Catalytic cracking of alkylcyclohexanes: Modeling the reaction pathways and mechanisms

The cracking reaction pathways and mechanisms of ethylcyclohexane and 1-cyclohexyloctane with a rare earth Y (REY) catalyst were studied. Experiments at 500°C indicated that the dominant reactions were ring opening with subsequent secondary cracking, cracking in the alkyl side chain, isomerization, and hydrogen transfer. A kinetic model of the catalytic cracking of 1-cyclohexyloctane was developed using a novel mechanism-based lumping scheme that exploits the chemical similarities within reaction families. The formal application of 17 reaction family matrices, which correspond to 13 reaction family classes, to the matrix representations of the reactants and derived products generated the model. The reaction family concept was further exploited to constrain the kinetics within each reaction family to follow a quantitative structure/reactivity Polanyi relationship. Ultimately, nine Polanyi relationship parameters and three coking/deactivation parameters were determined by optimizing the model fit to the experimental data. The resulting model correlations were excellent, as the overall parity between experimental and model values was y_Model=−0.000470+0.986y_Exp with a correlation coefficient of 0.971. © 1997 John Wiley & Sons, Inc. Int J Chem Kinet 29: 545–560, 1997.     

Synthesis and characterization of new polyimides containing calix[4]arenes in the polymer backbone

Two diaminocalix[4]arene monomers were synthesized from p-tert-butylcalix[4]arene through a 4-step reaction sequence. New copoly(amic acid)s containing calix[4]arene moieties on the polymer backbone were successfully synthesized in N-methyl-2-pyrrolidone by polycondensations of 4,4′-oxydiphthalic anhydride (ODPA) with the diaminocalix[4]arene monomers using 4,4′-oxydiphenylene diamine (ODA) as a comonomer. These copoly(amic acid)s were soluble in aprotic polar solvents, so that they can be processed in various ways. The copoly(amic acid) precursors were thermally converted to the corresponding copolyimides in films. The copolyimide films are amorphous, but insoluble in common solvents. They are thermally stable up to 366°C. The copolyimides exhibit relatively high TEC's, low T_g's, low refractive index, low dielectric constant, low optical anisotropy, low dielectric anisotropy, and low water uptake, compared to those of conventional ODPA-ODA polyimide. These property characteristics were interpreted in regard to bulky, cone-like calix[4]arene moieties and their effects on the chain conformation and morphological structure. The processability and property characteristics support that both of the copolyimides containing calix[4]arene moieties are potential candidate materials suitable for membranes, antioxidant additives, chemical sensor devices, and microelectronic devices. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 2013–2026, 1999     

A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler–Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler–Voigt equations also require less resolution than simulations of the 3D Euler equations for fixed values of the regularization parameter \(\alpha >0\). Therefore, the new blow-up criteria allow one to gain information about possible singularity formation in the 3D Euler equations indirectly, namely by simulating the better-behaved 3D Euler–Voigt equations. The new criteria are only known to be sufficient criterion for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well known to occur.     

The effect of two distinct fast time scales in the rotating,stratified Boussinesq equations: variations from quasi-geostrophy

Inspired by the use of fast singular limits in time-parallel numerical methods for a single fast frequency, we consider the limiting, nonlinear dynamics for a system of partial differential equations when two fast, distinct time scales are present. First-order slow equations are derived via the method of multiple time scales when the two small parameters are related by a rational power. We find that the resultant system depends only on the relationship of the two fast time scales, i.e. which fast time is fastest? Using the theory of cancellation of fast oscillations, we show that with the appropriate assumptions on the nonlinear operator of the full system, this reduced slow system is exactly that which the solution will converge to if each asymptotic limit is considered sequentially. The same result is also obtained via the method of renormalization. The specific example of the rotating, stratified Boussinesq equations is explored in detail, indicating that the most common distinguished limit of this system—quasi-geostrophy, is not the only limiting asymptotic system.     

Photochemical functionalization of gallium nitride thin films with molecular and biomolecular layers

We demonstrate that photochemical functionalization can be used to functionalize and photopattern the surface of gallium nitride crystalline thin films with well-defined molecular and biomolecular layers. GaN(0001) surfaces exposed to a hydrogen plasma will react with organic molecules bearing an alkene (C=C) group when illuminated with 254 nm light. Using a bifunctional molecule with an alkene group at one end and a protected amine group at the other, this process can be used to link the alkene group to the surface, leaving the protected amine exposed. Using a simple contact mask, we demonstrate the ability to directly pattern the spatial distribution of these protected amine groups on the surface with a lateral resolution of <12 mum. After deprotection of the amines, single-stranded DNA oligonucleotides were linked to the surface using a bifunctional cross-linker. Measurements using fluorescently labeled complementary and noncomplementary sequences show that the DNA-modified GaN surfaces exhibit excellent selectivity, while repeated cycles of hybridization and denaturation in urea show good stability. These results demonstrate that photochemical functionalization can be used as an attractive starting point for interfacing molecular and biomolecular systems with GaN and other compound semiconductors.     

