# Difference between revisions of "Physical ageing of the contact line on colloidal particles at liquid interfaces"

Spring 2012 entry - Anna Wang

## References

David M. Kaz, Ryan McGorty, Madhav Mani, Michael P. Brenner, and Vinothan N. Manoharan (2012) Physical ageing of the contact line on colloidal particles at liquid interfaces Nature Materials, Nature Materials advance online publication December 2011, http://www.nature.com.ezp-prod1.hul.harvard.edu/nmat/journal/vaop/ncurrent/full/nmat3190.html

## Introduction

It is commonly accepted that it is energetically favourable for particles to bind to fluid-fluid interfaces. The particle sits at an equilibrium position in between the two bulk phases, as predicted by Young's law. But how does a particle reach this equilibrium position from the bulk phase? In this paper, the authors examine the dynamics of how a particle reaches this position and find that the process is surprisingly slow and has parallels in ageing of glassy systems.

## Experimental setup

The experiments are performed in a custom-made trough, which allows for a pinned aqueous subphase and an oil superphase. Polystyrene microspheres (1.9um diameter) start in the aqueous phase and are pushed gently upwards towards the interface using radiation pressure from out-of-focus optical tweezers.

### Digital Holographic Microscopy

Figure 1. Digital holographic microscopy is used to image the microspheres

Digital Holographic Microscopy is used to capture the three-dimensional trajectory of the microspheres as they approach the interface at up to 5000 frames/sec. A high spatial precision of 2nm is achieved by refractive index matching the aqueous phase (~60% glycerol, 40% water, NaCl) to the decane. This minimises reflections within the sample, which would make hologram analysis much more complicated.

## Observations

### Approach

The approach of the particles towards the interface can be accounted for entirely by considering radiation pressure from the optical tweezers, and the opposing drag force as the particle moves. The particle's axial motion eventually plateaus and at low salt concentrations, the particles do not rise any further (Fig 1b.).

### Breach

For high salt concentrations (~100mM NaCl) the particle then rises sharply, which is interpreted as the particle breaching the interface. From here, the interfacial tension from the newly-formed three-phase contact line then drives the particle's motion upwards.

### Relaxation

The dynamics of the particle as it breaches the interface are shown in Figure 1d. The rise is logarithmic in time, and the particle does not reach the reported equilibrium contact angle (measured in experiments which introduce the particle with a spreading solvent) even after the tens of seconds the experiment lasts for; in fact, it would take months if we extrapolate from the logarithmic time dependence

## Analysis

After breaching the interface, the initial velocity is 1000 times smaller than hydrodynamics can account for, and a model taking into account enhanced viscous drag do not predict logarithmic behaviour. Instead the authors look to the analogy to ageing in non-equilibrium systems, and use a model based on the microscopic processes to predict the motion of the particles.

### Arrhenius model

As the contact line moves across the particle, it is pinned by various defects, topological or chemical, with an activation energy U. With enough of a thermal kick, the contact line can 'hop' over these defects, and then it gets pinned again. This molecular dissipation process is encapsulated in the expression V=v.exp(-U/kT+FA/2kT) where V is the velocity of the contact line, v is a molecular velocity scale, F the force on the contact line and A the 'defect area'.

Working with this, the equation of motion for the height of a particle becomes

 \begin{align} \frac{dz}{dt} &= v\sqrt{z(2R-z)} exp(-\frac{A {\gamma} z}{2RkT}) \end{align} 

This represents a logarithmic trajectory when the contact angle is close to equilibrium.

## Implications

Molecular dissipation affects wetting dynamics markedly in this situation, even though the contact angle change is large which is a regime that having hydrodynamic dissipation usually matters more. The slow relaxation time means that it can not be assumed that particles are at equilibrium during particle-interface self assembly experiments, an assumption which is usually taken for granted. This may help explain why particle-particle interactions vary over time when they are adsorbed to the interface, as both the amount of surface charge exposed and contact line distortions change over time.