Redlich Kister Polynomial Research Articles

Density, Speed of Sound, Refractive Index, and the Derived Properties of Binary Mixtures of N,N-Dimethylacetamide with 1-Butanol, 1-Pentanol, Furfural, or Furfuryl Alcohol at Different Temperatures.

The density (ρ), speed of sound (c), and refractive index (n D) of N,N-dimethylacetamide (DMA) with 1-butanol, 1-pentanol, furfural (FFL), or furfuryl alcohol (FA) as a function of composition and at T = 293.15 to 323.15 K with an interval of 10 K and atmospheric pressure were measured. From the experimental data, the excess molar volume (V m E), isentropic compressibility (κ s), intermolecular free length (L f), specific acoustic impedance (Ζ), relative association (R A), relaxation strength (r), Rao's molar sound function (R), excess isentropic compressibility (k s E), and excess refractive index (n D E) properties were calculated. These results were successfully fitted to the Redlich-Kister polynomial equation. The obtained results were discussed in terms of the nature of molecular interactions. The perturbed chain statistical associating fluid theory equation of state (PC-SAFT EoS) as a predictive approach was used for modeling the density of the binary mixtures. Schaaffs's collision factor theory (SCFT) and Nomoto's relation (NR) were successfully applied for predictive modeling the speed of sound of the binary mixtures, and four mixing rules were used for the modeling of the refractive index of the mixtures.

Excess properties, intermolecular interaction, and CO2 capture performance of diethylene glycol monomethyl ether + ethylenediamine binary mixed solutions

In this work, the density (ρ) and viscosity (η) values of diethylene glycol monomethyl ether (DEGME) (1) + ethylenediamine (EDA) (2) binary mixed solutions were experimentally measured over the temperature span of 298.15–318.15 K and at a constant pressure of 100.5 kPa. To delve into the physicochemical properties of the binary mixed solutions, the excess properties, including excess molar volume, viscosity deviation, and excess molar activation Gibbs free energy, and thermodynamic values, including activation Gibbs free energy, enthalpy change, entropy change, and activation energy, were systemically calculated. Furthermore, the relationship between mole fraction and temperature was modeled using the Jouyban-Acree (J-A) model and a least squares method. Additionally, the three-body McAllister, the four-body McAllister, the Eyring-Margules, and the Heric viscosity models were employed to establish a relationship between viscosity and mole fraction. The relationship between viscosity and temperature was determined utilizing the Arrhenius equation, and the Redlich-Kister (R-K) polynomial was applied to fit the excess molar volume, viscosity deviation, and excess molar activation Gibbs free energy values of the binary mixed solutions. To further validate the intermolecular interactions within the binary mixed solutions, Raman, UV, and 1H NMR spectroscopic analyses, and density-functional theory (DFT) calculations were also conducted. These comprehensive analyses collectively confirmed the presence of significant intermolecular hydrogen bonds (IHBs) between the DEGME and EDA molecules, which are characterized as the –OH⋯NH2– interaction. Ultimately, the CO2 absorption capacity of the binary mixed solutions was examined, revealing that diethylene glycol monomethyl ether (DEGME) (1) + ethylenediamine (EDA) (2) binary mixed solutions owned superior CO2 absorption efficiency, thus offering a promising approach for CO2 capture.

Machine Learning Enabled Operando Optical Microscopy for Determination of Lithium Transport in Battery Electrodes

Diffusion coefficients of electrode materials are often determined using galvanostatic (GITT) or potentiostatic intermittent titration technique (PITT), electrochemical impedance spectroscopy (EIS) or cyclic voltammetry (CV). However, these methods require special care, as each of their formal derivations use quite restrictive assumptions. As an alternative, a machine learning model is presented to extend a previously proposed optical method of studying lithium transport by operando microscopy. The herein reported model enables the measurement of concentration-dependent diffusion coefficients in a wide solubility range. For this purpose, a python code is developed that determines concentration profiles from RGB images using support vector regression (SVR), a flexible machine learning tool. To evaluate the diffusion coefficient, an inverse Boltzmann-Matano concept is applied. Representing the diffusion coefficient with generalized Redlich-Kister polynomials, concentration profiles are predicted and fit to the measured data. The method is demonstrated here on the example of delithiation of LiMn2O4, but it can, in-principle, be extended to any other battery material showing significant optical response on lithiation, which most of them do.

