Measuring the free energy of hard-sphere colloidal glasses

Free energy is a key thermodynamic observable that controls the elusive physics of the glass transition. However, measuring the free energy of colloidal glasses from microscopy images is challenging due to the difficulty of measuring the individual particle size in the slightly polydisperse glassy systems. In this paper, we carry out experiments and numerical simulations of colloidal glasses with the aim to find a practical approach to measure the free energy from colloidal particles at mild polydispersity. We propose a novel method which requires only the particle coordinates from a few confocal microscopy snapshots to estimate the average particle diameter and use it as an input for our experimental free energy measurements. We verify our free energy calculations from Cell Theory with the free energy obtained by Thermodynamic Integration. The excellent agreement between the free energies measured using the two methods close to the glass transition packing fraction highlights the dominant role played by \emph{vibrational} entropy in determining a colloidal glass's free energy. Finally, the noticeable free energy difference calculated from uniform and conjectured particle sizes emphasizes the sensitivity on particle free volumes when measuring free energy in the slightly polydisperse colloidal glass.

Direction-Dependent Properties in Inverted Carbon Nitride Colloidal Glasses with Gradient Porosity

It is well known that the step from a dense packing of colloidal beads to the inverted systems was important for the optimization of photonic crystal properties. Inverted opals made of high-refractive index semiconductors have attracted great attention due to their supreme optical features such as the occurrence of a photonic band-gap and because of an astonishing behavior in photocatalysis or for photovoltaics caused by so-called slow photons. It is much less known that photonic glasses, despite being disordered, exhibit unique optical properties too like random lasing or high-contrast structural colors. In analogy to opals and inverted opals, one can expect that inverted colloidal glasses may lead to an amplification of photonic properties as well or even to the emergence of unexpected features. An inverted photonic glass is characterized by a dense packing of monodisperse voids with colloidal dimensions without any long-range order. The preparation of inverse photonic glasses has rarely been reported by now and cases for materials composed of a semiconductor as a pore-wall material are unknown. The synthesis of porous carbon nitride (C₃N₄) with inverted colloidal glass structure is demonstrated here using a template approach. The formation of the template with glass-like order is achieved by analytical ultracentrifugation (AUZ) of size-selected silica colloids, followed by infiltration of a precursor sol, transformation to carbon nitride and the final removal of the template. The use of AUZ is particularly important because it even allows to use a mixture of differently sized template particles, which are gradually fractionated. Monoliths with optimized morphological features exhibiting a gradient porosity and highly accessible pores are obtained. The result are materials with a graded structure. What makes such functional gradient material interesting is, a dependence of the optical features on the position can be expected. In addition, the method presented here allows to synthesize materials with adjustable composition ranging from carbon over nitrogen-doped carbon to C₃N₄ with either graphitic or polymeric structure. Therefore, the optical band gap is highly adjustable and tunable with regards to the photonic properties, as confirmed by optical absorption and photoluminescence measurements.

Direction-Dependent Properties in Inverted Carbon Nitride Colloidal Glasses with Gradient Porosity

It is well known that the step from a dense packing of colloidal beads to the inverted systems was important for the optimization of photonic crystal properties. Inverted opals made of high-refractive index semiconductors have attracted great attention due to their supreme optical features such as the occurrence of a photonic band-gap and because of an astonishing behavior in photocatalysis or for photovoltaics caused by so-called slow photons. It is much less known that photonic glasses, despite being disordered, exhibit unique optical properties too like random lasing or high-contrast structural colors. In analogy to opals and inverted opals, one can expect that inverted colloidal glasses may lead to an amplification of photonic properties as well or even to the emergence of unexpected features. An inverted photonic glass is characterized by a dense packing of monodisperse voids with colloidal dimensions without any long-range order. The preparation of inverse photonic glasses has rarely been reported by now and cases for materials composed of a semiconductor as a pore-wall material are unknown. The synthesis of porous carbon nitride (C₃N₄) with inverted colloidal glass structure is demonstrated here using a template approach. The formation of the template with glass-like order is achieved by analytical ultracentrifugation (AUZ) of size-selected silica colloids, followed by infiltration of a precursor sol, transformation to carbon nitride and the final removal of the template. The use of AUZ is particularly important because it even allows to use a mixture of differently sized template particles, which are gradually fractionated. Monoliths with optimized morphological features exhibiting a gradient porosity and highly accessible pores are obtained. The result are materials with a graded structure. What makes such functional gradient material interesting is, a dependence of the optical features on the position can be expected. In addition, the method presented here allows to synthesize materials with adjustable composition ranging from carbon over nitrogen-doped carbon to C₃N₄ with either graphitic or polymeric structure. Therefore, the optical band gap is highly adjustable and tunable with regards to the photonic properties, as confirmed by optical absorption and photoluminescence measurements.

Microscopic pathways for stress relaxation in repulsive colloidal glasses

Residual stresses are well-known companions of all glassy materials. They affect and, in many cases, even strongly modify important material properties like the mechanical response and the optical transparency. The mechanisms through which stresses affect such properties are, in many cases, still under study, and their full understanding can pave the way to a full exploitation of stress as a primary control parameter. It is, for example, known that stresses promote particle mobility at small length scales, e.g., in colloidal glasses, gels, and metallic glasses, but this connection still remains essentially qualitative. Exploiting a preparation protocol that leads to colloidal glasses with an exceptionally directional built-in stress field, we characterize the stress-induced dynamics and show that it can be visualized as a collection of “flickering,” mobile regions with linear sizes of the order of ≈20 particle diameters (≈2 μm here) that move cooperatively, displaying an overall stationary but locally ballistic dynamics.

“Dense diffusion” in colloidal glasses: short-ranged long-time self-diffusion as a mechanistic model for relaxation dynamics

Individual particle dynamics are monitored during the colloidal glass transition, using a novel size-jump algorithm to quench from liquid to glass.