Lignin Oxidation Research Articles

Catalytic fractionation of Palm Kernel shell with Co and Cu over zeolite HY catalysts

Lignocellulosic biomass has the potential to be transformed valuable chemicals. This study extracted lignin from palm kernel shell with liquid phased oxidative fractionation in the presence of Co and Cu loaded over Zeolite HY catalysts. The oxidative fractionation was conducted at temperatures ranging from 140 °C to 180 °C, with various reaction times of 2–4 h. The GCMS analysis identified various products from the oxidative conversion including phenol derivatives (Butylated hydroxytoluene, 1,2-Benzenediol, etc.), phenolic aldehydes (Vanillin, Syringaldehyde, p-hydroxybenzaldehyde, etc.), and carboxylic acids (p-hydroxybenzoic acid, vanillic acid etc.). At a reaction temperature of 180 °C with a 2 h reaction time, Co/Zeolite HY catalyst yielded 9.81% and Cu/Zeolite HY catalyst yielded 13.53% for phenol derivatives. The optimal yield of lignin-derived compounds was achieved with a 5 wt% catalyst loading in the context of biomass weight, particularly with a 10% metal loading of Co and Cu over Zeolite HY support. Additionally, the total yield of lignin-derived compounds obtained was 32.85% for 10%Co/Zeolite HY and 23.89% for 10%Cu/Zeolite HY, catalysts respectively. This research displays incorporating metals into zeolite support subsequently boosts their catalytic efficiency in lignin oxidation.

Solvent screening for the extraction of aromatic aldehydes

The aromatic aldehydes vanillin, syringaldehyde, and p-hydroxybenzaldehyde find applicability in a broad field ranging from additives in food, cosmetics, and fragrances to precursors of electrochemically active substances used in organic redox flow batteries. These aldehydes can be obtained by wet oxidation of lignin a macromolecule present in woody biomass followed by the isolation via solvent extraction from the resulting acidic solutions.The present study investigates solvents grouped by esters, ethers, terpenes, and terpenoids, in addition to 1-octanol for their performance in extraction of the aromatic aldehydes vanillin, p-hydroxybenzaldehyde and syringaldehyde from an acidic aqueous solution. Solvent extractions are performed at 25 and 50 °C in double-walled tempered separation funnels. The overall extraction efficiency is determined by back-extractions performing a pH-swing at 25 °C. Aldehyde concentrations are measured by HPLC-UV. Karl-Fischer titration and total organic carbon measurements are used to account for the mutual solubility.The best-performing solvent in the case of aldehyde yields at low mutual solubility is given by the ester butyl acetate with extraction efficiencies of 96.53 % for p-hydroxybenzaldehyde, and > 95 % and > 93 % for vanillin and syringaldehyde, respectively. The highest overall extraction efficiency among all solvents suitable for alkaline back-extraction is achieved by cyclopentyl methyl ether with 94.73 % for p-hydroxybenzaldehyde, 94.04 % for vanillin and 87.91 % for syringaldehyde. The solvents geraniol, 1-octanol, ethyl acetate, and 2-methyl tetrahydrofuran show increased uptake of water with ethyl acetate, and 2-methyl tetrahydrofuran pointing out a high solvent loss with 9.82 vol% and 15.84 vol%, respectively. The terpene p-cymene showed preferable extraction of vanillin and syringaldehyde over p-hydroxybenzaldehyde with mutual solubility below 0.02 vol%, which makes it and interesting candidate for multistage solvent extraction.

A Metallomicellar Catalyst for Controlled Oxidation of Alcohols and Lignin Mimics in Water using Open Air as Oxidant.

Alcohol groups and β-O-4 (C-C) linkages are widespread in biomass feedstock that are abundant renewable resource for value-added chemicals. The development of sustainable protocols for direct oxidation or oxidative cleavage of feedstock materials in a controlled fashion, using open air as an oxidant is an intellectually stimulating task to produce industrially important value-added carbonyls. Further, the oxidative depolymerization of lignin into fine chemicals has evoked interest in recent times. Herein, we report the first example of a catalyst system that could activate molecular oxygen from atmospheric air for controlled oxidation and oxidative cleavage/depolymerization of feedstock materials such as alcohols, β-O-4 (C-C) linkages and real lignin in water under open air conditions. The selectivity of carbonyl products is controlled by altering the pH between ~7.0 and ~12.0. The current strategy highlights the non-involvement of any external co-catalyst, oxidant, radical additives, and/or destructive organic solvents. The catalyst shows a wide substrate scope and eminent functional group tolerance. The upscaled multigram synthesis using an inexpensive catalyst and easily available oxidant evidences the practical utility of the developed protocol. A plausible mechanism has been proposed with the help of a few controlled experiments, and kinetic and computational studies.

