Dilute solution characteristic viscosity

With appropriate caUbration the complex characteristic impedance at each resonance frequency can be calculated and related to the complex shear modulus, G, of the solution. Extrapolations to 2ero concentration yield the intrinsic storage and loss moduH [G ] and [G"], respectively, which are molecular properties. In the viscosity range of 0.5-50 mPa-s, the instmment provides valuable experimental data on dilute solutions of random coil (291), branched (292), and rod-like (293) polymers. The upper limit for shearing frequency for the MLR is 800 H2. High frequency (20 to 500 K H2) viscoelastic properties can be measured with another instmment, the high frequency torsional rod apparatus (HFTRA) (294). 

The dilute solution properties of copolymers are similar to those of the homopolymer. The intrinsic viscosity—molecular weight relationship for a VDC—AN copolymer (9 wt % AN) is [77] = 1.06 x 10 (83). The characteristic ratio is 8.8 for this copolymer. 

In the present chapter we shall be concerned with quantitative treatment of the swelling action of the solvent on the polymer molecule in infinitely dilute solution, and in particular with the factor a by which the linear dimensions of the molecule are altered as a consequence thereof. The frictional characteristics of polymer molecules in dilute solution, as manifested in solution viscosities, sedimentation velocities, and diffusion rates, depend directly on the size of the molecular domain. Hence these properties are intimately related to the molecular configuration, including the factor a. It is for this reason that treatment of intramolecular thermodynamic interaction has been reserved for the present chapter, where it may be presented in conjunction with the discussion of intrinsic viscosity and related subjects. 

ISO 1628-4 1999 Plastics - Determination of the viscosity of polymers in dilute solution using capillary viscometers - Part 4 Polycarbonate (PC) moulding and extrusion materials ISO 7391-1 1996 Plastics - Polycarbonate (PC) moulding and extrusion materials - Part 1 Designation system and basis for specifications ISO 7391-2 1996 Plastics - Polycarbonate (PC) moulding and extrusion materials - Part 2 Preparation of test specimens and determination of properties ISO 11963 1995 Plastics - Polycarbonate sheets - Types, dimensions and characteristics. 

Figure 8 illustrates the relationship between inherent viscosity (IV) and concentration for PBI/PAr/NMP solutions. It is interesting to note that the IV of all solution blends exhibited normal polymer solution characteristics. At a fixed concentration (0.5%), it was noted that the IV of the solution blends exceeded the rule of mixtures (see Fig. 9) suggesting that PBI and PAr exhibit specific interactions in a dilute solution, such that the resulting hydrodynamic sizes of the blends were greater than that of the calculated averages based on each component. 

Viscosity Measurements, Previous studies (2) have shown that dilute solutions of Pluronic F127 exhibit Newtonian flow characteristics and consequently, it is permissible that the viscosity of these solutions is measured by capillary viscometry. A suspended-level viscometer was used and solutions were thermostatted to within... 

The most important characteristic quantity in very dilute solutions is the limiting viscosity number, which is defined as ... 

The polymers were fractioned into 8-14 components by coacervate extraction from the benzene - methanol system. For fractions and nonfractioned polymers, characteristic viscosities [t ], were me-asured. Because that was the first example of studying conformations of macromolecules of this ty-pe in diluted solutions, authors of the work [56] paid much attention to selection of an equation, which would adequately describe hydrodynamic behavior of polymeric chains. Figure 10 shows de-pendencies of [q] on molecular mass (MM), represented in double logarithmic coordinates. Parame-ters of the Mark-Kuhn-Hauvink equation for toluene medium at 25°C were determined from the slo-pe and disposition of the straight lines. 

