A strategy for characterizing the mixing state of immiscible aerosol components and the formation of multiphase aerosol particles through coagulation

We demonstrate that the coagulation of two aerosol droplets of different chemical composition can be studied directly through the unique combination of optical tweezers and Raman spectroscopy. Multiple optical traps can be established, allowing the manipulation of multiple aerosol droplets. Spontaneous Raman scattering allows the characterization of droplet composition and mixing state, permitting the phase segregation of immiscible components in multiphase aerosol to be investigated with spatial resolution. Stimulated Raman scattering allows the integrity of the droplet and uniformity of refractive index to be probed. The combination of these spectroscopic probes with optical tweezers is shown to yield unprecedented detail in studies of the coagulation of decane and water droplets.     

凝并和成核机理下颗粒尺度分布的Monte Carlo求解

颗粒的凝并和成核现象影响其尺度分布,现有的MonteCarlo方法描述颗粒尺度分布的时间演变过程存在若干困难.提出了一种新的多重MonteCarlo(MMC)算法,基于时间驱动,利用加权的虚拟颗粒的思想,在模拟过程中保持虚拟颗粒总数不变和计算区域体积不变.利用该算法对“常凝并核,一阶成核”的情况下颗粒尺度分布的时间演变过程进行了数值求解,所得结果与数值解相符,表明MMC算法具有高且稳定的计算精度.另外,MMC算法由于跟踪比实际颗粒数目少得多的虚拟颗粒而具有较低的计算代价.     

Nanoparticle formation in water-in-oil microemulsions: experiments, mechanism, and Monte Carlo simulation

The dynamics of nanoparticle formation in water-in-oil microemulsions via temporal size evolution has been followed from UV-visible absorption spectra of CdS nanoparticles. Existing Monte Carlo (MC) simulations of nanoparticle formation are primarily based on the mechanism of nuclei formation and their growth by coalescence-exchange of drops, which alone do not predict particles of large size as observed in some experiments. Hence, we have included an additional size enlargement process, namely coagulation of nanoparticles during drop coalescence. We find that particle coagulation, constrained by microemulsion drop size, shows very good agreement with our experimental data on CdS nanoparticle size evolution, for different drop sizes. Thus a combined approach of spectroscopy and MC simulation is helpful in elucidating the mechanism of nanoparticle formation in these confined systems, leading to prediction of size-controlled nanoparticle synthesis.     

Interfaces in polymer blends

We investigate the structure and thermodynamics of interfaces in dense polymer blends using Monte Carlo (MC) simulations and self‐consistent field (SCF) calculations. For structurally symmetric blends we find quantitative agreement between the MC simulations and the SCF calculations for excess quantities of the interface (e.g., interfacial tension or enrichment of copolymers at the interface). However, a quantitative comparison between profiles across the interface in the MC simulations and the SCF calculations has to take due account of capillary waves. While the profiles in the SCF calculations correspond to intrinsic profiles of a perfectly flat interface the local interfacial position fluctuates in the MC simulations. We test this concept by extensive Monte Carlo simulations and study the cross‐over between “intrinsic” fluctuations which build up the local profile and capillary waves on long (lateral) length scales. Properties of structurally asymmetric blends are exemplified by investigating polymers of different stiffness. At high incompatibilities the interfacial width is not much larger than the persistence length of the stiffer component. In this limit we find deviations from the predictions of the Gaussian chain model: while the Gaussian chain model yields an increase of the interfacial width upon increasing the persistence length, no such increase is found in the MC simulations. Using a partial enumeration technique, however, we can account for the details of the chain architecture on all length scales in the SCF calculations and achieve good agreement with the MC simulations. In blends containing diblock copolymers we investigate the enrichment of copolymers at the interface and the concomitant reduction of the interfacial tension. At weak segregation the addition of copolymers leads to compatibilization. At high incompatibilities, the homopolymer‐rich phase can accommodate only a small fraction of copolymer before the copolymer forms a lamellar phase. The analysis of interfacial fluctuations yields an estimate for the bending rigidity of the interface. The latter quantity is important for the formation of a polymeric microemulsion at intermediate segregation and the consequences for the phase diagram are discussed.     

