What I Talk About When I Talk About Viscometry

Transcription

1 What I Talk About When I Talk About Viscometry André M. Striegel * National Institute of Standards & Technology *With apologies to Raymond Carver & Haruki Murakami

2 CHROMATOGRAPHIA issue with contributions of the International GPC Conference 2015: Participants are invited to submit manuscripts based on their oral or poster presentations for possible publication in CHROMATOGRAPHIA, with the intention of including them in a Topical Collection devoted to the International GPC Symposium Manuscripts will be subject to a regular refereeing procedure, editor will be André Striegel. Please consult the journal's homepage for more details. Manuscripts are to be delivered electronically not later than November 30, 2015 via the journal's online submission and reviewing system which is accessible at:

3 Outline Historical Background Viscometers Select Topics Universal calibration Polymer size Solution aggregation Detector sensitivities Oligomers Conclusions Et cetera

4 P 8 LQ r 4 0 Figures courtesy of Waters, Wyatt Technology, Malvern

5 Historical Background (or, How Did We Get Here From There?)

6 Isaac Newton ( ) The resistance which arises from the lack of slipperiness originating in a fluid, other things being equal, is proportional to the velocity by which the parts of the fluid are being separated from each other. Principia Mathematica (1687), translation by M. Reiner

7 The resistance which arises from the lack of slipperiness originating in a fluid, other things being equal, is proportional to the velocity by which the parts of the fluid are being separated from each other. resistance local stress, velocity by which the parts of the fluid are being separated velocity gradient, or change of velocity with position in the fluid, In one dimension, we can write: yx or yx d vx d y

8 Newton s Law of Viscosity Stress rate of strain Constant of proportionality: Viscosity, yx = Stress = Force (per unit area); strain rate = acceleration (change in velocity with position). Form of Newton s Second Law, F = ma

9 Navier & Stokes 1845: 150+ years after Newton s idea, George Gabriel Stokes ( ), also using work by Claude-Louis Navier ( ), among others, formulates viscosity law in three dimensions. Assumptions: Stress in the fluid is sum of a diffusing viscous term and a pressure term. Constant density (incompressible flow) and viscosity.

10 The Navier-Stokes Equation Local acceleration Convective acceleration Pressure force per unit volume Body force per unit volume Viscous force per unit volume v v v p g 2 v t Mass Sum of accelerations = Sum of forces (per unit volume)

11 The Navier-Stokes Equation In fluid dynamics, everything boils down to one canonical equation, the Navier-Stokes equation. It is a miracle of brevity, relating a fluid s velocity, pressure, density, and viscosity, but it happens to be nonlinear. Chaos: Making a New Science, James Gleick (1987)

12 Let s Make Some Assumptions Flow is laminar (Re < 2100). Density is constant ( incompressible flow ). Flow is time-independent ( steady state ). Fluid is Newtonian. End effects are neglected. Fluid behaves as a continuum. No wall slip. For additional info, see R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, rev. 2 nd ed. (2006)

13 Parabolic Flow Profile in Tube x L z r r 0 y Q 2 r r P 0 v r dr d z L 4 0

14 Poiseuille s Law P 8 LQ r 4 0 P: Pressure drop across capillary : Viscosity of liquid flowing through capillary L: Length of capillary Q: Volumetric flow rate through capillary r 0 : Inner radius of capillary

15 J Lesec, in Encyclopedia of Chromatography, 2nd ed., J Cazes, Ed. (2005) On-Line Viscometers Two basic types: Single-Capillary and Differential

16 Universal Calibration Z Grubisic, P Rempp, H Benoit, J. Polym. Sci.: Polym. Lett., 5 (1967) 1705

17 ( ) n OH O ( ) n HO HO O OH O OH O OH Polystyrene Cellulose

18 SEC/VISC/DRI Universal Calibration Plot: PS Standards JD Timpa, in Adv. Chem. Ser. 247, pp (1995)

19 SEC/VISC/DRI of Cellulose JD Timpa, in Adv. Chem. Ser. 247, pp (1995)

20 Dendrimer Characterization by SEC/VISC/DRI Universal Calibration using Pullulan Standards

21 Starburst (PAMAM) Dendrimers B Halford, C&EN, 83 (2005) 30

22 Calculating the Molar Mass of Dendrimers M M c N c M RU N G1 b N b 1 1 G1 M t Nb M: Theoretical average molar mass M c : Molar mass of initiator core M RU : Molar mass of repeat unit M t : Molar mass of terminal unit N c : Initiator core multiplicity N b : Branch-juncture multiplicity G: Dendrimer generation N RU : # of dendrimer repeat units (degree of polymerization) N RU N c N N G1 b b 1 1 DA Tomalia, AM Naylor, WA Goddard III, Angew. Chem., 29 (1990) 138

