Soil Thin Layer Research Articles

Availability of Metribuzin-Loaded Polymeric Nanoparticles in Different Soil Systems: An Important Study on the Development of Safe Nanoherbicides.

Nanoformulations have been used to improve the delivery of fertilizers, pesticides, and growth regulators, with a focus on more sustainable agriculture. Nanoherbicide research has focused on efficiency gains through targeted delivery and environmental risk reduction. However, research on the behavior and safety of the application of these formulations in cropping systems is still limited. Organic matter contained in cropping systems can change the dynamics of herbicide−soil interactions in the presence of nanoformulations. The aim of this study was to use classical protocols from regulatory studies to understand the retention and mobility dynamics of a metribuzin nanoformulation, compared to a conventional formulation. We used different soil systems and soil with added fresh organic material. The batch method was used for sorption−desorption studies and soil thin layer chromatography for mobility studies, both by radiometric techniques. Sorption parameters for both formulations showed that retention is a reversible process in all soil systems (H~1.0). In deep soil with added fresh organic material, nanoformulation was more sorbed (14.61 ± 1.41%) than commercial formulation (9.72 ± 1.81%) (p < 0.05). However, even with the presence of straw as a physical barrier, metribuzin in nano and conventional formulations was mobile in the soil, indicating that the straw can act as a barrier to reduce herbicide mobility but is not impeditive to herbicide availability in the soil. Our results suggest that environmental safety depends on organic material maintenance in the soil system. The availability can be essential for weed control, associated with nanoformulation efficiency, in relation to the conventional formulation.

Development of micro-zymography: Visualization of enzymatic activity at the microscopic scale for aggregates collected from the rhizosphere

AimsVisualization of enzymatic activity links microbial functioning to localization in heterogeneous soil habitats. To assess enzymatic reactions in soil thin layer at the microscopic level, we developed a micro-zymography approach and tested it by visualization of the potential activity of phosphomonoesterase for aggregates collected from the rhizosphere of Zea mays L.MethodsWe evaluated micro-zymography by applying fluorogenically-labeled substrate i) on individual soil aggregates freshly sampled from the rhizosphere, ii) on thin layers of aggregates (≈ 500 µm) saturated with substrate to assess the dynamics of phosphomonoesterase activity, and iii) on maize roots under laser scanning microscope upon the identified hotspots by membrane-based zymography.ResultsWe found super transparent silicon as the most appropriate fixative to prevent sample drying. We optimized microscope settings to eliminate the soil auto-fluorescence. The fluorescent signal shifted from the free liquid phase towards the aggregate boundaries within 30 min after substrate addition and was finally detectable at the surface of a few aggregates. This was probably due to higher microbial abundance and enzymatic activity on the soil aggregates compared to the liquid phase. The enzymatic activity appeared patchy at the aggregate and root surfaces indicating heterogeneous distribution of hotspots.ConclusionsThe methodology including calibration, sample preparation, fixation, and monitoring was developed. The novel membrane-free micro-zymography approach is a promising tool to identify functional specificity and niche differentiation on roots and soil aggregates. This approach revealed unexplained complexity of competing processes (biochemical, hydrolytic, and physical) due to differently charged reaction products and enzyme-clay complexes.

Effects of root exudates on the mobility of pyrene in mangrove sediment-water system

Mangrove ecosystems receive substantial polycyclic aromatic hydrocarbons (PAHs) from human activities. The mechanism of transport and translocation of PAHs within mangrove sediment is not well understood. In the present study, the mobility of pyrene in two typical mangrove sediments was studied using soil thin layer chromatography (TLC). The mobility of pyrene in the sediments displayed an inverse trend with organic carbon (foc) content. As one of the important fraction in sediment organic matter pool, the influence of root exudates on adsorption of pyrene within the tested sediments was also evaluated. In particular, root exudates significantly enhanced the bioavailability and mobility of pyrene in the sediments. The effectiveness of root exudates in promotion of pyrene mobility follows an order: citric acid>oxalic acid>malic acid>artificial root exudates (ARE). In addition, mobility factors of pyrene from root exudate treatments were significantly higher than the value determined in the control, and the magnitude of mobility factor (Rf) showed a positive correlation with root exudate concentrations. Results of this study could promote our understanding of the mobility of PAHs in contaminated mangrove sediments.

