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One of the frontiers of nanotechnology is advancing beyond the periodic self-assembly of materials. Icosahedral quasicrystals, aperiodic in all directions, represent one of the most challenging targets that have yet to be experimentally realized at the colloidal scale. Previous attempts have required meticulous human-designed building blocks and often resulted in interactions beyond current experimental capabilities. In this work, we introduce a framework for generating experimentally accessible designs that self-assemble into quasicrystalline arrangements. We present a design for icosahedral DNA-origami building blocks and demonstrate, through molecular simulations, their successful assembly into the target quasicrystalline structure. Our results highlight the feasibility of using automated design protocols to achieve complex quasicrystalline patterns, paving the way for new applications in material science and nanotechnology.

In the present work, with the intent of exploring the out-of-equilibrium polymerization of active patchy particles in linear chains, we study a suspension of active bivalent Brownian particles (ABBPs). At all studied temperatures and densities, ABBPs self-assemble in aggregating chains, as opposed to the uniformly space-distributed chains observed in the corresponding passive systems. The main effect of activity, other than inducing chain aggregation, is to reduce the chain length and favor alignment of the propulsion vectors in the bonding process. At low activities, attraction dominates over activity in the bonding process, leading self-assembly to occur randomly regardless of the particle orientations.Interestingly, we find that at the lowest temperature, as density increases, chains aggregate forming a novel state: MISP, i.e., Motility-Induced Spirals, where spirals are characterised by a finite angular velocity. On the contrary, at the highest temperature, density and activity, chains aggregate forming a different novel state (a spinning crystalline cluster) characterized by a compact and hexagonal ordered structure, both translating and rotating. The rotation arises from an effective torque generated by the presence of competing domains where particles self-propel in the same direction.

In recent years, the possibility of algorithmically preparing ultra-stable glasses (UG), i.e., states that lie very deep in the potential energy landscape, has considerably expanded our understanding of the glassy state. In this work, we report on a new protocol for ultrastable glass preparation that iteratively modifies the particle diameters to reduce local virial stress fluctuations. We apply the algorithm to an additive Lennard-Jones mixture and show that, compared to the states obtained via thermal annealing, virial homogenized glasses (VHG) are characterized by a considerable increase in both kinetic stability and the number of locally favored structures (icosahedra). We also consider the melting dynamics during heating ramps and show that it occurs via an accumulation of localized events. Our results highlight the connection between the thermodynamic and mechanical stability of ultra-stable glassy states.

Studies of water thermodynamics have long been tied to the identification of two distinct families of local structures, whose competition could explain the origin of the many thermodynamic anomalies and of the hypothesized liquid-liquid critical point in water. Despite the many successes and insights gained, the structural indicators proposed throughout the years were not able to unequivocally identify these two families over a wide range of conditions. We show that a recently introduced indicator, $\Psi$, which exploits information on the HB network connectivity, can reliably identify these two distinct local environments over a wide range of thermodynamic conditions (188 to 300 K and 0 to 13 kbar), and that close to the liquid-liquid critical point the spatial correlations of density fluctuations are identical to those of the $\Psi$ indicator. Our results strongly support the idea that water thermodynamic properties arise from the competition between two distinct and identifiable local environments., Comment: Published on The Journal of Chemical Physics. Main: 8 pages, 6 figures. SI: 10 pages, 6 figures

The presence of a second critical point in water has been a topic of intense investigation for the last few decades. The molecular origins underlying this phenomenon are typically rationalized in terms of the competition between local high-density (HD) and low-density (LD) structures. Their identification often require designing parameters that are subject to human intervention. Herein, we use unsupervised learning to discover structures in atomistic simulations of water close to the Liquid-Liquid Critical point (LLCP). Encoding the information of the environment using local descriptors, we do not find evidence for two distinct thermodynamic structures. In contrast, when we deploy non-local descriptors that probe instead heterogeneities on the nanometer length scale, this leads to the emergence of LD and HD domains rationalizing the microscopic origins of the density fluctuations close to criticality.

