# Enhance Your Polymer Analysis With Light Scattering

Whitepaper

Published: July 18, 2023

Static and dynamic light scattering (SLS/DLS) are powerful and robust tools for obtaining information about the molar mass, size and topology of biomolecules.

This whitepaper highlights how coupling light scattering techniques with size exclusion chromatography (SEC) can enhance polymer analysis and drive advancements in biopharma research.

**Download this whitepaper to discover:**

- Theoretical and practical considerations of light scattering in biopharma
- How to ensure robust quality control of complex polymer samples
- How to enhance real-time monitoring of biomolecules under physical conditions

White Paper
Author
Moritz Susewind
Agilent Technologies, Inc.
Introduction
Detection based on the principle of light scattering with size exclusion
chromatography (SEC) is a powerful technique to identify molar mass and
size distributions of synthetic polymers such as polystyrene (PS), polymethyl
methacrylate (PMMA), polycarbonate (PC), and biopolymers. Especially the latter
has received increased attention recently in the biopharmaceutical industry with
applications including bioconjugates, proteins, monoclonal antibodies (mAbs),
mRNA1
, viruses (adeno-associated viruses, AAVs), extracellular vesicles (EVs), and
liposomal nanoparticles (LNPs).
Light Scattering and Size Exclusion
Chromatography (SEC) in Biopharma
2
SEC in biopolymer analyses
What is the reason to use SEC as a measure to fractionate
complex polymer samples? Analysis based on SEC can both
identify and quantify higher aggregates of biomolecules,
of which further analyses can be done by elaborate light
scattering equipment. With that information, quality control of
biomolecules, including applications such as drug-to-antibody
ratio (DAR) analysis of antibody drug conjugates (ADCs), can
be done.2
The strategy, to first separate molecules by size
and then to analyze those single size fractions, leads to more
precise results than measurements in batch.
Use of calibrants for determination of molecular weights
in SEC
As SEC is a relative method in determination of molecular
weight, calibration of the chromatographic columns is
normally done with analytical standards consisting of
narrowly distributed polymers, which are available for a
broad range of analyte classes.3
Despite the universal
applicability, a major drawback of this method is the lack of
the primary information about size of the original molecules
under investigation and, if a standard matching the polymer
class is unavailable, accurate molar mass determination is
not available.
Light scattering for direct measurement of
physicochemical parameters
To circumvent the use of calibrants, analytical scientists
rely on light scattering detectors to not only determine the
weight average of molar mass (Mw) directly without needing
to calibrate the chromatographic column, but also to obtain
information about molecular size. The latter can be deduced
in static light scattering (SLS) by the radius of gyration Rg
and in dynamic light scattering (DLS) by the hydrodynamic
radius RH of the analytes. Also, based on the ratio of the two
size expressions, it is possible to deduce the topology of the
molecules, that is, if the polymer or polymer aggregate adapts
the morphology of a homogeneous sphere, a hollow sphere,
a random polymer coil, or something else.4
Alternatively,
this topological information can also be extracted either by
viscometry and a Mark-Houwink plot5
or by the Rg
-M relation,
which is analogous to the Mark-Houwink plot. Here, it can be
stated that DLS provides a more robust and easy-to-handle
system. It is important to note that both techniques,
multi-angle (20-angle) static light scattering and DLS, can be
implemented simultaneously in SEC by consecutive coupling.
Theoretical and practical considerations
of light scattering in biopharma
In this white paper, some theoretical and practical background
paired with selected examples from biopharma is shown to
exemplify the tremendous potential of light scattering as a
detection method in SEC. Using light scattering, molar mass,
size, and conformation of fractionated biomolecules under
physiological conditions can be monitored online.
