Understanding Dilute Solution Viscosity (DSV)

Definition of DSV

Dilute Solution Viscosity (DSV) is the viscosity measurement of dilute solutions of polymers. Typically, a sample is dissolved in a solvent at a specified concentration in the range 0.2 – 1.0 g/dl. Polymer solution viscosity is measured relative to the viscosity of the pure solvent. The Relative Viscosity (RV) is simply the ratio of the two measurements:

Where η is the polymer solution viscosity and η₀ is the viscosity of the pure solvent.

Traditional Glass Tubes Method of Measurement

With a traditional glass capillary tube viscometer, we measure the time it takes for the test liquid to flow through a capillary of a known diameter between 2 marked points.

Determining viscosity in this manner is both time-consuming and error-prone.

Glass capillary viscometers can not operate at very low concentrations and must therefore use several concentrations for a Huggins plot (see fig 2) to derive intrinsic viscosity by extrapolation to zero concentration.

The Viscotek Relative Viscometer is able to operate at low concentrations and will give intrinsic viscosity from one sample run by use of the Solomon-Gatesman equation.

DSV Calculations

Polymer solution viscosity is measured relative to the viscosity of the pure solvent.

Where η is the polymer solution viscosity and η₀ is the viscosity of the pure solvent.

Derived Functions of RV

The most common function of Relative Viscosity is called the inherent viscosity.

Another function of RV is the intrinsic viscosity, which is defined as the inherent viscosity in the limit of infinite dilution.

Intrinsic Viscosity

It is not viscosity!

• Note, the units are in dl/g.
• Viscosity is measured in Pa.s or centipoise.

It is the volume per unit mass that the polymer occupies in a solution.

• Inverse of molecular density.

It can be related to molecular weight by the empirical Mark-Houwink equation but for the molecular weight to be measured accurately the polymer structure must be known or assumed:

[η] = intrinsic viscosity.
k = Mark-Houwink constant.
a = Mark-Houwink constant relating to the polymer structure. As a guide to typical values:
0 to 0.1 = sphere, 0.35 to 0.80 = random coil, and 1.5 to 2 = rigid rod structure.
M_V = Viscosity average molecular weight.

Nomenclature for Polymer Solution Viscosity

Where η₀ = Solvent Viscosity and η = Polymer Solution Viscosity

Viscotek relative viscometer principle

A multi-capillary viscometer can measure the relative viscosity of the solution directly by measuring the solvent and sample viscosity simultaneously, avoiding errors due to temperature fluctuation and solvent variations.

Poiseulle’s Law:

For the two capillaries in series the pressure ratio will be:

Under baseline conditions, pure solvent flows through both R1 and R2. Therefore, η in both capillaries are equal and cancel. Since the capillaries are in series and liquid is non-compressible, the flow rates Q1 and Q2 are also equal and cancel. So this leaves:

Where k is the instrument constant.

After sample injection into the sample loop, the solvent is diverted from the sample loop by-pass route, and enters the sample loop to push sample across capillary 2, at which time the pressure on transducer will reach a maximum or plateau.

At the measurement plateau we know the relationship is still:

But now we also know the instrument constant, k:

So we can determine RV directly:

Systems for DSV:

Viscotek DSV Dilute solution viscometer for automated relative viscosity measurements This system can measure: Dilute Soultion Viscometry Solution viscosity range: <1mPas to 20mPas Measurement temperature range: 15°C to 160°C See the Viscotek DSV