Raman and Infrared Spectroscopic Investigation of Speciation in BeSO<Subscript>4</Subscript>(aq)

Measurements have been made of the Raman spectra of aqueous solutions of Be(ClO₄)₂, BeCl₂, (NH₄)₂SO₄ and BeSO₄ to 50 cm⁻¹. In some cases low concentrations (0.000770 mol⋅kg⁻¹) have been used and two temperatures (23 and 40 °C) were studied. In BeSO₄(aq), the ν ₁-SO₄^2-\mathrm{SO}_{4}^{2-} mode at 980 cm⁻¹ broadens with increasing concentration and shifts to higher wavenumbers. At the same time, a band at 1014 cm⁻¹ is detectable with this mode being assigned to [BeOSO₃], an inner-sphere complex (ISC). Confirmation of this assignment is provided by the simultaneous appearance of stretching bands for the Be²⁺-OSO₃^2-\mathrm{Be}^{2+}\mbox{-}\mathrm{OSO}_{3}^{2-} bond of the complex at 240 cm⁻¹ and for the BeO₄ skeleton mode of the [(H₂O)₃BeOSO₃] unit at 498 cm⁻¹. The ISC concentration increases with higher temperatures. The similarity of the n₁-SO₄^2-\nu_{1}\mbox{-}\mathrm{SO}_{4}^{2-} Raman bands for BeSO₄ in H₂O and D₂O is further strong evidence for formation of an ISC. After subtraction of the ISC component at 1014 cm⁻¹, the n₁-SO₄^2-\nu_{1}\mbox{-}\mathrm{SO}_{4}^{2-} band in BeSO₄(aq) showed systematic differences from that in (NH₄)₂SO₄(aq). This is consistent with a n₁-SO₄^2-\nu_{1}\mbox{-}\mathrm{SO}_{4}^{2-} mode at 982.7 cm⁻¹ that can be assigned to the occurrence of an outer-sphere complex ion (OSCs). These observations are shown to be in agreement with results derived from previous relaxation measurements. Infrared spectroscopic data show features that are also consistent with a beryllium sulfato complex such as the appearance of a broad and weak n₁-SO₄^2-\nu_{1}\mbox{-}\mathrm{SO}_{4}^{2-} mode at ∼1014 cm⁻¹, normally infrared forbidden, and a broad and asymmetric n₃-SO₄^2-\nu_{3}\mbox{-}\mathrm{SO}_{4}^{2-} band contour which could be fitted with four band components (including n₃-SO₄^2-(aq)\nu_{3}\mbox{-}\mathrm{SO}_{4}^{2-}(\mathrm{aq})). The formation of ISCs in BeSO₄(aq) is much more pronounced than in the similar MgSO₄(aq) system studied recently.     

Ethanol/water solutions as certified reference materials for breath alcohol analyzer calibration

The Federal Institute for Materials Research and Testing (BAM), Germany, has issued a series of large volume ethanol in water certified reference materials (CRMs), primarily developed for the calibration of evidential breath alcohol analyzers in Germany. The certified parameter is the ethanol mass concentration at 20 °C. When used in a wet bath simulator, the solutions deliver gas samples that meet the requirements set by the Organization of Legal Metrology for calibration of breathalyzers. The materials were prepared gravimetrically by spiking of ethanol into water in single 5 L units. A complete uncertainty budget for the preparation process has been established. The purity of the commercial ethanol stock solution was identified to be the main source of uncertainty. For stability and homogeneity measurements and for the verification of the gravimetric mass concentration of the CRMs, a robust high-precision gas chromatography, with flame-ionization detection method for ethanol determination in aqueous samples was developed and validated. The good performance of this method has been demonstrated in several international comparisons organized by the Consultative Committee for Amount of Substance—Metrology in Chemistry at the International Bureau of Weights and Measures.     

