1 Polimer Karakterizasyon Teknikleri GPC/SEC - Atomika Teknik · Polimer Karakterizasyon Teknikleri...
Transcript of 1 Polimer Karakterizasyon Teknikleri GPC/SEC - Atomika Teknik · Polimer Karakterizasyon Teknikleri...
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Polimer KarakterizasyonTeknikleri – GPC/SEC
Evren Depren, Aplikasyon Uzmanı
Atomika Teknik Cihazlar
Temmuz 2018
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The Triple DetectionTechnique
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› Hardware Schematic
› Mechanism of separation: size exclusion chromatography
› Overview of the detectors
� Concentration
� Light scattering
� Viscometer
› Equations governing the response of the detectors
OVERVIEW
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› Involves passing a mixture dissolved in a "mobile phase" through astationary phase,
� Separates the analyte to be measured from other molecules in themixture and allows it to be isolated.
› Separation takes place on size not molecular weight
› After the column, the separated molecules can be analysed by oneor more detectors.
› GPC is a solution-based technique. The polymer sample must bedissolved in a suitable solvent for the analysis.
› Molecular weight, Size and Structure of our macromolecule
GPC – Gel Permeation Chromatography
SEC – Size Exclusion Chromatography
GFC – Gel Filtration Chromatography
What is GPC/SEC?
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SE
PA
RA
TIO
ND
ET
EC
TIO
N
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SEC Instrument Schematic
Tetra Detection
ViscometerLight Scattering
Refractive Index
UltraViolet -PDA
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GPC SYSTEMS
Triple/Tetra detection
Conventional detection Advanced Triple/Tetra detection
RImax
OMNISEC
TDAmaxHT-GPC
Tetra detection at high temperatures
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SEPARATION
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SEPARATION: SEC
A
Sample loaded on column.
B
Sample components separated by hydrodynamic size.
C and D
Components elute from column and pass through detectors.
› Solution based technique.
› Purely physical separation.
Larger molecules elute first
› No interaction with column.
SAMPLE MIXTUREA B C D
DETECTORS
SOLVENT
FLOW
CHROMATOGRAM
RETENTION
VOLUMEA B C D
POROUS
PACKING
SIZE EXCLUSION CHROMATOGRAPHY
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THE SEPARATION PROCESS
Lo
gM
W
Retention Volume
V0
Vt
Exclusion Total Permeation
Mobile Phase Flow
Stationary Phase
Gel Particle
Vo = Void volume
Vt = Total column volume
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THINK!
A B
20 nm 5 nm
WHICH MOLECULE WOULD ELUTE FIRST IN GPC?
Hydrodynamic
size
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THINK!
WHAT WOULD THE CHROMATOGRAM LOOK LIKE?
Retention Time or Volume
De
tecto
r In
ten
sity
A
20 nm
B
5 nm
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THINK!
A B
20 nm 19 nm
WHICH MOLECULE WOULD ELUTE FIRST IN GPC?
Hydrodynamic
size
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THINK!
WHAT WOULD THE CHROMATOGRAM LOOK LIKE?
Retention Time or Volume
De
tecto
r In
ten
sity
A B
20 nm 19 nm
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THINK!
A B
20 nm 20 nm
B
HYDRODYNAMIC VOLUMESIZE & STRUCTURE!
WHICH MOLECULE WOULD ELUTE FIRST IN GPC?
Hydrodynamic
volume
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THINK!
WHAT WOULD THE CHROMATOGRAM LOOK LIKE?
Retention Time or Volume
De
tecto
r In
ten
sity
A
20 nm
B
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QUIZ!
200 KDa100 KDa
BBA
10 nm6 nm
6 nm10 nm
WHICH MOLECULE WOULD ELUTE FIRST IN GPC?
Molecular weight
Hydrodynamic size
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DETECTION
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DETECTOR OUTPUT
SSIZEIZE
IINTRINSICNTRINSIC
VVISCOSITYISCOSITYCCONCENTRATIONONCENTRATION
MMOLECULAR OLECULAR
WWEIGHTEIGHT
SECSEC--TDATDA
SSIZEIZE
IINTRINSICNTRINSIC
VVISCOSITYISCOSITYCCONCENTRATIONONCENTRATION
MMOLECULAR OLECULAR
WWEIGHTEIGHT
SECSEC--TDATDA
RI & UVVISCOMETER
VISCOMETER+LIGHT SCATTERING
LIGHT SCATTERINGRALS & LALS
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Concentration Detectors
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Sample
cell
Reference
cell
Incident Beam
Flow Cell
› Deflection of beam corresponds to
sample concentration
20
› Principle: Light travels at different
speeds in different media.
› This causes bending or refraction of the
light.
Differential Refractometer
No sample
Low conc.
High conc.
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Ultraviolet Spectroscopy
› Principle: The molecule absorbs light
at a specific wavelength.
› The detector measures the difference
between the intensity of light passed
through the reference and sample.
ItI0Reference
Sample
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HOW DO RI & UV DETECTORS GIVE CONCENTRATION?
Concentration profile
UVRI
2 4 6 8 10
Concentration
De
tecto
r re
sp
onse
2 4 6 8 10
Concentration
De
tecto
r re
sp
onse
Classical concentration determination:• The UV or RI responses of standards would be plotted against concentration.
