Effective potentials between nanoparticles in suspension

Results of molecular dynamics simulations are presented for the pair distribution function between nanoparticles in an explicit solvent as a function of nanoparticle diameter and interaction strength between the nanoparticle and solvent. The effect of including the solvent explicitly is demonstrated by comparing the pair distribution function of nanoparticles to that in an implicit solvent. The nanoparticles are modeled as a uniform distribution of Lennard-Jones particles, while the solvent is represented by standard Lennard-Jones particles. The diameter of the nanoparticle is varied from 10 to 25 times that of the solvent for a range of nanoparticle volume fractions. As the strength of the interactions between nanoparticles and the solvent increases, the solvent layer surrounding the nanoparticle is formed which increases the effective radii of the nanoparticles. The pair distribution functions are inverted using the Ornstein-Zernike integral equation to determine an effective pair potential between the nanoparticles mediated by the introduction of an explicit solvent.     

Coarse-grained simulation of amphiphilic self-assembly

The authors present a computer simulation study of amphiphilic self-assembly performed using a computationally efficient single-site model based on Gay-Berne [J. Chem. Phys. 74, 3316 (1981)] and Lennard-Jones particles. Molecular dynamics simulations of these systems show that free self-assembly of micellar, bilayer, and inverse micelle arrangements can be readily achieved for a single model parametrization. This self-assembly is predominantly driven by the anisotropy of the amphiphile-solvent interaction, amphiphile-amphiphile dispersive interactions being found to be of secondary importance. While amphiphile concentration is the main determinant of phase stability, molecular parameters such as head group size and interaction strength also have measurable affects on system properties.     

Molecular dynamics simulation of the forces between colloidal nanoparticles in n-decane solvent

Molecular dynamics is utilized to simulate solvation forces between two nanoparticles immersed in liquid n-decane. Three types of solvophilic nanoparticles are investigated with sizes in the 1-6 nm range: small and large amorphous spheres and crystalline cubes. We find that the solvation forces are negligible for the small spheres, which have diameters comparable to the end-to-end distance of all-trans decane, and we attribute this to the inability of the small spheres to induce decane ordering in the interparticle gap. The cubic nanoparticles (and to a lesser extent, the large spheres) are able to induce the formation of solidlike, n-decane layers in their gap for certain nanoparticle separations, and the transition between layered and disordered structures leads to solvation forces that oscillate between repulsion and attraction as the nanoparticle separation is varied. We find that the Derjaguin approximation [B. V. Derjaguin, Kolloid-Z. 69, 155 (1934)] is not effective at describing the dependence of the solvation forces on nanoparticle size and shape-contrasting results from a previous study involving these nanoparticles in Lennard-Jones solvent [Y. Qin and K. A. Fichthorn, J. Chem. Phys. 119, 9745 (2003)]. In particular, we find that for decane, the magnitude of the repulsive solvation forces is sensitive to nanoparticle size and shape, a phenomenon we attribute to the size and rigid-rod structure of n-decane, which makes its ordering in the interparticle gap sensitive to the size and the surface roughness of the nanoparticles.     

Structure and diffusion of nanoparticle monolayers floating at liquid/vapor interfaces: a molecular dynamics study

Large-scale molecular dynamics simulations are used to simulate a layer of nanoparticles floating on the surface of a liquid. Both a low viscosity liquid, represented by Lennard-Jones monomers, and a high viscosity liquid, represented by linear homopolymers, are studied. The organization and diffusion of the nanoparticles are analyzed as the nanoparticle density and the contact angle between the nanoparticles and liquid are varied. When the interaction between the nanoparticles and liquid is reduced the contact angle increases and the nanoparticles ride higher on the liquid surface, which enables them to diffuse faster. In this case the short-range order is also reduced as seen in the pair correlation function. For the polymeric liquids, the out-of-layer fluctuation is suppressed and the short-range order is slightly enhanced. However, the diffusion becomes much slower and the mean square displacement even shows sub-linear time dependence at large times. The relation between diffusion coefficient and viscosity is found to deviate from that in bulk diffusion. Results are compared to simulations of the identical nanoparticles in 2-dimensions.     

