Viscometry

Viscometry is the measurement of the viscosity ( strength ) of liquids or gases. This is determined in a measuring device, the viscometer , by measuring the flow rate through a defined volume, usually in a capillary , for a defined amount of liquid or gas . A flow sensor is often used in technology.

History and derivation

Isaac Newton first investigated viscosity, which is a measure of the internal friction of a material. For Newtonian media, he defined it as the proportionality factor, the shear stress σ ₁₂ and the shear rate .

${\displaystyle F=\eta \cdot A{\frac {dv}{dx}}=\eta \cdot a\cdot {\dot {\gamma }}}$

d v / d x corresponds to the shear rate. If a Newtonian liquid is sheared between two plates of area A with a force F, it begins to flow and a velocity gradient is created orthogonally to the direction of movement . η is referred to here as dynamic viscosity. Macromolecules are mobile due to the rotatability of the bonds and can take various forms. If you exert a shear stress on a ball, the macromolecules align themselves in the direction of the resulting flow and consequently the viscosity decreases. The dynamic viscosity depends on the temperature. As a rule, the solvent becomes thermodynamically better with increasing temperature; the ball becomes larger and thus the viscosity increases. It is therefore very important to carry out viscosity measurements at constant temperature and in the same solvent. ${\displaystyle {\tfrac {dv}{dx}}}$

Staudinger index

The Staudinger index, named after Hermann Staudinger and often also referred to as limiting viscosity or intrinsic viscosity, is obtained by extrapolating the concentration c of a dilute solution to zero. It is thus defined by:

${\displaystyle [\eta ]=\lim _{c,G\to 0}{\frac {\eta _{s}}{c}}}$

• [ η ] is the limit value of the reduced viscosity for c = 0 and G = 0
• G corresponds to the speed gradient
• the specific viscosity η _s results from the viscosity of the solution η and the viscosity of the solvent η _L as:

${\displaystyle \eta _{s}={\frac {\eta -\eta _{L}}{\eta _{L}}}}$

The extrapolation to c = 0 can be carried out graphically by plotting against η _s . In this way one often obtains a linear relationship. This method of extrapolation is called Schulz-Blaschke extrapolation. It is also common to plot against c, which is called extrapolation according to Huggins. ${\displaystyle {\tfrac {\eta _{s}}{c}}}$ ${\displaystyle {\tfrac {\eta _{s}}{c}}}$

The extrapolation from G → 0 can usually be dispensed with by choosing a suitable viscometer, since the value of G is thus kept small and constant.

Measurement

The measurement is carried out with a viscometer , of which there are different versions. When measuring with a capillary viscometer, the use of an Ubbelohde viscometer is the least expensive. The basis for measuring viscosity is provided by the Hagen-Poiseuille law :

${\displaystyle \eta ={\frac {\pi \cdot t\cdot r^{4}\cdot \Delta p}{8\cdot V\cdot l}}={\frac {\pi r^{4}\cdot g\cdot h}{8\cdot V\cdot l}}\cdot \rho \cdot t}$

r is the radius and l is the length of the capillary . Δ p is the pressure difference between the capillary ends and V is the volume of liquid that flows through the capillary during time t . All parameters can be kept constant because the acceleration due to gravity g and the height of the capillary h = l are constant and the difference in density (density = ρ ) between the solvent and the dilute solution can be neglected. This results in a proportionality and with the help of the equation of the specific viscosity results: ${\displaystyle \eta \,\alpha \,t}$

${\displaystyle \eta _{s}={\frac {t-t_{l}}{t_{l}}}}$

The actual measured variables are the processing times for a polymer- solvent mixture.

Individual evidence

1. ^ Cowie, Jan MG: Polymers: Chemistry and Physics of modern Materials. 3rd edition, CRC Press, 2008
2. ↑ Lechner, MD; Gehrke, K .; Nordmeier, EH; Macromolecular Chemistry, 3rd edition, Birkhäuser Verlag, 2003
3. ^ Tieke, Bernd: Makromolekulare Chemie. 2nd edition, Wiley-VCH, 2008