Theory of Size Dependent Deliquescence of Nanoparticles: Relation to Heterogeneous Nucleation and Comparison with Experiments

Spectral Characteristics of Unsaturated and Supersaturated Inorganic Aerosols: Insights into Deliquescence Kinetics

The deliquescence phase transition of atmospheric aerosols is crucial for radiative forcing and atmospheric chemistry. However, the deliquescence kinetics of micrometer-sized aerosols, especially the formation and evolution of surface solution films, remain poorly understood. In this study, IR spectral characteristics were employed for the first time to quantify the solute concentration evolution in surface solution films. At a constant relative humidity (RH) of ∼65%, solution films on NaCl crystals exhibited a very low solute concentration (3.06 ± 0.18 mol/L), comparable to aqueous NaCl droplets above 90% RH. These films reached saturation at ∼74% RH, i.e., the deliquescence RH of NaCl, maintaining a nearly constant saturation level during deliquescence. In contrast, amorphous NaNO3 solids showed supersaturated solution films before deliquescence. Following deliquescence, the saturation level of solution phases increased due to faster solid dissolution rates than liquid water condensation. These findings address knowledge gaps in the complex nonequilibrium dissolution processes of crystalline or amorphous atmospheric aerosols.

Free energy surface of two-step nucleation

We test the theoretical free energy surface (FES) for two-step nucleation (TSN) proposed by Iwamatsu [J. Chem. Phys. 134, 164508 (2011)] by comparing the predictions of the theory to numerical results for the FES recently reported from Monte Carlo simulations of TSN in a simple lattice system [James et al., J. Chem. Phys. 150, 074501 (2019)]. No adjustable parameters are used to make this comparison. That is, all the parameters of the theory are evaluated directly for the model system, yielding a predicted FES, which we then compare to the FES obtained from simulations. We find that the theoretical FES successfully predicts the numerically evaluated FES over a range of thermodynamic conditions that spans distinct regimes of behavior associated with TSN. All the qualitative features of the FES are captured by the theory, and the quantitative comparison is also very good. Our results demonstrate that Iwamatsu's extension of classical nucleation theory provides an excellent framework for understanding the thermodynamics of TSN.

Subsecond measurement on deliquescence kinetics of aerosol particles: Observation of partial dissolution and calculation of dissolution rates

The deliquescence behavior of atmospheric aerosols has significant effects on global climate and atmospheric heterogeneous chemistry but remains largely unclear. The deliquescence kinetics data of micron-sized particles are scarce owing to the difficulty on performing the time-resolved dissolution measurements. In view of this technique bottleneck, an applicable and powerful experimental technique, i. e., vacuum FTIR combining pulsed relative humidity (RH) change technique, is introduced for gaining deliquescence kinetics information of three inorganic salts. For NaCl and (NH₄)₂SO₄ aerosols, a solid-liquid mixing state derived from partial dissolution of NaCl and (NH₄)₂SO₄ crystals is present during deliquescence, and the recrystallization will occur once RH decreases. While for NaNO₃ particles, the recrystallization cannot occur as RH decreases owing to the formed amorphous NaNO₃ solids after dying. The dissolution rates of NaCl, (NH₄)₂SO₄ and NaNO₃ solid particles are calculated, as a first attempt, by the upward pulsed RH mode. The measured rates show a significant dependency on ambient RH with three orders of magnitude. For NaCl particles, the measured J values range from 1.41 × 10^-4 to 7.67 × 10^-1 s^-1 at RH of 73.41-75.15%. The J for (NH₄)₂SO₄ particles is 7.34 × 10^-3 to 2.46 × 10⁰ s^-1 over the RH range of 77.27%-80.13%. The J values for amorphous NaNO₃ solids range from 6.01 × 10^-3 to 2.63 × 10⁰ s^-1 as RH increases from 71.15% to 73.84%. Our results fill in the dataset of atmospheric models describing the kinetics features of deliquescence and provide an insight into dynamic solid-solution transition for PM2.5 particles.

