Kinetic Modeling of the Suspension Copolymerization of Styrene/Divinylbenzene with Gel Formation

Summary : Experimental and theoretical studies concerning the suspension copolymerization of styrene with divinylbenzene are reported. Experiments were carried out in a batch stirred reactor, at 1.2 dm³ scale, and extended beyond gelation in order to synthesize insoluble material. Looking for real time information concerning the building process of such materials, these polymerizations were In-line monitored using a FTIR-ATR immersion probe. Polymer samples collected before and after gelation were Off-line characterized using a SEC/RI/MALLS system allowing the measurement of monomer conversion, average molecular weights, MWD and also the z-average radius of gyration. The weight fraction of insoluble material (gel) was measured for samples with different reaction times. The experimental program has included the study of the influence of key polymerization parameters on the dynamics of gelation and some properties of the resulting networks, namely the initial mole fraction of crosslinker and the initial proportions between monomers and inert diluent. Variable n-heptane/toluene mixtures were used within this purpose. These experimental observations were complemented with theoretical studies using a general kinetic approach allowing the prediction of MWD and z-average radius of gyration before and also after gelation. Comparison of the experimental measurements with these predictions is being exploited to develop modeling tools useful for the design of operating conditions allowing the improvement of the performance of the final products.     

On Complex-valued 2D Eikonals. Part Four: Continuation Past a Caustic

Theories of monochromatic high-frequency electromagnetic fields have been designed by Felsen, Kravtsov, Ludwig and others with a view to portraying features that are ignored by geometrical optics. These theories have recourse to eikonals that encode information on both phase and amplitude — in other words, are complex-valued. The following mathematical principle is ultimately behind the scenes: any geometric optical eikonal, which conventional rays engender in some light region, can be consistently continued in the shadow region beyond the relevant caustic, provided an alternative eikonal, endowed with a non-zero imaginary part, comes on stage. In the present paper we explore such a principle in dimension 2. We investigate a partial differential system that governs the real and the imaginary parts of complex-valued two-dimensional eikonals, and an initial value problem germane to it. In physical terms, the problem in hand amounts to detecting waves that rise beside, but on the dark side of, a given caustic. In mathematical terms, such a problem shows two main peculiarities: on the one hand, degeneracy near the initial curve; on the other hand, ill-posedness in the sense of Hadamard.We benefit from using a number of technical devices: hodograph transforms, artificial viscosity, and a suitable discretization. Approximate differentiation and a parody of the quasi-reversibility method are also involved.We offer an algorithm that restrains instability and produces effective approximate solutions.     

Electrochemical investigation of melittin reconstituted into a mercury-supported lipid bilayer

The channel-forming peptide melittin was incorporated into a biomimetic membrane consisting of a mercury electrode coated with a thiolipid monolayer, with a lipid monolayer self-assembled on top of it. The thiolipid consisted of a hydrophilic tetraethyleneoxy chain terminated at one end with a disulfide group, for anchoring to the mercury surface, and covalently linked at the other end to two diphytanyl chains, which formed a lipid bilayer with the overhanging lipid monolayer. The conductance of the lipid bilayer in contact with aqueous 0.1 M KCl was measured by electrochemical impedance spectroscopy over a frequency range from 1 x 10(-2) to 1 x 10(5) Hz and a potential range of 0.7 V for different compositions of the outer lipid monolayer. The conductance increases abruptly above the background level at sufficiently negative applied potentials, attaining a maximum value that increases with the composition of the outer monolayer in the order PC/chol (60:40) < PC < PC/SM/chol (59:15:26) < PS, with PC = phosphatidylcholine, chol = cholesterol, SM = sphingomyelin, and PS = phosphatidylserine. The higher the maximum conductance, the less negative the applied potential at which it is attained. This behavior is also discussed using a model of the electrified interphase.     