Sophisticated statistical mechanics approaches and human intuition have demonstrated the possibility to self-assemble complex lattices or finite size constructs, but have mostly only been successful in silico. The proposed strategies quite often fail in experiment due to unpredicted traps associated to kinetic slowing down (gelation, glass transition), as well as to competing ordered structures. An additional challenge that theoretical predictions face is the difficulty to encode the desired inter-particle interaction potential with the currently available library of nano- and micron-sized particles. To overcome these issues, we conjugate here SAT-assembly -- a patchy-particle interaction design algorithm based on constrained optimization solvers -- with coarse-grained simulations of DNA nanotechnology to experimentally realize trap-free self-assembly pathways. As a proof of concept we investigate the assembly of the pyrochlore (also known as tetrastack) lattice, a highly coveted 3D crystal lattice due to its promise in construction of optical metamaterials. We confirm the successful assembly with two different patchy DNA origami designs via SAXS as well as SEM visualization of the silica-coated lattice. Our approach offers a versatile modeling pipeline that starts from patchy particles designed in silico and ends with wireframe DNA origami that self-assemble into the desired structure., Comment: main text: 8 pages, supplementary material: 53 pages

The control over the self-assembly of complex structures is a long-standing challenge of material science, especially at the colloidal scale, as the desired assembly pathway is often kinetically derailed by the formation of amorphous aggregates. Here we investigate in detail the problem of the self-assembly of the three Archimedean shells with five contact points per vertex, i.e. the icosahedron, the snub cube, and the snub dodecahedron. We use patchy particles with five interaction sites (or patches) as model for the building blocks, and recast the assembly problem as a Boolean satisfiability problem (SAT) for the patch-patch interactions. This allows us to find effective designs for all targets, and to selectively suppress unwanted structures. By tuning the geometrical arrangement and the specific interactions of the patches, we demonstrate that lowering the symmetry of the building blocks reduces the number of competing structures, which in turn can considerably increase the yield of the target structure. These results cement SAT-assembly as an invaluable tool to solve inverse design problems., Comment: 21 pages, 10 figures

Polymer chains decorated with a fraction of monomers capable of forming reversible bonds form transient polymer networks that are important in soft and biological systems. If chains are flexible and the attractive monomers are all of the same species, the network formation occurs continuously as density increases. By contrast, it has been recently shown [L. Rovigatti and F. Sciortino, Phys. Rev. Lett. 129, 047801 (2022)] that, if the attractive monomers are of two different and alternating types, the entropic gain of swapping intra-molecular bonds for inter-molecular connections induces a first order phase transition in the fully-bonded (\textit{i.e.} low-temperature or, equivalently, large monomer-monomer attraction strength) limit and the network forms abruptly on increasing density. Here we use simulations to show that this phenomenon is robust with respect to thermal fluctuations, disorder and change in the polymer architecture, demonstrating its generality and likely relevance for the wide class of materials that can be modelled as associative (transient) polymer networks., Comment: Resubmission to SciPost

Nucleation in systems with a metastable liquid-gas critical point is the prototypical example of a two-step nucleation process, in which the appearance of the critical nucleus is preceded by the formation of a liquid-like density fluctuation. So far, the majority of studies on colloidal and protein crystallization have focused on one-component systems, and we are lacking a clear description of two-step nucleation processes in multicomponent systems, where critical fluctuations involve coupled density and concentrations inhomogeneities. Here, we examine the nucleation process of a binary mixture of patchy particles designed to nucleate into a diamond lattice. By combining Gibbs-ensemble simulations and direct nucleation simulations over a wide range of thermodynamic conditions, we are able to pin down the role of the liquid-gas metastable phase diagram on the nucleation process. In particular, we show that the strongest enhancement of crystallization occurs at an azeotropic point with the same stoichiometric composition of the crystal., Comment: 9 pages, 7 figures

