,
'
90-
SEC-VISCOMETRY-RIGHT ANGLE LIGHT SCATTERING
(SEC-VISC-RALS)
M.A. Haney
Viscotek Corporation
1032, RussellDrive
Porter, TX 77365
C. Jackson and W.W. Yau1
E.I. du Pont de Nemours and Company
Central Research and Development
Experimental Station
P.O. Box 80228
Wilmington, DE 19880-0228
ABSTRACT
The two types of light scattering photometers currently being used
for on-line size-exclusion chromatographic (SEC) polymer detection are the
low-angle laser lightscattering (LALLS)photometer and the multi-angle laser
light scattering photometer (MALLS). In both of these approaches, the
attainment of the zero degree forward light scattering intensity is the
targeted goal for the experimental determination of polymer molecular
weight. However, for molecules with dimensions small in comparison to the
wavelength of the incident light (D < 1/20_ wavelength)the angular variation
of the scattered light becomes too smallto measure, and the light scattered
at a right-angle (90°), to the incident beam may be used to determine
molecular weight. With the addition of an on-line viscometer, the molecular
weight of molecules with dimensions larger than 1/20 thof the wavelength
of the incident light may be determined using the right-angle method. In the
proposed method, the scattered intensity is corrected for angular
asymmetry by using the combined measurements of intrinsic viscosity and
90° light-scattering intensity to estimate the molecular radius, and thus the
expected scattering asymmetry. This molecular weight method provides
increased precision over lower angle measurements due to the high signalto-noise of the right-angle scattering intensity, and is accurate to within a
i
1Technical consultant to Viscotek Corp., Porter, TX.
•
_
"
49
few percent for all spherical and linearflexible chain molecules. The concept
and the computer algorithm used are discussed. Data obtained using a
laser light scattering detector as Well as right angle scattering from a
fluorescence detector are presented.
INTRODUCTION
The light scattered by a polymer molecule in dilute solution in the
forward direction of the incident beam is proportional to the polymer
molecular weight [1]. Two methods are currently used to estimate this
intensity in conjunction with SEC.The scattered intensity at angles close to
the forward direction of the incident beam is practically the same as at zero
degrees. Thus a measurement of the light scattered at, typically 7°, can be
used to estimate molecular weight [2]. The second method takes advantage
of the fact that the angular distribution of the scattering from a polymer
solution is a monotonic function of angle described by the form factor, P(e).
Measurements of the scattered intensity at a number of angles, generally
in the range 30 - 150°, are used to extrapolate to the zero degree intensity.
Furthermore, in some cases, the variation of the scattered intensity with
angle can be used to determine the molecular radius of gyration [3]. This
angular variation of the scattered light is caused by destructive interference
between light scattered from different segments of the same molecule. As
a result, the scattered intensity decreases with increasing angle. The initial
slope of the scattered intensity as a function of sin2(e/2) is proportional to
the square of the radius of gyration. Figure 2 shows such a plot for a
flexible chain molecule with a root-mean-square radius of gyration of 33 nm.
Recently, a method for determiningpolymer molecular weight using
the scattering at 90° was described [4]. When the maximum distance
between two points of the molecule is less than 1/20th of the incident
wavelength ( e.g., 20-25 nm, depending on solvent refractive index, for the
632.8 nm band of a helium-neon laser, this corresponds to a radius of
gyration of about 10 nm for a flexible chain molecule ) the asymmetry in the
scattered intensity cannot be detected. Under these conditions, the
scattered intensity at any angle is the same as at zero degree, and may be
used equally well to determine molecular weight.
The method was demonstrated for a variety of biopolymers [4]. For
some compact proteins of molecular weights up to 1 x 106,the radius of
gyration is so small that the difference between zero and 90° scattering is
often less than 1%. A standard fluorescence detector was used as a light
scattering monitor by setting the emission monochrometer wavelength equal
to that of the excitation monochrometer wavelength. Using a wavelength of
5O
467 nm the signal to noise level in the light scattering signal was
comparable to that from the UV concentration detector. An excellent linear
relationship (correlation coefficient = 0.9998) was found between the
scattered light intensity and the literature molecular weights for a series of
biopolymers with molecular weights ranging from 29,000 to 1,000,000
g/mol. In addition to the simplicity of the apparatus and data handling, the
method has the advantage that the signal at 90° is much less prone to
noise caused by dust particles, column particulates, etc. than the light
scattering signals from lower angles. The 90° scattering measurement gives
higher signal to noise than both the low angle measurement used by
LALLS, and the 0° extrapolation used by MALLS. Furthermore, the rightangle measurement does not require the refraction corrections required at
other detection angles, or the problem of normalizing multiple detectors
inherent in MALLS.