Calorimetric study of the enthalpy of mixing in the liquid systems In-Li and In-Li-Sn

Enthalpies of mixing of liquid binary In-Li alloys at different temperatures as well as liquid ternary In-Li-Sn alloys at 1073 K were determined using drop calorimetry. The binary system was investigated over the whole composition range at 923 K and 1073 K. A common Redlich-Kister polynomial was used for fitting and to calculate the binary interaction parameters for In-Li. The system shows a quite strong exothermic behavior with a minimum molar mixing enthalpy of −20000 to −22000 J⋅mol−1, depending on the temperature, at xLi≈ 0.6. Limiting partial enthalpies of mixing were determined and associate formation was considered to explain temperature dependencies and different mixing behavior in the In- respectively Li-rich region. Eight sections in the ternary system In-Li-Sn were investigated at 1073 K. The respective binary starting concentrations for the sections were A: xLi/xSn ≈ 3:2, B: xLi/xSn ≈ 3:7, C: xIn/xSn ≈ 1:3, D: xIn/xSn ≈ 1:1, E: xIn/xSn ≈ 3:1, F: xIn/xLi ≈ 7:3, G: xIn/xLi ≈ 2:3, and H: xIn/xLi ≈ 3:7. The experimental ternary data was fitted based on a Redlich-Kister-Muggianu polynomial including ternary interactions. Additionally, a comparison with extrapolated binary data based on the Toop model and Muggianu model is presented.

Unravelling the influence of water: Investigating the physicochemical properties of deep eutectic solvents based on choline chloride and pyruvic acid/α-keto glutaric acid

In the vast and intricate world of solution chemistry, deep eutectic solvents (DESs) have established a unique standing due to the easy accessibility of their components, along with their non-hazardous nature, biodegradability, recyclability, and cost-effectiveness. The main objective of this study is to investigate the key physicochemical properties of DESs, particularly those composed of choline chloride (ChCl) and pyruvic acid (referred to as pyruline), as well as those formulated with α-keto glutaric acid (referred to as glutaline). The initial investigation encompasses a comprehensive analysis of the thermal stability of the proposed DESs at 1:1, 1:2, and 2:1 M ratio, which were systematically assessed using TGA and DSC. The findings indicated that all eutectic mixtures exhibit a glass transition phenomenon instead of conventional melting and undergo a two-stage decomposition process. Following the thermal analysis of the neat DESs, the other physicochemical properties, including density, ionic conductivity, and electrochemical stability, were exclusively evaluated for the aqueous pyruline (1:1) and aqueous glutaline (2:1) pseudo-binary mixtures. The density studies of both proposed DES/H2O pseudo-binary mixtures across the temperature range of 293.15–343.15 K show a decrease with increasing temperature, accompanied by a corresponding increase in the thermal expansion coefficients (αP). Furthermore, the nonideal behaviour of the aqueous DESs was investigated by calculating the excess molar volume (VE) derived from density values across various temperature range and differing H2O mole fractions. The obtained VE demonstrated an excellent correlation with the Redlich–Kister polynomial equation. Additionally, the temperature dependent ionic conductivity of DES/H2O pseudo-binary mixtures was studied over the temperature range of 298.15–333.15 K. The cyclic voltammetry analysis offers a comprehensive insight into the electrochemical stability of DESs. Ultimately, the examination of binding energy (BE) and frontier molecular orbitals (FMOs) through density functional theory (DFT) offers valuable insights into the intermolecular interactions, molecular structures, and stability of DES clusters at the molecular level.

Thermophysical properties: Viscosity, density, and excess properties of 2-propanol and n-Decane mixtures from 283.15 K to 343.15 K under atmospheric conditions

To study the effects of temperature as well as molecular interaction of a fluid system on the thermophysical properties of 2-propanol and n-Decane binary mixture, the density (ρ), dynamic viscosity (η), speed of sound (u), and refractive index (nD) of pure 2-propanol and n-Decane, along with their binary mixtures, were experimentally measured across the entire compositional range at temperatures from 283.15 to 343.15 K and atmospheric pressure. These experimental measurements helped in the evaluation of various thermophysical properties, such as excess molar volume (vE), coefficient of thermal expansion (αE), and isentropic compressibility (κsE). The experimental dynamic viscosity (η) and density (ρ) data were used to evaluate kinematic viscosity (v) and Gibbs free energy (ΔG) of flow with an equation based on Eyring's absolute state theory, and their corresponding excess properties. The excess properties of the binary mixtures were correlated using a Redlich-Kister type polynomial equation via the least-squares regression method, with fitting parameters determined for the binary system. Moreover, the Prigogine–Flory–Patterson theory (PFP) was utilized to identify the primary molecular interactions contributing to the excess molar volume at 293.15, 308.15, and 323.15 K for the binary mixtures. Additionally, the capability of the Eyring-NRTL model was tested to predict the viscosity as well as vapor-liquid equilibrium (VLE) of the binary system, and the correlated model results agreed with literature data.

