A Journey towards Salivary Fluoride Level Detection by Suitable Low Cost Chemosensor: From Molecule to Product

Fluoride is a ubiquitous anion and essential for us owing to its ability to protect human body from several health related issues. The safe limit of Fluoride ion for human body is 1.5 ppm, above it the ion becomes toxic and can cause dental‐skeletal fluorosis or urolithiasis. Several countries are facing such health hazard owing to the naturally abundant excess fluoride in ground water. As a consequence, habitants of such fluoride enriched zone needs to monitor the concentration of fluoride in their body by periodic analysis. In this regard, development of a chemosensor which can detect fluoride from human body fluid at easy‐instant‐economic way is an obvious mandate. For the first time, our group has developed a sensor kit and sensor station device as a deliverable product for individual and batch scale detection of salivary fluoride level by colorimetric method. The sensor station is the first device made by interfacing chemical output with electronics and the encrypted signal in digital version could be used as a level of fluoride in saliva. Our journey towards the development of suitable chemosensor for recognition of fluoride from human body fluid is summarized in this account.     

改水除氟效果三年动态监测分析

为及时，准确地了解湖北省饮水型氟中毒病区改水降氟效果，于１９９３～１９９５年连续三年对丹江口，枣阳，通城和罗田等四县市已改水的四个氟病区监测进行了改水工程的落实和降氟效果的监测，结果表明，四县市管理措施落实较好的改水工程占整个改水工程的８０％以上，８～１２岁儿童氟斑牙，尿氟和水氟逐年下降或维持正常水平，防治效果显著（Ｐ〈０．０５）。因此饮用低氟水，改水降氟是预防饮水型氟中毒的根本措施，而改水后保证     

Effect of acid on morphology of calcite during acid enhanced defluoridation

Fluoride removal from water by lime materials is a promising defluoridation process. Acid enhanced limestone defluoridation (AELD) technique involves precipitation of CaF₂ as well as adsorption of fluoride on the surface of limestone which is capable of reducing fluoride concentration to below the WHO guideline value of 1.5 mg/L. Acids such as acetic acid and citric acid are added to the fluoride water before filtration through limestone column to enhance the Ca²⁺ activity in solution for precipitation of fluoride as CaF₂. This paper describes the effects of these acids on the quality of the limestone during the AELD process, which has been studied to evaluate the reusability of the limestone. The reaction products that formed during the AELD process have also been analyzed. The detail study of the morphology of the limestone before and after use have been done using various analytical techniques, viz., X-ray diffraction, infrared spectroscopy, thermogravimetric analysis and scanning electron microscopy combined with energy dispersive X-ray spectroscopy. The study reveals that the limestone degrades to some extent in the process due to dissolution of calcium carbonate by the acids and adsorption of fluoride by the limestone. While appreciable quantity of the citrate salt of calcium was formed in the column, the acetate salt mostly remained dissolved in the water. Since mainly the surface of the limestone particles take part in the reaction, the limestone particles can be reused for the defluoridation process after cleaning the outer surface. The limestone after use remains also suitable as raw material for cement.     

Evaluation of the chronic intoxication of fluoride on human serum metabolome using untargeted metabolomics

Drinking water is the main source of fluoride intake for the human body and its regulated consumption helps in decreasing dental caries. However, excessive fluoride consumption over a prolonged time period causes fluorosis disease which adversely affects many tissues and organs of the body. This paper describes the evaluation of chronic intoxication of fluoride on human serum metabolome. The untargeted metabolomics approach using UPLC-QTOF-MS/MS is applied for metabolomic profiling, whereas the estimation of fluoride in serum samples was carried out using the ion-selective electrode (ISE). Fluoride concentration was found to be 0.16–1.25 mg/L in serum samples of 39 fluorosis patients and 0.008–0.045 mg/L in 20 healthy samples. A total of 47 metabolites were identified based on the high-resolution mass spectrometry analysis. A volcano plot was generated to discriminate features that are significantly different between the fluorosis and healthy groups at the probability of 0.05 and fold change ≥ 2. Among all identified metabolites, intensities of ten differential identified metabolites including inosine, α-linolenic acid, guanosine, octanoyl-L-carnitine, His-Trp, phytosphingosine, lauroyl-L-carnitine, hydrocortisone, deoxyinosine and dodecanedioic acid have been found altered in disease samples compared to healthy controls. Major pathways identified based on these metabolites include energy metabolism, fatty acid oxidation, purine degradation pathway, elevated protein degradation, and increased ω-6 fatty acid linoleate signatures were observed.     

