When spectroscopy fails: The measurement of ion pairing

Spectroscopic techniques such as UV/vis, NMR, and Raman are powerful tools for the investigation of chemical speciation in solution. However, it is not widely recognized that such techniques do not always provide reliable information about ion association equilibria. Specifically, spectroscopic measurements do not in general produce thermodynamically meaningful association constants for non-contact ion pairs, where the ions are separated by one or more solvent molecules. Such systems can only be properly quantified by techniques such as dielectric or ultrasonic relaxation, which can detect all ion-pair types (or equilibria), or by traditional thermodynamic methods, which detect the overall level of association. Various types of quantitative data are presented for metal ion/sulfate systems in aqueous solution that demonstrate the inadequacy of the major spectroscopic techniques for the investigation of systems that involve solvent-separated ion pairs. The implications for ion association equilibria in general are briefly discussed

Counterexamples to regularities for the derivative processes associated to stochastic evolution equations

In the recent years there has been an increased interest in studying regularity properties of the derivatives of stochastic evolution equations (SEEs) with respect to their initial values. In particular, in the scientific literature it has been shown for every natural number $n\in\mathbb{N}$ that if the nonlinear drift coefficient and the nonlinear diffusion coefficient of the considered SEE are $n$-times continuously Fr\'{e}chet differentiable, then the solution of the considered SEE is also $n$-times continuously Fr\'{e}chet differentiable with respect to its initial value and the corresponding derivative processes satisfy a suitable regularity property in the sense that the $n$-th derivative process can be extended continuously to $n$-linear operators on negative Sobolev-type spaces with regularity parameters $\delta_1,\delta_2,\ldots,\delta_n\in[0,1/2)$ provided that the condition $\sum^n_{i=1} \delta_i < 1/2$ is satisfied. The main contribution of this paper is to reveal that this condition can essentially not be relaxed

Heat capacities of aqueous sodium hydroxide/aluminate mixtures and prediction of the solubility constant of boehmite up to 300 °C

A modified commercial (Setaram C80) calorimeter has been used to measure the isobaric volumetric heat capacities of concentrated alkaline sodium aluminate solutions at ionic strengths from 1 to 6 mol kg-1, with up to 40 mol.% substitution of hydroxide by aluminate, at temperatures from 50 to 300 °C and a pressure of 10 MPa. Apparent molar heat capacities for the mixtures, Cpφ{symbol}, derived from these data were found to depend linearly on the aluminate substitution level, i.e., they followed Young's rule. These quantities were used to estimate the apparent molar heat capacities of pure, hypothetical sodium aluminate solutions, Cpφ{symbol} ('NaAl(OH)4'(aq)). Slopes of the Young's rule plots were invariant with ionic strength at a given temperature but depended linearly on temperature. The heat capacities of ternary aqueous sodium hydroxide/aluminate mixtures could therefore be modelled using only two parameters in addition to those needed for the correlation of Cpφ{symbol} (NaOH(aq)) reported previously from these laboratories. An assessment of the standard thermodynamic quantities for boehmite, gibbsite and the aluminate ion yielded a set of recommended values that, together with the present heat capacity data, accurately predicts the solubility of gibbsite and boehmite at temperatures up to 300 °C

Random Bit Multilevel Algorithms for Stochastic Differential Equations

We study the approximation of expectations \E(f(X)) for solutions $X$ of SDEs and functionals $f \colon C([0,1],\R^r) \to \R$ by means of restricted Monte Carlo algorithms that may only use random bits instead of random numbers. We consider the worst case setting for functionals $f$ from the Lipschitz class w.r.t.\ the supremum norm. We construct a random bit multilevel Euler algorithm and establish upper bounds for its error and cost. Furthermore, we derive matching lower bounds, up to a logarithmic factor, that are valid for all random bit Monte Carlo algorithms, and we show that, for the given quadrature problem, random bit Monte Carlo algorithms are at least almost as powerful as general randomized algorithms

Morphological Characterization of Materials using Low Voltage Scanning Electron Microscopy (LVSEM)

