Evaluation and validation of detailed and simplified models of the uncertainty of unified [Formula: see text] measurements in aqueous solutions.

The use of the unified pH concept, [Formula: see text] , applicable to aqueous and non-aqueous solutions, which allows interpreting and comparison of the acidity of different types of solutions, requires reliable and objective determination. The [Formula: see text] can be determined by a single differential potentiometry measurement referenced to an aqueous reference buffer or by a ladder of differential potentiometric measurements that allows minimisation of inconsistencies of various determinations. This work describes and assesses bottom-up evaluations of the uncertainty of these measurements, where uncertainty components are combined by the Monte Carlo Method (MCM) or Taylor Series Approximation (TSM). The MCM allows a detailed simulation of the measurements, including an iterative process involving in minimising ladder deviations. On the other hand, the TSM requires the approximate determination of minimisation uncertainty. The uncertainty evaluation was successfully applied to measuring aqueous buffers with pH of 2.00, 4.00, 7.00, and 10.00, with a standard uncertainty of 0.01. The reference and estimated values from both approaches are metrologically compatible for a 95% confidence level even when a negligible contribution of liquid junction potential uncertainty is assumed. The MCM estimated pH values with an expanded uncertainty, for the 95% confidence level, between 0.26 and 0.51, depending on the pH value and ladder inconsistencies. The minimisation uncertainty is negligible or responsible for up to 87% of the measurement uncertainty. The TSM quantified measurement uncertainties on average only 0.05 units larger than the MCM estimated ones. Additional experimental tests should be performed to test these uncertainty models for analysis performed in other laboratories and on non-aqueous solutions.

Seawater pH measurements with a combination glass electrode and high ionic strength TRIS-TRIS HCl reference buffers - An uncertainty evaluation approach.

The comparison of pH measurements in seawater collected at different locations or occasions, is meaningful if the same measurand (i.e. the quantity intended to be measured) is determined, if adequate measurement procedures are used, including the selection of calibrators, and if the measurement uncertainty is known. Depending on the purpose of this evaluation, the measurement uncertainty should be smaller than a defined target value. The measured pH should have a sound physical-chemical meaning to allow the adequate assessment of its impacts. In the present procedure TRIS-TRIS HCl solutions, of different molality ratios, prepared in artificial seawater with reference values estimated by primary measurements, were used to obtain proper calibrators for the pH meter used for the analysis of seawater samples. This work presents the uncertainty evaluation of pH measurements in seawater, performed by potentiometry using a combination glass electrode, from the interpolation uncertainty evaluated by the Least Squares Regression Model and by Monte Carlo Simulations of measured potentials and reference values. The uncertainty evaluation was critically assessed. The developed algorithms were implemented in a user-friendly MS-Excel file available as Electronic Supplementary Material. Seawater pH was measured with an expanded uncertainty of 0.019 enabling discriminating differences of pH of two samples larger than 0.029.

Designing valid and optimised standard addition calibrations: Application to the determination of anions in seawater.

A strategy for designing valid standard addition calibrations and for optimising their uncertainty is presented. The design of calibrations involves the development of models of the sensitivity and precision of the instrumental signal, in a wide range of analyte concentration (or any other studied quantity), and the definition of sample dilution and standard addition procedures that allow fulfilling the assumptions of the linear unweighted regression model in, typically, a smaller range of standard addition calibrations. Calibrators are prepared by diluting the sample and adding analyte with negligible uncertainty to fit in a concentration range where signals are homoscedastic. The minimisation of the uncertainty is supported on detailed measurement uncertainty models function of the calibrators preparation procedure and of analytical instrumentation performance. The number of collected signals replicates is defined by balancing their impact on the estimated expanded uncertainty, the resources needed and the target (maximum) uncertainty for the intended use of measurements. The calibration design strategy was successfully applied to the determination of the mass concentration (mg L(-1)) of Cl(-), Br(-), NO3(-) and SO4(-2) in seawater by ion chromatography. A target expanded uncertainty of 20% was defined for the determination of Cl(-), NO3(-) and SO4(-2), or 40% for the determination of the smaller mass concentration of Br(-). The developed measurement model produced reliable predictions of the measurement uncertainty from approximate concentration of the analyte in the sample, before its accurate quantification, thus proving optimisation is effective. Predictions are more prone to the variability of the measurement uncertainty estimation if based on low number of calibrators signals. The reported relative expanded uncertainty ranged from 7.1% to 49%.

Carotenoid stability in fruits, vegetables and working standards - effect of storage temperature and time.

