Multicomponent dynamical nucleation theory and sensitivity analysis

Vapor to liquid multicomponent nucleation is a dynamical process governed by a delicate interplay between condensation and evaporation. Since the population of the vapor phase is dominated by monomers at reasonable supersaturations, the formation of clusters is governed by monomer association and dissociation reactions. Although there is no intrinsic barrier in the interaction potential along the minimum energy path for the association process, the formation of a cluster is impeded by a free energy barrier. Dynamical nucleation theory provides a framework in which equilibrium evaporation rate constants can be calculated and the corresponding condensation rate constants determined from detailed balance. The nucleation rate can then be obtained by solving the kinetic equations. The rate constants governing the multistep kinetics of multicomponent nucleation including sensitivity analysis and the potential influence of contaminants will be presented and discussed.     

Molecular structure and dynamics in the low temperature (orthorhombic) phase of NH3BH3

Variable temperature 2H NMR experiments on the orthorhombic phase of selectively deuterated NH3BH3 spanning the static to fast exchange limits of the borane and amine motions are reported. New values of the electric field gradient (EFG) tensor parameters have been obtained from the static 2H spectra of V(zz) = 1.652 (+/-0.082) x 10(21) V/m(2) and eta = 0.00 +/- 0.05 for the borane hydrogens and V(zz) = 2.883 (+/-0.144) x 10(21) V/m(2) and eta = 0.00 +/- 0.05 for the amine hydrogens. The molecular symmetry inferred from the observation of equal EFG tensors for the three borane hydrogens and likewise for the three amine hydrogens is in sharp contrast with the C(s) symmetry derived from diffraction studies. The origin of the apparent discrepancy has been investigated using molecular dynamics methods in combination with electronic structure calculations of NMR parameters, bond lengths, and bond angles. The computation of parameters from a statistical ensemble rather than from a single set of atomic Cartesian coordinates gives values that are in close quantitative agreement with the 2H NMR electric field gradient tensor measurements and are more consistent with the molecular symmetry revealed by the NMR spectra.     

Water-soluble polymers. 71. pH responsive behavior of terpolymers of sodium acrylate,acrylamide, and the zwitterionic monomer 4-(2-acrylamido-2-methylpropanedimethylammonio)butanoate

Terpolymers of sodium acrylate (NaA), acrylamide (AM), and the zwitterionic monomer 4-(2-acrylamido-2-methylpropanedimethylammonio) butanoate (AMPDAB) were prepared by the free radical polymerization in 0.5M NaBr aqueous solution using potassium persulfate as the initiator. The feed ratio of AMPDAB : NaA : AM was varied from 5 : 5 : 90 to 40 : 40 : 20 mol %, with the total monomer concentration held constant at 0.45M. Terpolymer compositions were determined by ¹³C NMR. Molecular weights varied from 3.0 × 10⁵ to 9.7 × 10⁶ g/mol. All terpolymers were soluble in deionized water and salt solutions at all pH values. The dilute and semidilute solution behavior of the terpolymers was studied as a function of composition, pH, and added electrolytes. Polyelectrolyte behavior was observed for all terpolymers at pH 8.5, as evidenced by high viscosity values at low polymer concentrations and viscosity decrease in the presence of added electrolytes. The reduced viscosity as a function of decreasing pH exhibits a minimum as the terpolymer undergoes a polyanion/polyzwitterion/polycation transition. Comparison of the solution behavior of the terpolymers to terpolymers of 3-(2-acrylamido-2-methylpropane dimethylammonio)-1-propane sulfonate (AMPDAPS), AM, and NaA (AADAPS series) as well as copolymers of AMPDAB and AM (AMPDAB series) have been made. © 1997 John Wiley & Sons, Inc.     