Cluster pair correlation function of simple fluids: energetic connectivity criteria

We consider the clustering of Lennard-Jones particles by using an energetic connectivity criterion proposed long ago by Hill [J. Chem. Phys. 32, 617 (1955)] for the bond between pairs of particles. The criterion establishes that two particles are bonded (directly connected) if their relative kinetic energy is less than minus their relative potential energy. Thus, in general, it depends on the direction as well as on the magnitude of the velocities and positions of the particles. An integral equation for the pair connectedness function, proposed by two of the authors [Phys. Rev. E 61, R6067 (2000)], is solved for this criterion and the results are compared with those obtained from molecular dynamics simulations and from a connectedness Percus-Yevick-type integral equation for a velocity-averaged version of Hill's energetic criterion.     

Comparison of Brownian dynamics algorithms with hydrodynamic interaction

The hydrodynamic interaction is an essential effect to consider in Brownian dynamics simulations of polymer and nanoparticle dilute solutions. Several mathematical approaches can be used to build Brownian dynamics algorithms with hydrodynamic interaction, the most common of them being the exact but time demanding Cholesky decomposition and the Chebyshev polynomial expansion. Recently, Geyer and Winter [J. Chem. Phys. 130, 1149051 (2009)] have proposed a new approximation to treat the hydrodynamic interaction that seems quite efficient and is increasingly used. So far, a systematic comparison among those approaches has not been clearly made. In this paper, several features and the efficiency of typical implementations of those approaches are evaluated by using bead-and-spring chain models. The different sensitivity to the bead overlap detected for the different implementations may be of interest to select the suitable algorithm for a given simulation.     

Microphase separation induced by interfacial segregation of isotropic, spherical nanoparticles

In a recent experiment by Chung et al. [Nano Lett. 5, 1878 (2005)] and simulation by Stratford et al. [Science 309, 2198 (2005)] on immiscible blends containing nanoscale particles, it was shown that the phase separation of the two polymers can be prevented as a result of the aggregation of the nanoparticles at the interfaces between the two polymers. Motivated by these studies, we performed large scale systematic simulations, based on the dissipative particle dynamics approach, on immiscible binary (A-B) fluids containing moderate volume fractions of isotropic nanoscale spherical particles N. The nanoparticles preferentially segregate at the interfaces between the two fluids if the pairwise interactions between the three components are such that chi(AB)>/chi(AN)-chi(BN)/. We find that at later times, the average domain size saturates to a value, L approximately R(N)/phi(N), where R(N) and phi(N) are the radius and volume fraction of the nanoparticles, respectively. For small nanoparticles, however, full phase separation is observed.     

Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems

This series of papers is devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids with more than 90% correlation between their virial W and potential energy U fluctuations in the NVT ensemble. Paper IV [N. Gnan et al., J. Chem. Phys. 131, 234504 (2009)] showed that strongly correlating liquids have "isomorphs," which are curves in the phase diagram along which structure, dynamics, and some thermodynamic properties are invariant in reduced units. In the present paper, using the fact that reduced-unit radial distribution functions are isomorph invariant, we derive an expression for the shapes of isomorphs in the WU phase diagram of generalized Lennard-Jones systems of one or more types of particles. The isomorph shape depends only on the Lennard-Jones exponents; thus all isomorphs of standard Lennard-Jones systems (with exponents 12 and 6) can be scaled onto a single curve. Two applications are given. One tests the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. 131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence curve, whereas the agreement is less convincing on the solid side. A second application is the derivation of an approximate equation of state for generalized Lennard-Jones systems by combining the isomorph theory with the Rosenfeld-Tarazona expression for the temperature dependence of the potential energy on isochores. It is shown that the new equation of state agrees well with simulations.     

