Dilute solution viscosity limitations

Dilute Polymer Solutions. The measurement of dilute solution viscosities of polymers is widely used for polymer characterization. Very low concentrations reduce intermolecular interactions and allow measurement of polymer—solvent interactions. These measurements ate usually made in capillary viscometers, some of which have provisions for direct dilution of the polymer solution. The key viscosity parameter for polymer characterization is the limiting viscosity number or intrinsic viscosity, [Tj]. It is calculated by extrapolation of the viscosity number (reduced viscosity) or the logarithmic viscosity number (inherent viscosity) to zero concentration. 

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) ... 

A limited amount of structural information can be obtained via viscometry of polymer solutions. Molecular dimensions have been mentioned as the province of dilute solution viscosity. Flow properties of more concentrated solutions provide information on whether solvent drains freely from the polymer coils and on how solvent attractions compete with the interactions among macromolecules that are bound to occur (37. 38). 

Intrinsic viscosity in- trin-zik- (Umiting viscosity number) n. In measurements of dilute-solution viscosity, intrinsic viscosity is the limit of the reduced and inherent... 

Also known as limiting viscosity number. See also dilute-solution viscosity, Huggins equation, and viscosity-average molecular weight. 

Intrinsic Viscosity in- ltrin-zik- n (limiting viscosity number) In measurements of dilute-solution viscosity, intrinsic viscosity is the limit of the reduced and inherent viscosities as the concentration of polymer solute approaches zero. It represents the capacity of the polymer to increase viscosity. Interactions between solvent and polymer molecules give rise to different intrinsic viscosities for a given polymer in different solvents. Intrinsic viscosity is related to polymer molecular weight by the equation [77] = K -M, where the exponent a lies between 0.5 and 1.0, and, for many systems, between 0.6 and 0.8. Also known as Limiting Viscosity Number. See also... 

Applications and Limitations of Dilute Solution Viscosity Measurements... 

To understand polymer structure, polymers are often dissolved in appropriate solvents, allowing molecular weight or degree of polymerization to be determined from dilute solution viscosity. The relative viscosity, is the ratio of solution viscosity to that of the solvent. The specific viscosity, is the ratio of the difference in solution and solvent viscosities divided by the solvent viscosity. These dimensionless quantities are often divided by the mass concentration of the polymer to obtain several additional terms that have units of dilution or volume per unit mass concentration the reduced viscosity, which is ratio of the relative viscosity to the concentration the inherent viscosity, which is the ratio of the natural logarithm of the relative viscosity and the intrinsic viscosity, [77], which is the common limiting value of the reduced (Huggins definition) or inherent (Craemer s definition) viscosity at infinite dilution of the polymer. The intrinsic viscosity is a concentration ratio it has been used to estimate molecular... 

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 various physical methods in use at present involve measurements, respectively, of osmotic pressure, light scattering, sedimentation equilibrium, sedimentation velocity in conjunction with diffusion, or solution viscosity. All except the last mentioned are absolute methods. Each requires extrapolation to infinite dilution for rigorous fulfillment of the requirements of theory. These various physical methods depend basically on evaluation of the thermodynamic properties of the solution (i.e., the change in free energy due to the presence of polymer molecules) or of the kinetic behavior (i.e., frictional coefficient or viscosity increment), or of a combination of the two. Polymer solutions usually exhibit deviations from their limiting infinite dilution behavior at remarkably low concentrations. Hence one is obliged not only to conduct the experiments at low concentrations but also to extrapolate to infinite dilution from measurements made at the lowest experimentally feasible concentrations. 

There are some limitations to this technique. First, proper mixing can only be achieved with dilute, low viscosity polymer solutions (perhaps a few percent polymer by mass), so the final films are at most a few hundred nanometers thick. This can be a problem if confinement will create undesired effects in the blend behavior. 

The fluid resistance experienced by a macromolecular solute moving in dilute solution depends on the shape and size of the molecule. A number of physical quantities have been introduced to express this. Typical ones are intrinsic viscosity [ry], limiting sedimentation coefficient s0, and limiting diffusion coefficient D0. The first is related to the rotation of the solute, while the last two are concerned with the translational motion of the solute. A wealth of theoretical and experimental information about these hydrodynamic quantities is already available for randomly coiled chains (40, 60). However, the corresponding information on non-randomly coiled polymers is as yet rather limited in number and in variety. 

The peculiarity of this expression, however, is that it does not make sense for dilute solutions of Gaussian coil molecules. In fact, the free-draining case is characterized by the limit of infinetely smaE friction coefficient . For this case, the contributions of the chain molecules to the viscosity of the solution becomes zero. 

From the foregoing it becomes evident that only a measure of the magnitude of the form birefringence, but not of its influence on the extinction angle, can be given. For this purpose the reader may be reminded that the stress-optical coefficient of an infinitely dilute solution can be expressed by one half of the ratio of Maxwell constant to intrinsic viscosity [eq. (2.33)]. In the absence of the form birefringence the limiting... 

Limiting Viscosity Number (Intrinsic Viscosity) and Related Properties of Very Dilute Solutions... 

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

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