23 Starburst Molar Masses: Experimental vs. Theoretical M theor M w (UC-SEC) Ð [] (ml g -1 ) Starburst G Starburst G Starburst G In H 2 O % NaN 3, 50 o C. All M in g mol -1. Ð M w /M n AM Striegel, RD Plattner, JL Willett, Anal. Chem., 71 (1999) 978

24 (a) (b) TH Mourey et al., Macromolecules, 25 (1992) 2401

25 Analyzing Alternan, an Ultra-High Molar Mass Polysaccharide

26 Alternan Ultra-high-M polysaccharide (seems as if MMD may exceed 100 million g/mol!) Potential applications: Coating for time-released pharmaceuticals Binder for paints and inks Bulking agent for food and beverages Cost-effective substitute for gum arabic Long-chain branched polysaccharide, with backbone and branches consist of statistically alternating -(13) and -(16) D- anhydroglucose units. Aggregates in aqueous solution. Collaboration with Dr. Greg Côté (USDA).

27 A Measure of Size: The Viscometric Radius R 3 M 10 N A 1/ 3 []: Intrinsic viscosity of polymer solution M: Molar mass of polymer N A : Avogadro s number Radius of homogeneous hard sphere which changes viscosity of solvent by the same amount as change imparted by polymer.

28 Differential Weight Fraction Cumulative Weight Fraction MMD of Alternan 2.5 HDC-MALS Molar Mass (g/mol) SL Isenberg, AK Brewer, GL Côté, AM Striegel, Biomacromolecules, 11 (2010) 2505

29 ( ( Influence of Hyperbranching on Size HO HO O OH O OH HO HO O OH O OH HO HO O OH O HO HO O OH O OH HO HO O OH O OH HO HO O OH Alternan -(13), -(16) Pullulan -(14), -(16) O n

30 Influence of Hyperbranching on Size M w (x 10 6 g mol -1 ) [] w (ml g -1 ) R (nm) B a B a <1 Pullulan b <1 Pullulan (theor) c 334 All results in DMSO at 50 o C. a From off-line, batch-mode MALS. b From HDC/MALS c Calculated from [] = M (courtesy of P. Kilz) SL Isenberg, AK Brewer, GL Côté, AM Striegel, Biomacromolecules, 11 (2010) 2505

31 ( ( HO HO O OH O OH SEC/MALS/VISC/DRI O HO HO OH O OH of HO HO O OH Pullulan O HO HO O OH O OH HO HO O OH O OH HO HO O OH O n

32 MALS Sensitivity to Aggregates Fundamental equation of static light scattering: * K c R( ) 1 1 2A... 2c P( ) M w Tells us that static light scattering signal, R(), is directly proportional to molar mass, M: R() M w Because aggregates have higher molar mass than unaggregated molecules, aggregates will produce a larger static light scattering detector response than the unaggregated molecule, all other factors being equal.

33 SEC/MALS/VISC/DRI of Pullulan (DMAc/LiCl, 80 o C) DRI Pullulan aggregation, observed by MALS. VISC AM Striegel, JD Timpa, ACS Symp. Ser. 635 (1996)

34 SEC/MALS/VISC/DRI of Pullulan (DMAc/LiCl, 80 o C) DRI VISC BUT [] = KM a? If [] M, where is VISC signal for aggregate peak? AM Striegel, JD Timpa, ACS Symp. Ser. 635 (1996)

35 Mark-Houwink Relations Mark-Houwink Equation: [] = KM a Structure Mark-Houwink exponent a Linear random coil () 0.5 Linear random coil ( good ) ~ Rigid rod 2 Homogeneous hard sphere 0

36 Intrinsic viscosity, [] (ml/g) Mark-Houwink Plot of PMMA Latexes (Water, r.t.) PMMA latexes Slope = Molar mass, M (g/mol) AK Brewer, AM Striegel, J. Sep. Sci., 33, (2010) 3555

37 Mark-Houwink Plot of Linear and High-f Star Poly(isobutyl methacrylate) S Podzimek, LS, SEC & AF4 (2011)

38 SEC/MALS/VISC/DRI of Pullulan (DMAc/LiCl, 80 o C) DRI No DRI signal indicates aggregate is present at very low concentration. MALS peak at ~18 min indicates pullulan aggregation in solution. VISC No VISC signal indicates aggregate shape is likely spherical. AM Striegel, JD Timpa, ACS Symp. Ser. 635 (1996)

39 The Viscometer as an Orthogonal Detector

40 SEC/MALS/QELS/VISC/DRI Analysis of solution of PDMS. Analysis of blend of two samples of PDMS. Analysis of blend of PDMS and PS.

41 Differential refractive index Specific Refractive Index Increment (n/c) of PDMS and PS 1.0x10-3 PDMS (20 o C) 8.0x x10-4 PS (25 o C) THF, 0 = 658 nm n c PS ml g 4.0x x n c PDMS ml g Concentration (g ml -1 ) AM Striegel, L Pitkänen, Chromatographia, 78 (2015) 743

42 Viscometry vs. Spectroscopy Analyses being conducted at conditions of spectroscopic invisibility for PDMS. However, viscometric detection is based on hydrodynamic transport properties, not on spectroscopic principles. VISC is a truly orthogonal complement, or alternative, to MALS, QELS, DRI, etc.

