Kubelka-Munk Model Research Articles

A Z-scheme AgI/BiOI binary nanophotocatalyst for the Eriochrome Black T photodegradation: A scavenging agents study

The increased pollution of the environment, especially the aquatic ones, requires novel techniques/catalysts with high removal efficiency and low cost. For this goal, the construction of novel visible-light heterogeneous photocatalysts attracted particular interest. The binary AgI/BiOI coupled catalyst in nano dimension was prepared and used in Eriochrome Black T (EBT) photodegradation in this research work. Photoluminescence (PL) spectra confirmed that in the coupled system, the electron-hole (e/h) production was increased concerning BiOI alone, while the e/h recombination was decreased. The modified carbon paste electrodes with semiconductors confirmed that the cyclic voltammogram (CV) peak current could change in the case of the coupled system, ensuring an internal redox process between BiOI and AgI components. By applying the Kubelka-Munk model on the UV-Vis diffuse reflectance spectra (DRS), the band gap energies of 2.8, 1.5, and 2 eV were obtained for AgI, BiOI, and AgI-BiOI samples. A boosted photocatalytic activity was observed for the coupled system, which depended on the AgI:BiOI mole ratio. The effects of some scavenging agents, including ascorbic acid, sodium bicarbonate, KI, and KNO3 were studied on the photocatalytic efficiency. Ascorbic acid drastically decreased the overall process efficiency, confirming the vital role of superoxide radicals in the photodegradation process. Based on the potential positions of the CB and VB levels, the Z-scheme mechanism was the best model to describe the photodegradation mechanism.

Practical pigment mixing for digital painting

There is a significant flaw in today's painting software: the colors do not mix like actual paints. E.g., blue and yellow make gray instead of green. This is because the software is built around the RGB representation, which models the mixing of colored lights. Paints, however, get their color from pigments, whose mixing behavior is predicted by the Kubelka-Munk model (K-M). Although it was introduced to computer graphics almost 30 years ago, the K-M model has never been adopted by painting software in practice as it would require giving up the RGB representation, growing the number of per-pixel channels substantially, and depriving the users of painting with arbitrary RGB colors. In this paper, we introduce a practical approach that enables mixing colors with K-M while keeping everything in RGB. We achieve this by establishing a latent color space, where RGB colors are represented as mixtures ofprimary pigments together with additive residuals. The latents can be manipulated with linear operations, leading to expected, plausible results. We describe the conversion between RGB and our latent representation, and show how to implement it efficiently.

Determination of suitable wavelengths in dye concentration estimation by spectral analysis of K/S’s scalability

K/S and reflectance graphs are essential tools in characterizing the dyeing behavior. In textile coloration, estimating the dye concentration is poor using the Kubelka-Munk model due to its low scalability and deviation of the reflectance function from linearity after low dye concentrations, particularly in the wavelengths where the gradient of K/S against dye concentration is noticeable. This paper focused on extending the validity of the Kubelka-Munk function, which originates from the linearity of reflectance function against higher dye concentration. A data set of dyed polyester specimens with three disperse dyes in a dye concentration range was prepared. At the present work, K/S was analyzed by describing the scalability property, and the suitable wavelengths in the visible spectrum where K/S benefits from minor deviation from linearity were also discussed. It was observed that the K/S function is not always scalable and deviates in λ max after a specific dye concentration for K/S > 17. Accordingly, the wavelengths other than λ max were found that could be as important as λ max. For the K/S values > 25, no practical region was achieved.

Facile synthesis of Cu1-xCoxFe2O4 (0 ≤ x ≤ 0.5) nanoparticles with enhanced magnetic and photocatalytic performances for organic dye degradation

