A Neural-Network-Optimized Hydrogen Peroxide Pairwise Additive Model for Classical Simulations.

We have developed an all-atom pairwise additive model for hydrogen peroxide using an optimization procedure based on artificial neural networks (ANNs). The model is based on experimental molecular geometry and includes a dihedral potential that hinders the cis-type configuration and allows for crossing the trans one, defined between the planes that have the two oxygen atoms and each hydrogen. The model's parametrization is achieved by training simple ANNs to minimize a target function that measures the differences between various thermodynamic and transport properties and the corresponding experimental values. Finally, we evaluated a range of properties for the optimized model and its mixtures with SPC/E water, including bulk-liquid properties (density, thermal expansion coefficient, adiabatic compressibility, etc.) and properties of systems at equilibrium (vapor and liquid density, vapor pressure and composition, surface tension, etc.). Overall, we obtained good agreement with experimental data.

Controlling the anisotropic self-assembly of polybutadiene-grafted silica nanoparticles by tuning three-body interaction forces.

Recently, the significant improvements in polymer composites properties have been mainly attributed to the ability of filler nanoparticles (NPs) to self-assemble into highly anisotropic self-assembled structures. In this work, we investigate the self-assembly of core-shell NPs composed of a silica core grafted with polybutadiene (PB) chains, generating the so-called "hairy" NPs (HNPs), immersed in tetrahydrofuran solvent. While uncoated silica beads aggregate forming uniform compact structures, the presence of a PB shell affects the silica NPs organization to the point that by increasing the polymer density at the corona, they tend to self-assemble into linear chain-like structures. To reproduce the experimental observations, we propose a theoretical model for the two-body that considers the van der Waals attractive energy together with the polymer-induced repulsive steric contribution and includes an additional three-body interaction term. This term arises due to the anisotropic distribution of PB, which increases their concentration near the NPs contact region. The resulting steric repulsion experienced by a third NP approaching the dimer prevents its binding close to the dimer bond and favors the growth of chain-like structures. We find good agreement between the simulated and experimental self-assembled superstructures, confirming that this three-body steric repulsion plays a key role in determining the cluster morphology of these core-shell NPs. The model also shows that further increasing the grafting density leads to low-density gel-like open structures.

Extended law of corresponding states: square-well oblates.

The vapour-liquid coexistence collapse in the reduced temperature,Tr=T/Tc, reduced density,ρr=ρ/ρc, plane is known as a principle of corresponding states, and Noro and Frenkel have extended it for pair potentials of variable range. Here, we provide a theoretical basis supporting this extension, and show that it can also be applied to short-range pair potentials where both repulsive and attractive parts can be anisotropic. We observe that the binodals of oblate hard ellipsoids for a given aspect ratio (κ= 1/3) with varying short-range square-well interactions collapse into a single master curve in theΔB2*-ρrplane, whereΔB2*=(B2(T)-B2(Tc))/v0,B2is the second virial coefficient, andv0is the volume of the hard body. This finding is confirmed by both REMC simulation and second virial perturbation theory for varying square-well shells, mimicking uniform, equator, and pole attractions. Our simulation results reveal that the extended law of corresponding states is not related to the local structure of the fluid.

Scaling Laws in the Diffusive Release of Neutral Cargo from Hollow Hydrogel Nanoparticles: Paclitaxel-Loaded Poly(4-vinylpyridine).

We study the nonequilibrium diffusive release of electroneutral molecular cargo encapsulated inside hollow hydrogel nanoparticles. We propose a theoretical model that includes osmotic, steric, and short-range polymer-cargo attractions to determine the effective cargo-hydrogel interaction, ueff*, and the effective diffusion coefficient of the cargo inside the polymer network, Deff*. Using dynamical density functional theory (DDFT), we investigate the scaling of the characteristic release time, τ1/2, with the key parameters involved in the process, namely, ueff*, Deff*, and the swelling ratio. This effort represents a full study of the problem, covering a broad range of cargo sizes and providing predictions for repulsive and attractive polymer shells. Our calculations show that the release time through repulsive polymer networks scales with q2eßueff*/Deff* for ßueff* ≫ 1. In this case, the cargo molecules are excluded from the shell of the hydrogel. For attractive shells, the polymer retains the cargo molecules on its internal surface and its interior, and the release time grows exponentially with the attraction strength. The DDFT calculations are compared to an analytical model for the mean first passage time, which provides an excellent quantitative description of the kinetics for both repulsive and attractive shells without fitting parameters. Finally, we apply the method to reproduce experimental results on the release of paclitaxel from hollow poly(4-vinylpyridine) nanoparticles and find that the slow release of the drug can be explained in terms of the strong binding attraction between the drug and the polymer.

