Unsteady motion in single-line flow-injection systems

Unsteady motion in single-line flow-injection systems consisting of n tubular elements with valve or hydrodynamic injection is studied theoretically. A formula for the duration of the initial period of unsteady flow is derived. This initial period is much shorter than the mean residence time of the analyte in practical systems. It can therefore be neglected in mathematical modelling of such systems. Experimental data obtained with single-line systems with valve and hydrodynamic injection confirmed the validity of the theoretical equations.     

Developments in liquid-crystalline dimers and oligomers

ABSTRACT

Liquid-crystalline dimers and bimesogens have attracted much attention due to their propensity to exhibit the spontaneously chiral twist-bend mesophase (N_TB), most often by dimers with methylene spacers. Despite their relative ease of synthesis, the number of ether-linked twist-bend materials significantly lags behind those of methylene-linked compounds. In this work, we have prepared and studied a range of ether-linked bimesogens homologous in structure to the FFO9OCB; as with methylene-linked systems, it appears that it is molecular topology and the gross molecular shape that are the primary drivers for the formation of this phase of matter. Dimers and bimesogens are well studied within the context of the twist-bend phase; however, present understanding of this mesophase in oligomeric systems lags far behind. We report our recent efforts to prepare further examples of oligomeric twist-bend nematogens, including further examples of our ‘n+1’ methodology, which may allow the synthesis of high-purity, monodisperse materials of any given length to be prepared. We have observed that there is a tendency for these materials to exhibit highly ordered soft-crystalline mesophases as opposed to the twist-bend phase.     

On the permeation time lag for different transport equations by Frisch method

A constructive application of Frisch method for deriving permeation time lags for different transport equations is shown. Two main classes, i.e. parabolic and hyperbolic diffusional mass transport equations, are presented and compared. An influence of drift and chemical reaction terms on the time lag is discussed.     

A method to evaluate the Sachs formula

A rule-based method for evaluating the Sachs formula is introduced. For simple molecules, such as linear chains and monocycles, the Sachs formula can be evaluated by directly using the rules. For complex molecular systems, the Sachs formula can be evaluated by first breaking up the molecule into constituent pieces of sufficient simplicity so that data for them are available in the data base and then constructing the molecule from the known data by adding all pieces together, one at a time, via a series of binary rules. The method changes the way of evaluating the Sachs formula from a trial-and-error-type numerical search to a purely algebraic manipulation and thus tremendously reduces the computing times. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 19–36, 1997     

Comprehensive time-lag measurement as a diagnostic and analytical tool for non-Fickian transport studies: a salient porous barrier-gaseous permeant test case

Concentration-independent permeation of He, Ne and N2 through a porous barrier, specially constructed by multistep compaction of fine "Carbolac" carbon powder, has been studied. Emphasis was placed on measuring a variety of time lags, supplemented with transient permeation and sorption kinetics. Previous time-lag data, restricted to values of a single time-lag parameter, were instrumental in revealing deviations from Fick's law in similar solid barrier-penetrant systems; however, they could only provide indirect evidence as to the nature of the underlying causes, namely, time- or spatial dependence of the relevant transport parameters. Thus, an interpretation in terms of time-dependence (induced by the presence of blind pores) was proposed, predicated on calculations indicating that, in theory, spatial dependence (induced by non-uniform compaction) could be reduced to insignificance by adoption of a suitable multistep powder compaction technique. The comprehensive time-lag analysis approach applied here is a general diagnostic and analytical tool, previously successfully tested on graphite barriers, that can discriminate rigorously between the aforementioned non-Fickian functional dependences, as well as provide additional substantial information in either case. This capability is well illustrated by the results obtained in the system under study here, which provide unequivocal evidence of substantial spatial dependence. Furthermore, it is shown that the predicted functional form of the detected spatial dependence (i) can, in conjunction with an adequate physical model and with the results of a previous theoretical parametric study, account fully for all aspects of the observed non-Fickian time-lag behaviour and (ii) correlates satisfactorily with variation of local porosity across the barrier, detected by a suitable X-ray imaging technique. On the other hand, there is no evidence, from time lags or transient kinetics, of any significant time-dependence attributable to slow filling or emptying of blind pores or to other causes.     

A configurational temperature for molecules with hard-core or discontinuous interactions

We extend the usual formula for a configurational temperature so that it applies to condensates in which the molecules interact through hard-core or discontinuous potentials. The new formula involves extra terms which may be calculated during the course of a simulation. The formula is tested by its application to a number of systems with discontinuous or hard-core potentials in thermodynamic equilibrium. Metropolis Monte Carlo simulations were performed on these systems in a canonical ensemble and the configurational temperature is compared with the input temperature. The two are in agreement to within less than 0.1%.     