Utilising Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) to track the oxidation of lignin by an alkaliphilic laccase.

Lignin is a complex heteroaromatic polymer which is one of the most abundant and diverse biopolymers on the planet. It comprises approximately one third of all woody plant matter, making it an attractive candidate as an alternative, renewable feedstock to petrochemicals to produce fine chemicals. However, the inherent complexity of lignin makes it difficult to analyse and characterise using common analytical techniques, proving a hindrance to the utilisation of lignin as a green chemical feedstock. Herein we outline the tracking of lignin degradation by an alkaliphilic laccase in a semi-quantitative manner using a combined chemical analysis approach using Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) to characterise shifts in chemical diversity and relative abundance of ions, and NMR to highlight changes in the structure of lignin. Specifically, an alkaliphilic laccase was used to degrade an industrially relevant lignin, with compounds such as syringaresinol being almost wholly removed (95%) after 24 hours of treatment. Structural analyses reinforced these findings, indicating a >50% loss of NMR signal relating to β-β linkages, of which syringaresinol is representative. Ultimately, this work underlines a combined analytical approach that can be used to gain a broader semi-quantitative understanding of the enzymatic activity of laccases within a complex, non-model mixture.

Pathways for vanillin production through alkaline aerobic oxidation of a phenolic lignin model compound, guaiacylglycerol-β-guaiacyl ether, in concentrated aqueous alkali

There are at least two plausible pathways for vanillin production in the alkaline aerobic oxidation of lignin, as suggested by the degradation of model compounds.

Mass Transfer in the Processes of Native Lignin Oxidation into Vanillin via Oxygen

The influence of mass transfer intensity on the kinetics of the catalytic oxidation of flax shives with oxygen in alkaline media to aromatic aldehydes and pulp was studied. The process was carried out in two autoclaves, with moderate stirring (stirrer engine of 8 W) and intense stirring (stirrer engine of 200 W). The oxidation of flax shives into vanillin, syringaldehyde, and pulp was shown to proceed as a completely diffusion-controlled process under the studied conditions, both moderate and intense stirring. Depending on the process conditions, it can be limited by stages of oxygen transfer through the diffusion boundary layer near the gas–liquid interface (low intensity of mass transfer) as well as by reagents’ inner diffusion in the porous and solid matter of the flax shive particle (high intensity of mass transfer). The results on the influence of the stirring speed and volume of the reaction mass on the rates of oxygen consumption and vanillin accumulation were obtained. They were described using a known simple model connecting the intensity of mass transfer and the stirring power density in the bulk of the liquid phase in terms of algebra equations.

Selective electrocatalytic oxidation of C(OH)–C bond in lignin with Pt@CeO2 toward the synthesis of benzoic acid

The synthesis of carboxylic acid compounds by the selective electrooxidation cleavage of the C(OH)-C bond in lignin is significant to biomass conversion to produce high-value-added chemicals. However, it is challenging to selectively cleave the C(OH)-C bond due to its extremely high dissociation energy of 260–300 kJ mol−1. Herein, a simple and effective method of hydrothermal process and wet impregnation is proposed to synthesize Pt@CeO2 catalysts. The cleavage of the C(OH)-C bond by Pt@CeO2, a catalyst loaded with a small amount of noble metal, triggered the electrochemical oxidation of lignin, resulting in the highly selective synthesis of carboxylic acid compounds. Consequently, more reactive oxygen species (ROS) are produced in the electrocatalytic oxidation process, which enhances the cleavage of C(OH)-C bond and the oxidation of benzaldehyde. In addition, Pt@CeO2 can also be used for the electrochemical depolymerization of industrial alkali lignin to produce carboxylic acids. This research proposes an efficient way of producing carboxylic acids of high value by utilizing an electrocatalyst for the electrocatalytic oxidation of lignin.

