Rigid chain polymers intrinsic viscosity

The molar mass dependence of the intrinsic viscosity of rigid chain polymers cannot be described by a simple scaling relation in the form of Equation (36) with molar mass independent of K and a. over a broad molar mass range. Starting from the worm-like chain model, Bohdanecky proposed [29] the linearizing equation... 

Equations (4) and (5) show that when the parameter x = 2 L/A changes from 0 to the hydrodynamic properties of a worm-like chain change from those of a thin straight tod to those of an undrained Gaussian coil. In accordance with this the dependence of intrinsic viscosity (nl and diffusion coefficient D on molecular weight M of a rigid-chain polymer cannot be described by the usual Mark-Kuhn dependence... 

As it is known, the plots of Fig. 39 allow one to determine the values of intrinsic viscosity [rj] by the extrapolation to the polymer zero concentration c. Another method of [r ] evaluation is Shultz-Blashke Eq. (48). In Table 12, the comparison of [q] values, evaluated by two indicated methods, is adduced for polyarylate F-1 at three testing temperatures and polyamidobenzymidazole [94] at two concentrations of solution in sulfuric acid. As it follows from the data of Table 12, the values [q], calculated according to the Eqs. (47) and (48) showed a good correspondence, that allows one to use Shultz-Blashke equation for [q] values of semirigid- and rigid-chain polymers estimation. 

Figure 3.63 shows the intrinsic viscosity of poly(n-hexyl isocyanate) in toluene at 25°C." The polymer is semirigid with Lp = 37 nm and = 1.6 nm. The slope of the tangent decreases from 1.4 to 0.8 with an increasing M. The locally rigid chain follows the viscosity law of the flexible chain when the molecular weight is sufficiently high. 

The solution properties of dendrigraft polybutadienes are, as in the previous cases discussed, consistent with a hard sphere morphology. The intrinsic viscosity of arborescent-poly(butadienes) levels off for the G1 and G2 polymers. Additionally, the ratio of the radius of gyration in solution (Rg) to the hydrodynamic radius (Rb) of the molecules decreases from RJRb = 1.4 to 0.8 from G1 to G2. For linear polymer chains with a coiled conformation in solution, a ratio RJRb = 1.48-1.50 is expected. For rigid spheres, in comparison, a limiting value RJRb = 0.775 is predicted. 

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 exponent a in the intrinsic viscosity-molecular weight relationship ([rj] = K.M ) of a polymer is associated with the expansion of the polymer in solution, and hence with the conformation and stiffness of the polymer (Table 24). The a values of tobacco mosaic virus, Kevlar and helical poly(a-amino acids) are close to 2, which means that they take rigid-rod structures. The a values of vinyl polymers are usually 0.5-0.8, indicating randomly coiled structures. In contrast, the a values of substituted polyacetylenes are all about unity. This result indicates that these polymers are taking more expanded conformations than do vinyl polymers. This is atrributed to their polymer-chain stiffness stemming from both the alternating double bonds and the presence of bulky substituents. 

Another indication of a rigid-chain nature of polymers under consideration is the value of the exponent a of the molecular mass M in the Mark-Houwink Equation for the intrinsic viscosity ... 

The intrinsic viscosity of the polymer prepared using the phosphorylation reaction is 0.2 dl/g in NMP at 30°C. The physical properties of the materials prepared thus far are those expected for rigid chains of moderate molecular weight. Brittle films can be cast from aqueous ammonium hydroxide solution or from polar aprotic solvents. The films which form are brittle. 

The intrinsic viscosity (rj) is a characteristic value of a single macromolecule in a given solvent and it is a measure of the hydrodynamic volume occupied by the polymer itself. It depends primarily on the molar mass (Mw), chain rigidity, and solvent quality. For anionic polyelectrolytes the presence of macroions and counterions in aqueous media causes coil expansion by intrachain electrostatic repulsion and extra dissipation of energy, thus explaining why the intrinsic viscosity of a polyelectrolyte can be higher than that of a neutral rodlike macromolecule of equal size. Thus, (rj) usually increases with an increase in the charge density of the macroion. 

K is related to the polymer- solvent inteiation and is an indication of chain stiffiiess (e.g. for cellulose is ca. 1.5, indicating cellulose is a semi-rigid polymer). The value of K depends of the solvent in which the intrinsic viscosity is measured. K values for different solvents may be found in the Polymer Handbook (38). Some rate data for the acid hydrolysis of different cellulose samples are in Table I. 

---