Three-step melting of hard superdisks in two dimensions.

We explore the link between the melting scenarios of two-dimensional systems of hard disks and squares through replica-exchange Monte Carlo simulations of hard superdisks. The well-known melting scenarios are observed in the disk and square limits, while we observe an unusual three-step scenario for dual shapes. We find that two mesophases mediate the melting: a hexatic phase and another fluid phase with a D_{2} local symmetry, we call it rhombatic, where both bond and particle orientational orders are quasi-long-range. Our results show that not only can the melting process of liquid-crystal forming molecules be complicated, where elongated shapes stabilize several mesophases, but also that of anisotropic quasispherical molecules.

Massive replica exchange Monte Carlo algorithm: a tool to access high pressure thermodynamics of hard systems.

We have explored the idea of producing the equilibrium equation of state, i.e. the pressure as a function of packing fraction, ßP(φ), of a confined system up to very high pressures to yield the configuration that leads to the maximum packing fraction. For this purpose we have massively implemented the replica exchange Monte Carlo algorithm in graphics processing units (GPUs), in such a way that each GPU core handles a single simulation cell. This yields a very easy scheme to implement parallelization for a very large amount of replicas (thousands), which densely sample configuration space. We have tested this idea with a very well studied system, i.e. discs confined in a circular cavity, for a number of particles N ≤ 125. In all cases, our outcomes for configurations having maximum packing fractions are in perfect agreement with those already reported and conjectured optimal in the literature, for which there is no formal mathematical proof, strongly suggesting that they are indeed optimal configurations. Furthermore, in most cases, we have obtained the same function ßP(φ), by compressing loose random configurations and by decompressing copies of the configuration having the largest packing fraction. This reveals numerically that the so obtained maximum packing configurations are the correct answer.

Phase diagram of hard squares in slit confinement.

This work shows a complete phase diagram of hard squares of side length σ in slit confinement for H < 4.5, H being the wall to wall distance measured in σ units, including the maximal packing fraction limit. The phase diagram exhibits a transition between a single-row parallel 1-[Formula: see text] and a zigzag 2-[Formula: see text] structures for H c (2) = (2[Formula: see text] - 1) < H < 2, and also another one involving the 1-[Formula: see text] and 2-[Formula: see text] structures (two parallel rows) for 2 < H < H c (3) (H c (n) = n - 1 + [Formula: see text]/n is the critical wall-to-wall distance for a (n - 1)-[Formula: see text] to n-[Formula: see text] transition and where n-[Formula: see text] represents a structure formed by tilted rectangles, each one clustering n stacked squares), and a triple point for H t [Formula: see text] 2.005. In this triple point there coexists the 1-[Formula: see text], 2-[Formula: see text], and 2-[Formula: see text] structures. For regions H c (3) < H < H c (4) and H c (4) < H < H c (5), very similar pictures arise. There is a (n - 1)-[Formula: see text] to a n-[Formula: see text] strong transition for H c (n) < H < n, followed by a softer (n - 1)-[Formula: see text] to n-[Formula: see text] transition for n < H < H c (n + 1). Again, at H [Formula: see text] n there appears a triple point, involving the (n - 1)-[Formula: see text], n-[Formula: see text], and n-[Formula: see text] structures. The similarities found for n = 2, 3 and 4 lead us to propose a tentative phase diagram for H c (n) < H < H c (n + 1) (n ∈ [Formula: see text], n > 2), where structures (n - 1)-[Formula: see text], n-[Formula: see text], and n-[Formula: see text] fill the phase diagram. Simulation and Onsager theory results are qualitatively consistent.

Critical behavior of hard squares in strong confinement.