Lytic polysaccharide monooxygenase synergized with lignin-degrading enzymes for efficient lignin degradation

Even though the discovery of lytic polysaccharide monooxygenases (LPMOs) has fundamentally shifted our understanding of biomass degradation, most of the current studies focused on their roles in carbohydrate oxidation. However, no study demonstrated if LPMO could directly participate to the process of lignin degradation in lignin-degrading microbes. This study showed that LPMO could synergize with lignin-degrading enzymes for efficient lignin degradation in white-rot fungi. The transcriptomics analysis of fungi Irpex lacteus and Dichomitus squalens during their lignocellulosic biomass degradation processes surprisingly highlighted that LPMOs co-regulated with lignin-degrading enzymes, indicating their more versatile roles in the redox network. Biochemical analysis further confirmed that the purified LPMO from I.lacteus CD2 could use diverse electron donors to produce H2O2, drive Fenton reaction, and synergize with manganese peroxidase for lignin oxidation. The results thus indicated that LPMO might uniquely leverage the redox network toward dynamic and efficient degradation of different cell wall components.

Unraveling Electrochemical Lignin Degradation in Organic Solvent for Production of Valuable Fuels and Chemicals

Lignin is the second most abundant biopolymer in nature after cellulose. Due to its distinctive aromatic backbone, it is also one of the most unique biopolymers. The aromatic components in lignin provide structural support to plants and comprises about 30% of the plant material. These aromatic groups can be used to produce renewable aromatic compounds. Also, these aromatic compounds can be used to produce biofuels which can be promising alternative to fossil-based fuels and chemicals. Besides, from previous studies it is found that about 40 to 60 million tons of lignin are generated from pulp and paper industry, mostly as wastes. So, developing novel and attractive strategies for fragmentation of lignin is gaining increased interest among scientific community for valorizing this underexploited material. Also, by valorizing lignin the sustainability of biorefinery and paper industry can be enhanced. However, the present technologies used for degradation of lignin generally requires the use of metallic catalysts at high temperatures and harsh reaction conditions. As a result, catalyst recovery and decomposition often become difficult under such harsh conditions and the process becomes impractical. Also, these technologies suffer from poor selectivity and usually produce the desired fragmentation products in low yields. Compared to the thermocatalytic transformation of lignin, electrocatalytic approaches have several advantages like it is environmentally friendly, have mild reaction conditions and the cost is low. Besides, there is a lack of studies incorporating electrocatalytic oxidation and reduction of lignin in organic solvent. In this project, the main goal was to overcome the challenge of using isolated lignin from various industrial processes by electrochemical depolymerization of lignin in organic solvent like tetrahydrofuran. Tetrahydrofuran is mainly used in Co-solvent Enhanced Lignocellulosic Fractionation (CELF) process. So, electrocatalytic degradation of lignin in this solvent is beneficial because the product from CELF process can be directly used here and thus it can work as a secondary treatment process for CELF process. Cyclic voltammetry (CV) and Chronoamperometry (CA) which are important tools for identifying redox reactions happening in the system is used here. In this presentation, for varying concentrations of Lignin, Tetrahydrofuran and sulfuric acid the results found from CV and CA will be discussed with practical significance.Keywords: Recalcitrant biopolymer, Lignin in organic solvent, controlled electrocatalysis, secondary treatment for CELF process, Cyclic Voltammetry

Catalytic oxidation of different lignin over Ni-MOFs based catalyst in oxygen: Effect of catalysts and solvents

The industrial production of monophenols was mainly dependent on fossil resources, due to growing energy demand and escalating environmental issues, more efficient and sustainable strategy, such as utilization of biomass as raw materials to economically produce monophenols, was desired, which could liberate us from the reliance on fossil resource and was of great industrial and social significance. Herein, a novel strategy was reported to produce biomass-derived monophenols from lignin by directly deconstructing C-O bond under mild conditions. A series of NiM-MOFs (M=Co, Mo, and Cu) derived bimetallic catalysts were synthesized via a simple hydrothermal method, which were characterized by XRD, SEM, TEM, XPS and NH3-TPD. The synergistic effect between the Ni and Mo greatly improved the catalytic activity and inhibited the transformation to by-products. In addition, we explored a new binary solvents system of MeOH-THF to effectively enhance the selectivity of monophenols. Under optimal catalytic conditions, Ni4Mo1/C-BN catalyst could break the C-O bonds in lignin dimer under 160 ℃ to afford phenol and benzoic acid, and the possible reaction pathway was proposed. The high yield of lignin oil from the oxidation of various realistic lignin also confirmed the superiority of this catalytic system. The lignin depolymerization products were characterized by element analysis, GPC and GC-MS, confirming the presence of mainly guaiacyl-type (G) products, while the highest yield was assigned to vanillin.

