Multi-detector GPC
Characterization
Drew Poche’
Outline
• Basics-On the mechanism of GPC
• Detection
– Light Scattering
– Viscometry
• Putting it together- multi-detector GPC
• Lots of numbers-What’s it good for?
How big is big?
Drew Poche’
Materials Characterization
Dow Chemical, Plaquemine
Alphabet Soup
SEC-Size Exclusion Chromatography
• Includes rigid stationary phases
GPC-Gel Permeation Chromatography
• “Soft” gel stationary phases
GFC-Gel Filtration Chromatography
• Separation of biological molecules (nature’s polymers) in an
aqueous environment
HPLC? You bet.
Mobile phase pump
auto-injector
column(s)
detector(s)
Temperature control
data acquisition
Putting it in perspective
• Typical organic molecule vs typical polymer
molecule
Measuring size and molar mass
•Mass spec
•GC-MS, LC-MS
•NMR
•Modeling, quantum
mechanics
•Other colligative
property based
measurements
EASY
TOUGH
Polymer standards--Column Calibration
GPC Calibration
120
8
log(Mw ) = 0.0009V e3 - 0.0534V e2 + 0.6303V e + 6.8161
2
100
R = 0.9996
7
6
80
5
60
4
3
40
2
20
1
0
0
14
16
18
20
22
Ve [mL]
24
26
28
log(Mw)
Detector Response
Rtn Vol Peak Mw
15.739 7500000
15.728 7500000
16.878 2560000
16.879 2560000
17.92
841700
17.935
841700
18.95
320000
18.953
320000
19.605
148000
19.62
148000
20.387
59500
20.386
59500
20.581
50000
20.583
50000
20.583
50000
21.073
28500
21.087
28500
22.008
10850
22.005
10850
23.359
2930
23.378
2930
24.832
580
24.838
580
Can it get worse?
•Typical synthetic organic molecules in a pure sample are all the
same molar mass
•Typical synthetic polymer molecules in a pure sample may differ not only
in molar mass but also in molecular shape
Ordinary small molecule sample
Ordinary synthetic polymer sample
GPC Mechanism
Wiggling (chain conformations)
determines average dimensions
and pore permeation
Eliminate enthalpic interactions
Entropic effects alone govern
Getting it right
Problems, Problems
•Polymer chains are not created equal
Ma
=
Mb
=
Mc
Va
>
Vb
<
Vc
Solutions
•Absolute molecular weight detectors (light scattering, viscometry)
•Universal calibration
Bent out of Shape
First, let’s select a couple of chain conformations...
Then, stuff them into a confined space and see what
happens
Center of mass too
close to wall
Forbidden
conformation
Allowed
conformation
Loss of conformational entropy dictates partitioning
between pore and non-pore space
Let’s clarify
Gibbs Free energy change of a process,
Gpo  Hpo  TSpo
Gibbs free energy change of permeation of
the pores at equilibrium conditions (sufficient
time for diffusion into and out of pores)
Gpo  RT ln KGPC
KGPC is the fraction of internal pore volume
penetrated (equilibrium constant)
With non-enthalphic interactions squelched,
Gpo  TSpo
so, KGPC  e
Spo / R
L
2
where, As is surface area/pore volume
L
is the mean molecular projection of
the chain in solution
o
Also, Sp  RAs
Bottom line:
KGPC  log( L)
or
Ve  log(L)
Who wants to be a millionaire?
If the polymer chains are restricted to one
configuration (e.g. rods), what drives the partitioning
between pore space and non-pore space?
a) rotational orientation
b) pore gremlins
c) there’s no such thing as rod d) Huh?
shaped chains
For the million dollars….
If GPC really separates by SIZE, which chain
dimension correlates with elution order?
•I don’t know
•It’s a rather complicated question because pore
characteristics and chain geometry influence the
magnitude of the equilibrium constant, KGPC
• Leading candidates:
•radius of gyration, Rg
•hydrodynamic volume, Rh3 or Vh (universal calibration)
Column selection
FIPA
Making sense of the chromatogram
•
Synthetic polymers are composed of a distribution of chain sizes
•
We use statistics to get average dimensions to describe the bulk
sample
•
Commonly computed from GPC: Mn the arithmetic mean
Mw weight average
•
Computing Mw and Mn is sensible since these averages “fall out”
naturally from experiments used to measure molar mass
– Mn from colligative or counting methods (NMR, osmometry, and
those boring experiments you did in freshman chem)
– Mw from methods sensitive to molecular size (LS,
centrifugation)
Time to count
Mn 
 xiMi 
 niMi
 ni
xi is the ith mole fraction
ni is the number of chains in the ith fraction
Mw 
 wiMi
niMi2


