Structure and energetics of nanometer size clusters of sulfuric acid with ammonia and dimethylamine

The structures of positively and negatively charged clusters of sulfuric acid with ammonia and/or dimethylamine ((CH(3))(2)NH or DMA) are investigated using a combination of Monte Carlo configuration sampling, semiempirical calculations, and density functional theory (DFT) calculations. Positively charged clusters of the formula [(NH(4)(+))(x)(HSO(4)(-))(y)](+), where x = y + 1, are studied for 1 ≤ y ≤ 10. These clusters exhibit strong cation-anion interactions, with no contribution to the hydrogen-bonding network from the bisulfate ion protons. A similar hydrogen-bonding network is found for the [(DMAH(+))(5)(HSO(4)(-))(4)](-) cluster. Negatively charged clusters derived from the reaction of DMA with [(H(2)SO(4))(3)(NH(4)(+))(HSO(4)(-))(2)](-) are also studied, up to the fully reacted cluster [(DMAH(+))(4)(HSO(4)(-))(5)](-). These clusters exhibit anion-anion and ion-molecule interactions in addition to cation-anion interactions. While the hydrogen-bonding network is extensive for both positively and negatively charged clusters, the binding energies of ions and molecules in these clusters are determined mostly by electrostatic interactions. The thermodynamics of amine substitution is explored and compared to experimental thermodynamic and kinetic data. Ammonia binds more strongly than DMA to sulfuric acid due to its greater participation in hydrogen bonding and its ability to form a more compact structure that increases electrostatic attraction between oppositely charged ions. However, the greater gas-phase basicity of DMA is sufficient to overcome the stronger binding of ammonia, making substitution of DMA for ammonia thermodynamically favorable. For small clusters of both polarities, substitutions of surface ammonium ions are facile. As the cluster size increases, an ammonium ion becomes encapsulated in the center of the cluster, making it inaccessible to substitution.     

Size-dependent reactions of ammonium bisulfate clusters with dimethylamine

The reaction kinetics of ammonium bisulfate clusters with dimethylamine (DMA) gas were investigated using Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS). Clusters ranged in size from 1 to 10 bisulfate ions. Although displacement of the first several ammonium ions by DMA occurred with near unit efficiency, displacement of the final ammonium ion was cluster size dependent. For small clusters, all ammonium ions are exposed to incoming DMA molecules, allowing for facile exchange ("surface" exchange). However, with increasing cluster size, an ammonium ion can be trapped in an inaccessible region of the cluster ("core" exchange), thereby rendering exchange difficult. DMA was also observed to add onto existing dimethylaminium bisulfate clusters above a critical size, whereas ammonia did not add onto ammonium bisulfate clusters. The results suggest that as the cluster size increases, di-dimethylaminium sulfate formation becomes more favorable. The results of this study give further evidence to suggest that ambient sub-3 nm diameter particles are likely to contain aminium salts rather than ammonium salts.     

Summation methods of Coulomb interactions in computer simulations of a system with one—dimensional periodic boundary conditions

The Ewald-type method, its modified version and the Lekner-type method for summing Coulomb interactions in a system periodic along one direction are presented and compared. Advantages and disadvantages of these methods are discussed, and the methods are tested in molecular dynamics simulations of acetone molecules confined to cylindrical silica pores.     

Electrostatic interactions in molecular dynamics simulation of a three-dimensional system with periodicity in one direction

The Mellin transform and Poisson summation formula are used to derive an expression for the Coulomb interaction energy of a three-dimensional system with periodicity in one direction. Initially, calculations are performed for interactions characterized by any inverse power and, using the analytical continuation of the energy function, one obtains the final expression for the interaction energy of charges. We consider also a special case when two different charges are located on a line parallel to the periodicity direction. The energy and force expressions are identical to those obtained from the Lekner summation which is simply a sum over reciprocal lattice terms. The convergence behaviour of the Lekner summation is compared with that based on the Ewald type approach.     

Coulomb interactions in a computer simulation of a system periodic in two directions

The integral representation of the gamma function and the Poisson summation formula are used to calculate the interaction energy of charged particles in a 3-dimensional system periodic in two directions. A parallelogram shape simulation box is considered. Calculations are carried out for interactions described by any inverse power, and analytical continuation of the energy function leads to the final expression for the Coulomb interaction energy. Summation over the simulation box replica along one or the other side of the box base is replaced by summation in reciprocal space. Therefore there are two equivalent formulas for the potential energy that offer the possibility of avoiding slowly convergent series. The energy expressions are identical to those obtained from the Lekner method. The special case is considered where the functions defining the energy are infinite, i.e. when two charges lie on a line parallel to the simulation box side that was chosen to convert real space summation into reciprocal space.