Beer-Lambert Equation Research Articles

An FT-IR and DFT based new approach for the detection of tautomer proportions in solution

Tautomer proportions of acetylacetone (acac) in six different solvents are investigated with a new method by means of experimental absorptions (A) and theoretical absorption coefficients (ε). The specific absorption bands (key bands) for keto and enol tautomers were obtained from recorded FT-IR spectra in related solution at room temperature. The molar absorption coefficients for key bands of both keto and enol tautomers were calculated, which is impossible to obtain with experimental methods for individual isomers in equilibrium. The Lambert–Beer equation is used to detect tautomer proportions. The obtained results are in consistence with literature. The most stable enol tautomer is found to be (86%) in CCl4 and the keto tautomer is found to be most stable in DMSO (48%).

The Optimal Attachment Position for a Fingertip Photoplethysmographic Sensor With Low DC

In this study, optimal position was approached by a search of a low-DC drift sensor attachment position for measuring photoplethysmography. DC and AC models were proposed by merging the Lambert-Beer equations at the conventional PPG onset and the peak into one equation. The position at which point the DC fluctuation is small and the AC component is large in the PPG was suggested. Among the lateral sides of four blood vessels, the dorsal, palmer, ulnar, and radial vessels region, the ulnar vessel region showed small DC amplitude and the largest AC amplitude and perfusion index.

Analysis of gypsum ore conversion with aid of gamma-ray transmission and CCRD

Nowadays, except for very few imported furnaces, the monitoring of the conversion of the produced plaster at the Pole Plaster of Araripe is not done with aid of online techniques. This research work shows a simulation of operational conditions with an online meter of chemically combined water in plaster, by means of Central Composite Rotatable Designs (CCRD) and nuclear technique of gamma-ray transmission. In the family of central composite rotatable designs, the CCRD is more efficient than the others, regarding uniformity of variances of the points at the same distance from the center of the design. This process is a simulation of operational conditions with an online meter of the chemically combined water in plaster, by means of gamma radiation transmission technique. Such determination can be achieved by the effect caused by the variation of the mass attenuation coefficient of the partially dehydrated material. An Americium-241 gamma source (60 keV) was simulated in the implementation of the Beer–Lambert equation. The nuclear data required for simulation were obtained from XMuDat software, available from the site of the International Atomic Energy Agency. A program in Matlab programming language has demonstrated the possibility of monitoring at all stages of the dehydration process, with measurements of the specific mass of the sample having an estimated error of the order of 1%. To verify the operating conditions suitable for the process, experiments were simulated using a CCRD. The independent variables were the sample thickness and the amount of chemically combined water in plaster. Optimal conditions of the process were determined, which allowed the derivation of a model represented by response surface of the gypsum conversion.

Relations between ac-dc components and optical path length in photoplethysmography

Photoplethysmography is used in various areas such as vital sign measurement, vascular characteristics analysis, and autonomic nervous system assessment. Photoplethysmographic signals are composed of ac and dc, but it is difficult to find research about the interaction of photoplethysmographic components. This study suggested a model equation combining two Lambert-Beer equations at the onset and peak points of photoplethysmography to evaluate ac characteristics, and verified the model equation through simulation and experiment. In the suggested equation, ac was dependent on dc and optical path length. In the simulation, dc was inversely proportionate to ac sensitivity (slope), and ac and optical path length were proportionate. When dc increased from 10% to 90%, stabilized ac decreased from 1 to 0.89 ± 0.21, and when optical path length increased from 10% to 90%, stabilized ac increased from 1 to 1.53 ± 0.40.

Research on the Photography Measurement of the Optical Parameters of the Vegetable Tissues

To measure the optical parameters of biological tissue, the laser imaging system of the diffusing reflection and the transmission measurements based on CCD was designed. The absorption coefficient (μa) and the reduced scattering coefficient (μ's) of the biological tissue simulating liquid (Intralipid-20% diluents) were derived from nonlinear regression of the diffusion equation with spatially resolved steady-state diffuse reflectance which was measured by CCD. At the same time, the reduced scattering coefficient (μ's) of the biological tissue simulating liquid (Intralipid-20% diluents) was also derived from linear regression of the Beer-Lambert equation with transmission light intensity of the biological tissue simulating liquid (Intralipid-20% diluents) which was measured by CCD for the different titer, which is used as the calibration of the non-invasively method. The optical parameters of the same sample measured by CCD diffusing reflection and transmission measurements were compared. The results of the two methods were approximately consistent. Furthermore, the optical parameters of Eggplant and Murphy were measured by CCD diffusing reflection measurements. So the technique of laser scattering imaging analysis is useful for measuring the optical properties of the vegetable tissues.