The combination of SEC with an on-line viscometer and a light
scattering detector (LALLS or MALLS) gives highly precise measurements
of molecular weight, intrinsic viscosity and radius distributions of a polymer
sample [5]. Because the method relies on direct measurement of physical
properties of the eluting sample, it is insensitive to many adverse variations
in SEC experimental conditions such as changes in flow rate, band
broadening, column degradation, etc. The molecular weight and intrinsic
viscosity at each slice can be used to calculate the hydrodynamic radius,
and for linear flexible chain molecules the radius of gyration. The combined
SEC-Visc-RALS instrument thus provides a very desirable method for
studying polymer conformation and branching.
For flexible linear polymers, the SEC-Visc-RALS method provides a
low-cost, reliable measurement of the radius of gyration. In addition, SECVisc-RALS gives improved measurement capability for small molecular sizes
over SEC-MALLS. The measurement has a wide size range and is precise.
The capability of SEC-Visc-RALS is extended to a wider range of
molecular shapes and sizes by the following computer algorithm: this is
done by repeatedly using the intrinsic viscosity and the right-angle light
scattering intensity to estimate the size of the molecule, and then using the
size value to correct for the angular asymmetry in scattered intensity [8].
In our software we have implemented the following steps to correct
for the light scattering asymmetry. The raw data consists of signals from the
concentration detector, the viscometer and the right-angle scattered
intensity for each chromatogram slice.
1.
Initially, the angular scattering function, P(e), is assumed to be equal
51
to 1 at 90°, and an initial molecular weight, Me=, is calculated for each
chromatogram slice from the light scattering intensity, R(e = 90o),measured
at 90°. Typical SEC concentrations, c, which are low, allow us to neglect the
effect of the second virial coefficient, and write,
M=,-R(o=9°_)
K*¢
(1)
where K* is an opticalconstant dependent on the solvent refractive index,
the polymer specificrefractive indexincrement,and the wavelengthof the
incidentlight.
2. The radius of gyration, R_=,is calculatedfrom the Flory-Foxequation
assuminga linearflexiblechain molecule.Usingthe above Me=valuefor the
molecularweightand the measuredintrinsicviscosity,[n], foreach slice,we
obtain,
RFF _
-
_
where _ is the Flory viscosityconstant.
3.
The valueof the asymmetryfunctioncorrespondingto the calculated
radiusof gyrationfor each slicethen is used to correct for the asymmetry
and providea new estimateof molecularweightfrom the 90° signal. The
completeP(e) functionderivedby Debyefor a flexiblecoil is used, avoiding
any systematic errors caused by unconstrained extrapolation from a
polynomialleast-squaresfit,
P(e)=_(e-'+x-l)
x"
(3)
where
4_n
=
,.=smO
(4)
where no is the solvent refractive index, and Io is the wavelength of the
52
•
.,(.
"
incident light.
4.
A new estimate of molecular weight is calculated from,
M=
M_
(5)
P(O
=9oD
5.
Steps 2 to 4 are repeated using the new estimate of molecular weight
until the molecular weight values no longer change significantly. This usually
requires three iterations.
The algorithm can be improved to take into account the different
degrees of expansion of the polymer chain described by the Ptitisyn-Eisner
modification of the Flow-Fox equation [7]. After the molecular weight values
are determined in each step, the Mark-Houwink exponent relating molecular
weight to intrinsic viscosity is calculated and used to modify the calculation
of the radius of gyration. This step has little effect on the final molecular
weight, but does improve the estimate of radius of gyration. However, the
sample must have some polydispersity to enable the Mark-Houwink
exponent to be calculated. Again it is noted that this software approach
gives the radius of gyration only when the sample is a linear flexible chain
structure. Otherwise, the method provides a measurement of an apparent
hydrodynamic radius of the molecule.
A more general version of the algorithm uses the radius of an
equivalent sphere for the asymmetry correction. In this case the
hydrodynamic radius is estimated from the measured value and the
scattering function for a sphere is used to correct for the scattering
asymmetry. Such a model can be applied to any molecular conformation as
well as branched molecules. The range of validity is currently being
investigated.
