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Nucleation is the rate-determining step in the kinetics of many self-assembly processes. However, the importance of nucleation in the kinetics of DNA-origami self-assembly, which involves both the binding of staple strands and the folding of the scaffold strand, is unclear. Here, using Monte Carlo simulations of a lattice model of DNA origami, we find that some, but not all, designs can have a nucleation barrier and that this barrier disappears at lower temperatures, rationalizing the success of isothermal assembly. We show that the height of the nucleation barrier depends primarily on the coaxial stacking of staples that are adjacent on the same helix, a parameter that can be modified with staple design. Creating a nucleation barrier to DNA-origami assembly could be useful in optimizing assembly times and yields, while eliminating the barrier may allow for fast molecular sensors that can assemble/disassemble without hysteresis in response to changes in the environment., Comment: 28 pages, 17 figures, accepted in Nano Letters with improved text and figure accessibility

Multi-component self-assembly mixtures offer the possibility of encoding multiple target structures with the same set of interacting components. Selective retrieval of one of the stored structures has been attempted by preparing an initial state that favours the assembly of the required target, through seeding, concentration patterning or specific choices of interaction strengths. This may not be possible in an experiment where on-the-fly reconfiguration of the building blocks to switch functionality may be required. In this paper, we explore principles of inverse design of a multi-component self-assembly mixture capable of encoding two competing structures that can be selected through simple temperature protocols. We design the target structures to realise the generic situation in which one of targets has the lower nucleation barrier while the other is globally more stable. We observe that to avoid the formation of spurious or chimeric aggregates, the number of neighbouring component pairs that occur in both structures should be minimal. Our design also requires the inclusion of components that are part only of one of the target structures, but we observe that to maximize the selectivity of retrieval, the component library itself should be maximally shared by the two targets. We demonstrate that temperature protocols can be designed which lead to the formation of either one of the target structures with high selectivity. We discuss the important role played by secondary aggregation products, which we term vestigial aggregates.

The methodology to simulate transport phenomena in bulk systems is well-established. In contrast, there is no clear consensus about the choice of techniques to model cross-transport phenomena and phoretic transport, mainly because some of the hydrodynamic descriptions are incomplete from a thermodynamic point of view. In the present paper, we use a unified framework to describe diffusio-osmosis(phoresis), and we report non-equilibrium Molecular Dynamics (NEMD) on such systems. We explore different simulation methods to highlight some of the technical problems that arise in the calculations. For diffusiophoresis, we use two NEMD methods: boundary-driven and field-driven. Although the two methods should be equivalent in the limit of very weak gradients, we find that finite Peclet-number effects are much stronger in boundary-driven flows than in the case where we apply fictitious color forces.

We study the kinetics of crystallization in deeply supercooled liquid silicon employing computer simulations and the Stillinger-Weber three body potential. The free energy barriers to crystallisation are computed using umbrella sampling Monte Carlo simulations, and for selected low temperature and zero pressure state points, using unconstrained molecular dynamics simulations to reconstruct the free energy from a mean first passage time formulation. We focus on state points that have been described in earlier work [Sastry and Angell, Nature Mater., 2, 739, 2003] as straddling a first order liquid-liquid phase transition (LLPT) between two metastable liquid states. It was argued subsequently [Ricci et al., Mol. Phys., 117, 3254, 2019] that the apparent phase transition is in fact due the loss of metastability of the liquid state with respect to the globally stable crystalline state. The presence or absence of a barrier to crystallization for these state points is therefore of importance to ascertain, with due attention to ambiguities that may arise from the choice of order parameters. We discuss our choice of order parameters and also our choice of methods to calculate the free energy at deep supercooling. We find a well-defined free energy barrier to crystallisation and demonstrate that both umbrella sampling and mean first passage time methods yield results that agree quantitatively. Our results thus provide strong evidence against the possibility that the liquids at state points close to the reported LLPT exhibit slow, spontaneous crystallisation, but they do not address the existence of a LLPT (or lack thereof). We also compute the free energy barriers to crystallisation at other state points over a broad range of temperatures and pressures, and discuss the effect of changes in the microscopic structure of the metastable liquid on the free energy barrier heights.

