Inertial deposition of nanoparticle chain aggregates: Theory and comparison with impactor data for ultrafine atmospheric aerosols

Nanoparticle chain aggregates (NCAs) are often sized and collected using instruments that rely on inertial transport mechanisms. The instruments size segregate aggregates according to the diameter of a sphere with the same aerodynamic behavior in a mechanical force field. A new method of interpreting the aerodynamic diameter of NCAs is described. The method can be used to calculate aggregate surface area or volume. This is useful since inertial instruments are normally calibrated for spheres, and the calibrations cannot be directly used to calculate aggregate properties. A linear relationship between aggregate aerodynamic diameter and primary particle diameter based on published Monte-Carlo drag calculations is derived. The relationship shows that the aggregate aerodynamic diameter is independent of the number of primary particles that compose an aggregate, hence the aggregate mass. The analysis applies to aggregates with low fractal dimension and uniform primary particle diameter. This is often a reasonable approximation for the morphology of nanoparticles generated in high temperature gases. An analogy is the use of the sphere as an approximation for compact particles. The analysis is applied to the collection of NCAs by a low-pressure impactor. Our results indicate the low-pressure impactor collects aggregates with a known surface area per unit volume on each stage. Combustion processes often produce particles with aggregate structure. For diesel exhaust aggregates, the surface area per unit volume calculated by our method was about twice that of spheres with diameter equal to the aerodynamic diameter. Measurements of aggregates collected near a major freeway and at Los Angeles International Airport (LAX) were made for two aerodynamic cutoff diameter diameters (d _a,50), 50 and 75 nm. (Aerodynamic cutoff diameter refers to the diameter of particles collected with 50% efficiency on a low-pressure impactor stage.) Near-freeway aggregates were probably primarily a mixture of diesel and internal combustion engine emissions. Aggregates collected at LAX were most likely present as a result of aircraft emissions. In both measurements, the aggregate aerodynamic diameters calculated from the primary particle diameter were fairly close to the stage cutoff diameter. The number of primary particles per aggregate varied one order of magnitude for particles depositing on the same stage. The average aggregate surface area per unit volume was 2.41 × 10⁶ cm⁻¹ and 2.59 × 10⁶ cm⁻¹ (50 nm d _a,50) and 1.81 × 10⁶ cm⁻¹ and 1.68 × 10⁶ cm⁻¹ (75 nm d _a,50) for near-freeway and LAX measurements, respectively. These preliminary measurements are consistent with values calculated from theory.     

Coalescing times for IID random variables with applications to population biology

We consider a coalescing particle model where particles move in discrete time. At each time period, each remaining ball is independently put in one of n bins according to a probability distribution p = (p₁, …, p_n), and all balls put into the same bin merge into a single ball. Starting with k balls, we are interested in the properties of E[N( p , k)], the expected time until all balls merge into one. We derive both upper and lower bounds for E[N( p , k)], some asymptotic results, and show that P{N( p , k) > t}, and thus E[N( p , k)], is a Schur concave function of p . Applications to population biology are noted. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 155–166, 2003     

Extending simulation uses of antithetic variables: partially monotone functions, random permutations, and random subsets

We show how to effectively use antithetic variables to evaluate the expected value of (a) functions of independent random variables, when the functions are monotonic in only some of their variables, (b) Schur functions of random permutations, and (c) monotone functions of random subsets.     

Toeplitz algebras on the disk

Let B be a Douglas algebra and let B be the algebra on the disk generated by the harmonic extensions of the functions in B. In this paper we show that B is generated by H^∞(D) and the complex conjugates of the harmonic extensions of the interpolating Blaschke products invertible in B. Every element S in the Toeplitz algebra TB generated by Toeplitz operators (on the Bergman space) with symbols in B has a canonical decomposition for some R in the commutator ideal CTB; and S is in CTB iff the Berezin transform vanishes identically on the union of the maximal ideal space of the Douglas algebra B and the set M₁ of trivial Gleason parts.     

