Long-lived Giant Number Fluctuations in a Swarming Granular Nematic

Coherently moving flocks of birds, beasts or bacteria are examples of living matter with spontaneous orientational order. How do these systems differ from thermal equilibrium systems with such liquid-crystalline order? Working with a fluidized monolayer of macroscopic rods in the nematic liquid crystalline phase, we find giant number fluctuations consistent with a standard deviation growing linearly with the mean, in contrast to any situation where the Central Limit Theorem applies. These fluctuations are long-lived, decaying only as a logarithmic function of time. This shows that flocking, coherent motion and large-scale inhomogeneity can appear in a system in which particles do not communicate except by contact.Comment: This is the author's version of the work. It is posted here by permission of the AAAS. The definitive version is to appear in SCIENC

Unsupervised machine learning for detection of phase transitions in off-lattice systems II. Applications

We outline how principal component analysis (PCA) can be applied to particle configuration data to detect a variety of phase transitions in off-lattice systems, both in and out of equilibrium. Specifically, we discuss its application to study 1) the nonequilibrium random organization (RandOrg) model that exhibits a phase transition from quiescent to steady-state behavior as a function of density, 2) orientationally and positionally driven equilibrium phase transitions for hard ellipses, and 3) compositionally driven demixing transitions in the non-additive binary Widom-Rowlinson mixture

Collective motion

We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the various facets of this highly multidisciplinary field, including experiments, mathematical methods and models for simulations, so that readers with a variety of background could get both the basics and a broader, more detailed picture of the field. The observations we report on include systems consisting of units ranging from macromolecules through metallic rods and robots to groups of animals and people. Some emphasis is put on models that are simple and realistic enough to reproduce the numerous related observations and are useful for developing concepts for a better understanding of the complexity of systems consisting of many simultaneously moving entities. As such, these models allow the establishing of a few fundamental principles of flocking. In particular, it is demonstrated, that in spite of considerable differences, a number of deep analogies exist between equilibrium statistical physics systems and those made of self-propelled (in most cases living) units. In both cases only a few well defined macroscopic/collective states occur and the transitions between these states follow a similar scenario, involving discontinuity and algebraic divergences.Comment: Submitted to Physics Reports, Jan, 201

Hybrid time-dependent Ginzburg-Landau simulations of block copolymer nanocomposites: nanoparticle anisotropy

Block copolymer melts are perfect candidates to template the position of colloidal nanoparticles in the nanoscale, on top of their well-known suitability for lithography applications. This is due to their ability to self-assemble into periodic ordered structures, in which nanoparticles can segregate depending on the polymer-particle interactions, size and shape. The resulting coassembled structure can be highly ordered as a combination of both the polymeric and colloidal properties. The time-dependent Ginzburg-Landau model for the block copolymer was combined with Brownian dynamics for nanoparticles, resulting in an efficient mesoscopic model to study the complex behaviour of block copolymer nanocomposites. This review covers recent developments of the time-dependent Ginzburg-Landau/Brownian dynamics scheme. This includes efforts to parallelise the numerical scheme and applications of the model. The validity of the model is studied by comparing simulation and experimental results for isotropic nanoparticles. Extensions to simulate nonspherical and inhomogeneous nanoparticles are discussed and simulation results are discussed. The time-dependent Ginzburg-Landau/Brownian dynamics scheme is shown to be a flexible method which can account for the relatively large system sizes required to study block copolymer nanocomposite systems, while being easily extensible to simulate nonspherical nanoparticles

Colloidal structures with novel functions

Over the last two decades, many kinds of environmentally responsive materials based on the chemical nature of gels and adsorption of surfactants at various interfaces are proposed. For the development of colloidal systems showing novel functionality we have designed various experimental systems for imaging the adsorption of surfactant at the interface between a nematic liquid crystal (LC) and water, self.propelling stimuli - responsive hydrogels and Janus particles. Optical textures changes produced by adsorption of a range of surfactants at the LC-water interface have been investigated using polarised and fluorescence microscopy to develop a novel sensor to detect various interfacial phenomena without requiring labelling of the analyte and the use of electroanalytical apparatus