Insights into Production of Hydroxybenzaldehydes via Lignin Oxidation

Insights into Production of Hydroxybenzaldehydes via Lignin Oxidation

Waste to wealth: H2S-free fabrication of Fe-ZnS/NC by industrial lignin self S-doping for efficient lignin aerobic oxidation

Industrial lignin mostly contains sulfur, which poisons metal catalysts easily. Metal sulfides with good S-resistance could be used as efficient catalysts for lignin oxidation, while metal sulfides preparation involved corrosive H2S. Here in, we proposed H2S-free fabrication of bimetallic Fe-ZnS/NC by industrial lignin self S-doping. The Fe-ZnS/NC 650 exhibited efficient oxidation activity (> 99% conversion) for β-O-4 cleavage and good S-resistance for industrial lignin oxidation. Density functional theory revealed the synergistic effect of FeS and ZnS in lignin oxidation, where FeS tended to activate O2 into superoxide radical (O2-•) and ZnS contributed to the polarization of β-O-4. The dual sites greatly reduced the migration distance of O2-• to the polarized β-O-4, facilitating the C-O/C-C cleavage. Hence, Fe-ZnS/NC 650 selectively converted lignin into carbonyl-containing aromatics with up to 92% selectivity under alkaline-free condition. This work developed a novel strategy using lignin-derived metal sulfide without external sulfur source for efficient lignin degradation.

Linkages between fluorescent dissolved organic matter and lignin phenols in the Canada Basin, Arctic Ocean

Lignin is one of the more refractory components of dissolved organic matter (DOM) and its concentration and composition are used to trace terrigenous DOM in the ocean. In this study, lignin oxidation products (LOP), and chromophoric and fluorescent DOM were measured in Polar Mixed Layer (PML), Atlantic water (AW), and Canada Basin Deep Water (CBDW) layers in the Canada Basin to elucidate the composition and source of terrestrial DOM. Significant differences in total lignin phenol concentration (Σ11) and cinnamyl to vanillyl ratio (C/V) measured with CuO oxidation in PML, AW, and CBDW samples were found. The fluorescence intensities of humic-like C1 were correlated with Σ11 in PML, congruent with the humic-like terrestrial origin. However, no significant correlation was found when all layers are considered (p > 0.05), suggesting a change in the molecular composition of C1. The protein-like C3 and C5 intensities were strongly correlated with Σ11 (rs = 0.55–0.64) corroborating that lignins can contribute to the protein-like fluorescence in the water column. The principal component analysis (PCA) confirmed the origin and composition of DOM vary between the different water masses, especially in terms of C/V, DOC, and fluorescent components. Significant relationships between humic-like fluorescence intensities and C/V reveal the significant contribution of woody sources to humic material in the Canada Basin. Elevated S/V and humic-like C6 levels were associated with a cold eddy DOM sample but further studies are required to validate the use of these DOM characteristics to trace deep eddy.

Effect of Substituents on Molecular Reactivity during Lignin Oxidation by Chlorine Dioxide: A Density Functional Theory Study.