Effect of Soil Chemical and Physical Properties on Cd Mobility Studied by Soil Thin-Layer Chromatography

Heavy metals contamination threat to the environment is a big concern. Predicting the movement of heavy metals such as Cd in soil is an important goal. In this study the effect of soil chemical and physical properties on Cd mobility were done using a thin layer chromatography (Soil TLC). The soils used in this research have a wide range of organic matter (2.1-29 g/kg), pH value (4.9-8.8), CEC (4.1-99 cmol/kg), bases saturation, iron and aluminum oxides to examines its effect on Cd mobility. The (Rf) values obtained from soil thin layer chromatography ranged from 0.25 to 0.95 and it showed that Cd was slightly mobile in 64 %, moderately mobile in 29 % and very mobile in 7 % of the soils. The Rf indicates that Cd mobility would decrease with increasing amounts of iron oxide fractions; silt % and exchangeable Mg2+ in the soils. Rcd values increased with increasing amounts of the iron oxide fractions (Feo, Fep, and Fed); silt % and exchangeable Mg2+ in the soils. Finally, both Rcd and Rf factors showed Cd mobility to be higher in those soils with a high percentage of sand.

Effect of CPC, Brij-35, and SDBS Surfactants on the Adsorption and Movement of Carbofuran in Indian Soils

Laboratory studies were conducted to determine adsorption and movement of carbofuran in aqueous surfactant-free and surfactant [(cationic, cetyl pyridinium chloride (CPC), non-ionic, polyoxyethylene lauryl ether (Brij-35) and anionic, sodium dodecyl benezene sulphonate (SDBS)] solutions of different critical micellar concentrations (1/2 × CMC, 1.0 × CMC, and 2 × CMC) in four different Indian soils using batch shake and soil thin layer chromatography (soil TLC) techniques. The measured equilibrium adsorption isotherms were in agreement with the Freundlich equation. Higher adsorption of carbofuran in both systems was observed on FRI silt loam (FSL) soil followed by Alampur silt loam (ASL), Kalai loam (KL), and Bhoran sandy loam (BSL) soils, as anticipated from Freundlich constant KF and distribution coefficient KD, in surfactant-free systems and KF* and KD* in surfactant-soil-water systems. The adsorption of carbofuran in surfactant-soil-water systems followed the order cationic > anionic > non-ionic at all CMCs studied. The Rf values obtained from soil TLC studies confirmed the above order of adsorption. The KD and KD* values were used to evaluate remediation efficiency (KD*/KD) of surfactants. Non-ionic surfactant, Brij-35, and anionic surfactant, SDBS, are favorable for remediating soil contaminated with carbofuran as KD*/KD ratio is less than 1.

The Environmental Risk Assessment of Herbicide Anilofos on Various Chinese Cultivated Soils

Anilofos is the organophosphorus herbicide widely used in China. However, little is known on the processes governing the environmental fate of anilofos in soils and its environmental risk for groundwater. Several environmental fate studies were performed concerning the degradation, sorption, photolysis and mobility of anilofos in soils. The degradation of anilofos in three Chinese soil samples followed first-order kinetics, with half-lives between 64.2 d-161.2 d. The adsorption coefficient (KF) values for the three soils were 10.67 (loam), 31.29 (clay) and 11.63 (sand). No notable photolysis of anilofos occurred on soil surface. Leaching tests, performed in manually packed soil glass-plate, indicated that anilofos moved very slowly on the three types of soil thin layer. Thus, the leaching behavior of anilofos coincided well with the results of the batch sorption and degradation experiments. The data generated from this study could be helpful for risk assessment studies of the pesticide in the environment.

Photoinduced Oxidation of the Insecticide Phenothrin on Soil Surfaces

Photodegradation profiles of the pyrethroid insecticide phenothrin on a moistened U.S. soil thin layer was investigated by using its predominant component, the 1R-trans-isomer (I), under continuous exposure to light at >290 nm from a xenon arc lamp. Its degradation was moderately accelerated by irradiation with half-lives of 5.7-5.9 days (dark control 21-24 days), mainly via successive oxidation of the 2-methylprop-1-enyl group and ester cleavage followed by mineralization to carbon dioxide. Spectroscopic and cochromatographic analyses showed that the major degradates were the alcohol and ketone derivatives of I formed via photoinduced oxidation of the 2-methylprop-1-enyl group by singlet oxygen. The photoinduced generation of singlet oxygen in/on the soil surface was confirmed by using chemical trapping reactions together with ESR spectroscopy.