Influence of Generic Scale Invariance on Classical and Quantum Phase Transitions

This review discusses a paradigm that has become of increasing importance in the theory of quantum phase transitions; namely, the coupling of the order-parameter fluctuations to other soft modes, and the resulting impossibility of constructing a simple Landau-Ginzburg-Wilson theory in terms of the order parameter only. The soft modes in question are manifestations of generic scale invariance, i.e., the appearance of long-range order in whole regions in the phase diagram. The concept of generic scale invariance, and its influence on critical behavior, is explained using various examples, both classical and quantum mechanical. The peculiarities of quantum phase transitions are discussed, with emphasis on the fact that they are more susceptible to the effects of generic scale invariance than their classical counterparts. Explicit examples include: the quantum ferromagnetic transition in metals, with or without quenched disorder; the metal-superconductor transition at zero temperature; and the quantum antiferromagnetic transition. Analogies with classical phase transitions in liquid crystals and classical fluids are pointed out, and a unifying conceptual framework is developed for all transitions that are influenced by generic scale invariance.Comment: 55pp, 25 eps figs; final version, to appear in Rev Mod Phy

Entropy-Driven Phase Transitions in Colloidal Systems

This thesis can be divided into two independent parts. In the first part of this thesis, we focus on studying the kinetic pathways of nucleation in colloidal systems. In Chapter 2, we briefly introduce the relevant theory of nucleation, i.e., classic nucleation theory. Then in Chapter 3, we investigate the crystal nucleation in the "simplest" model system for colloids, i.e., the monodisperse hard-sphere system, by using three different simulation methods, i.e., molecular dynamics, forward flux sampling and umbrella sampling simulations. Subsequently, we apply our simulation methods to a more realistic system of colloidal hard spheres in Chapter 4. Furthermore, we study the nucleation in a variety of systems consisting of hard particles, i.e., hard dumbbells (Chapter 5), hard rods (Chapter 6), hard colloidal polymers (Chapter 7) and binary hard-sphere mixtures (Chapter 8). In the second part of this thesis, we study the phase behavior of several colloidal systems. In Chapter 9, we study the equilibrium phase diagram of colloidal hard superballs whose shape interpolates from cubes to octahedra via spheres. We investigate the micellization of asymmetric patchy dumbbells induced by the depletion attraction in Chapter 10.Comment: PhD thesis, Utrecht University, July 2012. 188 page

Role of the anisotropy in the interactions between nano- and micro-sized particles

