A new look at effective interactions between microgel particles

Thermoresponsive microgels find widespread use as colloidal model systems, because their temperature-dependent size allows facile tuning of their volume fraction in situ. However, an interaction potential unifying their behavior across the entire phase diagram is sorely lacking. Here we investigate microgel suspensions in the fluid regime at different volume fractions and temperatures, and in the presence of another population of small microgels, combining confocal microscopy experiments and numerical simulations. We find that effective interactions between microgels are clearly temperature dependent. In addition, microgel mixtures possess an enhanced stability compared to hard colloid mixtures - a property not predicted by a simple Hertzian model. Based on numerical calculations we propose a multi-Hertzian model, which reproduces the experimental behavior for all studied conditions. Our findings highlight that effective interactions between microgels are much more complex than usually assumed, displaying a crucial dependence on temperature and on the internal core-corona architecture of the particles.

Modelling realistic microgels in an explicit solvent

Thermoresponsive microgels are polymeric colloidal networks that can change their size in response to a temperature variation. This peculiar feature is driven by the nature of the solvent-polymer interactions, which triggers the so-called volume phase transition from a swollen to a collapsed state above a characteristic temperature. Recently, an advanced modelling protocol to assemble realistic, disordered microgels has been shown to reproduce experimental swelling behavior and form factors. In the original framework, the solvent was taken into account in an implicit way, condensing solvent-polymer interactions in an effective attraction between monomers. To go one step further, in this work we perform simulations of realistic microgels in an explicit solvent. We identify a suitable model which fully captures the main features of the implicit model and further provides information on the solvent uptake by the interior of the microgel network and on its role in the collapse kinetics. These results pave the way for addressing problems where solvent effects are dominant, such as the case of microgels at liquid-liquid interfaces.

Force-Induced Unravelling of DNA Origami

The mechanical properties of DNA nanostructures are of widespread interest as applications that exploit their stability under constant or intermittent external forces become increasingly common. We explore the force response of DNA origami in comprehensive detail by combining AFM single molecule force spectroscopy experiments with simulations using oxDNA, a coarse-grained model of DNA at the nucleotide level, to study the unravelling of an iconic origami system: the Rothemund tile. We contrast the force-induced melting of the tile with simulations of an origami 10-helix bundle. Finally, we simulate a recently proposed origami biosensor, whose function takes advantage of origami behavior under tension. We observe characteristic stick-slip unfolding dynamics in our force-extension curves for both the Rothemund tile and the helix bundle and reasonable agreement with experimentally observed rupture forces for these systems. Our results highlight the effect of design on force response: we observe regular, modular unfolding for the Rothemund tile that contrasts with strain-softening of the 10-helix bundle which leads to catastropic failure under monotonically increasing force. Further, unravelling occurs straightforwardly from the scaffold ends inward for the Rothemund tile, while the helix bundle unfolds more nonlinearly. The detailed visualization of the yielding events provided by simulation allows preferred pathways through the complex unfolding free-energy landscape to be mapped, as a key factor in determining relative barrier heights is the extensional release per base pair broken. We shed light on two important questions: how stable DNA nanostructures are under external forces and what design principles can be applied to enhance stability.

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

The numerical investigation of the statics and dynamics of systems in non-equilibrium 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.

How to simulate patchy particles⋆

Patchy particles is the name given to a large class of systems of mesoscopic particles characterized by a repulsive core and a discrete number of short-range and highly directional interaction sites. Numerical simulations have contributed significantly to our understanding of the behaviour of patchy particles, but, although simple in principle, advanced simulation techniques are often required to sample the low temperatures and long time-scales associated with their self-assembly behaviour. In this work we review the most popular simulation techniques that have been used to study patchy particles, with a special focus on Monte Carlo methods. We cover many of the tools required to simulate patchy systems, from interaction potentials to biased moves, cluster moves, and free-energy methods. The review is complemented by an educationally oriented Monte Carlo computer code that implements all the techniques described in the text to simulate a well-known tetrahedral patchy particle model.

