1. Research Article Applied Optics 1
Multi-angle laser light scattering: determining the
molecular weight of polymers
TYLER PETERSON1,* AND QIANTING CHEN1,*
1Applied Optics Track, Graduate Internship Program, University of Oregon, 1252 University of Oregon, Eugene OR 97403
*Corresponding authors: tbp@uoregon.edu; qchen3@uoregon.edu
Compiled September 7, 2015
Molecular weight and size, or radius of gyration, are two properties that are commonly used to charac-
terize polymers. Static light scattering analysis is an absolute method to obtain these measurements. In
this experiment, two polystyrene standard solutions were examined, having molecular weights of 382,000
g/mol and 891,000 g/mol, using a Wyatt Dawn Enhanced Optical System. The measured molecular weights
were 388,300±16,500 g/mol and 915,300±44,800 g/mol, both within 2.7% of the known values.
OCIS codes: (290.5820) Scattering measurements
Polymers are macromolecules whose chemical structures
are composed of repeating units. The ability to specifically
arrange these repeat units allows for the optimization of a given
polymer material for an array of purposes. As early as 1600
B.C.E., ancient Mesoamerican civilizations had unintentionally
discovered the wide range of applications polymer materials
have. Rubber balls were used often for sporting events, liquid
rubber was used for writing and painting, and rubber bands
were used to fasten stone ax heads to wooden handles. Chemical
analysis of these materials has shown the main ingredients to
be latex acquired from the Castilla elastica tree and juice from
Ipomoea alba, a species of morning glory vine. On its own,
latex becomes too brittle to retain its shape upon drying, but
the Mesoamerican peoples discovered that the added juice
counteracted this material shortcoming. Modern mechanical
analysis has shown increased strength and elasticity in these
items as a result of the purification of latex, a natural polymer,
within the material [1].
The first instance of a more controlled approach to manu-
facturing polymers came in 1841, when Charles Goodyear’s
process of vulcanization was successfully implemented [2].
The idea came to Goodyear after accidentally bringing a
rubber sample into contact with a hot stove and observing
a charring effect similar to leather, which inspired him to
investigate the effect of heat on similar compounds [4]. The
crosslinking induced by the addition of sulfur atoms to polymer
backbone chains through the vulcanization process yields
enhanced modulus of elasticity, tensile strength, and resistance
to degradation by oxidation [5]. Wide scale production of
polymer materials did not really take off, however, until 1910,
when Leo H. Baekeland invented Bakelite, a combination of
phenol and formaldehyde that could be thermoset to hold any
form. The increased applicability inspired Baekeland to market
his product as the “Material of a thousand Uses” [6]. While
Bakelite eventually fell from the spotlight as the material of
choice, Baekeland is still considered the true father of synthetic
plastics. In today’s world, countless products are made from
polymer materials. Possibly the largest number of them fall
into the category of plastics, having a large variety of different
property combinations. Plastics are found everywhere, from
polycarbonate safety helmets and photographic film, to acrylic
aircraft enclosures. Elastomers, or rubbers, are polymers that
have a characteristic elasticity, or the ability to be deformed
drastically and spring back to their original form. Fibers are the
third major category of polymers, describing materials that can
be drawn into very long filaments which are typically used in
the textile industry for the manufacturing of clothing [5].
The microstructure of polymers is what determines the
macroscopic behavior of synthesized materials. The ability to
finely adjust this microstructure is what allows engineers to
design materials for very specific purposes, but it is important to
ensure that the synthesized polymer has the intended properties.
During the polymerization process, molecules can form very
short or long polymer chains, so the molecular weight is a
good starting point for characterization. For example, tensile
strength, elasticity, resistance to deformation, and many other
mechanical properties are dependent on molecular weight, so
its accurate determination can be crucial in the engineering
process [7]. Static light scattering is one technique through
which this property may be determined, and is the focus of this
study. Polymer molecules, when mixed in a solution that is
illuminated by a laser, will gain an induced dipole moment and
begin to emit light through a process known as scattering. In
static light scattering, this emitted light is collected at a range of

2. Research Article Applied Optics 2
angles and analyzed to determine the average radius of gyration
and weight average molar mass of the molecules.
When light interacts with matter, five different phenomena
take place, depending the size of that matter: absorption,
reflection, diffraction, refraction, and scattering [8]. When
considering matter on the scale of polymer macromolecules,
scattering effects dominate these interactions. Observing the
resultant scattering patterns can be very indicative of the size
and structure of macromolecules, as described by the measured
values for both the weight average molecular weight and the
RMS radius of gyration [9].