Calculation of probability density functions for nonlinear vibration systems

Technical systems are subjected to a variety of excitations that cannot generally be described in deterministic ways. Random excitations such as road roughness, wind gusts or loads on marine structures are commonly described by stochastic differential equations (SDEs). Given a set of SDEs, the main task is in finding probability density functions (PDFs), which yield statistical information about the system states. Monte-Carlo simulations represent a general way of generating PDFs, however, reliable integration methods can be time-consuming for complex systems. An alternative way of finding PDFs lies in the analysis of the Fokker-Planck equation, a partial differential equation of the PDF. Linear problems under Gaussian excitation can be solved analytically, which is the case only for a small class of nonlinear problems. As a result, there are a number of methods of approximating PDFs for general problems. Most of these are restricted to comparably low dimensions, such as d=4 ("curse of dimensionality"), limiting the relevance to technical applications. This paper presents solutions to problems of dimensions up to d=10, applying a Galerkin-method that expands approximate solutions into orthogonal polynomials. Problems include polynomial nonlinearities in damping and restoring terms, such as classical Duffing-elements, as well as other types of nonlinearities, demonstrated on a typical problem in vehicle dynamics. All results are compared with results from Monte-Carlo simulations or exact solutions, where available. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ends of iterated function systems

Guided by classical concepts, we define the notion of ends of an iterated function system and prove that the number of ends is an upper bound for the number of nondegenerate components of its attractor. The remaining isolated points are then linked to idempotent maps. A commutative diagram illustrates the natural relationships between the infinite walks in a semigroup and components of an attractor in more detail. We show in particular that, if an iterated function system is one-ended, the associated attractor is connected, and ask whether every connected attractor (fractal) conversely admits a one-ended system.     

T-groups,polycyclic groups,and finite quotients

A group is called a T-group if all of its subnormal subgroups are normal. In this note we consider the following question: Assume that G is a polycyclic group. What can be said about G if all finite epimorphic images H of G satisfy one of the following conditions: (i) H is a T-group,(ii) \({H/\Phi (H)}\) is a T-group,(iii) H/Z _*(H) is a T-group. We will see that the prime 2 will play a particular role in (ii) and (iii), see Theorems C and D.     

The hydrological response of heavy clay grassland soils to rainfall in south‐west England using δ2H

Stable isotopes of water have been previously used in catchment studies to separate rain‐event water from pre‐event groundwater. However, there are a lack of studies at the smaller scale looking at the separation of event water from pre‐event water. This is particularly relevant for heavy clay soil systems through which the movement of water is uncertain but is thought to be rainwater‐dominated. The data presented here were collected at a rural site in the south‐west of England. The historic rainfall at the site was isotopically varied but similar to the global meteoric water line, with annual weighted means of ?37‰ for δ²H and ?5.7‰ for δ¹⁸O and with no seasonal variation. Drainage was sampled from the inter‐flow (surface runoff + lateral through‐flow) and drain‐flow (55 cm deep mole drains) pathways of two 1 ha lysimeters during two rainfall events, which had δ²H values of ?68‰ and ?92‰, respectively. The δ²H values of the lysimeter drainage water suggest that there was no contribution of event water during the first, small discharge (Q) event; however, the second larger event did show isotopic variation in δ²H values negatively related to Q indicating that rainwater was contributing to Q. A hydrograph separation indicated that only 49–58% of the inter‐flow and 18–25% of the drain‐flow consisted of event water. This was surprising given that these soil types are considered retentive of soil water. More work is needed on heavy clay soils to understand better the nature of water movement from these systems. Copyright © 2010 John Wiley & Sons, Ltd.     

Certification of reference materials for ochratoxin A analysis in coffee and wine

Mycotoxins are important non-anthropogenic food and feed contaminants, which can be present on almost every agricultural commodity. Effective consumer protection therefore essentially depends on food surveillance by reliable quantitative analysis enabled by appropriate quality control. Certified (matrix) reference materials (CRMs) are versatile tools to support quality assurance. However, in the case of ochratoxin A (OTA), a hepato- and nephrotoxic mycotoxin, which is regulated in various foods, there is a lack of suitable CRMs. This lack has now been overcome by the development of two European Reference Materials (ERM^?) for the determination of OTA in roasted coffee (ERM^?-BD475) and red wine (ERM^?-BD476). This article discusses the material preparation process as well as the results of homogeneity and stability testing. Furthermore, the results of the in-house certification studies carried out at BAM Federal Institute for Materials Research and Testing are presented and discussed. Interlaboratory comparison studies involving selected expert laboratories with documented expertise in the field of mycotoxin analysis were conducted to confirm the certified values determined by BAM. The certified ochratoxin A values and their corresponding expanded uncertainties (k?=?2) were assigned in full compliance with the requirements of ISO Guide 35 and are as follows: (6.0?±?0.6)???g?kg^?1 for roasted coffee, ERM^?-BD475, and (0.52?±?0.11)???g?L^?1 for red wine, ERM^?-BD476.