Aggregation dynamics, structure, and mechanical properties of bigels

Recently we have introduced bigels, inter-penetrating gels made of two different colloidal species. Even if particles with simple short-range isotropic potential are employed, the selective interactions enable the tunability of the self-assembly, leading to the formation of complex structures. In the present paper, we explore the non-equilibrium dynamics and the phenomenology underlying the kinetic arrest under quench and the formation of bigels. We demonstrate that the peculiar bigel kinetics can be described through an arrested spinodal decomposition driven by demixing of the colloidal species. The role played by the presence of a second colloidal species on the phase diagram, as expanded to account for the increased number of parameters, is clarified both via extensive numerical simulations and experiments. We provide details on the realisation of bigels, by means of DNA-coated colloids (DNACCs), and the consequent imaging techniques. Moreover we evidence, by comparison with the usual one-component gel formation, the emergence of controllable timescales in the aggregation of the bigels, whose final stages are also experimentally studied to provide morphological details. Finally, we use numerical models to simulate the bigel response to mechanical strain, highlighting how such a new material can bear significantly higher stress compared to the usual one-component gel. We conclude by discussing possible technological uses and by providing insights on the viable research steps to undertake for more complex and yet tuneable multi-component colloidal systems.

Bose-Einstein condensation of microcavity polaritons

Davide Sarchi

This thesis presents a theoretical description of the phase transition, with formation of long-range spatial coherence, occurring in a gas of exciton-polaritons in a semiconductor microcavity structure. The results and predictions of the theories developed in this thesis suggest that this phase transition, recently observed in experiments, can be interpreted as the Bose-Einstein Condensation (BEC) of microcavity polaritons. Our theoretical framework is conceived as a generalization to the microcavity polariton system of the standard theories describing the BEC of a weakly interacting Bose gas. These latter are reviewed in Chapter 2, where an introduction to the physics of polaritons is also given. The polariton system is peculiar, basically due to three main features, i.e. the composite nature of polaritons, which are a linear superposition of photon and exciton states, their intrinsic 2-D nature, and the presence of two-body interactions, arising both from the mutual interaction between excitons and from the saturation of the exciton oscillator strength. Therefore it is not clear whether the observed phase transition can be properly described in terms of BEC of a trapped gas. To clarify this point, one has to describe self-consistently the linear exciton-photon coupling giving rise to polariton quasiparticles, and the exciton-nonlinearities. This is made in Chapter 3, where a bosonic theory is developed by generalizing the Hartree-Fock-Popov description of BEC to the case of two coupled Bose fields at thermal equilibrium. Hence, we derive the classical equations describing the condensate wave function and the Dyson-Beliaev equations for the field of collective excitations. In this way, for each value of the temperature and of the total polariton density, a self-consistent solution can be obtained, fixing the populations of the condensate and of the excited states. In particular, the theory allows to describe simultaneously the properties of the polariton, the exciton and the photon fields, this latter being directly investigated in the typical optical measurements. The predicted phase diagram, the energy shifts, the population energy distribution and the behavior of the resulting first order spatial correlation function agree with the recent experimental findings [Kasprzak 06, Balili 07]. These results thus support the idea that the observed experimental signatures are a clear evidence of polariton BEC. However, from a quantitative pint of view, the measured coherence amount in the condensed regime is significantly lower than the predicted one. This discrepancy could be due to deviations from the weakly interacting Bose gas picture and/or to deviations from the thermal equilibrium regime. In particular, these latter are expected to be strong in current experiments, because polaritons have a short radiative lifetime, while the rate of the energy-relaxation mechanisms is very slow. To investigate how the deviations from equilibrium could affect the condensate fraction and the formation of off-diagonal long-range correlations, in Chapter 4, we develop a kinetic theory of the polariton condensation, accounting for both the relaxation mechanisms and for the field dynamics of fluctuations. Within the Hartree-Fock-Bogoliubov limit, we derive a set of coupled equations of motion for the one-particle populations and for the two particle correlations describing quantum fluctuations. We account for the relaxation processes due both to the polariton-phonon coupling and to the exciton-exciton scattering. The actual spectrum of the system is evaluated within the Popov limit, during the relaxation kinetics. Within this model, we solve self-consistently the populations kinetics and the dynamics of the excitation field, for typical experimental conditions. In particular, we show that the role of quantum fluctuations is amplified by non-equilibrium, resulting in a significant condensate depletion. This behavior could explain the partial suppression of off-diagonal long-range coherence reported in experiments [Kasprzak 06, Balili 07]. We complete the analysis, by studying how the deviations from equilibrium depend on the system parameters. Our results show that the polariton lifetime plays a crucial role. In particular, we expect that the increase of the polariton lifetime above 10 ps would lead to thermal-equilibrium polariton BEC in realistic samples. In Chapter 5, devoted to the conclusions, we discuss which issues of BEC could be clarified, by achieving polariton BEC at thermal-equilibrium, and which extensions of the present work would be most promising in this respect.