Response = k • C
Slope
Unknown C = Response
k
In triple detection:
Refractive index k ~ dn/dc
Ultraviolet k = dA/dc
These values allow us to determine the concentration of polymer at every point in the chromatogram
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EQUATIONS GOVERNING THE DETECTORS
RI Output (mV) = KRI • dn/dc • Concentration
UV Output (mV) = KUV • dA/dc • Concentration
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Light Scattering Detectors
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› Photons from an incident beam is absorbed by a macromolecule and re-emitted in all directions
LIGHT SCATTERING DETECTOR
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LIGHT SCATTERING THEORY
› The relationship between light scattering and molecular weight is defined by the Rayleigh equation:
› Where:
� C = the sample concentration
� θ is the measurement angle
� Rθ = the Rayleigh ratio (the ratio of scattered light intensity to incident light intensity) at the measurement angle θ
� Mw = molecular weight
� A2 = the second virial coefficient
� Pθ = a term that defines angular dependence
� K = a constant (which is expanded on the next slide…)
��
��
= �
��+ 22�
�
�
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LIGHT SCATTERING THEORY
› K is an constant dependent on the system, solvent and the sample being measured
› Where:
� λ = the wavelength of the laser in a vacuum
� NA = Avogadro’s number
� n0 = is the refractive index of the solvent
› This term contains the value of dn/dc which is a measure of the difference in refractive index between the sample and the solvent
› dn/dc is squared in the equation meaning it is very important to have an accurate value
� = ���
����
�
�0��
��2
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LIGHT SCATTERING THEORY
› The Rayleigh equation can be used to measure molecular weight by measuring the intensity of the light scattered by the sample if all the other parameters are known
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ANGULAR DISSYMMETRY
› The consequence of the 1/Pθ term is that different molecules scatter
light in different directions with different intensity
� Smaller molecules scatter light evenly in all directions (isotropic scattering)
� Larger molecules scatter light in different directions with different intensities (anisotropic scattering)
› This is dependent on:
� The molecule’s size
� The measurement angle
� The laser wavelength
› Only the light scattered at zero degrees does not suffer interference
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LIGHT SCATTERING THEORY
› 1/Pθ is a term that defines the angular dependence of
the scattered light
› Where
� n0 = the refractive index of the solvent
� Rg = the sample’s radius of gyration
� λ0 = the wavelength of the laser in a vacuum
� θ = the measurement angle
› The result of this is that light scattered by larger
molecules at higher angles has a different intensity
› If we are going to measure the Mw, we must account
for this effect
�
�
= 1+�����
���
��
���� sin2 �
�
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ISOTROPIC SCATTERERS
› Molecules that are small with respect to the laser wavelength scatter light isotropically (i.e. evenly in all directions)
� ‘small’ means < 1/20th of the laser wavelength
› Any measurement of the light scattering intensity should be sufficient to determine the molecular weight
� 1/Pθ is very close to 1 so has no effect on the result
Sin2 θ/2 (essentially – angle)K
C/R
θ
Mw measured
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RIGHT-ANGLE LIGHT SCATTERING (RALS)
› RALS measures the intensity of scattered light at 90°
› RALS is limited to ‘small’ molecules (<15nm radius)� Isotropic scatterers
› This level of scattering is assumed to be the same as 0°
› RALS has excellent signal-to-noise
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ANISOTROPIC SCATTERERS
› Larger molecules scatter light in different directions with different intensities
� ‘large’ means >1/20th of the laser wavelength
› In large molecules, the light is scattered by the different mass cores within the molecule
› Individual scattered photons interfere with each other to change the overall light scattering intensity
› Pθ ≠ 1 and so affects the calculated molecular weight
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ACCOUNTING FOR ANISOTROPIC SCATTERING
› By plotting KC/Rθ as a function of sin2(θ/2) we can see the change in scattering intensity with angle
› Mw can be calculated from the KC/Rθ at the intercept
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ACCOUNTING FOR ANISOTROPIC SCATTERING
› We must account for the anisotropic scattering in some way in order to calculate the correct molecular weight
› The Rayleigh equation tells us that if θ = 0 then the scattered light intensity relates directly to the sample’s molecular weight
› We can’t measure at θ = 0 because the incident light is too bright
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LOW-ANGLE LIGHT SCATTERING
› LALS measure the scattered light intensity at an angle as close to 0° as possible
› This level of scattering is assumed to the be the same as 0° as 1/Pθ will be very close to 1
› LALS has good signal-to-noise
› LALS works for all molecules, large and small
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RALS/LALS
› A RALS/LALS detector has the sensitivity of RALS
for small molecules AND can account for anisotropy
for large moleculesSmall molecules
Large molecules
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LIGHT SCATTERING PROPERTIES OF DIFFERENT
MOLECULES
Hyaluronic Acid (1 MDa) ~ 60nm
LALS (7 deg)
RALS (90 deg)
12,0 15,0 18,0 21,0 24,0 27,0
-1,0
14,3
29,5
44,8
60,0
Retention Volume (mL)
PEO (23 kDa ~ 5nm)
LALS (7 deg)
RALS (90 deg)
17,0 20,0 23,0 26,0 29,0 32,0
-0,5
2,8
6,0
9,3
12,5
Re
sp
on
se
(m
V)
Isotropic scatterersEither RALS or LALS provides correct Mw
Non -isotropic scatterersLALS provides correct Mw
2
0 '
×∝
dc
dnCKMR w
The OmniSEC software automatically detects the transition
between RALS and LALS
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› For small molecules (e.g. polymers < 200kDa) there is no
angular dependence of the LS signal
� Molecular weight can be measured directly and accurately using RALS
� RALS always give highest signal-to-noise
› For larger molecules (e.g. polymers >200kDa) you need
to:
� Molecular weight is measured directly at low angle (7º) using LALS
� LALS minimises angular dependence
SUMMARY OF ANGULAR DEPENDENCE
39
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The Viscometer
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› Invented by Max Haney in 1983
› Based on the Wheatstone bridge principle
› Used to determine the Intrinsic Viscosity of sample
THE 4 CAPILLARY DIFFERENTIAL VISCOMETER
+ -
-+
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Viscosity is an inherent property of the solvent and specific!!
Imagine that these solvent molecules are arranged in sheets that are
trying to flow over one another.
42
WHAT IS VISCOSITY?
Solvent
e.g: water
The resistance to this flow is
the solvent’s viscosity.
VISCOMETERY
Which is more resistant to flow:
Milk
Or
Honey?
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43
WHAT IS INTRINSIC VISCOSITY?
Solute (polymer) dissolved in Solvent
When a solute is dissolved in the solvent, the ability of these sheets to
flow over one another is changed.
This contribution of the solute to the overall viscosity of the solution is
known as the intrinsic viscosity of the solute.
VISCOMETERY
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Traditional Solution Viscosity Measurements
c
relinh
)ln(ηη =1−= relsp ηη
Set Volume
Capillary
Reservoir
00 t
trel ==
η
ηη
Solution Drop Time
Solvent Drop Time
Derived from relative viscosity
Ubbelohde Tube
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45
Intrinsic viscosity is the concentration normalized ‘specific’ viscosity of the polymer in solution at infinite dilution.
η sp is called the specific viscosity of the solution whose concentration is C.
η o is the Solvent Viscosity.
η is the Solution Viscosity.
[ ]0→
==c
sp
cIV
ηη
0
0
η
ηηη
−=sp
In GPC, concentrations of solutions are
sufficiently dilute that the extrapolation
to zero concentration is negligible.
HOW DO WE DEFINE IV?
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46
HOW CAN WE RELATE IV TO STRUCTURE?
Intrinsic viscosity has the units:
dL/g
We can look at structure in these terms:
IV ∝ volumemass
Intrinsic viscosity is inversely proportional to molecular density:
Which of these two molecules with the same mass occupies the largest volume of space?
IV ∝ 1 Cdensity
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IP+ -
DP-+GPC IN OUT
Solvent
Sample
HOW DO WE MEASURE IV?4-capiliary viscometer bridge - The Wheatstone Bridge Concept
The viscometer detects changes in pressure when the sample travels though the viscometer.
Relationship of the output from the pressure transducers and specific viscosity
Relationship of the specific viscosity and intrinsic viscosity
DPIP
DPsp 2
4
−=η IVC ×=
47
0
0
η
ηηη
−=sp
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WHAT DOES THE IV TELL US ABOUT OUR SAMPLE?
CONFORMATION
Molecule folded on itself ⇒ high density – low IV
In general: IV rod > IV coil > IV sphere
› Since the hydrodynamic volume is smaller, with the same mass enclosed
with the same total chain length, the density must be higher, producing a
lower Intrinsic Viscosity
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WHAT DOES THE IV TELL US ABOUT OUR SAMPLE?