Some comments on nature of the structural relaxation and glass transition

We report on an experiment and new formula revealing dynamic and structural heterogeneity observed in liquids and polymeric systems. The formula applied to data obtained by mechanical spectroscopy reveals the glass-forming system behaviour giving the parameters previously postulated. The presented results are compared with data obtained for liquids (oligomers) confined to nanoporous media. To explain the behaviour of the polymeric systems the three-phase model is considered.     

Calculations of heat of solvation by a simple electrostatic approach to molecular interactions

An extremely simple formula to estimate the heat of formation of complexes between anion and a polar molecule or between highly polar systems is presented.The formula is entirelyelectrostatic and the expression used is verified by means of perturbation theory.This formula is test-ed for several ion-molecule and molecule-molecule pairs.It is also applied to estimate the heat ofhydration of simple salts.     

A general statistical test for correlations in a finite-length time series

The statistical properties of the autocorrelation function from a time series composed of independently and identically distributed stochastic variables has been studied. Analytical expressions for the autocorrelation function's variance have been derived. It has been found that two common ways of calculating the autocorrelation, moving-average and Fourier transform, exhibit different uncertainty characteristics. For periodic time series, the Fourier transform method is preferred because it gives smaller uncertainties that are uniform through all time lags. Based on these analytical results, a statistically robust method has been proposed to test the existence of correlations in a time series. The statistical test is verified by computer simulations and an application to single-molecule fluorescence spectroscopy is discussed.     

Three-dimensional Ewald method with correction term for a system periodic in one direction

A three-dimensional Ewald summation formula with a shape-dependent correction term for Coulomb interactions in systems with one-dimensional periodicity is derived. Test molecular dynamics simulations of acetone molecules in cylindrical silica pores show that the formula is efficient only when size of the system in a plane perpendicular to the periodicity direction is small in comparison with the periodicity length.     

三元系中两相区边界上活度之间的关系以及该关系与结线方位的依从性

本文研究了三元系中两相区边界上某组元的活度与三个组元的活度积φ之间的关系, 并导出了表示上述关系的重要公式, 该公式是一个将各种类型的三元系两相区的公式都概括进去的普遍式. 同时本文还详细地分析了结线的方位对活度之间关系的影响. 又应用了θ函数克服沿两相区边界上积分中的困难. 此外还完善了Krivsky和schuhmann规则。     

Dynamic NMR: A new intensity ratio for evaluation of lifetime in paripartite A ⇌ B systems

A simple formula for evaluation of rates of exchange in paripartite A ? B systems is introduced. It is concerned only with the intensity ratio in a two-site system in much the same way as that of Rogers and Woodbrey, but the new formula is also applicable above the coalescence point of the spectrum. The formula has been applied to the classical case of N,N-dimethyltrichloroacetamide. An error analysis demonstrates that the approximations inherent in the derivation of the new formula lead to smaller errors than do those of Rogers and Woodbrey.     

Dynamics of polymeric systems

Using dielectric and mechanical relaxation data of polymeric systems, an alternative formula is examined. The formula describes the experimental data with a high degree of accuracy, not received by the other model functions (Arrhenius and non-Arrhenius type) under investigation. The proposed formula gives the answer on questions concerning a supermolecular structure and the nature of the structural relaxation. New definition of the glass-transition temperature is proposed. It is shown how we should combine the results of different experimental methods to conduct an unambiguous analysis of polymeric systems.     

The error function for fitting of models to immittance data

In statistical calculations for fitting a model to experimental immittance data (admittance and/or impedance data) the key issue is the error function, which as a result of calculations should attain its minimum value ( ? 0). Different formulae for the error function, recently used in calculations, are analyzed and a new formula is proposed. The principal feature of the new formula is that for the admittance data and the impedance data the same results of calculations are obtained; this formula takes into account the possibility of correlation of errors of the two components of the immittance vector.The usefulness of the proposed formula is experimentally verified and demonstrated on immittance data measured for two actual systems.     

Metals and coordination compounds as modifiers for epoxy resins

This review concentrates on the use of metals in the formulation of epoxy resin systems and the effect that this has on the physical and mechanical properties of the polymer system. Epoxy resins are one of the most important higher performance polymer systems in use today, ranging from simple two-part adhesives and sports equipment to high-tech applications such as formula one racing cars and the aerospace industry. Epoxy resins are capable of undergoing homopolymerisation, although this process generally yields products with inadequate properties for high-tech applications. Consequently, in many cases catalysts, additives and co-curing-agents are formulated with the epoxy resin to significantly increase the storage stability, decrease the cure time and improve the final properties. The use of metals to formulate resin systems with excellent storage stability is discussed, along with the use of coordination compounds to improve cured resin properties such as fracture toughness, thermal stability and water absorption, etc.     