We examine the phase behavior of a quasi-one-dimensional system of hard squares with side-length σ, where the particles are confined between two parallel walls and only nearest-neighbor interactions occur. As in our previous work [Gurin, Varga, and Odriozola, Phys. Rev. E 94, 050603 (2016)]2470-004510.1103/PhysRevE.94.050603, the transfer operator method is used, but here we impose a restricted orientation and position approximation to yield an analytic description of the physical properties. This allows us to study the parallel fluid-like to zigzag solid-like structural transition, where the compressibility and heat capacity peaks sharpen and get higher as H→H_{c}=2sqrt[2]-1≈1.8284 and p→p_{c}=∞. Here H is the width of the channel measured in σ units and p is the pressure. We have found that this structural change becomes critical at the (p_{c},H_{c}) point. The obtained critical exponents belong to the universality class of the one-dimensional Ising model. We believe this behavior holds for the unrestricted orientational and positional case.

Conformation change of an isotactic poly (N-isopropylacrylamide) membrane: Molecular dynamics.

In this work, isotactic Poly (N-Isopropylacrylamide)-PNIPAM-in neat water and in electrolyte solutions is studied by means of molecular dynamics simulations. This is done for an infinitely diluted oligomer and for an assembly of several PNIPAM chains arranged into a planar membrane configuration with a core-shell morphology. We employed two different force fields, AMBER (assisted model building with energy refinement) and OPLS-AA (all atom - optimized potentials for liquid simulations) in combination with extended simple point charge water. Despite the more water insoluble character of isotactic oligomers, our results support the existence of a coil to globule transition for the isolated 30-mer. This may imply the existence of an oligomer rich phase of coil-like structures in equilibrium with a water rich phase for temperatures close but below the coil to globule transition temperature, TΘ. However, the obtained coil structure is much more compact than that corresponding to the syndiotactic chain. Our estimations of TΘ are (308±5) K and (303±5) K for AMBER and OPLS-AA, respectively. The membrane configuration allows one to include chain-chain interactions, to follow density profiles of water, polymer, and solutes, and accessing the membrane-water interface tension. Results show gradual shrinking and swelling of the membrane by switching temperature above and below TΘ, as well as the increase and decrease of the membrane-water interface tension. Finally, concentration profiles for 1M NaCl and 1M NaI electrolytes are shown, depicting a strong salting-out effect for NaCl and a much lighter effect for NaI, in good qualitative agreement with experiments.

Colloid-polymer mixtures under slit confinement.

We report a NVT molecular dynamic study of colloid-polymer mixtures under slit confinement. For this purpose, we are employing the Asakura-Oosawa model for studying colloidal particles, polymer coils, and hard walls as the external confining field. The colloid-polymer size ratio, q, is varied in the range 1⩾q⩾0.4 and the confinement distance, H, in 10σc⩾H⩾3σc, σc being the colloidal diameter. Vapor-liquid coexistence properties are assessed, from which phase diagrams are built. The obtained data fulfill the corresponding states law for a constant H when q is varied. The shift of the polymer and colloidal chemical potentials of coexistence follows a linear relationship with (H-σc)-1 for H≳4σc. The confined vapor-liquid interfaces can be fitted with a semicircular line of curvature (H-σc)-1, from which the contact angle can be obtained. We observe complete wetting of the confining walls for reservoir polymer concentrations above and close to the critical value, and partial wetting for reservoir polymer concentrations above and far from it.

Competition between excluded-volume and electrostatic interactions for nanogel swelling: effects of the counterion valence and nanogel charge.

