concentration of chain units within a single chain upon collapse transition), similar to the Boyle point of the non-ideal gas. We can perform Virial expansion on the osmotic pressure of dilute polymer solutions, as... 

Therefore, the construction of appropriate equilibrium configurations of polymer chains in a lattice model is always a problem. For a dilute solution under good solvent conditions the excluded volume interaction between all monomers of the chain can no longer be ignored. It leads to a swelling of the chain with respect to its size in the melt or in theta solution. Thus, Eq. (5) does not hold, but has to be replaced by... 

For sufficiently dilute polymer solutions, the only difference between the new approach and the original Flory-Huggins theory is in the second term. According to theoretical considerations and in accord with experimental findings, becomes zero under theta conditions (where the coils assume their unperturbed dimensions) and the conformational relaxation no longer contributes to... 

As well as controlling chain dimensions, solvent quality affects the thermodynamics of dilute polymer solutions. This is because interactions between polymer chains are modified by the presence of solvent molecules. In particular, solvent molecules will change the excluded volume for a polymer coil, i.e. how much volume it takes up and prevents neighbouring chains from occupying. In a theta solvent, the excluded volume is zero (this holds for the excluded volume for a polymer segment or the whole coil). The solution is said to he ideal if the excluded volume vanishes. Deviations from ideality for polymer solutions are described in terms of a virial equation, just as deviations from ideal gas behaviour are. The virial equation for a polymer solution in terms of polymer concentration is given by Eq. (2.9). The second virial coefficient depends on interactions between pairs of molecules in particular it is proportional to the excluded volume. Therefore, in a theta solvent, = 0. If the solvent is good then Ai > 0, but if it is poor Ai < 0. If the solvent quality varies as a function of temperature and theta (0) conditions are attained, this occurs at the theta temperature. 

A distinct mechanism, which also leads to attractive forces between adsorption layers, was investigated in experiments with dilute polymer solutions in bad solvents. An example is given by PS in cyclohexane below the theta temperature [51]. The subsequently developed theory [52] showed that the adsorption layers attract each other since the local concentration in the outer part of the adsorption layers is enhanced over the dilute solution and lies in the unstable two-phase region of the bulk phase diagram. Similar experiments were repeated at the theta temperature [53]. 

While the Rouse model was originally intended to describe dilute polymer solutions, Bueche [6] noted that the freely-jointed chain model should be able to describe the behavior of an unentangled melt. It has been found experimentally that the static interactions between a polymer molecule and its surroundings are normally the same in the melt as in a solution in its theta state, although Krishnamoorti et al. [7] have noted a few cases where chain dimensions are different in the melt and at the theta state. They attribute this to the ability of some theta solvents to induce a conformer population different from what is favored in the melt state . 

The formulation of the hydrodynamic constant theta and the definition of the Theta Point, where excluded volume effects are neutrahzed. These results were particularly important, because they allow a rational interpretation of physical measurements of dilute polymer solutions. 

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). 

A. Milchev, W. Paul, K. Binder. Off-lattice Monte Carlo simulation of dilute and concentrated polymer solutions under theta conditions. J Chem Phys 99 4786-4798, 1993. 

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. 

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