LENGTH OF CHAIN
Increasing length ⇒ density decrease – IV increase
BRANCHINGS (INCLUDING DENDRIMERS)
Branchings ⇒ more compact structure
⇒ higher density, lower IV
M
log [η]
log M
Mark-Houwink equation relates Mw to IV :
[η] = kMa
log [η] = log k + a logM
M – H a = Related to the way chains are added to the backbone of a polymer
M – H K = Density of the backbone
Average over whole or part of the molecular weight range
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Triple Detection
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Multi Detector SEC
› Addition of advanced detectors enhances GPC/SEC
greatly
� Light Scattering – Molecular Weight
� Viscometer – Molecular Structure
› Triple Detection – Light Scattering and Viscometer
› Tetra Detection – Addition of 2nd Concentration Det.
� Copolymers, Blends
� Conjugates, PEGylation, PDCs
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TRIPLE DETECTION DATA: OUTPUT FROM ALL
DETECTORS
50
75
100
125
150
175
200
225
250
275
Re
fra
ctive
In
de
x (
mv)
80
100
120
140
160
180
200R
igh
t A
ng
le L
igh
t S
ca
tte
rin
g (
mv)
90
100
110
120
130
140
150
160
Lo
w A
ng
le L
igh
t S
ca
tte
rin
g (
mv)
-360
-340
-320
-300
-280
-260
-240
-220
Vis
co
me
ter
- D
P (
mv)
0 5 10 15 20 25 30 35 40 45 50Retention Volume (mL)
RI
LS
IV
Detectors respond to different properties of a macromolecule
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EQUATIONS GOVERNING THE DETECTORS
› Concentration Detectors
› Absolute Molecular Weight Measurement� Static light scattering
› Hydrodynamic Size and Intrinsic Viscosity� Four-capillary viscometer
ii Cdc
dn
n
KRI ⋅⋅=
0
ii Cdc
dAKA ⋅⋅=
CPP
P
i
sp ⋅=∆−
∆=
−= ][
2
4
0
0 ηη
ηηη
Differential Refractive Index UV-Vis
Right Angle (90°) and Low Angle (7°) Light Scattering
Intrinsic Viscosity
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54
EQUATIONS GOVERNING THE DETECTORS
RI Output (mV) = KRI • dn/dc • Concentration
UV Output (mV) = KUV • dA/dc • Concentration
Visc. Output (mV) = KVisc • IV • Concentration
LS Output (mV) = KLS • Mw • (dn/dc)2 • Concentration
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� Absolute molecular weight� Molecular weight distribution� Intrinsic viscosity� Molecular size� Long-chain branching� Mark-Houwink coefficients� % Polymer
-1.0
210.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
110.0
120.0
130.0
140.0
150.0
160.0
170.0
180.0
190.0
200.0
Re
fra
ctive
In
de
x R
esp
on
se
(m
V)
3.000
7.000
3.200
3.400
3.600
3.800
4.000
4.200
4.400
4.600
4.800
5.000
5.200
5.400
5.600
5.800
6.000
6.200
6.400
6.600
6.800
Lo
g M
ole
cu
lar
Weig
ht
-1.0
175.0
8.0
16.0
24.0
32.0
40.0
48.0
56.0
64.0
72.0
80.0
88.0
96.0
104.0
112.0
120.0
128.0
136.0
144.0
152.0
160.0
168.0
Ultra
Vio
let @
26
0.0
nm
Re
sp
on
se
(m
V)
-1.0
90.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
55.0
60.0
65.0
70.0
75.0
80.0
85.0
Vis
co
me
ter
- D
P R
esp
on
se
(m
V)
-1.0
95.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
55.0
60.0
65.0
70.0
75.0
80.0
85.0
90.0
Lo
w A
ng
le L
igh
t S
ca
tte
rin
g R
esp
on
se
(m
V)
-1.0
145.0
7.0
14.0
21.0
28.0
35.0
42.0
49.0
56.0
63.0
70.0
77.0
84.0
91.0
98.0
105.0
112.0
119.0
126.0
133.0
140.0
Rig
ht A
ng
le L
igh
t S
ca
tte
rin
g R
esp
on
se
(m
V)
12.00 20.20
Retention Volume (mL)
12.6 12.9 13.2 13.5 13.8 14.1 14.4 14.7 15.0 15.3 15.6 15.9 16.2 16.5 16.8 17.1 17.4 17.7 18.0 18.3 18.6 18.9 19.2 19.5 19.8
Data File: 2008-07-18_17;03;55_PS_273K_01.vdt Method: PDACopoly3-0000.vcm
SEC Chromatogram Using OmniSECTM Software
DRI
UV-Vis
[η]
RALS
LALS
Mn - (Da) 142,344Mw - (Da) 273,337Mz - (Da) 419,713Mp - (Da) 239,145Mw / Mn 1.92[η] - (dL/g) 0.92Rh - (nm) 15.1Rg - (nm) 21.4Wt Fr (Peak) 1.0a 0.74logK -4.04Branches 0.00Branch Freq. 0.00dn/dc - (mL/g) -0.104
Results Table
Triple/Tetra Detection GPC/SEC by Malvern
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Molecular size by Triple Detection (random coil
polymers)
Pe x
x
x
( )( )θ =
− −−
212
Rh Rg
2
)2/sin(n
Rg3
8x
θλ
π=Where:
Rg from LS (only above ~10-15nm)
Rh from LS and Visc. (no limits)
Rh3
•3
10= π]M[η •ΝΑ
IV Mw Constants
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Size Measurements - Rg and Rh
› Radius of Gyration (Rg)
� Rg is the root-mean-square of the radii from the centre of the mass to the different mass cores within the molecule.
� Direct measurement by changes in scattered light intensities with observation angle
� Limitations:
• Requires good S/N light scattering signal
• Lower size detection limit = 10-15 nm
• Large structures require non-linear curve fitting
� A good estimate can be made using viscometry and the Flory-Fox equation
› Hydrodynamic Radius (Rh)
� RH is the radius of an equivalent sphere that diffuses with the same speed as the molecule of interest.
� Measured two ways
• Dynamic Light Scattering
• Triple Detection SEC/GPC – IV and Mw
� Triple Detection
• Analyze hydrodynamic size from < 1 nm to the exclusion limit of the SEC
column (~200 nm)
• No extrapolation or fitting parameters57
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› Triple detection technique uses 3 detectors:
RI + Light Scattering + Viscometer
› The signals are processed together at each data slice
� 5 Hz
› Specific equations govern each detector which allow concentration, Mw, intrinsic viscosity and molecular size to be determined across the entire distribution.
› Adding a fourth detector – UV – allows for compositional analysis in copolymer samples.