We present a neural network (NN) potential based on a new set of atomic fingerprints built upon two- and three-body contributions that probe distances and local orientational order respectively. Compared to existing NN potentials, the atomic fingerprints depend on a small set of tuneable parameters which are trained together with the neural network weights. To tackle the simultaneous training of the atomic fingerprint parameters and neural network weights we adopt an annealing protocol that progressively cycles the learning rate, significantly improving the accuracy of the NN potential. We test the performance of the network potential against the mW model of water, which is a classical three-body potential that well captures the anomalies of the liquid phase. Trained on just three state points, the NN potential is able to reproduce the mW model in a very wide range of densities and temperatures, from negative pressures to several GPa, capturing the transition from an open random tetrahedral network to a dense interpenetrated network. The NN potential also reproduces very well properties for which it was not explicitly trained, such as dynamical properties and the structure of the stable crystalline phases of mW., Comment: 14 pages, 11 figures

The goal of inverse self-assembly is to design inter-particle interactions capable of assembling the units into a desired target structure. The effective assembly of complex structures often requires the use of multiple components, each new component increasing the thermodynamic degrees of freedom and hence the complexity of the self-assembly pathway. In this work we explore the possibility to use azeotropy, i.e. a special thermodynamic condition where the system behaves effectively as a one-component system, as a way to control the self-assembly of an arbitrarily number of components. Exploiting the mass-balance equations we show how to select patchy particle systems that exhibit azeotropic points along the desired self-assembly pathway. As an example we map the phase diagram of a binary mixture that, by design, fully assembles into cubic (and only cubic) diamond crystal via an azeotropic point. The ability to explicitly include azeotropic points into artificial designs opens novel pathways to the self-assembly of complex structures., Comment: 21 pages, 10 figures, 4 supplementary figures

Single-chain nanoparticles (SCNP) are a new class of bio and soft-matter polymeric objects in which a fraction of the monomers are able to form equivalently intra- or inter-polymer bonds. Here we numerically show that a fully-entropic gas-liquid phase separation can take place in SCNP systems. Control over the discontinuous (first-order) change -- from a phase of independent diluted (fully-bonded) polymers to a phase in which polymers entropically bind to each other to form a (fully-bonded) polymer network -- can be achieved by a judicious design of the patterns of reactive monomers along the polymer chain. Such a sensitivity arises from a delicate balance between the distinct entropic contributions controlling the binding., Comment: The submission also contains the SI

Empty liquids represent a wide class of materials whose constituents arrange in a random network through reversible bonds. Many key insights on the physical properties of empty liquids have originated almost independently from the study of colloidal patchy particles on one side, and a large body of theoretical and experimental research on water on the other side. Patchy particles represent a family of coarse-grained potentials that allows for a precise control of both the geometric and the energetic aspects of bonding, while water has arguably the most complex phase diagram of any pure substance, and a puzzling amorphous phase behavior. It was only recently that the exchange of ideas from both fields has made it possible to solve long-standing problems and shed new light on the behavior of empty liquids. Here we highlight the connections between patchy particles and water, focusing on the modelling principles that make an empty liquid behave like water, including the factors that control the appearance of thermodynamic and dynamic anomalies, the possibility of liquid-liquid phase transitions, and the crystallization of open crystalline structures., Comment: 21 pages, 10 figures, first submitted version, for final article see Reports on Progress in Physics https://doi.org/10.1088/1361-6633/ac42d9

We propose a general framework for solving inverse self-assembly problems, i.e. designing interactions between elementary units such that they assemble spontaneously into a predetermined structure. Our approach uses patchy particles as building blocks, where the different units bind at specific interaction sites (the patches), and we exploit the possibility of having mixtures with several components. The interaction rules between the patches is determined by transforming the combinatorial problem into a Boolean satisfiability problem (SAT) which searches for solutions where all bonds are formed in the target structure. Additional conditions, such as the non-satisfiability of competing structures (e.g. metastable states) can be imposed, allowing to effectively design the assembly path in order to avoid kinetic traps. We demonstrate this approach by designing and numerically simulating a cubic diamond structure from four particle species that assembles without competition from other polymorphs, including the hexagonal structure., Comment: 12 pages, 4 figures