Effect of polar-dissolved organic matter fractions on the mobility of prometryne in soil

Purpose Using two fractions of dissolved organic matter (DOM) with different polarity, we carried out the experiments with standard batch equilibration, soil column leaching, and soil thin layer chromatography to investigate the behavior of the herbicide prometryne in soils. The purpose of the study was to: (1) separate DOM into hydrophilic matter and hydrophobic acid forms and characterize their chemical properties; (2) analyze interaction between the DOM fractions and prometryne in soils.

Adsorption and movement of carbaryl in soils: A verification of cosolvent theory and comparison of batch equilibrium and soil thin layer chromatography results

Batch equilibrium and soil thin layer chromatography (TLC) techniques were used to investigate the influence of different volume fractions of organic cosolvents (acetone and methanol) on the adsorption and movement of carbaryl in four different types of Indian soils. L-shaped isotherms were obtained for both the cosolvent–water mixtures at all f s values and were in close agreement with the Freundlich equation. Higher adsorption was observed on F.R.I. soil (FSL) followed by Alampur soil (ASL), Kalai soil (KL), and Bhoran soil (BSL) at all f s values for both the cosolvent systems as was anticipated from the K and K D values. The K and K D values also confirmed that carbaryl adsorption was higher in methanol–water mixture than acetone–water mixture and decreased with increasing f s values. The frontal R f values obtained from soil TLC studies were inversely proportional to the K and K D values for both the cosolvent systems. The higher K and K D values and lower R f values in methanol–water mixtures relative to acetone–water mixtures for all the soils indicated that acetone had a greater potential for ground water contamination compared to methanol. The adsorption data were used to evaluate the cosolvent theory for describing adsorption of carbaryl in acetone–water and methanol–water mixtures. The aqueous phase partition coefficients, K DW (mol g−1), normalized with respect to f oc for carbaryl was evaluated by extrapolating f s → 0.

Evaluation of the Effect of Surfactants on the Adsorption and Movement of Carbaryl in Soils of Divergent Texture

The adsorption and movement of carbaryl on soils in surfactant-free and surfactant (cationic, non-ionic, anionic) solutions of different critical micelle concentrations (CMCs) has been studied using batch equilibrium and soil thin layer chromatography (soil TLC) techniques. The adsorption of carbaryl in surfactant-soil-water systems followed the order cationic > anionic > non-ionic as anticipated from the Freundlich constant, KF, and distribution coefficient, KD, values. The Rf values obtained from soil TLC studies were inversely proportional to the KF and KD values. The affinities of carbaryl towards organic carbon and the clay content of the soil were compared using the KOC and KC values. The behaviour of carbaryl in surfactant-soil-water systems mainly depends on the degree of hydrophobicity of the pesticide and the type and concentration of surfactant used. The K*D/KD ratios were used to evaluate the remediation efficiency of surfactants and it was found that anionic surfactant is a better choice for ...

Adsorption and Movement of Carbofuran in Four Different Soils Varying in Physical and Chemical Properties

Laboratory studies were conducted to determine the adsorption and movement of carbofuran on four divergent textured Indian soils at a fixed volume fraction (fs = 0.1) of methanol/water mixtures using batch equilibrium and soil thin layer chromatography (soil TLC) techniques. The measured equilibrium adsorption isotherms for silt loam (FSL and ASL) and loam (KL) soils were L-shaped and for sandy loam (BSL) soil S-shaped, all being well fitted by the Freundlich isotherm. A higher adsorption of carbofuran was observed on FSL followed by ASL, KL and BSL soils as anticipated by the values obtained for the Freundlich constant, KF and partition coefficient, KD. The Frontal Retardation factor (FRf) values obtained from soil TLC studies were inversely proportional to the KF and KD values. The affinity of carbofuran towards organic carbon, organic matter and clay content of the soils was evaluated by calculating the KOC, KOM and KC values. The negative magnitude of the Gibbs'free energy (ΔG0) indicated the spontaneity of the adsorption of carbofuran onto the soils studied. The leaching index (LI) of carbofuran calculated for the soils studied indicated its high potential to leach into shallow aquifers and ground water. Pearson's correlations calculated for KF and KD against the soil properties showed a highly significant correlation with the clay + silt content of the soils. Multiple regression of KF and KD against the soil properties indicated that the mineral content of the soils (clay and clay + silt) is the best predictor of carbofuran adsorption, followed by soil pH. Predicted log KOM values were also evaluated by using the aqueous solubility, the 1-octanol/ water partition coefficient (KOW), the adsorbability index (AI) and the first-order molecular connectivity index (1χ) of carbofuran. Use of the aqueous solubility, and the 1-octanol/water partition coefficient (KOW) to predict the extent of adsorption gave values which displayed a considerable error in comparison to those measured experimentally, whereas the use of the adsorbability index (AI) and the first-order molecular connectivity index (1χ) of carbofuran improved the predictions considerably.