SUMMARY
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Conventional GPC
59 59
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Hardware Schematic Conventional GPC
GPC PumpVacuum
Degasser
Solvent
Autosampler
Injection Loop
Column Oven and Columns
Waste
RI Detector
1.00
LOW PRESSURE
HIGH PRESSURE 60
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Separation Mechanism
Columns
Detection
Calibration
Summary
Conventional GPC
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(A) (B) (C) (D) RETENTIONTIME
(A) (B) (C) (D)
POROUS
PACKING
SAMPLE MIXTURE
+
CONCENTRATION
DETECTOR
CHROMATOGRAM
SOLVENT
FLOW
unlike HPLC,
NO chemical
interaction
with the GPC
column is
permitted.
GPC relies on a
pure physical
separation
principle.
Separation Mechanism
RETENTION
VOLUME
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Example data output – Broad distribution polystyrene sample
8.53
18.88
29.23
39.58
49.93
60.28
70.63
Re
fra
ctiv
e In
de
x (
mV
)
Retention Volume (mL)
5.00 10.00 15.00 20.00 25.00
0.00
0.19
0.39
0.58
0.77
0.97
1.16W
F /
dL
og
MW
Log Molecular Weight
3.00 4.00 5.00 6.00 7.00
Raw
Chromatogram
Calculated
Molecular Weight
Distribution
Data reversed!
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Gel Permeation Chromatography
SEC - Size Exclusion Chromatography
GFC - Gel Filtration Chromatography (LP)
HPSEC - High Pressure/Performance SEC
GPC/SEC retention is an equilibrium, entropy-controlled size exclusion process
Separation takes place on size not molecular weight
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Temp.=65 0CTemp.=65 0C
Temp.=10 0CTemp.=10 0C
Effect of Temperature on SEC Mechanism
Sharper peaks at higher temperature
due to improved diffusion.
Sharper peaks at higher temperature
due to improved diffusion.
Retention volume is not strongly dependent on temperature
Retention volume is not strongly dependent on temperature
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Effect of flow rate on SEC mechanism
Flow Rate
Increase
Flow Rate
Increase
Increasing flow rate will reduce resolution but not change elution volumeIncreasing flow rate will reduce resolution but not change elution volume
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Conventional GPC
Separation Mechanism
Columns
Detection
Calibration
Summary
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GPC Column Selection
Need to match sample/solvent combination to
column selected.
Two broad categories:� Organic - Dominated by Styrene Divinyl Benzene
� Aqueous - More variety
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GPC Column Selection
Columns available either:
� Packed with gel (packing) having pores all of the same size. - Single Porosity columns. These are generally used as a ‘set’ of different pore sizes to cover the required range for the application.
� Packed with a mixture of gels with different pore sizes. -Linear or Mixed-Bed columns. These can be used as a single column for ‘screening’ but are often combined in sets of 2 or 3 to give additional resolution.
Typical column dimensions 8mm x 300mm.
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GPC Column Selection
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Conventional GPC
Separation Mechanism
Columns
Detection
Calibration
Summary
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Types of Concentration Detectors for GPC
Diode Array or UV/Vis. - Probably second most commonDiode Array or UV/Vis. - Probably second most common
Infrared Spectrometer - Probably least commonInfrared Spectrometer - Probably least common
Evaporative Mass - Linearity problemsEvaporative Mass - Linearity problems
Refractive Index - Almost universalRefractive Index - Almost universal
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RI Detectors - Schematic
Beam Splitter
Zero Glass
Diverting Mirror
Flow Cell Concave
Mirror
Photodiode
Photodiode LED
nsnr
Beam
Splitter
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Separation Mechanism
Columns
Detection
Calibration
Summary
Conventional GPC
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To use the technique quantitatively the column retention volume must be calibrated in some way.
Use polymer standards of known molecular weight.� (Remember though, the columns separate by size not
molecular weight so the calibration is only relative.)
Flow rate must be controlled carefully.
Conventional Calibration
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Refr
active I
ndex
Response (
mV
)
Retention Volume (mL )
12,50 15,00 17,50 20 ,00 22,50 25,00 27,50 30,00 32,50
150 ,55
138 ,97
127 ,40
115 ,82
104 ,24
92,66
81,08
69,51
57,93
162 ,13
46,35
10,00 35,00
Size Exclusion Chromatography
RI Detector
170.000
46.500
5.450
Exclusion Limit
Total Permeation
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Narrow Standards Calibration
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Weight Average (Mw)
∑∑
=ii
i
Mc
cMn
/
∑∑
=i
ii
c
McMw
Number Average (Mn)
Z-Average (Mz)
Retention Volume
RI
Hei
gh
t (W
eig
ht
Fra
ctio
n)
Mi
ci
Lo
g (
Mo
lecu
lar
Wei
gh
t)
∑∑
=ii
ii
Mc
McMz
2
MWD’s using Conventional Calibration.
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1) Simple Setup.
(Only one detector required - RI or UV)
2) Solution concentration not a variable.
(Approximate concentrations are good enough)
3) Excellent precision (repeatability)
(Related to column and pump performance)
Advantages of Conventional Calibration
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2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
18 20 22 24 26 28 30Retention Volume (ml)
Lo
g (
Mo
lecu
lar
Weig
ht)
PSPAMSPMM
API
PPBDPP
G
Overlay of Conventional Calibration Curves
Each Polymer has its own size to
Molecular weight relationship:Vh ≈ [η]xM
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Effect of molecular shape on GPC
retention volume
Structural changes will affect
results
Columns separate on
size not MWt.
Sphere
Coil
Rod
Retention volume
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1) Each polymer has its own calibration line,
so the Molecular Weight values are only
accurate for the same sample type:
only relative MW obtained
2) Any structural change such as branching
will affect the accuracy of this value:
gives incorrect relative MW!
3) Does not give any structural information.
Disadvantages of Conventional Calibration
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Conventional Calibration GPC - Summary
Simple technique to give whole polymer distribution
� Need to take care with sample/solvent/column
compatibility
� Comparison of samples is easy
Calibration is main difficulty
� Data is therefore only relative
No structural information
� Not useful for branched polymers
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Universal GPC
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Hardware Schematic Universal Calibration
GPC PumpVacuum
Degasser
Solvent
Autosampler
Injection Loop
Column Oven and Columns
Waste
Viscometer Detector
RI Detector
1.001.00
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Universal Calibration
•Why Universal Calibration
•Theory
•Viscosity Detector
•Examples
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Why Universal Calibration?Size Exclusion Chromatography (SEC)
(A) (B) (C) (D) RETENTIONTIME
(A) (B) (C) (D)
POROUS
PACKING
SAMPLE MIXTURE
+
CONCENTRATION
DETECTOR
CHROMATOGRAM
SOLVENT
FLOW
unlike HPLC,
NO chemical
interaction
with the GPC
column is
permitted.
GPC relies on
a pure
physical
separation
principle.