An Accurate Estimate of the Free Energy and Phase Diagram of All-DNA Bulk Fluids

We present a numerical study in which large-scale bulk simulations of self-assembled DNA constructs have been carried out with a realistic coarse-grained model. The investigation aims at obtaining a precise, albeit numerically demanding, estimate of the free energy for such systems. We then, in turn, use these accurate results to validate a recently proposed theoretical approach that builds on a liquid-state theory, the Wertheim theory, to compute the phase diagram of all-DNA fluids. This hybrid theoretical/numerical approach, based on the lowest-order virial expansion and on a nearest-neighbor DNA model, can provide, in an undemanding way, a parameter-free thermodynamic description of DNA associating fluids that is in semi-quantitative agreement with experiments. We show that the predictions of the scheme are as accurate as those obtained with more sophisticated methods. We also demonstrate the flexibility of the approach by incorporating non-trivial additional contributions that go beyond the nearest-neighbor model to compute the DNA hybridization free energy.

Internal structure and swelling behaviour of in silico microgel particles

Microgels are soft colloids that, by 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.

In Silico Synthesis of Microgel Particles

Microgels are colloidal-scale particles individually made of cross-linked polymer networks that can swell and deswell in response to external stimuli, such as changes to temperature or pH. Despite a large amount of experimental activities on microgels, a proper theoretical description based on individual particle properties is still missing due to the complexity of the particles. To go one step further, here we propose a novel methodology to assemble realistic microgel particles in silico. We exploit the self-assembly of a binary mixture composed of tetravalent (cross-linkers) and bivalent (monomer beads) patchy particles under spherical confinement in order to produce fully bonded networks. The resulting structure is then used to generate the initial microgel configuration, which is subsequently simulated with a bead-spring model complemented by a temperature-induced hydrophobic attraction. To validate our assembly protocol, we focus on a small microgel test case and show that we can reproduce the experimental swelling curve by appropriately tuning the confining sphere radius, something that would not be possible with less sophisticated assembly methodologies, e.g., in the case of networks generated from an underlying crystal structure. We further investigate the structure (in reciprocal and real space) and the swelling curves of microgels as a function of temperature, finding that our results are well described by the widely used fuzzy sphere model. This is a first step toward a realistic modeling of microgel particles, which will pave the way for a careful assessment of their elastic properties and effective interactions.

Free energy calculations for rings and chains formed by dipolar hard spheres

We employ a method based on Monte Carlo grand-canonical simulations to precisely calculate partition functions of non-interacting chains and rings formed by dipolar hard spheres (DHS) at low temperature. The extended low temperature region offered by such cluster calculations, compared to what had been previously achieved with standard simulations, opens up the possibility of exploring a part of the DHS phase diagram which was inaccessible before. The reported results offer the unique opportunity of verifying well-established theoretical models based on the ideal gas of cluster approximation in order to clarify their range of validity. They also provide the basis for future studies in which cluster-cluster interactions will be included.

Condensation and Demixing in Solutions of DNA Nanostars and Their Mixtures

We present a numerical/theoretical approach to efficiently evaluate the phase diagram of self-assembling DNA nanostars. Combining input information based on a realistic coarse-grained DNA potential with the Wertheim association theory, we derive a parameter-free thermodynamic description of these systems. We apply this method to investigate the phase behavior of single components and mixtures of DNA nanostars with different numbers of sticky arms, elucidating the role of the system functionality and of salt concentration. Specifically, we evaluate the propensity to demix, the gas-liquid phase boundaries and the location of the critical points. The predicted critical parameters compare very well with existing experimental results for the available compositions. The approach developed here is very general, easily extensible to other all-DNA systems, and provides guidance for future experiments.

Small-angle neutron scattering and molecular dynamics structural study of gelling DNA nanostars

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 of 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 nanostar concentration where the system forms a tetravalent equilibrium gel. We also perform molecular dynamics simulations of one isolated tetramer to evaluate the form factor numerically, 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.

Connectivity, dynamics, and structure in a tetrahedral network liquid

We report a detailed computational study by Brownian dynamics simulations of the structure and dynamics of a liquid of patchy particles which forms an amorphous tetrahedral network upon decreasing the temperature. The highly directional particle interactions allow 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 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.

