Rethinking the application of the first nucleation theorem to particle formation

The critical cluster is the threshold size above which a cluster will be more likely to grow than to evaporate. In field and laboratory measurements of new particle formation, the number of molecules of a given species in the critical cluster is commonly taken to be the slope of the log-log plot of the formation rate versus the concentration of the species. This analysis is based on an approximate form of the first nucleation theorem, which is derived with the assumption that there are no minima in the free energy surface prior to the maximum at the critical size. However, many atmospherically relevant systems are likely to exhibit such minima, for example, ions surrounded by condensable vapour molecules or certain combinations of acids and bases. We have solved numerically the birth-death equations for both an electrically neutral one-component model system with a local minimum at pre-critical sizes and an ion-induced case. For the ion-induced case, it is verified that the log-log slope of the nucleation rate versus particle concentration plot gives accurately the difference between the cluster sizes at the free energy maximum and minimum, as is expected from the classical form of the ion-induced nucleation rate. However, the results show that applying the nucleation theorem to neutral systems with stable pre-nucleation clusters may lead to erroneous interpretations about the nature of the critical cluster.     

Minimal Surfaces in the Round Three-Sphere by Doubling the Equatorial Two-Sphere,II

In a previous paper, new closed embedded smooth minimal surfaces in the round three-sphere were constructed, each resembling two parallel copies of the equatorial two-sphere joined by small catenoidal bridges, with the catenoidal bridges concentrating along two parallel circles, or the equatorial circle and the poles. In this sequel, we generalize those constructions so that the catenoidal bridges can concentrate along an arbitrary number of parallel circles, with the further option to include bridges at the poles. The current constructions follow the linearized doubling (LD) methodology developed in the previous paper. The LD solutions constructed here can be modified readily for use to doubling constructions of rotationally symmetric minimal surfaces with asymmetric sides [15]. In particular, they allow us to develop doubling constructions for the catenoid in Euclidean three-space, the critical catenoid in the unit ball, and the spherical shrinker of the mean curvature flow. Unlike in the previous paper, our constructions here allow for sequences of minimal surfaces where the catenoidal bridges tend to be “densely distributed,” that is, they do not miss any open set of in the limit. This in particular leads to interesting observations that seem to suggest that it may be impossible to construct embedded minimal surfaces with isolated singularities by concentrating infinitely many catenoidal necks at a point. © 2019 Wiley Periodicals, Inc.     

An experimental and theoretical analysis of molecular separations by diffusion through ultrathin nanoporous membranes

Diffusion based separations are essential for laboratory and clinical dialysis processes. New molecularly thin nanoporous membranes may improve the rate and quality of separations achievable by these processes. In this work we have performed protein and small molecule separations with 15 nm thick porous nanocrystalline silicon (pnc-Si) membranes and compared the results to 1- and 3- dimensional models of diffusion through ultrathin membranes. The models predict the amount of resistance contributed by the membrane by using pore characteristics obtained by direct inspection of pnc-Si membranes in transmission electron micrographs. The theoretical results indicate that molecularly thin membranes are expected to enable higher resolution separations at times before equilibrium compared to thicker membranes with the same pore diameters and porosities. We also explored the impact of experimental parameters such as porosity, pore distribution, diffusion time, and chamber size on the sieving characteristics. Experimental results are found to be in good agreement with the theory, and ultrathin membranes are shown to impart little overall resistance to the diffusion of molecules smaller than the physical pore size cutoff. The largest molecules tested experience more hindrance than expected from simulations indicating that factors not incorporated in the models, such as molecule shape, electrostatic repulsion, and adsorption to pore walls, are likely important.     

Synthesis and characterization of multiblock copolymers based on hydrophilic disulfonated poly(arylene ether sulfone) and hydrophobic partially fluorinated poly(arylene ether ketone) for fuel cell applications

Sulfonated fluorinated multiblock copolymers based on high performance polymers were synthesized and evaluated for use as proton exchange membranes (PEMs). The multiblock copolymers consist of fully disulfonated poly(arylene ether sulfone) and partially fluorinated poly(arylene ether ketone) as hydrophilic and hydrophobic segments, respectively. Synthesis of the multiblock copolymers was achieved by a condensation coupling reaction between controlled molecular weight hydrophilic and hydrophobic oligomers. The coupling reaction could be conducted at relatively low temperatures (e.g., 105 °C) by utilizing highly reactive hexafluorobenzene (HFB) as a linkage group. The low coupling reaction temperature could prevent a possible trans‐etherification, which can randomize the hydrophilic‐hydrophobic sequences. Tough ductile membranes were prepared by solution casting and their membrane properties were evaluated. With similar ion exchange capacities (IECs), proton conductivity and water uptake were strongly influenced by the hydrophilic and hydrophobic block sequence lengths. Conductivity and water uptake increased with increasing block length by developing nanophase separated morphologies. Atomic force microscopy (AFM) and transmission electron microscopy (TEM) experiments revealed that the connectivity of the hydrophilic segments was enhanced by increasing the block length. The systematic synthesis and characterization of the copolymers are reported. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 214–222, 2010     