(A) Injection
(B) Separation
(C) Elution of
large
molecules
(D) Elution of
small
molecules
Polymer separation
based on SIZE
(hydrodynamic volume)
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2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
18 20 22 24 26 28 30Retention Volume (ml)
Lo
g (
Mo
lecu
lar
Weig
ht)
PSPAMSPMMAPIPPBDPPG
Overlay of Conventional Calibration Curves
Each Polymer has its own size to
Molecular weight relationship:Vh ≈ [η]xM
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Universal CalibrationUniversal Calibration was first demonstrated
and proven by Benoit in 1967, who showed
that a wide range of polymer structures
eluted on the same calibration curve when
the intrinsic viscosity is included.
It does not matter whether the polymer is
linear, branched, block copolymer,
heterogeneous copolymer, or whatever...
105
106
107
108
109
Lo
g [
η]
M
18 20 22 24 26 28 30
ELUTION VOLUME
PS “Comb”PS
PS “Star”
Hetero-Graft CopolymerPolyMethylMethacrylatePolyVinylChlorideGraft Copolymer: PS/PMMAPolyPhenylSiloxane
Polybutadiene
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Universal CalibrationIntrinsic Viscosity
Intrinsic viscosity is the concentration normalized
viscosity of the polymer in solution at infinite dilution.
ηsp is called the specific viscosity of the solution whose concentration is C.
ηo is the Solvent Viscosity.
η is the Solution Viscosity.
[ ]0→
==c
sp
cIV
ηη
0
0
η
ηηη
−=sp
In GPC, concentrations of solutions are
sufficiently dilute that the extrapolation
to zero concentration is negligible.
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Universal Calibration
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Universal Calibration4- capillary Differential Viscosity Detector
IP
+ -
DP-+GPC IN OUT
Solvent
Wheatstone bridge concept - M. Haney, 1984Wheatstone bridge concept - M. Haney, 1984
Sample
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Universal CalibrationCalculation of Viscosity
Intrinsic Viscosity is Determined by the Viscometer Detector Signal.
[ ]ηη
= =IVC
sp
IVCDPIP
DP
o
o
sp×=
−=
−=
24
ηηη
η
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ViscometerDelay
Volume
IP (-)IP (+)
DP (-)
DP (+)
Inlet Outlet
Pump pulsation noise cancels
At DP transducer:
This is a direct pneumatic cancellation
The bridge doesn’t see solvent differences
It only sees actual polymer differences
Four Capillary Viscometer
5.0 7.0 9.0 11.0 13.0 15.0
Retention Volume (mL)
Det
ecto
r R
esp
on
se
Pump Noise
is cancelled out
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Universal CalibrationDual Detector Response
Detector Responses VISC ∝ IV x C
RI ∝ dn/dc x C
Polystyrene
850,000
15.0 17.0 19.0 21.0 23.0 25.0
0
50
100
150
200
250
Retention Volume (mL)
Det
ecto
r R
esp
on
se (
mV
)
Refractomete
rPolystyrene
30,000
Viscometer
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Universal Calibration – RI response
RI ChromatogramPS10-1 RIps1-1 RIps11-1 RIps12-1 RIps2-1 RIps3-1 RIps4-1 RIps5-1 RIps6-1 RIps7-1 RIps8-1 RIps9-1 RI
8,0 10,2 12,4 14,7 16,9 19,1 21,3 23,6 25,8 28,0-20
-2
15
33
50
68
86
103
121
138
Retention Volume (mL)
Res
ponse
(m
V)
Date of Run: Tue May 04 199909:26:17
Viscotek Corporation
Viscotek PolyCal standards
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Viscosity ChromatogramPS10-1 DPps1-1 DPps11-1 DPps12-1 DPps2-1 DPps3-1 DPps4-1 DPps5-1 DPps6-1 DPps7-1 DPps8-1 DPps9-1 DP
8,0 10,2 12,4 14,7 16,9 19,1 21,3 23,6 25,8 28,0-70
-29
12
52
93
134
175
216
257
298
Retention Volume (mL)
Res
ponse
(m
V)
Date of Run: Tue May 04 199909:26:17Viscotek PolyCal standards
Universal Calibration – Viscometer Response
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Universal Calibration Line
1,000
8,000
2,100
2,800
3,500
4,200
4,900
5,600
6,300
7,000
Log
( M
p x
IV
)
17,000 28,000
Retention Volume (mL)
19,000 20,000 21,000 22,000 23,000 24,000 25,000 26,000
1,870 e 6
940,000
400,000
170,000
94,400
46,500
18,000
5,450
2,560
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Retention
Volume
Log MxIV
IV MW IVxMW
Polymer A (Standard)
1.0 250,000 250,000
Polymer B (Sample)
0.83 300,000 250,000
MWAIVA = MWBIVB
Universal CalibrationCalculation
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Universal CalibrationResults
Differential MWD
3,81 4,21 4,61 5,02 5,42 5,82 6,230,00
0,27
0,53
0,79
1,06
Log(Molecular Weight)
d(W
f) /
d(L
og
M)
Differential IVD
3,81 4,29 4,78 5,26 5,74 6,230,00
0,30
0,60
0,89
1,19
1,49
Log(Molecular Weight)
d(W
f)/d
(Log
IV)
Size Distribution
3,81 4,29 4,78 5,26 5,74 6,230,00
0,37
0,74
1,11
1,49
1,86
Log(Molecular Weight)
d(W
f)/d
(Log
Rg
)
Mark-HouwinkPS250K-1 IV LS
3,81 4,29 4,78 5,26 5,74 6,23-1,21
-0,86
-0,52
-0,17
0,17
0,52
Log(Molecular Weight)
Lo
g (
IV)
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Universal CalibrationStructure Analysis Mark-Houwink Plot
PS250K-1 IV LSpsrr1-1 IV LSnbs706-1 IV LS
3,80 4,23 4,66 5,08 5,51 5,94 6,36-1,22
-0,76
-0,30
0,16
0,62
Log(Molecular Weight)
Log[I
ntr
isic
Vis
cosi
ty]
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Universal CalibrationSummary
Advantages:
•True molecular weight/intrinsic viscosity
•MH a and K values (broad distributions)
•Structure/branching information
•Sensitive from high to low Mw (< 1000)
•No dn/dc needed
Disadvantages:
•True size exclusion separation necessary
•Standards in the same Mw(Vh) range as unknown
•Need to know concentration
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Branching
103
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Types of Polymer Branching
1. Short Chain 2. Long Chain - Star
4. Long Chain - Comb3. Long Chain Random
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The Kuhn–Mark–Houwink–Sakurada equation
αη MwK ×= ][
› [η] is the Intrinsic Viscosity (IV)
› K and α are the MH parameters which depend on the nature of the polymer & solvent
› Mw is the weight average molar mass (molecular weight)
› a describes the relationship between molecular weight and IV, K is the intercept, describing the flexibility of the backbone.