Assessment and Validation of a Hygroscopic Growth Model with Different Water Activity Estimation Methods

Hygroscopic growth models are currently of interest as aids for targeting the deposition of inhaled drug particles in preferred areas of the lung that will maximize their pharmaceutical effect. Mathematical models derived to estimate hygroscopic growth over time have been previously developed but have not been thoroughly validated. For this study, model validation involved a comparison of modeled values to measured values when the growing droplet had reached equilibrium. A second validation process utilized a novel system to measure the growth of a droplet on a microscope coverslip relative to modeled values when the droplet is undergoing the initial rapid growth phase. Various methods currently used to estimate the water activity of the growing droplet, which influences the droplet growth rate, were also compared. Results indicated that a form of the hygroscopic growth model that utilizes coupled-differential equations to estimate droplet diameter and temperature over time was valid throughout droplet growth until it reached its equilibrium size. Accuracy was enhanced with the use of a polynomial expression to estimate water activity relative to the use of a simplified estimate of water activity based on Raoult's Law. Model accuracy was also improved when constraining the film of salt solution surrounding the dissolving salt core at saturation.

Nonclassical Nucleation in a Solid-Solid Transition of Confined Hard Spheres

A solid-solid phase transition of colloidal hard spheres confined between two planar hard walls is studied using a combination of molecular dynamics and Monte Carlo simulation. The transition from a solid consisting of five crystalline layers with square symmetry (5□) to a solid consisting of four layers with triangular symmetry (4△) is shown to occur through a nonclassical nucleation mechanism that involves the initial formation of a precritical liquid cluster, within which the cluster of the stable 4△ phase grows. Free-energy calculations show that the transition occurs in one step, crossing a single free-energy barrier, and that the critical nucleus consists of a small 4△ solid cluster wetted by a metastable liquid. In addition, the liquid cluster and the solid cluster are shown to grow at the planar hard walls. We also find that the critical nucleus size increases with supersaturation, which is at odds with classical nucleation theory. The △-solid-like cluster is shown to contain both face-centered-cubic and hexagonal-close-packed ordered particles.

A novel approach to the theory of homogeneous and heterogeneous nucleation

A new approach to the theory of nucleation, formulated relatively recently by Ruckenstein, Narsimhan, and Nowakowski (see Refs. [7-16]) and developed further by Ruckenstein and other colleagues, is presented. In contrast to the classical nucleation theory, which is based on calculating the free energy of formation of a cluster of the new phase as a function of its size on the basis of macroscopic thermodynamics, the proposed theory uses the kinetic theory of fluids to calculate the condensation (W(+)) and dissociation (W(-)) rates on and from the surface of the cluster, respectively. The dissociation rate of a monomer from a cluster is evaluated from the average time spent by a surface monomer in the potential well as obtained from the solution of the Fokker-Planck equation in the phase space of position and momentum for liquid-to-solid transition and the phase space of energy for vapor-to-liquid transition. The condensation rates are calculated using traditional expressions. The knowledge of those two rates allows one to calculate the size of the critical cluster from the equality W(+)=W(-) as well as the rate of nucleation. The developed microscopic approach allows one to avoid the controversial application of classical thermodynamics to the description of nuclei which contain a few molecules. The new theory was applied to a number of cases, such as the liquid-to-solid and vapor-to-liquid phase transitions, binary nucleation, heterogeneous nucleation, nucleation on soluble particles and protein folding. The theory predicts higher nucleation rates at high saturation ratios (small critical clusters) than the classical nucleation theory for both solid-to-liquid as well as vapor-to-liquid transitions. As expected, at low saturation ratios for which the size of the critical cluster is large, the results of the new theory are consistent with those of the classical one. The present approach was combined with the density functional theory to account for the density profile in the cluster. This approach was also applied to protein folding, viewed as the evolution of a cluster of native residues of spherical shape within a protein molecule, which could explain protein folding/unfolding and their dependence on temperature.

