A kinetic model of the formation of organic monolayers on hydrogen-terminated silicon by hydrosilation of alkenes

We have analyzed a kinetic model for the formation of organic monolayers based on a previously suggested free radical chain mechanism for the reaction of unsaturated molecules with hydrogen-terminated silicon surfaces (Linford, M. R.; Fenter, P. M.; Chidsey, C. E. D. J. Am. Chem. Soc 1995, 117, 3145). A direct consequence of this mechanism is the nonexponential growth of the monolayer, and this has been observed spectroscopically. In the model, the initiation of silyl radicals on the surface is pseudo first order with rate constant, ki, and the rate of propagation is determined by the concentration of radicals and unreacted Si-H nearest neighbor sites with a rate constant, kp. This propagation step determines the rate at which the monolayer forms by addition of alkene molecules to form a track of molecules that constitute a self-avoiding random walk on the surface. The initiation step describes how frequently new random walks commence. A termination step by which the radicals are destroyed is also included. The solution of the kinetic equations yields the fraction of alkylated surface sites and the mean length of the random walks as a function of time. In mean-field approximation we show that (1) the average length of the random walk is proportional to (kp/ki)1/2, (2) the monolayer surface coverage grows exponentially only after an induction period, (3) the effective first-order rate constant describing the growth of the monolayer and the induction period (kt) is k = (2ki kp)1/2, (4) at long times the effective first-order rate constant drops to ki, and (5) the overall activation energy for the growth kinetics is the mean of the activation energies for the initiation and propagation steps. Monte Carlo simulations of the mechanism produce qualitatively similar kinetic plots, but the mean random walk length (and effective rate constant) is overestimated by the mean field approximation and when kp > ki, we find k approximately ki0.7kp0.3 and Ea = (0.7Ei+ 0.3Ep). However the most striking prediction of the Monte Carlo simulations is that at long times, t > 1/k, the effective first-order rate constant decreases to ki even in the absence of a chemical termination step. Experimental kinetic data for the reaction of undec-1-ene with hydrogen-terminated porous silicon under thermal reflux in toluene and ethylbenzene gave a value of k = 0.06 min(-1) and an activation energy of 107 kJ mol(-1). The activation energy is in reasonable agreement with density functional calculations of the transition state energies for the initiation and propagation steps.     

Non-aqueous capillary electrophoretic separation of enantiomeric amines with (-)-2,3:4,6-di-O-isopropylidene-2-keto-L-gulonic acid as chiral counter ion

(-)-2,3:4,6-Di-O-isopropylidene-2-keto-L-gulonic acid [(-)-DIKGA] has been introduced as a chiral counter ion in non-aqueous capillary electrophoresis. High enantioresolutions (R(s)> or =3) were obtained for amines, e.g., pronethalol, labetalol and bambuterol. Methanol containing NaOH and (-)-DIKGA was used as the background electrolyte. The counter ion concentration and the nature of the injection medium were found to affect the chiral separation. Covalent coating of the fused-silica capillary reduced the electro-osmotic flow resulting in improved enantioresolutions.     

Photostabilisation mechanisms in polymers: A review

Key degradative processes for various polymers are itemised, together with photostabilisation mechanisms which can minimise these processes. Polymers can be conveniently classified as inherent absorbers, which absorb large amounts of solar uv, and as ‘non-absorbers’, that is polymers transparent in the near uv. The former group which includes aramids, polycarbonates and polyesters is predominantly photodegraded by primary processes causing direct bond scission and stabilisation is best effected by the use of uv absorbing additives or opaque pigments. The ‘non-absorbers’ include polyolefins and poly(vinylchloride) which are degraded as the result of oxidative chain processes initiated by chromophoric impurities. For polypropylene the dominant photooxidation product is hydroperoxide which photocleaves to initiate further oxidation. Various uv. stabilisers for polyolefins appear to owe their effectiveness to their ability to decompose hydroperoxide groups and/or to their ability to scavenge free radical intermediates in the oxidative process.     

Optical characterisation of the photolytic decomposition of ferrocene into nanoparticles

Optical emission from the photolytic dissociation of ferrocene Fe(C₅H₅)₂, often abbreviated as FeCp₂, in argon atmosphere was studied. The dissociation was performed by using an ArF excimer laser, operating at a wavelength of 193 nm. Two pressure regions were examined. At low (0.1 mbar) pressure, several emission lines of Fe could be identified, however no C, C₂, or CH emission lines/bands were found. At a higher (20 mbar) pressure of the FeCp₂/Ar gas mixture, a broadband emission identified as blackbody radiation was observed. This blackbody radiation originates from nanoparticles with a mean size of 30 nm, which consist of both metallic iron and amorphous carbon. The initial colour temperature of the particles was 2600 K.     

Confocal scanning microfluorometry of dual-labelled specimens using two excitation wavelengths and lock-in detection technique

A new technique for simultaneous recording of multiple fluorophores has been implemented in a confocal scanning laser microscope. Dual excitation wavelengths, intensity-modulated at different frequencies and two lock-in amplifiers tuned to the corresponding frequencies are used. In this way two fluorophores can be independently, albeit simultaneously, excited. This technique, Intensity-modulated Multiple-beam Scanning (IMS) microfluorometry, has the potential to virtually eliminate the cross-talk between fluorophores that often occurs when recording multiple-labelled specimens. Furthermore, it will offer simultaneous information about both the excitation and emission spectra of the fluorophores used. Also, variations in decay time over the image area can be studied independently and simultaneously for two fluorophores.     

Oriented polyolefin laminates: A refractometry and infrared study

A series of polypropylene-copolymer laminates produced by biaxial orientation in the 120–155°C range has been characterized by refractometry and infrared (IR) spectroscopy. The copolymer was a random ethylene-propylene resin and the IR techniques included tilted-film transmission as well as internal reflection, both using polarized radiation. The IR techniques yielded spectra corresponding to the machine, transverse, and through directions. Similarly, the refractometry gave refractive indices of both components of each laminate along all three axes. Results from the three techniques were compared and contrasted and the validity of the calculated internal reflectance spectra discussed. Practical methods to estimate the source and extent of errors in the latter technique from false radiation and contact problems were explored.     

The Theory of Multidimensional Persistence

Persistent homology captures the topology of a filtration—a one-parameter family of increasing spaces—in terms of a complete discrete invariant. This invariant is a multiset of intervals that denote the lifetimes of the topological entities within the filtration. In many applications of topology, we need to study a multifiltration: a family of spaces parameterized along multiple geometric dimensions. In this paper, we show that no similar complete discrete invariant exists for multidimensional persistence. Instead, we propose the rank invariant, a discrete invariant for the robust estimation of Betti numbers in a multifiltration, and prove its completeness in one dimension. The first author was partially supported by NSF under grant DMS-0354543. The second author was partially supported by DARPA under grant HR 0011-06-1-0038 and by ONR under grant N 00014-08-1-0908. Both authors were partially supported by DARPA under grant HR 0011-05-1-0007.     

Second-harmonic generation in vortex-induced waveguides

We study the second-harmonic generation and localization of light in a reconfigurable waveguide induced by an optical vortex soliton in a defocusing Kerr medium. We show that the vortex-induced waveguide greatly improves conversion efficiency from the fundamental to the second-harmonic field.