The equation describes the dependence of the intrinsic
viscosity of a polymer to molecular weight
6TH INTERNATIONAL CONFERENCE ON THE HISTORY OF CHEMISTRY Staudinger - Mark - Kuhn: Historical Notes from the Development of Macromolecular Chemistry105
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Branching AnalysisMark-Houwink Plots
Log M
Lo
g I
V
Log M
Lo
g I
V
Non-Uniform Branching
Typical for
random long chain branching
Uniform Branching
Typical for
short chain branching
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Effect of Branching on Molecular Size
› Difference in volume between a linear chain and a
branched chain with the same total chain length
› Since the hydrodynamic volume is smaller, with the
same mass enclosed, the density must be higher,
producing a lower Intrinsic Viscosity
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Star Branched PS
Decrease in
Viscosity
Area
Equivalent Molecular Weight Star Branched PS vs. Linear PS
Star Viscosity
Linear Viscosity
Retention Volume (mL)
Dete
ctor
Resp
onse
Equivalent
Molecular Weight
Areas
Decrease in Retention Volume (Rg)
Star LS
Linear LS
Mw IV star IV linear IV ratio Bn
340,000 0.805 1.162 0.693 4
100,000 0.318 0.497 0.639 5
+2,500,000 1.308 4.632 0.282 10
IV linear equivalent measured from MH-Coefficients of linear polystyrene. Star branch viscosities
measured directly with the differential viscometer detector.
Three Star Branched PS
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The Zimm-Stockmayer theory defines the g factor as the ratio of the radius of gyration of
the branched polymer to the radius of gyration of the linear polymer, at the same
molecular weight.
The radius of gyration can be measured by light scattering from the initial slope of the
Zimm plot.
The practical difficulty here is that Rg measured by light scattering does not extend to
molecules below Rg = 15 nm.
M
=
(lin) R
(br) R g
2
g
2
g
Long Chain Branching - Zimm-Stockmayer
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Long Chain Branching - Zimm-Stockmayer
The Zimm-Stockmayer theory also defines the g factor in terms of the intrinsic viscosity
ratio
.
Where ε is a shape factor, generally taken as ~0.75.
This formulation is not as rigorous as that using the RG, considering that ε is ill-defined
by the theory. However, it is more practical in the sense that intrinsic viscosity can be
measured over nearly the entire distribution of the polymer.
[ ][ ]
ε
η
η1/
Ml,
Mb,
g
=
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Equations of Zimm-Stockmayer for g
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Values of Epsilon in the g Equation
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Calculation of branching – Zimm Stockmayer
› Branching ratio (g) defined in terms of Rg (radius of gyration)• Not an easy parameter to measure
accurately – initial slope of Zimm plotat Θ = 0° not overall slope!
• Impossible to measure below ~15nm
› Branching ratio can also be defined in terms of Intrinsic Viscosity (g’)• More practical solution• Easier to measure across entire size
range 1nm to >100nm• Better sensitivity (density, not size)• More reproducible
› ….but need to use shape factor (ε)• Typically 0.75 used for PE• Results are only relative, unless ε
can be determined absolutely• Can check from Rg estimate if large
enough
linM
brM
Rg
Rgg
,2
,2
=
[ ][ ]
ε
η
η1/
Ml,
Mb,
g
=
[ ][ ] linM
brM
Mg,
,'
η
η=
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Long-Chain Branching Parameters
› Star Branching
• For regular distribution of arms, Number of Arms ‘f’ (or Bn)
• For random distribution of arms:
2/)23( ffg −=
( )( )21
6
++=
ff
fg
f (or Bn) = 2f (or Bn) = 2
f (or Bn) = 3
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› The number of branches per molecule (Bn) is
determined for random tri-functional branching using:
Long-Chain Branching Parameters
( )
( )g
B
B
B
B B
B Bn
n
n
n n
n n
=+
+ +
+ −
−
6 1
2
2 2
2
1
1
2
1
2
1
2
1
2
1
2
ln
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Branching Frequency
Constant Number of Branches per Molecule
(not likely)Constant Branching Frequency (Density)
e.g. For polyethylene we set
R=14,000 to give ‘branches per
1000 C atomsM
BR nM
⋅=λ
Branching frequency (f or λ) can also be determined
(How many branches are there as you go along backbone)
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Example
› Branching in polyethylene
› NIST standards
• NBS 1475 – Linear
• NBS 1476 – Branched
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0.1
0.2
0.3
1
2
3
10
Intr
insic
Vis
co
sity (
dL
/g)
410
42x10
43x10
510
52x10
53x10
610
Molecular Weight (Da)
Comparison of NBS 1475 (Linear) and 1476 (Branched) using M-H plot
300
350
400
450
500
550
600
650
700
750
Vis
com
ete
r -
DP
(m
v)
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Retent ion Volume (mL)
300
350
400
450
500
550
600
650
700
750
Vis
com
ete
r -
DP
(m
v)
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Retention Volume (mL)
Refractive IndexViscosityLow Angle LS
160°C TCB2.5 mg/ml, 200ul
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Branching Module in OmniSEC™
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Reproducibility determined by Mark Houwink plot
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1. What is the minimum length of long chain branches in this method?
Ans: 6-12 carbons in length.
1. What is the minimum length of long chain branches in this method?
Ans: 6-12 carbons in length.
2. What can I use for a linear reference if I do not know whether any of my polymers are linear?
Ans: Use the Mark-Houwink constants of a close relative polymer.
Or : Use the least branched polymer that you have as a reference.
Then the values will be useful on a relative basis.
2. What can I use for a linear reference if I do not know whether any of my polymers are linear?
Ans: Use the Mark-Houwink constants of a close relative polymer.
Or : Use the least branched polymer that you have as a reference.
Then the values will be useful on a relative basis.
3.What if I see apparent differences in branching in my samples but other information suggests that they are not branched?
Ans: May be some copolymer, blending or other chemical
heterogeneity present in the samples.
Or: There is some other variable that affects the density of the
molecule.
3.What if I see apparent differences in branching in my samples but other information suggests that they are not branched?
Ans: May be some copolymer, blending or other chemical
heterogeneity present in the samples.
Or: There is some other variable that affects the density of the
molecule.
Common Questions regarding Branching
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Branching Summary
› Triple detection can be used to measure branching
› Comparison of Mark-Houwink plots is often enough
› Quantitative analysis requires a linear reference, either
• Linear polymer sample, or
• Mark-Houwink ‘a’ and ‘log k’ values
› Branching number (Bn) gives branches per molecule
• Most useful for star branching
• Less useful for random branching
› Branching frequency (λ) more useful
• Gives branches per selected repeat unit
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Copolymer Analysis
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Sample Types
PROTEIN POLYMER
DNA
Homogenous, mono-constituent molecules
Homopolymer Copolymer – Conjugate Analysis
PROTEIN/
POLYMER
Heterogeneous, multi-constituent complexes
PROTEIN/
PROTEIN
PROTEIN/
DNAPOLYMER/
POLYMER
PROTEIN/
DETERGENT
DNA/
DETERGENT
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Copolymers: What are they?
› Homo-polymer� chemical homogeneity in the distribution independent
of molecular weight.
› Copolymer� chemical composition can change with respect to
molecular weight.