Fluoride removal from water by chitosan derivatives and composites: A review

Fluoride is an essential element, indispensable for maintenance of dental health. Nevertheless, fluoride concentrations in drinking water above 1.5 mg L⁻¹ may be detrimental to human health. Many methods have been developed for removing excessive fluoride from drinking water, adsorption seems to be an effective, environmentally friendly and economical one. Since the sorption capacity of fluoride below 2 mg L⁻¹ on most conventional adsorbents is not satisfactory, much effort has been devoted to develop new and cost-effective fluoride adsorbents. This review reports the recent developments in the F⁻ removal in water treatment, using chitosan derivatives and composites in order to provide useful information about the different technologies. When possibly the adsorption capacity of chitosan derivatives and composites under different experimental conditions is reported to help to compare the efficacy of the fluoride removal process. A comparison with the adsorption capacity of other low cost adsorbents is also tabled.     

Determination of fluoride in drinking water and in urine of adolescents living in three counties in Northern Chihuahua Mexico using a fluoride ion selective electrode

This study was carried out to determine fluoride in drinking water and in urine of adolescents, ages 15-20 years, living in Northern Chihuahua Mexico. Participants are from a cross-sectional study on health effects of chronic fluoride exposure from drinking water. A total of 201 participants (106 female and 95 male) in the study were recruited from three counties. Samples of drinking water of each county were collected and analyzed using the U.S. EPA Fluoride Ion-Selective Method. Statistically significant difference of fluoride content in water was found among the three counties of recruitment (Cd. Juarez; 0.3 mg/L, Samalayuca, 1.0 mg/L, and Villa Ahumada, 5.3 mg/L). Fluoride content in wells and tap water samples of Villa Ahumada ranged from 5.0 to 5.7 mg/L. Fluoride content of these samples was above the level permitted by Mexican regulations. The fluoride content in bottled water obtained from local stores in Villa Ahumada ranged from 0.3 to 3.7 mg/l.Fluoride in urine samples of each participant was also analyzed using the U.S. EPA Ion-Selective Method. The mean fluoride urine concentration (reported in mg/g creatinine) in adolescents living in these counties was 0.792±0.39, 1.33±0.67 and 2.22±1.16 (Cd. Juarez, Samalayuca and Villa Ahumada), respectively. The high fluoride urinary levels found in participants from Villa Ahumada may be associated to the high fluoride level (5.3 mg/L) in dinking water.The accuracy of measurements was assessed with reference materials in water and in urine. Mean fluoride recovery was 99.0% and 99.6% in water and in urine, respectively. The levels obtained were within the assayed 5% confidence levels.     

Adsorption equilibrium modeling and solution chemistry dependence of fluoride removal from water by trivalent-cation-exchanged zeolite F-9

Fluoride in drinking water above permissible levels is responsible for human dental and skeletal fluorosis. In this study, therefore, the large internal surface area of zeolite was utilized to create active sites for fluoride sorption by exchanging Na+-bound zeolite with Al3+ or La3+ ions. Fluoride removal from water using Al3+- and La3+-exchanged zeolite F-9 particles was subsequently investigated to evaluate the fluoride sorption characteristics of the sorbents. Equilibrium isotherms such as the two-site Langmuir (L), Freundlich (F), Langmuir-Freundlich (LF), Redlich-Peterson (RP), Toth (T), and Dubinin-Radushkevitch (DR) were successfully used to model the experimental data. Modeling results showed that the isotherm parameters weakly depended on the solution temperature. From the DR isotherm parameters, it was considered that the uptake of fluoride by Al3+-exchanged zeolite proceeded by an ion-exchange mechanism (E = 11.32-12.13 kJ/mol), while fluoride-La3+-exchanged zeolite interaction proceeded by physical adsorption (E = 7.41-7.72 kJ/mol). Factors from the solution chemistry that affected fluoride removal from water were the solution pH and bicarbonate content. The latter factor buffered the system pH at higher values and thus diminished the affinity of the active sites for fluoride. Natural groundwater samples from two Kenyan tube wells were tested and results are discussed in relation to solution chemistry. In overall, Al3+-exchanged zeolite was found to be superior to La3+-exchanged zeolite in fluoride uptake within the tested concentration range.     