Static light scattering (SLS) in SEC
When incident light scatters with soft matter quasi-elastically
(see Figure 1), the scattered light intensity is proportional to
the weight average of molar mass Mw, the concentration c,
and the scattering contrast factor K. The latter is the product
of a constant (4π2
)⁄NL
, the refractive index of the solvent
n0
2
, the refractive index increment of the polymer in solution
(δnp
⁄δc)2
, and the wavelength of the incident laser light λ–4.
This applied to the screening of polymer-solvent interactions,
referring to this fundamental equation (Equation 1) with A2
,
the second virial coefficient, it can easily be shown that by the
sum of all scattering components it is possible to attain the
weight average of molar mass Mw.
Kc 1 = + 2A2
c Rθ M
Equation 1.
Scattering
volume
Laser
Detector
Polarization
Scattering
angle
Figure 1. Scheme of a classical light scattering setup with scattering angle θ.
3
This simple term is only valid for isotropic scatterers (Rayleigh
scattering). If molecules become larger than d >λ⁄20,
interference of scattered light from more than a single
scattering center lets us introduce the particle form factor
P(q). This means that the scattered light intensity becomes
angle-dependent (see Figure 2).
Pair-wise summation of all scattering centers and
introduction of a center of mass coordinate system leads us
to a series expansion (Equation 2), which can be terminated
for particles with a radius of gyration Rg
<50 nm.4
P(q) = 1 – + …
Rg
2 q2
3
Equation 2.
Replacing scattering vector q by the scattering angle θ and
introducing polymer-solvent interactions by the second virial
coefficient A2
, we end up with the final static light scattering
equation (Equation 3).
Rg
2
zsin2
( Kc 1 π θ 2 n0
2 16 = + 2A2 1 + ) c Rθ Mw λ 2 2 3 [ ]
Equation 3.
Double extrapolation of term Kc⁄Rθ versus θ & 0 and c &0
according to Zimm yields the inverse weight average of
molar mass. From the slope of Kc⁄Rθ versus θ, one gets the
z-average of the radius of gyration squared and from the
slope of the c-dependent linear extrapolation, the second
virial coefficient.
In practice, software like the Agilent WinGPC Software
is doing this analysis automatically for each slice in the
chromatographic elugram when a multi-angle light scattering
(MALS) detector has been used for data acquisition. So,
for each chromatographic slice, Mw and Rg
are determined
from the angle-dependent scattering intensity plot by
extrapolation of θ & 0. The reason for this limit is that
particle form factor P(q) & 1 means that scattering intensity
becomes independent of particle size and shape. It should
be mentioned though, that size determination is only valid
above a lower limit of Rg
>10 nm, and molecular weight can
also be determined for isotropic scatterers such as bovine
serum album (BSA), which is often used as an isotropic
standard molecule.
It is important to note that for polydisperse samples
consisting of Ni
species of molar mass Mi
, one gets the
z-average of the squared radius of gyration according to
Equation 4.6
∑i
wi
Mi
Rg
2
z= ∑i
wi
Mi Rg
2
i
Equation 4.
Thereby each species has its own mean squared radius of
gyration over all conformations.
Again, for practical purposes, software such as the WinGPC
Software automatically determines the conformational
averages Rg
2
i for each chromatographic slice, since
those can be considered as monodisperse. The overall
elugram average size is then the z-average of the squared
Figure 2. Scattering intensity distribution of an isotropic scatterer (A) and of a scattering molecule with d >λ/20 (B).
A B
4
radius of gyration. This size is considered from a center of
mass-based coordinate system according to Equation 5 and
naturally differs from the geometric or microscopic radius R.
Calculations of those can be found in literature.4
∑j
mj
Rg
2
i
=
∑j
mj
rj
2
Equation 5.
As mentioned before, series expansion of the particle form
factor and use of Guinier approximation 1⁄(1 – x) = 1 + x
in Equation 3 is only valid for qR <<1. For larger molecules,
solutions for the particle form factor depend on their particle
topology. For example, scattering intensity of homogeneous
spherical particles possess local minima and maxima,
depending on the scattering angle according to Equation 6.4
9 P(q) = 2
sin(qR) – qRcos(qR) (qR)6 [ ]
Equation 6.