 niMi
wi is the ith weight fraction
Where do ni and Mi come from?
Mn 
 xiMi 
 niMi
 ni

 hi
hi
M
i
Mw 
 wiMi
niMi2


 niMi

 hiMi
 hi
hi is the concentration of the ith fraction
Multiple numbers of standards
Column Calibration
• That’s one source of Mi
Problem: only equivalent Mi is obtained
E pluribus unum
• Universal Calibration
• Gives molar mass without
regard to chain architecture
• Valid? Nearly always.
• Suggests: L  Vh
Wait a minute!
• If I don’t know how M and [h] are related for my polymer,
how do I use universal calibration?
YOU DON’T
• Mark-Houwink (empirical power law)
a
and
std
[h]std  Kstd Mstd
since [h]std Mstd  [h]unk Munk
Munk
 [h] M
  std std
 Kunk
1 / 1  aunk




a
unk
[h]unk  Kunk Munk
“…too much dancing and not nearly enough
prancing...”
C. Montgomery Burns, commenting on GPC prior
to molar mass sensitive detectors
• Visible light scattering used for polymer
characterization has been around almost as
long as chemists have believed in polymers
• However, GPC detectors based upon the technique
are relatively new (1970s)
• Light scattering, by its nature, returns the
weight average molar mass
Visible Light vs. polymer chain
Particle view: Incident light
“pushes” electrons, producing
transient dipoles
Thermo view: Incident light
couples to concentration
gradient found in real solutions
How to get Mw from the measurement
1
2
Kc 1

 2A2c
R M
q2Rg2
Kc 1


R M 3M
as q approaches 0
Scattering
as c approaches 0
contains dn/dc
3
Kc
1

 2A2c
R MP(q)
Particle form factor
MALLS uses Eq 1 and 2 and returns Mw and Rg
LALLS and RALLS use Eq 3 and return Mw
caveat: RALLS requires a shape correction when Rg approaches (lo/50)n
How LS returns other molar mass
averages
• Simple assumption….monodisperse fractions
from the GPC columns. Therefore,
Mw,i = Mi
• This assumption may lead to an overestimation of Mn
“I’m going to describe the apparatus first before I set it
motion. Then you’ll be able to follow the proceedings better.”
Franz Kafka
• Advantages
– MALLS gives molecular architecture information without
assumptions IF there is a measurable angular dependence
on the scattered light intensity
– RALLS is more forgiving of dusty samples
and returns essentially the same information as LALLS IF
the polymer is small compared to lo
– LALLS is more sensitive, requires no correction over a
huge range of molar mass
“Do you suppose,” the Walrus said, “that they
could get it clear?”
“I doubt it,” said the Carpenter, and shed a
bitter tear.
Lewis Carroll
DUST, GELS, or assorted particulate vs. Light Scattering
"...died a dusty death!"
Relative Response
100
00713T-2 LS
80
60
40
20
0
11.1
16.3
21.5
26.6
Retention Volume (mL)
31.8
37.0
Column Calibration? Not!
PS 50K vs. 100K DRI detection
373
00628X-2 RI
00628y-2 RI
Response 3(mV) x10
315
Response (mV)
PS 50K vs. 100K LALLS Detection
1.54
258
200
142
00628X-2 LS
00628y-2 LS
1.21
0.88
0.56
0.23
-0.10
85
4.9
9.8
14.6
19.5
Retention Volume (mL)
24.4
29.2
4.9
9.8
14.6
19.5
Retention Volume (mL)
24.4
29.2
Specific refractive index increment
dn
n 