Defluoridation in aqueous solution by a composite of reduced graphene oxide decorated with cuprous oxide via sonochemical

The World Health Organization (WHO) has recommended the fluoride level in drinking water (1.5 mg/L) and defluoridation of water is an essential to remove of fluoride from contaminated water. Hence, the effective and rapid adsorbent Cuprous oxide-reduced graphene oxide (Cu₂O-RGO) composite was developed to overwhelm this concern. Sonochemical approach was adopted for the synthesis of desirable composite which was further characterized by XRD, FTIR, SEM, and EDS. The optimized composite (30 mg) shown the significant adsorption capacity of 34 mg/g of F⁻ solution (pH = 9), 70% removal of F⁻ solution from real experiment and Freundlich model was fitted than Langmuir and Temkin isotherms. The experimental results corroborate that adsorbent is the most effective for removal of fluoride from its polluted water.     

Indirect determination of fluoride in waters with lanthanum alizarin complexone and inductively-coupled plasma emission spectrometry

Fluoride is determined indirectly by measurement of the La II 333.75-nm line in the lanthanum/alizarin complexone/fluoride complex. The ternary complex is extracted into hexanol containing N,N-diethylaniline and the extract is introduced directly into the plasma. Related to water samples, the detection limit (3σ, concentration factor 5) is 0.59 ng ml^?1 fluoride, calibration is linear up to 1.2 μg ml^?1 and the relative standard deviation for 0.04 μg ml^?1 is 2.6%. Alkali, alkali elements and most anions do not interfere. The method is applied in the analysis of river water, coastal seawater and drinking water.     

Potentiometric determination of ultratrace amounts of fluoride enriched by zirconia in a flow system

A satisfactory method was described for separation and preconcentration of ultratrace amounts of fluoride ions enriched by zirconia (ZrO₂) as an inorganic ion exchanger. Fluoride ions can be adsorbed rapidly and selectively on zirconia from an acidic solution (pH 4.8) then reversibly desorbed by increasing pH up to 13. A flow system consisting of a column packed with zirconia impregnated on cellulose fibers and an ion-selective electrode was used for the determination of fluoride. The RSD was found to be 1.6% and the detection limit defined by S/N = 3 was 3 × 10⁻⁹ mol L⁻¹. The interference effects of various ions, such as nitrate, sulfate, halides, alkaline, and alkaline earth ions, which may be found in the environmental water, were studied, and it was found that they were tolerated even at high concentrations. The method was applied to determine fluoride in drinking water, which contains ultratrace amounts of fluoride. The concentration of fluoride was found to be 42 μg L⁻¹, which is confirmed by spiking 2 μmol fluoride to the drinking water with a recovery of 99%. Published in Russian in Zhurnal Analiticheskoi Khimii, 2006, Vol. 61, No. 2, pp. 179–183. The text was submitted by the authors in English.     

Removal of fluoride from water by electrocoagulation using Mild Steel electrode

Electrocoagulation process was used for defluoridation of synthetic fluoride containing water. In the process Mild Steel (MS) was used as sacrificial electrode and experiments were performed with different varying parameters such as pH and current density (CD). The fluoride removal efficiency was found to be maximum at pH 6 and CD 75.44 A/m² (2 A). At these conditions fluoride concentration reduces from initial concentration of 50 ​mg/dm³ to 5.2 ​mg/dm³. Kinetic study of electrocoagulation process revealed that the order of the reaction was in the range 1.61–1.64 with respect to fluoride concentration. It was observed that fluoride removal efficiency of the present MS electrode is comparable to the other electrodes used in electrocoagulation process available in the literature.     

Selective sorption of fluoride using Fe(III) loaded carboxylated chitosan beads

Chitosan beads (CB) as such have very low defluoridation capacity (DC) of 52 mgF⁻/kg have been suitably modified by carboxylation followed by chelation with Fe³⁺ ion (Fe-CCB), in order to effectively utilize both hydroxyl and amine groups for defluoridation. The modified beads showed enhanced DC to a very significant level of 4230 mgF⁻/kg. The fluoride removal process is governed by both adsorption and complexation mechanism. The sorbent was characterized using Fourier transform infrared spectrometer (FTIR) and scanning electron microscope (SEM) analysis. The experimental data have been analysed using isotherm and kinetic models. Thermodynamic parameters such as ΔG°, ΔH° and ΔS° were calculated to predict the nature of sorption. A field trial was carried out with fluoride water collected from a nearby fluoride-endemic village.     