Lignin is a polymer with a complex structure. It is widely present in lignocellulosic biomass, and it has a variety of functional group substituents and linkage forms. Especially during the oxidation reaction, the positioning effect of the different substituents of the benzene ring leads to differences in lignin reactivity. The position of the benzene ring branched chain with respect to methoxy is important. The study of the effect of benzene substituents on the oxidation reaction's activity is still an unfinished task. In this study, density functional theory (DFT) and the m062x/6-311+g (d) basis set were used. Differences in the processes of phenolic oxygen intermediates formed by phenolic lignin structures (with different substituents) with chlorine dioxide during the chlorine dioxide reaction were investigated. Six phenolic lignin model species with different structures were selected. Bond energies, electrostatic potentials, atomic charges, Fukui functions and double descriptors of lignin model substances and reaction energy barriers are compared. The effects of benzene ring branched chains and methoxy on the mechanism of chlorine dioxide oxidation of lignin were revealed systematically. The results showed that the substituents with shorter branched chains and strong electron-absorbing ability were more stable. Lignin is not easily susceptible to the effects of chlorine dioxide. The substituents with longer branched chains have a significant effect on the flow of electron clouds. The results demonstrate that chlorine dioxide can affect the electron arrangement around the molecule, which directly affects the electrophilic activity of the molecule. The electron-absorbing effect of methoxy leads to a low dissociation energy of the phenolic hydroxyl group. Electrophilic reagents are more likely to attack this reaction site. In addition, the stabilizing effect of methoxy on the molecular structure of lignin was also found.

Direct extraction of biphasic organosolv lignin for producing aromatic aldehydes via alkaline oxidation

Lignin can be a sustainable source of aromatic compounds, whereas the utilization is limited because of its complex three-dimensional structure. Organosolv method is promising for the valorization of lignin because of its mild conditions as compared with industrial pulping processes. Aromatic aldehydes, widely used in various industries, are obtained by catalytic oxidation of lignin. Organosolv treatment of various types of lignocellulose in water/1-butanol solvent was conducted using a batch type reactor. During the solvent removal from 1-butanol phase containing organosolv lignin, the concentrated lignin was denatured, which was evaluated by measuring particle size distribution and thermal decomposition behavior of the lignin. The recovery procedure of lignin was improved, and the extraction of organosolv lignin from 1-butanol phase to alkaline solution was developed. The improved extraction method definitely showed a higher yield of aromatic compounds regardless of the type of lignocellulose, yielding 14 C-mol% of aromatic aldehydes after alkaline oxidation of willow-derived lignin. After the alkaline oxidation reaction, a simple solvent fractionation was applied for refining the oxidized products. The solvent fractionation of the oxidized products was achieved using ethyl acetate and n-heptane. n-Heptane-soluble fraction selectively contained the lighter fraction with maintaining the content of aromatic compounds.

Touch wood: Conversion of lignin to dicarboxylic acids using biochar-based solid-acid photo-Fenton catalysts

The depolymerization of lignin into dicarboxylic acids (DCA) by the Fenton oxidation process is a promising approach to valorising lignin. However, Fenton oxidation is challenging due to the demand for acidic reaction conditions and homogeneous Fe2+ catalysts, which cannot be recovered. Herein, we fabricated a biochar-based solid-acid catalyst (SBC) from the pyrolysis of rice straw biomass followed by H2SO4 treatment. This novel catalyst achieved an enhanced catalytic performance in the activation of H2O2 under circumneutral pH, visible-light irradiation and Fe-free conditions. Under optimum conditions, a cumulative yield of 40.1 μ mol. gcat−1. h−1 of malonic, maleic, fumaric, succinic and gallic acid was obtained using 40 mM H2O2, 1 g/L catalyst loading and 4 h reaction time, which is comparable to yields reported in the literature under elevated temperatures and pressures. The activity of SBC stems from the synergy of oxygenated surface functional groups and persistent free radicals (PFRs), which can chemisorb and subsequently activate H2O2 and dissolved O2 to yield •OH and 1O2. Addition of NaN3 scavenger for 1O2 enhanced the cumulative DCA yields to 282.4 μ mol. gcat−1.h−1, suggesting that 1O2 is the main reactive oxygen species in the reaction. Finally, the SBC catalysts remained stable at the said reaction conditions and could be recycled without significant deactivation. After five cycles, the lignin conversion and cumulative DCA yields decreased by 19.7% and 23% respectively. These results show that Fe-free, visible-light Fenton-like catalytic oxidation of lignin with acid-modified biochars is a promising way to produce high-value platform chemicals.