We numerically investigate the metastable equilibrium structure of deep supercooled and glassy water under pressure, covering the range of densities corresponding to the experimentally produced high-density and very-high-density amorphous phases. At $T = 188$ K, a continuous increase in density is observed on varying pressure from $2.5$ to $13$ kbar, with no signs of first-order transitions. Exploiting a recently proposed approach to the analysis of the radial distribution function -- based on topological properties of the hydrogen-bond network -- we are able to identify well-defined local geometries that involve pair of molecules separated by multiple hydrogen bonds, specific of the high and very high density structures., Comment: Main text: 5 pages, 6 figures. Supplemental material: 19 pages, 18 figures. Accepted for publication in Physical Review Letters

It has recently been shown that the TIP4P/Ice model of water can be studied numerically in metastable equilibrium at and below its liquid-liquid critical temperature. We report here simulations along a subcritical isotherm, for which two liquid states with the same pressure and temperature, but different density, can be equilibrated. This allows for a clear visualisation of the structural changes taking place across the transition. We specifically focus on how the topological properties of the H-bond network change across the liquid-liquid transition. Our results demonstrate that the structure of the high-density liquid, characterised by the existence of interstitial molecules and commonly explained in terms of the collapse of the second neighbour shell, actually originates from the folding back of long rings, bringing pairs of molecules separated by several hydrogen-bonds close by in space., Comment: 13 pages, 12 figures. Accepted for publication in Journal of Chemical Physics

By means of Langevin dynamics simulations, we investigate the gel formation of randomly functionalized polymers in solution, with the ability to form both intra- and intermolecular reversible bonds. Under highly dilute conditions, these polymers form soft nano-objects (so-called single-chain nanoparticles, SCNPs), resulting from the purely intramolecular cross-linking of the reactive functional groups. Here we show that the competition between intra- and intermolecular bonds at finite concentration is governed by a delicate balance of various entropic contributions and leads to a density dependent effective valence. System-spanning networks are formed at relatively low monomer densities and their stability is mediated by just a small number of intermolecular connections per chain. The formation of intermolecular bonds furthermore can induce a non-monotonic dependence of the polymer size on the density for long bond lifetimes. Concomitantly, the polymers in the percolating cluster adopt an intramolecular structure characteristic for self-avoiding chains, which constitutes a strong contrast to the fractal globular behavior of irreversible SCNPs in crowded solutions with purely topological interactions (no intermolecular bonds). Finally, we study the dynamics of the system, which displays signatures expected for reversible gel-forming systems. An interesting behavior emerges in the reorganization dynamics of the percolating cluster. The relaxation is mostly mediated by the diffusion over long distances, through breaking and formation of bonds, of chains that do not leave the percolating cluster. Regarding the few chains that are transiently free, the time they spend until they reattach to the cluster is solely governed by the bond strength., Comment: 40 single-column pages, 15 figures

Taking advantage of the base-pairing specificity and tunability of DNA interactions, we investigate the spontaneous formation of hyperbranched clusters starting from purposely designed DNA tetravalent nanostar monomers, encoding in their four sticky-ends the desired binding rules. Specifically, we combine molecular dynamics simulations and Dynamic Light Scattering experiments to follow the aggregation process of the DNA nanostars at different concentrations and temperatures. At odd with the Flory-Stockmayer predictions, we find that, even when all possible bonds are formed, the system does not reach percolation due to the presence of intracluster bonds. We present an extension of the Flory-Stockmayer theory that properly describes the numerical and the experimental results., Comment: The Supplementary Information is included in the pdf file