Removal of fluoride ions using cuttlefish bones

Because of the high toxicity of fluoride to mankind, there is an urgent need to treat fluoride-contaminated drinking water to make it safe for human consumption. This work investigated the possibility of eliminating, by sorption, the excess of fluoride in overloaded water according to World Health Organization WHO recommendations. We tested the cuttlefish bone as an adsorbent material (available in Tunisia) for the defluoridation of water. Initially, we determined the optimal conditions of use (contact time, pH effect, adsorbent dose, initial fluoride concentration) of the cuttlefish bone on synthetic solutions of sodium fluoride. The second step was to verify the effectiveness of the sorption process on the cuttlefish bone by testing it on natural waters loaded with fluoride. The results obtained showed that sorption on the cuttlefish bone could be an effective method for the removal of fluoride. The efficacy of cuttlefish bone to remove fluoride from water was found to be 80% at pH 7.2, 1 h contact time, 15 g L⁻¹ adsorbent dose and 5 mg L⁻¹ initial fluoride concentration. Despite the different anions (Cl⁻ and SO₄²⁻) generally present in natural waters, a fluoride concentration in agreement with the norm (<1.5 mg L⁻¹) could be reached whatever the water treated. The regeneration of the cuttlefish bone was performed with a NaOH solution (10 g of cuttlefish bone/1000 mL NaOH 3 M). After 1 h of agitation, 95% of fluorides were desorbed. Following regeneration, the adsorbent can be used for further removal of fluoride.     

Study on the fluoride adsorption of various apatite materials in aqueous solution

The aim of this study was to evaluate the defluoridation efficiencies of various sorbents in aqueous solution. These sorbents include synthetic nano-hydroxyapatite (n-HAp), biogenic apatite (bone meal), treated biogenic apatite (bone meal prepared by H₂O₂ oxidation) and geogenic apatite (rock phosphate), which were characterized by XRD, FTIR, TEM and SEM. It has been observed that the defluoridation capacities follow the order: n-HAp > BH₂O₂ > B > rock phosphate. The controlling factors, sorbent dose, initial fluoride concentration, pH, contact time and temperature were investigated. The defluoridation capacities increased with the increase in the initial fluoride concentration and contact time, decreased with the increase in the sorbent dose. The optimum pH range for removal of fluoride on various apatite sorbents was considered to be 5.0-6.0. The fluoride adsorption can be explained by Langmuir, Freundlich isotherms, and the adsorption kinetic data follow the pseudo-second-order model. Thermodynamic parameters such as ΔH⁰, ΔS⁰ and ΔG⁰ indicated that the adsorption on various apatite sorbents was spontaneous and endothermic. These results showed that bone meal is a promising material for fluoride adsorption.     

Soil adsorption defluoridation of drinking water for an Ethiopian rural community

Content of fluoride compounds in some typical Ethiopian water sources was analysed and several commonly available soils were characterized for their adsorption properties regarding the water defluoridation. Various soils were collected in different Ethiopian sites and the samples were analysed by X-ray diffractometry for their mineralogical composition. Batch experimental runs at room temperature were performed to evaluate the adsorption capacity of each soil sample as well as to deduce the adsorption isotherms of fluoride ions with respect to the examined soils. The best soil was identified in terms of adsorption capacity and considered for the design of two different adsorption apparatuses. Considering the water consumption of a small rural community, the capacity of the adsorption unit was selected to assure a reduction of the fluoride concentration in drinking water to the limits recommended by the World Health Organization and to allow a suitable working time of the adsorption unit before the replacement of adsorbent would be necessary. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