Magnetic nanoparticles are found to have tremendous applications towards opto-magnetic-photocatalytic fields. Hence, herein authors make the efforts to prepare CuFe2O4 (CFe) nanoparticles (NPs) with different Co contents Cu1-xCoxFe2O4 (0 ≤ x ≤ 0.5) (CCFe NPs) through microwave combustion process for the first time. Mono phasic preparation of CFe NPs at all Co contents was confirmed via structural analysis. The oxidations states of the prepared NPs were carried out via X-ray photoelectron spectroscopy(XPS). The morphological analysis and chemical compositions of the prepared samples were observed by high resolution scanning electron microscopy (HRSEM) with energy dispersive X-ray spectroscopy (EDX) respectively. Kubelka-Munk model was used to estimate energy gap and found between 2.30 and 2.50 eV. The electron and hole pairs recombination rate and presence of defects were studied via Photoluminescence spectra. The saturation magnetization, MS, remanant magnetization, Mr and coercivity, HC were obtained to be improved from 17.40 to 24.80 emu/g, 5.18 to 8.73 emu/g & 331.89 to 1698.12 Oe, respectively. A detailed photocatalytic nature of the prepared CFe and CCFe NPs via hazardous RhB dye degrading beneath of irradiation of visible light (λ > 420 nm) was carried out. The possible mechanism of RhB dye degradation along with optimum Co doping in CFe and commanding active species has been discussed. These outcomes reveal that the Co doping play a key role in improving the optical band gap, magnetic and photocatalytic properties of CFe NPs.

Numerical Pathology in Selected Kubelka–Munk Formulas, and Strategies for Mitigation

Causes of numerical pathology in formulas for reflectance factor (R), transmittance factor (T), and reflectance factor over a perfectly black background (R 0 ) under the Kubelka-Munk model are posited, and alternate formulas believed less prone to these pathologies are introduced. Suggestions are offered not only for R, T, and R 0 , but also for intermediate or adjunct quantities used in the main formulas. Computational experiments were performed to verify that the new models produce the same results as the existing ones under non-pathological conditions, exhibit acceptable levels of precision in a customary floating-point environment, and are more robust with respect to edge cases where an input quantity is zero. The new formulas performed well, with some evidence that the new hyperbolic forms provide better accuracy than their exponential counterparts.

A novel manganese(II) bisthiocarbohydrazone complex: Crystal structures, Hirshfeld surface analysis, DFT and molecular docking study with SARS-CoV-2

A novel Mn(II) complex [Mn(H2L)Cl2]•H2O (1) of a ditopic ligand 1,5-bis(2-benzoylpyridine) thiocarbohydrazone (H2L) was synthesized and characterised physico-chemically. A part of the mother solution of the complex 1 and THF yielded single crystals in a triclinic space group and are found same from the crystals obtained from another mixture of the mother solution and ethyl acetate. Single crystal XRD studies have confirmed the mononuclear complex formation and absence of any interactions between the Mn(II) centers. A solution of the complex 1 in chloroform, conversely, yielded a crystallographically different complex [Mn(H2L)Cl2]•CHCl3 (1a) in monoclinic and is also characterised with single crystal XRD. The ligand is coordinated through thione sulfur atom to form a square pyramidal geometry around Mn(II) center in both the complexes. The molecular packing of the complexes is found influenced by the nature of solvent inclusion, and are stabilized by different non-covalent interactions in the lattice. The intermolecular interactions are quantified by Hirshfeld surface analyses, which reveal that H•••Cl interactions has maximum contribution to the total Hirshfeld surface in the complex 1a. This is the first crystal structure study of a manganese(II) complex of a bisthiocarbohydrazone ligand. The molecular and electronic structures of the complexes are studied by DFT quantum chemical calculations. The band gap (Eg) of the complex 1 was estimated as 2.45 eV using Kubelka-Munk model and is in agreement with the electronic spectral calculations of the complex at TD-DFT level. Molecular docking studies of both the ligand and the complex reveal their greater propensity towards SARS-CoV-2 main protease compared to B-DNA dodecamer. Also, the binding potential of the ligand and the complex with SARS-CoV-2 main protease is found higher than that with chloroquine and hydroxychloroquine.

Electronic and optical properties of organic-inorganic (CuII /ReVII)-heterobimetallic L-Arginine complex: Experimental and Computational studies

Recently, organic-inorganic hybrid materials have emerged as a new promising class of materials for optoelectronic applications, due to their excellent chemical and physical properties. The novel trans-[Cu(L-Arg)2(ReO4)2] has been studied using density functional theory (DFT), within the generalized gradient approximation (GGA-PBE). The experimental band gap estimated from the Kubelka-Munk function is found to be in good agreement with the calculated band gap found by DFT. The density of states, band structure, density of charge, absorption coefficient, and reflectivity are presented and analyzed in detail. The partial densities of states show that ReO4− ligand in the material plays a crucial role in different properties of the trans-[Cu(L-Arg)2(ReO4)2] material. Moreover, the experimental reflectance is employed to estimate the scattering coefficient using a semi-empirical Kubelka-Munk (K-M) model.

