Theta solvent, polymers zero value

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. 

Negative or near zero A2 values have been obtained showing a behavior typically exhibited by polymers dissolved in thermodynamically poor or theta solvents. Negative values may indicate an association effect, but light scattering alone is insufficient to ascertain association of lignin. The results listed in Table... 

Figure 3.13 Linear viscoelastic data (symbols) for polystyrene in two theta solvents, decalin and diocty Iphthalate, compared to the predictions (lines) of the Zimm theory with dominant hydrodynamic interaction, h = oo. The reduced storage and loss moduli and G are defined by = [G ]M/NAksT and G s [G"]M/A /cbT, where the brackets denote intrinsic values extrapolated to zero concentration, [G jj] = limc o(G /c) and [G j ] = limc +o[(G" — cor)s]/c), and c is the mass of polymer per unit volume of solution. The characteristic relaxation time to is given by to = [rj]oMrjs/NAkBT. For frequencies ro

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. 

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. 

This means that the critical concentration is shifted to lower values with increasing segment number (molar mass) of the polymer and becomes zero for infinite molar mass. Equation [4.4.61] explains also why the x(T)-function becomes 0.5 for infinite molar mass. The critieal temperature of these conditions is then called theta-temperature. Solvent activities can be calculated from critical %(T)-function data via Equation [4.4.13]. However, results are in most cases of approximate quality only. 

The chemical structure of a polymer can also cause a contraction of the polymer coil compared to the unperturbed dimensions at theta-conditions. In this case the exponent a of the [ ]]-M-relationship shows values of a<0.5. A contraction of the coil occurs if the attractive intramolecular interactions between the polymer segments become larger than the interactions with the solvent molecules. In extreme cases, the solvent is forced out of the polymer coil and the chain segments start to form compact aggregates. The density of the polymer coil is then independent of the molar mass and the intrinsic viscosity is constant. In this case the exponent a is zero. An example is shown in Fig. 6.12 for compact glycogen in aqueous solution. 

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