Theta solution/solvent

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. 

In a better solution than that provided by a theta solvent the polymer coil will be more expanded. The radius of gyration will exceed the which is characteristic of the bulk amorphous state or a theta solution. If the polymer radius in a good solvent is times its unperturbed /-g, then the ratio of hydrodynamic volumes will be equal to a and its intrinsic viscosity will be related to [ /] by... 

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. 

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... 

An analogous situation is encountered in a theta-solution, with the quantity of interest now being the effective interaction potential between two solute molecules, or in the polymer case, between two monomers. The curve (b) in Fig. 2.11 represents the situation in a good solvent, where the potential is repulsive at all distances. Each solute molecule is surrounded by a hydrate-shell of solvent molecules and this shell has to be destroyed when two solvent molecules are to approach each other. The situation in a poor solvent is different, due to there being a preference for solute-solute contacts. Here, the solute molecules effectively attract each other and repulsion occurs only at short distances, then for the same reason as for the real gases, namely the presence of hard core interactions. For poor solvents, therefore, u r) has an appearance similar to the pair interaction potential in a van-der-Waals gas and a shape like curve (a) in Fig. 2.11. 

A2 is an indicator of the polymer-solvent interactions and is useful for the determination of the solvent-polymer interaction parameter [A2 h- (1 - 2x)l a solution with A2 = 0 is called a theta solution, and the polymer is said to be in the theta state. The temperature at which A2 = 0 is the theta temperature (0), and the solvent becomes a theta solvent at this precise temperature. These are called 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... 

Electrolyte Effect on Polymer Solution Rheology. As salt concentration in an aqueous poly(1-amidoethylene) solution increases, the resulting brine becomes a more Theta-solvent for the polymer and the polymer coil compresses(47) This effect is particularly pronounced for partially hydrolyzed poly(l-amidoethylene). The... 

Comparison of the limiting viscosity numbers determined in deionized water with those determined in 1 molar sodium nitrate shows a 20 per cent decrease in copolymer intrinsic viscosity in the saline solution. These results are consistent with previous studies using aqueous saline solutions as theta solvents for 2-propenamide polymers(47) Degree of hydrolysis controls the value of limiting viscosity number for the hydrolyzed copolymers in distilled water. 

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. 

If the polymer concentration increases so that the number of high order bead-bead interactions is significant, c>>c =p, (when c is expressed as the polymer volume fraction. Op), the fluctuations in the polymer density becomes small, the system can be treated by mean-field theory, and the ideal model is applicable at all distance ranges, independent of the solvent quaUty and concentration. These systems are denoted as concentrated solutions. A similar description appHes to a theta solvent, but in this case, the chains within the blobs remain pseudoideal so that =N (c/c ) and Rg=N, i.e., the global chain size is always in-... 

The osmotic second virial coefficient A2 is another interesting solution property, whose value should be zero at the theta point. It can be directly related with the molecular second virial coefficient, expressed as B2=A2M /N2 (in volume units). For an EV chain in a good solvent, the second virial coefficient should be proportional to the chain volume and therefore scales proportionally to the cube of the mean size [ 16]. It can, therefore, be expressed in terms of a dimensionless interpenetration factor that is defined as... 

Then we address the dynamics of diblock copolymer melts. There we discuss the single chain dynamics, the collective dynamics as well as the dynamics of the interfaces in microphase separated systems. The next degree of complication is reached when we discuss the dynamic of gels (Chap. 6.3) and that of polymer aggregates like micelles or polymers with complex architecture such as stars and dendrimers. Chapter 6.5 addresses the first measurements on a rubbery electrolyte. Some new results on polymer solutions are discussed in Chap. 6.6 with particular emphasis on theta solvents and hydrodynamic screening. Chapter 6.7 finally addresses experiments that have been performed on biological macromolecules. 

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. 

Staudinger showed that the intrinsic viscosity or LVN of a solution ([tj]) is related to the molecular weight of the polymer. The present form of this relationship was developed by Mark-Houwink (and is known as the Mark Houwink equation), in which the proportionality constant K is characteristic of the polymer and solvent, and the exponential a is a function of the shape of the polymer in a solution. For theta solvents, the value of a is 0.5. This value, which is actually a measure of the interaction of the solvent and polymer, increases as the coil expands, and the value is between 1.8 and 2.0 for rigid polymer chains extended to their full contour length and zero for spheres. When a is 1.0, the Mark Houwink equation (3.26) becomes the Staudinger viscosity equation. 

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. 

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]. 

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