Affinity interactions in counterion‐polyelectrolyte systems: Competition between different counterions

Non‐bonding, specific interactions between linear polyelectrolytes and different species of counterions (of equal or different valence) are considered in the framework of the counterion condensation theory. It is assumed that these interactions are of short distance nature and that, within our theoretical approach, they apply only to the counterions territorially associated (condensed) to the polyion, which are free to move within the condensation volume V_p around it. It is found that a simple additive term in the total free energy is sufficient to account for this interaction, resulting in a modulation of the polyelectrolytically determined population of territorially bound counterions. The distribution of free and condensed counterions as well as its variation with the physicochemical variables of the solution can be readily calculated. Analysis of literature data on titrations of poly(methacrylic acid) and dextran sulfate in aqueous solution with different species of monovalent and divalent counterions show that both polyanions appear to have a modest affinity free energy (of about RT) for Ca⁺⁺ counterions when compared with Na⁺. On the other hand, polyion interactions with the Mg⁺⁺/Na⁺ pair are well described by bare polyelectrolytic interactions.     

Inhibition of Cellobiohydrolases from Trichoderma reesei. Synthesis and Evaluation of Some Glucose-, Cellobiose-, and Cellotriose-Derived Hydroximolactams and Imidazoles

The lactam 16 , the hydroximolactams 8 , 20 , 23 , and 27 , and the imidazole 32 were prepared following known methods. They were tested together with the known tetrazole 35 and the hydroximolactams 2 and 36 as inhibitors of the cellobiohydrolases Cel7A and Cel6A from Trichoderma reesei. Cel7A is only weakly inhibited by these compounds. Comparing their inhibitory activity evidences the importance of occupying subsites +1 and +2. The results strongly suggest that the shape of none of the variants of the lactone-type inhibitor motif embodied by these inhibitors is complementary to the subsite −1, i. e., analogous to the transition state. Cel6A is rather strongly inhibited by the cellobiose analogues 20 , 23 , and 32 , and by the cellotriose analogue 27 . Their relative inhibitory activities evidence that binding at subsite −2 depends upon the shape of the moiety occupying subsite −1. There is only a small difference between the inhibition by the hydroximolactams 20 and 23 , which may be (partially) protonated by the catalytic acid of either anti- or syn-protonating glycosidases, and the imidazole 32 , which can only be protonated by anti-protonating glycosidases. The results strongly suggest that shape requirements must be met by glycosidase inhibitors before they can be used to characterize the proton trajectory of glycosidases.     

Inspection games in arms control

An inspection game is a mathematical model of a situation in which an inspector verifies the adherence of an inspectee to some legal obligation, such as an arms control treaty, where the inspectee may have an interest in violating that obligation. The mathematical analysis seeks to determine an optimal inspection scheme, ideally one which will induce legal behavior, under the assumption that the potential illegal action is carried out strategically; thus a non-cooperative game with two players, inspector and inspectee, is defined. Three phases of development in the application of such models to arms control and disarmament may be identified. In the first of these, roughly from 1961 through 1968, studies that focused on inspecting a nuclear test ban treaty emphasized game theory, with less consideration given to statistical aspects associated with data acquisition and measurement uncertainty. The second phase, from 1968 to about 1985, involves work stimulated by the Treaty on the Non-Proliferation of Nuclear Weapons (NPT). Here, the verification principle of material accountancy came to the fore, along with the need to include the formalism of statistical decision theory within the inspection models. The third phase, 1985 to the present, has been dominated by challenges posed by such far-reaching verification agreements as the Intermediate Range Nuclear Forces Agreement (INF), the Treaty on Conventional Forces in Europe (CFE) and the Chemical Weapons Convention (CWC), as well as perceived failures of the NPT system in Iraq and North Korea. In this connection, the interface between the political and technical aspects of verification is being examined from the game-theoretic viewpoint.     

Methodology in studying improvement of polyacrylates biodegradability

The biodegradability of polyacrylic acid derivatives may be improved through introduction of some fragility points within the main carbon chains. These weakness points can be either hydrolizable bonds or oxidizable sites. Enzymatic hydrolysis and oxydative biomimetic degradation tests have been set up in order to quickly evaluate new polymeric structures, before their possible evaluation through microbial degradation by Candida tropicalis.     

