Intrinsic viscosity limiting values

Viscosity, intrinsic Also called limiting viscosity number. For a plastic, it is the limiting value of an infinite dilution. It is the ratio of the specific viscosity of the plastic solution to its concentration in moles per liter. 

If the intrinsic viscosity is large (i.e., greater than about 4 deciliters per gram), the viscosity is likely to be appreciably dependent on the rate of shear in the range of operation of the usual capillary viscometer. Measurements in a viscometer permitting operation at a series of rates of shear extending to very low rates are then required in order to extrapolate nsp/c to its limiting value at a shear rate of zero. Extrapolation to infinite dilution does not eliminate the effect on this ratio of a dependence on shear rate. 

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 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. 

The intrinsic viscosity is the Einstein value [rj] = 2.5 and the packing fraction cpm(0) is that in the low shear limit. As the volume fraction approaches the maximum packing fraction, the viscosity rapidly... 

The experimental determination of polymer intrinsic viscosity is done through the measurement of polymer solution viscosity. The connotation of intrinsic viscosity [hi/ however, is very different from the usual sense of fluid viscosity. Intrinsic viscosity, or sometimes called the limiting viscosity number, carries a far more reaching significance of providing the size and MW information of the polymer molecule. Unlike the fluid viscosity, vdiich is commonly reported in the poise or centipoise units, the [h] value is reported in the dimension of inverse concentration xinits of dl/g, for exanple. The value of [hi for a linear polymer in a specific solvent is related to the polymer molecular weight (M) through the Mark-Houwink equation ... 

Note that all the desired properties depend directly or Indirectly on the ratio A/n and therefore, on the relative response factors and signal to noise ratios of the spectrophotometer and the differential refractometer. In general, spectrophotometers are more sensitive than differential refractometers, therefore, the ratio A/n at the tails of the chromatogram, that is, the refractometer signal will be zero while there still be a signal from the spectrophotometer. In addition, equations 9 and 10 are hyperbolic functions of the concentration. Thus, as the concentration decreases the apparent values of Mw and [n] will increase, increasing the uncertainty in the estimates of the molecular weights and the intrinsic viscosities (see Appendix I and references 26-29). In the limit when A/n - (or n/A 0), the polymer... 

The intrinsic viscosity contains a contribution of concentration that we note by writing [rj]ex = (r]sp)ex/cex for which it is understood that this is a limiting value. If the sample is polydis-perse, both (rjsp)ex and cex are made up of contributions from molecules in different molecular weight classes, which we designate by the subscript i that is, we can write... 

After having reached the equilibrium ratio polymer/monomer the intrinsic viscosity shows its maximum value, depending on the temperature, concentration and sort of catalyst (29, 49, 94). By prolonged heating the intrinsic viscosity decreases and after a very sharp decrease during the first stage the viscosity approaches a certain limiting value which depends on the m temperature and on the sort and concentration of j- 7 catalyst (fig. 2). This decrease is a result of... 

Note from Table 6.8 that the reduced viscosity gives the relative increase in the viscosity of the solution over the solvent, per unit of concentration. Since r/ is the limiting value of the reduced viscosity, it is a measure of the first increment of viscosity due to the dispersed particles and is therefore characteristic of the particles. Equation (6.33) predicts that the intrinsic viscosity should equal 2.5 for spherical particles. If the dispersed phase volume fraction is used to reflect the dry-weight concentration of particles that may become solvated when dispersed, then intrinsic viscosity measurements can be used to determine the extent of solvation as follows. Suppose the mass of colloidal solute in a solution is converted to the volume of unsolvated material using the dry density. If the particles are assumed to be uniformly solvated throughout the dispersion then the solvated particle volume exceeds that of the unsolvated particle volume by the factor 1 + (m], b/m2)(p2/Pi) where my, is the mass of bound solvent, m2 is the mass of the solute particle, p2 is the density of the particle and pi is the density of the solvent. Since 4>[Pg.185]

Here, the intrinsic viscosity [r ] is defined as the infinite dilution limit of the reduced viscosity and kH is Huggins coefficient. This result is valid up to the second order in concentration. The PFPE solvent interaction is related to kfj [r ]2. For flexible polymer chains in a theta solvent, kn has been found to vary from 0.4 to 1.0 [110]. From the intercept and slope, we obtain [r ] and kH. These values... 

In a purely mathematical sense, the lower limit of [ij] predicted by Eq. (58) or Eq. (6) is zero at M — 0. But this is physically meaningless and the intrinsic viscosity curve should stop at a finite non-zero value as the molecular weight approaches the monomer weight. As remarked by Sadron and Remmp, this effect can be expressed empirically by the equation1 [t)] = D + K M, (93)... 

The relationship between the intrinsic viscosity of DNA and the amount ( r ) of bound tilorone was studied28. The intrinsic viscosity of the complex increases with r up to a limiting value of about 0.05. The maximum relative enhancement of viscosity was about 1.7. In addition, at the same ionic strength and at a ligand to DNA-P molar ratio of 0.1, the sedimentation rate of DNA was decreased to 78% of the value in the absence of ligand. 

Another very useful approach to molar mass information of complex polymers is the coupling of SEC to a viscosity detector [55-60]. The viscosity of a polymer solution is closely related to the molar mass (and architecture) of the polymer molecules. The product of polymer intrinsic viscosity [r ] times molar mass is proportional to the size of the polymer molecule (the hydrodynamic volume). Viscosity measurements in SEC can be performed by measuring the pressure drop AP across a capillary, which is proportional to the viscosity r of the flowing liquid (the viscosity of the pure mobile phase is denoted as r 0). The relevant parameter [r ] is defined as the limiting value of the ratio of specific viscosity (qsp= (n-noVflo) and concentration c for c—> 0 ... 

It is well known [3], however, that the MAES measurements begin to fail in the determination of once Yg falls below about 8-10 nm, even though the M values generated still remain precise. This lack of precision is due to the limitations of the laser ruler to resolve a size much below about one-twentieth of the incident wavelength. The trouble with empirical relations, such as the relation between intrinsic viscosity and molar mass, is that they too are often limited to regions where such concepts are applicable. For very small molar... 

In order to relate viscosity to molecular weight, the value of reduced (or inherent) viscosity is extrapolated to zero concentration. This parameter is called the intrinsic viscosity, [77], and is usually expressed in deciliters per gram (dL/g) (the lUPAC preferred term is limiting viscosity number, mL/g) ... 

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