To become independent of the particle form factor P(q), the
scattering intensity is extrapolated versus q & 0, where the
particle form factor equals 1.
Agilent InfinityLab GPC/SEC Solutions, including data
acquisition by the Agilent 1260 Infinity II Multi-Angle Light
Scattering Detector run with WinGPC Software, can do this
extrapolation precisely, as 20 scattering angle plots can be
acquired and then processed.
Further, the range of scattering angles is of great importance.
Since the q-vector scales as an inverse length scale,
resolution becomes better at higher angles and more
details such as conformational changes are seen. In
contrast, a more reliable mass information (a particle form
factor-independent scattering intensity) is given at small
angles in good approximation. The 1260 Infinity II Multi-Angle
Light Scattering Detector spans a wide range of 20 angles
from 12° up to 164°. Especially in the small angle region, the
1260 Infinity II Multi-Angle Light Scattering Detector offers
three more angles of 12°, 20°, and 28°, making molar mass
determination more accurate.
An issue faced with some light scattering detector types
is the cell design, resulting in correction terms due to
changing refractive indices at the liquid/glass interface. In
the 1260 Infinity II Multi-Angle Light Scattering Detector, this
is circumvented by placing the photodiodes planar on the
cylindrical glass cell, so that the detector angle equals the
scattering angle. Further, by the design of the cell, scattering
contributions from contaminations such as dust are reduced,
making the signals less noisy. With a red wavelength 660 nm
120 mW laser diode, the detector also has enough power
for weakly scattering samples. Figure 3 shows the LS trace
chromatogram of the monoclonal antibody bevacizumab
primary structure on a mAb SiO2
3 µm analytical column in
PBS buffer. The results of the corresponding slice-wise Zimm
plots given by 20 angles for each chromatographic slice yields
the molar mass fit given in Figure 4. By this technique, it is
possible to deduce the true molar mass of 147 kDa with only
approximately a 1% deviation from the literature.7
The radius
of gyration for the primary structure of bevacizumab yields
Rg z = 11 nm.
2.6 2.8 3.0 3.2 3.4
Ve
(mL)
RID signal
SLS 12° SLS 20° SLS 28° SLS 36° SLS 44° SLS 52° SLS 60° SLS 68° SLS 76° SLS 84° SLS 90° SLS 100°
SLS 108°
SLS 116°
SLS 124°
SLS 132°
SLS 140°
SLS 148°
SLS 156°
SLS 164°
SLS signal
Figure 3. Light scattering intensities of 20 angles of 5 g/L bevacizumab on a
mAb SiO2
3 µm microbore column in 34 mM PBS + 0.3 M NaCl.
2.7 2.8 2.9 3.0 3.1 3.2
102
103
104
105
106
107
Ve
(mL)
RID signal
Mw (g/mol)
Figure 4. Molar mass fit of bevacizumab elugram from light scattering
detector with Mw = 147 kDa.
5
Dynamic light scattering (DLS) in SEC
For molecules ranging from 1 nm up to micrometers in size,
dynamic light scattering (DLS) can also be a good choice for
size determination. Generally, DLS spans a much wider range
in size determination than SLS from a few nanometers to
the micrometer scale. The sizes (the hydrodynamic radius
RH) are calculated from the diffusion coefficient D of the
molecule due to its Brownian motion. RH is then given by the
Stokes-Einstein equation (Equation 7).
D =
kT
6πηRH
Equation 7.