Zur Konjugation in makrocyclischen Bindungssystemen [1]

A simple formula (14) has been derived for the calculation of the perturbed first order orbitals, which is applicable to systems with degenerate unperturbed eigenvalues. With formula (14) it is possible to calculate second order energy-derivatives like chemical shifts or magnetic susceptibilities for systems with degenerate eigenvalues without any extrapolations. This formula has been applied to the calculation of ¹H-chemical shifts of Circumpolyacenes, which have degenerate HMO- and SCF-eigenvalues.

Wir danken der Deutschen Forschungsgemeinschaft für die Unterstützung dieser Arbeit und dem Rechenzentrum der Universität Heidelberg für die Gewährung von Rechenzeit auf der IBM 360/44 und IBM 360/67.     

A multiple time-gated system for pulsed digital gamma-ray spectroscopy

Neutron activation analysis (NAA) systems that use pulsed neutron generators (NGs) employ spectrum gating procedures to segregate nuclear processes by acquiring gamma-ray spectra separately when the generator is on (HIGH gate) and off (LOW gate). Often, the actual neutron burst lags the leading edge of the HIGH gate signal by a few μs. Thus, count rates vary not only between the on and off states of the NG, but within them as well. Recent advances in digital gamma-ray spectrometers that allowed the concurrent acquisition of data by sorting events into two separate spectra based on gate status suggested that a time-resolved analysis that further subdivided the neutron pulse cycle could obtain further information to separate gamma-rays produced by different nuclear reactions. In this paper we introduce a gating system for time-resolved NAA that is capable of concurrently acquiring as many as 16 spectra from up to 8 user-defined time intervals during each of the HIGH gate and LOW gate periods, each with all required timing and count rate information. We present the new gating system’s implementation, operation and some first experimental test results.     

An exact formulation of hyperdynamics simulations

We introduce a new formula for the acceleration weight factor in the hyperdynamics simulation method, the use of which correctly provides an exact simulation of the true dynamics of a system. This new form of hyperdynamics is valid and applicable where the transition state theory (TST) is applicable and also where the TST is not applicable. To illustrate this new formulation, we perform hyperdynamics simulations for four systems ranging from one degree of freedom to 591 degrees of freedom: (1) We first analyze free diffusion having one degree of freedom. This system does not have a transition state. The TST and the original form of hyperdynamics are not applicable. Using the new form of hyperdynamics, we compute mean square displacement for a range of time. The results obtained agree perfectly with the analytical formula. (2) Then we examine the classical Kramers escape rate problem. The rate computed is in perfect agreement with the Kramers formula over a broad range of temperature. (3) We also study another classical problem: Computing the rate of effusion out of a cubic box through a tiny hole. This problem does not involve an energy barrier. Thus, the original form of hyperdynamics excludes the possibility of using a nonzero bias and is inappropriate. However, with the new weight factor formula, our new form of hyperdynamics can be easily implemented and it produces the exact results. (4) To illustrate applicability to systems of many degrees of freedom, we analyze diffusion of an atom adsorbed on the (001) surface of an fcc crystal. The system is modeled by an atom on top of a slab of six atomic layers. Each layer has 49 atoms. With the bottom two layers of atoms fixed, this system has 591 degrees of freedom. With very modest computing effort, we are able to characterize its diffusion pathways in the exchange-with-the-substrate and hop-over-the-bridge mechanisms.     

中药色谱指纹图谱相似度计算中保留时间校正方法的研究

从保留时间校正方法对线性推移、非线性推移和时间延迟的校正效果方面探讨了保留时间校正方法的适用范围。认为一点法校正仅能校正线性推移;两点法可以校正时间延迟和线性推移,并能部分校正非线性推移。多点法使用分段线性逼近的方法对非线性推移有良好的校正效果。     

Statistical representation of atomic systems structure. II. classification of the representation; entropy dependence of the total energy for isoelectronic series

The energies of the ground states of the mononuclear atomic systems, until now determined merely by approximate methods, turn out to exhibit some almost exact interdependencies. A simple statistical functional of the electronic structure (the “γ representation”) turns out to be decisive for the system energy. In this paper that interdependence is further traced for the N-electron systems in isoelectronic series (with constant N and varying Z). The resulting “combinatorial formula” reproduces the experimental data with the errors at least ten times smaller than those of the conventional Hartree–Fock approximation. The reason why there is such an exact formula for the ground-state energy remains to be clarified. The limiting behavior of our energy formula for large Z exhibits consistency with the Thomas–Fermi and the Z^?1perturbation expansion models.