Formation of silver nanoparticles at the air-water interface mediated by a monolayer of functionalized hyperbranched molecules

Nanofibrillar micellar structures formed by the amphiphilic hyperbranched molecules within a Langmuir monolayer were utilized as matter for silver nanoparticle formation from the ion-containing water subphase. We observed that silver nanoparticles were formed within the multifunctional amphiphilic hyperbranched molecules. The diameter of nanoparticles varied from 2-4 nm and was controlled by the core dimensions and the interfibrillar free surface area. Furthermore, upon addition of potassium nitrate to the subphase, the Langmuir monolayer templated the nanoparticles' formation along the nanofibrillar structures. The suggested mechanism of nanoparticle formation involves the oxidation of primary amino groups by silver catalysis facilitated by "caging" of silver ions within surface areas dominated by multibranched cores. This system provides an example of a one-step process in which hyperbranched molecules with outer alkyl tails and compressed amine-hydroxyl cores mediated the formation of stable nanoparticles placed along/among/beneath the nanofibrillar micelles.     

1H, 13C, and 73Ge NMR spectral analysis of substituted aryltrimethylgermanes

NMR chemical shifts of 1H, 13C, and 73Ge are reported for a series of monosubstituted aromatic trimethylgermanes of the type XC6H4Ge(CH3)3; X = p-N(CH3)2, p-OCH3, p-OC2H5, p-C(CH3)3, p-Si(CH3)3, p-Ge(CH3)3, p-Sn(CH3)3, p-CH3, m-CH3, -H, m-OCH3, p-Cl, p-Br, m-F, m-CF3, p-CF3, o-OCH3, and o-CH3. The relatively narrow 73Ge resonances show a strong correlation with Hammett sigma constants, with a correlation coefficient of 0.976 and 0.876 for 73Ge chemical shifts in meta- and para-substituted derivatives, respectively. The 13C chemical shifts of the methyl carbons bonded to germanium also display a relationship, with correlation coefficients of 0.904, 0.993, and 0.911 for para-, meta- and all derivatives, respectively. Comparisons of the Hammett plots for the homologous series XC6H4M(CH3)3; M = C, Si, Ge, Sn, show that, in general, correlation coefficients decrease while slopes increase significantly down the group, presumably reflecting the corresponding increase in chemical shift range of the group 14 atom. The Hammett constant derived for the p-Ge(CH3)3 group of +0.13 compares with the NMR-derived constants of -0.12 for p-C(CH3)3, +0.14 for p-Si(CH3)3, and -0.14 for p-Sn(CH3)3. The indication of electron release by carbon and tin can be rationalized through traditional hyperconjugative arguments for carbon and by the low electronegativity and consequent inductive effect of tin. The small electron attraction suggested by the positive constants for silicon and germanium can be simply, and perhaps naively, attributed to pi-acceptor interactions with the benzene ring.     

High-Resolution Infrared-Vacuum Ultraviolet Photoion and Pulsed Field Ionization-Photoelectron Methods for Spectroscopic Studies of Neutrals and Cations

We show that by scanning the frequency of a single mode infrared (IR) optical parametric oscillator (IR-OPO) laser to excite the molecular species of interest and fixing the frequency of a vacuum ultraviolet (VUV) laser to photoionize the IR excited species, high-resolution IR spectra of polyatomic neutrals can be obtained with high sensitivity. The fact that this IR-VUV-photoion (IR-VUV-PI) method is based on VUV photoionization probe, and thus, allows the identification of the neutral IR absorber, makes it applicable for IR spectroscopy measurements of isotopemers, radicals, and clusters, which usually exist as impure samples. The highly resolved IR-VUV-PI measurements achieved using the single mode IR-OPO laser have made possible the selection of single rovibrational states of CH3X (X=Br and I), C2H4, and C3H4 for VUV-pulsed field ionization-photoelectron (VUV-PFI-PE) measurements, resulting in rovibrationally resolved photoelectron spectra for these polyatomic molecules. These experiments show that the signal-to-noise ratios of the IR-VUV-PI and IR-VUV-PFI-PE spectra obtained by employing the high-resolution IR-OPO laser are significantly higher than those observed in previous IR-VUV-PI and IR-VUV-PFI-PE studies using a low-resolution IR-OPO laser. Further improvement in sensitivity of IR-VUV-PI and IR-VUV-PFI-PE measurements by using the collinear arrangement of IR-VUV lasers and molecular beam is discussed.