Stochastic transition states: reaction geometry amidst noise

Classical transition state theory (TST) is the cornerstone of reaction-rate theory. It postulates a partition of phase space into reactant and product regions, which are separated by a dividing surface that reactive trajectories must cross. In order not to overestimate the reaction rate, the dynamics must be free of recrossings of the dividing surface. This no-recrossing rule is difficult (and sometimes impossible) to enforce, however, when a chemical reaction takes place in a fluctuating environment such as a liquid. High-accuracy approximations to the rate are well known when the solvent forces are treated using stochastic representations, though again, exact no-recrossing surfaces have not been available. To generalize the exact limit of TST to reactive systems driven by noise, we introduce a time-dependent dividing surface that is stochastically moving in phase space, such that it is crossed once and only once by each transition path.     

Nanoparticle formation and ultrathin film electrodeposition of carbazole dendronized polynorbornenes prepared by ring-opening metathesis polymerization

We report on the synthesis, electropolymerization, and nanoparticle formation of a series of electroactive carbazole-terminated dendronized linear polynorbornenes prepared by living ring-opening metathesis polymerization (ROMP). The molecular weight (MW) of the dendronized polymers was controlled by varying the feed ratio between the dendronized monomer and first-generation Grubbs' catalyst. Ultrathin films were prepared by electrodeposition. The electrochemical behavior and viscoelastic properties of such films were found to be highly dependent on the dendron generation and linear polymer MW as studied by electrochemical quartz crystal microbalance (E-QCM). Moreover, nanoparticle formation and size/shape control were observed by tuning the surface wetting properties of the substrate during adsorption and by intramolecular cross-linking via chemical oxidation in solution.     

Temperature-dependent interfacial properties of hydrophobically end-modified poly(2-isopropyl-2-oxazoline)s assemblies at the air/water interface and on solid substrates

We describe herein the properties at the air/water (A/W) interface of hydrophobically end-modified (HM) poly(2-isopropyl-2-oxazoline)s (PiPrOx) bearing an n-octadecyl chain on both termini (telechelic HM-PiPrOx) or on one chain end (semitelechelic HM-PiPrOx) for different subphase temperatures and spreading solvents using the Langmuir film balance technique. The polymer interfacial properties revealed by the π–A isotherms depend markedly on the architecture and molecular weight of the polymer. On cold water subphases (14 °C), diffusion of PiPrOx chains onto water takes place for all polymers in the intermediate compressibility region (5 mN m⁻¹). At higher subphase temperatures (36 and 48 °C), the HM-PiPrOx film exhibited remarkable stability with time. Brewster angle microscopy (BAM) imaging of the A/W interface showed that the polymer assembly was not uniform and that large domains formed, either isolated grains or pearl necklaces, depending on the polymer structure, the concentration of the spreading solution and the subphase temperature. The Langmuir films were transferred onto hydrophilic substrates (silica) by the Langmuir–Blodgett (LB) technique and onto hydrophobic substrates (gold) by Langmuir–Schaefer (LS) film deposition, resulting in the formation of adsorbed particles ranging in size from 200 to 500 nm, depending on the polymer architecture and the substrate temperature. The particles presented “Janus”-like hydrophilic/hydrophobic characteristics.     

Enumerations of peaks and valleys on non-decreasing Dyck paths

A valley in a Dyck path is a local minimum, and a peak is a local maximum. A Dyck path is non-decreasing if the $y$-coordinates of the valleys of the path valley form anon-decreasing sequence. In this paper we provide some statistics about peaks and valleys in non-decreasing Dyck paths, such as their total number, the number of low and high valleys, low and high peaks, etc. Our methods include bijective proofs, recursive relations, and the symbolic method for generating functions.     

Design, synthesis, and photochemical behavior of poly(benzyl ester) dendrimers with azobenzene groups throughout their architecture

A new class of dendrons and dendrimers containing azobenzene units (bearing up to 29 azobenzene groups for four generations) were designed and synthesized with the convergent method, which uses azobenzene derivatives as monomers and benzyl ester groups as linkages leading to photoresponsive dendrons and dendrimers with azobenzene units throughout their architecture. Photochemical isomerization experiments revealed that all of the dendrons and dendrimers undergo trans-cis isomerization by irradiation and cis-trans isomerization by either irradiation or heating.     

