BETTER THAN SEC’s Paul S. Russo Louisiana State University Texas Polymer Center Freeport, TX...
-
Upload
walter-sutton -
Category
Documents
-
view
215 -
download
2
Transcript of BETTER THAN SEC’s Paul S. Russo Louisiana State University Texas Polymer Center Freeport, TX...
BETTER THAN SEC’s
Paul S. RussoLouisiana State University
Texas Polymer CenterFreeport, TX
October 31, 2001
Obligatory Equation
SEC = GPC = GFCSize Exclusion Chromatography
Gel Permeation ChromatographyGel Filtration Chromatography
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?
Osmometry: Real Science
Semipermeable membrane: stops polymers, passes solvent.
h V = n R T
n = g/M
c = g/V
= c R T ...)1
( 2 cAM
Light Scattering: Osmometer without the membrane100,000
x
c
...)21
( 2,
1
cAM
cRTc
IpT
s
q
2
)2/sin(π4 o
nq
LS adds optical effects Size
q = 0 in phase Is maximum
q > 0 out of phase, Is goes down 3
122g
s
RqI
Scattering Envelope for a Single Slice
0.0 0.2 0.4 0.6 0.8 1.00
20000
40000
60000
80000
100000
120000
140000
c = 0.044 mg/mLM = 130000 g/mol
R/K
c
sin2( /2)
Universal Calibration
Grubisic, Rempp & Benoit,
JPS Pt. B, 5, 753 (1967)
One of of the most importantPapers in polymer science.Imagine the work involved!6 pages long w/ 2 figures.Selected for JPS 50th Anniv. Issue.
Universal Calibration Equations
[] = KM a
[]AMA = []SMS= f
(Ve)
11 SA aSS
aAA MKMK
Mark-Houwink Relation
Universal Calibration A = analyte; S = standard
Combine to get these two equations, useful only if universal calibration works!1
11
AS
S
a
A
aS
A K
MKM
Objectives
• Use -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?
Severe test of universal calibration: compare rods & coils
Combine M’s from GPC/MALLS with []’s from literature Mark-Houwink relations.
Strategy
Ld
Hydrodynamic volume
Polymers Used
[NH-CHR-C]x
O
R = (CH2)2COCH2
[CH-CH]x
R = (CH2)2CO(CH2)CH3
Polystyrene (expanded random coil)Solvent: THF = tetrahydrofuran
Homopolypeptides (semiflexible rods)
PBLG = poly(benzylglutamate)Solvent: DMF=dimethylformamide
PBLG = poly(stearylglutamate)Solvent: THF = tetrahydrofuran
Mark-Houwink Relations
[] = 0.011·Mw0.725 for PS
[] = 1.26·10-5·Mw
1.29 for PSLG
[] = 1.58 10-5·Mw
1.35 for PBLG
Polystyrene Standards: the UsualTable 1. GPC/LS Parameters for PS in THF
Mw Mw/Mn
Vendor
Specified This Worka This Workb
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 GPC/LS bSensitive to baseline and peak selection.
Polypeptide Samples Were Reasonably Monodisperse
Table 2. PSLG Molecular Weights
Mw Mw/Mn
13370 2.044 17570 2.044 51080 1.04 67700 1.022 93090 1.256 138400 1.019 150800 1.24 176000 1.125 249000 1.03
Table 3. PBLG Molecular Weights
Mw
Mw/Mn
10670 1.233 13690 1.267 18520 1.233 29980 1.07 45990 1.046 70870 1.119 86000 1.018 95920 1.05
265000 1.176 327500 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
12 14 16 18 20 22
4
6
8
10lo
g([
]M /
ml-
mol
-1)
Ve /ml
PS PSLG PBLG PBLG Mixture
2nd Virial Coefficient Equations
A2, = M 2A2 /Na
= kT(1 + A2, + …)
A2, = dL2/4
12
/
12,
ocalcg
MMLR
Osmotic pressure in numberdensity concentration () units
Relationship to the “normal” 2nd virial coefficient for conc.in mass per volume units.
Onsager 2nd virial coefficient for rods (L= length, d = dia.)
