General Order Kinetics Equation Research Articles

Studies on luminescence properties and photo-thermo transfer phenomena in fluorapatite

This study reports the structure, composition, photoluminescence (PL), thermoluminescence (TL), and optically stimulated luminescence (OSL) properties of the Brazilian natural fluorapatite. Also, the existence of photo-thermo transfer phenomena is investigated from TL/OSL emission mechanisms. X-ray diffraction (XRD) pattern reveals that the sample has a hexagonal system with a crystallite size of about 46 nm calculated using the Scherrer formula. The presence of several elements including the rare earths such as Ce, Nd, and Er are identified using total X-ray fluorescence (TXRF) spectroscopy results. Ce3+ ions are associated with the emission band at 371 nm when excited at 300 nm. Fluorapatite exhibits intense TL and OSL signals when irradiated with beta particles and shows linear dose-response from 1 up to 50 Gy. The TL glow curves are deconvoluted to six peaks centered at 99, 147, 188, 242, 329, and 431 °C using general order kinetic equation. The corresponding activation energies vary between 0.68 and 1.11 eV. An anomalous fading is noticed for the first TL peak, which decays completely in 6 h; the second TL glow peak decays about 59% within 12 h and other high temperature peaks are more stable. Continuous-wave OSL (CW-OSL) is constituted of three components, having decay times (τ) of 0.39, 5, and 64 s. The deconvoluted linearly modulated OSL (LM-OSL) has four peaks, with peak maxima (tm) at 2.85, 7.4, 27, and 130 s. Further, it is noticed the phenomenon of phototransferred TL (PTTL) at 30 °C, due to the optical transfer of electrons related to the traps of 329 and 431 °C peaks to the main peak at 242 °C. The temperature-induced PTTL using thermally assisted OSL (TA-OSL) at 170 °C with 400 s of blue stimulation depicted a transfer of trapped electrons from very deep traps (VDTs), located at temperatures higher than 500 °C, to the main peak. Here, the luminescence intensity increases with the beta dose.

Influence of scatter data and temperature lag on the analysis of thermoluminescence glow peak: A Monte Carlo simulation study

The effects of the scattering data that might appear at the low radiation doses and the temperature lag that might occur between the heater pan and the detector on the thermoluminescence (TL) glow-curve have been addressed. The scattering data were mathematically induced in the TL glow curve using the Monte Carlo (MC) algorithm. While the phenomenon of the temperature lag has been simulated, assuming an exponential function. The deconvolution analysis has been carried out by TL expressions based on a presumed kinetics order value in comparison with the general-order kinetics equation. It has been found that even though the glow peak is known to obey the first- or second-order kinetics model, using the general-order kinetics equation in the deconvolution analysis is better than using the corresponding model equation.

Determination of Thermoluminescence Kinetic Parameters of La2O3 Doped with Dy3+ and Eu3.

Thermoluminescence (TL) properties of La2O3: Dy3+, Li+, and La2O3: Eu3+, Li+, exposed to 5.12 Gy of beta radiation, and recorded at different heating rates 0.5, 1, 2, 3, 4, and 5 °C s−1 (from Molefe et al., paper 2019), were analyzed and the trap parameters were determined in this study. These parameters include the order of kinetics b, the activation energy E (eV), the frequency factor S (s−1), or the pre-exponential factor S″ (s−1), and the initial concentration of trapped electrons no (cm−3). A new non-linear curve fitting technique, based on the general order kinetic equation and the outcomes of Hoogenstraaten’s Method, was established and applied on the TL glow peaks of La2O3: Dy3+, Li+. The fitting technique was evaluated by calculating the R-square and figure of merit (FOM) values. The results revealed that the FOM values are <1%, and the R-square values are >0.997, which demonstrates an excellent convergence between experimental and fitted curves. A modified technique based on the three-points analysis method was exploited to deconvolute complex TL glow curves of La2O3: Eu3+, Li+, and in turn, to determine the trap parameters the method disclosed that each TL glow curve consists of four peaks. The trap parameters of the individual peaks were numerically determined. The fading, as a function of storage temperature and time, from the TL signals of the investigated materials was predicted and discussed based on the calculated trap parameters. The results support the value of the materials for employment in radiation dosimeter applications with a low fading fraction.