Multiparticle moves in acceptance rate optimized monte carlo

Molecular Dynamics (MD) and Monte Carlo (MC) based simulation methods are widely used to investigate molecular and nanoscale structures and processes. While the investigation of systems in MD simulations is limited by very small time steps, MC methods are often stifled by low acceptance rates for moves that significantly perturb the system. In many Metropolis MC methods with hard potentials, the acceptance rate drops exponentially with the number of uncorrelated, simultaneously proposed moves. In this work, we discuss a multiparticle Acceptance Rate Optimized Monte Carlo approach (AROMoCa) to construct collective moves with near unit acceptance probability, while preserving detailed balance even for large step sizes. After an illustration of the protocol, we demonstrate that AROMoCa significantly accelerates MC simulations in four model systems in comparison to standard MC methods. AROMoCa can be applied to all MC simulations where a gradient of the potential is available and can help to significantly speed up molecular simulations. © 2015 Wiley Periodicals, Inc.     

Simulation of droplet heating and desolvation in an inductively coupled plasma — Part I

The total desolvation rate of sample droplets in an argon inductively coupled plasma (Ar ICP) is investigated through the development of a two-phase continuum flow computer model. The desolvation model is supplemented by equations used to determine the trajectories of particles through the plasma. The model is used to calculate the behavior of aerosol droplets from a direct injection high efficiency nebulizer (DIHEN), a micronebulizer used to inject microliter quantities of samples that are toxic, expensive, or of limited volume. We use the combination of desolvation and transport models to present the first predicted spatial distribution of droplet concentrations and evaporation rates in an ICP flow. These data are compared with the behavior of a DIHEN spray in an environment with no net argon gas flow to determine the importance of gas flow rates to overall droplet concentration profiles in the ICP. In addition, two separate techniques (Stokes’ equation and the direct simulation Monte Carlo treatment) for determining droplet trajectories are contrasted.     

Formation of junction zones in thermoreversible methylcellulose gels

To analyze the structure of junction zones formed in methylcellulose (MC) gel, the modified Eldridge–Ferry method was applied to phase diagrams for aqueous solutions of different molecular weight MCs derived from micro‐DSC, small‐angle X‐ray scattering, and visual inspection. The results suggested that junctions in MC gels took thin, rodlike fringed‐micellar crystallites. The junction multiplicity s decreased from 4.3 for low‐temperature melting gels to 2.0 for high‐temperature melting gels. With increasing molecular weight, the number ζ of statistical units in a junction along a single chain increased from 27 to 54. Because the number depends sensitively on the enthalpy of bonding per mole of the repeat units of MC, our estimate is considered to give an upper bound to the junction length. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 943–946, 2001     

Nonequilibrium Monte Carlo simulation of lattice block copolymer chains subject to oscillatory shear flow

This paper has extended nonequilibrium Monte Carlo (MC) approach to simulate oscillatory shear flow in a lattice block copolymer system. Phase transition and associated rheological behaviors of multiple self-avoiding chains have been investigated. Stress tensor has been obtained based upon sampled configuration distribution functions. At low temperatures, micellar structures have been observed and the underlying frequency-dependent rheological properties exhibit different initial slopes. The simulation outputs are consistent with the experimental observations in literature. Chain deformation during oscillatory shear flow has also been revealed. Although MC simulation cannot account for hydrodynamic interaction, the highlight of our simulation approach is that it can, at small computing cost, investigate polymer chains simultaneously at different spatial scales, i.e., macroscopic rheological behaviors, mesoscopic self-assembled structures, and microscopic chain configurations.     

Simulation of droplet heating and desolvation in inductively coupled plasma—part II: coalescence in the plasma

A numerical model is developed to consider for the first time droplet coalescence along with transport, heating and desolvation in an argon inductively coupled plasma (Ar ICP). The direct simulation Monte Carlo (DSMC) method and the Ashgriz–Poo model are used, respectively, to compute droplet–droplet interactions and to determine the outcome of droplet collisions. Molecular dynamics (MD) simulations support the use of the Ashgriz–Poo coalescence model for small droplet coalescence. Simulations predict spatial maps of droplet number and mass densities within an Ar ICP for a conventional nebulizer-spray chamber arrangement, a direct injection high efficiency nebulizer (DIHEN), and a large bore DIHEN (LB-DIHEN). The primary findings are: (1) even at 1500 W, the collisions of the droplets in the plasma lead primarily to coalescence, particularly for direct aerosol injection; (2) the importance of coalescence in a spray simulation exhibits a complex relationship with the gas temperature and droplet size; (3) DIHEN droplets penetrate further into the Ar ICP when coalescence is considered; and (4) droplets from a spray chamber or the LB-DIHEN coalesce less frequently than those from a DIHEN. The implications of these predictions in spectrochemical analysis in ICP spectrometry are discussed.     