In this work the equilibrium distribution of ions around a thermo-responsive charged nanogel particle in an electrolyte aqueous suspension is explored using coarse-grained Monte Carlo computer simulations and the Ornstein-Zernike integral equation theory. We explicitly consider the ionic size in both methods and study the interplay between electrostatic and excluded-volume effects for swollen and shrunken nanogels, monovalent and trivalent counterions, and for two different nanogel charges. We find good quantitative agreement between the ionic density profiles obtained using both methods when the excluded repulsive force exerted by the cross-linked polymer network is taken into account. For the shrunken conformation, the electrostatic repulsion between the charged groups provokes a heterogeneous polymer density profile, leading to a nanogel structure with an internal low density hole surrounded by a dense corona. The results show that the excluded-volume repulsion strongly hinders the ion permeation for shrunken nanogels, where volume exclusion is able to significantly reduce the concentration of counterions in the more dense regions of the nanogel. In general, we demonstrate that the thermosensitive behaviour of nanogels, as well as their internal structure, is strongly influenced by the valence of the counterions and also by the charge of the particles. On the one hand, an increase of the counterion valence moves the swelling transition to lower temperatures, and induces a major structuring of the charged monomers into internal and external layers around the crown for shrunken nanogels. On the other hand, increasing the particle charge shifts the swelling curve to larger values of the effective radius of the nanogel.

Anomalous structural transition of confined hard squares.

Structural transitions are examined in quasi-one-dimensional systems of freely rotating hard squares, which are confined between two parallel walls. We find two competing phases: one is a fluid where the squares have two sides parallel to the walls, while the second one is a solidlike structure with a zigzag arrangement of the squares. Using transfer matrix method we show that the configuration space consists of subspaces of fluidlike and solidlike phases, which are connected with low probability microstates of mixed structures. The existence of these connecting states makes the thermodynamic quantities continuous and precludes the possibility of a true phase transition. However, thermodynamic functions indicate strong tendency for the phase transition and our replica exchange Monte Carlo simulation study detects several important markers of the first order phase transition. The distinction of a phase transition from a structural change is practically impossible with simulations and experiments in such systems like the confined hard squares.

Thermodynamic properties of triangle-well fluids in two dimensions: MC and MD simulations.

With the aim of providing complementary data of the thermodynamics properties of the triangular well potential, the vapor/liquid phase diagrams for such potential with different interaction ranges were calculated in two dimensions by Monte Carlo and molecular dynamics simulations; also, the vapor/liquid interfacial tension was calculated. As reported for other interaction potentials, it was observed that the reduction of the dimensionality makes the phase diagram to shrink. Finally, with the aid of reported data for the same potential in three dimensions, it was observed that this potential does not follow the principle of corresponding states.

Entropy Driven Self-Assembly in Charged Lock-Key Particles.

In this work we study the lock-key model successfully used in supramolecular chemistry and particles self-assembly and gain further insight into the infinite diluted limit of the lock and key, depletant mediated, effective attraction. We discuss the depletant forces and entropy approaches to self-assembly and give details on the different contributions to the net force for a charged lock and key pair immersed in a solvent plus a primitive model electrolyte. We show a strong correlation of the force components behavior and the underlying processes of co-ion and solvent release from the cavity. In addition, we put into context the universal behavior observed for the energy-distance curves when changing the lock and key to solvent size ratio. Basically, we now show that this behavior is not always achieved and depends on the particular system geometry. Finally, we present a qualitative good agreement with experiments when changing the electrolyte concentration, valence, and cavity-key size ratio.

Effect of orientational restriction on monolayers of hard ellipsoids.

The effect of out-of-plane orientational freedom on the orientational ordering properties of a monolayer of hard ellipsoids is studied using the Parsons-Lee scaling approach and replica exchange Monte Carlo computer simulation. Prolate and oblate ellipsoids exhibit very different ordering properties, namely, the axes of revolution of prolate particles tend to lean out, while those of oblate ones prefer to lean into the confining plane. The driving mechanism of this is that the particles try to maximize the available free area on the confining surface, which can be achieved by minimizing the cross section areas of the particles with the plane. In the lack of out-of-plane orientational freedom the monolayer of prolate particles is identical to a two-dimensional hard ellipse system, which undergoes an isotropic-nematic ordering transition with increasing density. With gradually switching on the out-of-plane orientational freedom the prolate particles lean out from the confining plane and destabilisation of the in-plane isotropic-nematic phase transition is observed. The system of oblate particles behaves oppositely to that of prolates. It corresponds to a two-dimensional system of hard disks in the lack of out-of-plane freedom, while it behaves similar to that of hard ellipses in the freely rotating case. Solid phases can be realised by lower surface coverage due to the out-of-plane orientation freedom for both oblate and prolate shapes.

Phase diagram of two-dimensional hard ellipses.