Structural and luminescence properties of Y2O3:Eu3+red phosphor by incorporation of Ga3+ and Bi3+ions

The cationic substitution of Y3+simultaneously with Bi3+/Ga3+ ions on the crystal structure of the Y2O3:Eu3+ phosphor and its effect on the structure, the luminescence and thermoluminescence properties was investigated. Four samples were prepared by using a sol-gel combustion method. The substitution of Bi3+/Ga3+ ions modified the Y2O3:Eu3+ phosphor structure, which showed a transition phase structure. In addition, the presence of Bi3+/Ga3+ ions simultaneously in the Y2O3:Eu3+ phosphor structure affected the optical properties. The excitation at 305 nm gave the characteristic emission peaks of the Eu3+ ions with a remarkable increase in the intensity of the peak at 628 nm compare to the same peak that was excited using the Bi3+excitation at 330 nm. The Judd-Ofelt theory was used to estimate the photometric parameters. The TL glow curves of UV-irradiated samples showed a low temperature peak at about 402 K and a high temperature peak at 543 K. A significantly change in the TL intensities for the different dopants in the Y2O3 was observed. The TL kinetics parameters were calculated by a deconvolution computer fitting program using the general order kinetic equation. Different dopants in the Y2O3 was observed with defect levels ranging from 0.8 to 1.8 eV.

A study on thermoluminescence behaviour of Eu doped LaB3O6 irradiated with beta particles

Lantanium triborate (LaB3O6) samples doped with Eu3+ ions are synthesized via combustion route. This study primarily reports the thermoluminescence (TL) behaviour of LaB3O6 host. X-ray diffraction (XRD) pattern reveals that LaB3O6 exhibits a single phase matched with JCPDS card 98-002-3609. Dose response, reusability and trap parameters of TL glow curves are evaluated to clearly reveal the TL features. The results show that the peak positions of TL glow curves are affected by varying the concentration of Eu. The experimental results obtained from the dose-response of LaB3O6:Eu3+ (1%) which has given high TL intensity reveal that the intensity of TL given by the total area under glow curves shows a good linearity (b= 0.997) up to 20 Gy. In addition, the minimum detectable dose (MDD) value has been calculated as 1.45 mGy with a standard deviation of 0.8%. Main TL peak maxima is observed around 197 °C with heating rate (HR) of 2 °Cs−1. An anomalous HR effect is observed for this peak in the range of 0.5–20 °Cs−1 with beta dose of 5 Gy. To find the overlapping peak numbers and determine the kinetic parameters of the main peak of LaB3O6:Eu3+ (1%), Initial Rise (IR) method using Tm−Tstop experiment and CGCD analysis have been performed for HRs of 0.5 and 2 °Cs−1. It can be said that the results of the methods are in good agreement when same trap numbers (at least eight separate peaks for both) and close energy values are taken into consideration. Deconvolution procedure of LaB3O6: Eu3+(1%) is performed using general order kinetic equation by R studio ‘tgcd’. Additionally, the lifetimes of each deconvolved peaks by CGCD of Eu activated LaB3O6 (1%) have been calculated. Based on the results it can be put forth that TL characteristics of Eu doped LaB3O6 can be used as a promising material for thermoluminescence dosimetry-environmental applications.

Enhanced dyes adsorption from wastewater via Fe3O4 nanoparticles functionalized activated carbon.

Fe3O4 nanoparticles functionalized activated carbon (Fe3O4/AC) as an adsorbent was prepared and used for fast and effectively removing rhodamine B (RhB) and methyl orange (MO) from aqueous solution. Its physical and chemical properties characterized indicate that the adsorbent possesses abundant surface functional groups, sensitive magnetic response and enhanced specific surface area. Batch experiments were carried out to investigate the adsorption capacity and mechanisms. The obtained experimental data fitted well with the general-order kinetic equation and Liu's isotherm model with a maximum adsorption capacity of 182.48 mg g-1 for RhB and 150.35 mg g-1 for MO, respectively. The thermodynamic parameter was analyzed further and it showed an exothermic and spontaneous adsorption process. This composite with high adsorption efficiency and rapid magnetic separation can be a promising and recyclable adsorbent for practical wastewater treatment and purification processes.

Glow curve analysis of glassy system dosimeter subjected to photon and electron irradiations

Abstract The current paper illustrates glow curve analysis of newly developed Borate glass dosimeters. A series of dosimetric properties including dose response for photons and electrons, energy response, optical fading, and precision were determined. Glow curve deconvolution based on the general order kinetics equation was applied to extract the trapping parameters. Excellent fitting was obtained with the superposition of three-second order glow peaks. The quality of fitting was monitored through the r2 value which is always in excess of 0.9998. Thermoluminescence (TL) measurements showed that the material exhibits good linear dose–response over the delivered range of absorbed dose from 0.5 to 4 Gy for photons and electrons irradiation with low energy dependence. The material exhibits large signal loss when exposed to direct sunlight and moderate signal loss when exposed to fluorescent light. Therefore, it is recommended to use the current dosimeters indoor and to avoid prolonged direct exposure to fluorescent light. This combination of properties makes the material suitable for radiation dosimetry.