The free energy of glasses cannot be estimated using thermodynamic integration, as glasses are intrinsically not in equilibrium. We present numerical simulations showing that, in contrast, plausible free-energy estimates of a Kob-Andersen glass can be obtained using the Jarzynski relation. Using the Jarzynski relation, we also compute the chemical potential difference of the two components of this system, and find that, in the glassy regime, the Jarzynski estimate matches well with the extrapolated value of the supercooled liquid. Our findings are of broader interest as they show that the Jarzynski method can be used under conditions where the thermodynamic integration approach, which is normally more accurate, breaks down completely. Systems where such an approach might be useful are gels and jammed, glassy structures formed by compression., Comment: 4 pages, 2 figures

Hard-sphere model systems are well-suited in both experiment and simulations to investigate fundamental aspects of the crystallization of fluids. In experiments on colloidal models of hard-sphere fluids, the uid is unavoidably at contact with the walls of the sample cell, where heterogeneous crystallization may take place. In this work we use simulations to investigate the competition between homogeneous and heterogeneous crystallization. We report simulations of wall-induced nucleation for different confining walls. Combining the results of these simulations with earlier studies of homogeneous allows us to asses the competition between homogeneous and heterogeneous nucleation as a function of wall type, fluid density and the system size. On at walls, heterogeneous nucleation will typically overwhelm homogeneous nucleation. However, even for surfaces randomly coated with spheres with a diameter that was some three times larger than that of the fluid spheres - as has been used in some experiments - heterogeneous nucleation is likely to be dominant for volume fractions smaller than 0.535. Only for a disordered coating that has the same structure as the liquid holds promise did we find the nucleation was likely to occur in the bulk. Hence, such coatings might be used to suppress heterogeneous nucleation in experiments. Finally, we report the apparent homogeneous nucleation rate taking into account the formation of crystallites both in the bulk and at the walls. We find that the apparent overall nucleation rates coincides with those reported in "homogeneous nucleation" experiments. This suggests that heterogeneous nucleation at the walls could partly explain the large discrepancies found between experimental measurements and simulation estimates of the homogeneous nucleation rate.

Building upon recent developments of force-based estimators with a reduced variance for the computation of densities, radial distribution functions or local transport properties from molecular simulations, we show that the variance can be further reduced by considering optimal linear combinations of such estimators. This control variates approach, well known in Statistics and already used in other branches of computational Physics, has been comparatively much less exploited in molecular simulations. We illustrate this idea on the radial distribution function and the one-dimensional density of a bulk and confined Lennard-Jones fluid, where the optimal combination of estimators is determined for each distance or position, respectively. In addition to reducing the variance everywhere at virtually no additional cost, this approach cures an artefact of the initial force-based estimators, namely small but non-zero values of the quantities in regions where they should vanish. Beyond the examples considered here, the present work highlights more generally the underexplored potential of control variates to estimate observables from molecular simulations., Comment: 4 Pages and 2 Figures

Using a recently developed technique to estimate the equilibrium free energy of glassy materials, we explore if equilibrium simulation methods can be used to estimate the solubility of amorphous solids. As an illustration, we compute the chemical potentials of the constituent particles of a two-component Kob-Andersen model glass former. To compute the chemical potential for different components, we combine the calculation of the overall free energy of the glass with a calculation of the chemical potential difference of the two components. We find that the standard method to compute chemical potential differences by thermodynamic integration yields not only a wide scatter in the chemical potential values but, more seriously, the average of the thermodynamic integration results is well above the extrapolated value for the supercooled liquid. However, we find that if we compute the difference of the chemical potential of the components with the the non-equilibrium free energy expression proposed by Jarzynski, we obtain a good match with the extrapolated value of the supercooled liquid. The extension of the Jarzynski method that we propose opens a potentially powerful route to compute free-energy related equilibrium properties of glasses. We find that the solubility estimate of amorphous materials obtained from direct coexistence simulations is only in fair agreement with the solubility prediction based on the chemical potential calculations of a hypothetical "well-equilibrated glass". In direct coexistence simulations, we find that, in qualitative agreement with experiments, the amorphous solubility decreases with time and attains a low solubility value., Comment: 8 pages, 3 figures

We present simulations indicating that it should be possible to construct a switchable nano-scale fluid pump, driven by exothermic surface reactions. Such a pump could, for instance, be controlled electro-chemically. In our simulations we explore a simple illustration of such a pump. We argue that the simplicity of the pump design could make it attractive for micro/nano-fluidics applications.