Laser blow-off injections of aluminum and tungsten have been performed on the DIII-D tokamak to investigate the variation of impurity transport in a set of dedicated ion and electron heating scans with a fixed value of the external torque. The particle transport is quantified via the Bayesian inference method, which, constrained by a combination of a charge exchange recombination spectroscopy, soft X-ray measurements, and VUV spectroscopy provides a detailed uncertainty quantification of the transport coefficients. Contrasting discharge phases with a dominant electron and ion heating reveal a factor of 30 increase in midradius impurity diffusion and a 3-fold drop in the impurity confinement time when additional electron heating is applied. Further, the calculated stationary aluminum density profiles reverse from peaked in electron heated to hollow in the ion heated case, following a similar trend as electron and carbon density profiles. Comparable values of a core diffusion have been observed for W and Al ions, while differences in the propagation dynamics of these impurities are attributed to pedestal and edge transport. Modeling of the core transport with non-linear gyrokinetics code CGYRO [J. Candy and E. Belly J. Comput. Phys. 324,73 (2016)], significantly underpredicts the magnitude of the variation in Al transport. The experiment demonstrates a 3-times steeper increase of impurity diffusion with additional electron heat flux and 10-times lower diffusion in ion heated case than predicted by the modeling. However, the CGYRO model correctly predicts that the Al diffusion dramatically increases below the linear threshold for the transition from the ion temperature gradient (ITG) to trapped electron mode (TEM)., Comment: submitted to Physics of Plasmas

The stability-limit conjecture (SLC) proposes that the liquid spinodal of water returns to positive pressure in the supercooled region, and that the apparent divergence of water's thermodynamic response functions as temperature decreases are explained by the approach to this reentrant spinodal. Subsequently, it has been argued that the predictions of the SLC are inconsistent with general thermodynamic principles. Here we reconsider the thermodynamic viability of the SLC by examining a model equation of state for water first studied to clarify the relationship of the SLC to the proposed liquid-liquid phase transition in supercooled water. By demonstrating that a binodal may terminate on a spinodal at a point that is not a critical point, we show that the SLC is thermodynamically permissible in a system that has both a liquid-gas and a liquid-liquid phase transition. We also describe and clarify other unusual thermodynamic behavior that may arise in such a system, particularly that associated with the so-called "critical-point-free" scenario for a liquid-liquid phase transition, which may apply to the case of liquid Si., Comment: 11 pages, 11 figures

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 material

The potential energy landscape (PEL) formalism is a statistical mechanical approach to describe supercooled liquids and glasses. Here we use the PEL formalism to study the pressure-induced transformations between low-density amorphous ice (LDA) and high-density amorphous ice (HDA) using computer simulations of the TIP4P/2005 molecular model of water. We find that the properties of the PEL sampled by the system during the LDA-HDA transformation exhibit anomalous behavior. In particular, at conditions where the change in density during the LDA-HDA transformation is approximately discontinuous, reminiscent of a first-order phase transition, we find that (i) the inherent structure (IS) energy, $e_\text{IS}(V)$, is a concave function of the volume, and (ii) the IS pressure, $P_\text{IS}(V)$, exhibits a van der Waals-like loop. In addition, the curvature of the PEL at the IS is anomalous, a non-monotonic function of $V$. In agreement with previous studies, our work suggests that conditions (i) and (ii) are necessary (but not sufficient) signatures of the PEL for the LDA-HDA transformation to be reminiscent of a first-order phase transition. We also find that one can identify two different regions of the PEL, one associated to LDA and another to HDA. Our computer simulations are performed using a wide range of compression/decompression and cooling rates. In particular, our slowest cooling rate (0.01 K/ns) is within the experimental rates employed in hyperquenching experiments to produce LDA. Interestingly, the LDA-HDA transformation pressure that we obtain at $T=80$ K and at different rates extrapolates remarkably well to the corresponding experimental pressure., Comment: Manuscript and Supplementary Material