Thermophysical study for Binary mixtures of Dimethyl carbonate with Anisole, Butyl vinyl ether, Diisopropyl ether and Dibutyl ether at 303.15, 308.15 and 313.15 K

Ultrasonic velocity, density and viscosity have been determined for the binary compositions of dimethyl carbonate+ butyl vinyl ether, + diisopropyl ether, + anisole and + dibutyl ether at T= 303.15, 308.15 and 313.15 K. The inventive data is applied to assess the excess molar volume VmE, deviation in viscosity Δη and the acoustical parameters namely isentropic compressibility (Ks), free volume (Vf ), free length (Lf ) and internal pressure (πi). The excess or deviation properties are contoured to the Redlich-Kister polynomials and the outcomes are elucidated in terms of molecular interactions present in compositions.

Thermodynamic and transport properties of binary mixtures containing 1,2-propanediol with 2-methoxyethanol and 2-ethoxyethanol at different temperatures

In the present investigation density, speed of sound, and viscosity have been reported for binary liquid mixtures of 1,2-propanediol (1,2-PD) with 2-methoxyethanol (2-ME) and 2-ethoxyethanol (2-EE) over the entire composition range at T= (298.15–323.15) K. From the experimental data, excess molar volume, (VmE), excess isentropic compressibility, (κsE), excess molar isentropic compressibility, (κs,mE), excess speed of sound, (uE), excess isobaric thermal expansion,αpE, and deviation in viscosity (Δη) of liquid mixtures have been calculated. The excess partial molar volume,V¯m,1E, V¯m,2E , excess partial molar isentropic compressibility, K¯s,m,1EK¯s,m,2E over the whole composition range together with partial molar volume,V¯m,10, V¯m,20, partial molar isentropic compressibility K¯s,m,10,K¯s,m,20, excess partial molar volume,V¯m,10E, V¯m,20E and excess partial molar isentropic compressibility, K¯s,m,10E,K¯s,m,20E at infinite dilution have also been calculated. All excess properties have been correlated using the Redlich-Kister smoothing polynomial equation. The VmE results are analysed in the light of Prigogine-Flory-Patterson theory. Analysis of each of the three contributions viz. interactional, free volume, and P* to VmE has shown that interactional contribution and free volume effect are negative for all the mixtures, and P* contribution is positive for the mixtures of 2-ME. The variations of these parameters with changes in composition and temperature have been discussed in terms of intermolecular interactions prevailing in these mixtures. Further, the viscosities of these binary mixtures were correlated theoretically by using various empirical and semi-empirical models and the results were compared with the experimental findings.

Ultrasonic Velocity of Acrylates with Decane-2-ol at 313.15 K

Thermodynamic data involving ultrasonic velocities of binary liquid mixtures of methyl acrylate, ethyl acrylate and butyl acrylate with decane-2-ol have been measured at 313.15 K and at atmospheric pressure. Study of thermodynamic properties involves challenges of interpreting the excess quantities as a means of understanding the nature of intermolecular interactions among the mixed components. Experimental values of ultrasonic velocities were correlated with recently proposed Jouyban-Acree model. Deviations in isentropic compressibility were calculated and have been fitted to Redlich-Kister polynomial equation. Excess parameters like specific acoustic impendence, intermolecular free length, available volume, intrinsic pressure, molecular association and molar sound velocity were also calculated. Graphical representations of excess derived thermodynamic parameters used to explain the type and extent of intermolecular interactions

Physicochemical properties of binary mixtures of cation-fluorinated ionic liquids with their non-fluorinated analogues