Excimer laser ablation of single crystal 4H-SiC and 6H-SiC wafers

A 248 nm, 23 ns pulsed excimer laser was used to compare the ablation characteristics of single crystal wafers of the polytypes 4H-SiC and 6H-SiC over a wide range of energy fluence (0.8–25 J cm−2). Photothermal models based on Beer–Lambert equation using thermal diffusivity and absorption coefficient, energy balance, and heat transfer were presented to predict the ablation mechanisms. Micromachining of trenches was demonstrated at 7 J cm−2 to demonstrate the potential of UV laser ablation. Results indicate that the ablation process is characterized by two well-defined threshold fluences: (a) decomposition threshold ~1 J cm−2 and (b) melting threshold ~1.5 J cm−2 for both polytypes. Contrary to the modeling expectations, the ablation rates were lower and did not increase rapidly with energy fluence. Four types of ablation mechanisms—chemical decomposition, vaporization, explosive boiling, and plasma shielding—either singly or in combination occur as a function of energy fluence. The predictions of photothermal models were not in good agreement with the experimental data implying that a complex interplay among various physical phenomena occurs during ablation. Micromachined trench exhibited ripple patterns, microcracks and recast layers, most of which could be eliminated by a subsequent chemical cleaning process. It is concluded that excimer laser ablation is an effective but slow material removal process for SiC wafers compared to other lasers such as 1064 nm Nd:YAG.

Influence of Dye Concentration on Display Characteristic in Wax-Base Electrophoretic Rewritable Media

Wax-based electrophoretic rewritable media has been studied with the expectation of good preservation characteristics. The thinning thickness condition of the rewritable media thickness is studied. The samples of dye concentration 0, 0.03, 0.07wt% against wax and weight ratio of TiO2 2.5, 5 and 10wt% are prepared with the thickness of 0.1 and 0.2mm. Displaying characteristics are estimated. Concerning the dependence of dyed side on dye concentration, Lambert-Beer equations is applied and the absorption coefficient of dye is obtained. The thinning condition of rewritable media is discussed as the reflection ratio of dyed side and white TiO2 side of the media can be realized to 10 at the condition of media thickness less than 0.1mm around dye concentration 0.1wt%.

The application of artificial neural networks technique to estimate mass attenuation coefficient of shielding barrier

This study aims to investigate comparison of radiation attenuation property of harzburgite mineral calculated by Monte Carlo (MCNP) and Artificial Neural Network (ANN). Slab sample modeled in MCNP with 1, 2 and 4 cm thickness was irradiated with parallel beam of monoenergetic particles. Incoming and outgoing particle fluxes were computed with F1 tally. Beer-Lambert equation was used to obtain mass attenuation coefficients for photon energies between 40 keV and 20 MeV. Optimum ANN model was obtained after trying different structures in terms of iterations and hidden layer numbers. For ANN calculation, parameters considered in the study are dose, thickness and mass attenuation coefficient. Dose and thickness are used as inputs to ANN for the estimation of mass attenuation coefficient. Model results are evaluated using root mean square errors (RMSE) and determination coefficient (R2) statistics. The estimates of selected ANN model were compared with MCNP results. Based on the comparison results, ANN was found good in prediction of mass attenuation coefficient for shielding material. Relationship between observed MCNP values and ANN estimates is noticeable with a high determination coefficient (R2) of 1 and has a root mean square error (RMSE) of 0.0033. Key words: Monte Carlo, artificial neural network, mass attenuation coefficient, radiation shielding.

