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

Accurate phase diagram of tetravalent DNA nanostars

We evaluate, by means of molecular dynamics simulations employing a realistic DNA coarse-grained model, the phase behaviour and the structural and dynamic properties of tetravalent DNA nanostars, i.e. nanoconstructs completely made of DNA. We find that, as the system is cooled down, tetramers undergo a gas--liquid phase separation in a region of concentrations which, if the difference in salt concentration is taken into account, is comparable with the recently measured experimental phase diagram [S. Biffi \textit{et al}, Proc. Natl. Acad. Sci, \textbf{110}, 15633 (2013)]. We also present a mean-field free energy for modelling the phase diagram based on the bonding contribution, derived by Wertheim in its studies of associating liquids, combined with mass action law expressions appropriate for DNA binding and a numerically evaluated reference free energy. The resulting free energy qualitatively reproduces the numerical data. Finally, we report information on the nanostar structure, e.g. geometry and flexibility of the single tetramer and of the collective behaviour, providing a useful reference for future small angle scattering experiments, for all investigated temperatures and concentrations.Comment: 10 pages, 11 figure

Internal structure and swelling behaviour of in silico microgel particles

Microgels are soft colloids that, in virtue of their polymeric nature, can react to external stimuli such as temperature or pH by changing their size. The resulting swelling/deswelling transition can be exploited in fundamental research as well as for many diverse practical applications, ranging from art restoration to medicine. Such an extraordinary versatility stems from the complex internal structure of the individual microgels, each of which is a crosslinked polymer network. Here we employ a recently-introduced computational method to generate realistic microgel configurations and look at their structural properties, both in real and Fourier space, for several temperatures across the volume phase transition as a function of the crosslinker concentration and of the confining radius employed during the `in-silico' synthesis. We find that the chain-length distribution of the resulting networks can be analytically predicted by a simple theoretical argument. In addition, we find that our results are well-fitted to the fuzzy-sphere model, which correctly reproduces the density profile of the microgels under study

qq-independent slow-dynamics in atomic and molecular systems

Investigating million-atom systems for very long simulation times, we demonstrate that the collective density-density correlation time ($\tau_{\alpha}$) in simulated supercooled water and silica becomes wavevector independent ($q^0$) when the probing wavelength is several times larger than the interparticle distance. The $q$-independence of the collective density-density correlation functions, a feature clearly observed in light-scattering studies of some soft-matter systems, is thus a genuine feature of many (but not all) slow-dynamics systems, either atomic, molecular or colloidal. Indeed, we show that when the dynamics of the density fluctuations is due to particle-type diffusion, as in the case of the Lennard Jones binary mixture model, the $q^0$ regime does not set in and the relaxation time continues to scale as $\tau_{\alpha} \sim q^{-2}$ even at small $q$.Comment: Includes the supplementary materia

Soft self-assembled nanoparticles with temperature-dependent properties

The fabrication of versatile building blocks that are reliably self-assemble into desired ordered and disordered phases is amongst the hottest topics in contemporary material science. To this end, microscopic units of varying complexity, aimed at assembling the target phases, have been thought, designed, investigated and built. Such a path usually requires laborious fabrication techniques, especially when a specific funcionalisation of the building blocks is required. Telechelic star polymers, i.e., star polymers made of a number $f$ of di-block copolymers consisting of solvophobic and solvophilic monomers grafted on a central anchoring point, spontaneously self-assemble into soft patchy particles featuring attractive spots (patches) on the surface. Here we show that the tunability of such a system can be widely extended by controlling the physical and chemical parameters of the solution. Indeed, at fixed external conditions the self-assembly behaviour depends only on the number of arms and/or on the ratio of solvophobic to solvophilic monomers. However, changes in temperature and/or solvent quality makes it possible to reliably change the number and size of the attractive patches. This allows to steer the mesoscopic self-assembly behaviour without modifying the microscopic constituents. Interestingly, we also demonstrate that diverse combinations of the parameters can generate stars with the same number of patches but different radial and angular stiffness. This mechanism could provide a neat way of further fine-tuning the elastic properties of the supramolecular network without changing its topology.Comment: 8 pages, 7 figures. Submitted to Nanoscal

On the effect of the thermostat in non-equilibrium molecular dynamics simulations

The numerical investigation of the statics and dynamics of systems in nonequilibrium in general, and under shear flow in particular, has become more and more common. However, not all the numerical methods developed to simulate equilibrium systems can be successfully adapted to out-of-equilibrium cases. This is especially true for thermostats. Indeed, even though thermostats developed to work under equilibrium conditions sometimes display good agreement with rheology experiments, their performance rapidly degrades beyond weak dissipation and small shear rates. Here we focus on gauging the relative performances of three thermostats, Langevin, dissipative particle dynamics, and Bussi-Donadio-Parrinello under varying parameters and external conditions. We compare their effectiveness by looking at different observables and clearly demonstrate that choosing the right thermostat (and its parameters) requires a careful evaluation of, at least, temperature, density and velocity profiles. We also show that small modifications of the Langevin and DPD thermostats greatly enhance their performance in a wide range of parameters.Comment: 13 pages, 9 figure

Self-assembly in chains, rings and branches: a single component system with two critical points

We study the interplay between phase separation and self-assembly in chains, rings and branched structures in a model of particles with dissimilar patches. We extend Wertheim's first order perturbation theory to include the effects of ring formation and theoretically investigate the thermodynamics of the model. We find a peculiar shape for the vapor-liquid coexistence, featuring re-entrant behavior in both phases and two critical points, despite the single-component nature of the system. The emergence of the lower critical point is caused by the self-assembly of rings taking place in the vapor, generating a phase with lower energy and lower entropy than the liquid. Monte Carlo simulations of the same model fully support these unconventional theoretical predictions.Comment: 5 pages, 3 figure

How soft repulsion enhances the depletion mechanism

We investigate binary mixtures of large colloids interacting through soft potentials with small, ideal depletants. We show that softness has a dramatic effect on the resulting colloid-colloid effective potential when the depletant-to-colloid size ratio $q$ is small, with significant consequences on the colloidal phase behaviour. We also provide an exact relation that allows us to obtain the effective pair potential for {\it any} type of colloid-depletant interactions in the case of ideal depletants, without having to rely on complicated and expensive full-mixture simulations. We also show that soft repulsion among depletants further enhances the tendency of colloids to aggregate. Our theoretical and numerical results demonstrate that --- in the limit of small $q$ --- soft mixtures cannot be mapped onto hard systems and hence soft depletion is not a mere extension of the widely used Asakura-Oosawa potential.Comment: Accepted for publication in Soft Matte

Surface wave excitations and backflow effect over dense polymer brushes

Polymer brushes are being increasingly used to tailor surface physicochemistry for diverse applications such as wetting, adhesion of biological objects, implantable devices and much more. Here we perform Dissipative Particle Dynamics simulations to study the behaviour of dense polymer brushes under flow in a slit-pore channel. We discover that the system displays flow inversion at the brush interface for several disconnected ranges of the imposed flow. We associate such phenomenon to collective polymer dynamics: a wave propagating on the brush surface. The relation between the wavelength, the amplitude and the propagation speed of the flow-generated wave is consistent with the solution of the Stokes equations when an imposed traveling wave is assumed as the boundary condition (the famous Taylor's swimmer)