This work reports an investigation of the physicochemical properties (density, viscosity, refractive index and thermal stability) of four binary mixtures having a common acetate ([OAc]¯), trifluoromethanesulfonate ([OTf]¯) or bis(trifluoromethylsulfonyl)imide ([NTf2]¯) anion with either cation-fluorinated and non-fluorinated methylimidazolium (MIm) or pyridinium (Py) cations respectively, at various temperatures. The mixing behaviour of the binary mixtures was analysed by 1H and 19F Nuclear magnetic resonance (NMR) spectrometry, and the excess properties of the mixtures were calculated from the physicochemical data. The binary mixtures of fluorinated ionic liquids (FILs) with their non-fluorinated or alkyl-substituted analogues (AILs) showed an increase in density and viscosity but a decrease in refractive index with an increase in mole fraction of the pure FILs. The thermal stability of the AILs was higher than the FILs, however, an increase in the mole fraction of the pure FILs in the binary mixtures made a negligible impact on the thermal stability of the binary mixtures. These binary mixtures were found to deviate from ideal behaviour for the different physicochemical properties tending to vary between the extremes of the pure components. The large differences in properties of FILs compared with their non-fluorinated analogues were shown to be associated with the size of the fluorine atoms in the fluoro-alkyl chain, the tendency of the fluoro-alkyl chain to form aggregates with fluorinated anions, and the hydrogen bond acceptor strength of the anions. The excess properties were fitted to the Redlich-Kister polynomial equation, and no significant deviation was obtained. This study shows that the physicochemical properties of the fluorinated ionic liquids can conveniently be adjusted for specific applications by simply varying the amount of the cation-fluorinated component in binary mixtures.

Properties of La2F4Se, B–LaFSe phases. Phase diagram of the LaF3–La2Se3 system

Lanthanum selenidofluorides belong to wide-gap semiconductors and are promising for optoelectronics. La2F4Se, B–LaFSe compounds were obtained by the ampoule method from binary compounds. Crystals La2F4Se, R-3m, a = 4.18245(11) Å, c = 23.2939(6) Å, Z = 3, B–LaFSe P63/mmc, a = 4.21989(5) Å, c = 8.19140(10) Å, Z = 2 have a layered grain structure, their microhardnesses are 340 and 450 HV, which allows samples processing. The optical bandgap of La2F4Se is 4.5 eV. The optical bandgaps of La2F4Se and B–LaFSe were analyzed by comparing the calculated absorption spectra and the experimental Kubelka-Munk Functions. It was shown that this approach is attractive in explaining optical properties in the vicinity of fundamental absorption onset and in neighboring regions. In LaF3–La2Se3 system, temperatures and enthalpies of five phase transformations were determined, and their balance equations were obtained. It was shown that La2F4Se, B–LaFSe compounds melt incongruently and that an eutectic is formed between the phases. A phase diagram of LaF3–La2Se3 system was constructed. The liquidus calculated by Redlich-Kister polynomial agrees with the data of differential scanning calorimetry.

Thermodynamic, Structural and Surface Properties of Liquid Al-Sr Alloy at Different Temperatures

Thermodynamic functions like excess Gibbs free energy of mixing (∆GxsM) and activity (a) of liquid Al-Sr alloy were studied in the temperature range 1323-1623 K in the frame work of Redlich-Kister (R-K) polynomial. The compositional and temperature dependence of structural functions like concentration fluctuation in long wavelength limit (Scc(0)), Warren-Cowley short range order parameter (α) and ratio of mutual to intrinsic diffusion coefficients (Dm/Did) were computed and analysed using the same approach. The surface tension (σ) and surface segregation (xsi) tendencies of the atoms in the liquid mixture were computed and studied using Butler’s model. Present investigations revealed that association tendency among the atoms of metallic mixture gradually decreased with increase in temperature.

Molecular interaction study using density, viscosity, speed of sound and FT-IR in 2-methyl-2-butanol + alkoxyethanols: Experimental and modelling approach

In this article, the intermolecular interactions in the binary liquid mixtures of 2-methyl-2-butanol with alkoxyethanols viz., 2-ethoxyethanol, 2-propoxyethanol and 2-butoxyethanol have been interpreted using thermophysical properties. Density (ρ), viscosity (η) and speed of sound (u) of pure components and their binary mixtures have been measured over the entire range of composition at 298.15, 303.15 and 308.15 K and at pressure p = 0.10 MPa. The experimental data were used to calculate the thermophysical properties such as excess molar volume (VmE), excess molar isentropic compressibility (Ks,mE), excess speed of sound (uE), deviation in viscosity (Δη) and excess Gibbs free energy of activation for viscous flow (ΔG∗E). The changes in these properties with composition and temperature of the liquid mixtures were discussed in terms of intermolecular interactions. Also, the effect of increase in alkyl chain length of alkoxyethanol molecule on these properties has been studied. The excess functions and their deviations have been correlated using Redlich-Kister type polynomial equation. The experimentally measured values of viscosities have been correlated with various semi-empirical relations such as Grunberg-Nissan, Tamura-Kurata, Hind et al., Katti-Chaudhri, McAllister’s two parameter model, Heric-Brewer and McAllister’s three parameter model. Apart from this, Prigogine-Flory-Patterson (PFP) theory has been used for the estimation of VmE values for studied binary mixtures. FT-IR spectra of these liquid mixtures have also been studied.