Thermodynamical and structural properties of imidazolium based ionic liquids from molecular simulation

We have performed molecular dynamics simulations to determine the densities and heat of vaporization as well as structural information for the 1-alkyl-3-methyl-imidazolium based ionic liquids [amim][Cl] and [amim][BF(4)] in the temperature range from 298 to 363 K. In this simulation study, we used an united atom model of Liu et al. [Phys. Chem. Chem. Phys. 8, 1096 (2006)] for the [emim(+)] and [bmim(+)] cations, which we have extended for simulation in [hmim]-ILs and combined with parameters of Canongia Lopes et al. [J. Phys. Chem. B 108, 2038 (2004)] for the [Cl(-)] anion. Our simulation results prove that both the original united atoms approach by Liu et al. and our extension yield reasonable predictions for the ionic liquid with a considerably reduced computational expense than that required for all atoms models. Radial distribution functions and spatial distribution functions where employed to analyze the local structure of this ionic liquid, and in which way it is influenced by the type of the anion, the size of the cation, and the temperature. Our simulations give evidence for the occurrence of tail aggregations in these ionic liquids with increasing length of the side chain and also increasing temperature.     

Universal scaling behaviour of surface tension of molecular chains

We use and extend the universal relationship recently proposed by Galliero [G. Galliero, J. Chem. Phys. 133, 074705 (2010)], based on a combination of the corresponding-states principle of Guggenheim [E. A. Guggenheim, J. Chem. Phys. 13, 253 (1945)] and the parachor approach of Macleod [J. Macleod, Trans. Faraday Soc. 19, 38 (1923)], to predict the vapour-liquid surface tension of fully flexible chainlike Lennard-Jones molecules. In the original study of Galliero, the reduced surface tension of short-chain molecules formed by up to five monomers is expressed as a unique function of the difference between the liquid and vapour coexistence densities. In this work, we extend the applicability of the recipe and demonstrate that it is also valid for predicting the surface tension of two different chainlike molecular models, namely, linear tangent chains that interact through the Lennard-Jones intermolecular potential and fully flexible chains formed by spherical segments interacting through the square-well potential. Computer simulation data for vapour-liquid surface tension of fully flexible and rigid linear Lennard-Jones, and fluid flexible square-well chains is taken from our previous works. Our results indicate that the universal scaling relationship is able to correlate short- and long-chain molecules with different degrees of flexibility and interacting through different intermolecular potentials.     

Simulation of interaction forces between nanoparticles in the presence of Lennard-Jones polymers: freely adsorbing homopolymer modifiers

The force between two nanoscale colloidal particles dispersed in a solution of freely adsorbing Lennard-Jones homopolymer modifiers is calculated using the expanded grand canonical Monte Carlo simulation method. We investigate the effect of polymer chain length (N), nanoparticle diameter (sigma(c)), and colloid-polymer interaction energy (epsilon(cp)) on polymer adsorption (Gamma) and polymer-induced forces (F(P)(r)) between nanoparticles in the full thermodynamic equilibrium condition. There is a strong correlation between polymer adsorption and the polymer-mediated nanoparticle forces. When the polymer adsorption is weak, as in the case of smaller diameters and short polymer chain lengths (sigma(c) = 5, N = 10), the polymers do not have any significant effect on the bare nanoparticle interactions. The adsorbed amount increases with increasing particle diameter, polymer chain length, and colloid-polymer interaction energy. In general, for strong polymer-particle adsorption the polymer-governed force profiles between nanoparticles show short-range repulsion and long-ranged attraction, suggesting that homopolymers would not be ideal for achieving stabilization in nanoparticle dispersions. The attraction is likely due to bridging, as well as polymer segment-segment interactions. The location and magnitude of attractive minimum in the force profile can be controlled by varying N and epsilon(cp). The results show partial agreement and some marked differences with previous theoretical and experimental studies of forces in the limit of flat walls in an adsorbing polymer solution. The difference could be attributed to incorporation of long-ranged colloid-polymer potential in our simulations and the influence of the curvature of the nanoparticles.     

