Use of Light Scattering in First-Year Courses
The Physics Department's first-year and intermediate
seminars provide potential physics majors and other students
with an early opportunity to acquaint themselves with cutting
edge topics in physics. This year's focus is on biological
physics. In these courses, students learn about the role of
physical principles in the world of biology. We aim to
understand the elaborate machinery of a living cell and other
amazing biological systems in terms of structure, forces,
energy, and system design. We discuss topics in current research
on protein folding and nucleotide conformations, biopolymers,
biomembranes, membrane transport processes, diffusion of
molecules in liquids, chemical forces and self-assembly,
propagation of nerve impulses and briefly survey topics in
nanotechnology and soft materials. The courses are a combination
of lectures, discussion of assigned readings, small group
problem-solving sessions, demonstrations, and experimental work
with biophysical techniques.
The light scattering apparatus is used in experiments that test the
elementary concepts of probability theory, entropy, random
walks, fluid dynamics and Boltzmann statistics; these physical
concepts are particularly relevant in biological systems. Early
in the semester, the students perform basic experiments on ideal
gas law, osmosis across semi-permeable membranes, motion of
particles due to thermal fluctuations and drift under constant
force (e.g. electrophoretic mobility in electric fields and
sedimentation under gravity). Toward the end of the semester,
their experience culminates in performing experiments using the
state-of-the-art light scattering instrument to confirm some of
their previous results involving macroscopic variables (e.g.
temperature, pressure, viscosity, diffusion, etc.) with data
gained from measurements on microscopic scale (e.g. direct
measurement of size via scattering and diffusion constants via
photon counting).
In the first part of the experiment, students measure the size of latex
spheres in a colloidal solution by simple observation under a
microscope. Although they cannot resolve the nano-scaled size of
the spheres, they can see speckles of scattered (nanowatt) laser
light that passes through the solution. By recording the motion
of speckles with a camera, they can analyze the trajectory of
individual spheres and determine their diffusion constants from
the two-dimensional diffusion law: <∆r2> = 4Dt. Using
the Stoke’s formula, ζ = 6πηR, and the Einstein relation, ζD =
kT, they can calculate the sphere’s radius R (see
Handout). These
measurements setup the conceptual framework needed to understand
the basic physical principles behind the operation of the
dynamic light scattering later.
In the second part of the experiment, the students measure the size of
the spheres using the dynamic light scattering (DLS). While the
full mathematical treatment of the correlation-fluctuation data
analysis obtained from statistics of photon counting is beyond
the scope of the introductory course, we outline the process
diagrammatically. The students pick up the physical ideas with
ease, partly because they have worked through the concrete set
of conceptually related exercises using the microscope, and
partly because they are allowed to get their “hands on” the
experiment, from preparing the colloidal solutions to operating
the instrument. Once they insert their samples and open the
shutter, the instrument reports the relaxation constant Γ that
is related to the translational diffusion constant, D, via the
relation Γ = Dq2 , where q is the magnitude of the scattering
vector (see Handout).
The experience of determining the sub-micron particle size
almost “instantly” lies in contrast to the laborious (often
imprecise, impractical and sometimes impossible) task of
analyzing data obtained by the microscope.
In the final part of the lab using the DLS, students determine the
Boltzmann constant, a fundamental constant stemming from nearly
all statistical formulations of physics. This experiment closely
mimics the conceptually related experiments suggested by
Einstein in his 1905 Nobel prize-winning result. The product ζD
is a falsifiable prediction of the hypothesis that heat is
disordered molecular motion, incidentally, first observed in a
jiggly motion of a pollen particle by biologist Robert Brown.
The students prepare colloidal solution of latex spheres and
systematically vary the viscosity, η, of their solutions by
adding sugar. Measuring the spheres’ diffusion constants and
utilizing the Stoke and Einstein relations, they construct a
plot of Γ vs. n2/η (n is the solution’s index of
refraction) and determine the Boltzmann constant (see
Handout). A
representative plot of actual data collected by a group of
students is shown below.
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| Figure 1: : Data collected by
students using DLS. The relaxation constant Γ is
measured by the instrument. The Boltzmann constant can
be obtained from the slope and is measured to be 1.20×10-23
J/K, a little lower than the accepted value |
 
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