We report the phase diagram of two-dimensional hard ellipses as obtained from replica exchange Monte Carlo simulations. The replica exchange is implemented by expanding the isobaric ensemble in pressure. The phase diagram shows four regions: isotropic, nematic, plastic, and solid (letting aside the hexatic phase at the isotropic-plastic two-step transition [E. P. Bernard and W. Krauth, Phys. Rev. Lett. 107, 155704 (2011)]). At low anisotropies, the isotropic fluid turns into a plastic phase which in turn yields a solid for increasing pressure (area fraction). Intermediate anisotropies lead to a single first order transition (isotropic-solid). Finally, large anisotropies yield an isotropic-nematic transition at low pressures and a high-pressure nematic-solid transition. We obtain continuous isotropic-nematic transitions. For the transitions involving quasi-long-range positional ordering, i.e., isotropic-plastic, isotropic-solid, and nematic-solid, we observe bimodal probability density functions. This supports first order transition scenarios.

Simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres.

A recent proposal in which the equation of state of a polydisperse hard-sphere mixture is mapped onto that of the one-component fluid is extrapolated beyond the freezing point to estimate the jamming packing fraction ϕJ of the polydisperse system as a simple function of M1M3/M22, where Mk is the kth moment of the size distribution. An analysis of experimental and simulation data of ϕJ for a large number of different mixtures shows a remarkable general agreement with the theoretical estimate. To give extra support to the procedure, simulation data for seventeen mixtures in the high-density region are used to infer the equation of state of the pure hard-sphere system in the metastable region. An excellent collapse of the inferred curves up to the glass transition and a significant narrowing of the different out-of-equilibrium glass branches all the way to jamming are observed. Thus, the present approach provides an extremely simple criterion to unify in a common framework and to give coherence to data coming from very different polydisperse hard-sphere mixtures.

Empty liquid phase of colloidal ellipsoids: the role of shape and interaction anisotropy.

We study the effect of anisotropic excluded volume and attractive interactions on the vapor-liquid phase transition of colloidal ellipsoids. In our model, the hard ellipsoid is embedded into an ellipsoidal well, where both the shape of the hard ellipsoid and that of the added enclosing ellipsoidal well can be varied independently. The bulk properties of these particles are examined by means of a van der Waals type perturbation theory and validated with replica exchange Monte Carlo simulations. It is shown that both the critical volume fraction (ηc) and the critical temperature (Tc) of the vapor-liquid phase transition vanish with increasing shape anisotropy for oblate shapes, while ηc → 0 and Tc ≠ 0 are obtained for very elongated prolate shapes. These results suggest that the chance to stabilize empty liquids (a liquid phase with vanishing density) is higher in suspensions of rod-like colloidal ellipsoids than in those of plate-like ones.

Constant-force approach to discontinuous potentials.

Aiming to approach the thermodynamical properties of hard-core systems by standard molecular dynamics simulation, we propose setting a repulsive constant-force for overlapping particles. That is, the discontinuity of the pair potential is replaced by a linear function with a large negative slope. Hence, the core-core repulsion, usually modeled with a power function of distance, yields a large force as soon as the cores slightly overlap. This leads to a quasi-hardcore behavior. The idea is tested for a triangle potential of short range. The results obtained by replica exchange molecular dynamics for several repulsive forces are contrasted with the ones obtained for the discontinuous potential and by means of replica exchange Monte Carlo. We found remarkable agreements for the vapor-liquid coexistence densities as well as for the surface tension.

Statistical mechanics approach to lock-key supramolecular chemistry interactions.

In the supramolecular chemistry field, intuitive concepts such as molecular complementarity and molecular recognition are used to explain the mechanism of lock-key associations. However, these concepts lack a precise definition, and consequently this mechanism is not well defined and understood. Here we address the physical basis of this mechanism, based on formal statistical mechanics, through Monte Carlo simulation and compare our results with recent experimental data for charged or uncharged lock-key colloids. We find that, given the size range of the molecules involved in these associations, the entropy contribution, driven by the solvent, rules the interaction, over that of the enthalpy. A universal behavior for the uncharged lock-key association is found. Based on our results, we propose a supramolecular chemistry definition.