Pressure derivatives in the classical molecular-dynamics ensemble

The calculation of thermodynamic state variables, particularly derivatives of the pressure with respect to density and temperature, in conventional molecular-dynamics simulations is considered in the frame of the comprehensive treatment of the molecular-dynamics ensemble by Lustig [J. Chem. Phys. 100, 3048 (1994)]. This paper improves the work of Lustig in two aspects. In the first place, a general expression for the basic phase-space functions in the molecular-dynamics ensemble is derived, which takes into account that a mechanical quantity G is, in addition to the number of particles, the volume, the energy, and the total momentum of the system, a constant of motion. G is related to the initial position of the center of mass of the system. Secondly, the correct general expression for volume derivatives of the potential energy is derived. This latter result solves a problem reported by Lustig [J. Chem. Phys. 109, 8816 (1998)] and Meier [Computer Simulation and Interpretation of the Transport Coefficients of the Lennard-Jones Model Fluid (Shaker, Aachen, 2002)] and enables the correct calculation of the isentropic and isothermal compressibilities, the speed of sound, and, in principle, all higher pressure derivatives. The derived equations are verified by calculations of several state variables and pressure derivatives up to second order by molecular-dynamics simulations with 256 particles at two state points of the Lennard-Jones fluid in the gas and liquid regions. It is also found that it is impossible for systems of this size to calculate third- and higher-order pressure derivatives due to the limited accuracy of the algorithm employed to integrate the equations of motion.     

Molecular dynamics simulations of the melting of aluminum nanoparticles

Molecular dynamics simulations are performed to determine the melting points of aluminum nanoparticles of 55-1000 atoms with the Streitz-Mintmire [Phys. Rev. B 1994, 50, 11996] variable-charge electrostatic plus potential. The melting of the nanoparticles is characterized by studying the temperature dependence of the potential energy and Lindemann index. Nanoparticles with less than 850 atoms show bistability between the solid and liquid phases over temperature ranges below the point of complete melting. The potential energy of a nanoparticle in the bistable region alternates between values corresponding to the solid and liquid phases. This bistability is characteristic of dynamic coexistence melting. At higher temperatures, only the liquid state is stable. Nanoparticles with more than 850 atoms undergo a sharp solid-liquid-phase transition characteristic of the bulk solid phase. The variation of the melting point with the effective nanoparticle radius is also determined.     

Dissipative particle dynamics simulations of polymer-protected nanoparticle self-assembly

Dissipative particle dynamics simulations were used to study the effects of mixing time, solute solubility, solute and diblock copolymer concentrations, and copolymer block length on the rapid coprecipitation of polymer-protected nanoparticles. The simulations were aimed at modeling Flash NanoPrecipitation, a process in which hydrophobic solutes and amphiphilic block copolymers are dissolved in a water-miscible organic solvent and then rapidly mixed with water to produce composite nanoparticles. A previously developed model by Spaeth et al. [J. Chem. Phys. 134, 164902 (2011)] was used. The model was parameterized to reproduce equilibrium and transport properties of the solvent, hydrophobic solute, and diblock copolymer. Anti-solvent mixing was modeled using time-dependent solvent-solute and solvent-copolymer interactions. We find that particle size increases with mixing time, due to the difference in solute and polymer solubilities. Increasing the solubility of the solute leads to larger nanoparticles for unfavorable solute-polymer interactions and to smaller nanoparticles for favorable solute-polymer interactions. A decrease in overall solute and polymer concentration produces smaller nanoparticles, because the difference in the diffusion coefficients of a single polymer and of larger clusters becomes more important to their relative rates of collisions under more dilute conditions. An increase in the solute-polymer ratio produces larger nanoparticles, since a collection of large particles has less surface area than a collection of small particles with the same total volume. An increase in the hydrophilic block length of the polymer leads to smaller nanoparticles, due to an enhanced ability of each polymer to shield the nanoparticle core. For unfavorable solute-polymer interactions, the nanoparticle size increases with hydrophobic block length. However, for favorable solute-polymer interactions, nanoparticle size exhibits a local minimum with respect to the hydrophobic block length. Our results provide insights on ways in which experimentally controllable parameters of the Flash NanoPrecipitation process can be used to influence aggregate size and composition during self-assembly.     