The effects of freezing and storage temperature on the mass fraction of α- and ß-carotene, ß-cryptoxanthin, lutein, lycopene and zeaxanthin in minimally processed fresh food products, were evaluated after sample preparation, extraction and saponification (only when strictly necessary). Effects of freezing and long-term stability were studied at two temperatures, -20 and -70°C, using high performance liquid chromatography (reversed phase columns, UV-Vis diode array detector) at time points during storage; measurement uncertainty was included in the evaluation. Stability of working standard solutions was also examined. Freezing did not affect the carotenoid mass fraction under the conditions studied. Carotenoids in orange, cherry, peach, apple, and kale were stable (except α-carotene and zeaxanthin in peach) for 13, 9.7, 5.7, 2.5 and 7.5months, respectively. For these food sample matrices, no significant difference between the freezing/storage at -20 and -70°C was observed. Standard solutions (0.05-5µg/mL) were stable for at least 6months at -70°C, except lycopene which at 0.05µg/mL was apparently stable only for six weeks.

Weighted calibration with reduced number of signals by weighing factor modelling: application to the identification of explosives by ion chromatography.

The linear weighted regression model (LW) can be used to calibrate analytical instrumentation in a range of quantities (e.g. concentration or mass) wider than possible by the linear unweighted regression model, LuW (i.e. the least squares regression model), since this model can be applied when signals are not equally precise through the calibration range. If precision of signals varies within the calibration range, the regression line should be defined taking into account that more precise signals are more reliable and should count more to define regression parameters. Nevertheless, the LW requires the determination of the variation of signals precision through the calibration range. Typically, this information is collected experimentally for each calibration, requiring a large number of replicate collection of signals of calibrators. This work proposes reducing the number of signals needed to perform LW calibrations by developing models of weighing factors robust to daily variations of instrument sensibility. These models were applied to the determination of the ionic composition of the water soluble fraction of explosives. The adequacy of the developed models was tested through the analysis of control standards, certified reference materials and the ion balance of anions and cations in aqueous extracts of explosives, considering the measurement uncertainty estimated by detailed metrological models. The high success rate of the comparisons between estimated and known quantity values of reference solutions, considering results uncertainty, proves the validity of developed metrological models. The relative expanded measurement uncertainty of single determinations ranged from 1.93% to 35.7% for calibrations performed along 4 months.

Evaluation of the performance of the determination of anions in the water soluble fraction of atmospheric aerosols.

The knowledge of the mass of particulate matter in air, its chemical composition and emission sources is of relevance for taking decisions concerning air quality management in urban areas. The interpretation of these data is a function of the quality of the measurement results expressed by their uncertainties. This study aimed at developing models of the performance of the determination of anions in the water-soluble fraction of atmospheric aerosols, capable of determining, separately, the contribution of aerosols sampling, extraction of water-soluble fraction of atmospheric aerosols and quantification, by ion chromatography, of anions in the extract. The sampling procedure was assessed from the dispersion of results of duplicate parallel sampling after subtracting the analytical component of this dispersion. These models are used to evaluate the adequacy of the measurement procedure for the determination of urban aerosol composition and to support strategies for reducing measurement uncertainty or cost of analysis. The method performance was studied for the following ranges considering extract dilution up to five times: 0.23-8 µg m(-3) for chloride and nitrate, and 0.093-3.25 µg m(-3) for sulphate. Measurements are fit for the analysis of urban aerosols since the relative expanded measurement uncertainty is smaller than a maximum value of 40%. The percentage contribution of the uncertainty components varies with the analyte and its mass concentration, the major components being 24-93% for the extraction, 43-59% for sampling, 0.2-28% for the interpolation of the sample signal in the calibration curve and 4-8% for air volume measurement. The typical composition of analysed air is: (1.12±0.26) µg m(-3), (1.02±0.30) µg m(-3) and (0.76±0.22) µg m(-3) of chloride, nitrate and sulphate in the water soluble fraction of aerosol, respectively, for a confidence level of approximately 95% considering a coverage factor of 2.

Optimization of the determination of chemical oxygen demand in wastewaters.

Chemical oxygen demand (COD) is one of the most relevant chemical parameters for the management of wastewater treatment facilities including the control of the quality of an effluent. The adequacy of decisions based on COD values relies on the quality of the measurements. Cost effective management of the minor sources of uncertainty can be applied to the analytical procedure without affecting measurement quality. This work presents a detailed assessment of the determination of COD values in wastewaters, according to ISO6060:1989 standard, which can support reduction of both measurement uncertainty and cost of analysis. This assessment includes the definition of the measurement traceability chain and the validation of the measurement procedure supported on sound and objective criteria. Detailed models of the measurement performance, including uncertainty, developed from the Differential Approach, were successfully validated by proficiency tests. The assumption of the measurement function linearity of the uncertainty propagation law was tested through the comparison with the numerical Kragten method. The gathered information supported the definition of strategies for measurement uncertainty or cost reduction. The developed models are available as electronic supplementary material, in an MS-Excel file, to be updated with the user's data.

Critical assessment of three high performance liquid chromatography analytical methods for food carotenoid quantification.