 lim

c

0
dc
 c  l ,T
n = n - no
•The bigger the better
•Depends on:
•solvent
•temperature
•light wavelength
If polymer solvent combo is isorefractive, no scattering
will be observed
Why dn/dc matters
FIPA LS data (similar concentration)
324
PS 50 K
SBS 50K
Response (mV)
297
271
245
218
192
0.19
0.87
1.56
2.25
Retention Volume (mL)
2.94
3.63
The plot thickens-Viscosity
• Viscometers as GPC detectors are
based upon the measurement of a
differential pressure between pure
solvent and polymer solution
  hsp
How to get [h]i
• Software computes both hsp,i and hrel,i
• Solomon-Gottesman
[h]i = 21/2(hsp,i-ln(hrel,i)1/2/c
Important point: hsp and hrel are concentration
dependent
[h] is, by definition, a “zero”
concentration property
Like LS, the viscometer is sensitive to
bigger chains
PS 50K vs. 100K DRI detection
373
00628X-2 RI
00628y-2 RI
00628X-2 DP
00628y-2 DP
101
Response (mV)
315
Response (mV)
PS 50K vs. 100K VIS Detection
117
258
200
85
69
53
142
37
85
4.9
9.8
14.6
19.5
Retention Volume (mL)
24.4
29.2
4.9
9.8
14.6
19.5
Retention Volume (mL)
24.4
29.2
All that work for two numbers?
• Re-visit universal calibration…units analysis
Mw
x
[h]

(Rh)3
gmol-1
x
cm3g-1
=
cm3mol-1
From two simple measurements we can estimate size
or volume!
Implication: chain architecture elucidation
Let the fun begin
• Getting Mi and [n]i from GPC fractionation mean:
–
–
–
–
–
Rapid M-H relationships
Molecular architecture determinations
Calculation of other polymer dimensions
Correlation to physical properties
Identification of tiny fractions of high molar mass
material
From a few months to a few minutes!
PS 1683
0.75
00828C-2 RI
00828C-2 DP
00828C-2 LS
Log[Intrinsic Viscosity]
Relative Response
100
80
60
40
20
-0
7.8
10.0
12.2
14.5
Retention Volume (mL)
16.7
18.9
M-H Plot from single run PS 1683
0.37
-0.01
-0.40
-0.78
-1.17
3.86
4.42
4.98
5.55
Log(Molecular Weight)
6.11
6.67
Behold the Power of M-H
[h] = KMa
• a parameter:
approaching 0 ; spheres
0.5 ;theta condition for linear
chains
0.7-0.8 ; expanded coils
1.8 ; ideally rigid rod
a may or may not change with branching
• K parameter:
shifts with comonomer
composition or branching density
What happens when branches are
present
Star branched
Had enough?
Linear vs. Random LCB
More commonly encountered
long chain branching
-1
Log[Intrinsic Viscosity]
x10
7.42
4.66
Linear
Branched
1.90
-0.86
-3.62
-6.38
4.49
4.90
5.31
5.72
6.13
Log(Molecular Weight)
Have you noticed that the hydrodynamic dimensions of a branched
polymer are “shrunken” compared to its linear counterpart?
6.54
Branching? YIKES!
• Triple detection GPC measurements (LS,VIS, DRI)
• Determine [h]-Mw relationship (M-H values)
• Compare [h]-Mw relationship to that of a linear sample
• Apply appropriate branching model to calculate branching
density
 Possibilities: star, off-center star, comb, random long
chain branching, H, super-H, Pom-Pom
Dependence of Performance Properties on Molar
Mass
Tensile Strength
Elongation
Yield Strength
Toughness
Brittleness
Hardness
Abrasion Resistance
Softening Temp
Melt Viscosity
Adhesion
Chemical Resistance
Solubility
+ property increase
- property decrease
o little change
Increase molar mass
+
+
+
+
+
+
+
+
+
-
+
-
Narrow the MWD
+
-
-
+
-
-
+
+
+
-
+
o