Mobility of Prometryne in Soil As Affected by Dissolved Organic Matter

Incorporation of organic fertilizers/amendments in soils has been, and will continue to be, a popular strategy for improving the quality of arable soils. However, the mechanism by which the dissolved organic matters (DOMs) affect soil properties or interact with other substances in soils is largely unknown. In this study, a batch equilibrium experiment was performed to evaluate the effect of two types of DOMs on the behavior of prometryne (a herbicide) in soils. Two sorts of DOMs were derived from lakebed sludge (SL) and rice straw (ST), respectively. The results show that sorption capacity in one soil for prometryne was significantly reduced by application of DOMs, whereas desorption of prometryne was promoted by DOM treatments. To understand the mobility behavior of prometryne in soils with DOMs, a column leaching experiment was carried out. It is shown that both DOMs enhanced the solubility and migration of prometryne in soils. To confirm the role of DOMs in regulating the mobility of prometryne in soils, a soil thin-layer chromatography was performed. The migration of prometryne was promoted by DOMs, which were used as a developing solvent or directly incorporated in the soil thin layer. The data indicate that DOM extracts can modify the mobility of prometryne in soil.

Adsorption and Movement of Endosulfan in Soils: A Verification of the Co-Solvent Theory and a Comparison of Batch Equilibrium and Soil Thin Layer Chromatography Results

Batch equilibrium and soil thin-layer chromatography (soil TLC) techniques were used to investigate the influence of different volume fractions (fs = 0.25, 0.50, 0.75 and 1.0) of organic co-solvents (acetone and methanol) on the adsorption and movement of endosulfan in three different types of Indian soils (silt loam, loam and sandy loam).The measured equilibrium adsorption isotherms for all three soils studied were L-shaped for both co-solvent/water mixtures at all fs values. All isotherms were in close agreement with the Freundlich equation. Higher adsorption of endosulfan was observed on silt loam soil followed by loam and sandy loam soils at all fs values for both co-solvent systems, as was anticipated from the values of the Freundlich constants, K, and the partition coefficients, KD. The order of the K and KD values also confirmed that endosulfan adsorption was higher in methanol/water mixtures than in acetone/water mixtures and decreased with increasing fs values.The Rf values obtained from soil TLC...

Relationship between mobility factors ( R f) of two hydrophobic termiticides and selected field and artificial soil parameters

Mobility of two commonly used hydrophobic termiticides, chlorpyrifos and fenvalerate, was carried out by soil thin layer chromatograph using 3 field soils and 7 artificial soil as absorbent phases. Mobility factors ( R f ) were measured, and single- and multi-variable linear regression equations were then established. The result indicated that chlorpyrifos removed faster than fenvalerate in both field and artificial soils. In field soils negative correlation coefficients ( r) was found between R f and organic matter (OM) content, pH, cationic exchange capacity (CEC), and clay content. It was noticeable, however, that correlation coefficient ( r) derived from single-variable equations were not a reliable criterion for evaluation of relative importance of individual soil parameter in R f determination. One could see, in multi-variable regression, a functional superposition of OM and CEC in pesticide/soil interaction, and the influence of soil pH was overwhelmed by joint action of the other 3 parameters. R f of the two hydrophobic termiticides could therefore be predicted with adequate accuracy by either of the combinations of the two parameter: 1) OM content and clay content, 2) CEC and clay content. Introducing field soil properties into equations established from artificial soils one could see that the four-variable equations, which toke sphagnum as the only source of CEC, gave better prediction of field soil R f . In spite of that these equations were different in two points with those from field soils: Firstly the parameter of soil pH could not be deprived, and secondly, R f of chlorpyrifos was positively correlated with the level of clay content.