Free Path Lengths in Quasicrystals

Previous studies of kinetic transport in the Lorentz gas have been limited to cases where the scatterers are distributed at random (e.g., at the points of a spatial Poisson process) or at the vertices of a Euclidean lattice. In the present paper we investigate quasicrystalline scatterer configurations, which are non-periodic, yet strongly correlated. A famous example is the vertex set of a Penrose tiling. Our main result proves the existence of a limit distribution for the free path length, which answers a question of Wennberg. The limit distribution is characterised by a certain random variable on the space of higher dimensional lattices, and is distinctly different from the exponential distribution observed for random scatterer configurations. The key ingredients in the proofs are equidistribution theorems on homogeneous spaces, which follow from Ratner’s measure classification.     

Hexasulfanyl analogues of cyclotriveratrylene

The synthesis of four 3,4-di(alkylsulfanyl)benzyl alcohol derivatives is described, in five steps from methyl 3,4-di(hydroxy)benzoate via a Newman–Kwart rearrangement. Incubation of these derivatives in formic acid affords 2,3,7,8,12,13-hexakis(alkylsulfanyl)-10,15-dihydro-5H-tribenzo[a,d,g]cyclononene products, which are hexa-sulfanyl analogues of the well-known supramolecular cavitand host, cyclotriveratrylene (CTV). The yield of this cyclization depends strongly on the alkylsulfanyl substituents present, in the order SMe > SEt ≈ SiPr ? SBn. A crystal structure determination of one of the cyclotrimers shows a mode of self-association that is commonly exhibited by CTV itself.     

The crystal and molecular structure of tris[(triphenylstannyl)methyl]methane

The title compound, C₅₈H₅₂Sn₃, belongs to the triclinic space group P$\text{1}$, with a 10.165, b 13.365, c 18.670 Å, α 96.28, β 93.88, γ 103.15°, V = 2443.8 ų, f_w = 1105.1, Z = 2, D_calc 1.501 g cm^?3, m.p. 206.5–208°C, λ(Mo-K_$\text{α}$) 0.71069 Å. The structure was refined on 2684 nonzero reflections to an R factor of 0.044. The crystal contains molecules in which the (SnCH₂)₃CH core possesses an approximate C₃ symmetry. The three SnC(H₂) bonds are gauche to the C(4)-H bond. Repulsive interactions involving the bulky Ph₃Sn substituents lead to large SnC(H₂)C(H) angles (av. 117.3°), whereas the C(H₂)C(H)C(H₂) angles at the tertiary carbon average 111.3°. Little distortion of the Ph₃Sn groups themselves is present, since the PhSnPh angles (av. 109.8°) are almost equal to the C(H₂)SnPh angles (av. 109.9°). The molecule as a whole has no symmetry because the aromatic rings in the three Ph₃Sn groups have different orientations. The phenyl groups create a pocket in the middle of the molecule which encloses and shields the tertiary hydrogen atom. The resulting inaccessibility of this hydrogen accounts in part for the low reactivity of the title compound in redox reactions.     

A nonlocal species concentration theory for diffusion and phase changes in electrode particles of lithium ion batteries

A nonlocal species concentration theory for diffusion and phase changes is introduced from a nonlocal free energy density. It can be applied, say, to electrode materials of lithium ion batteries. This theory incorporates two second-order partial differential equations involving second-order spatial derivatives of species concentration and an additional variable called nonlocal species concentration. Nonlocal species concentration theory can be interpreted as an extension of the Cahn–Hilliard theory. In principle, nonlocal effects beyond an infinitesimal neighborhood are taken into account. In this theory, the nonlocal free energy density is split into the penalty energy density and the variance energy density. The thickness of the interface between two phases in phase segregated states of a material is controlled by a normalized penalty energy coefficient and a characteristic interface length scale. We implemented the theory in COMSOL Multiphysics\(^{\circledR }\) for a spherically symmetric boundary value problem of lithium insertion into a \(\hbox {Li}_x\hbox {Mn}_2\hbox {O}_4\) cathode material particle of a lithium ion battery. The two above-mentioned material parameters controlling the interface are determined for \(\hbox {Li}_x\hbox {Mn}_2\hbox {O}_4\), and the interface evolution is studied. Comparison to the Cahn–Hilliard theory shows that nonlocal species concentration theory is superior when simulating problems where the dimensions of the microstructure such as phase boundaries are of the same order of magnitude as the problem size. This is typically the case in nanosized particles of phase-separating electrode materials. For example, the nonlocality of nonlocal species concentration theory turns out to make the interface of the local concentration field thinner than in Cahn–Hilliard theory.