EPFL2007

Static and dynamical correlation functions behaviour in attractive colloidal systems from theory and simulation

Giuseppe Foffi, Francesco Sciortino

We present comparisons of theoretical and simulation results for static and dynamical correlation functions for a very simple model of attractive colloidal systems, the short-ranged square-well potential. In the region of the phase diagram investigated, the system displays slow (glassy) dynamics. In particular, we compare the static structure factor calculated by Percus-Yevick closure versus the simulation results, both in the small-and large-wavevector ranges. For the same model, we also compare the non-ergodicity parameter, i.e. the long-time limit of the dynamical density correlators, as calculated by mode-coupling theory and by simulation, confirming the presence of two distinct glassy phases.

2003

A DNA Coarse-Grain Rigid Base Model and Parameter Estimation from Molecular Dynamics Simulations

Daiva Petkeviciute

Sequence dependent mechanics of DNA is believed to play a central role in the functioning of the cell through the expression of genetic information. Nucleosome positioning, gene regulation, DNA looping and packaging within the cell are only some of the processes that are believed to be at least partially governed by mechanical laws. Therefore it is important to understand how the sequence of DNA affects its mechanical properties. For exploring the mechanical properties of DNA, various discrete and continuum models have been, and continue to be, developed. A large family of these models, including the model considered in this work, assume that bases or base pairs of DNA are rigid bodies. The most standard are rigid base pair models, with parameters either obtained directly from experimental data or from Molecular Dynamics (MD) simulations. The drawback of current experimental data, such as crystal structures, is that only small ensembles of configurations are available for a small number of sequences. In contrast, MD simulations allow a much more detailed view of a larger number of DNA sequences. However, the drawback is that the results of these simulations depend on the choice of the simulation protocol and force field parameters. MD simulations also have sequence length limitations and are currently too intensive for (linear) molecules longer than a few tens of base pairs. The only way to simulate longer sequences is to construct a coarse-grain model. The goal of this work is to construct a small parameter set that can model a sequence- dependent equilibrium probability distribution for rigid base configurations of a DNA oligomer with any given sequence of any length. The model parameter sets previously available were for rigid base pair models ignoring all the couplings beyond nearest neighbour interactions. However it was shown in previous work, that this standard model of rigid base pair nearest neighbour interactions is inconsistent with a (then) large scale MD simulation of a single oligomer [36]. In contrast we here show that a rigid base nearest neighbour, dimer sequence dependent model is a quite good fit to many MD simulations of different duration and se- quence. In fact a hierarchy of rigid base models with different interaction range and length of sequence-dependence is discussed, and it is concluded that the nearest neighbour, dimer based model is a good compromise between accuracy and complexity of the model. A full parameter set for this model is estimated. An interesting feature is that despite the dimer dependence of the parameter set, due to the phenomenon of frustration, our model predicts non local changes in the oligomer shape as a function of local changes in the sequence, down to the level of a point mutation.