Volcanic Rock Materials for Defluoridation of Water in Fixed-Bed Column Systems

Consumption of drinking water with a high concentration of fluoride (>1.5 mg/L) causes detrimental health problems and is a challenging issue in various regions around the globe. In this study, a continuous fixed-bed column adsorption system was employed for defluoridation of water using volcanic rocks, virgin pumice (VPum) and virgin scoria (VSco), as adsorbents. The XRD, SEM, FTIR, BET, XRF, ICP-OES, and pH Point of Zero Charges (pH_PZC) analysis were performed for both adsorbents to elucidate the adsorption mechanisms and the suitability for fluoride removal. The effects of particle size of adsorbents, solution pH, and flow rate on the adsorption performance of the column were assessed at room temperature, constant initial concentration, and bed depth. The maximum removal capacity of 110 mg/kg for VPum and 22 mg/kg for VSco were achieved at particle sizes of 0.075–0.425 mm and <0.075 mm, respectively, at a low solution pH (2.00) and flow rate (1.25 mL/min). The fluoride breakthrough occurred late and the treated water volume was higher at a low pH and flow rate for both adsorbents. The Thomas and Adams–Bohart models were utilized and fitted well with the experimental kinetic data and the entire breakthrough curves for both adsorbents. Overall, the results revealed that the developed column is effective in handling water containing excess fluoride. Additional testing of the adsorbents including regeneration options is, however, required to confirm that the defluoridation of groundwater employing volcanic rocks is a safe and sustainable method.     

Fluoride removal using lanthanum incorporated chitosan beads

Highly selective material based on naturally occurring biomaterial namely chitosan has been designed for the defluoridation of water. Lanthanum incorporated chitosan beads (LCB) were prepared using precipitation method. The synthesis was optimized by varying different synthesis parameters namely lanthanum loading, complexation and precipitation time, strength of ammonia solution used for precipitation, drying time, etc. Lanthanum incorporated chitosan beads were characterized using SEM, FTIR, XRD and EDX. Surface area of LCB was observed to be 2.76 m² g⁻¹. The equilibrium adsorption data fitted well to Langmuir adsorption isotherm and showing maximum fluoride adsorption capacity of 4.7 mg g⁻¹ with negligible lanthanum release. Kinetic study reveals that adsorption of fluoride is fast and follows pseudo-first-order kinetics. The effect of pH was also studied and the best efficiency was observed at pH 5. Presence of sulphate, nitrate and chloride marginally affected the removal efficiency, however drastic reduction in fluoride uptake was observed in the presence of carbonate and bicarbonate. Negative value of change in free energy (ΔG°) and positive value of change in entropy (ΔS°) suggest the adsorption of fluoride by LCB is feasible and spontaneous process. Positive value of change in enthalpy (ΔH°) suggests the process of fluoride adsorption is endothermic in nature. Regeneration study reveals that 1 M ammonium chloride solution appears to be the promising regeneration media showing 81.22% regeneration. The adsorption capacity of LCB was similar in fluoride-contaminated ground water collected from Dhar district of Madhya Pradesh, India, as compared to simulated water.     

由单层薄水铝石制备的活性氧化铝处理水中氟离子

The preparation of high-efficiency and low-cost adsorbents for the defluoridation of drinking water remains a huge challenge. In this study, single-layer and multi-layer boehmite were first synthesized via an organic-free method, and active alumina used for fluoride removal from water was obtained from the boehmite. The advantage of a single layer is that more aluminum is exposed to the surface, which can provide more adsorption sites for fluoride. The active alumina adsorbent derived from single-layer boehmite exhibits a high specific surface area and excellent adsorption capacity. The high surface area ensures a high adsorption capacity, and the organic-free synthesis method lowers the preparation cost. The as-prepared adsorbent was characterized by X-ray powder diffraction (XRD), scanning electron microscopy (SEM), high-resolution transmission electron microscopy (HRTEM), Fourier-transform infrared spectroscopy (FTIR) and nitrogen adsorption-desorption analysis. The single-layer structure of boehmite was determined from the simulated XRD diffraction pattern of single-layer boehmite. The disappearance of the (020) diffraction peak of boehmite illustrates that the dimensions in the b direction are extremely small, and according to the XRD simulation results, the single-layer structure of boehmite could be determined. Single-layer boehmite with a surface area of 789.4 m²·g^-1 was formed first. The active alumina obtained from the boehmite had a surface area of 678.4 m²·g^-1, and the pore volume was 3.20 cm³·g^-1. The fluoride adsorption of the active alumina was systematically studied as a function of the adsorbent dosage, contact time, concentration, co-existing anions, and pH. The fluoride adsorption capacity of the active alumina obtained from the single-layer boehmite reached up to 67.6 mg·g^-1, which is higher than those of most alumina adsorbents reported in the literature. The adsorption capacities of the active alumina are related to the specific surface area and the number of hydroxyl groups on the surface. Dosages of 0.6, 1.0, and 2.6 g·L^-1 of active alumina were able to lower the 10, 20, and 50 mg·L^-1 fluoride solutions, respectively, below the maximum permissible limit of fluoride in drinking water in China (1.0 mg·L^-1), suggesting that the active alumina synthesized in this work is a promising adsorbent for defluoridation of drinking water. In addition, the fluoride adsorption is applicable in a wide pH range from 4 to 9 and is mainly interfered by SO₄^2- and PO₄^3-. Further investigation suggested that the fluoride adsorption of the active alumina follows the pseudo second-order model and Langmuir isotherm model     

