Studies of solute self-association by sedimentation equilibrium: allowance for effects of thermodynamic non-ideality beyond the consequences of nearest-neighbor interactions

A sedimentation equilibrium study of a-chymotrypsin self-association in acetate-chloride buffer, pH 4.1 I 0.05, has been used to illustrate determination of a dimerization constant under conditions where thermodynamic non-ideality is manifested beyond the consequences of nearest-neighbor interactions. Because the expressions for the experimentally determinable interaction parameters comprise a mixture of equilibrium constant and excluded volume terms, the assignment of reasonable magnitudes to the relevant virial coefficients describing non-associative cluster formation is essential for the evaluation of a reliable estimate of the dimerization constant. Determination of these excluded volume parameters by numerical integration over the potential-of-mean-force is shown to be preferable to their calculation by approximate analytical solutions of the integral for this relatively small enzyme monomer with high net charge (+ 10) under conditions of low ionic strength (0.05 M). (C) 2001 Elsevier Science B.V. All rights reserved.

The equilibrium penetration of monolayers. Is equilibrium really established?

In studying the penetration of water-soluble surfactants into water-insoluble monolayers the main theoretical problem is to find a relationship that would enable the amount of surfactant that has entered the monolayer to be calculated from a set of equilibrium surface pressure-area isotherms. Despite many attempts, no current theory gives satisfactory results when applied to experimental data (Langmuir 14 (1998) 2148). One possible reason is that equilibrium had not been established when the surface pressure-area curves were measured. The three experiments reported here suggest that equilibrium is extremely difficult to establish in such systems when the area is low or the surface pressure is high. The essence of these experiments is to try to reach the same final condition by two different routes. In the first route, the one nearly always used in equilibrium penetration measurements, the surfactant is injected under the expanded monolayer, which is then slowly compressed in steps, with time allowed at each step for a steady surface pressure to be attained. In the second procedure, the monolayer is first compressed to a high surface pressure and the surfactant then injected. A stepped expansion isotherm may then be observed. Surface pressure-area per monolayer molecule isotherms, reflection spectra, and slow neutron reflectivity data all show the same pattern: if the surfactant was allowed to penetrate while the monolayer was in an expanded state, it was not completely removed when the monolayer was compressed; but if the monolayer was in a highly compressed state when exposed to the surfactant little penetration took place until the film was expanded. There thus appear to be very large energy barriers to the ejection of surfactant from a compressed monolayer and to the penetration of surfactant into a compressed monolayer. Although these experiments have some limitations, it now seems likely that at least some of the penetration data used in evaluating the various thermodynamic treatments of equilibrium penetration were not equilibrium data. (C) 2001 Elsevier Science B.V. All rights reserved.

Quantum criticality

We investigate the theory of quantum fluctuations in non-equilibrium systems having large critical fluctuations. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction, and also to envisage future tests of quantum theory in regions of macroscopic quantum fluctuations. A long-term objective of this research is to identify suitable physical systems in which macroscopic 'Schrodinger cat'-like behaviour may be observed. We investigate two systems in particular of much current experimental interest, namely the degenerate parametric oscillator near threshold, and the evaporatively cooled (BEC). We compare the results obtained in the positive-P representation, as a fully quantum mechanical calculation, with the truncated Wigner phase space equation, also known as semi-classical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. In the region where the largest quantum fluctuations and Schrodinger cat-like behaviour might be expected, we find that the quantum predictions correspond very closely to the semi-classical theory. Nature abhors observing a Schrodinger car.

Generation of eigenstates using the phase-estimation algorithm

The phase estimation algorithm is so named because it allows an estimation of the eigenvalues associated with an operator. However, it has been proposed that the algorithm can also be used to generate eigenstates. Here we extend this proposal for small quantum systems, identifying the conditions under which the phase-estimation algorithm can successfully generate eigenstates. We then propose an implementation scheme based on an ion trap quantum computer. This scheme allows us to illustrate two simple examples, one in which the algorithm effectively generates eigenstates, and one in which it does not.

A novel method for solid-phase synthesis of oligosaccharides using the N-1-(4,4-dimethyl-2,6-dioxocyclohexylidene)ethyl (Dde) linker

The application of the N-1-(4,4-dimethyl-2,6-dioxocyclohexylidene)ethyl (Dde) linker for the solid-phase synthesis of oligosaccharides is described. The oligosaccharide products can be cleaved from the resin by hydrazine, ammonia or primary amines, but the linker is stable under the conditions of oligosaccharide synthesis. The first sugar can be attached to the resin linker via a vinylogous amide bond, or by ether linkage using a p-aminobenzyl alcohol converter. (C) 2001 Elsevier Science Ltd. All rights reserved.

