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