Multi-detector GPC Characterization

1. Multi-detector GPC Characterization Drew Poche’

2. Outline • Basics-On the mechanism of GPC • Detection • Light Scattering • Viscometry • Putting it together- multi-detector GPC • Lots of numbers-What’s it good for?

3. How big is big? Drew Poche’ Materials Characterization Dow Chemical, Plaquemine

4. Alphabet Soup SEC-Size Exclusion Chromatography • Includes rigid stationary phases GPC-Gel Permeation Chromatography • “Soft” gel stationary phases GFC-Gel Filtration Chromatography • Separation of biological molecules (nature’s polymers) in an aqueous environment

5. HPLC? You bet. Mobile phase pump auto-injector column(s) detector(s) data acquisition Temperature control

6. Putting it in perspective • Typical organic molecule vs typical polymer molecule Measuring size and molar mass • Mass spec • GC-MS, LC-MS • NMR • Modeling, quantum • mechanics • Other colligative • property based • measurements EASY TOUGH

7. Polymer standards--Column Calibration

8. Can it get worse? • Typical synthetic organic molecules in a pure sample are all the • same molar mass • Typical synthetic polymer molecules in a pure sample may differ not only • in molar mass but also in molecular shape Ordinary small molecule sample Ordinary synthetic polymer sample

9. GPC Mechanism Wiggling (chain conformations) determines average dimensions and pore permeation Eliminate enthalpic interactions Entropic effects alone govern

10. Getting it right • Problems, Problems • Polymer chains are not created equal Mc = Ma Mb = < Vc Va > Vb • Solutions • Absolute molecular weight detectors (light scattering, viscometry) • Universal calibration

11. Bent out of Shape First, let’s select a couple of chain conformations... Then, stuff them into a confined space and see what happens Center of mass too close to wall Forbidden conformation Allowed conformation Loss of conformational entropy dictates partitioning between pore and non-pore space

12. Let’s clarify Bottom line: or

13. Who wants to be a millionaire? If the polymer chains are restricted to one configuration (e.g. rods), what drives the partitioning between pore space and non-pore space? a) rotational orientation b) pore gremlins c) there’s no such thing as rod d) Huh? shaped chains

14. For the million dollars…. If GPC really separates by SIZE, which chain dimension correlates with elution order? • I don’t know • It’s a rather complicated question because pore • characteristics and chain geometry influence the • magnitude of the equilibrium constant, KGPC • Leading candidates: • radius of gyration, Rg • hydrodynamic volume, Rh3 or Vh (universal calibration)

15. Column selection FIPA

16. Making sense of the chromatogram • Synthetic polymers are composed of a distribution of chain sizes • We use statistics to get average dimensions to describe the bulk sample • Commonly computed from GPC: Mnthe arithmetic mean Mw weight average • Computing Mw and Mn is sensible since these averages “fall out” naturally from experiments used to measure molar mass • Mn from colligative or counting methods (NMR, osmometry, and those boring experiments you did in freshman chem) • Mw from methods sensitive to molecular size (LS, centrifugation)

17. Time to count

18. Where do ni and Mi come from?

19. Multiple numbers of standards Column Calibration • That’s one source of Mi Problem: only equivalent Mi is obtained

20. E pluribus unum • Universal Calibration • Gives molar mass without regard to chain architecture • Valid? Nearly always. • Suggests: L  Vh

21. Wait a minute! • If I don’t know how M and [h] are related for my polymer, how do I use universal calibration? YOU DON’T • Mark-Houwink (empirical power law)

22. “…too much dancing and not nearly enough prancing...”C. Montgomery Burns, commenting on GPC prior to molar mass sensitive detectors • Visible light scattering used for polymer characterization has been around almost as long as chemists have believed in polymers • However, GPC detectors based upon the technique are relatively new (1970s) • Light scattering, by its nature, returns the weight average molar mass

23. Visible Light vs. polymer chain Particle view: Incident light “pushes” electrons, producing transient dipoles Thermo view: Incident light couples to concentration gradient found in real solutions

24. How to get Mw from the measurement Scattering contains dn/dc Particle form factor MALLS uses Eq 1 and 2 and returns Mw and Rg LALLS and RALLS use Eq 3 and return Mw caveat: RALLS requires a shape correction when Rg approaches (lo/50)n

25. How LS returns other molar mass averages • Simple assumption….monodisperse fractions from the GPC columns. Therefore, Mw,i = Mi • This assumption may lead to an over-estimation of Mn

26. “I’m going to describe the apparatus first before I set it motion. Then you’ll be able to follow the proceedings better.” Franz Kafka • Advantages • MALLS gives molecular architecture information without assumptions IF there is a measurable angular dependence on the scattered light intensity • RALLS is more forgiving of dusty samples and returns essentially the same information as LALLS IF the polymer is small compared to lo • LALLS is more sensitive, requires no correction over a huge range of molar mass

27. “Do you suppose,” the Walrus said, “that they could get it clear?” “I doubt it,” said the Carpenter, and shed a bitter tear. Lewis Carroll DUST, GELS, or assorted particulate vs. Light Scattering

28. Column Calibration? Not!

29. Specific refractive index increment • The bigger the better • Depends on: • solvent • temperature • light wavelength Dn = n- no If polymer solvent combo is isorefractive, no scattering will be observed

30. Why dn/dc matters

31. The plot thickens-Viscosity • Viscometers as GPC detectors are based upon the measurement of a differential pressure between pure solvent and polymer solution  hsp

32. How to get [h]i • Software computes both hsp,i and hrel,i • Solomon-Gottesman [h]i = 21/2(hsp,i-ln(hrel,i)1/2/c Important point: hsp and hrel are concentration dependent [h] is, by definition, a “zero” concentration property

33. Like LS, the viscometer is sensitive to bigger chains

34. All that work for two numbers? • Re-visit universal calibration…units analysis Mw x [h]  (Rh)3 gmol-1 x cm3g-1 = cm3mol-1 From two simple measurements we can estimate size or volume! Implication: chain architecture elucidation

35. Let the fun begin • Getting Mi and [n]i from GPC fractionation mean: • Rapid M-H relationships • Molecular architecture determinations • Calculation of other polymer dimensions • Correlation to physical properties • Identification of tiny fractions of high molar mass material

36. From a few months to a few minutes!

37. Behold the Power of M-H[h] = KMa • a parameter: approaching 0 ; spheres 0.5 ;theta condition for linear chains 0.7-0.8 ; expanded coils 1.8 ; ideally rigid rod a may or may not change with branching • K parameter: shifts with comonomer composition or branching density

38. What happens when branches are present Star branched

39. Had enough? More commonly encountered long chain branching Have you noticed that the hydrodynamic dimensions of a branched polymer are “shrunken” compared to its linear counterpart?

40. Branching? YIKES! • Triple detection GPC measurements (LS,VIS, DRI) • Determine [h]-Mw relationship (M-H values) • Compare [h]-Mw relationship to that of a linear sample • Apply appropriate branching model to calculate branching density • Possibilities: star, off-center star, comb, random long chain branching, H, super-H, Pom-Pom

41. Dependence of Performance Propertieson Molar Mass