Engineered Surface Chemistry and Enhanced Energetic Performance of Aluminum Nanoparticles by Nonthermal Hydrogen Plasma Treatment.

Extracting the maximum chemical energy from aluminum nanoparticles (Al NPs) during oxidation is essential for their use in energetic applications. However, the shell of native Al2O3 limits the release of chemical energy by acting as a diffusion barrier and dead weight. Engineering the surface properties of Al NPs by modifying their shell chemistry can reduce the inhibiting effects of the oxide shell on the rate and heat release of oxidation. Here, we employ nonthermal hydrogen plasma at high power and a short time to alter the shell chemistry by doping it with Al-H, as examined and confirmed by HRTEM, FTIR, and XPS. Thermal analysis (TGA/DSC) shows that Al NPs with modified surfaces exhibit augmented oxidation and heat release (33% higher than those of untreated Al NPs). The results demonstrate the promising effect of nonthermal hydrogen plasma in engineering the shell chemistry of Al NPs to improve their overall energetic performance during oxidation.

Combinatorics and Statistical Mechanics of Integer Partitions.

We study the set of integer partitions as a probability space that generates distributions and, in the asymptotic limit, obeys thermodynamics. We view ordered integer partition as a configuration of cluster masses and associate them with the distribution of masses it contains. We organized the set of ordered partitions into a table that forms a microcanonical ensemble and whose columns form a set of canonical ensembles. We define a functional of the distribution (selection functional) that establishes a probability measure on the distributions of the ensemble, study the combinatorial properties of this space, define its partition functions, and show that, in the asymptotic limit, this space obeys thermodynamics. We construct a stochastic process that we call exchange reaction and used it to sample the mean distribution by Mote Carlo simulation. We demonstrated that, with appropriate choice of the selection functional, we can obtain any distribution as the equilibrium distribution of the ensemble.

Nanoenergetic Materials: Enhanced Energy Release from Boron by Aluminum Nanoparticle Addition.

Boron has the highest enthalpy of oxidation per unit mass (and volume) among metals and metalloids and is an excellent candidate as a solid fuel. However, the native oxide present on the surface limits the available energy and rate of its release during oxidation. Here, we report a simple and effective method that removes the oxide in situ during oxidation via an exothermic thermite reaction with aluminum that enriches the particle in B at the expense of Al. B/Al blends with different compositions are optimized using thermogravimetry and differential scanning calorimetry, and the best sample in terms of energy release is characterized by high-resolution transmission electron microscopy, X-ray photoelectron spectroscopy, energy-dispersive spectroscopy, and X-ray diffraction. All compositions release more energy than the individual components, and the blend containing 10% Al by weight outperforms pure B by 40%. The high energy release is due to the synergistic effect of B oxidation and thermite reaction between Al and B2O3. We demonstrate the formation of ternary oxide by the oxidation of the B/Al blend that provides porous channels for the oxidation of B, thereby maximizing the contact of the metal and oxidizer. Overall, the results demonstrate the potential of using B/Al blends to improve the energetic performance of B.

Enhanced Energetic Performance of Aluminum Nanoparticles by Plasma Deposition of Perfluorinated Nanofilms.

The performance of Al as nanoenergetic material in solid fuel propulsion or additive in liquid fuels is limited by the presence of the native oxide layer at the surface, which represents a significant weight fraction, does not contribute to heat release during oxidation, and acts as a diffusion barrier to Al oxidation. We develop an efficient technique in which the oxide layer is effectively turned into an energetic component via a reaction with fluorine that is coated in the form of a fluorocarbon nanofilm on the Al surface by plasma-enhanced chemical vapor deposition. Perfluorodecalin vapors are introduced in a low-pressure plasma reactor to produce nanofilms on the surface of Al nanoparticles, whose thickness is controlled with nanolevel precision as demonstrated by high-resolution transmission electron microscopy images. Coated particles show superior heat release, with a maximum enhancement of 50% at a thickness of 10 nm. This significant improvement is attributed to the chemical interaction between Al2O3 and F to form AlF3, which removes the oxide barrier via an exothermic reaction and contributes to the amount of heat released during thermal oxidation. The chemistry and mechanism of the enhancement effect of the plasma nanofilms are explained with the help of X-ray photoelectron spectroscopy, X-ray diffraction, high-angle annular dark-field scanning transmission electron microscopy-energy dispersive spectroscopy, thermogravimetric analysis, and differential scanning calorimetry.

