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 A membrane osmometer is a device used to indirectly measure the number average molecular weight ( M n displaystyle M_ n ) of a polymer sample. One chamber contains pure solvent and the other chamber contains a solution in which the solute is a polymer with an unknown M n displaystyle M_ n . The osmotic pressure of the solvent across the semipermeable membrane is measured by the membrane osmometer. This osmotic pressure measurement is used to calculate M n displaystyle M_ n for the sample.Contents1 Basic operation 2 Virial equations 3 Different membrane osmometry devices3.1 Static membrane osmometry 3.2 Dynamic membrane osmometry4 Limitations of membrane osmometry 5 ReferencesBasic operation 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. The osmotic pressure is measured and used to calculate M n displaystyle M_ n . In an ideally dilute solution, van ‘t Hoff’s law of osmotic pressure can be used to calculate M n displaystyle M_ n from osmotic pressure. lim c → 0 ( Π c ) = R T M n displaystyle lim _ cto 0 Big ( Pi over c Big ) = RT over M_ n M n displaystyle M_ n , number average molecular weight, mass/mole R displaystyle R , gas constant T displaystyle T , absolute temperature, typically Kelvin c displaystyle c , concentration of polymer, mass/volume Π displaystyle Pi , osmotic pressure Virial equations In practice, the osmotic pressure produced by an ideally dilute solution would be too small to be accurately measured. For accurate M n 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 M n 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: Π c = R T ( 1 M n + A 1 c + A 2 c 2 + A 3 c 3 + … ) displaystyle Pi over c =RT( 1 over M_ n +A_ 1 c+A_ 2 c^ 2 +A_ 3 c^ 3 +dots ) where A n displaystyle A_ n are constants and c displaystyle c is still the concentration of polymer 1. This virial equation may be represented in different additional forms: Π c = A M n + B c + C c 2 + D c 3 + … displaystyle Pi over c = A over M_ n +Bc+Cc^ 2 +Dc^ 3 +dots Π c = M n ( Γ 1 + Γ 2 c + Γ 3 c 2 + Γ 4 c 3 + … ) displaystyle Pi over c =M_ n (Gamma _ 1 +Gamma _ 2 c+Gamma _ 3 c^ 2 +Gamma _ 4 c^ 3 +dots ) where B displaystyle B and Γ displaystyle Gamma are constants and R T A 2 = B = R T M n Γ 2 displaystyle RTA_ 2 =B= RT over M_ n Gamma _ 2 . Different membrane osmometry devices Static membrane osmometry Capillary tubes are attached to both the solvent and the solution compartments. In this case the osmotic pressure is provided by the additional pressure of the fluid in the solution compartment. The difference in the height of the fluid in the capillary tube of solution compartment versus the height of the fluid in the capillary tube of the solvent compartment is measured once the solution reaches equilibrium to calculate the osmotic pressure. Π = Δ H ρ g displaystyle Pi =Delta Hrho g Π displaystyle Pi , osmotic pressure Δ H displaystyle Delta H , change in height ρ displaystyle rho , density g displaystyle g , acceleration due to gravity The main disadvantage of static osmometry is the long time it takes for equilibrium to be reached. It often takes 3 or more hours after the solute is added for the static osmometer to reach equilibrium. Dynamic membrane osmometry In a dynamic osmometer flow of solvent is measured and a counteracting pressure is created to stop the flow. Flow rate of the solvent is measured by the movement of an air bubble in a capillary tube of the solvent. The pressure of the solvent compartment is directly changed by raising or lowering a reservoir of solvent connected to the solvent compartment. The pressure difference between the two compartments is the osmotic pressure. This can be calculate by measuring the change in height or measured directly with a flexible diaphragm. Since the pressure is directly changed, an accurate measurement of osmotic pressure can be achieved in 10 - 30 minutes. Limitations of membrane osmometry Membrane osmometry measurements are best used for 30,000 < M n < displaystyle

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