Molecular Weight Distribution Summary

1. Molecular Weight Distribution Summary

2. Colligative Properties and Mn For an ideal solution (dilute): DV = 0 and DH = 0 Mole fraction of i. Standard chemical potential of pure component i. For the solvent in a polymer solution: Thus: Also: Molar volume of solvent. Molecular weight of solute.

3. So for ideal solutions (DV=0 and DH=0): This is known as a virial equation and the property (m1-m1o) relates to the colligative properties osmotic pressure, boiling point elevation, freezing point depression and pressure lowering. For osmotic pressure, it can be shown that: where P is the osmotic pressure. So,

4. For real solutions (DV and DH not 0): where A2 and A3 are second and third virial coefficients. These equations are also written as: Or:

5. Colligative Properties and Mn Osmotic Pressure: Boiling Point Elevation: Freezing Point Depression: Vapor Pressure Lowering:

6. Membrane Osmometry (pp. 37-44 in Shaw) P semi-permeable membrane! watch your units!! Recall... Assume A2, A3 … are equal to 0. Q: What would be the osmotic pressure for a10 g/L solution of Polystyrene of 200,000 g/mol in toluene at 25C?

7. Answer: At 25C: RT ~ 23 L x atm C ~ 10 g/L x 1 mol/200,000 g = 5 x 10-5 M P ~ 10-3 atm P ~ 14 mm toluene Modern osmometers can measure with accuracy of ~ 0.2 mm so the error here is ~ 0.15%. For this same sample: DTb ~ 1 x 10-4 C DP ~ 2 x 10-4 mm Hg (2.7 x 10-3 Pa) Neither which can be measured with great accuracy!

8. slope of A2 c • Practical considerations: • Solvent • low viscosity, equilibrates fast • Membrane • strength (i.e. 1M NaCl P=0.42 atm) • no leakage or attack by solvent • does it pass what you want? mechanism? • possible membranes • cellophane • animal membranes • polyurethane

9. Measurement • Capillary effects • Temperature effects • Impurities • Depends on number of particles, • high MW sample can be contaminated • by relatively (by mass) small amounts • of low MW impurity. Practical limits-- M=104-106 Two types of osmometers available: (1) Static -

10. (2) Dynamic – Pressure is adjusted on one side of membrane to cancel the solvent flow. (1 transparency from the Web) • Raw osmometry data are in cm (mm) of solvent: P = r g h Recall: So called Flory-Huggins parameter

11. better solvent P/c2 so called theta (Q) solvent Is this possible? c2 lower molecular weight in the same solvent P/c2 c2 What kind of results are possible?

12. In Summary: Upper limit depends on smallest pressure that can be measured. Lower limit depends on permeability of the membrane.

13. Donnan Equilibria Problems occur when a solution of diffusible and non-diffusible ions are introduced in an osmometer (say in the case of measuring on proteins). Unrealistically low molecular weights are determined due to the excess of diffusible ions on the side of the macromolecule. Working with moderately low protein concentrations and moderately high salt concentrations will solve this difficulty.

14. Donnan Equilibria 1 2 Na+ = a Pr- = a Na+ = a + x Pr- = a Cl- = x Na+ = b Cl- = b Na+ = b - x Cl- = b - x Before Equb’m At Equb’m Excess of ions in compartment 1 over compartment 2 (text)

15. Reverse Osmosis - Desalination 2270 m3/day, at P = 400 psi P>P Note: P is not transmitted through membrane!