Homo-polymer Co-polymers
Alternating
Block
Random
Grafted
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Multi Detector SEC
› Addition of advanced detectors enhances GPC/SEC
greatly
� Light Scattering – Molecular Weight
� Viscometer – Molecular Structure
› Triple Detection – Light Scattering and Viscometer
› Tetra Detection – Addition of 2nd Concentration Det.
� Copolymers, Blends
� Conjugates, PEGylation, PDCs
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Copolymers - Introduction› Some types of copolymers can be treated like
homopolymers:
� Copolymers with alternating sequence
� (A-B-A-B, or A-A-B-A-A-B-, ......)
� Copolymers with MW independent composition
� Copolymers with negligible dn/dc difference of the different monomeric units e.g. Polylactide/glycolide
› For some block-copolymers, blends, copolymers with MW
dependent composition dn/dc is not a constant. Therefore:
� RI chromatogram is not a concentration chromatogram
› The MWD’s of co-polymers derived from LS and a
concentration detector (RI or UV ) are incorrect, because
the dn/dc of the polymer is different for each elution
volume.
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Why do we need an accurate concentration profile?
› Concentration for each slice is needed to calculate Molecular weight.
-1,0
43,0
5,0
10,0
15,0
20,0
25,0
30,0
35,0
Lo
w A
ng
le L
igh
t S
ca
tte
rin
g R
esp
on
se
(m
V)
0,0
22,0
3,0
6,0
9,0
12,0
15,0
18,0
Re
fra
ctive
In
de
x R
esp
on
se
(m
V)
0,0
64,0
7,0
14,0
21,0
28,0
35,0
42,0
49,0
56,0
Ultra
Vio
let R
esp
on
se
(m
V)
11,50 20,80
Retention Volume (mL)
13,0 14,0 15,0 16,0 17,0 18,0 19,0
MwM c
c
i i
i
=∑∑
2)/(.
ResponseLS
dcdnconcKMi
××=
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129
EQUATIONS GOVERNING THE DETECTORS
RI Output (mV) = KRI • dn/dc • Concentration
UV Output (mV) = KUV • dA/dc • Concentration
Visc. Output (mV) = KVisc • IV • Concentration
LS Output (mV) = KLS • Mw • (dn/dc)2 • Concentration
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Why Can’t We Use The Homopolymer Method?
DE
TE
CT
OR
RE
SP
ON
SE
RI LS
Direct relationship
between the molecule
and detector response
Both constituents of the
complex contribute to the
response of the signals
RI LS
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Why Can’t We Use The Homopolymer Method?
dn/dc = RI Output (mV)
KRI • Conc.
Mw = LS Output (mV)
KLS • (dn/dc)2 • Concentration
Not usually known for
copolymers
Cannot determine
concentration of
copolymer
We need to find dn/dc copolymer
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Describing dn/dc and dA/dc In Copolymers
B
A
dn
dc copolymer
=dn
dc A
dn
dc B
+11 + δ
δ
1 + δ
We don’t know δ
dA
dc copolymer
=dA
dc A
dA
dc B
+11 + δ
δ
1 + δ
Copolymer = 1 + δ
Equation A
Equation B
A = Homopolymer A
B = Homopolymer B
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Describing dn/dc In Terms Of Detector Responses
dn
dc copolymer
= RI
?
Change in RI response
Concentration of copolymer=
dA
dc copolymer
= UVccopolymer
Substitute for ccopolymer
Equation C
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Describing dn/dc In Terms Of Detector Responses
dn
dc copolymer
= RI • (dA/dc) copolymer
UV=
RI
UVdA
dc A
dA
dc B
+11 + δ
δ
1 + δ
Derived in Equation B
Equation D
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Solve For δ
Combining Equations A and D gives
dn
dc A
dn
dc B
+11 + δ
δ
1 + δRI
UVdA
dc A
dA
dc B
+11 + δ
δ
1 + δ=
dn/dcA, dA/dcA, dn/dcB, dA/dcB, RI and UV output all known….
Solve for δ and determine the dn/dccopolymer using equation A.
dn
dc copolymer
=RI
UVdA
dc A
dA
dc B
+11 + δ
δ
1 + δ
Equation D
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Determination of Mwcopolymer & MwA
Conccopolymer = RI Output (mV)
KRI • dn/dc copolymer
Mwcopolymer = LS Output (mV)
KLS • (dn/dc)copolymer2 • Conccopolymer
Mwcopolymer = (1 + δ) • MwA
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Example: PS/PMMA Copolymer Blend: 50:50
› PMMA 122K broad distribution
› PS 250K broad distribution
- 1 ,0
48 ,0
5 ,0
10 ,0
15 ,0
20 ,0
25 ,0
30 ,0
35 ,0
40 ,0
Response (
mV
)
11 ,50 20 ,80
Retention Volume ( mL )
12 ,6 13 ,3 14 ,0 14 ,7 15 ,4 16 ,1 16 ,8 17 ,5 18 ,2 18 ,9 19 ,6
Refractive Index
Ultra Violet
Low Angle Light Scattering
Viscometer DP
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PS/PMMA Copolymer Blend :Total of Responses
RIHT = Height of RI Chromatogram
UVHT = Height of UV Chromatogram
ARI = RI Response Factor for Polymer A
BRI = RI Response Factor for Polymer B
AUV = UV Response Factor for Polymer A
BUV = UV Response Factor for Polymer B
HT A UV B UV
RIHT = CA ARI + CB BRI (1)
UVHT = CA AUV + CB BUV (2)
For each slice of data
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PS/PMMA Copolymer Blend Calculation of true concentration profile
0,0
6,9 e-5
1,0 e-5
2,0 e-5
3,0 e-5
4,0 e-5
5,0 e-5
6,0 e-5
Conc P
S
0,0
6,9 e-5
1,0 e-5
2,0 e-5
3,0 e-5
4,0 e-5
5,0 e-5
6,0 e-5
Conc (
PS
+P
MM
A)
0 ,0
6,9 e-5
1,0 e-5
2,0 e-5
3,0 e-5
4,0 e-5
5,0 e-5
6,0 e-5
Conc P
MM
A
0 ,0
22 ,0
3,0
6,0
9,0
12 ,0
15 ,0
18 ,0
Refr
active Index R
esponse (
mV
)
11 ,50 20 ,80
Retention Volume (mL )
12 ,8 13 ,6 14 ,4 15 ,2 16 ,0 16 ,8 17 ,6 18 ,4 19 ,2
Conc PS
Conc (PS +PMMA)
Conc PMMA
Refractive Index
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PS/PMMA Copolymer Blend dn/dc distribution
0,100
0,200
0,110
0,120
0,130
0,140
0,150
0,160
0,170
0,180
0,190
dn
/dc o
f C
op
oly
me
r
0,0
22,0
2,0
4,0
6,0
8,0
10,0
12,0
14,0
16,0
18,0
20,0
Re
fra
ctive
In
de
x R
esp
on
se
(m
V)
11,50 20,80
Retention Volume (mL)
12,6 13,2 13,8 14,4 15,0 15,6 16,2 16,8 17,4 18,0 18,6 19,2 19,8
dn/dc PS = 0.185
dn/dc PMMA = 0.084
][][B
BA
B
ABA
A
i dcdn
CC
C
dcdn
CC
C
dcdn ×
++×
+=
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Copolymer Analysis - Summary of Results
› True RI concentration profile� difference in UV and RI response needed (UV1/UV2 or
RI/IR)
› dn/dc for each slice
› Co-polymer Mw
› % co-monomers (% A and B)
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Some Selected Application Examples
Synthetic Polymers
� Polystyrene
� Polycarbonate
� HT-GPC - Polyolefins
Natural Polymers
� DNA
� Polysaccharides
� Maltodextrins (Polysaccharide)
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Some Selected Application Examples
Synthetic Polymers
� Polystyrene
� Polycarbonate
� HT-GPC - Polyolefins
Natural Polymers
� DNA
� Polysaccharides
� Maltodextrins (Polysaccharide)
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Comparison of calculated Mw values for Polystyrene
2005-10-08_19;37;32_AT_comb-ps_BPS_B108-1_01.vdt: Refractive Index
-43.03
-6.10
30.82
67.75
104.67
141.59
Re
fra
ctiv
e In
de
x (
mV
)
Retention Volume (mL)
0.10 3.59 7.08 10.57 14.06 17.55 21.04 24.53 28.02 31.51 35.00
Conventional Calibration (RI only)
720,000 140,000
910,000 144,000Triple Detection
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Decrease in
Viscosity
Area
Star Viscosity
Star LS
Linear Viscosity
Linear LS
12.5 13.5 14.5 15.50
20
40
60
80
100
Retention Volume (mL)
Det
ecto
r R
espon
se
Equivalent
Molecular Weight
Areas
Decrease in Retention Volume (Rg)
Star Branched PolymersAt the same molecular weight,
a star branched polymer has a
much lower intrinsic viscosity.
