Theta solvent, polymers

Under whieh eireumstanees is the predietion of Eq. (6) eorreet, at least on a qualitative level It turns out that the predietion for D, Eq. (6), obtained within the simple mean-field theory, is eorreet if the attraetive tail of the substrate potential in Eq. (3) deeays for large values ofz slower than the entropie repulsion in Eq. (4) [24]. In other words, the mean-field theory is valid for weakly adsorbed polymers only for T < 1/v. This ean already be guessed from the funetional form of the layer thiekness, Eq. (6), beeause for t > 1/v the layer thiekness D goes to zero as b diminishes. Clearly an unphysieal result. For ideal polymers (theta solvent, v = 1 /2), the validity eondition is t < 2, whereas for swollen polymers (good solvent eonditions, v = 3/5), it is T < 5/3. For most interaetions (ineluding van der Waals interaetions with t = 3) this eondition on T is not satisfied, and fluetuations are in faet important, as is dis-eussed in the next seetion. 

For each polymer, theta solvents are given in alphabetical order no attempt was made to convert commonly used solvent names into systematic names (e.g. dioxane = 1,4-dioxane). In mixed solvents, the liquid Hsted first may thus be a solvent or a nonsolvent. Compositions of mixed solvents are given in vol./vol. unless otherwise noted (ex w/w indicates weight per weight). 

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. 

Expansion of Thickness of the Adsorbed Layer. In the low salt concentration the large thickness compared with the case of the Theta solvent (4.17 M NaCl) is considered to be due to the electrostatic repulsion, i.e., the excluded volume effect of the adsorbed NaPSS chains. Usually, the expansion factor at, defined by the ratio of the thickness in good solvent and that in the Theta solvent, is used to quantitatively evaluate the excluded volume effect for the adsorbed polymers. 

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 new information necessary to make this approach quantitative is the dependence of the effective entanglement molecular weight on the concentration, (j) of unrelaxed segments. This is known from experiments on dilution of polymer melts by theta-solvents to be approximately which corre-... 

In particular it has been conjectured that the terminal relaxation of star polymers might be the most sensitive test of the dilution exponent P in Go theta solvents suggest a mean value of nearer 2.3 [32]. A physically reasonable scahng assumption for the density of topological entanglements in a melt of Gaussian chains leads to a value of 7/3 [31]. 

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. 

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. 

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. 

However, if the original temperature is below the theta temperature, the viscosity will increase when the mixture of polymer and solvent is heated to a temperature slightly above the theta temperature. 

What is the value of the exponent a in the Mark-Houwink equation for polymers in theta solvents ... 

If c and dc/dx are known as a function of x and the measurement is carried out in a theta solvent, the molecular weight M of monodisperse polymers can now be calculated precisely. If the solvent is not a theta solvent, the obtained value of M is an apparent molecular weight from which the true value can be calculated upon plotting 1/M vs. c and extrapolation to c —> 0. For polydisperse samples, one has to insert the average of dc/dx in the above equation, and the thus calculated molecular weight represents a weight-average,... 

An alternative approach for determining the molecular weight of a polymer in theta solvents includes the determination of the polymer s concentration at the meniscus (c ,) and at the bottom ic, ) (or alternatively at two other positions Xi and X2) in the cell. These two outstanding positions have a distance of x ix ) and Xh(x2), respectively, from the center of rotation. Then, one obtains the weight-average molecular weight of a polydisperse polymer sample via the equation ... 

As demonstrated by numerous experiments, temperature does not well influence the exclusion processes (compare Equation 16.6) in eluents, which are thermodynamically good solvents for polymers. In this case, temperature dependence of intrinsic viscosity [ii] and, correspondingly, also of polymer hydrodynamic volume [p] M on temperature is not pronounced. The situation is changed in poor and even theta solvents (Section 16.2.2), where [p] extensively responds to temperature changes. 

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]. 

Relations between g and go are semi empirical and approximate (19,20). It is assumed that g is independent of solvent conditions and that a theta solvent for a linear polymer is also a theta solvent for its branched analogues. Neither of these assumptions is well founded (19). In practical applications, exponential relations between g and go of the form... 

Most liquid-crystalline polymer solutions have a large second virial coefficient ( > 10 4 cm 3mol/g2) [41], which means that it is rather difficult to find poor or theta solvents for these polymers and that liquid-crystalline polymers in solution interact repulsively. This fact is essential in formulating their static solution properties (osmotic pressure, phase separation, etc.). 

N) indicates that the polymer is insoluble. h(0) indicates theta-solvent. 

Fig. 5.1. Intrinsic moduli for narrow distribution polystyrene (M = 860000) in two theta solvents (114). This comparison with theory is equivalent to that of reduced moduli described in the text. [Reproduced from Polymer J. 1,747 (1970).]...

Some relationship between viscosity crossover in theta solvents and polymer polarity is suggested by the results, supporting the idea of enhanced intermolecular association in poor solvents. However, from the data on hand, one could also infer a correlation with the glass transition temperature of undiluted polymer,... 

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. 

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