Soft sticky dipole-quadrupole-octupole potential energy function for liquid water: an approximate moment expansion

A new, efficient potential energy function for liquid water is presented here. The new model, which is referred here as the soft sticky dipole-quadrupole-octupole (SSDQO) model, describes a water molecule as a Lennard-Jones sphere with point dipole, quadrupole, and octupole moments. It is a single-point model and resembles the hard-sphere sticky dipole potential model for water by Bratko et al. [J. Chem. Phys. 83, 6367 (1985)] and the soft sticky dipole model by Ichiye and Liu [J. Phys. Chem. 100, 2723 (1996)] except now the sticky potential consists of an approximate moment expansion for the dimer interaction potential, which is much faster than the true moment expansion. The object here is to demonstrate that the SSDQO potential energy function can accurately mimic the potential energy function of a multipoint model using the moments of that model. First, the SSDQO potential energy function using the dipole, quadruple, and octupole moments from SPC/E, TIP3P, or TIP5P is shown to reproduce the dimer potential energy functions of the respective multipoint model. In addition, in Monte Carlo simulations of the pure liquid at room temperature, SSDQO reproduces radial distribution functions of the respective model. However, the Monte Carlo simulations using the SSDQO model are about three times faster than those using the three-point models and the long-range interactions decay faster for SSDQO (1/r(3) and faster) than for multipoint models (1/r). Moreover, the contribution of each moment to the energetics and other properties can be determined. Overall, the simplicity, efficiency, and accuracy of the SSDQO potential energy function make it potentially very useful for studies of aqueous solvation by computer simulations.     

Local ordering of polymer-tethered nanospheres and nanorods and the stabilization of the double gyroid phase

We present results of Brownian dynamics simulations of tethered nanospheres and tethered nanorods. Immiscibility between tether and nanoparticle facilitates microphase separation into the bicontinuous, double gyroid structure (first reported by Iacovella et al. [Phys. Rev. E 75, 040801(R) (2007)] and Horsch et al. [J. Chem. Phys. 125, 184903 (2006)], respectively). We demonstrate the ability of these nanoparticles to adopt distinct, minimal energy local packings, in which nanospheres form icosahedral-like clusters and nanorods form splayed hexagonal bundles. These local structures reduce packing frustration within the nodes of the double gyroid. We argue that the ability to locally order into stable structures is key to the formation of the double gyroid phase in these systems.     

Systematic coarse-graining of nanoparticle interactions in molecular dynamics simulation

A recently developed multiscale coarse-graining procedure [Izvekov, S.; Voth, G. A. J. Phys. Chem. B 2005, 109, 2469] is extended to derive coarse-grained models for nanoparticles. The methodology is applied to C(60) and to carbonaceous nanoparticles produced in combustion environments. The coarse-graining of the interparticle force field is accomplished applying a force-matching procedure to data obtained from trajectories and forces from all-atom MD simulations. The CG models are shown to reproduce accurately the structural properties of the nanoparticle systems studied, while allowing for MD simulations of much larger self-assembled nanoparticle systems.     

Reversible voltage-induced assembly of au nanoparticles at liquid/liquid interfaces

The voltage-induced assembly of mercaptosuccinic acid-stabilized Au nanoparticles of 1.5 +/- 0.4 nm diameter is investigated at the polarizable water/1,2-dichloroethane interface. Admittance measurements and quasi-elastic laser scattering (QELS) studies reveal that the surface concentration of the nanoparticle at the liquid/liquid boundary is reversibly controlled by the applied bias potential. The electrochemical and optical measurements provide no evidence of irreversible aggregation or deposition of the particles at the interface. Analysis of the electrocapillary curves constructed from the dependence of the frequency of the capillary waves on the applied potential and bulk particle concentration indicates that the maximum particle surface density is 3.8 x 10(13) cm(-2), which corresponds to 67% of a square closed-pack arrangement. This system provides a unique example of reversible assembly of nanostructures at interfaces, in which the density can be effectively tuned by the applied potential bias.     

Interactions between nanocolloidal particles in polymer solutions: effect of attractive interactions

We present a density-functional theory study of nanoparticle interactions in a concentrated polymer solution. The polymers are modeled as freely jointed tangent chains; all nonbonded interactions between polymer segments and nanoparticles are described by Lennard-Jones potentials. We test several recently proposed methods of treating attractive interactions within the density-functional theory framework by comparing theoretical results with recent simulation data. We find that the simple van der Waals approach provides the most accurate results for the polymer-mediated potential of mean force between two dilute nanoparticles. We employ this approach to study nanoparticle interactions as a function of nanoparticle-segment interaction strength and polymer solution density and temperature.