Exact quantum phase model for mesoscopic Josephson junctions

Starting from the two-mode Bose-Hubbard model, we derive an exact version of the standard Mathieu equation governing the wave function of a Josephson junction. For a finite number of particles N, we find an additional cos 2 phi term in the potential. We also find that the inner product in this representation is nonlocal in phi. Our model exhibits phenomena, such as pi oscillations, which are not found in the standard phase model, but have been predicted from Gross-Pitaevskii mean-field theory.

A modified pore-filling isotherm for liquid-phase adsorption in activated carbon

This article modifies the usual form of the Dubinin-Radushkevich pore-filling model for application to liquid-phase adsorption data, where large molecules are often involved. In such cases it is necessary to include the repulsive part of the energy in the micropores, which is accomplished here by relating the pore potential to the fluid-solid interaction potential. The model also considers the nonideality of the bulk liquid phase through the UNIFAC activity coefficient model, as well as structural heterogeneity of the carbon. For the latter the generalized adsorption integral is used while incorporating the pore-size distribution obtained by density functional theory analysis of argon adsorption data. The model is applied here to the interpretation of aqueous phase adsorption isotherms of three different esters on three commercial activated carbons. Excellent agreement between the model and experimental data is observed, and the fitted Lennard-Jones size parameter for the adsorbate-adsorbate interactions compares well with that estimated from known critical properties, supporting the modified approach. On the other hand, the model without consideration of bulk nonideality, or when using classical models of the characteristic energy, gives much poorer bts of the data and unrealistic parameter values.

The use of liquid phase adsorption isotherms for characterization of activated carbons

The characterization of three commercial activated carbons was carried out using the adsorption of various compounds in the aqueous phase. For this purpose the generalized adsorption isotherm was employed, and a modification of the Dubinin-Radushkevich pore filling model, incorporating repulsive contributions to the pore potential as well as bulk liquid phase nonideality, was used as the local isotherm. Eight different flavor compounds were used as adsorbates, and the isotherms were jointly fitted to yield a common pore size distribution for each carbon. The bulk liquid phase nonideality was incorporated through the UNIFAC activity coefficient model, and the repulsive contribution to the pore potential was incorporated through the Steele 10-4-3 potential model. The mean micropore network coordination number for each carbon was also determined from the fitted saturation capacity based on percolation theory. Good agreement between the model and the experimental data was observed. In addition, excellent agreement between the bimodal gamma pore size distribution and density functional theory-cum-regularization-based pore size distribution obtained by argon adsorption was also observed, supporting the validity of the model. The results show that liquid phase adsorption, using adsorptive molecules of different sizes, can be an effective means of characterizing the pore size distribution as well as connectivity. Alternately, if the carbon pore size distribution is independently known, the method can be used to measure critical molecular sizes. (C) 2001 Elsevier Science.

Characterization of activated carbons using liquid phase adsorption

A modification of the Dubinin-Radushkevich pore filling model by incorporation of the repulsive contribution to the pore potential, and of bulk non-ideality, is proposed in this paper for characterization of activated carbon using liquid phase adsorption. For this purpose experiments have been performed using ethyl propionate, ethyl butyrate, and ethyl isovalerate as adsorbates and the microporous-mesoporous activated carbons Filtrasorb 400, Norit ROW 0.8 and Norit ROX 0.8 as adsorbents. The repulsive contribution to the pore potential is incorporated through a Lennard-Jones intermolecular potential model, and the bulk-liquid phase non-ideality through the UNIFAC activity coefficient model. For the characterization of activated carbons, the generalized adsorption isotherm is utilized with a bimodal gamma function as the pore size distribution function. It is found that the model can represent the experimental data very well, and significantly better than when the classical energy-size relationship is used, or when bulk non-ideality is neglected. Excellent agreement between the bimodal gamma pore size distribution and DFT-cum-regularization based pore size distribution is also observed, supporting the validity of the proposed model. (C) 2001 Elsevier Science Ltd. All rights reserved.

