Transcript Universal Calibration - LSU Macromolecular Studies Group

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
4πn
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
2
g
q R
3
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]AMA = [h]SMS= 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
A2,n / 10
-24
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.