We study the evolution of dynamic fluctuations averaged over different space lengths and time scales to characterize spatially and temporally heterogeneous behavior of TIP4P/2005 water in liquid and supercooled states. Analysing a million particle simulated system we provide evidence of the existence, upon supercooling, of a significant enhancement of spatially localized dynamic fluctuations stemming from regions of correlated mobile molecules. We show that both the magnitude of the departure from the value expected for the system-size dependence of an uncorrelated system and the molecular size at which such trivial regime is finally recovered clearly increase upon supercooling. This provides a means to estimate an upper limit to the maximum length scale of influence of the regions of correlated mobile molecules. Notably, such upper limit grows two orders of magnitude on cooling, reaching a value corresponding to a few thousand molecules at the lowest investigated temperature.

An important goal of self-assembly is to achieve a preprogrammed structure with high fidelity. Here, we control the valence of DNA-functionalized emulsions to make linear and branched model polymers, or `colloidomers'. The distribution of cluster sizes is consistent with a polymerization process in which the droplets achieve their prescribed valence. Conformational dynamics reveals that the chains are freely-jointed, such that the end-to-end length scales with the number of bonds $N$ as $N^{\nu}$, where $\nu\approx3/4$, in agreement with the Flory theory in 2D. The chain diffusion coefficient $D$ approximately scales as $D\propto N^{-\nu}$, as predicted by the Zimm model. Unlike molecular polymers, colloidomers can be repeatedly assembled and disassembled under temperature cycling, allowing for reconfigurable, responsive matter.

We propose a coarse-grained model to investigate stress relaxation in star-polymer networks induced by dynamic bond exchange processes. We show how the swapping mechanism, once activated, allows the network to reconfigure, exploring distinct topological configurations, all of them characterised by complete extent of reaction. Our results reveal the important role played by topological defects in mediating the exchange reaction and speeding up stress relaxation. The model provides a representation of the dynamics in vitrimers, a new class of polymers characterized by bond swap mechanisms which preserve the total number of bonds, as well as in other bond-exchange materials., Comment: 5 pages, 5 figures, with 6 pages SI appended

We report an exhaustive numerical study of the statistical properties of the potential energy landscape of TIP4P/2005, one of the most accurate rigid water models. We show that, in the region where equilibrated configurations can be generated, a Gaussian landscape description is able to properly describe the model properties. We also find that the volume dependence of the landscape properties is consistent with the existence of a locus of density maxima in the phase diagram. The landscape-based equation of state accurately reproduces the TIP4P/2005 pressure-vs-volume curves, providing a sound extrapolation of the free-energy at low T. A positive-pressure liquid-liquid critical point is predicted by the resulting free-energy.

We introduce a new and robust approach for characterizing spatially and temporally heterogeneous behavior within a system based on the evolution of dynamic fuctuations once averaged over different space lengths and time scales. We apply it to investigate the dynamics in two canonical systems as the glass transition is approached: simulated Lennard-Jones liquids and experimental dense colloidal suspensions. We find that in both cases the onset of glassines is marked by spatially localized dynamic fluctuations originating in regions of correlated mobile particles. By removing the trivial system size dependence of the fluctuations we show that such regions contain tens to hundreds of particles for time scales corresponding to maximally non-Gaussian dynamics., Comment: New analysis technique introduced, and applied to previously published data

The proper design of DNA sequences allows for the formation of well defined supramolecular units with controlled interactions via a consecution of self-assembling processes. Here, we benefit from the controlled DNA self-assembly to experimentally realize particles with well defined valence, namely tetravalent nanostars (A) and bivalent chains (B). We specifically focus on the case in which A particles can only bind to B particles, via appropriately designed sticky-end sequences. Hence AA and BB bonds are not allowed. Such a binary mixture system reproduces with DNA-based particles the physics of poly-functional condensation, with an exquisite control over the bonding process, tuned by the ratio, r, between B and A units and by the temperature, T. We report dynamic light scattering experiments in a window of Ts ranging from 10{\deg}C to 55{\deg}C and an interval of r around the percolation transition to quantify the decay of the density correlation for the different cases. At low T, when all possible bonds are formed, the system behaves as a fully bonded network, as a percolating gel and as a cluster fluid depending on the selected r., Comment: 15 pages, 11 figures