Controlling and characterizing the coagulation of liquid aerosol droplets

We demonstrate that optical tweezers can be used to control and characterize the coagulation and mixing state of aerosols. Liquid aerosol droplets of 2-14 mum in diameter are optically trapped and characterized by spontaneous and stimulated Raman scatterings, which together provide a unique signature of droplet size and composition. From the conventional bright field image, the size of the trapped droplet can be estimated and compared with that determined from stimulated Raman scattering, and the motion of the particle within the trapping plane can be recorded. A maximum of four droplets can be manipulated in tandem by forming multiple optical traps through rapid beam steering. The coagulation of two droplets can be studied directly by controlling two droplets. The limiting conditions under which optical forces and capillary forces dominate the aerosol coagulation event are explored by varying the relative optical trap strengths and characterizing the coagulation of different droplet sizes. Finally, we demonstrate that the coagulation of different aerosol components can be compared and the mixing state of the final coagulated droplet can be investigated. In particular, we compare the outcome of the coagulation of an aqueous sodium chloride aerosol droplet with a second aqueous droplet, with an ethanol droplet or with a decane droplet.     

Aggregate size distribution evolution for Brownian coagulation-sensitivity to an improved rate constant

Brownian motion causes small aggregates to encounter one another and grow in gaseous environments, often under conditions in which the coalescence rate (say, spheroidization by "sintering") cannot compete. The polydisperse nature of the aerosol population formed by this mechanism is typically accounted for by formulating an evolution equation for the joint PDF of the state variables needed for describing individual particles. In the simple case of fractal-like aggregates (prescribed morphology and state, characterized just by the number of aggregated spherules, or total aggregate volume), we use the quadrature method of moments and Monte Carlo simulations to show that recent improvements in the laws governing free molecule regime coagulation frequency (rate "constant") of these aggregates cause systematic changes in the shape of the asymptotic aggregate size distribution, with significant implications for the light-scattering power and inertial impaction behavior of such aggregate populations.     

Monte carlo simulation of macromolecular ionization by nanoelectrospray

Electrospray ionization (ESI) is commonly used in macromolecular mass spectrometry, yet the dynamics of macromolecules in ESI droplets are not well understood. In this study, a Monte Carlo based model was developed, which can predict the efficiency of electrospray ionization for macromolecules, i.e., the number of macromolecular ions produced per macromolecules electrosprayed. The model takes into account ESI droplet evaporation, macromolecular diffusion within the droplet, droplet fissions, and the statistical nature of the ESI process. Two idealized representations of macromolecular analytes were developed, describing cluster prone, droplet surface inactive macromolecules and droplet surface active macromolecules, respectively. It was found that surface active macromolecules are preferentially ionized over surface inactive cluster prone macromolecules when the initial droplet size is large and the analyte concentration in solution is high. Simulations showed that ESI efficiency decreases with increasing initial droplet size and analyte molecular weight, and is influenced by analyte surface activity, the properties of the solvent, and the variance of the droplet size distribution. Model predictions are qualitatively supported by experimental measurements of macromolecular electrospray ionization made previously. Overall, this study demonstrates the potential capabilities of Monte Carlo based ESI models. Future developments in such models will allow for more accurate predictions of macromolecular ESI intensity.     

Methodology of predicting approximate shapes and size distribution of micelles: illustration for simple models

We propose an efficient methodology for predicting approximate shapes and size distribution of micelles. The methodology is a judicious combination of a conventional thermodynamic approach, the reference interaction site model (RISM) theory, and the Monte Carlo (MC) simulated annealing technique. Solvent effects are fully incorporated using the RISM theory with our robust and very efficient algorithm for solving the RISM equations, and the MC technique is applied only to surfactant molecules. The methodology is potentially applicable to realistic models of surfactant and solvent molecules with all-atom potentials. As the first step, however, it is illustrated for simplified models having only essential characteristics of the amphiphiles. We estimate the critical micelle concentration, approximate shapes, and size distributions at some surfactant concentrations. Roles of the solvent and effects due to the type of the surfactant molecule are discussed in detail.     

On the solvation of ions in small water droplets

The solvations of positively and negatively charged model ions in water droplets have been studied using Monte Carlo simulations performed with a polarizable intermolecular potential function model. Special focus has been placed on the position of the ion in the water droplet. It was found that the sign of the ionic charge is of minor importance but an increased ionic charge localizes the ion to the central regions of the droplet, whereas a large polarizability and a large ionic radius favor locations close to the surface of the water droplet.     