Limiting the valence: advancements and new perspectives on patchy colloids, soft functionalized nanoparticles and biomolecules

Artistic representation of limited valance units consisting of a soft core (in blue) and a small number of flexible bonding patches (in orange).

Void-Based Assembly of Colloidal Crystals: Using Structure-Directing Agents to Direct the Assembly of Open Colloidal Crystals

We have used computer simulations to reveal how colloidal crystals may be assembled by engineering the shape and charge of polymeric additives, which act as structure-directing agents (SDAs). Using these agents, only a single desired polymorph may be obtained from a crystallizing mixture of colloids and polymers, which would otherwise result in a defective crystal in the absence of these agents. Building on previous work, which demonstrated this principle in the limiting case of high-density, close-packed crystals, we have now achieved this control over low-density, open crystals, which have broad utility especially in optical applications. These results reveal the general utility of the SDA paradigm in assembling tailored colloidal crystals, which represents a new design method that does not rely on any modification of the colloids themselves.

Bottom-Up Colloidal Crystal Assembly with a Twist

Globally ordered colloidal crystal lattices have broad utility in a wide range of optical and catalytic devices, for example, as photonic band gap materials. However, the self-assembly of stereospecific structures is often confounded by polymorphism. Small free-energy differences often characterize ensembles of different structures, making it difficult to produce a single morphology at will. Current techniques to handle this problem adopt one of two approaches: that of the "top-down" or "bottom-up" methodology, whereby structures are engineered starting from the largest or smallest relevant length scales, respectively. However, recently, a third approach for directing high fidelity assembly of colloidal crystals has been suggested which relies on the introduction of polymer cosolutes into the crystal phase [Mahynski, N.; Panagiotopoulos, A. Z.; Meng, D.; Kumar, S. K. Nat. Commun. 2014, 5, 4472]. By tuning the polymer's morphology to interact uniquely with the void symmetry of a single desired crystal, the entropy loss associated with polymer confinement has been shown to strongly bias the formation of that phase. However, previously, this approach has only been demonstrated in the limiting case of close-packed crystals. Here, we show how this approach may be generalized and extended to complex open crystals, illustrating the utility of this "structure-directing agent" paradigm in engineering the nanoscale structure of ordered colloidal materials. The high degree of transferability of this paradigm's basic principles between relatively simple crystals and more complex ones suggests that this represents a valuable addition to presently known self-assembly techniques.

Direct Simulation of the Self-Assembly of a Small DNA Origami

By using oxDNA, a coarse-grained nucleotide-level model of DNA, we are able to directly simulate the self-assembly of a small 384-base-pair origami from single-stranded scaffold and staple strands in solution. In general, we see attachment of new staple strands occurring in parallel, but with cooperativity evident for the binding of the second domain of a staple if the adjacent junction is already partially formed. For a system with exactly one copy of each staple strand, we observe a complete assembly pathway in an intermediate temperature window; at low temperatures successful assembly is prevented by misbonding while at higher temperature the free-energy barriers to assembly become too large for assembly on our simulation time scales. For high-concentration systems involving a large staple strand excess, we never see complete assembly because there are invariably instances where two copies of the same staple both bind to the scaffold, creating a kinetic trap that prevents the complete binding of either staple. This mutual staple blocking could also lead to aggregates of partially formed origamis in real systems, and helps to rationalize certain successful origami design strategies.

Soft self-assembled nanoparticles with temperature-dependent properties

The fabrication of versatile building blocks that reliably self-assemble into desired ordered and disordered phases is amongst the hottest topics in contemporary materials 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 specific functionalisation of the building blocks is required. Telechelic star polymers, i.e., star polymers made of a number of f 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, under fixed external conditions the self-assembly behaviour depends only on the number of arms and on the ratio of solvophobic to solvophilic monomers. However, changes in temperature and/or solvent quality make it possible to reliably change the number and size of the attractive patches. This allows the steering of 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.

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 provide an exact relationship that allows us to obtain the effective pair potential for any type of colloid-depletant interaction 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.

Temperature-induced structural transitions in self-assembling magnetic nanocolloids

With the help of a unique combination of density functional theory and computer simulations, we discover two possible scenarios, depending on concentration, for the hierarchical self-assembly of magnetic nanoparticles on cooling.