Stochastic Theory of Discrete Binary Fragmentation-Kinetics and Thermodynamics.

We formulate binary fragmentation as a discrete stochastic process in which an integer mass k splits into two integer fragments j, k-j, with rate proportional to the fragmentation kernel Fj,k-j. We construct the ensemble of all distributions that can form in fixed number of steps from initial mass M and obtain their probabilities in terms of the fragmentation kernel. We obtain its partition function, the mean distribution and its evolution in time, and determine its stability using standard thermodynamic tools. We show that shattering is a phase transition that takes place when the stability conditions of the partition function are violated. We further discuss the close analogy between shattering and gelation, and between fragmentation and aggregation in general.

Surface-Functionalized Boron Nanoparticles with Reduced Oxide Content by Nonthermal Plasma Processing for Nanoenergetic Applications.

The development of an in situ nonthermal plasma technology improved the oxidation and energy release of boron nanoparticles. We reduced the native oxide layer on the surface of boron nanoparticles (70 nm) by treatment in a nonthermal hydrogen plasma, followed by the formation of a passivation barrier by argon plasma-enhanced chemical vapor deposition (PECVD) using perfluorodecalin (C10F18). Both processes occur near room temperature, thus avoiding aggregation and sintering of the nanoparticles. High-resolution transmission electron microscopy (HRTEM), high-angular annular dark-field imaging (HAADF)-scanning TEM (STEM)-energy dispersive spectroscopy (EDS), and X-ray photoelectron spectroscopy (XPS) demonstrated a significant reduction in surface oxide concentration due to hydrogen plasma treatment and the formation of a 2.5 nm thick passivation coating on the surface due to PECVD treatment. These results correlated with the thermal analysis results, which demonstrated a 19% increase in energy release and an increase in metallic boron content after 120 min of hydrogen plasma treatment and 15 min of PECVD of perfluorodecalin. The PECVD coating provided excellent passivation against air and humidity for 60 days. We conclude in situ nonthermal plasma reduction and passivation lead to the amelioration of energy release characteristics and the storage life of boron nanoparticles, benefits conducive for nanoenergetic applications.

The Smoluchowski Ensemble-Statistical Mechanics of Aggregation.

We present a rigorous thermodynamic treatment of irreversible binary aggregation. We construct the Smoluchowski ensemble as the set of discrete finite distributions that are reached in fixed number of merging events and define a probability measure on this ensemble, such that the mean distribution in the mean-field approximation is governed by the Smoluchowski equation. In the scaling limit this ensemble gives rise to a set of relationships identical to those of familiar statistical thermodynamics. The central element of the thermodynamic treatment is the selection functional, a functional of feasible distributions that connects the probability of distribution to the details of the aggregation model. We obtain scaling expressions for general kernels and closed-form results for the special case of the constant, sum and product kernel. We study the stability of the most probable distribution, provide criteria for the sol-gel transition and obtain the distribution in the post-gel region by simple thermodynamic arguments.

Mass-based finite volume scheme for aggregation, growth and nucleation population balance equation.

In this paper, a new mass-based numerical method is developed using the notion of Forestier-Coste & Mancini (Forestier-Coste & Mancini 2012, SIAM J. Sci. Comput. 34, B840-B860. (doi:10.1137/110847998)) for solving a one-dimensional aggregation population balance equation. The existing scheme requires a large number of grids to predict both moments and number density function accurately, making it computationally very expensive. Therefore, a mass-based finite volume is developed which leads to the accurate prediction of different integral properties of number distribution functions using fewer grids. The new mass-based and existing finite volume schemes are extended to solve simultaneous aggregation-growth and aggregation-nucleation problems. To check the accuracy and efficiency, the mass-based formulation is compared with the existing method for two kinds of benchmark kernels, namely analytically solvable and practical oriented kernels. The comparison reveals that the mass-based method computes both number distribution functions and moments more accurately and efficiently than the existing method.