If)/ is independent of shear history, the material is said to be time independent. Such liquids can exhibit different behavior patterns, however, if, as is frequently the case with polymers, )/ varies with shear rate. A material whose viscosity is independent of shear rate, e.g., water, is a Newtonian fluid. Figure 11-26 illustrates shear-thickening, Newtonian and shear-thinning rj-y relations. Most polymer melts and solutions are shear-thinning. (Low-molecular-weight polymers and dilute solutions often exhibit Newtonian characteristics.) Wet sand is a familiar example of a shear-thickening substance. It feels hard if you run on it, but you can sink down while standing still. 

Many foods contain high-molecular weight polymers, such as proteins, pectins, and others. Often, they contribute significantly to the structure and viscosity of foods. In dilute solutions, the polymer chains are separate and the intrinsic viscosity, denoted as [ ], of a polymer in solution depends only on the dimensions of the polymer chain. Because [ ] indicates the hydrodynamic volume of the polymer molecule and is related to the molecular weight and to the radius of gyration, it reflects important molecular characteristics of a biopolymer. The concentrations of polymers used should be such that the relative viscosities of the dispersions are from about 1.2 to 2.0 to assure good accuracy and linearity of extrapolation to zero concentration (Morris and Ross-Murphy, 1981 da Silva and Rao, 1992). Intrinsic viscosity can be determined from dilute solution viscosity data as the zero concentration-limit of specific viscosity (ijsp) divided by concentration (c) ... 

Physico-Chemical Properties of Salvarsan Solutions.— These solutions show the characteristic properties of colloids, dialysis through a parchment membrane showing but slight diffusion, w hiist in methyl alcohol solution diffusion takes place more readily. The disodium salt diffuses about four times as quickly as the free hydrochloride. Hie idscosity of aqueous solutions of Salvarsan increases from the moment of preparation until an approximately constant value is reached. This value is much higher than the initial value. As the concentration of the solution increases, the initial velocity of increase of scosity and the final value are affected, and the presence of acid or alkali also has a marked effect. With rise of temperature the viscosity more quickly attains its maximum value, but this value is diminished The viscosity of dilute solutions diminishes on keeping. The ps value of Salvarsan is 7-60 of the dihydrochloride, 2-41 of the monohydrochloride, 3-00 of the monosodium salt, 10-88 and of tlie disodium salt, 11 43. The presence of an isoelectric point at ps value about 3 4 is indicated. ... 

It can be shown that for most dilute solutions there exists a simple correlation between dynamic and steady state flow characteristics (16). For most detergent solutions the magnitude of the complex viscosity 1 n I at a certain angular frequency CO coincides with the steady state viscosity n, at the corresponding shear rate "f (12, 17). 

A characteristic feature of a dilute polymer solution is that its viscosity is considerably higher than that of either the pure solvent or similarly dilute solutions of small molecules. The magnitude of the viscosity increase is related to the dimensions of the polymer molecules and to the polymer-solvent interactions. Viscosity measurements thus provide a simple means of determining polymer molecular dimensions and thermodynamic parameters of interactions between polymer and solvents. These aspects will also be considered in a later part of this chapter. 

As discussed in the Introduction to this paper, different viscosity versus concentration behavior is observed for SFS solutions in toluene/methanol and in DMF. Folyelectrolyte behavior is observed only in the latter solvent. The ESR spectrum of a 2.65 mole % Mn-SPS in these two solvents was studied at various concentrations. For both lvents, the hyperfine structure characteristic of isolated Mn ions was observed in very dilute solutions and at concentrations for which Lundberg and Phillips(10) observed strong intermolecular interactions. The ESR data indlcat that in dilute solution in both DMF and toluene/methanol, the Mn exists mainly as Isolated cations. In addition, the IR spectra indicated that the cation is removed from the anion to a similar degree in both solvents. Yet, a polyelectrolyte effect is observed experimentally only in DMF solutions. Although there was some dipole-dipole broadening of the toluene/methanol spectrum, the line width and the g-factor (g 2,000) in both cases were ldent fal. The g-factor of 2.000 is characteristic of an isolated Mn in solution ). 