EXPERIMENTAL
Data were collected on two separate systems. One using a MALLS
detector and the other using a fluorometer as the LS detector. The SEC and
detector configuration is shown in Fig. 2. In the first system three PL gel 5
/_mmixed-bed linear columns were used (Polymer Labs, Amherst, MA). The
refractometer was a Waters _(Waters
Associates, Milford, MA). The
multi-angle laser light scattering d_{ector was a Model F laser photometer
f
53
(Wyatt Technology Corporation, Santa Barbara CA) with a helium-neon
laser ( 632.8 nm wavelength ) as the incident light source. The viscometer
was a Model 110 (Viscotek Corporation, Porter TX). The mobile phase was
toluene at 30°C. The broad molecular weight standard was polystyrene 706
(National Institute of Standards and Technology, Bethseda MD).
The second system consisted of three TSKgel PW columns, 2500,
3000, and 5000 ('l'osoHaas, Philadelphia, PA). The concentration detector
was a Knauer refractometer. The 90° scattered light intensity was measured
on a Hitachi F-1050 Fluorescence Spectrophotometer (Hitachi Ltd., Tokyo,
Japan) with both the emission and the excitation wavelengths set to 300
nm. The viscometer was a Model 110 (Viscotek Corporation, Porter TX).
The mobile phase was water. The samples used were poly(ethylene oxide),
(American Polymer Standards, Mentor, OH) and dextran (Pharmacia
Corporation, Uppsala, Sweden) molecular weight standards.
RESULTS
Figure 3 compares the radius of gyration calculated by using the
Flory-Fox equation using intrinsicviscosityand molecular weight value
measured by MALLS, comparedto that measured usingonly SEC-MALLS
resultsfor polystyrene706. The two setsof data agree withinexperimental
error. The increased precision of the SEC-Visc-LS integration in the
measurementfor the lowerhalfof the distributionisclearlyapparent. Figure
4 showsthe plotof molecularweightagainstelutionvolumefor polystyrene
706. The lowerline showsthe initialmolecularweightestimate,from the 90°
scattering uncorrectedfor angular asymmetry.The higher line shows the
final molecularweight calculatedusingthe correction algorithm. Figure 5
compares the molecularweightcalculatedby extrapolationfrom multi-angle
measurementsto thatobtainedby the LS-asymmetrycorrected right-angle
determination. The values are the same across the molecular weight
distribution,and the improvedsignal-to-noiseof the right-anglemethod is
apparent at the low molecularweight end of the MWD.
Figures6 and 7 show the LS and RI chromatogramsobtainedfrom
the second system usingthe fluorometeras a right-anglelight scattering
detector. Fig. 6 showsa PEO standard ( MW = 10,000 ) and Fig. 7 shows
a T-500 dextran (nominalMW = 500,000 ) respectively.The signal-to-noise
level of the light-scatteringsignal is comparableto the RI, showingthat the
detector is sensitiveenoughfor SEC sample concentrations.Also note the
asymmetricalshape of the LS chromatogramfor the dextranT-500 sample.
The slightshoulder on the left-hand-sideof the peak could be caused by
54
branching or ion exclusion of dextran containing carboxylic acid
functionality. This feature would have been present but unnoticeable with
conventional SEC using only an RI detector. Even without making a
correction for scattered intensity asymmetry, this apparent branching can
be detected by the right-angle light scattering detector.
To illustrate the applicability ofthe LS-asymmetry correction for RALS,
the algorithm was evaluated using literature experimental values of
molecular weight, intrinsic viscosity and radius of gyration for different
molecular conformations from the literature [8,9,10]. Measurements made
under both good solvent, and e conditions were used. The measured radius
of gyration and molecular weight were used to determine the 90° intensity
by means of the angular scattering function for the appropriate
conformation. Then this value was used as an initial molecular weight
estimate and was corrected using the intrinsic viscosity and the modified
Flory-Fox equation. The molecular weights calculated using the right-angle
scattering and the intrinsic viscosity are shown in Table I, along with the
percentage difference from the experimental values. As expected, the
accuracy of the estimated molecular weights is well within the experimental
errors for flexible coils and spherical molecules with molecular weights up
to many millions. For rod-shaped polymers the Flory-Fox relation breaks
down for molecular weights above a few hundred thousand. In fact the
values obtained by successive iterationsfail to converge for data from DNA.
If additional information is known about the molecular conformation
then this can be used to select the appropriate model for the asymmetry
correction. As mentioned above, for polydisperse samples, the MarkHouwink exponent can be used to determine conformation, and in the case
of branched samples the g' factor can be used to determine the relationship
between radius of gyration and intrinsic viscosity [11]. When the appropriate
equations for the intrinsic viscosity and scattering function of rigid rods are
used in the calculation, the results in Table I are improved. Thus if the
moleculesare knownto be rod shaped,or if this can be determinedfrom
the relationshipof the 90° molecular weight to intrinsic viscosity, the
correspondingtheoreticalmodelcan be usedto calculatemolecularweight
values. Similarlyfor the sphericalmoleculesin Table I, if the moleculeswere
known to be so compact the estimate of molecular weight from the 90°
scatteringcould be used,as it isclearthatmakingan asymmetrycorrection
in this case actually increasesthe error in the molecularweight estimate.