We calculate the components of the microscopic pressure tensor as a function of radial distance r from the centre of a spherical water droplet, modelled using the TIP4P/2005 potential. To do so, we modify a coarse-graining method for calculating the microscopic pressure [T. Ikeshoji, B. Hafskjold, and H. Furuholt, Mol. Simul. 29, 101 (2003)] in order to apply it to a rigid molecular model of water. As test cases, we study nanodroplets ranging in size from 776 to 2880 molecules at 220 K. Beneath a surface region comprising approximately two molecular layers, the pressure tensor becomes approximately isotropic and constant with r. We find that the dependence of the pressure on droplet radius is that expected from the Young-Laplace equation, despite the small size of the droplets., Comment: 10 pages, 6 figures

It is common practice in molecular dynamics and Monte Carlo computer simulations to run multiple, separately-initialized simulations in order to improve the sampling of independent microstates. Here we examine the utility of an extreme case of this strategy, in which we run a large ensemble of $M$ independent simulations (a "swarm"), each of which is relaxed to equilibrium. We show that if $M$ is of order $10^3$, we can monitor the swarm's relaxation to equilibrium, and confirm its attainment, within $\sim 10\bar\tau$, where $\bar\tau$ is the equilibrium relaxation time. As soon as a swarm of this size attains equilibrium, the ensemble of $M$ final microstates from each run is sufficient for the evaluation of most equilibrium properties without further sampling. This approach dramatically reduces the wall-clock time required, compared to a single long simulation, by a factor of several hundred, at the cost of an increase in the total computational effort by a small factor. It is also well-suited to modern computing systems having thousands of processors, and is a viable strategy for simulation studies that need to produce high-precision results in a minimum of wall-clock time. We present results obtained by applying this approach to several test cases., Comment: 12 pages. To appear in Eur. Phy. J. E, 2017

Gels are low-packing arrested states of matter which are able to support stress. On cooling, limited valence colloidal particles form open networks stabilized by the progressive increase of the interparticle bond lifetime. These gels, named equilibrium gels, are the focus of this review article. Differently from other types of colloidal gels, equilibrium gels do not require an underlying phase separation to form. Oppositely, they form in a region of densities deprived of thermodynamic instabilities. Limited valence equilibrium gels neither coarsen nor age with time.

The potential energy landscape (PEL) formalism is a valuable approach within statistical mechanics for describing supercooled liquids and glasses. Here we use the PEL formalism and computer simulations to study the pressure-induced transformations between low-density amorphous ice (LDA) and high-density amorphous ice (HDA) at different temperatures. We employ the ST2 water model for which the LDA-HDA transformations are remarkably sharp, similar to what is observed in experiments, and reminiscent of a first-order phase transition. Our results are consistent with the view that LDA and HDA configurations are associated with two distinct regions (megabasins) of the PEL that are separated by a potential energy barrier. At higher temperature, we find that low-density liquid (LDL) configurations are located in the same megabasin as LDA, and that high-density liquid (HDL) configurations are located in the same megabasin as HDA. We show that the pressure-induced LDL-HDL and LDA-HDA transformations occur along paths that interconnect these two megabasins, but that the path followed by the liquid is different than the path followed by the amorphous solid. At higher pressure, we also study the liquid-to-ice-VII first-order phase transition, and find that the behavior of the PEL properties across this transition are qualitatively similar to the changes found during the LDA-HDA transformation. This similarity supports the interpretation that the LDA-HDA transformation is a first-order-like phase transition between out-of-equilibrium states., Comment: 29 pages, 8 figures