Researches on a practical system for concentration detection of human exhaled CO<sub>2</sub> gas

In clinics, especially in the emergency department, carbon dioxide (CO2) is considered as the sixth vital sign in evaluating a patient's medical status. However, its wide applications in developing countries are dissatisfactory due to their high cost compared to their economic growth. In order to develop a practical system for concentration detection of human exhaled CO2 gas for our own, we studied the detection principle based upon the non-dispersive infrared (NDIR) measuring technique and related Lambert-Beer's equation carefully, gave out our functional circuit design of the system, and provided the corresponding graphical user interface (GUI) for CO2 detection. Finally, the experiment shows that it may be a practical system, and will give benefits for the development of our medical care in the future.

The influence of seasonal changes in canopy structure on interception loss: Application of the revised Gash model

Interception loss from a multi-species, deciduous, broad-leaved secondary forest in Japan was derived from gross rainfall, throughfall, and stemflow. The seasonal changes in the canopy structure were expressed using the leaf area index, which ranged from 1.65 to 4.31. In addition, the relationship between leaf area index (LAI) and relative light index (RLI) was examined using the Beer-Lambert equation. We established that RLI was associated with the canopy cover fraction. The relationships between throughfall, stemflow, and interception loss and gross rainfall were approximated by a linear regression equation for the growing and dormant seasons. Spatial variability in throughfall could be estimated from the relationship between the ratios of throughfall and RLI or LAI measured at many points, and had a high coefficient of variation. For stemflow, the regression coefficient and constant were strongly related to the diameter at breast height and were approximated by exponential equations. The differences in interception loss between seasons were small despite the distinct differences in LAI (the percentages of the total gross rainfall were 17.6 and 14.3% in the growing and dormant seasons, respectively). The revised Gash model was used to estimate interception loss more precisely by dividing the calculation period into (i) the entire study period, (ii) the growing and dormant seasons, and (iii) 3-month periods. The estimated interception loss was over- and underestimated by 7.8% for (i), 1.4% for (ii), and −2.2% for (iii). Regarding the parameters in revised Gash model, the canopy storage capacity varied with changes in LAI, and the evaporation rate was related not only to meteorological conditions, but also to the canopy structure in terms of aerodynamic resistance.

Contribution of hemodynamics and light scattering to the changes in optical intrinsic signal during cortical spreading depression in rats

Optical intrinsic signals (OIS) imaging has been shown a powerful method for characterizing the spatial and temporal pattern of the propagation of cortical spreading depression (CSD) with high resolution. However, the possible physiological mechanisms underlying these OIS during CSD still remain incompletely understood. In this study, spectroscopic recording of the changes in OIS during pinprick induced CSD were performed at the exposed cortex of -chloralose/urethane anesthetized Sprague-Dawley rats (male, n=12) using a fiber optic reflectance spectrometer (PC-1000, Ocean Optics Inc.) to estimate the contribution of hemodynamics and light scattering to the changes in OIS. The fiber probe (source-detector fiber separation: 0.2 mm) was placed at cortical parenchyma site avoiding large blood vessels. For each animal, five CSDs were elicited with an interval of half an hour. On each CSD induction, the spectra data was collected over a 400 seconds period at the rate of 2 Hz. The changes in the concentration of HbO2 and Hb, and changes in light scattering was estimated by fitting the experimental reflectance spectra data to a modified Beer-Lambert equation using a linear least squares fitting procedure, for a spectral range of 460630 nm. The fit was good with a residual error less than 5% in most experiments. In this experiment, four-phasic changes in OIS were observed at 460 nm 570 nm, but triphasic changes were observed at longer wavelength. The fitting results showed that the CSD induced an initial increase in concentration of HbO2 (amplitude: 9.03.7%), which was 26.218.6 s earlier than the onset of increase of Hb concentration. The increase in concentration of Hb reached its maximum value 47.25.9 s earlier than that of HbO2. Whereas the concentration of HbO2 showed a four-phasic change, the light scattering showed a triphasic change and the concentration of Hb only showed a biphasic change. The timing relationship between OIS and concentration of HbO2 and Hb indicated that the initial phase of the decreased IOS at 550 nm was only caused by the concentration increase of oxygenated hemoglobin at cortical parenchyma sites. But during the second phase of the increased optical reflectance at 550 nm, more complicated physiological mechanisms may be involved, not only the changes in concentration of HbO2, Hb and Hbt, but also the changes in light scattering contributed significantly to the increase of optical reflectance. When the concentration of HbO2 shows a small decrease (7.84.5%), the concentration of Hb increased 24.510.8%, simultaneously with a significant increase of light scattering. Interestingly, in our previous studies, a slight constriction of the pial arteries was observed during this phase of OIS. The constriction of the pial artery and the increase of concentration of total hemoglobin at cortical parenchyma site suggest that the regulations of the pial artery and capillary during this phase may be controlled by different mechanisms. During the followed third phase of light decrease at 550 nm, an increase of blood volume (concentration of total hemoglobin), an increase of oxygenation and decrease of scattering all contributed to the change of intrinsic optical signal.

