Recent Developments in
Polymer Characterization
And how we may have to modify
them for nanoparticles
Obligatory Equation
SEC = GPC = GFC
Size Exclusion Chromatography
Gel Permeation Chromatography
Gel Filtration Chromatography
A riddle
After a hurricane, many trees fall over and
bend into a river. Also, a cow and a dog
fall into a flooded river. Which one reaches
Moo!
the ocean first, cow or dog?
Woof!
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/MALLS in the Hands of a Real Expert
Macromolecules, 29, 7323-7328 (1996)
ap  15 nm
Much less
than PBLG
Midpoint
The new power of SEC/Something Else experiments is very real.
SEC is now a method that even the most skeptical physical
chemist should embrace. For example, our results (not shown)
favor higher rather than lower values for persistence length of
one polymer (PBLG). This helps to settle about 30 years of
uncertainty.
So, SEC is good enough for physical measurements, but is it still
good enough for polymer analysis?
What about nanoparticles, especially large ones, in GPC?
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.
Atlanta, Georgia
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.
Large,
molecules
Small, slow
fast molecules
Is
t
It’s fluctuations again, but now fluctuations over time!
DLS diffusion coefficient, inversely proportional to size.
 kT 

Rh  
 6πηo D 
Molecular Weight Distribution by
DLS/Inverse Laplace Transform--B.Chu, C. Wu, &c.
Where:
G() ~ cMP(qRg)
 = q2D  q2kT/(6phRh)
Rh = XRg
g (t )   G (  ) exp(  t )d
g(t)
ILT
G()
log10t
log10D
q2D
1/2
c
MAP
CALIBRATE
log10M
M
Hot Ben Chu / Chi Wu Example
Macromolecules, 21, 397-402 (1988)
MWD of PTFE
Special solvents
at ~330oC
Problems:
•Only “works” because MWD is broad
•Poor resolution.
•Low M part goofy.
•Some assumptions required.
Reptation: inspired enormous advances in
measuring polymer speed…and predicts
More favorable results for polymers in a matrix.
There once was a theorist from France
Who wondered how molecules dance.
"They're like snakes," he observed,
"as they follow a curve,
the large ones can hardly advance."*
D ~ M-2
deGennes
More generally, we could write D ~ M- where
 increases as entanglements strengthen
*With apologies to Walter Stockmayer
Matrix Diffusion/Inverse Laplace Transformation
Goal: Increase magnitude of 
Difficult in DLS because matrix
log10D
Solution: 1/2
D
D
Matrix: 
log10M
Stretching 
scatters, except special cases.
Difficult anyway: dust-free matrix
not fun!
Still nothing you can do about
visibility of small scatterers
DOSY not much better
Replace 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)
Painting Molecules* Makes Life Easier
*R. S. Stein
Small Angle Neutron Scattering
Forced Rayleigh Scattering
Fluorescence Photobleaching
Recovery
Index-matched DLS
match solvent & polymer refractive
index
can't do in aqueous systems
Depolarized DLS
works for optically anisotropic probes
works for most matrix polymers
Fluorescence Photobleaching Recovery
C t   C (0)e t  B
10
9
8
6
5
4
3
2
1
0
0
50
100
150
200
t/s
  DK 2
0.40
0.35
0.30
Dapp < Dapp
-1
0.25
/s
C(t)
7
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.
0.20
Dapp
0.15
0.10
0.05
0.00
0.0
0.5
1.0
1.5
2
2.0
5
2.5
3.0
-2
K / 10 cm
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.
FPR for Pullulan (a polysaccharide)
1
10
5
10
4
M
-7
Dapp / 10 cm s
2 -1
10
0.1
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)
0.01
4
10
10
5
0.1
1
10
-7
M
Probe Diffusion: Polymer physics
2
Dapp / 10 cm s
-1
Calibration: polymer analysis
FPR Chromatogram
Pullulan, 5%w/w Dextran Matrix, 50/50 mix of 380K and 11.8K
45
40
CONTIN Analysis
Exponential Analysis
Exponential Analysis
35
FArbitrary Units
30
25
20
15
10
5
0
1000
10000
100000
M
1000000
 Indicates targeted M.
GPC vs. FPR for a Nontrivial Case
0.9
20
0.8
18
0.7
16
Mw = 1,400
PDI = 1.08
Total Amplitude % = 20.7
14
0.6
% Amplitude
Relative Concentration
1.0
0.5
0.4
0.3
Mw = 52,000
PDI = 1.04
Total Amplitude % = 46.5
Mw = 15,000
PDI = 1.03
Total Amplitude % = 27.2
12
Mw = 250,000
PDI = 1.03
Total Amplitude % = 5.5
10
8
6
0.2
4
0.1
2
0
0.0
4
10
M / g mol
-1
5
10
PL Aquagel 40A & 50A
3
10
4
10
5
M
10
6
10
User-chosen CONTIN
25% Matrix
20,000 & 70,000 Dextran
Pullulan, 8% HPC Solution, M=12,200 and 48,000
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.
What about separating cows and
elephants? Either will float around
the trees. How do you separate
Moo!
them then?
Eeee!
Field Flow Fractionation, that’s how!
In FFF, large nanoparticles are made
to flow between plates.
One plate is porous, and a crossflow is arranged.
What happens?
Little nanoparticles come out first!
Potential Advantages of FFF
Handles a wider range of particles.
May be easier for some aggressive solvents.
Conclusion
GPC is essential in any Nano Lab
GPC may eventually get replaced.
Matrix FPR
FFF
Thank you!
L
S
U