Friction Coefficient of a Dense 2D Colloidal System
Hydrodynamic Damping of Collective Motion in a
Quasi-Two-Dimensional Dense Colloidal Particle SuspensionMichael
RyanUndergraduate StudentWest Chester University
Kevin AptowiczWest Chester UniversityArjun YodhTim
StillUniversity of Pennsylvania
Hi, my name is Michael Ryan, Im an undergraduate at West Chester
University working on finding the friction coefficient of a dense
2D colloidal crystal.1
BackgroundHydrodynamic properties of colloidal system are not
the same as atomic crystalColloidal CrystalAtomic
CrystalHydrodynamic forcesShared electronsFriction of surrounding
waterNo analogous form
A.M. Alsayed, M.F. Islam, J. Zhang, P.J. Collings, and A.G.
Yodh, Premelting at defects within bulk colloidal crystals, Science
309, 1207-1210, (2005)
System: 2D Colloidal CrystalDensely packed PNIPAm particles
sandwiched between two coverslips
5 m
Spheres are soft (deformable)
The kind of colloidal crystal I am working with is PNIPAM
particles sandwiched between two coverslips. Observed through a
microscope, one of mine looks like this picture. I take pretty long
video of 1500-3000 particles, about 100 seconds at 1000 frames per
second.3
Video Microscopy
(Sped up 30x)5 m 1500-3000 particles1770 normal modes1000 fpsLow
frequencymodeHigh frequencymode
We analyze video andcompute eigenvectorsPrevious work using this
method: Chen et al., PRL, 2010; Kyay et al., Science, 2010; A.
Ghosh et al., PRL, 2010
The motion of the colloidal crystal is dependent on the
temperature of the system; as it increases, the particles shrink
and move with thermal motion. Using particle tracking and IDL, I
can create a covariance matrix and use it to find eigenmodes and
eigenvectors of the system.4
Mode Dynamics
Displacement (Pixels)Time (s)
Histogram of mode:Displacement (Pixels)
mkT,
Lag time (s)Autocorrelation of DisplacementWe know:k,m,T.We can
find:
3rd mode5
Mode NumberDisplacementHistogramAutocorrelation1410001500
Dynamics of Multiple Modes
Lag Time (s)Lag Time (s)Lag Time (s)Displacement (px)
Displacement (px)Displacement (px)
i=12, 999,1699
These are three modes out of the 2248 for the section of the
video I analyzed. Lower modes look fairly Gaussian, but curve
fitting seems to default to overdamped for even the lowest modes.
The reason for this is unclear, but it remains possible that all
modes may be overdamped.6
qaSpring constant (kBT/m2)
qaDecay Time (s)
qaFriction coff. (kBTs/m2)LongitudinalStill et al., Phys. Rev.
E, 2014Main ResultTransverse(Averaged over all q-vector
directions)
A Similar System
Baumgartl et al., Soft Matter, 2008
Baumgartl et al.Our SystemSphere
TypePolystyrenePNIPAmInteraction MethodCharged
spheresMechanical
A paper in Soft Matter also created a crystal, but with an
interference pattern to hold them in their lattice and with charged
spheres. The paper determined the friction coefficient of these
spheres and approximated that the dynamics of normal modes would be
overdamped; in other words, the expected shape of the
autocorrelation function should decay exponentially for all
modes.8
Experimental Stokes Law Friction*(~15.5
kBTs/m2)ConclusionsqaFriction coff. (kBTs/m2)
Plot by Baumgartl et al:LongitudinalTransverse* Nakroshis et
al., American Journal of Physics, 2003LongitudinalTransverseUnlike
Baumgartl et al., our friction coefficient does not appear to
vanish.
Black is longitudinal9