Quantitative measurements on wetted thin layer chromatography plates using a charge coupled device camera

This paper presents the first study of imaging of spots on thin-layer chromatographic plates whilst still wet with solvent. Imaging and quantification of Sudan II after development with dichloromethane was carried out in both reflectance and transmission modes, using a charge coupled device (CCD) camera. The relationship between peak area and sample loading was established at low sample loading, and found to be linear over an order of magnitude for both wet and dry modes with r 2-values > 0.99. All data processing was carried out using the Beer–Lambert equation. Curvature at high loadings in the plots of integrated absorbance as a function of sample loading was accounted for using an empirical expression designed for use with the Kubelka–Munk treatment and apparent absorbance of the stationary phase due to scattering. Results are consistent with an effective pathlength significantly longer than the thickness of the sorbent layer. The limit of detection on a dry plate (0.5 ng) was found to be lower than on a wetted plate (2 ng). Precision was found to be 1–4% RSD intra-plate and 8–14% RSD inter-plate. Results are compared with quantification of the same analyte on dried plates.

IRMS–TPD of ammonia for characterization of acid site in β-zeolite

IR (infrared spectroscopy) and MS (mass spectroscopy) were measured together during TPD (temperature programmed desorption) of ammonia in order to simultaneously follow the thermal behavior of not only the adsorbed ammonia species but also the desorbed ammonia. The change of IR intensity with respect to temperature, i.e., IR–TPD, and MS–TPD gave us information of structure, number, and strength of acid sites, effectively. On a β-zeolite, three kinds of adsorbed ammonia species were detected at ca. 1620, 1450, and 1320 cm −1, assignable to NH 3 weakly adsorbed on the Lewis acid site, NH 4 + on the Brønsted acid site, and NH 3 strongly adsorbed on and/or interacted with the dislodged Al, respectively. A hydroxyl group interacted with each adsorbed ammonia was also detected; from the finding, the structure of acid site was discussed. Extinction coefficient of the NH 4 + at ca. 1450 cm −1 in the Lambert–Beer equation was determined. Catalytic activity for octane cracking was related to the amount of strong Brønsted acid site. Discussion was made on the availability of the present method to characterize the solid acidity.

NUMERICAL SIMULATION ON PRIMARY PRODUCTION AND INTERSPECIFIC COMPETITION OF STREAM PERIPHYTON

A numerical simulation model is presented to describe primary production and species transition of stream periphyton communities, in which the net growth rate of periphyton biomass is estimated by the balance of primary production, immigration, respiration and detachment of the periphyton biofilm. The interspecific competition of filamentous periphyton and non-filamentous periphyton is included in the model via the differences of the algal densities and the immigration patterns to the substrate. The solar radiation inside the periphyton biofilm is estimated by the Lambert-Beer's equation, and the nutrient distribution inside the biofilm is calculated from the diffusion equations of nutrients. The physiological parameters used in the present computations are evaluated from the laboratory data on periphyton growth. The results of the computation show that the model can predict the temporal variation of periphyton biomass and the species transition from the non-filamentous periphyton to filamentous periphyton well.

