A hybrid finite-element–volume-of-fluid method for simulating free surface flows and interfaces

A numerical technique is developed for the simulation of free surface flows and interfaces. This technique combines the strength on the finite element method (FEM) in calculating the field variables for a deforming boundary and the versatility of the volume-of-fluid (VOF) technique in advection of the fluid interfaces. The advantage of the VOF technique is that it allows the simulation of interfaces with large deformations, including surface merging and breaking. However, its disadantage is that is solving the flow equations, it cannot resolve interfaces smaller than the cell size, since information on the subgrid scale is lost. Therefore the accuracy of the interface reconstruction and the treatment of the boundary conditions (i.e. viscous stresses and surface tension forces) become grid-size-dependent. On the other hand, the FEM with deforming interface mesh allows accurate implementation of the boundary conditions, but it cannot handle large surface deformations occurring in breaking and merging of liquid regions. Combining the two methods into a hybrid FEM-VOF method eliminates the major shortcomings of both. The outcome is a technique which can handle large surface deformations with accurate treatment of the boundary conditions. For illustration, two computational examples are presented, namely the instability and break-up of a capillary jet and the coalescence collision of two liquid drops.     

Literal‐paraconsistent and literal‐paracomplete matrices

We introduce a family of matrices that define logics in which paraconsistency and/or paracompleteness occurs only at the level of literals, that is, formulas that are propositional letters or their iterated negations. We give a sound and complete axiomatization for the logic defined by the class of all these matrices, we give conditions for the maximality of these logics and we study in detail several relevant examples. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis and comparative solution properties of single‐, twin‐, and triple‐tailed associating ionic polymers based on diallylammonium salts

The cycloterpolymerizations of single‐, twin‐, and triple‐tailed hydrophobes with hydrophilic monomer N,N‐diallyl‐N‐carboethoxymethylammonium chloride and sulfur dioxide afforded a series of cationic polyelectrolytes (CPEs) in excellent yields. These CPEs, upon the acidic hydrolysis of the pendent ester groups, gave the corresponding pH‐responsive cationic acid salts, which, upon a treatment with sodium hydroxide, were converted to polybetaines (PBs), anionic polyelectrolytes (APEs), and PB/APE polymers containing various proportions of zwitterionic (PB) and anionic fractions (APE) in the polymer chain. At a shear rate of 0.36 s⁻¹ at 30 °C, salt‐free water solutions of the CPEs (2 g/dL) containing 8, 4, and 2.67 mol % of the single‐, twin‐, and triple‐tailed hydrophobes (all having 8 mol % octyloxy tails) had apparent viscosity values of 70, 2800, and 396,000 cps, respectively. The PB/APE polymer with a ratio of 33:67 for the zwitterionic and anionic fractions in the polymer chain gave the highest viscosity value. The superior viscosity behavior of the polymers containing the triple‐tailed hydrophobe was attributed to the blocky nature of the comonomer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5480–5494, 2006     

The phase diagram of a single polymer chain: New insights from a new simulation method

We present simulation results for the phase behavior of a single chain for a flexible lattice polymer model using the Wang-Landau sampling idea. Applying this new algorithm to the problem of the homopolymer collapse allows us to investigate not only the high temperature coil–globule transition but also an ensuing crystallization at lower temperature. Performing a finite size scaling analysis on the two transitions, we show that they coincide for our model in the thermodynamic limit corresponding to a direct collapse of the random coil into the crystal without intermediate coil–globule transition. As a consequence, also the many chain phase diagram of this model can be predicted to consist only of gas and crystal phase in the limit of infinite chain length. This behavior is in agreement with findings on the phase behavior of hard-sphere systems with a relatively short-ranged attractive square well. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2542–2555, 2006     

Nitroxide‐mediated radical polymerization of 2‐(dimethylamino)ethyl acrylate and its sequential block copolymerization with styrene and N‐butyl acrylate

Nitroxide‐mediated radical polymerization (NMRP) of 2‐(dimethylamino)ethyl acrylate (DMAEA) was carried out at 100–120 °C, initiated by MONAMS, an alkoxyamine based on N‐tert‐butyl‐N‐(1‐diethyl phosphono‐2,2‐dimethylpropyl)nitroxide, SG1. Controlled polymerization can be achieved by the addition of free SG1 (the initial molar ratio of SG1 to MONAMS ranged from 0.06 to 0.12), giving a linear first‐order kinetic plot up to 55–70% conversion depending on the reaction conditions. The molecular weights show a near linear increase with conversion; however, they deviate to some extent with theoretical values. SG1‐mediated polymerization of DMAEA at 112 °C is also controlled in organic solvents (N,N‐dimethylformide, anisole, xylene). Polymerization rate increases with increasing solvent polarity. Chain transfer to polymer produces ～1 mol % branches in bulk and 1.2–1.9 mol % in organic solvents, typical of those for acrylates. From poly(styrene) (pS) and poly(n‐butyl acrylate) (pBA) macroinitiators, amphiphilic di‐ and triblock copolymers p(S‐b‐DMAEA), p(DMAEA‐b‐S‐b‐DMAEA), p(BA‐b‐DMAEA), and p(DMAEA‐b‐BA‐b‐DMAEA) were synthesized via NMRP at 110 °C. Polymers were characterized by GPC, NMR, surface tension measurements, and DSC. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 414–426, 2006     

Synthesis and characterization of multiblock copolymers composed of poly(5‐methyl‐5‐benzyloxycarbonyl‐1,3‐dioxan‐2‐one) outer blocks and poly(L‐lactide) inner blocks

