THE MINOR INFLUENCE OF CALCIUM DOPED PHOSPHATE TUNGSTEN BRONZE ON THE BRIGGS-RAUSCHER REACTION DYNAMICS

The Briggs-Rauscher (BR) oscillatory reaction is the oxidation of malonic acid in the presence of hydrogen peroxide and iodate in the acidic environment, which is catalyzed by ions of manganese. This reaction is very sensitive to the presence of additives. In this paper, the BR reaction has been used to investigate the phosphate tungsten bronze as well as calcium doped tungsten bronze, obtained by thermal treatment. The addition (0.01-0.08 g) of phosphate tungsten bronze and calcium doped phosphate tungsten bronze has a different effect on the dynamics of the Briggs-Rauscher reaction. In the case of the addition of phosphate tungsten bronze in the Briggs-Rauscher reaction, the linear dependence of the length of the oscillatory period on the mass of the added bronze was obtained, while in the case of addition of calcium doped phosphate tungsten bronze, the oscillatory period does not significantly change with an increase of added mass. The mechanism of calcium doped and undoped phosphate tungsten bronze action in BR reaction is probably adsorptive, and it will be the subject of future work. Keywords: oscillatory reactions, Briggs-Rauscher reaction, phosphate tungsten bronze, calcium doped phosphate tungsten bronze, thermal treatment.

Oscillatory reaction as a system detector for doped and undoped phosphate tungsten bronzes

Phosphate tungsten bronzes, obtained by thermal treatment, are insufficiently investigated bronzes and there is scarce literature data on their chemical behavior and structure. Due to high-sensitivity of the Briggs-Rauscher (BR) reaction to addition of different analytes, this oscillatory reaction presents a potentially important chemical system for investigation and characterization of phosphate-tungsten bronzes, doped and undoped. The reaction mixture for the oscillatory BR reaction typically consists of H2O2, HClO4, KIO3, Mn(II) (catalyst), and CH2(COOH)2 (malonic acid, as an organic substrate). This paper deals with phosphate tungsten bronzes (PWB) and lithium doped phosphate tungsten bronzes (LiPWB) and their effects on the Briggs-Rauscher reaction dynamics. It is shown that the addition of phosphate tungsten bronzes decreases the oscillatory period length in this reaction. Furthermore, the obtained results show that PWB has a stronger influence on the BR reaction dynamics then LiPWB. In both cases, the oscillatory period is a linear function of the added bronze mass. The obtained linear functions can be successfully used for determination of the unknown bronze mass. Furthermore, due to different slopes of these functions, the Briggs-Rauscher reaction can be used as a system-detector for lithium doped and undoped phosphate tungsten bronzes. In order to elucidate the mechanism of bronze action, the inductively coupled plasma optical emission spectrometry (ICP-OES) was used to measure the total contents of K, Mn, W, Li. The aliquots of the above solution (i.e. CH2(COOH)2, MnSO4, HClO4, KIO3 but without H2O2) with the identical masses of PWB and LiPWB were examined. For the sake of comparison, contents of the metals in the solution without the bronze addition were measured, as well. Results obtained by the ICP-OES analysis show that the bronze structure is disturbed in the strong oxidizing environment (iodate in acidic solution) so that both, tungsten and lithium, leach into the BR solution. Accordingly, the proposed mechanism of the bronze action is probably by the reaction of tungsten ion with hydrogen-peroxide resulting in formation of a tungsten-peroxo complex. This complex is a stronger oxidizing agent then hydrogen peroxide itself. Thus, formation of the tungsten-peroxo complex potentially affects the kinetics of the Briggs-Rauscher reaction.

Asymptotic trends in time-varying oscillatory period for a dual-staged torsional system

The primary goal of this article is to propose a new analysis tool that estimates the asymptotic trends in the time-varying oscillatory period of a non-linear mechanical system. The scope is limited to the step-response of a torsional oscillator containing a dry friction element and dual-staged spring. Prior work on the stochastic linearization techniques is extended and modified for application in time domain. Subsequently, an instantaneous expected value operator and the concept of instantaneous effective stiffness are proposed. The non-linear system is approximated at some instant during the step-response by a linear time-invariant mechanical system that utilizes the instantaneous effective stiffness concept. The oscillatory period of the non-linear step-response at that instant is then approximated by the natural period of the corresponding linear system. The proposed method is rigorously illustrated via two computational example cases (a near backlash and near pre-load non-linearities), and the necessary digital signal processing parameters for time domain analysis are investigated. Finally, the feasibility and applicability of the proposed method is demonstrated by estimating the softening and hardening trends in the time-varying oscillatory period of the measured response for two laboratory experiments that contain clearance elements and multi-staged torsional springs.