Field determination of fluoride in drinking water using a polymeric aluminium complex of 5-(2-carboxyphenylazo)-8-hydroxyquinoline impregnated paper

A simple field method which allows the determination of fluoride in drinking water with a small handheld instrument called Arsenator was developed. Arsenator is a commercially available instrument which was used successfully for reliable determination of arsenic. In the proposed method the functionality of the Arsenator which is based on a photometric measurement of a spot on the reagent paper is expanded to analyse fluoride. A polymeric aluminium complex of 5-(2-carboxyphenylazo)-8-hydroxyquinoline (LH₂) has been prepared as a new specific reagent for fluoride. Job's method of continuous variation was adopted for the determination of the composition of the coloured complex, which was further characterized by UV-VIS spectroscopic studies. The molar absorptivity of the complex formation is 8.48?×?10³?L?mol^?1?cm^?1 at 410?nm. The coloured complex reacts with fluoride on an impregnated paper where its colour changes are dependent on the concentration of fluoride in water samples. The change in the colour was measured using the Arsenator. The method allows a reliable determination of fluoride in the range 0.3 to 2.0?mg?L^?1. Further spectophotometric determinations of fluoride in drinking water were also studied. The determination is based on the reaction of aluminium complex with fluoride in the examined samples. Beer's law is obeyed in the range 0.3 to 2.0?mg?L^?1 of fluoride at 495?nm. Sensitivity, detection limit and quantitation limit of the method were found to be 0.251?±?0.007?µg^?1?mL, 0.1?mg?L^?1 and 0.3?mg?L^?1, respectively. The optimum reaction conditions and other analytical conditions were evaluated. The effect of interfering ions on the determination is described. There is no interference by nitrate or chloride. Sulphate interfered only at high concentrations which are not expected in drinking water.     

Adsorption kinetics of fluoride on iron(III)-zirconium(IV) hybrid oxide

Fluoride occurs in some drinking water sources at levels that are hazardous to health. Tests were conducted to assess the ability of a mineral-based adsorbent to take-up fluoride ion. Consequently, in search of novel adsorbent media, crystalline and hydrous iron(III)-zirconium(IV) hybrid oxide (IZHO) was synthesized, and tested to determine its capacity and kinetics for fluoride adsorption. The Fourier Transform Infrared (FTIR) spectrum of IZHO indicated the presence of Fe–O–Zr linkage which showed hybrid nature of the synthetic oxide. The optimum pH range for fluoride adsorption was ranged between 4.0 and 7.0. The analyses of the isotherm equilibrium data using the Langmuir and the Redlich–Peterson model equations by linear and non-linear methods showed that the data fitted better with latter model than the former. Thermodynamic analysis showed spontaneous nature of fluoride adsorption, and that took place with the increase of entropy. The kinetic data obtained for fluoride adsorption on IZHO at pH 6.8 (±0.1) and room temperature (303±2 K) described both the pseudo-first order and the reversible first-order equations equally well (r ²= ∼0.98–0.99), and better than pseudo second order equation (r ²= ∼0.96–0.98) for higher concentrations (12.5 and 25.0 mg/dm³) of fluoride. The kinetics of fluoride adsorption on the mixed oxide took place with boundary layer diffusion. External mass transport with intra-particle diffusion phenomena governed the rate limiting process, which has been confirmed from the Boyd poor non-linear kinetic plots.