Analysis of heterogeneous uptake by nanoparticles via differential mobility analysis–drift tube ion mobility spectrometry

Tandem differential mobility analysis–drift tube ion mobility spectrometry enables examination of heterogeneous vapor uptake by nanoscale particles.

Vapor condensation onto a non-volatile liquid drop

Molecular dynamics simulations of miscible and partially miscible binary Lennard-Jones mixtures are used to study the dynamics and thermodynamics of vapor condensation onto a non-volatile liquid drop in the canonical ensemble. When the system volume is large, the driving force for condensation is low and only a submonolayer of the solvent is adsorbed onto the liquid drop. A small degree of mixing of the solvent phase into the core of the particles occurs for the miscible system. At smaller volumes, complete film formation is observed and the dynamics of film growth are dominated by cluster-cluster coalescence. Mixing into the core of the droplet is also observed for partially miscible systems below an onset volume suggesting the presence of a solubility transition. We also develop a non-volatile liquid drop model, based on the capillarity approximations, that exhibits a solubility transition between small and large drops for partially miscible mixtures and has a hysteresis loop similar to the one observed in the deliquescence of small soluble salt particles. The properties of the model are compared to our simulation results and the model is used to study the formulation of classical nucleation theory for systems with low free energy barriers.

Heterogeneous nucleation in multi-component vapor on a partially wettable charged conducting particle. I. Formulation of general equations: electrical surface and line excess quantities

Thermodynamics is applied to formulate general equations for internal energies and grand potential for a system consisting of a dielectric liquid nucleus of a new phase on a charged insoluble conducting sphere within a uniform macroscopic one- or multicomponent mother phase. The currently available model for ion-induced nucleation assumes complete spherical symmetry of the system, implying that the seed ion is immediately surrounded by the condensing liquid from all sides. We take a step further and treat more realistic geometries, where a cap-shaped liquid cluster forms on the surface of the seed particle. To take into account spontaneous polarization of surface layer molecules we introduce the electrical surface and line excess quantities.

Generalization of the Gibbs-Kelvin-Kohler and Ostwald-Freundlich equations for a liquid film on a soluble nanoparticle

A derivation of chemical equilibrium equations for a spherical thin film of solution around a soluble solid nanoparticle is presented. The equations obtained generalize the Gibbs-Kelvin-Kohler and Ostwald-Freundlich equations for a soluble particle immersed in the bulk phase. The generalized equations describe the dependence of the chemical potentials of a condensate and dissolved nanoparticle matter in the thin solution film, the condensate saturated pressure, and the solubility of the nanoparticle matter on the film thickness, and the nanoparticle size with account of the disjoining pressure of the liquid film.

Anomalous hygroscopic growth of fine particles of MgSO4 aerosols investigated by FTIR/ATR spectroscopy

This paper demonstrates an approach for investigating the hygroscopic growth of MgSO4 aerosols deposited on ZnSe substrate by using attenuated total reflection Fourier transform infrared (FTIR/ATR) spectroscopy. The experimental setup based upon a refitted standard FTIR/ATR accessory was adopted for the hygroscopic study of aerosols. It has been found that the "predeliquescence" of fine MgSO4 aerosol particles with the mean spreading diameter around 500 nm occurred before roughly 15% RH. In contrast, the abrupt water absorption of coarse MgSO4 particles with the mean diameter larger than about 10 microm was reported to occur at roughly 42% RH, which was reproduced in this study. Up to now, both theoretical and experimental investigations were rare and immature for fine particles, but the method we used in this study worked very well for the fine particles of MgSO4 aerosols. It has been found that the possible reason for the "predeliquescence" fine particles of MgSO4 aerosols is that the initial state or phase of fine particles is different from coarse ones after desiccation. This research demonstrates that the approach based on the ATR technique is very convenient, accurate and requires only a little amount of lab supplies.