Quantitative affinity chromatography

The objective of this review is to summarize developments in the use of quantitative affinity chromatography to determine equilibrium constants for solute interactions of biological interest. Affinity chromatography is an extremely versatile method for characterizing interactions between dissimilar reactants because the biospecificity incorporated into the design of the affinity matrix ensures applicability of the method regardless of the relative sizes of the two reacting solutes. Adoption of different experimental strategies, such as column chromatography, simple partition equilibrium experiments, solid-phase immunoassay, and biosensor technology, has led to a situation whereby affinity chromatography affords a means of characterizing interactions governed by an extremely broad range of binding affinities-relatively weak interactions (binding constants below 10(3) M-1) through to interactions with binding constants in excess of 10(9) M-1. In addition to its important role in solute separation and purification, affinity chromatography thus also possesses considerable potential for investigating the functional roles of the reactants thereby purified. (C) 2001 Elsevier Science B.V. All rights reserved.

Predicting coal ash slag flow characteristics (viscosity model for the Al2O3-CaO-'FeO'-SiO2 system)

A model has been developed which enables the viscosities of coal ash slags to be predicted as a function of composition and temperature under reducing conditions. The model describes both completely liquid and heterogeneous, i.e. partly crystallised, slags in the Al2O3-CaO-'FeO'-SiO2 system in equilibrium with metallic iron. The Urbain formalism has been modified to describe the viscosities of the liquid slag phase over the complete range of compositions and a wide range of temperatures. The computer package F * A * C * T was used to predict the proportions of solids and the compositions of the remaining liquid phases. The Roscoe equation has been used to describe the effect of presence of solid suspension (slurry effect) on the viscosity of partly crystallised slag systems. The model provides a good description of the experimental data of fully liquid, and liquid + solids mixtures, over the complete range of compositions and a wide range of temperatures. This model can now be used for viscosity predictions in industrial slag systems. Examples of the application of the new model to coal ash fluxing and blending are given in the paper. (C) 2001 Elsevier Science Ltd. All rights reserved.

Coupled experimental and thermodynamic study of the Zn-Fe-Si-O system

Experimental and thermodynamic modeling studies have been carried out on the Zn-Fe-Si-O system. This research is part of a wider program to characterize zinc/lead industrial slags and sinters in the PbO-ZnO-SiO2-CaO-FeO-Fe2O3 system. Experimental investigations involve high-temperature equilibration and quenching techniques followed by electron probe X-ray microanalysis (EPMA). Liquidus temperatures and solid solubilities of the crystalline phases were measured in the temperature range from 1200 °C to 1450 °C (1473 to 1723 K) in the zinc ferrite, zincite, willemite, and tridymite primary-phase fields in the Zn-Fe-Si-O system in air. These equilibrium data for the Zn-Fe-Si-O system in air, combined with previously reported data for this system, were used to obtain an optimized self-consistent set of parameters of thermodynamic models for all phases.

Optimal input states and feedback for interferometric phase estimation

We derive optimal N-photon two-mode input states for interferometric phase measurements. Under canonical measurements the phase variance scales as N-2 for these states, as compared to N-1 or N-1/2 for states considered bq previous authors. We prove, that it is not possible to realize the canonical measurement by counting photons in the outputs of the interferometer, even if an adjustable auxiliary phase shift is allowed in the interferometer. However. we introduce a feedback algorithm based on Bayesian inference to control this auxiliary phase shift. This makes the measurement close to a canonical one, with a phase variance scaling slightly above N-2. With no feedback, the best result (given that the phase to be measured is completely unknown) is a scaling of N-1. For optimal input states having up to four photons, our feedback scheme is the best possible one, but for higher photon numbers more complicated schemes perform marginally better.

The effects of time delays in adaptive phase measurements

It is not possible to make measurements of the phase of an optical mode using linear optics without introducing an extra phase uncertainty. This extra phase variance is quite large for heterodyne measurements, however it is possible to reduce it to the theoretical limit of log (n) over bar (4 (n) over bar (2)) using adaptive measurements. These measurements are quite sensitive to experimental inaccuracies, especially time delays and inefficient detectors. Here it is shown that the minimum introduced phase variance when there is a time delay of tau is tau/(8 (n) over bar). This result is verified numerically, showing that the phase variance introduced approaches this limit for most of the adaptive schemes using the best final phase estimate. The main exception is the adaptive mark II scheme with simplified feedback, which is extremely sensitive to time delays. The extra phase variance due to time delays is considered for the mark I case with simplified feedback, verifying the tau /2 result obtained by Wiseman and Killip both by a more rigorous analytic technique and numerically.