The use of lower energy (0.5 to 10 keV) electron beams in the scanning electron microscope (LVSEM) provides a number of advantages in the imaging of materials, including increased topographic contrast and reduced specimen charging. Application of LVSEM to materials analysis was difficult in the past due to a number of instrumental difficulties, including low gun brightness, the increased effect of chromatic aberration upon lower energy beams, and the increased sensitivity of such electron beams to stray fields. Improvements in design have led to commercial instruments which provide the microscopist with the capability to analyze materials in this low-energy regime. LVSEM has been applied to the analysis of a variety of specimens, all of which would have proven quite difficult or impossible by classical higher-energy (15-35 keV) SEM. Examples discussed include an ion-implanted cemented carbide, a surface-modified glassy carbon electrode, a semiconductor (III-V) layered structure, and a macroscopic polymer crystal

Postive Behavioral Interventions and Supports in Out of School Time: Providing Professional Development via Consultation and Performance Feedback

American youth are in need of supervision after the school day concludes. After School Programs (ASPs) provide students with safe and supportive venues that have the potential for encouraging student growth and development. ASPs across the country struggle to find high quality professionals to staff their programs; adequate training for these professionals is also limited. There is also significant evidence linking strong teacher-student relationships to both academic and social success. Positive Behavioral Interventions and Supports (PBIS) is a framework that has a strong evidence base to support success in promoting a proactive approach to behavior management within school settings. The purpose of this study was to examine the effect of two variables that can improve ASP staff professional development opportunities and the quality of staff-student relationships in after-school settings: active supervision and consultation with performance feedback. A multiple-baseline design across five after-school counselors was utilized to evaluate the effects of an intervention involving training in PBIS as it relates to after school settings and visual performance feedback on the counselors’ engagement in active supervision, provision of reinforcement, statements of correction, and statements of behavioral expectations during daily snack time. The study also examined counselor perceptions of utility and relevance of the training and feedback process. As expected based on previous research, the intervention was somewhat effective in increasing and sustaining high levels of active supervision amongst most counselors. Overall rates of reinforcement increased across all counselors, use of correction was less affected, and statements of behavior expectations remained low throughout the study. Results of the social validity measures indicated positive feelings about the relevance of the training, but mixed perceptions related to the specific application of the skills to snack time. Findings from the current study provide early evidence that after-school professionals would benefit from the opportunity to engage in professional development in the area of behavior management, when combined with consultation and performance feedback. Limitations of the study, contributions to the field, and directions for future research are presented

Decomposition of Bayer process organics: Phenolates, polyalcohols, and additional carboxylates

The degradation of nineteen low-molecular-weight phenolates, polyalcohols and selected aliphatic and aromatic carboxylates of relevance to the Bayer process has been studied in 6 mol kg-1 NaOH(aq) at 90 °C for up to 36 days, and (for some species) at 180 °C for up to 12 days, using HPLC and 13C NMR spectroscopy. Aliphatic polyalcohols degraded readily at 90 °C to lactate, oxalate, acetate, and formate. As observed previously, aliphatic carboxylates with hydroxyl groups also degraded readily at 90 °C but there is evidence that the position of the hydroxyl group may be important. The observed degradation products for most, but not all, of these species can be explained in terms of well-known organic reaction mechanisms. Phenolate and 5-hydroxyisophthalate were stable at 180 °C but other phenolic species degraded partially at 90 °C. However, the reaction products could not be identified and no trends in reactivity were discernible. Consistent with previous studies both aliphatic and aromatic carboxylates without hydroxyl groups were generally stable in NaOH(aq) even at 180 °C

Random Bit Quadrature and Approximation of Distributions on Hilbert Spaces

We study the approximation of expectations \E(f(X)) for Gaussian random elements $X$ with values in a separable Hilbert space $H$ and Lipschitz continuous functionals $f \colon H \to \R$. We consider restricted Monte Carlo algorithms, which may only use random bits instead of random numbers. We determine the asymptotics (in some cases sharp up to multiplicative constants, in the other cases sharp up to logarithmic factors) of the corresponding $n$-th minimal error in terms of the decay of the eigenvalues of the covariance operator of $X$. It turns out that, within the margins from above, restricted Monte Carlo algorithms are not inferior to arbitrary Monte Carlo algorithms, and suitable random bit multilevel algorithms are optimal. The analysis of this problem leads to a variant of the quantization problem, namely, the optimal approximation of probability measures on $H$ by uniform distributions supported by a given, finite number of points. We determine the asymptotics (up to multiplicative constants) of the error of the best approximation for the one-dimensional standard normal distribution, for Gaussian measures as above, and for scalar autonomous SDEs