Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. The paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.     

Studies on the Oral Anticancer Drug JM-216: Synthesis and Characterization of Isomers and Related Complexes

The complex cis,trans,cis-[PtCl(2)(OAc)(2)NH(3)(c-C(6)H(11)NH(2))] (JM-216) is currently undergoing clinical evaluation as an antitumor agent. In support of characterization and analysis of this complex a study of its isomers and other complexes [PtCl(m)()(OAc)((4)(-)(m)()())NH(3)(c-C(6)H(11)NH(2))] (m = 0-4) has been undertaken. The complexes have been obtained by a variety of synthetic routes which now extend the scope for the preparation of platinum(IV) antitumor complexes. As platinum(IV) complexes are very stable to substitution in the absence of catalysis, use has been made of both light and base catalysis to promote substitution. Oxidative addition to platinum(II) using hypervalent iodine reagents has also been used. The stereochemistry of the complexes has been confirmed by spectroscopic studies, primarily NMR including natural abundance (15)N NMR spectroscopy.     

Transfer of amido groups from isolated rhodium(I) amides to alkenes and vinylarenes

The reaction of monomeric and dimeric rhodium(I) amido complexes with unactivated olefins to generate imines is reported. Transamination of {(PEt(3))(2)RhN(SiMePh(2))(2)} (1a) or its -N(SiMe(3))(2) analogue 1b with p-toluidine gave the dimeric [(PEt(3))(2)Rh(mu-NHAr)](2) (Ar = p-tolyl) (2a) in 80% isolated yield. Reaction of 2a with PEt(3) generated the monomeric (PEt(3))(3)Rh(NHAr) (Ar = p-tolyl) (3a). PEt(3)-ligated arylamides 2a and 3a reacted with styrene to transfer the amido group to the olefin and to form the ketimine Ph(Me)C=N(p-tol) (4a) in 48-95% yields. The dinuclear amido hydride (PEt(3))(4)Rh(2)(mu-NHAr)(mu-H) (Ar = p-tolyl) (5a) was formed from reaction of 2a in 95% yield, and a mixture of this dimeric species and the (PEt(3))(n)RhH complexes with n = 3 and 4 was formed from reaction of 3a in a combined 75% yield. Propene reacted with 2a to give Me(2)C=N(p-tol) (4b) and 5a in 90 and 57% yields. Propene also reacted with 3a to give 4b and 5a in 65 and 94% yields. Analogues of 2a and 3a with varied electronic properties also reacted with styrene to form the corresponding imines, and moderately faster rates were observed for reactions of electron-rich arylamides. Kinetic studies of the reaction of 3a with styrene were most consistent with formation of the imine by migratory insertion of olefin into the rhodium-amide bond to generate an aminoalkyl intermediate that undergoes beta-hydrogen elimination to generate a rhodium hydride and an enamine that tautomerizes to the imine.     

Isotope fractionation of water during evaporation without condensation

The microscopic events engendering liquid water evaporation have received much attention over the last century, but remain incompletely understood. We present measurements of isotope fractionation occurring during free molecular evaporation from liquid microjets and show that the isotope ratios of evaporating molecules exhibit dramatic differences from equilibrium vapor values, strong variations with the solution deuterium mole fraction, and a clear temperature dependence. These results indicate the existence of an energetic barrier to evaporation and that the evaporation coefficient of water is less than unity. These new insights into water evaporation promise to advance our understanding of the processes that control the formation and lifetime of clouds in the atmosphere.     