Electropolymerization of layer‐by‐layer precursor polymer films

The layer‐by‐layer (LbL) self‐assembly has been used to fabricate polymer thin films on any solid substrates. The multilayer polymer thin films are constructed by alternating adsorption of anionic and cationic polymers. Polyelectrolyte multilayer ultrathin films containing anionic poly[2‐(thiophen‐3‐yl)ethyl methacrylate‐co‐methacrylic acid]; P(TEM‐co‐MA) and cationic poly[4‐(9H‐carbazol‐9‐yl)‐N‐butyl‐4‐vinyl pyridium bromide]; P4VPCBZ, were fabricated. The growth of multilayer ultrathin films was followed by UV–Vis absorption spectrophotometer and surface plasmon resonance spectroscopy (SPR). The deposition of P(TEM‐co‐MA)/P4VPCBZ as multilayer self‐assembled ultrathin films regularly grow which showed linear growth of absorbance and thickness with increasing the number of layer pair. Cross‐linking of the layers was verified by cyclic voltammetry (CV), UV–Vis spectrophotometry and electrochemical surface plasmon resonance (EC‐SPR) spectroscopy with good electro‐copolymerizability. This was verified by spectroelectrochemistry. The SPR angular‐reflectivity measurement resulted in shifts to a higher reflectivity according to the change in the dielectric constant of the electropolymerized film. Copyright © 2011 John Wiley & Sons, Ltd.     

Properties of single‐walled carbon nanotube‐based poly(phenylene vinylene) electroluminescent nanocomposites

Devices with varying concentrations of single‐walled carbon nanotubes (SWNTs) dispersed in three derivatives of poly(p‐phenylene vinylene) are prepared, and their electroluminescent properties evaluated. Increasing the concentration of SWNTs improves the electrical conductivity of the nanocomposites. However, an undesired increase in the electroluminescence (EL) turn‐on voltage is observed for the hybrids, possibly due to photoluminescence quenching of excitons by the SWNTs. At relatively low concentrations of SWNTs, there is an increase in the EL lifetime; in contrast, at relatively high concentrations of SWNTs, due to photoluminescence quenching by the nanotubes, significant reduction in brightness and faster degradation of the EL performance of the devices is observed. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Facile approach to graphene oxide and poly(N-vinylcarbazole) electro-patterned films

A facile approach of making scalable nanocomposite and electro-patterned films using graphene oxide (GO) and poly(N-vinylcarbazole) (PVK) is reported. The method involves the layering of polystyrene colloidal templates, electrodeposition of the composite film on template array, and finally removal of the sacrificial templates to reveal the patterned GO-PVK arrays.     

QCM sensing of a chemical nerve agent analog via electropolymerized molecularly imprinted polythiophene films

The highly selective and sensitive detection of a chemical nerve agent analog pinacolyl methylphosphonate (PMP) was demonstrated using an electrochemically molecularly imprinted polymer (MIP) polythiophene film onto a quartz crystal microbalance (QCM) transducer surface. The fabrication and optimization of the sensor film was monitored by in situ electrochemistry‐QCM (EC‐QCM) measurements, which determined the change in mass and simultaneous change in redox properties of the polymer film. The film deposition, template loading, and template removal were evidenced by a combination of surface characterization techniques such as the attenuated total reflection infrared spectroscopy and high‐resolution X‐ray photoelectron spectroscopy. The fabricated MIP film demonstrated a limit of detection and a limit of quantification of ～60 and ～197 μM, respectively. The linear sensing range is between 125 and 250 μM concentration of PMP. Finally, theoretical modeling (AM1 semiempirical quantum calculations) studies revealed that a stable prepolymerization complex is formed in solution with the existence of H‐bonding interactions using the 2:1 monomer‐to‐template ratio. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012