Light scattering is a process by which electromagnetic
waves incident on a material induce electron oscillations within
that material, which then act as independent emitters of light.
Because the induced electron oscillations are dependent on
the frequency of the incident waves, the emitted light will
have that same frequency. In addition, this scattering is elastic,
so no absorption takes place. Such behavior is known as
Rayleigh scattering, and is taken advantage of heavily in the
characterization of polymers [10].
The intensity of scattered light is a good measure to use for
experimentally determining the molecular weight of polymer
macromolecules [3]. When a laser is incident upon multiple,
unconnected molecules, the induced oscillations will not
necessarily be in phase, resulting in incoherent scattered light,
which reduces the intensity. With increased molecular weight,
however, these molecules will be chained together to form larger
polymers. This forces all of the charge within the polymer to
subsequently oscillate in phase, thus providing a more intense
scattered beam [15].
The architecture of the polymer can be implied from the
angular dependence of the intensity of scattered light. Because
the individual monomers will act as emitters of light, an interfer-
ence pattern will manifest from the polymer as a whole [15]. By
collecting light at multiple angles, this angular dependence may
be observed. Both the weight average molecular weight and
RMS radius of gyration can be obtained by constructing a Zimm
plot. Zimm plots are created using the following equation [13]:
Rθ
K∗c
= MP(θ) − 2A2cM2
P2
(θ) (1)
Where c is the concentration of the solute molecules in the
solvent (g/mL), M is the weight average molar mass (g/mol),
A2 is the second virial coefficient (mol mL / g2) (a measure of
how good the polymer-solvent relationship is), P(θ) is a form
factor dependent on the size and shape of the polymer, and the
Rayleigh ratio, Rθ, which is defined by [13]:
Rθ = Nθ ACSCC(
Vθ − Vθ,baseline
Vlaser − Vlaser,dark
) (2)
Where ACSCC is defined as the configuration specific
calibration constant. This constant depends on the type of
solvent and flow cell being used, whose determination will be
described shortly. Vθ, Vθ,baseline, Vlaser, and Vlaser,dark relate to
voltages output by photodetectors at different angles with the
laser turned on and turned off, which will be elaborated on in
the section regarding calibration. The Zimm equation is also
dependent on the optical constant, K*, which is defined by [13]:
K∗
=
4π2n2
0(dn
dc )2
λ2
0NA
(3)
Where dn/dc is the relative change in index of refraction
with respect to the change in solution concentration, λ0 is the
wavelength of incident light, NA is Avogadro’s number, and n0
is the index of refraction of the solvent in vacuum.
While there are many different fits to characterize light
scattering patterns, such as the Debye, Berry, and Random Coil
fits, the Zimm fit is the most accurate for particles whose radius
is between 20 – 50 nm. The polystyrene standards used in this
experiment fell in this size range, so the other fits are out of the
scope of this report.
A Wyatt DAWN Enhanced Optical System (EOS) is the
multi-angle static light scattering instrument that was used to
run the experiment. The sample under consideration is pumped
into a flow cell contained within the instrument from a glass
syringe using an infusion pump. A laser of wavelength 780.88
nm, as measured by a spectrometer, illuminates the sample.
The emitted light from this process is collected by 18 hybrid
transimpedance photodetectors surrounding the sample, which
convert the scattered light intensity into voltages that may be
analyzed.
ASTRA 4.90, provided by Wyatt Technology, was the
software used to collect and analyze data from the DAWN EOS.
Four main steps are taken to obtain molecular weight, radius
of gyration, and second virial coefficient information. First,
the instrument must be calibrated in order to determine the
Rayleigh ratio. A beam splitter placed before the sample yields
the incident light intensity, which is then compared against the
scattered intensities. To correct for ambient light, the laser is
then turned off and the voltages measured by the photodetectors
are used to determine the dark offset, which will be subtracted
from final measurements. Once this is complete, a normalization
is carried out to ensure the detectors are operating properly
in conjunction with each other. A low molecular weight, high
concentration polymer solution is injected into the flow cell.
The solvent in this step must be the same solvent that will be
used to mix solutions for analysis. A low molecular weight
polymer must be used to ensure that it will scatter isotropically,
which will be the case for any molecule with a radius below
10 nm [13]. The geometry of the flow cell is such that each
detector is aligned to view a different scattering volume, which
is defined as the intersection between an incident beam of light
and the scattered beam of light. Because scattered intensity is
proportional to the scattering volume, each detector will report
a slightly different voltage. This, along with refraction effects,
is accounted for by a set of normalization coefficients for the
detectors produced by the normalization collection. After the
detectors have been calibrated and normalized, the instrument
is ready to collect data on the sample under consideration.