Photodegradation of Rotenone in Soils under Environmental Conditions

An environmental fate study was performed to analyze the effects of soil components on the photochemical behavior of rotenone. Photodegradation experiments were carried out on three types of soil collected in southern Italy, Valenzano (VAL), Turi (TUR), and Conversano (CON), from April to June 2006. Soil thin-layer plates (1 mm thick) were spiked with 1.5 mg/kg of rotenone and exposed under natural conditions of sunlight and temperature. The plates were removed from the sunlight at predetermined intervals of continuous irradiation. Other soil samples, control and sterilized, were kept in the dark to evaluate possible effects of chemical and microbiological degradation during the irradiation experiment. The time for 50% loss of the initially applied rotenone varied from 5 to 7 h, following the order TUR < CON < VAL. In environmental studies, changes in temperature and/or moisture affected the degradation rate and caused deviations from first-order kinetics. The photolysis reaction fit the two compartment or the multiple compartment model pathways better. A fast initial decrease during the first 5 h of rotenone irradiation was followed by a much slower decline, which clearly indicates the rather complex chemical process of rotenone photodegradation on soil surfaces. Also, the degradation was shown to be directly related to the soil concentration of clay and organic matter. Rotenolone (12abeta-hydroxyrotenone) was detected by HPLC/DAD/MS analysis as the only photodegradation byproduct of rotenone in soil thin layers. Results provide additional insights on the rates and the mechanisms of rotenone degradation, aiming to describe more clearly the degradation performance of chemical residues in the environment.

Study of MCPA and MCPP Herbicides Mobility in Soils from North‐West Croatia as Affected by Presence of Fertilizers

The mobility of acid herbicide (4‐chloro‐2‐methylphenoxy)acetic acid [MCPA] and 2‐(4‐chloro‐2‐methylphenoxy)propionic acid [MCPA] in soils of North‐West Croatia has been studied by soil thin‐layer chromatography (STLC). Mobility of MPCA and MCPP was influenced by the change in concentration of soluble salts and the effect of mineral composition of the system studied, i.e. content of kaolin and sand in soil thin layer. The objective of this work was also to investigate how the mobility of phenoxy herbicides MCPA and MCPP is altered by the presence of fertilizers when both coexist in soil as a result of human activity. It has been found that mobility of acidic herbicides increases with application of fertilizers especially on soil with low clay and low organic matter content.

ADSORPTION, DESORPTION, AND MOBILITY OF TWO INSECTICIDES IN MALAYSIAN AGRICULTURAL SOILS

Laboratory studies utilizing radioisotopic techniques were conducted to determine the adsorption, desorption, and mobility of endosulfan (6,7,8,9,10,10-hexachloro-1,5,5a,6,9,9a-hexahydro-6,9-methano-2,4,3-benzodioxanthiepin3-oxide) and methamidophos (O,S-dimethyl phosphorothioate) in sandy loam and clay soils of the Cameron Highlands and the Muda rice-growing area, respectively. High Freundlich adsorption distribution coefficients [Kads (f)] for endosulfan (6.74 and 18.75) and low values for methamidophos (0.40 and 0.98) were obtained in the sandy loam and clay soils, respectively. The observed Koc values for endosulfan were 350.85 (sandy loam) and 1143.19 (clay) while Koc values of 20.92 (sandy loam) and 59.63 (clay) were obtained for methamidophos. Log Kow of 0.40 and 1.25 were calculated for endosulfan as well as −1.96 and −1.21 for methamidophos in the sandy loam and clay soils, respectively. Desorption was common to both pesticides but the desorption capacity of methamidophos from each soil type far exceeded that of endosulfan. Soil thin layer chromatography (TLC) and column studies showed that while methamidophos was very mobile in both soils, endosulfan displayed zero mobility in clay soil.