Rg for rods
2nd Virial Coefficient (Excluded Volume Limit) is Another Universal Descriptor
12 13 14 15 16 17 18 19 20 21 22104
105
106
107
108
109
PS PSLG PBLG PBLG Mixture
A2, /
10-2
4 cm
3
Ve /ml
Persistence Length ap from Rg
)]1(1[2
3/
3
22 paLppp
pg e
L
a
L
aa
LaR
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”
0 100000 200000 300000 400000 5000000
20
40
60
80
100
ap = 70 nm
ap = 120 nm
ap = 240 nm
Rod
Rg /
nm
M
What the biggest polymers in our sample would look like at this ap
SEC/MALLS in the Hands of a Real Expert
ap 15 nm
Much less than PBLG
Macromolecules, 29, 7323-7328 (1996)
ConclusionsThe 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?
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
Sizing by Dynamic Light Scattering—a 1970’s advance in measuring motion, driven by need to measure sizes, esp. for small particles.
D
kTRh
oπη6
t
Is
It’s fluctuations again, but now fluctuations over time!DLS diffusion coefficient, inversely proportional to size.
Large, slow moleculesSmall, fast molecules
Molecular Weight Distribution byDLS/Inverse Laplace Transform--B.Chu, C. Wu, &c.
Where: G() ~ cMP(qRg)
= q2D
q2kT/(6Rh)
Rh = XRgg(t)
log10t
ILT
q2
D
G()
CALIBRATE MAP
M
c
log10M
log10D
Hot Ben Chu / Chi Wu Example
MWD of PTFESpecial solvents at ~330oC
Macromolecules, 21, 397-402 (1988)
This only “works” because of that wide, wide M distribution.Main problem with DLS/Laplace inversion is poor resolution.Things kinda go to pot at low M, too. Some assumptions have to be made to do this.
Reptation: inspired enormous advances in measuring polymer speed…and predicts More favorable results for polymers in a matrix.
There once was a theorist from FranceWho wondered how molecules dance."They're like snakes," he observed,"as they follow a curve,the large ones can hardly advance."*
D ~ M-2deGennes
More generally, we could write D ~ M- where increases as entanglements strengthen
*With apologies to Walter Stockmayer
Matrix Diffusion/Inverse Laplace TransformationGoal: Increase magnitude of
Difficult in DLS because matrix scatters, except special cases.Difficult anyway: dust-free matrix not fun!Still nothing you can do about visibility of small scatterersDOSY not much betterReplace DLS with FPR.Selectivity supplied by dye.Matrix = same polymer as analyzed, except no label.No compatibility problems.G() ~ c (sidechain labeling)G() ~ n (end-labeling)log10M
log10D
Stretching
Solution:
Matrix:
Painting Molecules* Makes Life Easier*R. S. Stein
Small Angle Neutron ScatteringForcedRayleighScattering
Fluorescence Photobleaching Recovery
Index-matched DLSmatch solvent & polymer refractive
indexcan't do in aqueous systems
Depolarized DLSworks for optically anisotropic probesworks for most matrix polymers
Fluorescence Photobleaching RecoveryFluorescence Photobleaching Recovery
0 50 100 150 2000
1
2
3
4
5
6
7
8
9
10
C(t
)
t / s
0.0 0.5 1.0 1.5 2.0 2.5 3.00.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
Dapp
< Dapp
Dapp
/ s
-1
K2 / 105 cm-2
2DK
1. An intense laser pulse photobleaches a striped pattern in the fluorescently tagged sample.
2. A decaying sine wave is produced by moving the illumination pattern over the pattern written into the solution.
3. An exponential decay is produced by monitoring the amplitude of the decaying sine wave. Fitting this curve produces from which D can be calculated.
BeCtC t )0(
FPR for Pullulan (a polysaccharide)FPR for Pullulan (a polysaccharide)
104 105
0.01
0.1
1
10
NaN3(aq) solution ( = 0.537 ± 0.035)
5% Matrix solution ( = 0.822 ± 0.018) 10% Matrix solution ( = 0.907 ± 0.038) 15% Matrix solution ( = 0.922 ± 0.037)
Dap
p / 1
0-7 c
m2 s
-1
M
0.1 1 1010
4
105
MD
app / 10
-7 cm
2 s
-1
Probe Diffusion: Polymer physics Calibration: polymer analysis
FPR ChromatogramFPR Chromatogram
1000 10000 100000 10000000
5
10
15
20
25
30
35
40
45 CONTIN Analysis Exponential Analysis Exponential Analysis
Pullulan, 5%w/w Dextran Matrix, 50/50 mix of 380K and 11.8K
FA
rbit
rary
Uni
ts
M Indicates targeted M.
