Solution Viscosity
The overall shape of a macromolecule in solution can be deduced from the viscosity of solutions of the macromolecular substance.
Measurement of the viscosities, of solutions of macromolecular substances leads us to information on the overall shape of the molecule in the solution.
Intrinsic viscosity: when the viscosities of solutions are studied so that the properties of the solute molecules can be deduced, viscosities are obtained for the pure solvent and for solutions of various concentrations. At each concentration the effect of the solute can be conveniently shown by calculating
where η and η0 are the viscosities of the solution and the solvent, respectively.
The properties of solutions of macromolecules are often affected by the interaction of these large solute particles. Results that affect the properties of the individual particles rather than their interactions are obtained by extrapolating measured quantities to infinite dilution. Here this is done by using concentration c, the mass per unit volume, rather than as the chemically more common molar concentration. The viscosity effect per unit concentration of the solute can now be expressed as
And the value extrapolated to infinite dilution is represented by [η], where
If c is in grams per millimeter, the values of [η] are not really a viscosity. It depends on the ratio η/η_{0} and thus does not contain viscosity units. The intrinsic viscosity of a solution of a given macromolecule is used to deduce the shape and sometimes the molecular mass of the molecule.
Effect of shape and specific volume: the addition of a macromolecular solute to a solvent invariably increases the viscosity. This qualitative result seems reasonable in view of the familiar thickening that accompanies the formation of such solutions. The thickening, however, is usually the result of molecular interactions and is not related to the intrinsic viscosity effect.
The molecular explanation of the increase in viscosity that results from the addition of macromolecules is based on the disruption of the flow pattern or velocity gradient they produce.
When this approach is developed quantitatively, the fraction of the volume of the solution attributable to the solute is most directly related to the viscosity effect. If veff is introduced as the effective specific volume of the macromolecular material in solution, i.e. the volume per unit mass, then since c is the mass of solute per unit volume of solution, cveff is the volume of solute per unit volume of solution.
According to derivations by A, Einstein and by R. Simha, the extrapolation of viscosities of solutions of molecules that have spherical or ellipsoidal shapes should conform to
Where v is a shape dependent parameter. If v_{eff} is removed from the extrapolation term and treated separately, we can write
Or, with equation
[η] = cv_{eff}
Additional factors must be taken into account if viscosities deduced from high flow rate studies considered. In such cases the flow is said to be nonnewtonian, implying that the proportionality between driving force and flow rate does not hold. The molecular interpretation of viscosities obtained under such conditions must allow for an alignment of molecules with the flow lines. Such effects are not considered here.
The effective specific volume term veff raises some difficulties. The specific volume of the dry solute, which we denote v_{2}, is the proportional of the density of the dry solute and can be measured. In solution many types of macromolecules hold solvent molecules in their cavities and on their surface. If we introduce to represent the mass of solvent that is bound in this way per unit volume of solute and v1 to represent the specific volume of the solvent, we can write
v_{eff} = v_{2} + v_{1}
Then equation can be written as
[η] = v(v_{2} + v_{1})
Application of this result is awkward because of the two unknown v and . A variety of procedures can be followed. For example, we can consider a particular class of compounds, say proteins in aqueous solutions. Then we can proceed by using representative values of v_{2} = 0.75 mL g^{-1}, = 0.2, and v_{1} = 1 mL g^{-1 }then we have
[η] = v(0.95) ≈ v
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