Optical spectroscopic studies on poly(methyl methacrylate) doped by charge transfer complex

Polymeric sheets of poly(methyl methacrylate) (PMMA) doped by charge-transfer (CT) complex of perylene/iodine (pyr/I 2 ), perylene/picric acid (pyr/PA) and perylene/chloranilic acid (pyr/CLA) were synthesized in methanol solvent at room temperature. The optical spectroscopic studies on PMMA polymer doped by charge transfer complex are determined by UV–Vis–NIR spectroscopy, Photoluminescence spectroscopy (PL), Vis–NIR diffused reflectance spectroscopy (DRS) and FTIR spectroscopy. The diffused reflectance spectroscopy (DRS) of the polymeric sheet samples is analyzed based on the Kubelka–Munk model. The indirect allowed optical band gaps of the polymeric sheet samples are estimated by applying absorption spectrum fitting (ASF) and Tauc's methods. Here we report the optical spectroscopic studies on PMMA polymer doped by charge transfer complex as potential materials to be used in optoelectronic devices. • Charge-transfer complexes have an important role in solar energy storage and organic semiconductors fields. • Polymeric sheets of PMMA doped by charge-transfer complex were synthesized. • Optical spectroscopic studies on PMMA polymer doped by charge transfer were investigated. • The optical band gap of polymeric sheets was calculated by the DRS, ASF and Tauc's equations. • The spectral behaviour of the refractive index and the specific polarizability were obtained.

Investigation on structural, morphological and electrochemical properties of Mn doped WO3 nanoparticles synthesized by co-precipitation method for supercapacitor applications

The work reported here, demonstrates the synthesis of pristine WO3 and Manganese (Mn)-doped through the hydraulic acid-assisted precipitation method. Structural, morphological, compositional, optical and electrochemical properties of the synthesized samples were analysed. The structural analysis through X-ray diffraction studies confirmed the monoclinic phase of WO3 as well as the substitutional incorporation of Mn inWO3 lattice. A bandgap value of 2.9 eV was estimated from Optical analysis using Kubelka-Munk model. The defect centered luminescence as a consequences of Mn doping was analyzed using photoluminescence spectroscopy (PL). FT Raman Spectroscopic data also reconfirmed the monoclinic structure of the sample and incorporation of Mn into the lattice of Mn-doped WO3. The surface morphological study was performed using Field Emission Scanning Electron Microscope (FESEM), which exhibits the development of mesoporous networks. The Conductivity, dielectric and electrochemical studies were performed on these mesoporous structures to inveterate the impact of Mn doping. A dynamic increment in AC conductivity was observed with doping even at room temperature. Most significantly, we prove that Mn doped WO3 for the first time, Nanoparticles are an outstanding candidate for applications for supercapacitors. Pure and Mn doped WO3 electrochemical properties cyclic voltammetry measurements have been used to analyze samples. The results showed the excellent electrochemical efficiency on 1 wt% Mn doped WO3 electrode (1178 F/g specific capacitance at 2 mA/cm2 and charge transfer ability) for supercapacitors.

Microwave-assisted synthesis of Cu doped PbS nanostructures with enhanced dielectric and electrical properties for optoelectronic applications

Herein, facile CTAB surfactant-assisted synthesis of Pb1-xCuxS (x = 0, 0.1, 0.5, 1.0, 2.5 & 5.0 wt%) nanostructures (NSs) via a microwave route within 10 mins was attained and investigated for their structural, optical, vibrational, dielectric and electrical properties using X-ray diffraction, FT-Raman, UV–VIS, impedance and I-V measurements. Structural study with Rietveld refinement confirms the synthesis of PbS predominantly with cubic phase; however, at higher content of Cu some CuS peaks are detected. The values crystallite size of all Pb1-xCuxS specimens were determined between 19 and 25 nm and the specific surface area between 31 and 40 m2/g. Vibrational modes are noticed at 59.59, 74.05, 127.04, 268.82, 426.96, 601.49 cm−1 in all specimens confirmed cubic PbS NSs synthesis. As received powders were tested through DRS to evaluate the energy gap values via Kubelka-Munk model and noticed between 1.02 ± 0.01 to 1.37 ± 0.01 eV tuned with crystallite size. Dielectric studies reveal that the Cu doping enhanced the capacitance/dielectric constant and ac electrical conductivity of PbS NSs. Moreover, the I-V nature of the prepared Pb1-xCuxS NSs was measured, and dc conductivity was calculated and noticed to be enriched with Cu doping. The enhanced dielectric and electrical properties make the prepared materials useful for optoelectronic devices.