Sure this is easy. Also easy for GPC.But not for DLS or DOSY!
Separation ResultsSeparation ResultsPullulan M = 50/50 mix of 11,800 and 380,000
Two ExponentialMatrix M1 / 1000 M2 / 1000
NaN3 (aq) 14.0 ± 1.0 (56.8%) 374.0 ± 37.2 (43.2%)5% w/w 12.2 ± 0.8 (52.3%) 313.9 ± 17.4 (47.7%)10% w/w 11.6 ± 0.6 (52.3%) 269.1 ± 20.9 (47.7%)15% w/w 12.0 ± 0.8 (51.1%) 261.4 ± 40.7 (48.9%)
CONTINMatrix M1 / 1000 M2 / 1000
NaN3 (aq) 14.1 ± 1.0 (54.5%) 393.1 ± 49.6 (42.1%)5% w/w 10.2 ± 1.3 (53.0%) 292.3 ± 23.4 (47.0%)10% w/w 10.0 ± 1.0 (50.3%) 221.4 ± 20.1 (47.5%)15% w/w 10.3 ± 1.1 (48.5%) 205.3 ± 38.3 (48.1%)
Better Resolution “Soon”?
Indicates targeted M.
1000 10000 100000 10000000.0
0.2
0.4
0.6
0.8
1.0
Pullulan, 8% HPC Solution, M=12,200 and 48,000
CONTIN Exponential Exponential
F Arb
itra
ry U
nits
M
Improvement in resolution is observed at lower concentrations due to a more viscous characteristic. A compatibility problem is seen though at higher concentrations.
Simulation of FPR ResultsSimulation of FPR Results(Most Desirable Situation)(Most Desirable Situation)
y = -0.4998x + 1.1518
0
1
2
3
4
5
6
-10 -8 -6 -4 -2 0
log D
log M
y = -2.0009x + 2.3045
-12
-10
-8
-6
-4
-2
0
2
4
0 2 4 6 8
log M
log
D
1000 10000 1000000.0
0.5
1.0
1.5
2.0
M = 10,000 and 20,000
CONTIN 2 Exponential
F Arb
itrar
y U
nits
M
1000 10000 100000 10000000.0
0.5
1.0
1.5
2.0
M = 10,000 and 160,000
CONTIN 2 Exponential
F Arb
itra
ry U
nits
M
1000 10000 1000000.0
0.5
1.0
1.5
2.0
M = 10,000 and 57,000
CONTIN 2 Exponential
F Arb
itrar
y U
nits
M
Examples of Examples of Separation Results Separation Results
from Simulation Datafrom Simulation Data
Indicates targeted M.
Ultimate Goal: A Black Box for MWDUltimate Goal: A Black Box for MWD
Matrix FPREasily Maintained
AccuratePrecise
Simple ConceptExpedient
Easy System SwitchBasic Info Obtained
MiniaturizableDetect Large MassesLabeling Required
GPCAccurate
Simple ConceptMiniaturizable
No Labeling RequiredBroad Distributions
PumpsParts
Press for MWD
DLSForm Factor
Index MatchingLong Acquisition for
Multiangle ExperimentsPrecise
Accurate
DOSYEasy System Switch
PreciseAccurate
Obtain Basic InfoLabeling Required
ConclusionsConclusionsFor a limited number of cases, this could really work.
We may not always need leaking pumps and large parts bins for polymer characterization.
What is good about GPC (straight GPC) is the simple concept; Matrix FPR keeps that—just replaces Ve with D.
Better than SEC’sMonday, January 29, 2001
Physical Info from SEC
Elena TemyankoHolly Ricks
N$F
Replacing SEC
Garrett Doucet
David Neau
Wieslaw Stryjewski