Soft colloids make strong glasses
Edited by Qichao Hu
September 27th, 2010
There are some similarities between hard sphere colloids and molecular systems, when it comes to glass formation. For hard sphere colloids, the glass phase transition is controlled by an increase in volume fraction, and for molecular systems, it is controlled by a decrease in temperature. The difference is that molecular glasses exhibit a wider variety of behavior when the supercooled molecular liquids approach glassy state. These behaviors include viscosity and structural relaxation time, or in general called "fragility".
For fragile molecular liquids, the relaxation time is highly sensitive to changes in temperature, while for non-fragile, or strong molecular liquids, the relaxation time has a lower temperature dependence. On the other hand, hard sphere colloids are characterized as fragile, and limited by their volume fraction dependence. This fragile nature limits the use of hard sphere colloids in glass formation.
This paper demonstrates that instead of using hard sphere colloids, soft sphere colloids (deformable) can exhibit the same amount of variation in fragility by varying their concentration at fixed temperature as molecular liquids by varying the temperature at fixed volume. The fragility of these soft sphere colloids is determined by the elastic properties of the individual particles. This relation between fragility and elasticity also has an analogy in molecular liquids.
In molecular liquids, the concept of fragility is understood as the log slope in an Arrhenius plot when temperature is the glass transition temperature. For colloidal systems, fragility needs to have a concentration dependence rather than a temperature dependence.
Several notations used in this study are:
<math>\eta</math>: particle concentration
<math>\phi</math>: volume fraction
<math>V_P</math>: volume of each particle
<math>n</math>: number density of each particle
For hard sphere colloids, the total volume fraction is simply
However, for soft sphere colloids, the volume is not fixed and we need to use concentration
where <math>V</math> is the volume of an undeformed particle. Thus at low concentrations <math>\eta=\phi</math>, since each particle's volume is independent of the concentration.
In the figure below, dynamic light scattering is used to study the deforming behavior of soft sphere colloids.
The behaviors for both hard and soft sphere colloids are similar. As concentration increases, there are dramatic changes in the dynamics. A two-step relaxation is observed, which is characteristic of glass-forming materials near glass transition temperature. It is noted that the final decay, which is related to the structural relaxation is strongly dependent on the concentration. At very high concentration, the final decay occurs on a time scale longer than experimental accessible range, and glass formation happens.
For hard sphere colloids, a small change in volume fraction leads to a large slowing of the structural relaxation. But for soft sphere colloids, they are dynamically arrested over a large range of concentrations. This is shown in the figure below, where the concentration dependences of the structural relaxation times for a hard sphere (diamond) and soft sphere (circle) are compared.
The concentration dependence of relaxation time follows a Vogel-Fulcher-Tammann (VFT) behavior
Unlike the Arrhenius behavior in molecular liquids, here the temperature dependence of <math>T</math> is replaced with the concentration dependence of <math>1/\eta</math>. Also when <math>\eta_0\gg\eta</math> the Arrhenius behavior is recovered.
This confirms that the concept of fragility can be extended to colloidal systems through varying concentration. For molecular liquids, the x-axis in the Arrhenius plot is conveniently scaled by <math>T_g</math>, indicating the relaxation time near glass transition. Similarly, for colloids, the x-axis in the VFT plot can be scaled by <math>\eta_g</math>. In both cases the relaxation time to long to be experimentally accessible is defined as 100s in this study.
The follow figure shows the role of particle elasticity on the dynamic arrest. The figures show elastic energy as functions of concentration.
A direct correlation between the growth of the elastic energy and fragility is observed, the softer the colloids, the stronger the suspension. Moreover, the elastic energy dominates over thermal energy near the glass transition for hard, soft colloids, and molecular liquids. This suggests that the thermal activation controls fragility. In colloidal systems, it is dependent on concentration. While in molecular liquids, it is dependent on temperature.