Comments on ‘Derivation of general order kinetics equation using probability theory by Longjam Lovedy Singh’

ABSTRACTComments on “Derivation of general order kinetics equation using probability theory by Longjam Lovedy Singh” regarding its limitations are described. It has been found that the value of η or α (ratio of An/Am) need not be ≤1 and the use of α(N−n) for estimating empty trap population will lead to wrong estimation of the concentration/population of empty traps, i.e., <N for α < 1 and >N for α > 1 even when n = 0.

Reply to the comments of Munish Kumar of “Derivation of general order kinetics equation using probability theory by Longjam Lovedy”

ABSTRACTA reply to the Munish Kumar's comments on “Derivation of general order kinetics equation using probability theory by Longjam Lovedy Singh” is presented hereby. The conceptual error made by Munish Kumar regarding his in ability to define the range of or (ratio of ) has been clarified, and it is shown why the value of or must be and not as suggested by him. Lastly, the conceptual error made by Munish Kumar regarding his inability to differentiate between N and has also been clarified.

Derivation of general order kinetics equation using probability theory

ABSTRACTIn this paper the general order kinetics (GOK) equation has been derived using the probability theory. The advantage of using the probability theory to derive the GOK equation is that it does not require the quasiequilibrium equation. Secondly, it helps in determining the range of α, which is , and lastly it helps in finding the mathematical error of the May and Partridge GOK equation.

Adsorption of anti-inflammatory nimesulide by graphene materials: a combined theoretical and experimental study.

Interactions of anti-inflammatory nimesulide (NM) with different graphene material species were explored employing both ab initio calculations, based on Density Functional Theory (DFT), and a batch adsorption process. The adsorption of NM onto graphene, with and without a vacancy, reduced graphene oxide (rGO) and functionalized graphene nanoribbons was simulated, providing a good understanding of the adsorption process of the NM molecule onto graphene material surfaces. The theoretical results indicate a physisorption interaction between NM and all of the evaluated adsorbents. Based on batch adsorption experiments, it was found that rGO, obtained via a modified Hummers method, is a good nanoadsorbent for the removal of the anti-inflammatory NM from aqueous solutions. The general-order kinetic equation displays the best fit to the experimental data compared with pseudo-first order and pseudo-second order kinetics. The equilibrium data fitted well into the Liu isotherm equation, and the maximum sorption capacity for the adsorption of NM by rGO was 82.4 mg g-1 at 25 °C. Our results of the first principle calculations and the batch adsorption experiments point out that graphene materials are promising nanomaterials for extracting NM from aqueous solutions.

Adsorption of Alizarin Red S Dye by Carbon Nanotubes: An Experimental and Theoretical Investigation

This study evaluated the feasibility of removing Alizarin Red S dye (ARS) from aqueous solutions, using nanoadsorbents such as single and multiwalled carbon nanotubes (SWCNT and MWCNT, respectively). The effect of pH, shaking time, and temperature on adsorption was studied. The pH 2.0 was observed to show optimum removal for both of the carbon nanotubes. The equilibrium time (298–318 K) was fixed at 65 and 100 min for SWCNT and MWCNT, respectively. The kinetics of adsorption was calculated using pseudo-first-order, pseudo-second-order, and general-order equations. The calculations revealed that the general-order kinetic equation best-fit the adsorption data. The Liu isotherm model best fit the equilibrium data (298–318 K). The maximum sorption capacity at 318 K for ARS dye was 312.5 and 135.2 mg g–1 for SWCNT and MWCNT, respectively. Change in entropy (ΔS°), Gibb’s free energy change (ΔG°), and enthalpy (ΔH°) were calculated for the adsorption of ARS dye. The electrostatic interaction between nanoadsorben...