An FPGA-Integrated Time-to-Digital Converter Based on a Ring Oscillator for Programmable Delay Line Resolution Measurement

We describe the architecture of a time-to-digital converter (TDC), specially intended to measure the delay resolution of a programmable delay line (PDL). The configuration, which consists of a ring oscillator, a frequency divider (FD), and a period measurement circuit (PMC), is implemented in a field programmable gate array (FPGA) device. The ring oscillator realized in loop containing a PDL and a look-up table (LUT) generates periodic oscillatory pulses. The FD amplifies the oscillatory period from nanosecond range to microsecond range. The time-to-digital conversion is based on counting the number of clock cycles between two consecutive pulses of the FD by the PMC. Experiments have been conducted to verify the performance of the TDC. The achieved relative errors for four PDLs are within 0.50%–1.21% and the TDC has an equivalent resolution of about 0.4 ps.

Activation energies as the validity criterion of a model for complex reactions that can be in oscillatory states

Modeling of any complex reaction system is a difficult task. If the system under examination can be in various oscillatory dynamic states, the apparent activation energies corresponding to different pathways may be of crucial importance for this purpose. In that case the activation energies can be determined by means of the main characteristics of an oscillatory process such as pre-oscillatory period, duration of the oscillatory period, the period from the beginning of the process to the end of the last oscillation, number of oscillations and others. All is illustrated on the Bray-Liebhafsky oscillatory reaction.

Effects of Chloride and Bromide Ions on Sequential Oscillations in the Uncatalyzed Bromate Oscillator

The uncatalyzed system BrO3--phenol-H2SO4 exhibits an astonishing variety of dynamic behaviour, including sequential oscillations in a closed, stirred batch reactor. The effect of initial addition of chloride and bromide ions on a sequential oscillating system has been studied. Various results were obtained, depending on the initial chloride and bromide concentrations. Increasing the concentration of chloride ions (from 5 × 10-5 to 6 × 10-4 mol dm-3), the parameters of sequential oscillations changed. The number of first oscillations increased from 4 to 21 and their amplitude decreased. The duration of the non-oscillatory period and the number of second oscillations decreased from 96 to 26 min and from 8 to 1, respectively. In the concentration range 3.5 mmol dm-3 < [Br-]o < 8.0 mmol dm-3, the system displays a dual-frequency, dual-amplitude and aperiodic oscillations with a transition period between high- and low-frequency oscillations. The induced oscillations were also observed when the system was perturbed by chloride or bromide ions. The oxidation of pyrocatechol with bromate is an autocatalytic reaction; the rate constants corresponding to the uncatalyzed and catalyzed reactions were evaluated and used in numerical simulations.

Improvement of Nonrigid-Earth Nutation Theory by Adding a Model Free Core Nutation Term

From the analysis of VLBI observational data compiled by USNO (U.S. Naval Observatory) from MJD 44089.994 to 51618.250 (McCarthy, 2000), we showed that a strong peak around –400 sidereal days in the spectrum of its differences from the IERS96 nutation theory could be explained by adding a model Free Core Nutation (FCN) term in the form of a single damped oscillation. Then we developed a new analytical theory of the nonrigid-Earth nutation including the derived FCN model. We adopted RDAN98 (Roosbeek and Dehant, 1998) as the rigid Earth nutation theory. It was convolved with a transfer function using numerical convolution in the time domain (Shirai and Fukushima, 2000). The form of the transfer function was the same as that of Herring (1995). However, its free parameters such as the complex amplitude and frequency of the FCN were readjusted by fitting to the above VLBI data. Even after truncating the forced nutation series so as to contain only 180 terms, the WRMS (Weighted Root Mean Square) of the complex residuals for the new nutation series is 0.312 mas, which is significantly smaller than 0.325 mas, that of the IERS96 nutation theory. As for the FCN term, we estimated its oscillatory period as –430.8±0.6 sidereal days, and its Q-value as 16200 ± 1600. Also we estimated the correction of the precession constants as −0.29297±0.00047”/cy in longitude and −0.02430±0.00019”/cy in obliquity, respectively.