Theta condition solvent

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. 

The adsorption of block and random copolymers of styrene and methyl methacrylate on to silica from their solutions in carbon tetrachloride/n-heptane, and the resulting dispersion stability, has been investigated. Theta-conditions for the homopolymers and analogous critical non-solvent volume fractions for random copolymers were determined by cloud-point titration. The adsorption of block copolymers varied steadily with the non-solvent content, whilst that of the random copolymers became progressively more dependent on solvent quality only as theta-conditions and phase separation were approached. 

Colloid stability conferred by random copolymers decreased as solvent quality worsened and became increasingly solvent dependent around theta-conditions. However, dispersions maintain some stability at the theta-point but destabilize close to the appropriate phase separation condition. 

A theoretical expression for the concentration dependence of the polymer diffusion coefficient is derived. The final result is shown to describe experimental results for polystyrene at theta conditions within experimental errors without adjustable parameters. The basic theoretical expression is applied to theta solvents and good solvents and to polymer gels and polyelectrolytes. 

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 deterioration of the solvent qnality, that is, the weakening of the attractive interactions between the polymer segments and solvent molecules, brings about the reduction in the coil size down to the state when the interaction between polymer segments and solvent molecules is the same as the mutual interaction between the polymer segments. This situation is called the theta state. Under theta conditions, the Flory-Huggins parameter % assumes a value of 0.5, the virial coefficient A2 is 0, and exponent a in the viscosity law is 0.5. Further deterioration of solvent quality leads to the collapse of coiled structure of macromolecules, to their aggregation and eventually to their precipitation, the phase separation. 

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]. 

Theta conditions correspond to a solvent so poor that precipitation would occur for a polymer of infinite molecular weight. 

Although a is ordinarily greater than unity, fractional values are also possible. The range of fractional values is more limited, however, since the polymer tends to precipitate rather than squeeze out much more solvent under conditions poorer than theta conditions. Incorporating a into Equation (89) gives... 

Summary The classical treatment of the physicochemical behavior of polymers is presented in such a way that the chapter will meet the requirements of a beginner in the study of polymeric systems in solution. This chapter is an introduction to the classical conformational and thermodynamic analysis of polymeric solutions where the different theories that describe these behaviors of polymers are analyzed. Owing to the importance of the basic knowledge of the solution properties of polymers, the description of the conformational and thermodynamic behavior of polymers is presented in a classical way. The basic concepts like theta condition, excluded volume, good and poor solvents, critical phenomena, concentration regime, cosolvent effect of polymers in binary solvents, preferential adsorption are analyzed in an intelligible way. The thermodynamic theory of association equilibria which is capable to describe quantitatively the preferential adsorption of polymers by polar binary solvents is also analyzed. 

Keywords Solution properties Conformational analysis Theta condition Excluded volume Good and poor solvent Thermodynamic theories Preferential adsorption Cosolvent effect... 

For polymer chains in two dimensions in good solvents, the theoretical predictions point to a v value narrowly centered in 0.75 [61], Monte Carlo simulations predicts a value of 0.753 [66], while by the matrix-transfer method a value of 0.7503 is predicted. In the case of theta condition the situation is not clear, the predictions are less precise. Monte Carlo simulation [66] has suggested ve 0.51 while matrix-transfer data suggest ve 0.55 [67],... 

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. 

When the concentration of the free polymer is set equal to zero, the situation corresponds to pure steric stabilization. The free energy of interaction due to the interpenetration of the adsorbed polymer chains has a range of 26, where 6 is the thickness of the adsorbed layer. This free energy is proportional to the quantity (0.5 - x), where x is the Flory interaction parameter for the polymer-solvent system. Thus, a repulsive potential is expected between two particles when x < 0.5 and this repulsion is absent when x = 0.5. For this reason, it was suggested [25] that instabilities in sterically stabilized dispersions occur for x > 0.5, hence for theta or worse-than-theta conditions. However, the correlation with the theta point only holds when the molecular weight of the added polymer is sufficiently high... 

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. 

Only in the so-called theta solvents or 0-solvents, or more precisely under theta conditions, the volume expansion can be offset. A 0-solvent is a specially selected poor solvent at... 

At theta conditions where the molecule exists in the form of a completely closed-up (compact) random coil R = R0) a is 0.5. In a good solvent a is 0.8 and maximally about 1.0. For rods a is 1.8. 

Other experiments with block copolymers (Hadziioannou et al., 1986 Tirrell et al., 1987 Patel et al., 1988 Ansarifar and Luckham, 1988) provide similar results in good solvents and strong, but shorter range repulsions at theta conditions. The behavior in poor solvents, i.e., the delineation between attractive and repulsive potentials, remains to be resolved. 

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. 

Under theta conditions the polymer coil is not expanded (or contracted) by the solvent and is said to be in its unperturbed state. The radius of gyration of such a macromolecule is shown in Section 4.4.1 to be proportional to the square root of the number of bonds in the main polymer chain. That is to say, if M is the polymer molecular weight and A/q is the formula weight of its repeating unit, then... 

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