Surface tension of polymers with long unbranched side chains

The surface tension of polymers having long unbranched side chains was measured by a contact-angle technique. It ranges between 20–29 dynes/cm and is almost entirely due to dispersion forces. At the lower end of this range the side chains are attached to every other carbon atom of the main chain and the structure is characterized by extended alkyl side chains at right angles to the main chain with methyl groups forming the interface. As the spacing frequency of the side chains increases and the main chain becomes the site of other bulky groups, this structure becomes less ordered and the surface tension increases to the high twenties. The same effect, to a lesser extent, is observed when the length of the side chains is gradually diminished to 12 carbon atoms from 21. A sudden increase of the polar force contribution of the surface tension at 10–12 carbon atoms indicates collapse of the ordered side-chain structure.     

A Categorification of the Boson–Fermion Correspondence via Representation Theory of sl(∞)

In recent years different aspects of categorification of the boson–fermion correspondence have been studied. In this paper we propose a categorification of the boson–fermion correspondence based on the category of tensor modules of the Lie algebra sl(∞) of finitary infinite matrices. By \({\mathbb{T}^{+}}\) we denote the category of “polynomial” tensor sl(∞)-modules. There is a natural “creation” functor \({{\mathcal{T}_{N}} : {\mathbb{T}^{+}} \to {\mathbb{T}^{+}}}\), \({M \mapsto N \otimes M, \quad M,N \in \mathbb{T}^{+}}\). The key idea of the paper is to employ the entire category \({\mathbb{T}}\) of tensor sl(∞)-modules in order to define the “annihilation” functor \({{\mathcal{D}_{N}} : {\mathbb{T}^{+}} \to {\mathbb{T}^{+}}}\) corresponding to \({{\mathcal{T}_{N}}}\). We show that the relations allowing one to express fermions via bosons arise from relations in the cohomology of complexes of linear endofunctors on \({{\mathbb{T}^{+}}}\).     

Formation of Pd/Au nanostructures from Pd nanowires via galvanic replacement reaction

Bimetallic nanostructures with non-random metal atoms distribution are very important for various applications. To synthesize such structures via benign wet chemistry approach remains challenging. This paper reports a synthesis of a Au/Pd alloy nanostructure through the galvanic replacement reaction between Pd ultrathin nanowires (2.4 +/- 0.2 nm in width, over 30 nm in length) and AuCl3 in toluene. Both morphological and structural changes were monitored during the reaction up to 10 h. Continuous changes of chemical composition and crystalline structure from Pd nanowires to Pd68Au32 and Pd45Au55 alloys, and to Au nanoparticles were observed. More interestingly, by using combined techniques such as high-resolution transmission electron microscopy (HRTEM), X-ray diffraction (XRD), energy dispersive X-ray spectrometry (EDS), UV-vis absorption, and extended X-ray absorption fine structure (EXAFS) spectroscopy, we found the formation of Pd68Au32 non-random alloy with Au-rich core and Pd-rich shell, and random Pd45Au55 alloy with uniformly mixed Pd and Au atom inside the nanoparticles, respectively. Density functional theory (DFT) calculations indicated that alkylamine will strongly stabilize Pd to the surface, resulting in diffusion of Au atoms into the core region to form a non-random alloy. We believe such benign synthetic techniques can also enable the large scale preparation of various types of non-random alloys for several technically important catalysis applications.     

Synthesis of <Emphasis Type="Italic">N</Emphasis>-and <Emphasis Type="Italic">C</Emphasis>-trimethylsilyl-substituded anililes

N-Metallation of bromoanilines with ethylmagnesium bromide followed by a reaction with trimethylchlorosilane provided N-mono and N-bis(trimethylsilyl)bromoanilines depending on the structure of substrate. The metallation of bissilylated bromoanilines with butyllithium permitted the introduction of a trimethylsilyl substituent in the aromatic ring. Previously unknown 2-bromo-N,N-bis(trimethylsilyl)aniline, 2,6-dibromo-N-trimethylsilylaniline, 2,6-dibromo-N,N-bis(trimethylsilyl)aniline, 2-bromo-6-trimethylsilylaniline, 2-bromo-6-trimethylsilyl-N,N-bis(trimethylsilyl)aniline, 2-bromo-6-trimethylsilyl-N-trimethylsilylaniline, 2,4,6-tribromo-N-trimethylsilylaniline, and 2,4,6-tribromo-N,N-bis(trimethylsilyl)aniline were prepared. The structures of the compounds obtained were established by the chromato-mass spectrometry and ¹H, ¹³C, and ²⁹Si NMR spectroscopy.     

