Theta condition temperature

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... 

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. 

The stability of these dispersions has been investigated. A strong dependence of critical flocculation conditions (temperature or volume fraction of added non-solvent) on particle concentration was found. Moreover, there seems to be little or no correlation between the critical flocculation conditions and the corresponding theta-conditions for the stabilising polymer chains, as proposed by Napper. Although a detailed explanation is difficult to give a tentative explanation for this unexpected behaviour is suggested in terms of the weak flocculation theory of Vincent et al. 

It is however possible to find conditions, called unperturbed or theta conditions (because for each polymer-solvent pair they correspond to a well-defined temperature called d temperature) in which a tends to 1 and the mean-square distance reduces to Q. In 6 conditions well-separated chain segments experience neither attraction nor repulsion. In other words, there are no long-range interactions and the conformational statistics of the macromolecule may be derived from the energy of interaction between neighboring monomer units. For a high molecular weight chain in unperturbed conditions there is a simple relationship between the mean-square end-to-end distance < > and the mean-... 

The unconventional applications of SEC usually produce estimated values of various characteristics, which are valuable for further analyses. These embrace assessment of theta conditions for given polymer (mixed solvent-eluent composition and temperature Section 16.2.2), second virial coefficients A2 [109], coefficients of preferential solvation of macromolecules in mixed solvents (eluents) [40], as well as estimation of pore size distribution within porous bodies (inverse SEC) [136-140] and rates of diffusion of macromolecules within porous bodies. Some semiquantitative information on polymer samples can be obtained from the SEC results indirectly, for example, the assessment of the polymer stereoregularity from the stability of macromolecular aggregates (PVC [140]), of the segment lengths in polymer crystallites after their controlled partial degradation [141], and of the enthalpic interactions between unlike polymers in solution (in eluent) [142], as well as between polymer and column packing [123,143]. 

Experimentally, good solvent conditions have been observed [22,23,27,28, 34,35]. On the other hand, none has been reported for the prediction of the theta condition, y = 101, whereas the prediction of poor solvent conditions giving rise to y > 3 has been reported. These all have y < 20 except for two they are poly(methyl acrylate) at lower temperatures [34] and poly(dimethyl siloxane) [24]. Others have failed to reproduce them since. A caveat needs to be raised with these results. Since the semi-dilute regime is so narrow in r before the collapse state sets in whereby the power exponent is commonly deduced for a r range less than one full decade hence, the r scaling is at best qualitative in the static characterization. 

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 method outlined above is now well established. Its application, however, is often limited by the difficulty of finding appropriate theta solvents. This limitation becomes especially serious for the investigation of crystalline polymers with high melting points, because for such polymers the theta condition can rarely be attained at ordinary temperatures. It is therefore highly desirable to develop a method for estimating the unperturbed dimensions without the aid of theta-solvent experiments. 

Theta conditions are of great theoretical interest because the diameter of the polymer chain random coil in solution is thenequal to the diameter it would have in the amorphous bulk polymer at the same temperature. The solvent neither expands nor contracts the macromolecule, which is said to be in its unperturbed state. The theta solution allows the experimenter to obtain polymer molecules which are unperturbed by solvent but separated from each other far enough not to be entangled. Theta solutions are not normally used for molecular weight measurements, because they are on the verge of precipitation. The excluded volume vanishes under theta conditions, along with the second virial coelTicient. 

Bishop and Clarke employed Brownian dynamics to study the end-to-end distribution function of two-dimensional linear chains in different regimes excluded volume, theta condition, and collapsed. The results show that Mazur s function fits the first regime while the collapsed condition is satisfactorily represented by a Gaussian. However, the changeover in behavior between these two conditions appears to occut at temperatures that are well above the expected theta point. 

Determine for the polymer-solvent system, (a) the temperature at which theta conditions are attained, (b) the entropy of dilution parameter 1/) and (c) the heat of dilution parameter k at 27°C. [Specific volume of polymer = 0.96 cm /g molar volume of cyclohexane at 27°C = 108.7 cm /mol.]... 

Theta conditions occur at a particular temperature T = 6, known as the theta (or Flory) temperature, for which (jj,i — = 0. It means... 

Conditions that cause the extended polymer segments to become insoluble in the medium will also, in general, give rise to flocculation and even coalescence of the emulsion. Flory (3) defined theta conditions as conditions of temperature and solvent composition under which the free energy of interaction between polymer segments equals the free energy of polymer-solvent interaction. Under theta conditions, the soluble segments of a steric stabilizer would collapse, the repulsion between droplets would diminish, and flocculation of the system would be expected to ensue. This prediction has been demonstrated experimentally (20, 21). 

Equations 70 and 72 are numerically very similar using the value v = 2.5 for any particle with spherical symmetry and have been reported to accurately describe kf of PS and poly-a-methylstyrene in cyclohexane at the theta temperature (84) based on sedimentation data. However, recent translational diffusion measurements of polystyrene/ cyclohexane solutions under theta conditions using QLLS indicate experimental kf values which lie between the extremes represented by Equation 71 on one hand and Equations 70 and 72 on the other (34). For smaller molecular weights, the values are closer to the Pyun Fixman or Freed theory for high molecular weights, they are closer to the Yamakawa-Imai result. 

The change in viscosity of these solutions is due to changes in the dimensions of the coils of polymer molecules in solution. Depending on the type of solvent, the polymer molecules will either seek more contact with the solvent molecules (the coil will swell) or with itself (coils become more compact). Under certain, the so-called theta, conditions, the coil has undisturbed, ideal dimensions. A solvent in which at room temperature a polymer forms such undisturbed coils is named a theta solvent for this polymer. In principle such a solvent has exactly the same solubility parameters as the polymer in question. 

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