According to Einstein’s law of the movement of dispersed
particles in quiescent liquids, RH is considered the radius of
an equivalent sphere.8
In the simplest form for monodisperse
hard spheres, the diffusion coefficient D is part of a relaxation
time τ = 1⁄Dq2
with the scattering vector q of a normalized
single-exponential decaying function g1
(t), which is given
by comparing two scattering intensities each after certain
incremental time intervals Δt respectively, which are averaged
over the whole correlator run time for each correlator channel
according to Equation 8 with A the baseline (the scattering
intensity correlation for t & ∞, I(q,t) 2
).4,6
g2
(t) – 1 = = g1
(t)2
= exp(–2t/τ) I(q,t)I(q,t + Δt – A
A
Equation 8.
The rightmost term of Equation 8 is also called dynamic
structure factor squared. Figure 5 shows the normalized
autocorrelation function of an SEC-fractionated
immunoglobulin G (IgG) primary structure with RH = 6 nm and
a higher associate of RH = 11 nm.
10–3 10–2 10–1 100 101 102
0
0.5
1.0
g1(t)
t [ms]
Slow mode RH = 11 nm
Fast mode RH = 6 nm
Bi-exponential fit function
Figure 5. Single autocorrelation functions of SEC-separated IgG fractions of
RH = 6 nm (fast mode) and RH = 11 nm (slow mode).
As mentioned earlier, this simple equation is only valid
for monodisperse hard spheres. For nonmonodisperse or
nonspherical polymers9,10, the dynamic structure factor can
be expressed as the sum of single mono-exponential decay
functions i, weighted by its scattering intensity contribution,
which depends on the particle number density ni
, molar mass
Mi
, and particle form factor Pi
(q),4
so one gets Equation 9.1
g1
(t) = ∑i
ni
Mi
2
Pi
(q)g1,i(t)
∑i
ni
Mi
2
Pi
(q)
Equation 9.
For simplicity, one can rewrite the equation as shown in
Equation 10.6
g1
(t) =∑ m
i = 1 ai
exp(–t)⁄τi
)
Equation 10.
Equation 10 can be solved in the form of a series expansion
taking logarithm of g1
(t) with the first cumulant being the
average diffusion coefficient at a fixed scattering vector.4
For most broad monomodal correlation functions, a
bi-exponential fitting approach with m = 2 is fully sufficient.1
Since for each molar mass Mi
we find a diffusion coefficient
Di
, the average diffusion coefficient can be defined as shown
in Equation 11.
= ∑i
ni
Mi
2
Pi
(q) Di
∑i
ni
Mi
2
Pi
(q)
Dapp(q)
Equation 11.
6
Since for polydisperse samples the dynamic structure
factor g1
(t) as well as the apparent diffusion coefficient
Dapp(q) become q-dependent due to polydispersity or internal
segmental or rotational modes of motion, Dapp(q) must be
extrapolated for q & 0. In this limit, the apparent diffusion
coefficient becomes a z-average according to Equation
12,1
where the particle form factor also equals Pi
(q) = 1 and
neither segment fluctuations nor rotational terms must
be considered.
= ∑i
ni
Mi
2
Di
lim ∑i
ni
Mi
D z Dapp 2 (q) q & 0
=
Equation 12.
According to Stokes-Einstein, we get the z-average of the
inverse hydrodynamic radius RH z
–1 . The angular dependency
of the diffusion coefficient becomes relevant for particles
larger than RH >20 nm.1
Most particle sizers that can be used
as online instruments are designed as single angle machines
(sla-DLS). Typically, correlation is performed on the 90° static
light scattering signal. Since in SEC molecules are separated
by size, a mono-exponential decay function can be assumed
for each slice. Nevertheless, the scattering contribution of
segmental or rotational modes of motion can also become
relevant for isotropic flexible polymers or anisotropic particles
larger than 20 nm. Only at small qR-regimes, those terms can
be neglected. One option to circumvent this problem is to
measure at low scattering angle, for instance θ = 15°, where
one gets true molar masses and diffusion coefficients. In
the presence of larger particle fractions, which in SEC can
sometimes be caused by column bleeding or dust particles,
smaller fractions are unseen due to the molar mass weighted
scattering intensity. With increasing scattering angle, particle
form factor may decay first for larger particles, so that the
scattering contribution decreases in favor of smaller particle
fractions. The dual angle dynamic light scattering detector
(LSD) (θ = 15° and 90°) offered with the Agilent 1260 Infinity II
Bio-SEC Multidetector System takes θ = 90° as a good
compromise for collecting correlation data. The results for
that correlation hold true with only moderate deviation for
flexible biomolecules in size range of RH <40 nm or hard
spheres independent of size.1
It is important to note that dynamic light scattering yields
diffusion coefficients from which sizes are calculated. It
provides no information about molar mass—this is only done
by static light scattering.
