On-line Detector Methods…and a peak at possibly better things to come. Theme: being average (and averages generally) suck. Reference: Study of Rodlike Homopolypeptides by Gel Permeation Chromatography with Light Scattering Detection: Validity of Universal Calibration and Stiffness Assessment E. Temyanko, P. S. Russo and H. Ricks, Macromolecules, 34, 582-586 (2001) GPC •Solvent flow carries molecules from left to right; big ones come out first while small ones get caught in the pores. •It is thought that particle volume controls the order of elution. •But what about shape? Simple SEC c log10M c DRI Ve c degas pump injector log10M Osmometry: Real Science h pV = n R T n = g/M c = g/V 1 p = c R T ( A2c ...) M Semipermeable membrane: stops polymers, passes solvent. Light Scattering: Osmometer without the membrane 100,000 c x 2p q 1 p Is cRT ( 2 A2c ...) M c T , p 1 q 4 πn o sin( / 2) LS adds optical effects Size q = 0 in phase Is maximum 2 q > 0 out of phase, Is goes down Is 1 q R 3 2 g SEC/MALLS MALLS DRI DRI degas pump injector SEC/MALLS 3D Plot - PBLG Scattered intensity 6 7 16 15 14 13 12 11 10 9 8 5 4 Scattering Envelope for a Single Slice 140000 120000 R/Kc 100000 80000 60000 c = 0.044 mg/mL M = 130000 g/mol 40000 20000 0 0.0 0.2 0.4 0.6 sin ( /2) 2 0.8 1.0 SEC/RALS/VIS DP h viscometer LS90o DRI degas pump injector Universal Calibration Grubisic, Rempp & Benoit, JPS Pt. B, 5, 753 (1967) One of of the most important Papers in polymer science. Imagine the work involved! 6 pages long w/ 2 figures. Selected for JPS 50th Anniv. Issue. Universal Calibration Equations [h]AMA = [h]SMS= f (Ve) Universal Calibration A = analyte; S = standard [h] = KM a Mark-Houwink Relation K A M Aa A 1 K S M SaS 1 K S M SaS 1 MA KA 1 a A 1 Combine to get these two equations, useful only if universal calibration works! Objectives • Use a-helical rodlike homopolypeptides to test validity of universal calibration in GPC. • Can GPC/Multi-angle Light Scattering arbitrate between disparate estimates of stiffness from dozens of previous attempts by other methods? Strategy d L Hydrodynamic volume Severe test of universal calibration: compare rods & coils Combine M’s from GPC/MALLS with [h]’s from literature Mark-Houwink relations. Polymers Used Polystyrene (expanded random coil) Solvent: THF = tetrahydrofuran [CH-CH]x [NH-CHR-C]x Homopolypeptides (semiflexible rods) O R = (CH2)2COCH2 PBLG = poly(benzylglutamate) Solvent: DMF=dimethylformamide R = (CH2)2CO(CH2)CH3 PBLG = poly(stearylglutamate) Solvent: THF = tetrahydrofuran Mark-Houwink Relations [h] = 0.011·Mw0.725 for PS [h] = 1.26·10-5·Mw1.29 for PSLG [h] = 1.58 10-5·Mw1.35 for PBLG Polystyrene Standards: the Usual Table 1. GPC/LS Parameters for PS in THF Mw Mw/Mn Vendor This Worka This Workb Specified 3105 N/A 1.14 6207 N/A 1.03 10300 10250 1.03 43900 45900 1.01 102000 105800 1.02 212000 240900 1.01 170000 174700 1.01 422000 483900 1.02 929000 935900 1.01 1600000 1639000 1.16 1971000 2226000 1.03 2145000 2171000 1.1 a b GPC/LS Sensitive to baseline and peak selection. Polypeptide Samples Were Reasonably Monodisperse Table 2. PSLG Molecular Weights Table 3. PBLG Molecular Weights Mw Mw/Mn Mw Mw/Mn 13370 17570 51080 67700 93090 138400 150800 176000 249000 2.044 2.044 1.04 1.022 1.256 1.019 1.24 1.125 1.03 10670 13690 18520 29980 45990 70870 86000 95920 265000 327500 