Solution Dynamics

1. Solution Dynamics Richard Thompson Department of Chemistry University of Durham r.l.thompson@dur.ac.uk

2. Dynamics of Polymer SolutionsHow fast will a process happen? “…as soon as it got wet it became more of a problem” A seaside town was swamped with semolina after a factory blasted out 2 tonnes of the dessert ingredient. People living in Great Yarmouth woke up to find their town covered in the fine white grain. But council staff who tried to clear up the mess made the mistake of adding water - accidentally turning the powder into a slippery pudding! The grain is thought to have been chucked out because of a problem with a huge container at a nearby factory. A council spokesperson said: "It looked like there had been a heavy frost. Everywhere was just white, even the grass. "We had 10-15 people trying to clear it up, but as soon as it got wet it became more of a problem." The semolina was eventually cleared up and Great Yarmouth is now back to normal.

3. Overview • This lecture provides a link between • molecular characterisation techniques • concerned with how to measure properties of polymers • and polymer physics • concerned with understanding how polymers behave once their characteristics are known • A good starting point are dilute solutions allows us to consider polymers in isolation

4. Dilute solutions • Chains do not overlap • Can consider that each chain acts in isolation • Dynamic considerations: Movement of polymers - diffusion Solutions under flow - viscosity • In semi-dilute solutions • concentration is sufficient for chains to just overlap

5. Measuring DiffusionDynamic Light Scattering (DLS, PCS, QELS etc) • Light scattered from polymer chains in dilute solution interferes producing a speckle pattern • Diffusion causes shimmering of speckle pattern as polymer chains undergo Brownian motion • Can also view this as Doppler shift to frequency of scattered light • Measure rate of shimmering with autocorrelation function

6. ( ) ( ) t = + - t 2 G 1 exp 2 Dq p 4 = q q sin l kT 1 = D ph 6 R e Interpretation of DLS data • Autocorrelation function G(t) leads to effective hydrodynamic radius of polymer coil in solution. • where h is the viscosity, … I(t) t t G(t) t

7. Dilute Solution Viscosity • A step towards understanding dynamics in polymers • A useful practical tool for rapid measurement of molecular weights • Important relationship for relative viscosity:

8. Suspended level dilution viscometry B C A • Solution pumped into E from A with pressure and C closed • Pressure removed from A and C opened • Solution flows back from E into D • Viscosity determines time for height of solution to change from x to y • Measurements can be repeated for different concentrations by diluting the solution via A x E y F D Ubbelohde Viscometer

9. Relative, specific, intrinsic … • Relative viscosity • Specific viscosity • Intrinsic viscosity solution viscosity solvent viscosity extrapolated to zero concentration

10. Viscosity measures hrel h 1 hsp h0 slope = [h] conc.

11. Spheres • Einstein: for a solution of dilute non-interacting spheres • Viscosity increases according to... • v2 is the volume fraction of spheres • What is the intrinsic viscosity?

12. The equivalent sphere model I • Consider that each polymer chain is impenetrable to solvent • with an effective hydrodynamic radius, Re • and volume • For polymer equivalent spheres, Einstein relation can be rewritten Re Number of molecules/ unit volume

13. constant (in freely jointed chain models) The equivalent sphere model II • Since the number of molecules per unit volume is also given by • then the intrinsic viscosity is molecular weight

14. The equivalent sphere model III • From the solution thermodynamics lecture • and • Hence intrinsic viscosity theta solvent good solvent

15. The Mark-Houwink Relationship • Flory showed that in a good solvent • equivalent to • Typically state • So a log [h] vs log M plot is normally linear • where 0.5 < a < 0.8 theta solvent a = 0.5 good solvent a=0.8

16. Highly Branched Polymers • Quite different viscosity / molecular weight properties are seen for highly branched polymers • Shown here for both dendrimers and hyperbranched • (Hobson & Feast, Chem Comm 1997, p2067) • Intrinsic viscosity begins to fall with increasing Mw at high Mw.

17. Summary • Polymer structure and solvent interactions have a huge effect on dynamics, even in dilute systems • Light scattering can quantify diffusion and effective size of polymer chains • Viscometry provides a simple but effective method for molecular size characterisation • Simple measurements like these can provide a profound insight into the physical properties of polymers in solution

18. Resources Thermodynamics and Dynamics of Polymer Solutions • DLS • N.C. Ford, Jr., in Dynamic Light Scattering. Applications of Photon Correlation Spectroscopy. Edited by R. Pecora, Plenum 1985 • Viscometry • Polymers: Chemistry and Physics of Modern Materials, 2nd Ed, J.M.G. Cowie, Blackie, 1991 • Hobson and Feast, Chem Comm, 1997, p 2067. • Freely Jointed Chain Models • Polymer Physics, M. Rubinstein and R. H. Colby, Oxford, 2003 (see also J.M.G. Cowie’s book) • ‘Solution’ Properties of Semolina: • Source: CBBC website(!) • See also Jordan and Brant, Macromolecules, 13, 3, (1980) p 491. for serious discussion of Amylose solutions.