Attenuated total reflection fourier transform infrared spectroscopy to investigate water uptake and phase transitions in atmospherically relevant particles

In this study, attenuated total reflection Fourier transform infrared (ATR-FT-IR) spectroscopy is used to investigate water uptake and phase transitions for atmospherically relevant particles. Changes in the ATR-FT-IR spectra of NaCl, NH(4) NO(3), (NH(4))(2)SO(4), Ca(NO(3))(2), and SiO(2) as a function of relative humidity (RH) are presented and discussed. For these various particles, water can (1) become adsorbed on the particle surface; and/or (2) become absorbed in the particle structure to form a hydrate salt; and/or (3) become absorbed by the particle to form a liquid solution. Spectral features and analyses that distinguish these various processes are discussed. For the salts that do undergo a solid to liquid phase transition (deliquescence), excellent agreement is found between the measurements made here with ATR-FT-IR spectroscopy, a relatively simple, inexpensive, and readily available analytical tool, compared to more expensive, elaborate aerosol flow reactor systems using tandem differential mobility analyzers. In addition, for particles that adsorb water, we show here the utility of coupling ATR-FT-IR measurements with simultaneous quartz crystal microbalance (QCM) measurements. This coupling allows for the quantification of the amount of water associated with the particle as a function of relative humidity (f(RH)) along with the spectroscopic data.

Theoretical Investigation of Substrate Effect on Deliquescence Relative Humidity of NaCl Particles

A theoretical investigation is conducted for the first time to explore the deliquescence of particles deposited on a substrate. The formulation incorporates the Kelvin effect with the assumption that the dry and wet particles are both spherical caps in shape. Unlike the deposited particles larger than 500 nm, the deliquescence relative humidity (DRH) of smaller particles can substantially depend on the particle size, the contact angles, and the surface tension between the particle and the atmosphere. At certain contact angles, small particles depositing on a substrate could deliquesce at a much lower RH, posing a potential corrosion problem for metallic substrates.

Confocal Raman Observation of the Efflorescence/Deliquescence Processes of Individual NaNO3 Particles on Quartz

Confocal Raman spectroscopy was used to study the structural changes of bulk NaNO3 solutions with molar water-to-solute ratios (WSRs) of 54.0-12.3 and NaNO3 droplets (10-100 microm) with WSRs of 9.5-1.0 on a quartz substrate. Upon reduction of the WSR, a blue shift of the symmetric stretching band (nu(1)(NO3-)) from approximately 1048 to approximately 1058 cm(-1) was observed in the confocal Raman spectra with high signal-to-noise ratios. Accordingly, the full width at half-height of the nu(1)(NO3-) band increased from approximately 8.4 cm-1 for the dilute solution (WSR = 54.0) to approximately 15.6 cm-1 for the extremely supersaturated droplet (WSR = 1.0), suggesting the formation of contact ion pairs with different structures. For the O-H stretching band, the ratio of weak hydrogen-bonding components to strong ones, i.e., I(3488)/I(3256), increased from approximately 1.2 at WSR = 54.0 to approximately 7.3 at WSR = 1.0, indicating that the strong hydrogen bonds were heavily destroyed between water molecules especially in the supersaturated droplets. In the humidifying process, two hygroscopic behaviors were observed depending on the morphology of solid NaNO3 particles. No surface water was detected for a solid NaNO3 particle with rhombohedral shape at relative humidities (RHs) below 86%. When the RH increased from 86% to 93%, it suddenly absorbed water and turned into a solution droplet. For a maple-leaf-shaped NaNO3 particle with a rough surface, however, a trace of residual water originally remained on the rough surface even at very low RH according to its Raman spectrum. Its initial water uptake from the ambient occurred at approximately 70% RH. The small amount of initially adsorbed water induced surface rearrangement of the maple-leaf-shaped particle. A further increase of RH made the particle gradually turn into a regular solid core swathed in a solution layer. Eventually, it completely deliquesced in the RH region of 86-93%, similar to the case of the NaNO3 particle with rhombohedral shape.