Formation of Reversible Clusters with Controlled Degree of Aggregation.

We develop a reversible colloidal system of silica nanoparticles whose state of aggregation is controlled reproducibly from a state of fully dispersed nanoparticles to that of a colloidal gel and back. The surface of silica nanoparticles is coated with various amino silanes to identify a silane capable of forming a monolayer on the surface of the particles without causing irreversible aggregation. Of the three silanes used in this study, N-[3-(trimethoxysilyl)propyl]ethylenediamine was found to be capable of producing monolayers up to full surface coverage without inducing irreversible aggregation of the nanoparticles. At near full surface coverage the electrokinetic behavior of the functionalized silica is completely determined by that of the aminosilane. At acidic pH the ionization of the amino groups provides electrosteric stabilization and the system is fully dispersed. At basic pH, the dispersion state is dominated by the hydrophobic interaction between the uncharged aminosilane chains in the aqueous environment and the system forms a colloidal gel. At intermediate pH values the dispersion state is dominated by the balance between electrostatic and hydrophobic interactions, and the system exists in clusters whose size is determined solely by the pH. The transformation between states of aggregation is reversible and a reproducible function of pH. The rate of gelation can be controlled to be as fast as minutes while deaggregation is much slower and takes several hours to complete.

Abrupt percolation in small equilibrated networks.

Networks can exhibit an abrupt transition in the form of a spontaneous self-organization of a sizable fraction of the population into a giant component of connected members. This behavior has been demonstrated in random graphs under suppressive rules that passively or actively attempt to delay the formation of the giant cluster. We show that suppressive rules are not a necessary condition for a sharp transition at the percolation threshold. Rather, a finite system with aggressive tendency to form a giant cluster may exhibit an instability at the percolation threshold that is relieved through an abrupt and discontinuous transition to the stable branch. We develop the theory for a class of equilibrated networks that produce this behavior and find that the discontinuous jump is especially pronounced in small networks but disappears when the size of the system is infinite.

Statistical thermodynamics of irreversible aggregation: the sol-gel transition.

Binary aggregation is known to lead, under certain kinetic rules, to the coexistence of two populations, one consisting of finite-size clusters (sol), and one that contains a single cluster that carries a finite fraction of the total mass (giant component or gel). The sol-gel transition is commonly discussed as a phase transition by qualitative analogy to vapor condensation. Here we show that the connection to thermodynamic phase transition is rigorous. We develop the statistical thermodynamics of irreversible binary aggregation in discrete finite systems, obtain the partition function for arbitrary kernel, and show that the emergence of the gel cluster has all the hallmarks of a phase transition, including an unstable van der Waals loop. We demonstrate the theory by presenting the complete pre- and post-gel solution for aggregation with the product kernel.

Statistical thermodynamics of clustered populations.

We present a thermodynamic theory for a generic population of M individuals distributed into N groups (clusters). We construct the ensemble of all distributions with fixed M and N, introduce a selection functional that embodies the physics that governs the population, and obtain the distribution that emerges in the scaling limit as the most probable among all distributions consistent with the given physics. We develop the thermodynamics of the ensemble and establish a rigorous mapping to regular thermodynamics. We treat the emergence of a so-called giant component as a formal phase transition and show that the criteria for its emergence are entirely analogous to the equilibrium conditions in molecular systems. We demonstrate the theory by an analytic model and confirm the predictions by Monte Carlo simulation.

Passivation of aluminum nanoparticles by plasma-enhanced chemical vapor deposition for energetic nanomaterials.