An open design microfabricated nib-like nanoelectrospray emitter tip on a conducting silicon substrate for the application of the ionization voltage

This paper describes a novel emitter tip having the shape of a nib and based on an open structure for nano-electrospray ionization mass spectrometry (nanoESI-MS). The nib structure is fabricated with standard lithography techniques using SU-8, an epoxy-based negative photoresist. The tip is comprised of a reservoir, a capillary slot and a point-like feature, and is fabricated on a silicon wafer. We present here a novel scheme for interfacing such nib tips to MS by applying the ionization voltage directly onto the semi-conductor support. The silicon support is in direct contact with the liquid to be analyzed at the reservoir and microchannel level, thus allowing easy use in ESI-MS. This scheme is especially advantageous for automated analysis as the manual step of positioning a metallic wire into the reservoir is avoided. In addition, the analysis performance was enhanced compared with the former scheme, as demonstrated by the tests of standard peptides (gramicidin S, Glu-fibrinopeptide B). The limit of detection was determined to be lower than 10(-2) microM. Due to their enhanced performance, these microfabricated sources might be of great interest for analysis requiring very high sensitivity, such as proteomics analysis using nanoESI-MS.     

Enantiospecific approach toward pentalenolactone

[reaction: see text] The enantiospecific assembly of the pentalenolactones' carbon skeleton was achieved in 17 steps and 16% overall yield from methyl alpha-D-glucopyranoside. The synthetic strategy relies on two highly efficient key steps: an exo-diastereoselective Diels-Alder reaction and a nonsymmetric ozonolysis.     

Highly diastereoselective Diels-Alder reaction using a chiral auxiliary derived from levoglucosenone

[reaction: see text] A new chiral auxiliary derived from levoglucosenone is reported. The compound is obtained by a cycloaddition reaction with 9-methoxy methylanthracene followed by a diastereoselective reduction of the C-2 keto function. The auxiliary has been used as a chiral template in an asymmetric Diels-Alder reaction of the corresponding acrylic ester derivative with cyclopentadiene. The results showed excellent diastereomeric excess even at room temperature when the reaction was promoted by Et(2)AlCl as the Lewis acid.     

Stationary isothermic surfaces and some characterizations of the hyperplane in the N-dimensional Euclidean space

We consider the entire graph S of a continuous real function over RN−1 with N?3. Let Ω be a domain in RN with S as a boundary. Consider in Ω the heat flow with initial temperature 0 and boundary temperature 1. The problem we consider is to characterize S in such a way that there exists a stationary isothermic surface in Ω. We show that S must be a hyperplane under some general conditions on S. This is related to Liouville or Bernstein-type theorems for some elliptic Monge-Ampère-type equation.     

Prediction and Experimental Characterization of the Molecular Architecture of FRP and ATRP Synthesized Polyacrylate Networks

Summary: This work reports experimental and modeling studies concerning the conventional (FRP) and atom transfer radical polymerization (ATRP) of acrylate/diacrylate monomers. In the framework of a recently developed general approach, kinetic models including crosslinking reactions and branching by chain transfer to polymer are discussed for FRP and ATRP polymerization systems. Besides molecular weight distribution (MWD), fairly good predictions of the z-average radius of gyration could be obtained for these non-linear polymers. A set of experiments was performed at 1 L scale in a batch reactor using n-butyl acrylate (BA) or methyl acrylate (MA) as monovinyl monomers and 1,6-Hexanediol diacrylate (HDDA) or bisphenol A ethoxylate diacrylate (BEDA) as crosslinkers. In FRP experiments, AIBN was used as initiator and ATRP polymerizations were initiated by ethyl 2-bromopropionate (EBrP) and mediated by CuBr using PMDETA (N,N,N′,N″,N″-pentamethyldiethylenetriamine) as ligant. Polymerizations were carried out in solution at 60 °C with different dilutions using toluene and DMF as solvents. Products formed at different polymerization times were analyzed by SEC/RI/MALLS yielding average MW, MWD, z-average radius of gyration and monomer conversion. Important differences in the molecular architecture of the synthesized FRP and ATRP highly branched polyacrylates have been identified. Comparisons of experimental results with predictions have put into evidence the important effect of intramolecular cyclizations at all dilutions, even with ATRP polymerizations.     

Translation planes admitting many homologies

The translation planes with spreads inPG(3,2 ^r ) that admit >2 ^r +1 axes (coaxes) of homologies of orderu1 are classified.Partially supported by FONDECYT Project No. 890-1061