A re-entrant gas-liquid spinodal was proposed as a possible explanation of the apparent divergence of the compressibility and specific heat on supercooling water. Such a counter intuitive possibility, e.g. a liquid that becomes unstable to gas-like fluctuations on cooling at positive pressure, has never been observed, neither in real substances nor in off-lattice simulations. More recently, such re-entrant scenario has been dismissed on the premise that the re-entrant spinodal would collide with the gas-liquid binodal in the pressure-temperature plane. Here we study, numerically and analytically, two previously introduced one-component patchy particle models that both show (i) a re-entrant spinodal and (ii) a re-entrant binodal, providing a neat in silico (and in charta) realization of such unconventional thermodynamic scenario., Comment: 6 pages, 5 figures

We report numerical results for the effective potential arising between two colloids immersed in a self-assembling cosolute which forms reversible clusters. The potential is evaluated at cosolute state points with different densities and temperatures but with the same connectivity properties. We find that the range of the resulting effective potential is controlled only by the cosolute thermal correlation length rather than by its connectivity length. We discuss the significant differences with previous results focused on cosolute forming irreversible clusters and we show that irreversible bond case represents a singular limit which cannot be accessed in equilibrium by continuously increasing the bond lifetime., Comment: 8 pages, 10 figures

We report a detailed computational study by Brownian Dynamics simulations of the structure and dynamics of a liquid of patchy particles which develops an amorphous tetrahedral network upon decreasing temperature. The highly directional particle interactions allows us to investigate the system connectivity by discriminating the total set of particles into different populations according to a penta-modal distribution of bonds per particle. With this methodology we show how the particle bonding process is not randomly independent but it manifests clear bond correlations at low temperatures. We further explore the dynamics of the system in real space and establish a clear relation between particle mobility and particle connectivity. In particular, we provide evidence of anomalous diffusion at low temperatures and reveal how the dynamics is affected by the short-time hopping motion of the weakly bounded particles. Finally we widely investigate the dynamics and structure of the system in Fourier space and identify two quantitatively similar length scales, one dynamic and the other one static, which increase upon cooling the system and reach distances of the order of few particle diameters. We summarize our findings in a qualitative picture where the low temperature regime of the viscoelastic liquid is understood in terms of an evolving network of long time metastable cooperative domains of particles., Comment: 19 pages, 17 panels and 29 figures

DNA oligomers with properly designed sequences self-assemble into well defined constructs. Here, we exploit this methodology to produce bulk quantities of tetravalent DNA nanostars (each one composed by 196 nucleotides) and to explore the structural signatures of their aggregation process. We report small-angle neutron scattering experiments focused on the evaluation of both the form factor and the temperature evolution of the scattered intensity at a nano star concentration where the system forms a tetravalent equilibrium gel. We also perform molecular dynamics simulations of one isolated tetramer to evaluate the form factor theoretically, without resorting to any approximate shape. The numerical form factor is found to be in very good agreement with the experimental one. Simulations predict an essentially temperature independent form factor, offering the possibility to extract the effective structure factor and its evolution during the equilibrium gelation., Comment: 9 pages, 5 figures

Many natural and industrial processes rely on constrained transport, such as proteins moving through cells, particles confined in nanocomposite materials or gels, individuals in highly dense collec- tives and vehicular traffic conditions. These are examples of motion through crowded environments, in which the host matrix may retain some glass-like dynamics. Here we investigate constrained transport in a colloidal model system, in which dilute small spheres move in a slowly rearranging, glassy matrix of large spheres. Using confocal differential dynamic microscopy and simulations, we discover a critical size asymmetry at which anomalous collective transport of the small particles appears, manifested as a logarithmic decay of the density autocorrelation functions. We demonstrate that the matrix mobility is central for the observed anomalous behaviour. These results, crucially depending on size-induced dynamic asymmetry, are of relevance for a wide range of phenomena ranging from glassy systems to cell biology., Comment: 13 pages, 7 figures