# Scaling of the current-current time correlation function of a suspension of hard sphere-like particles; Exposing when the motion of particles is Brownian

Condensed Matter lunchtime seminar

#### Scaling of the current-current time correlation function of a suspension of hard sphere-like particles; Exposing when the motion of particles is Brownian

• Event time: 1:00pm
• Event date: 12th October 2009
• Speaker: Bill van Megen (RMIT University Australia)
• Location: Room 2511,

### Event details

The current-current correlation function, C(q,$\tau$), is determined by dynamic light scattering for a suspension of particles with hard sphere-like interactions. Factorization of space and time variables provides direct support for the notion that the motion of suspended particles can be described in terms of uncorrelated Brownian encounters, the assumption that underpins the Smoluchowski equation. This applies to the suspension known to be in thermodynamic equilibrium ie, for volume fractions less than $\Phi_f=0.493$, the known first order freezing point of the hard-sphere system. In the metastable case, for $\Phi > \Phi_f$, non-monotonicity in C(q,$\tau$) obviates space-time factorization and signals the presence of another impediment to structural relaxation, one that is incompatible with loss of memory of the particles' momenta. Further evidence of such impediment is seen in previous studies of Newtonian [1] and colloidal [2] hard spheres. These expose the emergence, at $\Phi_f$, negative algebraic decays in the velocity auto-correlation function --features reminiscent flow in channels [3] and porous media [4]. In these cases the fluid is presented with a structural obstacle to momentum diffusion. In response, overdamped compression waves are excited in the suspending liquid, first, it would appear with wavevectors around the location of the main structure factor peak and then, with increasing volume fraction, spreading to other wavevectors [5]. [1]S.R. Williams, G. Bryant, I.K. Snook and W. van Megen, Phys. Rev. Lett. 96, 087801 (2006). [2]W.van Megen, Phys. Rev. E 73, 020503(R) (2006). [3]I.Pagonabarraga, M.H.J. Hagen, C.P. Lowe and D. Frenkel, Phys. Rev. E 59, 4458 (1999). [4] D.O. Riese and G.H. Wegdam, Phys. Rev. Lett. 82, 1676 (1999). [5] W. van Megen, V.A. Martinez and G. Bryant, Phys. Rev. Lett. 102, 168301 (2009).

### About Condensed Matter lunchtime seminars

This is a weekly series of informal talks given primarily by members of the soft condensed matter and statistical mechanics groups, but is also open to members of other groups and external visitors. The aim of the series is to promote discussion and learning of various topics at a level suitable to the broad background of the group. Everyone is welcome to attend..