Intrinsic viscosity vs. molecular weight

The intrinsic viscosity vs molecular weight dependence extracted from the SEC experiments curve of the intrinsic viscosity also often gives a straight line in the double logarithmic plot and can be described by the (KMHS) relationship ... 

A large number of papers has dealt with the question of molecular weight and molecular weight distribution in polyacrylonitrile. Recent discussions are those of Onyon 108), Krigbaum and Kotliar 90), Booth and Beason 33), Bamford, Jenkins, Johnston and White 19) and Kobayashi 87). The intrinsic viscosity vs. molecular weight relationship of Cleland and Stockmayer 41) is probably as well supported as any. Fortunately, much of the material in this review does not depend heavily on detailed knowledge of molecular weights or of their distributions. 

Linear dependence of intrinsic viscosity on molecular weight Maximum in the intrinsic viscosity vs. molecular weight relationship... 

Figure 4 Intrinsic viscosity vs. molecular weight M for polystyrene in toluene (O) at 2CC and THF (A) at 25 °C (reproduced by permission of the American Chemical Society from Macromolecules, 1979, 12, 968)...

It was shown that the logarithm of the product of intrinsic viscosity and molecular weight of polymers of different chemical and stereochemical composition, configuration, or molecular weight is linearly related to the elution volume.81 A plot of log (r) M) vs. elution volume provides a single calibration curve, useful for samples of similar composition, and is termed a universal... 

Grubisic et al. (3) showed that for many polymers a single calibration curve can be drawn through a plot of the product of intrinsic viscosity and molecular weight ( [7/] M) vs. retention volume. This relationship certainly supports the model of molecular separation based on hydro-dynamic volume since [77] M is proportional to the hydrodynamic volume of the molecule in solution. Hence, molecular weights of the two polymers (calibration standard polymer and sample) which have identical retention volume under identical GPC analytical conditions can be expressed in terms of each other by combining the Grubisic relationship ... 

This brings us to the relationship between the intrinsic viscosity and molecular weight This was first established empirically from plots of log r vs log Mol Wr., which were found to be linear (Figure 12-29), meaning that the relationship between the two quantities has the form (Equation 12-47) ... 

From a Mark-Houwink plot of intrinsic viscosities V5. molecular weight, [see Section 3.8.3 and equation (3.97)], values of K and a were estimated at 10 cm7g and 0.7, respectively (63). The dependence of the solution viscosity vs. concentration resembles that of ordinary polymer solutions. 

Figure I. Poly(vinyl chloride) resin general performance /property characteristics vs. molecular weight. Molecular weight was evaluated by intrinsic viscosity (ASTM D-1243-A).

Pig. 10. Double logarithmic plot of diffusion coeffF cient D (1) and intrinsic viscosity [q J (2) vs. molecular weight Mfot poly(p-phenylene-l,3,4-oxadia-zole) samples in sulfuric acid ). Curves 1 and 2 are theoretical curves ... 

Fig. 6. Intrinsic viscosity ( ) vs. number aqerage molecular weight Mn ...

The equation with pertinent constants for polychloroprene is used in determining the extent of branching. Thus, several linear polymers were made vmder extreme control conditions. The molecular weight distribution and intrinsic viscosities were determined for each polymer. A plot of In IV) vs molecular weight yielded a and If values ... 

Fig. 3. Solution viscosity vs concentration for ethylene oxide polymers (10). The molecular weight of the polymer is indicated on each curve. The dependence of the intrinsic viscosity [Tj] on molecular weight M for these polymers can be expressed by the Mark-Houwink relationship ...

Dead Volume. The dead volume difference between the viscometer and DRI must be accounted for. Otherwise systematic errors in Mark-Houwink parameters K and u can occur. In the previous paper (16), a method developed by Lesec and co-workers (38) based on injecting a known amount of a very high molecular weight polystyrene standard onto low porosity columns was used. From the viscometer and DRI chromatograms, the apparent intrinsic viscosity [h] was plotted against retention volume V. A series of [n] vs. V plots are then constructed assuming a range of dead volume, AV. 

In all cases, intrinsic viscosities were measured at 25 C in constant temperature baths controlled to +0.1°C or better, using suspended level Ubbelohde dilution viscometers with solvent flow times of at least 100 sec.. No kinetic energy corrections were made. Solution flow times were measured at four concentrations for each sample, and intrinsic viscosities were obtained from the classical double extrapolation of hg /c vs. c and (In hj.)/c vs. c to a single intercept value. Concentration ranges were varied somewhat with the molecular weights of the samples, but were chosen such that both functions were straight lines in all cases. 

Fig. 1.3 Double logarithmic plot of intrinsic viscosity [t ] (in dl g 1) vs. number average molecular weight M for poly(pentachlorophenyl methacrylate), (PPCIPh) in chlorobenzene (A), toluene (A), and benzene (o). (From ref. [44])...

An important dimensionless relationship between viscosity and concentration was found by Papkov et al. (1974) and reproduced in Fig. 16.30, where the variation of viscosity with polymer concentration for different molecular weights, expressed as intrinsic viscosities, is shown (left). The reduced viscosity t]/if vs. the reduced concentration c/c is shown on the right. The viscosity of the solution jumps down rapidly above the critical concentration as the nematic mesophase forms. The dimensionless relationship is remarkable. The relationship between the viscosity at the maximum and the intrinsic viscosity (see inset) appears to be r/max = 5.5b/]1 5, where rj is expressed in Ns/m2 and [77] in m3/kg. 

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