Often, biomolecules, including LNP, are more heterogeneous
and larger in size, so angular dependency arises. For those
molecules, only apparent diffusion coefficients are available,
which are larger than the true z-average, that is, molecules
are underestimated in size. This fact must be considered
in the size determination of bigger molecules, even when
monodispersity due to SEC separation is assumed. Figure 6
shows the 90° light scattering detector signal (purple curve)
of bovine serum albumin (BSA), which forms aggregates in
50 mM PBS buffer solution at pH = 7.4.
8 9 10 11
SLS 90° signal
VWD 290 nm
Detector signal
0
2
4
6
8
10
RH (nm)
Ve
(mL)
Figure 6. Chromatogram of partially associated bovine serum albumin (BSA)
revealed by dynamic light scattering (turquoise curve), UV-Vis signal 280 nm
(red curve), and light scattering signal 90° (purple curve).
An advantage for LS is the sensitivity of light scattering
detectors compared to UV-Vis detectors due to the molar
mass dependency of the scattering intensity.
The primary structure of BSA has a size of RH ~4 nm and the
associate a size of RH ~8 nm, which has been resolved on an
Agilent PROTEEMA 300 Å, 5 µm analytical column in 50 mM
PBS buffer. This molecule is considered to be an isotropic
scatterer and cannot be conclusively size determined by
static light scattering.
Another example is the separation and size determination
of higher associates of immunoglobulin G (IgG) from the
primary structure (RH = 5.5 nm) on a mAb SiO2
3 µm analytical
column. Shown in Figure 7, the RH curve (turquoise curve)
adapts an exponential decaying function over the elution
volume Ve
, which is in good agreement with theory.11
The relative stronger intensity of the 15° LS signal of
the higher associate of IgG (RH ~8 nm) in relation to the
concentration detector signal is again due to its higher mass
contribution. Note that the turquoise curve in Figure 7 is not
an intensity curve, but the calculated hydrodynamic radius of
the autocorrelator.
7
5.5 6.0 6.5 7.0 7.5
UV detector signal 265 nm
SLS signal 15°
Hypothetical exponential fit
4
6
8
10
12
RH (min)
Ve
(mL)
Figure 7. Chromatogram of IgG on a SiO2
3 µm analytical column in 34 mM
phosphate buffer pH = 6.6 + 0.5 M NaCl with UV signal (red), LS 15° signal
(green), and hypothetical exponential fit (gray).
It should be mentioned here that by combination of static
and dynamic light scattering, the topology of molecules can
be determined by the empirical dimensionless parameter ρ
(Equation 13), adapting ρ = 0.8 for homogeneous spheres and
ρ = 1.5 for random polymer coils.4
ρ =
Rg
RH
Equation 13.
This topological information can also be extracted online.
