Tame combing and almost convexity conditions

We give the first examples of groups which admit a tame combing with linear radial tameness function with respect to any choice of finite presentation, but which are not minimally almost convex on a standard generating set. Namely, we explicitly construct such combings for Thompson??s group F and the Baumslag?CSolitar groups BS(1, p) with p ??? 3. In order to make this construction for Thompson??s group F, we significantly expand the understanding of the Cayley complex of this group with respect to the standard finite presentation. In particular we describe a quasigeodesic set of normal forms and combinatorially classify the arrangements of 2-cells adjacent to edges that do not lie on normal form paths.     

Letters to the Editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to the editor-in-chieX Chandler Davis.     

Deformation of polybutene-1 spherulites

The deformation of fresh and aged polybutene-1 spherulitic samples has been investigated by microscopic observation, interferometry, studying macroscopic and spherulitic birefringence changes, and study of light-scattering patterns. The spherulite deformation is not affine, the microscopic deformation ratio being less than the macroscopic deformation ratio of the sample and greater in the equatorial regions of the spherulite than in the polar regions. The deviation from affine deformation is less for fresh spherulites than for the aged, where void formation occurs in the equatorial part of the spherulite. This gives rise to large scattering by this part of the spherulite and to form birefringence. The spherulite birefringence and its change with elongation is dependent upon the degree of aging of the sample. The spherulite birefringence is more negative for the aged sample. In the polar regions of the spherulite, this negative birefringence decreases and turns positive at higher elongations, characteristic of a reorientation of the crystals with their optic axes turning from being perpendicular to parallel to the spherulite radius. The spherulite birefringence in the equatorial direction becomes somewhat more negative on stretching a fresh sample but less negative on stretching an aged one. Spherulite distortion and orientation changes are apparent from the light-scattering patterns of films possessing small spherulites. The changes in V_v and H_v scattering patterns upon stretch are different for the fresh and aged samples. The V_v patterns of the fresh samples decrease in intensity with time after stretching a fresh sample with the H_v patterns do not.     

Steady shear rate rheology of suspensions, as described by the giant floc model

The break-down of a particle network by shear is described as the development of shear planes: a region able to withstand low shear stresses may break down under a larger stress; thus with increasing shear stress and shear rate, the mutual distance (A) between successive shear planes decreases until, at very high shear rates, A approaches the particle diameter. The shear planes are idealised as flat planes. Energy dissipation during shear is predominantly due to the energy dissipated through the movement of the particles; the energy dissipation due to breakage and renewed formation of bonds between particles is relatively small. A consideration of the energy dissipated during the encounters of particles during shear, including that dissipated by entrained particles, then leads to a relation between this energy dissipation and the average fraction L, over which a moving particle entrains a neighbour. L includes the effect of parts of the network which are rotating under the influence of the shear. In the limit of large shear rates, L is found to depend only to a small extent on whether the suspension is coagulated or not.     

The Electroviscous Behavior of Aqueous Dispersions of Amorphous Silica (Ludox)

The electroviscous effects in very dilute aqueous dispersions of amorphous silica (Ludox) were investigated at various levels of salt, pH, and volume fraction (<0.01) of solids. Viscosities were much higher than predicted from existing theories, which is ascribed to the formation of a thick, gel-like surface layer on the particle. The volume of a particle adjusts itself almost reversibly to the salt and pH levels of the liquid and can grow up to four times the dry volume. This explains the apparent discrepancy between published dry and wet particle sizes and also the reported anomalously large number of bound water layers around a particle. The existence of a gel layer leads to an abnormally large amount of surface conductance; this may explain the anomalities found in electrophoresis. The validity of the model is also supported by published results of the amount of nonbulk water as found with NMR. Copyright 2001 Academic Press.     