We propose a numerical technique to compute the equilibrium free energy of glasses that cannot be prepared quasi-reversibly. For such systems, standard techniques for estimating the free energy by extrapolation, cannot be used. Instead, we use a procedure that samples the equilibrium partition function of the basins of attraction of the different inherent structures (local potential energy minima) of the system. If all relevant inherent structures could be adequately sampled in the (supercooled) liquid phase, our approach would be rigorous. In any finite simulation, we will miss the lower-energy inherent structures that become dominant at very low temperatures. We find that our free energy estimates for a Kob-Andersen glass are lower than those obtained by very slow cooling, even at temperatures down to one third of the glass transition temperature. The current approach could be applied to compute the chemical potential of ultra-stable glassy materials, and should enable the estimation of their solubility., Comment: 7 pages, 4 figures

The existing kinetic theory of gases is based on an analytical approach that becomes intractable for all but the simplest molecules. Here we propose a simple numerical scheme to compute the transport properties of molecular gases in the limit of infinite dilution. The approach that we propose is approximate, but our results for the diffusivity $D$, the viscosity $\eta$ and the thermal conductivity $\lambda$ of hard spheres, Lennard-Jones particles and rough hard spheres, agree well with the standard (lowest order) Chapman-Enskog results. We also present results for a Lennard-Jones-dimer model for nitrogen, for which no analytical results are available. In the case of poly-atomic molecules (we consider n-octane), our method remains simple and gives good predictions for the diffusivity and the viscosity. Computing the thermal conductivity of poly-atomic molecules requires an approximate treatment of their quantized internal modes. We show that a well-known approximation that relates $\lambda$ to $D$ and $\eta$, yields good results. We note that our approach should yield a lower limit to the exact value of $D$, $\eta$ and $\lambda$. Interestingly, the most sophisticated (higher-order) Chapman-Enskog results for rough hard spheres seem to violate this bound.

Equilibrium molecular dynamics simulations, in combination with the Green-Kubo (GK) method, have been extensively used to compute the thermal conductivity of liquids. However, the GK method relies on an ambiguous definition of the microscopic heat flux, which depends on how one chooses to distribute energies over atoms. This ambiguity makes it problematic to employ the GK method for systems with non-pairwise interactions. In this work, we show that the hydrodynamic description of thermally driven density fluctuations can be used to obtain the thermal conductivity of a bulk fluid unambiguously, thereby bypassing the need to define the heat flux. We verify that, for a model fluid with only pairwise interactions, our method yields estimates of thermal conductivity consistent with the GK approach. We apply our approach to compute the thermal conductivity of a non-pairwise additive water model at supercritical conditions, and then of a liquid hydrogen system described by a machine-learning interatomic potential, at 33 GPa and 2000 K.

Gradients in temperature, concentration or electrostatic potential cannot exert forces on a bulk fluid; they can, however, exert forces on a fluid in a microscopic boundary layer surrounding a (nano)colloidal solute, resulting in so-called phoretic flow. Here we present a simulation study of phoretic flow around a spherical colloid held fixed in a concentration gradient. We show that the resulting flow velocity depends non-monotonically on the strength of the colloid-fluid interaction. The reason for this non-monotonic dependence is that solute particles are effectively trapped in a shell around the colloid and cannot contribute to diffusio-phoresis. We also observe that the flow depends sensitively on the anisotropy of solute-colloid interaction.

We report simulations of a spherical Janus particle undergoing exothermic surface reactions around one pole only. Our model excludes self-phoretic transport by design. Nevertheless, net motion occurs from direct momentum transfer between solvent and colloid, with speed scaling as the square root of the energy released during the reaction. We find that such propulsion is dominated by the system's short-time response, when neither the time dependence of the flow around the colloid nor the solvent compressibility can be ignored. Our simulations agree reasonably well with previous experiments.

During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides an interpretation of entropy in terms of probabilities. However, we cannot rely on the statistical-mechanical expressions for entropy in systems that are far from equilibrium. In this paper, we compare various extensions of the definition of entropy, which have been proposed for non-equilibrium systems. It has recently been proposed that measures of information density may serve to quantify entropy in both equilibrium and nonequilibrium systems. We propose a new "bit-wise" method to measure the information density for off lattice systems. This method does not rely on coarse-graining of the particle coordinates. We then compare different estimates of the system entropy, based on information density and on the structural properties of the system, and check if the various entropies are mutually consistent and, importantly, whether they can detect non-trivial ordering phenomena. We find that, except for simple (one-dimensional) cases, the different methods yield answers that are at best qualitatively similar, and often not even that, although in several cases, different entropy estimates do detect ordering phenomena qualitatively. Our entropy estimates based on bit-wise data compression contain no adjustable scaling factor, and show large quantitative differences with the thermodynamic entropy obtained from equilibrium simulations. Hence, our results suggest that, at present, there is not yet a single, structure-based entropy definition that has general validity for equilibrium and non equilibrium systems.