Effect of 100 MeV swift Si8+ ions on structural and thermoluminescence properties of Y2O3:Dy3+nanophosphor

ABSTRACTNanoparticles of Y2O3:Dy3+ were prepared by the solution combustion method. The X-ray diffraction pattern of the 900°C annealed sample shows a cubic structure and the average crystallite size was found to be 31.49 nm. The field emission scanning electron microscopy image of the 900°C annealed sample shows well-separated spherical shape particles and the average particle size is found to be in a range 40 nm. Pellets of Y2O3:Dy3+ were irradiated with 100 MeV swift Si8+ ions for the fluence range of 3 × 1011_3 × 1013 ions cm−2. Pristine Y2O3:Dy3+ shows seven Raman modes with peaks at 129, 160, 330, 376, 434, 467 and 590 cm−1. The intensity of these modes decreases with an increase in ion fluence. A well-resolved thermoluminescence glow with peaks at ∼414 K (Tm1) and ∼614 K (Tm2) were observed in Si8+ ion-irradiated samples. It is found that glow peak intensity at 414 K increases with an increase in the dopant concentration up to 0.6 mol% and then decreases with an increase in dopant concentration. The high-temperature glow peak (614 K) intensity linearly increases with an increase in ion fluence. The broad TL glow curves were deconvoluted using the glow curve deconvoluted method and kinetic parameters were calculated using the general order kinetic equation.

Variables and potential models for the bleaching of luminescence signals in fluvial environments

Luminescence dating of fluvial sediments rests on the assumption that sufficient sunlight is available to remove a previously obtained signal in a process deemed bleaching. However, luminescence signals obtained from sediment in the active channels of rivers often contain residual signals. This paper explores and attempts to build theoretical models for the bleaching of luminescence signals in fluvial settings. We present two models, one for sediment transported in an episodic manner, such as flood-driven washes in arid environments, and one for sediment transported in a continuous manner, such as in large continental scale rivers. The episodic flow model assumes that the majority of sediment is bleached while exposed to sunlight at the near surface between flood events and predicts a power-law decay in luminescence signal with downstream transport distance. The continuous flow model is developed by combining the Beer–Lambert law for the attenuation of light through a water column with a general-order kinetics equation to produce an equation with the form of a double negative exponential. The inflection point of this equation is compared with the sediment concentration from a Rouse profile to derive a non-dimensional number capable of assessing the likely extent of bleaching for a given set of luminescence and fluvial parameters. Although these models are theoretically based and not yet necessarily applicable to real-world fluvial systems, we introduce these ideas to stimulate discussion and encourage the development of comprehensive bleaching models with predictive power.

Determining fluvial sediment virtual velocity on the Mojave River using K-feldspar IRSL: Initial assessment

The Mojave River of Southern California was chosen as a field site to investigate the applicability of luminescence dating to sediment transport rate problems. Grains in the active channel of the river are expected to show signs of partial bleaching and this makes it difficult to determine time since deposition accurately. A modification of the multiple elevated temperature post-IR IRSL (METpIRIR) procedure, (Buylaert et al., 2009; Li and Li, 2011), was used for K-feldspar grains (175–200 μm) at temperature increments of 50, 95, 140, 185, and 230 °C in order to provide more information about relative signal bleaching among samples. The measurements show an exponential decrease in equivalent dose (De) with distance down the Mojave River. Higher temperature pIRIR signals are bleached more slowly than lower temperature ones (Buylaert et al., 2009). The De for samples at 50 °C is roughly constant along the river. These results suggest cyclical bleaching and burial as grains are transported downriver and higher energy (deeper) traps are vacated. The pattern of De values for the Mojave River can be used to constrain the sediment transport rate for this river by building a model of growth and bleach for each temperature increment. A bleaching experiment was run with multiple aliquot samples for direct sunlight exposure times of 0, 10, 30, 300, 1000, 3000, 10,000, and 30,000 s. The MET-pIRIR procedure was applied at each temperature increment for each exposure time aliquot and the results for all exposure times were fit to the general order kinetics equation using a non-linear regression. The bleaching parameters were used in conjunction with the SAR growth curves to build a model of partial bleaching of grains during transport that is fitted with a χ2 test to the pIRIR data from the Mojave River. This model is not a unique solution, but can be used to assess the likelihood of various sediment transport regimes.

Test of the accuracy of the computerized glow curve deconvolution algorithm for the analysis of thermoluminescence glow curves

The accuracy of the thermoluminescence (TL) kinetics parameters obtained using the computerized glow curve deconvolution (CGCD) algorithm was tested. The differential equation governing the electron traffic in the one trap–one recombination (OTOR) level model was solved with almost no approximation using the Fehlberg–Runge–Kutta method. A set of simulated glow peaks was generated for a wide range of kinetics parameter values. These glow peaks were then fitted using the general-order kinetics equation. Comparisons between the kinetics parameter values of the simulated glow peaks and those obtained by the CGCD method were made. The results show that the accuracy of the different kinetics parameters obtained by the CGCD method is not the same and that it varies according to the value of the kinetics order (b). The overlapping of two glow peaks with very close maximum peak positions (Tms) results in a glow peak with unexpected values for the kinetics parameters. A set of different cases of overlapping glow peaks is also discussed.