Preparative and 1H NMR Investigation on Regioselective Silylation of Starch Dissolved in Dimethyl Sulfoxide

Reaction of starch 1 dissolved in dimethyl sulfoxide (DMSO) with bulky thexyldimethylchlorosilane (TDSCl) in the presence of pyridine leads to regioselectively functionalized silyl ethers with a degree of substitution (DS) up to 1.8. The control of the DS_Si, of the regioselectivity, and of the reaction pathway is described in detail. The reaction proceeds homogeneously up to DS_Si of 0.6. With ongoing silylation the polymers form a separate phase incorporating the silylating agent to form TDS‐starches with DS_Si values higher than 1.0. After peracetylation of the silyl starches, the substitution pattern has been characterized not only in the anhydroglucose repeating units (AGU) but also in the non‐reducing terminal end groups (TEG) by means of two‐dimensional ¹H NMR techniques. Up to DS_Si 1.0, a very high regioselective functionalization of the primary 6‐OH groups in the AGU as well as in the TEG is detectable. With increasing silylation (DS_Si > 1.0), the subsequent silylation takes place at the 2‐OH groups of the AGU and at the 3‐OH groups of the TEG. These results are compared with our own investigations on the silylation of starch in the reaction system N‐methylpyrrolidone (NMP)/ammonia and on the silylation of cellulose in N,N‐dimethylacetamide (DMA)/LiCl/pyridine solution.     

Disappearing Polymorphs in Metal–Organic Framework Chemistry: Unexpected Stabilization of a Layered Polymorph over an Interpenetrated Three-Dimensional Structure in Mercury Imidazolate

The “disappearing polymorph” phenomenon is well established in organic solids, and has had a profound effect in pharmaceutical materials science. The first example of this effect in metal-containing systems in general, and in coordination-network solids in particular, is here reported. Specifically, attempts to mechanochemically synthesize a known interpenetrated diamondoid (dia) mercury(II) imidazolate metal–organic framework (MOF) yielded a novel, more stable polymorph based on square-grid (sql) layers. Simultaneously, the dia-form was found to be highly elusive, observed only as a short-lived intermediate in monitoring solvent-free synthesis and not at all from solution. The destabilization of a dense dia-framework relative to a lower dimensionality one is in contrast to the behavior of other imidazolate MOFs, with periodic density functional theory (DFT) calculations showing that it arises from weak interactions, including structure-stabilizing agostic C−H⋅⋅⋅Hg contacts. While providing a new link between MOFs and crystal engineering of organic solids, these findings highlight a possible role for agostic interactions in directing topology and stability of MOF polymorphs.     

Synthese von [(η-C5H5)2Ti(Cl)(CCSiMe3)]Ni(CO) und dessen Reaktionsverhalten gegenüber Phosphiten: die Festkörperstruktur von (CO)2Ni[P(OC6H4CH3-2)3]2

Treatment of [Ti](Cl)(CCSiMe₃) (1) {[Ti]=(η⁵-C₅H₅)₂Ti} with Ni(CO)₄ (2) in a 1:1 molar ratio produces the heterobimetallic early-late transition metal complex {[Ti](Cl)(CCSiMe₃)}Ni(CO) (3), which features a low-valent Ni(CO) entity stabilized by a datively bonded Cl and a η²-coordinated Me₃SiCC ligand. As side-products [Ti]Cl₂ (8) and {[Ti](CCSiMe₃)₂}Ni(CO) (5) are formed. The latter complex can also be synthesized by the reaction of [Ti](CCSiMe₃)₂ (4) with equimolar amounts of 2. If 3 is reacted with stoichiometric amounts of P(OR)₃ (6a, R=C₆H₅; 6b, R=C₆H₄CH₃-2; 6c, R=C₆H₄^tBu-2) the bis(alkynyl) titanocene 4, (CO)₂Ni[P(OR)₃]₂ (7a, R=C₆H₅; 7b, R=C₆H₄CH₃-2; 7c, R=C₆H₄^tBu-2), complex 8, {[Ti](μ,η¹:η²-CCSiMe₃)}₂ (9) along with Me₃SiCCCCSiMe₃ (10) is produced. A possible mechanism for the formation of these species is presented. The solid-state structure of 7b is reported. Complex 7b crystallizes in the tetragonalic space group P-42₁c with the following parameters: a=14.852(2), b=14.852(2), c=19.410(4) Å, V=4281.5(12) ų, Z=4 and ρ=1.271 g cm⁻³. Mononuclear 7b features a Ni(0) centre in a pseudo-tetrahedral environment, caused by the CO and P(OC₆H₄CH₃-2)₃ ligands.     