The present Thesis focuses on the thermodynamic and dynamic behaviour of anisotropically interacting colloids by means of theoretical and numerical techniques. Colloidal suspensions, i.e. micro-- and nano--sized particles dispersed in a continuous phase, are a topic of great interest in several fields, including material science, soft matter and biophysics. Common in everyday life in the form of soap, milk, cream, etc., colloids have been used for decades as models for atomic and molecular systems, since both classes of systems share many features like critical phenomena, crystallisation and glass transition. Experimental investigation of colloidal systems is made easier by the large size of colloids, which makes it possible to employ visible light as an experimental probe to investigate these systems. Moreover, since the mass of the particles controls the timescales of the dynamics, relaxation times of colloidal suspensions, ranging from seconds to years, orders of magnitude larger than their atomic counterparts, are more easily experimentally accessible. By exploiting this intrinsic slowness, with respect to molecular liquids, present day experimental techniques make it possible to follow in time trajectories of ensembles of particles with tools like confocal microscopy, thus effectively allowing to reconstruct the whole phase space trajectory of the system. In addition, it is also possible to manipulate single and multiple objects using techniques like optical tweezers, magnetic tweezers and atomic force microscopy. With single-molecule force spectroscopy one can arrange particles in ordered structures or measure properties like stiffness or mechanical responses (as in pulling experiments on RNA and DNA strands of particles and aggregates). A remarkable difference between the molecular and the colloidal world is that in the former the interactions between the basic constituents are fixed by nature, while in the latter the effective potential between two particles can be controlled by accurately designing and synthesizing the building blocks or tuned by changing the properties of the solvent. In the last decade many new sophisticated techniques for particle synthesis have been developed and refined. These recent advances allow for the creation of an incredible variety of non-spherically, i.e. anisotropically, interacting building blocks. The anisotropy can arise from shape, surface patterning, form of the interactions or a combination thereof. Examples are colloidal cubes, Janus particles, triblock Janus particles, patchy particles, magnetic spheres and many others. The recent blossoming of experimental, theoretical and numerical studies and research on the role of the anisotropy has highlighted the richness of phenomena that these systems exhibit. Relevant examples for the present Thesis are valence-limited building blocks, i.e colloids with a maximum number of bound neighbours, and non-spherical particles with an aspect ratio, i.e. the ratio of the width of a particle to its height, significantly different from $1$. The simplest example of valence-limited colloids is given by the so-called \textit{patchy} particles: colloids decorated with attractive spots (patches) on the surface. If the width and the range of the patches are chosen in such a way that each patch can form no more than one bond, then the total number of bound first neighbours per particle $M$ can not exceed the number of patches. For particles interacting through short-ranged isotropic potentials, $M \approx 12$. It has been shown that changing the valence $M$ has dramatic effects, both qualitative and quantitative, on the dynamic and thermodynamic properties of such systems. At high densities patchy colloids can self-assemble into a large variety of crystal structures, depending on valence, geometry and external parameters. We will mostly focus on low-density systems. The second class of systems pertinent to the present work comprises anisotropically shaped particles that, depending on the aspect ratio and the values of the external parameters, can exhibit liquid crystal phases which may display orientational long-range order. Nematic, in which there is no translational order, smectic, in which particles are ordered in layers and thus exhibit translational order in one dimension, and columnar phases, in which particles self-assemble into cylindrical aggregates which can in turn become nematic or form two-dimensional lattices, do not exist in isotropic systems, since the anisotropy in shape is a prerequisite for the breaking of the orientational symmetry. Liquid crystals, discovered at the end of the 19th century have been thoroughly investigated for decades, leading to technological breakthroughs like LCD displays. Recently it has been suggested that liquid crystal phases occurring in dense solutions of short DNA double strands could have played a role in the prebiotic chemical generation of complementary H-bonded molecular assemblies. The main goal of the present Thesis is to study the structural, thermodynamic and, to a lesser extent, dynamic properties of systems interacting through anisotropic potentials at low densities and temperatures. In particular, we focus on the low-density phase behaviour of valence-limited systems. We use a variegated approach, comprising state-of-the-art Monte Carlo and Molecular Dynamics techniques and theoretical approaches, to analyse and shed some light on the effect of the anisotropy on the phase diagram and on the dynamics of such systems. As the effect of the valence on the phase diagram plays a major role in the models investigated throughout this Thesis, each Chapter is devoted to the study of the dynamics and thermodynamics of systems having a fixed or effective maximum valence $M$. In the last years a lot of effort has been devoted to the study of end-to-end stacking interactions between different strands of nucleic acids, which play an important role in both physical and biological applications of DNA and RNA. In Chapter~1, building on the experimental work of Bellini \textit{et al.