Membrane osmometer

A low concentration solution is created by adding a small amount of polymer to a solvent. This solution is separated from pure solvent by a semipermeable membrane. Solute cannot cross the semipermeable membrane but the solvent is able to cross the membrane. Solvent flows across the membrane to dilute the solution. The pressure required to stop the flow across the membrane is called the osmotic pressure.[1] The osmotic pressure is measured and used to calculate ${\displaystyle M_{n}}$.

In an ideally dilute solution, van ‘t Hoff's law of osmotic pressure can be used to calculate ${\displaystyle M_{n}}$ from osmotic pressure.[1]

${\displaystyle \lim _{c\to 0}{\Big (}{\Pi \over c}{\Big )}={{RT} \over M_{n}}}$

${\displaystyle M_{n}}$, number average molecular weight, mass/mole

${\displaystyle R}$, gas constant

${\displaystyle T}$, absolute temperature, typically Kelvin

${\displaystyle c}$, concentration of polymer, mass/volume

${\displaystyle \Pi }$, osmotic pressure

In practice, the osmotic pressure produced by an ideally dilute solution would be too small to be accurately measured. For accurate ${\displaystyle M_{n}}$ measurements, solutions are not ideally dilute and a virial equation is used to account for deviations from ideal behavior and allow the calculation of ${\displaystyle M_{n}}$. The virial equation takes a form similar to van ‘t Hoff's law of osmotic pressure, but contains additional constants to account for non-ideal behavior:

${\displaystyle {\Pi \over c}=RT({1 \over M_{n}}+A_{1}c+A_{2}c^{2}+A_{3}c^{3}+\dots )}$

where ${\displaystyle A_{n}}$ are constants and ${\displaystyle c}$ is still the concentration of polymer 1. This virial equation may be represented in different additional forms:

${\displaystyle {\Pi \over c}={A \over M_{n}}+Bc+Cc^{2}+Dc^{3}+\dots }$

${\displaystyle {\Pi \over c}=M_{n}(\Gamma _{1}+\Gamma _{2}c+\Gamma _{3}c^{2}+\Gamma _{4}c^{3}+\dots )}$

where ${\displaystyle B}$ and ${\displaystyle \Gamma }$ are constants and ${\displaystyle RTA_{2}=B={RT \over M_{n}}\Gamma _{2}}$.

Membrane osmometry measurements are best used for 30,000 ${\displaystyle <M_{n}<}$ 1,000,000 grams/mole. For ${\displaystyle M_{n}}$ above 1,000,000 grams/mole, the solute is too dilute to create a measurable osmotic pressure.[1] For ${\displaystyle M_{n}}$ below 30,000 grams per mole, the solute permeates through the membrane and the measurements are inaccurate.[2]

Another issue for membrane osmometer is the limited membrane types. The most common membrane used is cellulose acetate; however, cellulose acetate can only be used with toluene and water.[3] While toluene and water are useful solvent for many compounds, not all polymers are miscible in toluene or water. Regenerated cellulose membranes can be used for many other solvents, but are hard to obtain.[3]