For branched polymers, the Rory-Fox equation is no longer
applicable, as the Flory viscosityconstantfor the branched polymer will
differfrom that for the linearform. Howeverunlessthe molecule is highly
55
branched ( > 50 branch points per molecule ) or highly uniform ( e.g., star
shaped polymers ) the error in the calculated molecular weight is generally
less than experimental errors. This is due to a number of reasons. Firstly,
the calculated radius of gyration is proportional to the cube root of the
inverse of the Flory constant, so errors are greatly reduced in the radius
value. Secondly, the asymmetry correction to the molecular weight value is
generally small ( < 30% for all flexible coil examples in Table I ), so that any
error in the estimated asymmetry is again reduced in the final estimate of
molecular weight. Finally, for a given molecular weight, the effect of
branching is to reduce the radius of gyration, tending more to a compact,
spherical conformation than a random coil. As a result the correction
required for a branched polymer is always less than for it's linear form at
the same molecular weight. This can be seen in Fig. 8 where the viscosity
branching factor, g', for an experimental branched polymer is shown as a
function of molecular weight. The branching factor calculated from the LSasymmetry corrected right-angle light scattering molecular weight gives the
same result as that calculated using the multi-angle molecular weight. The
weight-average number of branches per molecule is 20.
SUMMARY
The method of molecular weight determination using a right-angle
light scattering detector can be greatly extended by using an on-line
viscometer. The intrinsic viscosity can be used with the right-angle scattered
intensity to correct for any angular asymmetry in the scattering if such a
correction is needed. The results show that for flexible random coil and
spherical molecular configurations, the molecularweight results are accurate
up to molecular weights of many millions. In addition for random coil
configurations, the correct radius of gyration is determined. For rod-shaped
molecules, the method can calculate molecular weights within 5% accuracy
for rod lengths below 85 nm( Rg = 25 nm). For branched molecules, the
errors in molecular weight determination are negligible for moderate
degrees of random branching. Thus, for the majority of commercially
important polymers the incorporation of a right-angle light scattering
detector into a SEC system with an on-line viscometer provides a simple
and economical way of adding absolute molecular weight determination to
the system.
56
REFERENCES
[1] Kratochvil,P., Classical light scattering from polymer solutions, Elsevier,
Amsterdam 1987.
[2] Ouano, A.C., and W.J. Kaye, J. Polym. Sci., Part A-l, 12 : 1151 (1974)
[3] Wyatt, P.J., C. Jackson and G.K. Wyatt, Am. Lab., 20(5), 86 (1988),
Am. Lab., 20(6) 108 (1988).
[4] Jones, R., G. Dollinger, R. Cunico, and M. Kunitani, poster presentation
at Pittsburgh Conference, Chicago, March 4-8, 1991.
[5] Jackson, C., Barth, H.G., and Yau, W.W., Waters' International GPC
Symposium Proceedings 1991.
[6] Rory, P.J., Principles of polymer chemistry, Cornell University Press,
Ithaca, New York 1953 Ch. 7.
[7] Ptitsyn, O.B., and Y.E. Eizner, Sov. Phys. Tech. Phys. 4, 1020 (1960)
[8] Tanford, C.C., Physical chemistry of macromolecules, Wiley, New York
1961.
[9] Davidson, N.S., LJ. Fetters, W.G. Funk, N. Hadjichristidis, and W.W.
Graesley, Macromolecules, 20, 2614 (1987)
[10] Brandrup, J., and E.H. Immergut, eds., Polymer Handbook, 3rd ed.,
Wiley, New York 1989.
[11] W.H. Stockmayer, personal communication.
TABLE I
Evaluation of Algorithm for Molecular Weight Determination by
RALS with Asymmetry Correction
Literaturevalues
MW
Rg
[11]
(g/mol)
(nm) (dl/g)
Calculatedvalues
P(90°) MW
%
(g/tool) difference
Random coil molecules
Polystyrene
51,000
8
0.29
0.98
51,000
0%
Polystyrene
(e conditions)
420,000
19
0.52
0.95
415,000
-1%
Poly(methyl
methacrylate)
680,000
36
1.34 0.70
682,000
0%
Polyisoprene
-70% cis
940,000
48
4.6
945,000
0%
3
0.036 1.00
66,000
0%
12
0.034 0.98
11,200,000
+ 5%
0.56
Spherical molecules
Bovineserum
albumin
Bushy stunt virus
66,000
10,700,000
Rod-shsped molecules
Poly-_-benzyl
-L-glutamate
130,000
26
1.25 0.91
125,000
- 4%
Myosin
493,000
47
2.17
0.74
425,000
- 14%
DNA
4,000,000
117
50
0.35
5,600,000
+ 40%
58
FIGURE 1.