Small accessible quantum information does not imply security

The security of quantum key distribution is typically defined in terms of the mutual information between the distributed key S and the outcome of an optimal measurement applied to the adversary's system. We show that even if this so-called accessible information is small, the key S might not be secure enough to be used in applications such as one-time pad encryption. This flaw is due to a locking property of the accessible information: one additional (physical) bit of information can increase the accessible information by more than one bit.     

Phase coexistence of cluster crystals: beyond the Gibbs phase rule

We report a study of the phase behavior of multiple-occupancy crystals through simulation. We argue that in order to reproduce the equilibrium behavior of such crystals, it is essential to treat the number of lattice sites as a constraining thermodynamic variable. The resulting free-energy calculations thus differ considerably from schemes used for single-occupancy lattices. Using our approach, we obtain the phase diagram and the bulk modulus for a generalized exponential model that forms cluster crystals at high densities. We compare the simulation results with existing theoretical predictions. We also identify two types of density fluctuations that can lead to two sound modes and evaluate the corresponding elastic constants.     

Evidence for out-of-equilibrium crystal nucleation in suspensions of oppositely charged colloids

We report a numerical study of the rate of crystal nucleation in a binary suspension of oppositely charged colloids. Two different crystal structures compete in the thermodynamic conditions under study. We find that the crystal phase that nucleates is metastable and, more surprisingly, its nucleation free-energy barrier is not the lowest one. This implies that, during nucleation, there is insufficient time for subcritical nuclei to relax to their lowest free-energy structure. Such behavior is in direct contradiction with the common assumption that the phase that crystallizes most readily is the one with the lowest free-energy barrier for nucleation. The phenomenon that we describe should be relevant for crystallization experiments where competing solid structures are not connected by an easy transformation.     

Langlands duality for representations of quantum groups

We establish a correspondence (or duality) between the characters and the crystal bases of finite-dimensional representations of quantum groups associated to Langlands dual semi-simple Lie algebras. This duality may also be stated purely in terms of semi-simple Lie algebras. To explain this duality, we introduce an “interpolating quantum group” depending on two parameters which interpolates between a quantum group and its Langlands dual. We construct examples of its representations, depending on two parameters, which interpolate between representations of two Langlands dual quantum groups.     

In situ structural characterization of platinum dendrimer-encapsulated oxygen reduction electrocatalysts

In situ electrochemical extended X-ray absorption fine structure (EXAFS) was used to evaluate the structure of Pt dendrimer-encapsulated nanoparticles (DENs) during the oxygen reduction reaction (ORR). The DENs contained an average of just 225 atoms each. The results indicate that the Pt coordination number (CN) decreases when the electrode potential is moved to positive values. The results are interpreted in terms of an ordered core, disordered shell model. The structure of the DENs is not significantly impacted by the presence of dioxygen, but other electrogenerated species may have a significant impact on nanoparticle structure.     

Synthesis and characterization of [Ir(1,5-cyclooctadiene)(μ-H)]4: a tetrametallic Ir4H4-core, coordinatively unsaturated cluster

Reported herein is the synthesis of the previously unknown [Ir(1,5-COD)(μ-H)](4) (where 1,5-COD = 1,5-cyclooctadiene), from commercially available [Ir(1,5-COD)Cl](2) and LiBEt(3)H in the presence of excess 1,5-COD in 78% initial, and 55% recrystallized, yield plus its unequivocal characterization via single-crystal X-ray diffraction (XRD), X-ray absorption fine structure (XAFS) spectroscopy, electrospray/atmospheric pressure chemical ionization mass spectrometry (ESI-MS), and UV-vis, IR, and nuclear magnetic resonance (NMR) spectroscopies. The resultant product parallels--but the successful synthesis is different from, vide infra--that of the known and valuable Rh congener precatalyst and synthon, [Rh(1,5-COD)(μ-H)](4). Extensive characterization reveals that a black crystal of [Ir(1,5-COD)(μ-H)](4) is composed of a distorted tetrahedral, D(2d) symmetry Ir(4) core with two long [2.90728(17) and 2.91138(17) ?] and four short Ir-Ir [2.78680 (12)-2.78798(12) ?] bond distances. One 1,5-COD and two edge-bridging hydrides are bound to each Ir atom; the Ir-H-Ir span the shorter Ir-Ir bond distances. XAFS provides excellent agreement with the XRD-obtained Ir(4)-core structure, results which provide both considerable confidence in the XAFS methodology and set the stage for future XAFS in applications employing this Ir(4)H(4) and related tetranuclear clusters. The [Ir(1,5-COD)(μ-H)](4) complex is of interest for at least five reasons, as detailed in the Conclusions section.