The addition of the viscometer
provides a direct measurement
of size. The number of branches
(Bn) can then be determined.
PS PS-Star
Mw 100,000 100,000
IV(dL/g) 0.495 0.318
Rg(nm) 14 10
Equivalent Molecular WeightStar Branched PS Vs. Linear PS
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Polycarbonates
Polycarbonates are used in many applications including CD/DVDs, automotive and electronics.
Polycarbonates can exhibit branching which will affect the material properties.
Two samples are analysed - one linear, one has a very small level of branching.
Can we quantify the branching?
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Polycarbonates -Molecular weight comparison
Molecular Weight Distribution
PC 1 PC 2
3,00 3,40 3,80 4,20 4,60 5,00 5,40 5,80 0,00
0,20
0,40
0,60
0,80
1,00
1,20
1,40
Log(Molecular Weight)
Wf
/ [d
log
MW
]
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Polycarbonates - Structural comparison
Mark-Houwink-Plot
PC 1 PC 2 Polystyrene
3,20 3,60 4,00 4,40 4,80 5,20 5,60 6,00 6,40 6,80-1,70
-1,40
-1,10
-0,80
-0,50
-0,20
0,10
0,40
0,70
Log(Molecular Weight)
Log(I
ntr
insi
c V
isco
sity
)
Log I
VLog MW
Linear
Branched
Expanded scale
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Polycarbonates - Branching quantification
Number of Branches
4,20 4,40 4,60 4,80 5,00 5,20 5,40 5,60 0,00
0,40
0,80
1,20
1,60
2,00
2,40
2,80
Log(Molecular Weight)
Bn
Branching Frequency
4,20 4,40 4,60 4,80 5,00 5,20 5,40 5,60 0,50
0,70
0,90
1,10
1,30
1,50
1,70
1,90
2,10
2,30
2,50
Log(Molecular Weight)
Lam
bda
λ( )MRB
M
n=
R = 1000 D
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The Light Scattering Clearly Shows a
High Molecular Weight Species
at 2 Hours Dissolution.
Dissolved 2 Hours 24 Hours
Mz 13,000,000 3,000,000
Mw 155,000 154,000
Mn 38,000 38,000
IV(dL/g) 0.283 0.483
Rg(nm) 10 12
Analysis of GelsThe RI Chromatogram does not
Show any Differences Between
Samples Dissolved for 2 Hours
Versus 24 Hours.
Viscometer Chromatogram
10.0 12.0 14.0 16.0 18.0 20.0
0.0
2.0
4.0
6.0
8.0
10.0
Retention Volume (mL)
Res
pon
se (
mV
)
Refractometer Chromatogram
0.0
2.0
4.0
6.0
8.0
10.0
Res
pon
se (
mV
)
Light Scattering Chromatogram
0.00
1.00
2.00
3.00
4.00
5.00
Res
pon
se (
mV
)
2 Hours
24 Hours
Dissolution Time
2 Hours
24 Hours
Dissolution Time
2 Hours
24 Hours
Dissolution Time
The Large Increase in Viscosity
From 2 to 24 Hours Suggests that
the Molecules Were Not Fully
Solvated at 2 Hours.
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Polysaccharide Modification
Triple Chromatogramch2 RIch2 DPch2 LS
7.0 10.6 14.2 17.8 21.4 25.0-50
-10
30
70
110
150
Retention Volume (mL)
Rel
ativ
e R
esponse
GMPWxl x2
0.1M NaNO3+5%ACN
0.7ml/min
Mw = 32,500
IVw = 0.38
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Polysaccharide Modification
Triple Chromatogramch3 RIch3 DPch3 LS
7.0 10.6 14.2 17.8 21.4 25.0-50
-10
30
70
110
150
Retention Volume (mL)
Rel
ativ
e R
esp
on
se
GMPWxl x2
0.1M NaNO3+5%ACN
0.7ml/min
Mw = 139,000
IVw = 0.74
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Mark-Houwink Plot
CH2 IV LSCH3 IV LS
3.50 4.00 4.50 5.00 5.50 6.00 6.50-1.50
-0.88
-0.25
0.38
1.00
Log(Molecular Weight)
Log[I
ntr
isic
Vis
cosi
ty]
a = 0.699
a = 0.927
Polysaccharide Modification
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Triple Chromatogramch2 RIch2 DPch2 LS
7.0 10.6 14.2 17.8 21.4 25.0-50
-10
30
70
110
150
Retention Volume (mL)
Rel
ativ
e R
esp
on
se
Triple Chromatogramch3 RIch3 DPch3 LS
7.0 10.6 14.2 17.8 21.4 25.0-50
-10
30
70
110
150
Retention Volume (mL)
Rel
ativ
e R
esp
on
se
Polysaccharide
The difference in chain
stiffness can be clearly
seen in both the raw
chromatograms and
the M-H plot
Mark-Houwink Plot
3.50 4.00 4.50 5.00 5.50 6.00-2.00
-1.25
-0.50
0.25
1.00
Log(Molecular Weight)
Lo
g[I
ntr
isic
Vis
cosi
ty]
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Any questions?
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