Excess Thermodynamic Properties of Binary Liquid System Containing (Cyclic Ether + Octan-1-Ol) At Different Temperature

The ultrasonic velocity (u), density (ρ), and viscosity ( ) for the binary mixture 1,4-Dioxane (1) + Octan-1-ol (2) were measured over the whole composition range at temperature T = (298.15, 303.15 and 305.15) K. The experimental data have been used to calculate excess molar volume (VE), excess adiabatic compressibility ( ), excess viscosity ( ), excess intermolecular free length ( and excess internal pressure (PiE) over the entire composition range. These results have been fitted to the Redlich-Kister polynomial equation. Excess molar volume (VE), excess adiabatic compressibility ( ), excess viscosity ( ), excess intermolecular free length ( and excess internal pressure (PiE) were found to be negative for all temperatures. The results obtained have been discussed and interpreted in terms of the type and nature of the specific intermolecular interactions between the components.

A study on thermophysical properties of binary mixtures of n-hexane with benzene and some alkyl-substituted benzenes within temperature range (293.15–323.15) K: Experimental and modeling approach

The current work reports densities and sound speeds, and related thermodynamic excess properties, namely excess molar volumes and excess isentropic compressibilities, measured at temperatures from (293.15 to 323.15) K and under atmospheric pressure conditions for binary mixtures of n-hexane with benzene, toluene, ethylbenzene, o-xylene, m-xylene, and p-xylene. Redlich-Kister polynomial correlated the thermodynamic excess properties to test the quality of experimental data. Excess properties contributed to understanding molecular interactions between involved molecules and the peculiarities of their packing in the mixture. The Jouyban-Acree model was used to correlate the mixtures' experimental densities, sound speeds, and their related derived properties, namely isobaric thermal expansivities and isentropic compressibilities. The average absolute percentage deviation of the correlated values from the experimental ones was better than 0.036 %, 0.058 %, 0.040 %, and 0.146 % for density, sound speed, isobaric thermal expansivity, and isentropic compressibility, respectively, attesting to the robustness of the Jouyban-Acree correlations. Additionally, the Perturbed Chain Statistical Associating Fluid Theory Equation of State modeled the densities of the current mixtures. Schaaff's Collision Factor Theory and Nomoto's relation were compared for their ability to model the sound speeds of the mixtures. The efficacy of these models was tested by computing the average absolute percentage deviations between experimental and computed values. The modeled densities are reasonably concordant with experimental data, with an overall deviation of 0.02 %. Notably, Nomoto's relation exhibited superior performance over Schaaff's theory in modeling sound speeds of current mixtures, with an overall deviation of 0.33 %. The current findings underline the efficacy and versatility of the used models for thermodynamic modeling in systems of varying complexity.

Molecular Interaction Studies of Binary Mixtures of Diethyl Oxalate With Butyl Vinyl Ether, Diisopropyl Ether, Anisole and Dibutyl Ether in Terms of Thermodynamic, Transport and Acoustic Properties

Viscosity, the speeds of sound and density were measured in the binary mixtures of diethyl oxalate with butyl vinyl ether, diisopropyl ether, anisole and dibutyl ether at T = 303.15, 308.15 and 313.15 K. The experimental data were used to calculate the excess molar volume ,deviation in viscosity Δη and the acoustical parameters, namely isentropic compressibility (KS), free volume (Vf ), free length (Lf ) and internal pressure (πi). The excess or deviation properties were fitted to the Redlich-Kister polynomials and the results interpreted in terms of the molecular interactions present in mixtures. Theoretical viscosities were calculated using the Grunberg-Nissan, Lobe and Krishnan-Laddha models before their merits were studied in terms of interaction parameters.

Thermodynamic Modeling of the Au-Ge-X (X = In, Sb, Si, Zn) Ternary Systems.