Electroosmotic flow in channels with step changes in zeta potential and cross section

We consider the effects that step changes in zeta potential and cross section have on electroosmosis in long-and-narrow channels with arbitrary cross-sectional shapes. The Stokes equation of flow is solved analytically utilizing the thin Debye layer approximation to provide effective slip velocities on the channel walls. The effects of channel dimensions, surface potentials, applied pressure drop, and applied voltage are discussed. One anecdotal case, a two-region rectangular channel, is presented to illustrate the solution. The flow in each region is a combination of a uniform electroosmotic flow and a nonuniform pressure-driven flow. The electroosmotic pumping causes the pressure gradient in each region to adjust so that the flow rate is the same in each region and the overall applied pressure drop is met, resulting in convex velocity profiles in some regions and concave velocity profiles in other regions. By appropriate choice of the applied pressure drop, flat velocity profiles may be achieved in one or more regions.     

Theoretical calculation of electrode potentials: Electron-withdrawing compounds

The electrode potential of 2,3-dicyanobenzoquinone in aqueous solution has been calculated relative to parabenzoquinone using a thermodynamic cycle approach that includes accurate gasphase ab initio calculations and calculation of differences in free energies of hydration using the free-energy perturbation method. The discrepancy between the calculated and experimental electrode potential is disappointingly large (99 mV) compared to previous studies using this approach. This, along with the experimental evidence, suggests that the experimental value itself is too large and that theoretical approaches may indeed be as reliable as experimental ones for determining redox properties of molecules such as 2,3-dicyanobenzoquinone. In the light of this discrepancy we have examined the variation of the results with the basis set, inclusion of electron correlation and changes in the parameters used in the molecular dynamics free-energy simulations. The results are shown to be dependent upon the torsional parameters and especially dependent upon the basis set or semiempirical method used to obtain the electrostatic potential-derived charges. The best charge set was determined using the ab initio criteria of completeness—as far as it can be applied to large molecules—and also by studying the effect of hydration on these charges. This was done by allowing the solvent to perturb the wave function prior to the electrostatic potential determination. Thus, 3-21G and 6-31G * basis sets were found to give satisfactory results. Similar results were obtained using semiempirical and ab initio geometries.     

Computational and experimental studies of the effect of substituents on the singlet-triplet energy gap in phenyl(carbomethoxy)carbene

The effect of aromatic substitution on the singlet-triplet energy gap in substituted phenyl(carbomethoxy)carbene (X-Ph-C-CO(2)CH(3), PCC) has been explored by time-resolved infrared (TRIR) spectroscopy and gas-phase computational methods. The ground state of para-substituted PCC is calculated to change from the triplet state in p-NO(2)-PCC (Delta G(ST) = 6.1 kcal/mol) to the singlet state in p-NH(2)-PCC (Delta G(ST) = -2.8 kcal/mol). The absence of solvent perturbation in the TRIR spectra of p-N(CH(3))(2)-PCC (which should have electronic properties similar to p-NH(2)-PCC) and parent PCC is consistent with their ground states lying > +/-2 kcal/mol from the next available electronic state, in line with the computational results. The observation of solvent perturbation in the TRIR spectra of p-OCH(3)-PCC and p-CH(3)-PCC implies that their ground states lie < +/-1 kcal/mol from their next available electronic state. This is in agreement with our computational results, which predict a gas-phase Delta G(ST) of -0.8 and 1.6 kcal/mol for p-OCH(3)-PCC and p-CH(3)-PCC as compared to Delta G(ST) values of -3.9 and -1.3 kcal/mol from polarizable continuum model (PCM) calculations with acetonitrile as a solvent. Gas-phase computational results for the meta- and ortho-substituted PCC species are also presented, along with selected linear free energy (LFE) relationships for the para and meta species.     