Comment on “Photocatalytic degradation of RhB from an aqueous solution using Ag3PO4/N-TiO2 heterostructure” and “Evaluation of the effect of dose change of Fe3O4 nanoparticles on electrochemical biosensor compatibility using hydrogels as an experimental living organism model”

Two published papers in Journal of Molecular Liquids inappropriately named the same equation in different ways. These errors are clarified in this comment to avoid a misunderstanding involving the determination of the band gap energy from diffuse reflectance measurements using Kubelka Munk model and Tauc plot.

A camouflage coating with similar solar spectrum reflectance to leaves based on polymeric inorganic composite

To realize the hyperspectral camouflage under the background of vegetation, a camouflage polyvinyl alcohol coating containing lithium chloride and green pigment particles of chromium sesquioxide (Cr2O3) was prepared on a stainless-steel substrate. Based on the four flux Kubelka-Munk model, the reflectances of the coatings with different volume fractions of Cr2O3 (f c) were predicted and compared with those of the membranes without substrate. The results show that when f c reaches 0.8%, the 0.2 mm thick coating can conceal the reflectance characteristics of the stainless-steel substrate. The reflectances of the coatings with the volume fraction of water (f w) in the range from 0% to 50% were also calculated via the model. It is found that the reflectances around 1460 nm and 1940 nm decrease with increased f w due to the significantly enhanced absorption coefficient, and the correlation coefficient between the spectral reflectances of the camouflage coating and an Osmanthus fragrans leaf increases from 0.913 to 0.954, indicating that the coating camouflage performance can be improved by increasing f w.

Optical study to identify and quantify capsaicin in optical window

Capsaicin is an active compound in hot peppers. It has been studied for its health benefits for humans. Optical spectroscopy is an important tool for determining the optical properties or chemical composition of matter. The aim of this research is proposing an optical method to identify and quantify capsaicin in the visible range. To achieve this goal, we combined absorption and diffuse reflectance spectroscopy techniques to compute the extinction coefficient. Moreover, the concentration of the analytes was determined using the optical properties of capsaicin. Our method is a promising tool for developing a classification of capsaicin according to its percentage in chilies. The extinction coefficients are reported for 507nm and 663nm, which are the most significative. In addition, the coefficients to build the mathematical model for capsaicin are reported for Kubelka-Munk model. Finally, a comparison between capsaicin vs chilies spectra was obtained to identify spectral response. Diffuse reflectance signals allowed the identification of capsaicin and opened the possibility of this fast and easy to do method for classification and quantification of bioactive compounds.

Improved photocatalytic degradation of rhodamine B under visible light and magnetic properties using microwave combustion grown Ni doped copper ferrite spinel nanoparticles

Nanoparticles (NPs) of Cu1-xNixFe2O4 (0 ≤ x ≤ 0.5) have been facilely prepared via combustion through microwave technique. X-ray diffraction outcomes confirmed single-cubic phase synthesis of titled material and mean crystallites size and lattice constants were calculated in range of 19.37–22.69 nm and 8.319–8.248 Å, respectively. The XPS study confirms the chemical elements and oxidations states of Cu0.6Ni0.4Fe2O4 NPs. The high-resolutionSEM study reveals spherical NPs with agglomeration and composition of elements in Cu1-xNixFe2O4 (0 ≤ x ≤ 0.5) was confirmed through EDX study. The Kubelka-Munk model was employed to determine the energy gap of Cu1-xNixFe2O4 NPs and noticed to vary from 2.30 to 2.06 eV. Photoluminescence spectra study explained the rate of recombination of electron and hole pairs. The detailed magnetic study was carried out and magnetization of remanence (Mr), coercivity (Hc) & saturation (Ms) values were estimated through recording the hysteresis plots. The magnetic Mr & Ms values are noticed to be enhanced from 5.21 to 11.02 emu/g &17.37–31.37 emu/g with Ni content. Furthermore, the Cu1-xNixFe2O4 (0 ≤ x ≤ 0.5) NPs were studied by means of visible light induced RhB dye degradation and investigates major active species and a probable mechanism for degradation has been conferred. The photocatalytic activity of CuFe2O4 NPs has been improved via Ni doping. Photoluminescence spectra showed the rate of recombination of electron-hole pairs and presence of defects.