Debye plot of reduced Rayleigh ratio as a function of angle.
Solvent.__
Reservoir
I
0.2p Filter
Injection
Valve
SEC
Columns
Pump
Refractometer
Viscometer
LS Detector
_o,,,.to
1 I I
I I
,,ow
Solvent
Detector
Output
FIGURE 2.
i 1
Computer for Data
Acquisition and Analysis
Schematic of the SEC-Visc-LS instrument.
59
LO0• 0
LS-VIS RADIUSOF GYRATION
t0.0
/
i,_._
_
/
•
/
_
-
X
\
\
,.'_. ".'."
..:... _:
. _"
"__,
i. 000
I
2i
i9
I
23
I
25
I
27
I
29
I
3i
ELUTZON VOLUHE
FIGURE 3.
Radius of gyration as a function of elution volume for
polystyrene 706 measured by SEC-Visc-RALS and SECMALLS. The concentration profile of the sample is also shown.
LSASYMMETRYCORRECTEDMW
REFRACTOMI=/_-H
ixi0=6
-
J
5"
INmAL MWESTIMATE
txtO*5,,._,
.-.
...t
: ;: • • 2,:4,:.
ixt0"4
" ...... ,_..,,-.
• .'_.
. ..?- ; "..
_;._'.-.::.'.
...
1000
FIGURE 4.
1
10
i
t2
i
t4
. .
J
i6
Initial molecular weight (MW) values, calculated form the 90 °
scattering, and asymmetry corrected MW values, as a function
of elution volume for polystyrene 706• Note the increasing
asymmetry correction with increasing MW.
6O
.
__ -$
tx10_6
,._
..
ix10"5
MALLS MW
VISC-RALS
_000.
I
2!
t9
I
23
MW
I
25
I
27
ELUTION
FIGURE 5.
=
" 3!
VOLUME
Molecular weight values measured by SEC-MALLS and SECVisc-RALS for polystyrene 706. Note the close agreement for
all MW fractions. (The results are slightly offset for illustrative
_.oo
purposes),
o_,,_
_"
=
29
oU__CHROHATOGRAH
REFRACTOMETER
RALS . _""_
I
_..00
e_
J
•000 _L
t4.0
:
FIGURE 6.
--:
I •
_.7.0
"
I ".--"-_
: ' :
;20.0
:
:
23.0
: "
:
:
26.0
.
,
:
29.0
RETV0L(_}
RALS and RI chromatograms for 10,000 g/mol PEO standard.
61
VISCOTEK
CORP.
UCAL3._1
F'_.LENJO_E:
RUN i_
Trr_O-A
_
031_191it:31
30On=3 ¢o15
6.00
DUALC_OMATOBRAM
6.00
REFRACTOMETER
4:00
Z
--).
.--J
UJ
CC
2.00
"_
!
_
•000
14.0
_
17.0
_
_
20.0
_
23.0
26.0
29.0
BETVOL (ml)
FIGURE 7.
PALS and RI chromatograms for T-500 dextran. Note the
shoulder on the left-hand-side of the LS trace.
62
_"
:+
SEC-Visc-LS
s,,,-=
DETECTOR
Branching
SIGNALS
w
0,0
Report
MARK-HOUWINK
PLOT
I0
RALS
VISC
..
{
LINEAR
POLYMER
///:
._.-I
4.0
i
30
i
40
_
*
M
N
=
."
.-:"
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,' .'BRANCHED POLYMER
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issr4
i
I=111
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..
smlo'l
lespt
BRANCHING
FACTOR
sJ
Sample File
Samcle lO :
Contro2 File
Control IO :
8ranching
: ti-tGa._4
B_anched Polymer
: tJ-18a.,5
Linear Polymer
factor
g"
=
s.o
to
0.60
;-
..
%°
11.4
IJ
O.II
ulr4
--in
.rl
llillP
FIGURE 8.
Branching report showing the branching factor, g', as a
functionof molecularweightmeasuredusingSEC-Visc-RALS.
The Mark-Houwinkplotforthelinearcounterpartisalsoshown
in the top rightbox.
i
63
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