Computer-Assisted Solution of Chemical Problems—The Historical Development and the Present State of the Art of a New Discipline of Chemistry

The topic of this article is the development and the present state of the art of computer chemistry, the computer-assisted solution of chemical problems. Initially the problems in computer chemistry were confined to structure elucidation on the basis of spectroscopic data, then programs for synthesis design based on libraries of reaction data for relatively narrow classes of target compounds were developed, and now computer programs for the solution of a great variety of chemical problems are available or are under development. Previously it was an achievement when any solution of a chemical problem could be generated by computer assistance. Today, the main task is the efficient, transparent, and non-arbitrary selection of meaningful results from the immense set of potential solutions—that also may contain innovative proposals. Chemistry has two aspects, constitutional chemistry and stereochemistry, which are interrelated, but still require different approaches. As a result, about twenty years ago, an algebraic model of the logical structure of chemistry was presented that consisted of two parts: the constitution-oriented algebra of be- and r-matrices, and the theory of the stereochemistry of the chemical identity group. New chemical definitions, concepts, and perspectives are characteristic of this logic-oriented model, as well as the direct mathematical representation of chemical processes. This model enables the implementation of formal reaction generators that can produce conceivable solutions to chemical problems—including unprecedented solutions—without detailed empirical chemical information. New formal selection procedures for computer-generated chemical information are also possible through the above model. It is expedient to combine these with interactive methods of selection. In this review, the Munich project is presented and discussed in detail. It encompasses the further development and implementation of the mathematical model of the logical structure of chemistry as well as the experimental verification of the computer-generated results. The article concludes with a review of new reactions, reagents, and reaction mechanisms that have been found with the PC-programs IGOR and RAIN.     

A Rapid Gas-Chromatography/Mass-Spectrometry Technique for Determining Odour Activity Values of Volatile Compounds in Plant Proteins: Soy,and Allergen-Free Pea and Brown Rice Protein

Plant-based protein sources have a characteristic aroma that limits their usage in various meat-alternative formulations. Despite being the most popular plant-based protein, the allergenicity of soy protein severely restricts the potential adoption of soy protein as an animal substitute. Thereby, allergen-free plant-protein sources need to be characterized. Herein, we demonstrate a rapid solid-phase-microextraction gas-chromatography/mass-spectrometry (SPME-GC/MS) technique for comparing the volatile aroma profile concentration of two different allergen-free plant-protein sources (brown rice and pea) and comparing them with soy protein. The extraction procedure consisted of making a 1:7 w/v aqueous plant protein slurry, and then absorbing the volatile compounds on an SPME fibre under agitation for 10 min at 40 °C, which was subsequently injected onto a GC column coupled to an MS system. Observed volatile concentrations were used in conjunction with odour threshold values to generate a Total Volatile Aroma Score for each protein sample. A total of 76 volatile compounds were identified. Aldehydes and furans were determined to be the most dominant volatiles present in the plant proteins. Both brown rice protein and pea protein contained 64% aldehydes and 18% furans, with minor contents of alcohols, ketones and other compounds. On the other hand, soy protein consisted of fewer aldehydes (46%), but a more significant proportion of furans (42%). However, in terms of total concentration, brown rice protein contained the highest intensity and number of volatile compounds. Based on the calculated odour activity values of the detected compounds, our study concludes that pea proteins could be used as a suitable alternative to soy proteins in applications for allergen-free vegan protein products without interfering with the taste or flavour of the product.