SOIL PROPERTIES INFLUENCING THE ADSORPTION AND MOBILITY OF PENCONAZOLE IN VINEYARD SOILS

A study was made of the adsorption and mobility of the fungicide penconazole (1-[2-(2,4-dichlorophenyl)pentyl]-1H-1,2,4-triazole) in 19 vineyard soils with low organic matter contents (0.31-1.98%) and in seven uncropped soils from oak and beech forests or grasslands with higher organic matter contents (3.30-8.24%). Adsorption isotherms were obtained using the batch equilibrium technique, and mobility was studied using soil thin layer chromatography. The aim of this study was to evaluate the adsorption and mobility behavior of this relatively new fungicide in vineyard soils. The adsorption isotherms fit the Freundlich adsorption equation, the Kf values ranged between 10.3 and 151, and the nf values were always lower than unity. The Kf constants were correlated positively with the soil organic matter content. According to the r2 determination coefficients, the organic matter content accounted for 85% of the variance in adsorption when all soils were considered together and for 76% and 36%, respectively, when considering the natural and vineyard soils. In no case was any influence of clay or silt contents on adsorption observed. According to the Rf values obtained, penconazole is immobile in 8% of soils and slightly mobile in 92% of soils. Adsorption of the fungicide by individual soil components, clay minerals and humic acid, confirms the importance of the organic matter fraction as the only soil parameter that affects adsorption. The results obtained indicate that vertical leaching of penconazole is low. The fungicide may, however, cause surface pollution of the soil because of its accumulation. If its degradation rate is low, this accumulation may lead to the pollution of surface water through runoff of the sorbed pesticide.

Sorption of atrazine and dicamba in Delaware coastal plain soils: a comparison of soil thin layer and batch equilibrium results

The mobility and retention of atrazine and dicamba in six Atlantic Coastal Plain soils were estimated by soil thin-layer chromatography (soil-TLC). The soils studied were representative of the major agricultural regions in Delaware and were sampled, by horizon, to the water table. Four horizons from each profile were leached simultaneously with distilled water on one soil-TLC plate. Two values were obtained from each plate: the ratio of the distance traveled by the herbicide center of mass over that traveled by the solvent front (Rm), and a sorption distribution coefficient (Kd). The Rm values ranged from 0·06 to 0·94 for atrazine and from 0·80 to 0·94 for dicamba. Herbicide mobility was found to be greatest in coarse-textured soil horizons that contained low levels of organic matter, clay, and Fe and Al oxides. Correlation analysis indicated that effective cation exchange capacity, exchangeable acidity, exchangeable aluminum, and clay were useful predictive variables or both atrazine mobility and sorption. Organic matter was not useful for predicting soil-TLC derived sorption estimates; however, it was correlated to Kd-batch estimates. Distribution coefficients calculated from soil-TLC data were found to be in general agreement with Kd values obtained for the same soils by batch equilibrium techniques. The average Kd-soil-TLC values for atrazine and dicamba were 2·09(±2·24) and 0·03(±0·02), respectively. The ratio of the batch Kd to the soil-TLC Kd ranged from 0·1 to 19 (x̄=1·6, SD=3·8) for atrazine and from 2·9 to 38 (x̄=12·6, SD=8·7) for dicamba. Thus, although for some horizons agreement between the two methods was good, for other horizons significant discrepancies existed. It is suggested that the soil-TLC gives results under non-equilibrium conditions, whereas the batch procedure is, by definition, at quasi-equilibrium. These fundamental differences may account for the observed differences between the two methods. It is also suggested that, due to this difference, the soil-TLC procedure can provide additional information relevant to herbicide partitioning in the field environment that is not provided by traditional batch equilibrium techniques. © 1998 Society of Chemical Industry

Influence of cosolvent (acetone) on the adsorption and movement of cypermethrin on soils

Adsorption and movement of cypermethrin in three different types (silt loam, loam and sandy loam) of soils at various fs values of acetone-water mixtures have been studied by using batch shake and soil thin layer chromatographic techniques respectively. Higher adsorption and lower movement of cypermethrin in silt loam soil followed by loam and sandy loam soils was expected with Freundlich constants Km, partition coefficients Kd and Rf values. These values also confirm that cypermethrin adsorption decreases while movement increases with increase in fs values. The partition coefficient Kd values and Freundlich adsorption constant Km values were used to evaluate the cosolvent theory for describing the adsorption of cypermethrin in acetone-water mixtures. The aqueous phase partition coefficient Kdw (mol g−1) normalized with respect to foc and aqueous phase adsorption constant Kw for cypermethrin were evaluated by extrapolating to fs = 0.