Efflorescence Relative Humidity for Ammonium Sulfate Particles

The classical homogeneous nucleation theory was employed to calculate the efflorescence relative humidity (ERH) of airborne ammonium sulfate particles with a wide size range (8 nm to 17 microm) at room temperature. The theoretical predictions are in good agreement with the experimentally measured values. When the ammonium sulfate particle is decreased in size, the ERH first decreases, reaches a minimum around 30% for particle diameter equal to about 30 nm, and then increases. It is for the first time that the Kelvin effect is theoretically verified to substantially affect the ERH of ammonium sulfate particles smaller than 30 nm, while the aerosol size is the dominant factor affecting the efflorescent behavior of ammonium sulfate particles larger than 50 nm.

A kinetic approach to the theory of heterogeneous nucleation on soluble particles during the deliquescence stage

Deliquescence is the dissolution of a solid nucleus in a liquid film formed on the nucleus due to vapor condensation. Previously, the kinetics of deliquescence was examined in the framework of the capillarity approximation which involves the thermodynamic interfacial tensions for a thin film and the approximation of uniform density therein. In the present paper we propose a kinetic approach to the theory of deliquescence which avoids the use of the above macroscopic quantities for thin films. The rates of emission of molecules from the liquid film into the vapor and from the solid core into the liquid film are determined through a first passage time analysis whereas the respective rates of absorption are calculated through the gas kinetic theory. The first passage time is obtained by solving the single-molecule master equation for the probability distribution of a "surface" molecule moving in a potential field created by the cluster. Furthermore, the time evolution of the liquid film around the solid core is described by means of two mass balance equations which involve the rates of absorption and emission of molecules by the film at its two interfaces. When the deliquescence of an ensemble of solid particles occurs by means of large fluctuations, the time evolution of the distribution of composite droplets (liquid film+solid core) with respect to the independent variables of state is governed by a Fokker-Planck kinetic equation. When both the vapor and the solid soluble particles are single component, this equation has the form of the kinetic equation of binary nucleation. A steady-state solution for this equation is obtained by the method of separation of variables. The theory is illustrated with numerical calculation regarding the deliquescence of spherical particles in a water vapor with intermolecular interactions of the Lennard-Jones kind. The new approach allows one to qualitatively explain an important feature of experimental data on deliquescence, namely the occurrence of nonsharp deliquescence, a feature that the previous deliquescence theory based on classical thermodynamics could not account for.

Chemistry of particle inception and growth during alpha-pinene ozonolysis

A flow-tube reactor was used to study the formation of particles from alpha-pinene ozonation. Particle phase products formed within the first 3-22 s of reaction were analyzed online using a scanning mobility particle sizer and two particle mass spectrometers. The first, a photoionization aerosol mass spectrometer (PIAMS), was used to determine the molecular composition of nascent particles between 30 and 50 nm in diameter. The second, a nano-aerosol mass spectrometer (NAMS), was used to determine the elemental composition of individual particles from 50 nm to below 10 nm in diameter. Molecular composition measurements with PIAMS confirm that both the stabilized Criegee intermediate and hydroperoxide channels of alpha-pinene ozonolysis are operative. However, these channels alone cannot explain the high oxygen content of the particles measured with NAMS. The carbon-to-oxygen mole ratios of suspected nucleating agents are in the range of 2.25-4.0, while the measured ratios are from 1.9 for 9 nm particles to 2.5 and 2.7 for 30 and 50 nm particles, respectively. The large oxygen content may arise by cocondensation of small oxygenated molecules such as water or multistep reactions with ozone, water, or other species that produce highly oxygenated macromolecules. In either case, the increasing ratio with increasing particle size suggests that the aerosol becomes less polar with time.