The Lennard-Jones 12-6 potential (LJ) is arguably the most widely used pair potential in Molecular Simulations. In fact, it is so popular that the question is rarely asked whether it is fit for purpose. In this paper, we argue that, whilst the LJ potential was designed for noble gases such as argon, it is often used for systems where it is not expected to be particularly realistic. Under those circumstances, the disadvantages of the LJ potential become relevant: most important among these is that in simulations the LJ potential is always modified such that it has a finite range. More seriously, there is by now a whole family of different potentials that are all called Lennard-Jones 12-6, and that are all different - and that may have very different macroscopic properties. In this paper, we consider alternatives to the LJ 12-6 potential that could be employed under conditions where the LJ potential is only used as a typical short-ranged potential with attraction. We construct a class of potentials that are, in many respects LJ-like but that are by construction finite ranged, vanishing quadratically at the cut-off distance, and that are designed to be computationally cheap. Below, we present this potential and report numerical data for its thermodynamic and transport properties, for the most important cases: cut-off distance rc=2 (LJ-like) and rc=1.2 (a typical colloidal potential).

We report a numerical study of the diffusiophoresis of short polymers using non-equilibrium molecular dynamics simulations. More precisely, we consider polymer chains in a fluid containing a solute which has a concentration gradient, and examine the variation of the induced diffusiophoretic velocity of the polymer chains as the interaction between the monomer and the solute is varied. We find that there is a non-monotonic relation between the diffusiophoretic mobility and the strength of the monomer-solute interaction. In addition we find a weak dependence of the mobility on the length of the polymer chain, which shows clear difference from the diffusiophoresis of a solid particle. Interestingly, the hydrodynamic flow through the polymer is much less screened than for pressure driven flows.

We report a numerical study of thermo-osmotic slip, i.e. the particle flux induced by a thermal gradient along a solid-fluid interface. To facilitate comparison with theory, we consider a model of an ideal but viscous gas. We compare three numerical routes to obtain the slip coefficient: 1. by using the Onsager reciprocity relations 2. by using the appropriate Green-Kubo relation 3. via the excess enthalpy. The numerical results are found to be mutually consistent, and to agree with the theoretical prediction based on the assumption that hydrodynamics and thermodynamics are locally valid.

The optimal design of DNA origami systems that assemble rapidly and robustly is hampered by the lack of a model for self-assembly that is sufficiently detailed yet computationally tractable. Here, we propose a model for DNA origami that strikes a balance between these two criteria by representing these systems on a lattice at the level of binding domains. The free energy of hybridization between individual binding domains is estimated with a nearest-neighbour model. Double helical segments are treated as rigid rods, but we allow flexibility at points where the backbone of one of the strands is interrupted, which provides a reasonably realistic representation of partially and fully assembled states. Particular attention is paid to the constraints imposed by the double helical twist, as they determine where strand crossovers between adjacent helices can occur. To improve the efficiency of sampling configuration space, we develop Monte Carlo methods for sampling scaffold conformations in near-assembled states, and we carry out simulations in the grand canonical ensemble, enabling us to avoid considering states with unbound staples. We demonstrate that our model can quickly sample assembled configurations of a small origami design previously studied with the oxDNA model, as well as a design with staples that span longer segments of the scaffold. The sampling ability of our method should allow for good statistics to be obtained when studying the assembly pathways, and is suited to investigating in particular the effects of design and assembly conditions on these pathways and their resulting final assembled structures., Comment: 16 pages, 15 figures

We present a mean-field theory to explain the thermo-orientation effect in an off-centre Stockmayer fluid. This effect is the underlying cause of thermally induced polarisation and thermally induced monopoles, which have recently been predicted theoretically. Unlike previous theories that are based either on phenomenological equations or on scaling arguments, our approach does not require any fitting parameters. Given an equation of state and assuming local equilibrium, we construct an effective Hamiltonian for the computation of local Boltzmann averages. This simple theoretical treatment predicts molecular orientations that are in very good agreement with simulation results for the range of dipole strengths investigated. By decomposing the overall alignment into contributions from the temperature and density gradients, we shed further light on how the non-equilibrium result arises from the competition between the two gradients.