Some important properties of polymer chains in dilute solutions [steric hindrance parameter, characteristic ratio, persistence length, radius of gyration, statistical chain segment length (introduced earlier, in Chapter 11), intrinsic viscosity, and viscosity at small but finite concentrations] will be discussed, and new correlations will be presented for the steric hindrance parameter and the molar stiffness function, in Chapter 12. 

While in this brief section reference has been made only to viscosity and osmotic-pressure properties of polyelectrolytes, the difference between them and uncharged polymers persists in all dilute solution measurements. The characteristic effect is that in the absence of foreign salts in the polyelectrolyte system the behavior in dilute solutions is governed by the very long-range molecular interaction forces. 

In this chapter a method is proposed for finding the fractal dimension (D) of a macromolecular coil in solution, which uses only the characteristic viscosity of the polymer in an arbitrary solvent and a 0 solvent. Several examples are given to illustrate the applicahility of the proposed method to biopolymers of different classes. From D, one can determine a number of other important parameters characterising the behaviour of polymers in dilute solutions. 

Besides, let s add to this analysis the characteristic times of the segmental motion, estimated based on coefficient of the frictional component of viscosity of diluted solution ), concentrated solution and melt ( ). 

Kozlov, G. V Temiraev, K. B. Sozaev, V. A. The evaluation of fractal dimension of macromolecular coil in diluted solution by the characteristics of viscosity. Journal of Physical Chemistry, 1999, 73(4), 766-768. 

The sodium salts of polymer series of 4 and 8 were polyelectrolytes which had viscosity as well as electrophoretic characteristics. Reduced viscosities of the sodium salts of polymers 4a and 4b exhibited typical polyelectrolyte behavior as a function of concentrations in H O (Figure 4). By continuous dilution the reduced viscosities of the polymers decreased steadily and increased rapidly at concentrations below 0.5 g/dL in water. In neutral salt (NaCI, 5%) solution the reduced viscosity retained normal behavior. ... 

The viscosity of a dilute polymer solution depends on the nature of polymer and solvent, the concentration of the polymer, its average molecular mass and molecular mass distribution, the temperature, and the shear rate. The most important characteristic quantity in a very dilute solution, at vanishing shear rate, is the limiting viscosity number, which is defined as [1]... 

Measurements of polymer properties in dilute solution are often carried out on samples with a distribution of molecular weights. The properties of molecular-weight distributions and the characteristic averages of the distribution are presented. The relations between the measured quantity and the molecular-weight distribution are derived for light scattering, osmotic pressure, and viscosity. 

Solution Characteristics of Poiymers. The molar mass characterization techniques often provide additional information on the nature of the polymer species in solution. In most cases, the solutions used are sufficiently dilute so that the properties being measured are those of the isolated molecule. At infinite dilution the size of the polymer coil is dictated by both inter- and intramolecular interactions, the nature of the solvent used, and the temperature. In a viscosity or GPC/SEC experiment the properties being observed can be related to the hydro-dynamic volume of the poljmier coil. This hydrodynamic volume is the effective volume which the poljmier occupies in solution. The hydrodynamic volume is implicit in the Mark-Houwink relationship, which describes the value of the limiting infinitely dilute increment to the viscosity—the intrinsic viscosity [ j] to the molar... 

The behaviour of diluted solutions is related to the relation between the viscosity and the chain characteristics (structure, configuration, conformation, etc). Usually, the polymer solutions are treated as two-phase systems, consisting from mechanical elements, the macromolecules, immersed into a continuous media, the solvent. For long time, it was considered that the solvent acts to the polymer macromolecules in the same manner in which a fluid exerts forces about a small particle suspended in it. However, the extension of this model to the polymer solution is not adequate since, the ratio between the dimensions of macromolecules and those of solvent molecules essentially differs by that between the dimensions of a solid immersed particle and solvent molecules. On the other side, the flexible macromolecules, randomly coiled, can not be assimilated with the solid particles and therefore the typical relations applied to solid suspensions in liquids can not be used in this case. 

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