Water purification by membranes: The role of polymer science

Two of the greatest challenges facing the 21st century involve providing sustainable supplies of clean water and energy, two highly interrelated resources, at affordable costs. Membrane technology is expected to continue to dominate the water purification technologies owing to its energy efficiency. However, there is a need for improved membranes that have higher flux, are more selective, are less prone to various types of fouling, and are more resistant to the chemical environment, especially chlorine, of these processes. This article summarizes the nature of the global water problem and reviews the state of the art of membrane technology. Existing deficiencies of current membranes and the opportunities to resolve them with innovative polymer chemistry and physics are identified. Extensive background is provided to help the reader understand the fundamental issues involved. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Influence of filter ventilation on the chemical composition of cigarette mainstream smoke

Total yields of cigarette smoke constituents are greatly influenced by smoking behaviour, the tobacco blend as well as a variety of cigarette design parameters. Thereby, filter ventilation, i.e. diluting the smoke by providing a zone of microscopic holes around the circumference of the filter is one method to reduce the yield of ‘tar’ and other smoke compounds. However, little is known how these design variations influence the combustion conditions, and therefore, the overall chemical pattern of the smoke. In this paper single photon ionization-time-of-flight mass spectrometry (SPI-TOFMS) is used to characterize and compare cigarettes on a puff-by-puff basis, which differ only in filter ventilation magnitude. The research cigarettes investigated were made from Virginia tobacco and featured filter ventilations of 0% (no ventilation), 35%, and 70%. The cigarettes were smoked under two different puffing regimes, one using the puffing parameters of the conventional International Organization for Standardization (ISO) smoking regime and a more intense smoking condition. Results show that every variation entails a change of the chemical pattern, whereby, in general, cigarettes with 0% filter ventilation as well as the intense smoking regime lead to a more complete combustion compared to the ISO smoking conditions and the high ventilated cigarettes. Changes in the overall patterns can also be observed during the smoking for individual puffs. Some substances dominate the first puff, some species are more pronounced in the middle puffs, whereas others are preferably formed in the last puffs. This demonstrates the high complexity of the occurring processes. Results might help to understand the formation and decomposition reactions taking place when a cigarette is smoked and offer scope for targeted reduction strategies for specific toxicants or groups of toxicants in the smoke.     

Convergent synthesis of geometrically disassembling dendrimers using Cu(I)-catalyzed C-O bond formation

The convergent synthesis of geometrically degradable dendrimers based on the 2,4-bis(hydroxymethyl)phenol subunit is presented. The key step of the synthetic scheme involves the CuI/3,4,7,8-tetramethyl-1,10-phenanthroline-catalyzed coupling of aryl iodides and alcohols. The synthesis and disassembly of these compounds is discussed.     

Polymerisation of liquid crystalline phases in binary surfactant/water systems

The self-assembly behaviour of the polymerisable surfactant -undecenyltrimethylammonium bromide (-UTAB) both before and after polymerisation has been investigated. In addition polymerisation of the liquid crystalline phases formed by this surfactant in aqueous solution has been studied. Introduction of the carbon-carbon double bond at the end of the hydrocarbon chain increases the rigidity of the paraffinic chains such that the Krafft curve is shifted to higher temperatures compared with that of dodecyltrimethylammonium bromide, a nonpolymerisable analogue. Both the polymerised and non-polymerised forms have been observed to have the same phase progression, with the polymer being more soluble in water such that the liquid crystalline phases formed at high surfactant concentration are accessible at room temperature. Polymerisation of the liquid crystalline phases of -UTAB indicate that polymerisation proceeds to approximately 40% (in comparison) with 80% in a non-aggregated form) and that the original monomeric matrix is undisturbed upon partial polymerisation.     

Stereocontrolled synthesis and alkylation of cyclic beta-amino esters: asymmetric synthesis of a (-)-sparteine surrogate

A convenient method for the stereoselective synthesis of cyclic beta-amino esters from an iodo alphabeta-unsaturated ester and alpha-methylbenzylamine is described. Subsequent enolate generation and alkylation proceeds with complete stereocontrol, with the two stereogenic centres working together. In this way, a functionalised piperidine suitable for alkaloid natural product synthesis was prepared. The usefulness of the methodology is exemplified with the concise synthesis of a (-)-sparteine surrogate.