Mg impurity in helium droplets

Within the diffusion Monte Carlo approach, we have determined the structure of isotopically pure and mixed helium droplets doped with one magnesium atom. For pure (4)He clusters, our results confirm those of Mella et al. [J. Chem. Phys. 123, 054328 (2005)] that the impurity experiences a transition from a surface to a bulk location as the number of helium atoms in the droplet increases. Contrarily, for pure (3)He clusters Mg resides in the bulk of the droplet due to the smaller surface tension of this isotope. Results for mixed droplets are presented. We have also obtained the absorption spectrum of Mg around the 3s3p?(1)P(1) ← 3s(2)?(1)S(0) transition.     

On the definition of a Monte Carlo model for binary crystal growth

We show that consistency of the transition probabilities in a lattice Monte Carlo (MC) model for binary crystal growth with the thermodynamic properties of a system does not guarantee the MC simulations near equilibrium to be in agreement with the thermodynamic equilibrium phase diagram for that system. The deviations remain small for systems with small bond energies, but they can increase significantly for systems with large melting entropy, typical for molecular systems. These deviations are attributed to the surface kinetics, which is responsible for a metastable zone below the liquidus line where no growth occurs, even in the absence of a 2D nucleation barrier. Here we propose an extension of the MC model that introduces a freedom of choice in the transition probabilities while staying within the thermodynamic constraints. This freedom can be used to eliminate the discrepancy between the MC simulations and the thermodynamic equilibrium phase diagram. Agreement is achieved for that choice of the transition probabilities yielding the fastest decrease of the free energy (i.e., largest growth rate) of the system at a temperature slightly below the equilibrium temperature. An analytical model is developed, which reproduces quite well the MC results, enabling a straightforward determination of the optimal set of transition probabilities. Application of both the MC and analytical model to conditions well away from equilibrium, giving rise to kinetic phase diagrams, shows that the effect of kinetics on segregation is even stronger than that predicted by previous models.     

An apparent critical point in binary mixtures: experimental and simulation study

We report the experimental and simulation studies for the system of nitrobenzene-cyclododecane, showing an apparent critical point, which lies in their metastable, experimentally inaccessible state, below their melting point, affecting physical and chemical properties of this system in the stable liquid phase. The nonlinear dielectric effect (NDE) was measured in the mixture of nitrobenzene with cyclododecane. The mixture has been found to show an apparent critical point which lies below the melting point, manifested as anomalous NDE behavior in the vicinity of the critical concentrations in the stable liquid phase. The melting temperature of this system was estimated using the differential scanning calorimetry method. For such a system, we also performed Monte Carlo (MC) simulations that aimed to analyze the kinds of phase transitions observed and the conditions of their occurrence in Lennard-Jones mixture. The enthalpy, configurational energy, and radial distribution function have been estimated by the MC simulation method in the N-P-T system. Immiscibility conditions according to the approach by Schoen and Hoheisel [Mol. Phys. 57, 65 (1986)] are also discussed.     

Manipulation and characterization of aqueous sodium dodecyl sulfate/sodium chloride aerosol particles

Aerosol optical tweezers coupled with Raman spectroscopy can allow the detailed investigation of aerosol dynamics. We describe here measurements of the evolving size, composition, and phase of single aqueous aerosol droplets containing the surfactant sodium dodecyl sulfate and the inorganic salt sodium chloride. Not only can the evolving wet particle size be probed with nanometer accuracy, but we show that the transition to a metastable microgel particle can be followed, demonstrating that optical tweezers can be used to manipulate both spherical and non-spherical aerosol particles. Further, through the simultaneous manipulation and characterization of two aerosol droplets of different composition in two parallel optical traps, the phase behavior of a surfactant-doped particle and a surfactant-free droplet can be compared directly in situ. We also illustrate that the manipulation of two microgel particles can allow studies of the coagulation and interaction of two solid particles. Finally, we demonstrate that such parallel measurements can permit highly accurate comparative measurements of the evolving wet particle size of a surfactant-doped droplet with a surfactant-free droplet.     

Computer Study of Stimuli-Responsive Polyelectrolyte Micelles in Aqueous Media. Comparison of Monte Carlo and Self-Consistent Field Approaches

The behavior of polyelectrolyte micelles with kinetically frozen hydrophobic cores in aqueous solutions was studied by Monte Carlo (MC) simulations and self-consistent field (SCF) calculations. Some results have already been published. The structure of water-soluble shells formed by weak polyelectrolytes, both pure and containing a low fraction of strongly hydrophobic units arranged either in a short sequence or distributed uniformly in the shell-forming chains was studied in detail. In the case of sequenced system, the analysis of concentration profiles of individual species reveals strong segregation and important self-organization of hydrophobic units in the shell. A comparison and critical analysis of results of MC and SCF methods is presented.