Study of the enhancement of dipolar resonant excitation by linear ion trap simulations

Resolution improvements in dipolar resonant excitation have been examined in a round-rod quadrupolar collision cell for values of the Mathieu characteristic exponent beta equal to n/p, where n and m are small integers (prime beta values) versus other beta values where n and p are not small (ordinary beta values). The trajectories of ions moving in the time-varying electric fields of a quadrupole with and without buffer-gas molecules were calculated to determine the relationship of prime and ordinary beta values to frequency resolution for resonant ion excitation and ejection. For prime beta values, the ion trajectory in the hyperbolic quadrupole field will be exactly periodic with a period of at most 4 pi p/Omega, where Omega is the angular frequency of the main drive radio-frequency (RF) potential. Ion trajectory simulations with prime beta versus ordinary beta values show that the motion of ions with prime beta values have simpler trajectories of shorter periods. Frequency response profiles (FRPs) for round-rod quadrupoles at zero pressure show that dipolar resonant excitations with prime beta values exhibit significantly narrower bandwidths than those with ordinary beta values. Simulations show that at 0.05 to 0.8 mTorr of nitrogen, it is possible to reduce the FRP bandwidth by 20% (measured at 50% depth).     

The Quantum Formalism and the GRW Formalism

The Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse is known to provide a quantum theory without observers, in fact two different ones by using either the matter density ontology (GRWm) or the flash ontology (GRWf). Both theories are known to make predictions different from those of quantum mechanics, but the difference is so small that no decisive experiment can as yet be performed. While some testable deviations from quantum mechanics have long been known, we provide here something that has until now been missing: a formalism that succinctly summarizes the empirical predictions of GRWm and GRWf. We call it the GRW formalism. Its structure is similar to that of the quantum formalism but involves different operators. In other words, we establish the validity of a general algorithm for directly computing the testable predictions of GRWm and GRWf. We further show that some well-defined quantities cannot be measured in a GRWm or GRWf world.     

Experimental and computational study of the formation mechanism of the diammoniate of diborane: the role of dihydrogen bonds

The mechanism of formation of ammonia borane (NH(3)BH(3), AB) and the diammoniate of diborane ([H(2)B(NH(3))(2)][BH(4)], DADB) in the reaction between NH(3) and THF·BH(3) was explored experimentally and computationally. Ammonia diborane (NH(3)BH(2)(μ-H)BH(3), AaDB), a long-sought intermediate proposed for the formation of DADB, was directly observed in the reaction using (11)B NMR spectroscopy. The results indicate that dihydrogen bonds between the initially formed AB and AaDB accelerate the formation of DADB in competition with the formation of AB.     

A convenient synthesis and a NMR study of the diammoniate of diborane

DADB synthesis: The diammoniate of diborane (DADB) was synthesized in a new metathesis reaction between the diammoniate of monochloroborane and potassium borohydride in liquid ammonia. (1)H and (11)B?NMR spectra of DADB are reported. The stability in THF was examined by variable-temperature (11)B?NMR spectroscopy.     

Unusual cationic tris(dimethylsulfide)-substituted closo-boranes: preparation and characterization of [1,7,9-(Me2S)3-B12H9] BF4 and [1,2,10-(Me2S)3-B10H7] BF4

Rational syntheses of trisubstituted sulfur-bearing closo-boranes are presented. In the development of these syntheses unusual cationic closo-boranes [1,7,9-(Me(2)S)(3)-B(12)H(9)](+) (3) and [1,2,10-(Me(2)S)(3)-B(10)H(7)](+) (4) have been identified. These were initially recognized to be intermediates in the formation of the neutral trisubstituted species 1,7-(Me(2)S)(2)-9-(MeS)-B(12)H(9) (1) and 1,10-(Me(2)S)(2)-2-(MeS)-B(10)H(7) (2), respectively. Stable tetrafluoroborate salts were prepared and isolated, and their structures are presented. They are believed to represent the first structural determinations of cationic borane clusters of any type.