We present numerical simulations of diffusio-osmotic flow, i.e. the fluid flow generated by a concentration gradient along a solid-fluid interface. In our study, we compare a number of distinct approaches that have been proposed for computing such flows and compare them with a reference calculation based on direct, non-equilibrium Molecular Dynamics simulations. As alternatives, we consider schemes that compute diffusio-osmotic flow from the gradient of the chemical potentials of the constituent species and from the gradient of the component of the stress tensor parallel to the interface. We find that the approach based on treating chemical potential gradients as external forces acting on various species agrees with the direct simulations, thereby supporting the approach of Marbach et al. (J Chem Phys 146, 194701 (2017)). In contrast, an approach based on computing the gradients of the microscopic pressure tensor does not reproduce the direct non-equilibrium results., Comment: 7 Pages, 5 figures. arXiv admin note: text overlap with arXiv:1710.00355

Biological membranes typically contain a large number of different components dispersed in small concentrations in the main membrane phase, including proteins, sugars, and lipids of varying geometrical properties. Most of these components do not bind the cargo. Here, we show that such `inert' components can be crucial for precise control of cross-membrane trafficking. Using a statistical mechanics model and molecular dynamics simulations, we demonstrate that the presence of inert membrane components of small isotropic curvatures dramatically influences cargo endocytosis, even if the total spontaneous curvature of such a membrane remains unchanged. Curved lipids, such as cholesterol, as well as asymmetrically included proteins and tethered sugars can hence all be actively participating in controlling membrane trafficking of nanoscopic cargo. We find that even a low-level expression of curved inert membrane components can determine the membrane selectivity towards the cargo size, and can be used to selectively target membranes of certain compositions. Our results suggest a robust and general way to control cargo trafficking by adjusting the membrane composition without needing to alter the concentration of receptors nor the average membrane curvature. This study indicates that cells can prepare for any trafficking event by incorporating curved inert components in either of the membrane leaflets.

If a thermal gradient is applied along a fluid-solid interface, the fluid experiences a thermo-osmotic force. In steady state this force is balanced by the gradient of the shear stress. Surprisingly, there appears to be no unique microscopic expression that can be used for computing the magnitude of the thermo-osmotic force. Here we report how, by treating the mass $M$ of the fluid particles as a tensor in the Hamiltonian, we can eliminate the balancing shear force in a non-equilibrium simulation and therefore compute the thermo-osmotic force at simple solid-fluid interfaces. We compare the non-equilibrium force measurement with estimates of the thermo-osmotic force based on computing gradients of the stress tensor. We find that the thermo-osmotic force as measured in our simulations cannot be derived from the most common microscopic definitions of the stress tensor., Comment: 5 pages, 2 figures

A concentration gradient along a fluid-fluid interface can cause flow. On a microscopic level, this so-called Marangoni effect can be viewed as being caused by a gradient in the pressures acting on the fluid elements, or as the chemical-potential gradients acting on the excess densities of different species at the interface. If the interfacial thickness can be ignored, all approaches should result in the same flow profile away from the interface. However, on a more microscopic scale, the different expressions result in different flow profiles, only one of which can be correct. Here we compare the results of direct non-equilibrium Molecular Dynamics simulations with the flows that would be generated by pressure and chemical potential gradients. We find that the approach based on the chemical potential gradients agrees with the direct simulations, whereas the calculations based on the pressure gradients do not., Comment: 5 pages, 4 figures

We use the dynamic length and time scale separation in suspensions to formulate a general description of colloidal thermophoresis. Our approach allows an unambiguous definition of separate contributions to the colloidal flux and clarifies the physical mechanisms behind non-equilibrium motion of colloids. In particular, we derive an expression for the interfacial force density that drives single-particle thermophoresis in non-ideal fluids. The issuing relations for the transport coefficients explicitly show that interfacial thermophoresis has a hydrodynamic character that cannot be explained by a purely thermodynamic consideration. Our treatment generalises the results from other existing approaches, giving them a clear interpretation within the framework of non-equilibrium thermodynamics.