We have produced passivating coatings on 80-nm aluminum particles by plasma-enhanced chemical vapor deposition (PECVD). Three organic precursors--isopropyl alcohol, toluene, and perfluorodecalin--were used to fabricate thin films with thicknesses ranging from 5 nm to 30 nm. The coated samples and one untreated sample were exposed to 85% humidity at 25 °C for two months, and the active Al content was determined by thermogravimetric analysis (TGA) in the presence of oxygen. The results were compared with an uncoated sample stored in a glovebox under argon for the same period. We find that all three coatings provide protection against humidity, compared to the control, and their efficacy ranks in the following order: isopropyl alcohol < toluene < perfluorodecalin. This order also correlates with increasing water contact angle of the three solid coatings. The amount of heat released in the oxidation, measured by differential scanning calorimetry (DSC), was found to increase in the same order. Perfluorodecalin resulted in providing the best protection, and it produced the maximum enthalpy of combustion, ΔH = 4.65 kJ/g. This value is higher than that of uncoated aluminum stored in the glovebox, indicating that the coatings promote more complete oxidation of the core. Overall, we conclude that the plasma polymer coatings of this study are suitable passivating thin film for aluminum nanoparticles by providing protection against oxidation while facilitating the complete oxidation of the metallic core at elevated temperature.

Microbubble formation from plasma polymers.

We document the formation of liquid-like particles in a toluene glow discharge that subsequently solidify via a process that releases hydrogen to form a solid microbubble with micrometer-size diameter, nanometer-size shell thickness, and high volume fraction, in excess of 90%. Liquid-like particles are produced in a toluene plasma under conditions that promote low degree of cross-linking (low power, high pressure). When these are transferred for observation in TEM, they are seen to transform under irradiation by the electron beam into solid bubbles with diameter of about 3 µm. This transformation also takes place under laser irradiation of sufficient power and under heating. We present evidence that the formation of these microbubbles is due to solidification of the liquid-like precursor that is accompanied by release of hydrogen. This mechanism is supported by a geometric model that provides a quantitative description of the particle size before and after solidification. These unique stimuli-responsive particles exhibit the potential of using temperature, electron beam, or laser as a source to change their size and structure which may find application in thermal insulators, lightweight materials, and light scattering agents.

Encapsulation and permeability characteristics of plasma polymerized hollow particles.

In this protocol, core-shell nanostructures are synthesized by plasma enhanced chemical vapor deposition. We produce an amorphous barrier by plasma polymerization of isopropanol on various solid substrates, including silica and potassium chloride. This versatile technique is used to treat nanoparticles and nanopowders with sizes ranging from 37 nm to 1 micron, by depositing films whose thickness can be anywhere from 1 nm to upwards of 100 nm. Dissolution of the core allows us to study the rate of permeation through the film. In these experiments, we determine the diffusion coefficient of KCl through the barrier film by coating KCL nanocrystals and subsequently monitoring the ionic conductivity of the coated particles suspended in water. The primary interest in this process is the encapsulation and delayed release of solutes. The thickness of the shell is one of the independent variables by which we control the rate of release. It has a strong effect on the rate of release, which increases from a six-hour release (shell thickness is 20 nm) to a long-term release over 30 days (shell thickness is 95 nm). The release profile shows a characteristic behavior: a fast release (35% of the final materials) during the first five minutes after the beginning of the dissolution, and a slower release till all of the core materials come out.

Shifts in plasmon resonance due to charging of a nanodisk array in argon plasma.

A method for generating charge-induced plasmonic shifts, using argon plasma to charge nanoparticle arrays, is presented. Particles develop a negative charge, due to enhanced collisions with high-temperature electrons, in low-temperature plasmas. The negative charge generated causes a blue shift in the localized surface plasmon resonance. The dynamics of the shift were recorded and discussed. This effect could be used as a real-time method for studying the dynamics for charging in plasma.

Fokker-Planck equation for particle growth by monomer attachment.

The population balance equation (PBE) for growth by attachment of a monomeric unit is described in the discrete domain by an infinite set of differential equations. Transforming the discrete problem into the continuous domain produces a series expansion which is usually truncated past the first term. We study the effect of this truncation and we show that by including the second-order term one obtains a Fokker-Planck approximation of the continuous PBE whose first and second moments are exact. We use this truncation to study the asymptotic behavior of the variance of the size distribution with growth rate that is a power-law function of the particle mass with exponent a . We obtain analytic expressions for the variance and show that its asymptotic behavior is different in the regimes a<1/2 and a>1/2. These conclusions are corroborated by Monte Carlo simulations.