Thickness dependent morphological, structural and optical properties of SS/CuO nanocoatings as selective solar absorber

In this paper, selective solar absorber (SSA) of copper oxide (CuO) nanocoatings on stainless steel (SS) substrate are conveniently prepared by sputtering and chemical oxidation route for solar thermal energy harvesting. The copper (Cu) thin films were deposited on SS substrate by using RF sputtering for different thicknesses (i.e 300, 400, 500 and 600 nm), and then oxidized to form CuO nanocoatings. The AFM, SEM, EDS, XRD, Raman spectroscopy, UV–Vis–NIR, and FTIR techniques were employed to characterize the surface morphology, microstructure, and optical properties of the CuO nanocoatings. The morphological, structural, and optical properties are greatly influenced by the thickness of the coatings. Both SEM and AFM shows the presence of nanoflake as well as nanosheet-like structures, respectively. The crystallinity, lattice vibration and purity of the CuO nanocoatings are confirmed by XRD, Raman and EDS spectra, respectively. The optical properties the obtained nanocoatings are measured from spectral reflectance of UV–Vis–NIR as well as FTIR data’s and the absorption edge slightly shifts towards higher wavelength with a coating thickness, this enables to increase the solar absorptance (α), but at the same time emittance (ε) also increased. High solar absorptance (α) of 97.4% and emissivity (ε) of 40.8% is associated to the thickest coating of 600 nm. The optical band gap of the coatings is determined from diffuse reflectance by using Kubelka-Munk (K-M) model and the values are ranging between 1.27 and 1.62 eV.

Enforcing Kubelka–Munk constraints for opaque paints

AbstractThe Kubelka–Munk model relates the colours of paint mixtures to the absorption and scattering coefficients (K and S) of the constituent paints, and to their concentrations (C) in the mixtures. All Ks and Ss are non‐negative, and Cs are physically constrained to be between 0 and 1. Standard estimation procedures cast the Kubelka–Munk relationships as an overdetermined linear system and apply ordinary least squares (OLS). OLS, however, sometimes produces coefficients or concentrations that are less than 0 or greater than 1. These physically impossible solutions occur because OLS projects a target vector (such as a desired reflectance spectrum) onto a vector subspace, while in fact the set of physically realisable paint combinations is a convex polytope, which is a subset of that subspace. This paper reformulates Kubelka–Munk estimation problems geometrically, as the problem of finding the point on that polytope which is closest to a target vector. The solutions to the reformulated problem are always physically realisable. If feasible, a worker could solve the reformulated problem with a ready‐made commercial solver. Otherwise, the Gilbert–Johnson–Keerthi algorithm is recommended as particularly suitable for Kubelka–Munk estimation; this algorithm has been tested on some simple cases and released as open‐source code.

Reflectance and transmittance of flowable dental resin composite predicted by the two-flux model: on the importance of analyzing the effective measurement geometry

Flowable direct resin composite materials used in the dental domain are among materials that scatter light rather weakly, giving to millimeter-thick samples a certain translucent aspect. In order to predict the spectral reflectance and the color of such samples, the two-flux theory, i.e., Kubelka-Munk model (with Saunderson correction), remains the standard approach used in the dental domain, in spite of its known limitations when scattering is too weak. The present study, however, shows that a careful analysis of the light signal effectively measured on weakly scattering samples with instruments based, as usually recommended, on the d:8° measurement geometry, and a subsequent reevaluation of the parameters used in the Saunderson correction formulas with respect to the effective measurement geometry, can considerably improve the prediction accuracy of the model in both reflectance and transmittance modes, as confirmed by experiments carried out with samples of dental flowable resin composite material of different thicknesses. This broadens the applicability domain of the model, and might satisfy users preferring the simplicity of the two-flux model and the affordable equipment it needs to more relevant but more complex light scattering theories.