In this study, the CALPHAD approach was employed to model the thermodynamics of the Au-Ge-X (X = In, Sb, Si, Zn) ternary systems, leveraging experimental phase equilibria data and previous assessments of related binary subsystems. The solution phases were modeled as substitutional solutions, and their excess Gibbs energies were expressed using the Redlich-Kister polynomial. Owing to the unavailability of experimental data, the solubility of the third elements in the Au-In, Au-Sb, and Au-Zn binary intermetallic compounds was excluded from consideration. Additionally, stable ternary intermetallic compounds were not reported in the literature and, thus, were not taken into account in the present thermodynamic calculations. Calculations of liquidus projections, isothermal sections, and vertical sections for these ternary systems have been performed, aligning with existing experimental findings. These thermodynamic parameters form a vital basis for creating a comprehensive thermodynamic database for Au-Ge-based alloys, which is essential for the design and development of new high-temperature Pb-free solders.

Study of the intermolecular interaction in hydrophobic deep eutectic solvent of (2-n-octyl-4-isothiazolin-3-one + 1-decanol) from the density, viscosity, thermodynamic, spectroscopic and quantum chemical calculations

Hydrophobic deep eutectic solvents (HDESs) are considered as green solvents and have been developed rapidly in recent years, which are widely used in diverse applications. In this study, we introduce a binary system composed of 2-n-octyl-4-isothiazolin-3-one (OIT) as a novel hydrogen bond acceptor (HBA) and 1-decanol as a hydrogen bond donor (HBD) under atmospheric pressure. The fundamental physicochemical properties, including density and dynamic viscosity, of the binary systems with various mole ratios were measured at temperatures of 293.15 K, 303.15 K, 313.15 K, 323.15 K, and 333.15 K. The excess molar volume (VmE), viscosity deviation (Δη) and excess Gibbs free energy (ΔG∗E) for activation of viscous flow were calculated and fitted according to the Redlich-Kister type polynomial equation. Furthermore, the spectral analysis (FTIR, UV–vis and 1H NMR) confirmed the presence of intermolecular hydrogen bonding in the binary systems. In addition, quantum chemical calculations revealed that there may be multiple modes of hydrogen bond formation between OIT molecule and 1-decanol molecule. However, selecting the most energetically favorable point, the most prominent hydrogen bond was found to be between the amide O atom of OIT and the hydroxyl H atom of 1-decanol.

Density, Speed of Sound and Derived Properties of Binary Mixtures Propiophenone + Butoxyethanol at T = (303.15, 308.15, 313.15 and 318.15) K

The current study reports the experimental density (ρ) and sound speed (u) values for binary mixes of liquids propiophenone + 2-butoxyethanol at atmospheric pressure (0.1 MPa) and T = (303.15, 308.15, 313.15 and 318.15) K for the full spectrum of composition. densities and sound speed measurements from experiments have been used to estimate excess isentropic compressibility (κsE), excess molar volume (VEm), excess molar isentropic compressibility (KEs,m), excess isobaric thermal expansivity (αEp) and excess sound speed (uE). The Redlich-Kister polynomials were used to correlate excess parameters. Excess partial molar volume quantities (VEm,1 and VEm,2) at infinite dilution and their limiting values (V0Em,1 and V0Em,2) have been analytically determined using Redlich-Kister polynomials from the experimental density data. The results have been analyzed in light of strength and interactions among molecular entities scope and extent prevalent in these mixtures.

Machine learning-assisted measurement of lithium transport using operando optical microscopy

Diffusion coefficients of electrode materials are often determined using galvanostatic (GITT) or potentiostatic intermittent titration technique (PITT), electrochemical impedance spectroscopy (EIS) or cyclic voltammetry (CV). However, these methods require special care as for each, their formal derivations use quite restrictive assumptions. As an alternative, a machine learning model is developed to extend a previously proposed optical method of studying lithium transport by operando microscopy. The herein reported model enables the measurement of concentration-dependent diffusion coefficients. For this purpose, a python code is developed that determines concentration profiles from RGB images using support vector regression (SVR), a flexible machine learning tool. To evaluate the diffusion coefficient, an inverse Boltzmann-Matano concept is applied. Representing the diffusion coefficient with generalized Redlich-Kister polynomials, concentration profiles are predicted and fit to the measured data. The method is demonstrated here on the example of delithiation of LiMn2O4, but it can, in-principle, be extended to any other battery material showing significant optical response on lithiation, which most of them do.