Glow curve analysis of TLD-100H irradiated with radiation of different LET: Comparison between two theoretical method

In the present paper we show the result of study on the thermoluminescent signal of LiF:Mg,Cu,P (TLD-100H) after irradiation with beams of different LET (photons, electrons and protons). Through the analysis of the glow curve it is possible to obtain information on the LET of the radiation beam. To perform this analysis we have deconvoluted the glow curves adopting general order kinetic equation for the description of the peak shape. In addition a numerical simulation has been performed to find a connection among the physical parameters of the model (OTOR) and the parameters of the empirical expression used in the analysis of the experimental data (GOK). The methodology indicate that the kinetic order b of the glow peak depends on the LET.

The effect of the heating rate on the characteristics of some experimental thermoluminescence glow curves

The present work illustrates the effect of the different heating rates on the intensity and peak area of thermoluminescence (TL) glow peaks. In this work, we suggest that the kinetic equations for the TL intensity in their time-dependent forms I(t) are not adequate for comparison with experimental results I(t), where the TL is recorded versus temperature. The present work suggests that in the case of TL experiments, the first-order kinetics equation, I(t) = −dn/dt = nS exp(−E/kT), as well as the second- and general-order kinetics equation should be replaced by I(T) = −dn/dT = (nS/β) exp(−E/kT), and a similar change should be made in the second- and general-order case. Also, the present work distinguishes between the decrease in the intensity and the stability of the area of TL glow peaks as a result of increasing heating rates and the decrease in both the intensity and area of TL glow peaks as a result of thermal quenching with increasing heating rates. The present work illustrates the effect of changing the heating rate on the characterization of experimental glow curves of BeO (thermalox) for different heating rates.

Thermoluminescence characteristics and dose responses in MgSO4:Dy, P and MgSO4:Dy, P, Cu phosphors

The MgSO4:Dy, P and MgSO4:Dy, P, Cu phosphors have been developed and studied by the thermoluminescence (TL) glow curves and dose responses to gamma radiation. The TL sensitivity of MgSO4:Dy, P phosphor is higher than that of LiF:Mg, Ti. One main dosimetric peak at about 283.6 °C and a satellite peak at about 352.7 °C are involved in the TL glow curve of the MgSO4:Dy, P which was measured with a heating rate of 5 °C s-1 and deconvoluted by the general order kinetics equation to obtain the peak parameters and trap parameters of the elementary TL peaks. The dose responses to gamma rays in the dose range from 0.1 Gy to 20 kGy were obtained and fitted by the composite action dose response function to get the nonlinear characteristic parameters, one-hit factor R and characteristic dose D0, which indicate that the TL dose responses for the two peaks of MgSO4:Dy, P are supralinear. When a trace amount of Cu was co-doped into MgSO4:Dy, P the TL glow peak at 352.7 °C was suppressed and the TL sensitivity and the nonlinearity of dose response for the main dosimetric peak at 283.6 °C critically depends on the concentration of doped Cu. The dose response of MgSO4:Dy, P, Cu (0.1 mol%, 0.5 mol%, 0.01 mol%) phosphor is linear-sublinear. The MgSO4:Dy, P, Cu (0.1 mol%, 0.5 mol%, 0.004 mol%) phosphor has a wider linear range in the dose response than MgSO4:Dy, P (0.1 mol%, 0.5 mol%) and its TL sensitivity is close to MgSO4:Dy, P (0.1 mol%, 0.5 mol%). It may be a candidate with which to measure radiation dose under higher dose circumstances.

Improvement upon our previous method for auto-separating thermally stimulated current curves

In this paper we have introduced the following improvement on our previous method for auto-separating thermally stimulated current (TSC), namely, both the general-order kinetic equation of a thermally stimulated process (TSP) and the real peak found by calculating the activation energy varying with the increment of peak temperature are used to replace the first-order kinetic equation and the peak point obtained from the experimental TSC curve, respectively. Using this method we have separated successfully the experimental TSC curve of polyimide film, and found that this complex curve is composed of six sub-curves in the temperature range 250-500 K, one of which obeys second-order kinetics. Moreover, by comparing the parameters obtained with the cleaning peak method and our improved method it can be confirmed that the latter is very effective. As a result we believe that this improved method is more reasonable, and describes the real physical processes in a polymer much better than before.