Optimization of heterologous production of Bacillus ligniniphilus L1 laccase in Escherichia coli through statistical design of experiments

Laccases are powerful multi-copper oxidoreductases that have wide applicability as “green” biocatalysts in biotechnological, bioremediation, and industrial applications. Sustainable production of large amounts of functional laccases from original sources is limited by low yields, difficulties in purification, slow growth of the organisms, and high cost of production. Harnessing the full potential of these versatile biocatalysts will require the development of efficient heterologous systems that allow high-yield, scalable, and cost-effective production. We previously cloned a temperature- and pH-stable laccase from Bacillus ligniniphilus L1 (L1-lacc) that demonstrated remarkable activity in the oxidation of lignin and delignification for bioethanol production. However, L1-lacc is limited by low enzyme yields in both the source organism and heterologous systems. Here, to improve production yields and lower the cost of production, we optimized the recombinant E. coli BL21 strain for high-level production of L1-lacc. Several culture medium components and fermentation parameters were optimized using one-factor-at-a-time (OFAT) and Plackett-Burman design (PBD) to screen for important factors that were then optimized using response surface methodology (RSM) and an orthogonal design. The optimized medium composition had compound nitrogen (15.6 g/L), glucose (21.5 g/L), K2HPO4 (0.15 g/L), MgSO4 (1 g/L), and NaCl (7.5 g/L), which allowed a 3.3-fold yield improvement while subsequent optimization of eight fermentation parameters achieved further improvements to a final volumetric activity titer of 5.94 U/mL in 24 h. This represents a 7-fold yield increase compared to the initial medium and fermentation conditions. This work presents statistically guided optimization strategies for improving heterologous production of a bacterial laccase that resulted in a high-yielding, cost-efficient production system for an enzyme with promising applications in lignin valorization, biomass processing, and generation of novel composite thermoplastics.

Effect of Fenton oxidized lignin support on immobilized β-glucosidase activity.

In this study, the Fenton oxidized lignin was prepared to investigate the effect of Fenton oxidation modification on the activity of lignin immobilized β-glucosidase (β-GL). The results demonstrated that Fenton oxidation could significantly improve the activity and stability of immobilized β-GL. This is because the Fenton oxidation increased the electrostatic, hydrogen bonding, and hydrophobic forces between lignin and β-GL, resulting in increased lignin adsorption onto β-GL. The Fenton oxidation also changed the chemical structure of lignin, altering the lignin-β-GL binding site and reducing the negative effect of lignin on the β-GL catalytic domain. This research will improve understanding of the effect of Fenton lignin oxidation on immobilized β-GL activity and expand the use of lignin in enzyme immobilization.

The effect of oxygen bleaching on reactivity of syringyl and guaiacyl units of Eucalyptus tereticornis pulps lignin

Dioxin lignin of Eucalyptus tereticornis kraft pulps and its oxygen-treated pulps with kappa number 21.32, 12.84; 13.03, 12.18 were isolated and subjected to alkaline nitrobenzene oxidation studies to determine the structural changes during oxygen bleaching. HPLC quantitatively identified eight compounds during nitrobenzene oxidation of dioxin lignin in alkaline media. Lignin obtained from E. tereticornis has syringyl and guaiacyl units. Residual lignin composition in pulps was studied and found that during oxygen delignification, the syringyl unit was degraded more in comparison to guaiacyl and p-hydroxy phenyl unit, i.e., the molar ratio of syringyl unit is lower than guaiacyl and p-hydroxy phenyl unit. The results are adequately described in the research.

Structure of oxidized hydrolysis lignin

The main goal of this study was the elucidation of structures of products of oxidation of industrial hydrolysis lignin (HL) obtained in the system H2O2-H2SO4-H2O. It was found that the obtained oxidized hydrolysis lignin (OHL) contained structural fragments of muconic acid dilactone. The latter appeared as a result of the oxidation of aromatic ring of HL into unstable structures of 3,4-dihydroxyadipic acid, which are spontaneously cyclized into the corresponding fragments of muconic acid dilactone in acidic oxidative medium. Consequent reaction of OHL with aqueous sodium hydroxide (NaOH) led to the formation of sodium salt of OHL (Na-OHL), in which the muconic acid dilactone units of OHL opened into fragments of disodium salts of 3,4-dihydroxyadipic acid. The Na-OHL was transformed into the series of novel derivatives of lignins. Thus, the reaction of Na-OHL with thionyl chloride proceeded as a substitution of hydroxyl groups into chlorine atoms in the structure of OHL, that afforded chloro-derivative of OHL. The latter was transformed into amino-amide and ester-ether derivatives of OHL by nucleophilic substitution of chlorine atoms with amines and alcohols correspondingly.