Figure 8 shows the chromatogram of thyroglobulin in 10 mM
PBS buffer at pH = 7.4. For this measurement, a concentration
detector (VWD) was combined with the 20-angle 1260
Infinity II Multi-Angle Light Scattering Detector and a
dynamic light scattering detector (the 1260 Infinity II Bio-SEC
Multidetector System). The higher molar mass fractions of
associated thyroglobulin at lower elution volume are more
pronounced in the light scattering signal due to molar mass
dependency. The radius of gyration for each slice in the
chromatogram was detected by a 20-angle Zimm plot at a
known concentration each. That is why the Rg
plot is limited
to the range where the intensity of the concentration detector
is high enough, despite a strong light scattering signal. In
contrast, the reliability of the hydrodynamic results is better
for a higher dilution of an undisturbed diffusion process. The
RH plot spans a much broader range due to independency
of the concentration signal at lower elution volumes and a
clearly extended size range to smaller sizes at higher elution
volumes. For the primary structure of thyroglobulin, one gets
Rg
= 12 nm and RH = 9 nm, for the higher associate Rg
= 16 nm
and RH = 14 nm. By combining both curves (Rg
/RH), changes
in topology can be detected along the chromatogram
(ρ-ratio, blue curve). In the context of SEC, DLS provides a
robust and easy alternative to calibrate the column system
universally by plotting log VH versus elution volume Ve
, which
should be a universal linear decaying function independent
of the respective polymer-solvent combination.4
The only
prerequisite is a nonenthalpic SEC separation mechanism.
Ve
(mL)
7 8 9 10
VWD 280 nm/ MALS 90°
0.1
1
10
100
Rg
RH
ρ-ratio
Size (nm)
Figure 8. Chromatogram of thyroglobulin on an Agilent PROTEEMA 300 Å,
5 µm analytical column in 10 mM PBS pH = 7.4 equipped with static and
dynamic light scattering detectors.
Conclusion
Light scattering technique, static (SLS) and dynamic (DLS)
or the combination of both, is a powerful and robust tool
to get information about molar mass, size, and topology of
any biomolecule of interest. Following size separation by
SEC, size fractions can be measured individually, making a
precise analysis of the respective biological sample possible.
By the 20 angles of the Agilent 1260 Infinity II Multi-Angle
Light Scattering Detector, a precise extrapolation towards
zero scattering angle is possible, yielding an exact weight
average of molar mass and the radius of gyration. By these
data (molar mass and radius of gyration), the topology of the
molecule can also be analyzed by plotting the logarithm of the
radius of gyration versus logarithm of molar mass and getting
the topology by the slope in analogy to the Mark-Houwink
plot. In Agilent WinGPC Software, it is possible to implement
an extra dynamic light scatterer, the Agilent 1260 Infinity II
Bio-SEC Multidetector System, to monitor the sizes of the
sample fractions. One of the unique strengths of dynamic
light scattering in comparison to static light scattering is the
much broader size range from 1 to 2 nm up to micrometers
and the direct size information obtained in the software.
By the combination of the sizes from static and dynamic
www.agilent.com
RA45065.4247800926
This information is subject to change without notice.
© Agilent Technologies, Inc. 2023
Printed in the USA, May 30, 2023
5994-6110EN
light scattering, one can also conclude the topology of the
biomolecule associates. Concluding, all this is easily done in
a straightforward and precise way only by SEC with the right
choice of detector.
References
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Particle Sizing by Dynamic Light Scattering. Biomaterials
2016, 98, 79–91.
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Drug-to-Antibody Ratio (DAR) Analysis of Antibody Drug
Conjugates (ADCs). Agilent Technologies application note,
publication number 5994-0149EN, 2018.
3. Agilent GPC/SEC Standards home page. https://www.
agilent.com/en/product/gpc-sec-columns-standards/
gpc-sec-standards (accessed 2023).
4. Schärtl, W. Light Scattering from Polymer Solutions
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Heidelberg New York, 2007.
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Aflibercept and Bevacizumab Measured by TimeResolved Phosphorescence Anisotropy. Pharm. Res.
2016, 33, 2025–2032.
8. Einstein, A. Über die von der molekularkinetischen Theorie
der Wärme geforderte Bewegung von in ruhenden
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9. Borsali, R.; Nguyen, H.; Pecora, R. Small-Angle Neutron
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10. Lehner, D.; Lindner, H.; Glatter, O. Determination of the
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