Hydrogen bonding in 2‐amino‐4,6‐dimethoxypyrimidine, 2‐benzylamino‐4,6‐bis(benzyloxy)pyrimidine and 2‐amino‐4,6‐bis(N‐pyrrolidino)pyrimidine: chains of fused rings and a centrosymmetric dimer

Molecules of 2‐amino‐4,6‐di­methoxy­pyrimidine, C₆H₉N₃O₂, (I), are linked by two N—H?N hydrogen bonds [H?N 2.23 and 2.50 Å, N?N 3.106 (2) and 3.261 (2) Å, and N—H?N 171 and 145°] into a chain of fused rings, where alternate rings are generated by centres of inversion and twofold rotation axes. Adjacent chains are linked by aromatic π–π‐stacking interactions to form a three‐dimensional framework. In 2‐­benzylamino‐4,6‐bis(benzyloxy)pyrimidine, C₂₅H₂₃N₃O₂, (II), the mol­ecules are linked into centrosymmetric R(8) dimers by paired N—H?N hydrogen bonds [H?N 2.13 Å, N?N 2.997 (2) Å and N—H?N 170°]. Molecules of 2‐amino‐4,6‐bis(N‐pyrrolidino)­pyrimidine, C₁₂H₁₉N₅, (III), are linked by two N—H?N hydrogen bonds [H?N 2.34 and 2.38 Å, N?N 3.186 (2) and 3.254 (2) Å, and N—H?N 163 and 170°] into a chain of fused rings similar to that in (I).     

The steric and electronic effects of aliphatic fluoroalkyl groups

Ab initio calculations were performed on 18 fluorinated and unfluorinated alcohols at the B3LYP and HF levels with the 6-311G^∗∗ basis set. Molar volumes of the alcohols were computed at each level and averaged to produce a scale of relative size. From this, various isosteric replacements of potential use in drug design were suggested: ethyl by FCH₂CH₂ or HCF₂CH₂, propyl by CF₃CH₂, isopropyl by CF₃(CH₃)CH or (FCH₂)₂CH, isobutyl or t-butyl by (CF₃)₂CH, and 3-methyl-2-butyl by CF₃(CH₃)₂C. Calculation of the charge on oxygen and the Wiberg index of the CO bond allowed an electronegativity scale to be constructed for the fluoroalkyl groups. Electronegativity decreased in the order: (CF₃)₃C>(CF₃)₂CH>C₂F₅CH₂>CF₃CH₂>CH₃(CF₃)₂C>HCF₂CH₂>CF₃(CH₃)CH>(FCH₂)₂CH>FCH₂CH₂>CF₃(CH₃)₂C. This ranking agreed with literature acid dissociation data for the alcohols studied.     

Formation of Metallo-6(A)-((2-(bis(2-aminoethyl)amino)ethyl)amino)-6(A)-deoxy-beta-cyclodextrins and Their Complexation of Tryptophan in Aqueous Solution

A pH titration study shows that 6(A)-((2-(bis(2-aminoethyl)amino)ethyl)amino)-6(A)-deoxy-beta-cyclodextrin (betaCDtren) forms binary metallocyclodextrins, [M(betaCDtren)](2+), for which log(K/dm(3) mol(-)(1)) = 11.65 +/- 0.06, 17.29 +/- 0.05, and 12.25 +/- 0.03, respectively, when M(2+) = Ni(2+), Cu(2+), and Zn(2+), where K is the stability constant in aqueous solution at 298.2 K and I = 0.10 mol dm(-)(3) (NaClO(4)). The ternary metallocyclodextrins [M(betaCDtren)Trp](+), where Trp(-) is the tryptophan anion, are characterized by log(K/dm(3) mol(-)(1)) = 8.2 +/- 0.2 and 8.1 +/- 0.2, 9.5 +/- 0.3 and 9.4 +/- 0.2, and 8.1 +/- 0.1 and 8.3 +/- 0.1, respectively, where the first and second values represent the stepwise stability constants for the complexation of (R)- and (S)-Trp(-), respectively, when M(2+) = Ni(2+), Cu(2+), and Zn(2+). From comparisons of stabilities and UV-visible spectra, the binary and ternary metallocyclodextrins appear to be six-coordinate when M(2+) = Ni(2+) and Zn(2+) and five-coordinate when M(2+) = Cu(2+). The factors affecting the stoichiometries and stabilities of the metallocyclodextrins, are discussed and comparisons are made with related systems.