}, we make use of a theoretical framework recently developed to tackle the problem of the isotropic--nematic phase coexistence in solutions of short DNA duplexes (DNADs). We compare the parameter-free theoretical predictions with results from large scale numerical simulations on GPUs of a coarse-grained realistic model and find a good quantitative agreement at low concentrations. We then predict the phase boundaries for different DNAD lengths and compare the results with experimental findings. In Chapter~2 we investigate the structural and thermodynamic properties of systems having $M=2$, that is systems that undergo an extensive formation of linear structures as temperature is lowered. We focus on bi-functional patchy particles whose interaction details are chosen to qualitatively mimic the behaviour of the low-density, low-temperature dipolar hard sphere (DHS) model by analysing the outcomes of the simulations carried out in Chapter~3. In particular, we are interested in the interplay between chains and rings in equilibrium polymerization processes in a region of the phase diagram where the formation of the latter is favoured. The very good quantitative agreement found by comparing numerical results with theoretical, parameter-free predictions calls for an extension of the theory with the inclusion of branching, in order to understand how the presence of rings affects the phase separation. Chapter~3 is devoted to the investigation of the phase behaviour of dipolar fluids, i.e. systems interacting mainly through dipole-dipole potentials. For spheres, the lowest-energy configuration is the nose-to-tail contact geometry, and hence the ground state is an infinite chain or ring like in regular $M=2$ systems. For finite temperatures, on the other hand, thermal fluctuations allow for the appearance of defects like dangling ends and chain branching which, in the language of this Thesis, makes for a temperature-dependent valence. This general mechanism, under some specific conditions, can lead to a very peculiar phase separation, driven by a balance between these \textit{topological} defects rather than by the energy/entropy competition usually responsible for regular gas--liquid phase transitions. This topological phase transition has been recently observed in a model system of patchy particles but it is unclear whether such mechanism still holds in dipolar fluids in general and in the DHS model in particular. We focus on the DHS model, whose phase behaviour at low densities and temperatures has been studied for decades but still remains largely unknown. In particular, we look for the gas--liquid critical point by means of state-of-the-art Monte Carlo simulations in a region where it has long been thought to be. We find no evidence of a phase transition and we speculate that this is due to an abundance of rings, providing a remarkable example of phase separation suppressed by self-assembly. In Chapter~4 we study the dynamics of tetravalent patchy particles in the optimal network density region. For this fixed value of density the system is able to form a fully connected random network, i.e. an ideal gel. Indeed, as the temperature is lowered, a percolating network forms and the dynamics slows down. Although the observed dynamical arrest is different from the glass case, where excluded volume interactions are dominant, the decay of the self-- and collective correlation functions of the resulting fluid bears similarities with that observed in glassy systems. Remarkably, comparing the characteristic decay times of density-density correlation functions with the average bond life, we find that only at very low $T$ the decay of the density fluctuations requires the breakage of bonds. In Chapter~5 we introduce DNA as a building block that can be used to rationally design novel, self-assembling materials with tunable properties. In this Chapter, we study the phase behaviour and the dynamics of four-armed DNA constructs at low densities. We use the coarse-grained, realistic DNA model employed in Chapter~1 and state-of-the-art simulation techniques, as presented in Chapter~6, to investigate systems composed of thousands of nucleotides undergoing a two-step self-assembling process and we quantitatively compare the outcome with experimental results obtained for a very similar system. In Chapter~6 we introduce Graphics Processing Units (GPUs) as valuable tools for present day numerical investigations. We outline both the architecture of NVIDIA GPUs and NVIDIA CUDA, the software layer built on top of the hardware required to program these devices. We then present the techniques employed to write an efficient, general Molecular Dynamics code and compare its performances with a regular CPU code. The observed performance boost allows us to tackle the analysis of the dynamics and thermodynamics of very large systems without having to resort to massive CPU clusters (see Chapters~1,~4 and~5). Our work shows that it is possible to predict the location of thermodynamic and dynamic \textit{locii} of very complicated objects by means of numerical simulations. Since the available computational power keeps increasing at a steady pace, it will be soon possible to repeat the pioneering study presented in this Thesis on a more automated basis and for even more complicated system. For example, it will be possible to directly study the isotropic--nematic phase transition of short DNA duplexes investigated in Chapter~1 or design self-assembling DNA strands able to reproduce the behaviour of the patchy colloids or dipolar fluids studied throughout this Thesis. Being able to carefully design the building blocks and then predict beforehand the properties of a compound will greatly simplify the process of synthesising tomorrow's materials