High-LET radiolysis of liquid water with 1H+, 4He2+, 12C6+, and 20Ne9+ ions: effects of multiple ionization

Monte Carlo simulations are used to investigate the effects of multiple ionization of water molecules on the yields of formation of free radical and molecular species, including molecular oxygen, in the radiolysis of pure, deaerated liquid water by using different types of radiation (1H+, 4He2+, 12C6+, and 20Ne9+ ions) up to approximately 900 keV/microm, at neutral pH and 25 degrees C. Taking into account the double, triple, and quadruple ionizations of water, the primary (or "escape") yields (at 10(-6) s) of the various radiolytic species (G(e(aq)-), G(H*), G(H2), G(*OH), G(HO2*/O2*-), and G(H2O2) are calculated as a function of the linear energy transfer (LET) of the radiation. Our results quantitatively reproduce the large increase observed in G(HO2*/O2*-) at high LET. Under the conditions of this study, the mechanisms of triple and quadruple ionizations contribute only weakly to the production of HO2*/O2*-. With the exception of protons, our calculations also simultaneously predict a maximum in G(H2O2) corresponding to the LET of approximately 4.5-MeV helium ions (approximately 100 keV/microm) and approximately 110-MeV carbon ions (approximately 180 keV/microm). This maximum occurs where G(HO2*/O2*-) begins to rise sharply, suggesting, in agreement with previous experimental data, that the yields of HO2*/O2*- and H2O2 are closely linked. Moreover, our results show a steep increase in the initial and primary yields of molecular oxygen with increasing LET, giving support to the "oxygen in heavy-ion tracks" hypothesis. By contrast, it is found that, in the whole LET range considered, the incorporation of multiple ionization in the simulations has only little effect on the variation of our computed G(e(aq)-), G(H*), G(H2), and G(*OH) values as a function of LET. As expected, G(e(aq)-) and G(*OH) decrease continuously with increasing LET. G(H*) at first increases and then decreases at high LET. Finally, G(H2) monotonically rises with increasing LET. Our calculated yield values compare generally very well with experiment.     

Sandwich semigroups in locally small categories I: foundations

Fix (not necessarily distinct) objects i and j of a locally small category S, and write \(S_{ij}\) for the set of all morphisms \(i\rightarrow j\). Fix a morphism \(a\in S_{ji}\), and define an operation \(\star _a\) on \(S_{ij}\) by \(x\star _ay=xay\) for all \(x,y\in S_{ij}\). Then \((S_{ij},\star _a)\) is a semigroup, known as a sandwich semigroup, and denoted by \(S_{ij}^a\). This article develops a general theory of sandwich semigroups in locally small categories. We begin with structural issues such as regularity, Green’s relations and stability, focusing on the relationships between these properties on \(S_{ij}^a\) and the whole category S. We then identify a natural condition on a, called sandwich regularity, under which the set \({\text {Reg}}(S_{ij}^a)\) of all regular elements of \(S_{ij}^a\) is a subsemigroup of \(S_{ij}^a\). Under this condition, we carefully analyse the structure of the semigroup \({\text {Reg}}(S_{ij}^a)\), relating it via pullback products to certain regular subsemigroups of \(S_{ii}\) and \(S_{jj}\), and to a certain regular sandwich monoid defined on a subset of \(S_{ji}\); among other things, this allows us to also describe the idempotent-generated subsemigroup \(\mathbb E(S_{ij}^a)\) of \(S_{ij}^a\). We also study combinatorial invariants such as the rank (minimal size of a generating set) of the semigroups \(S_{ij}^a\), \({\text {Reg}}(S_{ij}^a)\) and \(\mathbb E(S_{ij}^a)\); we give lower bounds for these ranks, and in the case of \({\text {Reg}}(S_{ij}^a)\) and \(\mathbb E(S_{ij}^a)\) show that the bounds are sharp under a certain condition we call MI-domination. Applications to concrete categories of transformations and partial transformations are given in Part II.     

Rank and idempotent rank of finite full transformation semigroups with restricted range

Let T(X) be the full transformation semigroup on the set X and let T(X,Y) be the semigroup consisting of all total transformations from X into a fixed nonempty subset Y of X. In 2011, Sanwong studied the regular part $$F(X,Y)=\bigl\{\alpha\in T(X,Y): X\alpha\subseteq Y\alpha\bigr\}, $$ of T(X,Y) and described its Green’s relations and ideals. In this paper, we compute the rank of F(X,Y) when X is a finite set. Moreover, we obtain the rank and idempotent rank of its ideals.     