Structural, electrochemical and optical properties of 1,2,4-triazine derivative

Structural, optical and electrochemical properties of 4-amino-3-mercapto-6-(2-(2-thienyl)vinyl)-1,2,4-triazin-5(4H)-one donor (AMT) in powder and thin film forms are studied. The thermogravimetric curves (TGA and DTA) of AMT solid powder are performed for recognizing its thermal stability and thermal degradation kinetics. Integral method using Coats–Redfern and Horowitz–Metzger equations are applied in the dynamic thermal data analysis. The electrochemical reduction and oxidation potential of AMT organic material are investigated. AMT solid powder are characterized by means of optically diffused reflectance spectroscopy (DRS) based on the Kubelka–Munk model. Field emission scanning electron microscope image is characterized by the formation of nanostructure shape with average particle size 70 nm. The optical features of the AMT organic thin films are characterized by UV–Vis–NIR spectroscopy, Photoluminescence spectroscopy (PL) and Fourier transform infrared (FT-IR) spectroscopy. The optical properties such as absorption coefficient, optical gaps, refractive index, single effective oscillator energy (Eo) and dispersion energy (Ed) of the AMT organic thin films are estimated.

Investigating the transmission profiles of 808nm laser through different regions of the rat's head.

Studying light penetration in biological tissues became a very important concern in various medical applications. It is an essential factor required to resolve the optical dose in many diagnostic and therapeutic procedures. The absorption and scattering properties of the inspected tissue control how deep the light will travel inside the tissue. However, these optical properties are highly dependent on the wavelength of the light source. In this work, the light transmission through different regions of the rat's head was investigated and the minimum laser power required to reach different parts of the head is also determined using 808-nm semiconductor laser diode. The power variation in different regions of the head is estimated using Monte Carlo simulation. Absorption and scattering coefficients of the head layers were calculated using integrating sphere measurements and Kubelka-Munk model. The absorption coefficient of the skin was 0.19 ± 0.071mm-1, 0.024 ± 0.11mm-1 for skull, and 0.35 ± 0.13mm-1 for the brain, while the scattering coefficients were 7.35 ± 1.09, 2.71 ± 0.37, and 13.04 ± 0.36mm-1 for skin, skull, and brain, respectively. The obtained results provide a relationship between laser incident power and the depth in the rat's head showing a higher optical transmission at the frontal part of the head than the middle or back regions due to the variations in the skull thickness. Therefore, the study revealed that the transmitted power of 808nm laser at different incident locations on the head is nonlinear and variable due to different skull's thickness.

Light scattering as a Poisson process and first-passage probability

A particle entering a scattering and absorbing medium executes a random walk through a sequence of scattering events. The particle ultimately either achieves first-passage, leaving the medium, or it is absorbed. The Kubelka–Munk model describes a flux of such particles moving perpendicular to the surface of a plane-parallel medium with a scattering rate and an absorption rate. The particle path alternates between the positive direction into the medium and the negative direction back towards the surface. Backscattering events from the positive to the negative direction occur at local maxima or peaks, while backscattering from the negative to the positive direction occur at local minima or valleys. The probability of a particle avoiding absorption as it follows its path decreases exponentially with the path-length λ. The reflectance of a semi-infinite slab is therefore the Laplace transform of the distribution of path-length that ends with a first-passage out of the medium. In the case of a constant scattering rate the random walk is a Poisson process. We verify our results with two iterative calculations, one using the properties of iterated convolution with a symmetric kernel and the other via direct calculation with an exponential step-length distribution. We present a novel demonstration, based on fluctuation theory of sums of random variables, that the first-passage probability as a function of the number of peaks n in the alternating path is a step-length distribution-free combinatoric expression involving Catalan numbers. Counting paths with backscattering on the real half-line results in the same Catalan number coefficients as Dyck paths on the whole numbers. Including a separate forward-scattering Poisson process results in a combinatoric expression related to counting Motzkin paths. We therefore connect walks on the real line to discrete path combinatorics.