Analysis of the activation and heterolytic dissociation of H2 by frustrated Lewis pairs: NH3/BX3 (X = H, F, and Cl)

We performed a computational study of H(2) activation and heterolytic dissociation promoted by prototype Lewis acid/base pairs NH(3)/BX(3) (X = H, F, and Cl) to understand the mechanism in frustrated Lewis pairs (FLPs). Although the NH(3)/BX(3) pairs form strong dative bonds, electronic structure theories make it possible to explore the potential energy surface away from the dative complex, in regions relevant to H(2) activation in FLPs. A weakly bound precursor complex, H(3)N·H(2)·BX(3), was found in which the H(2) molecule interacts side-on with B and end-on with N. The BX(3) group is pyramidal in the case of X = H, similar to the geometry of BH(5), but planar in the complexes with X = F and Cl. The latter complexes convert to ion pairs, [NH(4)(+)][BHX(3)(-)] with enthalpy changes of 7.3 and -9.4 kcal/mol, respectively. The minimum energy paths between the FLP and the product ion pair of the chloro and fluoro complexes were calculated and analyzed in great detail. At the transition state (TS), the H(2) bond is weakened and the BX(3) moiety has undergone significant pyramidal distortion. As such, the FLP is prepared to accept the incipient proton and hydride ion on the product-side. The interaction energy of the H(2) with the acid/base pair and the different contributions for the precursor and TS complex from an energy decomposition analysis expose the dominant factors affecting the reactivity. We find that structural reorganization of the precursor complex plays a significant role in the activation and that charge-transfer interactions are the dominant stabilizing force in the activated complex. The electric field clearly has a role in polarizing H(2), but its contribution to the overall interaction energy is small compared to that from the overlap of the p(N), σ(H-H), σ*(H-H), and p(B) orbitals at the TS. Our detailed analysis of the interaction of H(2) with the FLP provides insight into the important components that should be taken into account when designing related systems to activate H(2).     

Study of ion specific interactions of alkali cations with dicarboxylate dianions

Alkali metal cations often show pronounced ion-specific interactions and selectivity with macromolecules in biological processes, colloids, and interfacial sciences, but a fundamental understanding about the underlying microscopic mechanism is still very limited. Here we report a direct probe of interactions between alkali metal cations (M(+)) and dicarboxylate dianions, (-)O(2)C(CH(2))(n)CO(2)(-) (D(n)(2-)) in the gas phase by combined photoelectron spectroscopy (PES) and ab initio electronic structure calculations on nine M(+)-D(n)(2-) complexes (M = Li, Na, K; n = 2, 4, 6). PES spectra show that the electron binding energy (EBE) decreases from Li(+) to Na(+) to K(+) for complexes of M(+)-D(2)(2-), whereas the order is Li(+) < Na(+) ≈ K(+) when M(+) interacts with a more flexible D(6)(2-) dianion. Theoretical modeling suggests that M(+) prefers to interact with both ends of the carboxylate -COO(-) groups by bending the flexible aliphatic backbone, and the local binding environments are found to depend upon backbone length n, carboxylate orientation, and the specific cation M(+). The observed variance of EBEs reflects how well each specific dicarboxylate dianion accommodates each M(+). This work demonstrates the delicate interplay among several factors (electrostatic interaction, size matching, and strain energy) that play critical roles in determining the structures and energetics of gaseous clusters as well as ion specificity and selectivity in solutions and biological systems.     

Understanding the chemical physics of nucleation

Observation and theory have steadily progressed our understanding of nucleation phenomena over the past 280 years. However, even more questions remain concerning the governing processes and mechanisms. The inherent instability and sensitivity of nucleation places a high premium on theoretical accuracy and experimental purity and similarly makes interpretation of both more challenging. The objective of the present paper is to contribute to the understanding of nucleation kinetics and thermodynamics with emphasis on cluster chemical physics within the context of Dynamical Nucleation Theory. Our hope is to share some insights that we have gained over the past several years concerning rate constants, molecular interactions, statistical mechanics and their consequences on nucleation.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.