The Use of a Low‐Molar‐Mass Self‐Assembled Template to Direct the Crystallisation of Poly(ε‐caprolactone)

Summary: We show that small quantities of dibenzylidene sorbitol dispersed in poly(ε‐caprolactone) provide a self‐assembling nanoscale framework to yield high levels of crystal orientation. During modest shear flow of the melt, the additive forms highly extended nanoparticles which adopt a preferred alignment with respect to the flow field and, on cooling, polymer crystallisation is directed by these particles. We speculate that atomistic level epitaxy is unlikely to be the only directing influence.

SAXS pattern of PCL/DBS in the melt at 80 °C and subjected to a shear flow of 10 s⁻¹ for 1 000 shear units. The flow direction is vertical.     

A novel one‐dimensional metal–organic framework with a μ‐cyanido‐argentate group: catena‐poly[[(5,5′‐dimethyl‐2,2′‐bipyridyl‐κ2N,N′)silver(I)]‐μ‐cyanido‐κ2N:C]

The design and synthesis of metal coordination and supramolecular frameworks containing N‐donor ligands and dicyanidoargentate units is of interest due to their potential applications in the fields of molecular magnetism, catalysis, nonlinear optics and luminescence. In the design and synthesis of extended frameworks, supramolecular interactions, such as hydrogen bonding, π–π stacking and van der Waals interactions, have been exploited for molecular recognition associated with biological activity and for the engineering of molecular solids.The title compound, [Ag(CN)(C₁₂H₁₂N₂)]_n, crystallizes with the Ag^I cation on a twofold axis, half a cyanide ligand disordered about a centre of inversion and half a twofold‐symmetric 5,5′‐dimethyl‐2,2′‐bipyridine (5,5′‐dmbpy) ligand in the asymmetric unit. Each Ag^I cation exhibits a distorted tetrahedral geometry; the coordination environment comprises one C(N) atom and one N(C) atom from substitutionally disordered cyanide bridging ligands, and two N atoms from a bidentate chelating 5,5′‐dmbpy ligand. The cyanide ligand links adjacent Ag^I cations to generate a one‐dimensional zigzag chain. These chains are linked together via weak nonclassical intermolecular interactions, generating a two‐dimensional supramolecular network.     

A unifying approach to the Margolis–Meakin and Birget–Rhodes group expansion

Let G be a group. We show that the Birget–Rhodes prefix expansion \(G^{Pr}\) and the Margolis–Meakin expansion M(X; f) of G with respect to \(f:X\rightarrow G\) can be regarded as inverse subsemigroups of a common E-unitary inverse semigroup P. We construct P as an inverse subsemigroup of an E-unitary inverse monoid \(U/\zeta \) which is a homomorphic image of the free product U of the free semigroup \(X^+\) on X and G. The semigroup P satisfies a universal property with respect to homomorphisms into the permissible hull C(S) of a suitable E-unitary inverse semigroup S, with \(S/\sigma _S=G\), from which the characterizing universal properties of \(G^{Pr}\) and M(X; f) can be recaptured easily.     

Synthesis and structure of the N-alkyl-2,6-dimethyl-4-oxopyridine-3-carboxylic acids

A range of N-alkyl-2,6-dimethyl-4-oxopyridine-3-carboxylic acids XV have been prepared via reactions of primary alkyl amines with differing 2,6-dimethyl-4-oxopyran-3-carboxylate esters IX . The quantity of desired product formed and the character of by-products formed are determined by the natures of the amine and ester IX respectively. X-ray crystallography data for the N-ethyl analogue of XV indicates very strong intramolecular hydrogen bonding to be present, with the heterocyclic ring exhibiting considerable aromaticity.     

The regular part of a semigroup of transformations with restricted range

Let T(X) be the full transformation semigroup on the set X and let T(X,Y) be the semigroup consisting of all total transformations from X into a fixed subset Y of X. It is known that $$F(X, Y)=\{\alpha\in T(X, Y): X\alpha\subseteq Y\alpha\},$$ is the largest regular subsemigroup of T(X,Y) and determines Green??s relations on T(X,Y). In this paper, we show that F(X,Y)?T(Z) if and only if X=Y and |Y|=|Z|; or |Y|=1=|Z|, and prove that every regular semigroup S can be embedded in F(S ¹,S). Then we describe Green??s relations and ideals of F(X,Y) and apply these results to get all of its maximal regular subsemigroups when Y is a nonempty finite subset of X.