43 DRI (V) QELS count rate (Hz) VISC (V) MALS 90 o (V) SEC/MALS/QELS/VISC/DRI of 116K PDMS -6.5x x x10-5 (a) PDMS 116 DRI MALS 90 o VISC QELS x x x x x x x x Retention volume (ml) AM Striegel, L Pitkänen, Chromatographia, 78 (2015) 743

44 DRI (V) QELS count rate (Hz) VISC (V) MALS 90 o (V) SEC/MALS/QELS/VISC/DRI of Blend of 116K and 440K PDMS -7.5x x10-5 PDMS 440 DRI MALS 90 o VISC QELS x x x10-5 PDMS x x x x Retention volume (ml) AM Striegel, L Pitkänen, Chromatographia, 78 (2015) 743

45 Normalized detector response SEC/MALS/QELS/VISC/DRI of Blend of 440K PDMS and 18K PS 1.0 (a) DRI MALS 90 o VISC QELS PDMS 440 PS Retention volume (ml) AM Striegel, L Pitkänen, Chromatographia, 78 (2015) 743

46 SEC/Viscometry Analysis of Oligomers

47 VISC Response (V) SEC/VISC of N-Acetylchitooligosaccharides Retention volume (ml) H 2 O, 37 o C, ph 7.4 MJ Morris, AM Striegel, Carbohydr. Polym., 106 (2014) 230

48 SEC/VISC of PE Oligomers in 135 o C MJ Smith, IA Haidar, AM Striegel, Analyst, 132 (2007) 455 DB Alward, AM Striegel, J. Liq. Chromatogr. Rel. Technol., 26 (2003) 157

49 Differential Viscometry Measurements Differential pressure signal proportional to specific viscosity: DP sp. Intrinsic viscosity [] defined through specific viscosity sp as per: [ ] lim c0 sp c Flow In R 2 R 3 DP Flow Out In turn, the viscometric radius R is defined through the intrinsic viscosity [] as per: R 1 R 4 R 3 M 10 N A 1/ 3 IP

50 SEC/VISC of PE Oligomers in 135 o C [] (dl/g) R (Å) PE PE MJ Smith, IA Haidar, AM Striegel, Analyst, 132 (2007) 455 DB Alward, AM Striegel, J. Liq. Chromatogr. Rel. Technol., 26 (2003) 157

51 SEC/VISC of PS Oligomers in 135 o C [] (dl/g) R (Å) PS PS MJ Smith, IA Haidar, AM Striegel, Analyst, 132 (2007) 455 DB Alward, AM Striegel, J. Liq. Chromatogr. Rel. Technol., 26 (2003) 157

52 SEC/VISC of PS Oligomers in 35 o C [] (dl/g) R (Å) PS PS Styrene PS 580 MJ Smith, IA Haidar, AM Striegel, Analyst, 132 (2007) 455 DB Alward, AM Striegel, J. Liq. Chromatogr. Rel. Technol., 26 (2003) 157

53 Viscosity (mpa-s) 1.00 Viscosity Plot of Styrene-DMAc/LiCl Solutions (35 o C) Volume Fraction Styrene DB Alward, AM Striegel, J. Liq. Chromatogr. Rel. Technol., 26 (2003) 157

54 What s Going On? Viscosity (mpas, 20 o C) Styrene 0.76 DMAc 0.97 DR Lide, CRC Handbook of Chemistry & Physics, 71 st ed. (1990)

55 PREDICTIVE MIXING RULE (ONE-PHASE BINARY MIXTURES) P A A B B A B, P A, A B B = Viscosity of solution = Viscosities of components A and B = Volume fractions of components A and B in mixture = Interaction parameter LE Nielsen, Predicting the Properties of Mixtures (1978)

56 Viscosity (mpa-s) 1.00 Viscosity Plot of Styrene-DMAc/LiCl Solutions (35 o C) Volume Fraction Styrene DB Alward, AM Striegel, J. Liq. Chromatogr. Rel. Technol., 26 (2003) 157

57 What s Going On Solutions are following mixing rule for one-phase binary mixtures. Small oligomeric solute is, essentially, becoming the solvent (diluent) in the solution. REM: Viscometric radius, R: Radius of homogeneous hard sphere which changes viscosity of solvent by the same amount as change imparted by polymer.

58 P 8 LQ r 4 0 Figures courtesy of Waters, Wyatt Technology, Malvern

59 Acknowledgements Collaborators Michael Krejsa Ronald Plattner JL Willett Amandaa Brewer Samantha Isenberg Gregory Côté Judy Timpa (dec d) Leena Pitkänen Mallory Morris David Alward Support Solutia USDA Library of Congress Agilent/Polymer Labs Daniela Held FSU

60 In Memoriam Donald D. Bly ( )

61