3. Research Article Applied Optics 3
A higher molecular weight polymer solution is mixed at a
number of different concentrations, which are introduced to
the system from highest to lowest concentration. A collection
is run on each concentration, resulting in a step-like total data
collection. This information is then converted into a Zimm
plot by entering the concentrations into the software. Once
these four steps have been completed, the calculated molecular
weight, RMS radius of gyration, and second virial coefficient
for the polymer is output. To yield the best results, a number of
measurements must be taken to minimize error.
Cleanliness is incredibly important in light scattering mea-
surements. The scattered intensity of a particle is proportional
to the sixth power of its radius, so any excess particulates in
the solution will nullify a data collection. To avoid this, an
acid-base wash was carried out for all scintillation vials used
to mix solutions. In addition, solvents were filtered before
solution mixing, and mixed solutions were filtered out of the
syringe immediately prior to entering the DAWN EOS. Also
important is the degree to which the concentrations of mixed
solutions are known. To ensure optimal accuracy in this regard,
all solutions should be weighed out by mass on an analytical
balance. Vibrations in the system will produce inconsistent
scattered intensities, so measurements should be carried out in
isolation from other scientists working in the same laboratory.
Samples, once injected, should be allowed to settle for sufficient
time for similar reasons. A sample was considered to be fully
settled when fluctuations in the 90 ◦ detector output voltage fell
below 0.02 V. Finally, the laser must be allowed adequate time to
reach thermal equilibrium. This was observed to take between
two to three hours, as determined by the signal stability in
measurements.
The experiment measured a polystyrene standard with
a molecular weight of 382,000 g/mol. We measured two
concentrations, 0.106 mg/mL and 0.479 mg/mL. The Zimm
plot in Fig. 1 reported the light scattering molecular weight of
this sample to be 388,300±16,500 g/mol, an error of 1.6% from
the known value. The radius of gyration was reported to be 0
nm for this solution, which we predict is due to errors in the
calibration and normalization constants.
Fig. 1. The Zimm plot of a polystyrene standard with molecu-
lar weight of 382,000 g/mol.
To check the reproducibility of our experiment, another
measurement was performed with a polystyrene standard
having molecular weight of 891,000 g/mol. We measured
two concentrations again, 0.101 mg/mL and 0.248 mg/mL.
The Zimm plot in Fig. 2 reported the molecular weight of this
sample to be 915,300±44,800 g/mol, an error of 2.7% from the
known value. The radius of gyration for this polymer solution
was reported to be 33.5±3.8 nm.
Fig. 2. The Zimm plot of a polystyrene standard with molecu-
lar weight of 891,000 g/mol.
The molecular weight of a polymer is an integral property
in determining how a material made from that polymer will
behave on a macroscopic scale. Therefore, being able to
measure it with high levels of accuracy is essential to ensure the
engineered material will perform as expected. Examining how
the polymer scatters light when illuminated by a laser is one
way to determine its molecular weight, as well as its molecular
architecture via the radius of gyration. A Wyatt DAWN EOS
static light scattering instrument was utilized to carry out
measurements on various polystyrene solutions, using toluene
as the solvent. Molecular weights were determined to within 3%
of the known values for two different polystyrene standards.
The immediate future direction of this experiment will
include further data collection on known polymer standards to
solidify reproducible procedural methods. A gel permeation
chromatography instrument will then be integrated in-line with
the DAWN EOS to reduce polydispersity in the samples yield
more accurate weight average molecular weights and radii of
gyration. Once a consistent procedure has been demonstrated,
the experimental setup will be used in collaboration with
polymer chemists and chemical engineers to test unknown
polymer and nanoparticle solutions for industry applications.
ACKNOWLEDGMENTS
We would like to acknowledge Dr. Chartoff and Dr. Check from
the University of Oregon Polymer Characterization Laboratory
for allowing access to their facilities for the duration of this
experiment, as well as for providing guidance along the way.
Chris Lundeen and Matthew Williams are polymer chemistry
students who collaborated on this project, lending chemistry-
specific advice and perspective the whole way through. Finally,
Dr. Nima Dinyari for establishing the collaboration between
the Optics and Polymer programs that allowed this project to
take place, in addition to acting as a mentor throughout the
experiment.

4. Research Article Applied Optics 4
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