1.233 1.267 1.233 1.07 1.046 1.119 1.018 1.05 1.176 1.04 NCA-ring opening was used to make these samples. Most were just isolated and used; a few were fractionated. Universal Calibration Works for These Rods and Coils PS PSLG PBLG PBLG Mixture -1 log([h]M /ml-mol ) 10 8 6 4 12 14 16 18 Ve /ml 20 22 nd 2 Virial Coefficient Equations p = nkT(1 + nA2,n + …) Osmotic pressure in number density concentration (n) units A2,n = M 2A2 /Na Relationship to the “normal” 2nd virial coefficient for conc. in mass per volume units. A2,n = Rg ,calc dL2/4 M / Mo L 12 12 Onsager 2nd virial coefficient for rods (L= length, d = dia.) Rg for rods 2nd Virial Coefficient (Excluded Volume Limit) is Another Universal Descriptor 9 10 8 10 7 10 6 10 5 10 4 -24 A2,n / 10 cm 3 10 PS PSLG PBLG PBLG Mixture 12 13 14 15 16 17 Ve /ml 18 19 20 21 22 Persistence Length ap from Rg R 2 g La p 3 a 2 p 2a p L 3 [1 ap L (1 e L / a p )] Persistence length is the projection of an infinitely long chain on a tangent line drawn from one end. ap = for true rod. Persistence Length of Helical Polypeptides is “Very High” 100 Rod ap = 240 nm 80 ap = 120 nm ap = 70 nm Rg / nm 60 40 What the biggest polymers in our sample would look like at this ap 20 0 0 100000 200000 300000 M 400000 500000 SEC/MALLS in the Hands of a Real Expert Macromolecules, 29, 7323-7328 (1996) ap 15 nm Much less than PBLG Conclusions The new power of SEC/Something Else experiments is very real. SEC is now a method that even the most jaded physical chemist should embrace. For example, our results favor higher rather than lower values for PBLG persistence length. This helps to settle about 30 years of uncertainty. Universal calibration works well for semiflexible rods spanning the usual size range, even when the rods are quite rigid. So, SEC is good enough for physical measurements, but is it still good enough for polymer analysis? They were young when GPC was. Small Subset of GPC Spare Parts To say nothing of unions, adapters, ferrules, tubing (low pressure and high pressure), filters and their internal parts, frits, degassers, injector spare parts, solvent inlet manifold parts, columns, pre-columns, pressure transducers, sapphire plunger, and on it goes… Other SEC Deficiencies • • • • 0.05 M salt at 10 am, 0.1 M salt at 2 pm? 45oC at 8 am and 50oC at noon? Non-size exclusion mechanisms: binding. Big, bulky and slow (typically 30 minutes/sample). • Temperature/harsh solvents no fun. • You learn nothing by calibrating. Must we separate ‘em to size ‘em? Your local constabulary probably doesn’t think so. I-85N at Shallowford Rd. Sat. 1/27/01 4 pm Better Resolution “Soon”? Pullulan, 8% HPC Solution, M=12,200 and 48,000 Improvement in resolution is observed at lower concentrations due to a more viscous characteristic. A compatibility problem is seen though at higher concentrations. 1.0 FArbitrary Units 0.8 CONTIN Exponential Exponential 0.6 0.4 0.2 0.0 1000 10000 100000 M 1000000 Indicates targeted M. M = 10,000 and 20,000 Examples of Separation Results from Simulation Data 2.0 FArbitrary Units 1.5 CONTIN 2 Exponential 1.0 0.5 0.0 1000 10000 M = 10,000 and 160,000 100000 M 2.0 M = 10,000 and 57,000 CONTIN 2 Exponential 1.5 FArbitrary Units 1.5 FArbitrary Units 2.0 CONTIN 2 Exponential 1.0 0.5 1.0 0.0 1000 0.5 10000 100000 1000000 M 0.0 1000 10000 M 100000 Indicates targeted M.