Contribution of blood volume changes to intrinsic optical signals

Hemodynamic responses evoked by neural activation are used to visualize active brain areas in various functional brain imaging techniques, such as PET, fMRI and intrinsic signal imaging. Though the major focus of these techniques is spatial localization of the active areas, the spatial precision of hemodynamic responses is not well understood. The purpose of this study was to investigate the spatial precision of hemodynamic responses by using intrinsic signal imaging. In particular, we focused on activity-dependent changes in the blood volume. We visualized sub-millimeter-scale functional structures such as orientation columns in the feline visual cortex using intrinsic signal imaging. To investigate the spatial precision of changes in the blood volume, we extracted the blood volume component from intrinsic signals using the Beer–Lambert equation, and directly visualized changes in the blood volume by observing absorption changes of an extrinsic dye infused into the bloodstream. In both cases, we succeeded in visualizing sub-millimeter-scale functional structures as changes in the blood volume. Taking into account that spatial separation of arteries is coarser than the spatial layout of sub-millimeter-scale functional structures, we believe these results suggest that there are supplementary control mechanisms of blood flow, probably in the capillary beds, in addition to arterial global control.

The Interaction of γ-Glycidoxypropyltrimethoxysilane with Oxidised Aluminium Substrates: The Effect of Drying Temperature

The interaction of γ-glycidoxypropyltrimethoxysilane (GPS) with oxidised aluminium substrates has been investigated in terms of the effect of the drying, or curing, temperature. Samples treated with aqueous solutions of GPS at concentrations of 1,4 and 8% v/v were cured at 25, 50, 93 and 120°C. X-ray photoelectron spectroscopy (XPS) and time-of-flight secondary ion mass spectrometry (ToF-SIMS) were used to construct adsorption isotherms and determine the thicknesses of the various GPS coatings. A temperature effect induces subtle changes in the structure of the resulting films. The uptake of GPS is increasing with increasing concentration of GPS. The structure of the films changes at a threshold temperature between 50 to 93°C. XPS and ToF-SIMS data both indicate that the interaction of the GPS film on aluminium is different for low and high temperatures drying regimes. Using the Beer-Lambert equation, it was found that increasing the curing temperature leads to the variation of the thickness of silane films. This is interpreted in terms of changes in the crosslink density of the films and in their state of hydration and/or degradation.

Appendix

Appendix

Multiple-scattering coefficients and absorption controlled diffusive processes

Multiple-scattering transmission and reflection coefficients (T,R) are introduced in addition to the diffusion coefficient D for the description of ballistic diffusion in the presence of absorption. For 1D (one-dimensional) systems, the measurement of only one between T and D imposes restrictions on the possible values of the other. If D is measured, then T is bounded between the Landauer and Lambert–Beer equations. Measurements of both (T,D) imply the theoretical knowledge of the microscopic absorption Σa and scattering rΣs cross sections.

Generalized Landauer equation: absorption-controlled diffusion processes.

The exact expression of the one-dimensional Boltzmann multiple-scattering coefficients, for the passage of particles through a slab of a given material, is obtained in terms of the single-scattering cross section of the material, including absorption. The remarkable feature of the result is that for multiple scattering in a metal, free from absorption, one recovers the well-known Landauer result for conduction electrons. In the case of particles, such as neutrons, moving through a weak absorbing media, Landuer's formula is modified due to the absorption cross section. For photons, in a strong absorbing media, one recovers the Lambert-Beer equation. In this latter case one may therefore speak of absorption-controlled diffusive processes.

Determination of the wavelength dependence of the differential pathlength factor from near-infrared pulse signals

For the calculation of changes in oxyhaemoglobin, deoxyhaemoglobin and the redox state of cytochrome-c-oxidase from attenuation data via a modified Beer-Lambert equation the wavelength dependence of the differential pathlength factor (DPF) has to be taken into account. The DPF, i.e. the ratio of the mean optical pathlength and the physical light source-detector separation at each wavelength, determines the crosstalk between the different concentrations and is therefore essential for a sensitive detection of chromophore changes. Here a simple method is suggested to estimate the wavelength dependence of the DPF from pulse-induced attenuation changes measured on the head of adult humans. The essence is that the DPF is the ratio of the attenuation changes over absorption coefficient changes, and that the spectral form of the pulse correlated absorption coefficient change can be assumed to be proportional to the extinction coefficient of blood. Indicators for the validity of the DPF derived for wavelengths between 700 and 970 nm are the stability of the calculated haemoglobin and cytochrome signals with variations of the wavelength range included for their calculation and its overall agreement with the data available from the literature.