Ethylene glycol (EG) initiated, hydroxyl‐telechelic poly(L ‐lactide) (PLLA) was employed as a macroinitiator in the presence of a stannous octoate catalyst in the ring‐opening polymerization of 5‐methyl‐5‐benzyloxycarbonyl‐1,3‐dioxan‐2‐one (MBC) with the goal of creating A–B–A‐type block copolymers having polycarbonate outer blocks and a polyester center block. Because of transesterification reactions involving the PLLA block, multiblock copolymers of the A–(B–A)_n–B–A type were actually obtained, where A is poly(5‐methyl‐5‐benzyloxycarbonyl‐1,3‐dioxan‐2‐one), B is PLLA, and n is greater than 0. ¹H and ¹³C NMR spectroscopy of the product copolymers yielded evidence of the multiblock structure and provided the lactide sequence length. For a PLLA macroinitiator with a number‐average molecular weight of 2500 g/mol, the product block copolymer had an n value of 0.8 and an average lactide sequence length (consecutive C₆H₈O₄ units uninterrupted by either an EG or MBC unit) of 6.1. For a PLLA macroinitiator with a number‐average molecular weight of 14,400 g/mol, n was 18, and the average lactide sequence length was 5.0. Additional evidence of the block copolymer architecture was revealed through the retention of PLLA crystallinity as measured by differential scanning calorimetry and wide‐angle X‐ray diffraction. Multiblock copolymers with PLLA crystallinity could be achieved only with isolated PLLA macroinitiators; sequential addition of MBC to high‐conversion L ‐lactide polymerizations resulted in excessive randomization, presumably because of residual L ‐lactide monomer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6817–6835, 2006     

Synthesis of poly(vinyl chloride)‐b‐poly(n‐butyl acrylate)‐b‐poly(vinyl chloride) by the competitive single‐electron‐transfer/degenerative‐chain‐transfer‐mediated living radical polymerization in water

The synthesis of a block copolymer poly(vinyl chloride)‐b‐poly(n‐butyl acrylate)‐b‐poly(vinyl chloride) is reported. This new material was synthesized by single‐electron‐transfer/degenerative‐chain‐transfer‐mediated living radical polymerization (SET‐DTLRP) in two steps. First, a bifunctional macroinitiator of α,ω‐di(iodo)poly (butyl acrylate) [α,ω‐di(iodo)PBA] was synthesized by SET‐DTLRP in water at 25 °C. The macroinitiator was further reinitiated by SET‐DTLRP, leading to the formation of the desired product. This ABA block copolymer was synthesized with high initiator efficiency. The kinetics of the copolymerization reaction was studied for two PBA macroinitiators with number–average molecular weight of 10 k and 20 k. The relationship between the conversion and the number–average molecular weight was found to be linear. The dynamic mechanical thermal analysis suggests just one phase, indicating that copolymer behaves as a single material with no phase separation. This methodology provides the access to several block copolymers and other complex architectures that result from combinations of thermoplastics (PVC) and elastomers (PBA). From industrial standpoint, this process is attractive, because of easy experimental setup and the environmental friendly reaction medium. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3001–3008, 2006     

Single electron transfer–degenerative chain transfer living radical polymerization of N‐butyl acrylate catalyzed by Na2S2O4 in water media

Living radical polymerization of n‐butyl acrylate was achieved by single electron transfer/degenerative‐chain transfer mediated living radical polymerization in water catalyzed by sodium dithionate. The plots of number–average molecular weight versus conversion and ln[M]₀/[M] versus time are linear, indicating a controlled polymerization. This methodology leads to the preparation of α,ω‐di(iodo) poly (butyl acrylate) (α,ω‐di(iodo)PBA) macroinitiators. The influence of polymerization degree ([monomer]/[initiator]), amount of catalyst, concentration of suspending agents and temperature were studied. The molecular weight distributions were determined using a combination of three detectors (TriSEC): right‐angle light scattering (RALLS), a differential viscometer (DV), and refractive index (RI). The methodology studied in this work represents a possible route to prepare well‐tailored macromolecules made of butyl acrylate in an environmental friendly reaction medium. Moreover, such materials can be subsequently functionalized leading to the formation of different block copolymers of composition ABA. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2809–2825, 2006     

Gold ultra-microelectrode arrays: application to the steady-state voltammetry of hydroxide ion in aqueous solution.

Gold ultra-microelectrode arrays are used to explore the electrochemical oxidation of hydroxide ions and are shown to be analytical useful. Two types of ultra-microelectrode arrays are used; the first consist of 256 individual electrodes of 5 microm in radius, 170 of which are electrochemically active in a cubic arrangement which are separated from their nearest neighbour by a distance of 100 microm. The second array compromises 2597 electrodes of 2.5 microm in radius and of which 1550 of which are electrochemically active in a hexagonal arrangement separated by the nearest neighbour by 55 microm. Well defined voltammetric waves are found with peak currents proportional to the concentration of hydroxide ions in the range 50 microM to 1 mM. Detection limits of 20 microM using the 170 ultra-microelectrode and 10 microM with the 1550 ultra-microelectrode array are shown to be possible but with a higher sensitivity of 4 mA M(-1) observed using the 1550 ultra-microelectrode array compared to 1.2 mA M(-1) with the 170 ultra-microelectrode array.     

Phase equilibria in the Tl-TlBr-S system

The polythermal sections TlBr-Tl₂S, TlBr-Tl₄S₃, TlBr-TlS, and Tl₆SBr₄-Tl; the isothermal section at 300 K of the phase diagram; and the projection of the liquidus surface of the Tl-S-Br system have been investigated in the composition region Tl-TlBr-S by DTA, X-ray powder diffraction analysis, and microhardness measurements. The primary crystallization regions, including that of the only ternary compound (Tl₆SBr₄), have been determined, and the types and coordinates of the invariant and univariant equilibria in the phase diagram are determined.