Three sets of extraction/saponification/HPLC conditions for food carotenoid quantification were technically and economically compared. Samples were analysed for carotenoids alpha-carotene, beta-carotene, beta-cryptoxanthin, lutein, lycopene, and zeaxanthin. All methods demonstrated good performance in the analysis of a composite food standard reference material for the analytes they are applicable to. Methods using two serial connected C(18) columns and a mobile phase based on acetonitrile, achieved a better carotenoid separation than the method using a mobile phase based on methanol and one C(18)-column. Carotenoids from leafy green vegetable matrices appeared to be better extracted with a mixture of methanol and tetrahydrofuran than with tetrahydrofuran alone. Costs of carotenoid determination in foods were lower for the method with mobile phase based on methanol. However for some food matrices and in the case of E-Z isomer separations, this was not technically satisfactory. Food extraction with methanol and tetrahydrofuran with direct evaporation of these solvents, and saponification (when needed) using pyrogallol as antioxidant, combined with a HPLC system using a slight gradient mobile phase based on acetonitrile and a stationary phase composed by two serial connected C(18) columns was the most technically and economically favourable method.

Uncertainty estimation and in-house method validation of HPLC analysis of carotenoids for food composition data production.

The method for separation and quantitative determination of the main carotenoids in food by high-performance liquid chromatography (HPLC) was in-house validated. Tomato (Lycopersicon esculentum M.) as food matrix was used to demonstrate its linearity, repeatability, intermediate precision, detection and quantification limits, sensitivity and bias. In addition, stability of carotenoids was studied in function of temperature and time. Method accuracy was quantified through measurement uncertainties estimate based on this validation study. Furthermore, a study was conducted to evaluate variability coming from location in an experimental field composed by 12 subfields. The use of two metal free reverse phase columns and an organic mobile phase based on acetonitrile, methanol and dichloromethane enabled the separation of the six target compounds (trans-α-carotene, trans-ß-carotene, ß-cryptoxanthin, all-lycopene, lutein, zeaxanthin) within a 30min run; detection at 450nm and external calibration allowed the quantification of the analytes. Carotenoids concentration and measurement uncertainty, in mg/100g, in tomato varieties "lido" and "for salad" were, respectively, 1.0±0.14 and 0.39±0.056 for trans-ß-carotene, 8±2.0 and 2.3±0.57 for all-lycopene and 0.10±0.017 and 0.08±0.015 for lutein; trans-α-carotene, ß-cryptoxanthin and zeaxanthin were not detected in both varieties (detection limits, in µg/100g, 0.81, 0.57 and 0.77, respectively). For ß-carotene and lutein, uncertainty associated with the entire process including small-scale within-region variation was statistically different, at a significance level of 5%, from measurement uncertainty (which includes sampling in the laboratory).

Effect of condensation phenomena on potentiometric measurements.

Results of potentiometric analysis, namely those of pH measurements, depend on temperature control of the experimental setup, as it is expressed in the analytical law, the Nernst equation, starting from the primary level, where reference values are conventionally assigned to standard solutions, through the whole traceability chain, down to the service laboratory. Fundamental studies of pH standards, based on the measurement of the potential of an electrochemical cell without transference, known as Harned cell, containing a platinum-hydrogen electrode and a silver-silver chloride reference electrode, refer condensation phenomena on the portions of the cell walls which are not immersed in the thermostatic bath, as one of the major sources of error in the assessment of both the silver-silver chloride electrode standard potential and on pH values. In this work such effect, which is bound to happen due to significant temperature differences between the ambient air temperature and the water bath, has been quantified, presenting an original contribution to the improvement of the quality of potentiometric analysis results. This was possible due to the availability of a climatic cabin "WALKIN" with a temperature control of +/-0.01 degrees C, which permitted that temperature gradients were built between the thermostat water bath (controlled to +/-0.005 degrees C) where cells filled to about 2/3 full were immersed up to 90% of their height, and the surrounding environment.

Worst case uncertainty estimates for routine instrumental analysis.

A methodology for the worst case measurement uncertainty estimation for analytical methods which include an instrumental quantification step, adequate for routine determinations, is presented. Although the methodology presented should be based on a careful evaluation of the analytical method, the resulting daily calculations are very simple. The methodology is based on the estimation of the maximum value for the different sources of uncertainty and requires the definition of limiting values for certain analytical parameters. The simplification of the instrumental quantification uncertainty estimation involves the use of the standard deviation obtained from control charts relating to the concentrations estimated from the calibration curves for control standards at the highest calibration level. Three levels of simplification are suggested, as alternatives to the detailed approach, which can be selected according to the proximity of the sample results to decision limits. These approaches were applied to the determination of pesticide residues in apples (CEN, EN 12393), for which the most simplified approach showed a relative expanded uncertainty of 37.2% for a confidence level of approximately 95%.