Secondary pH standards and their uncertainty in the context of the problem of two pH scales

Establishing a traceability route with all measurement and uncertainty relationships determined is an important aspect of traceability, and seems to be particularly striking in pH measurement. In this paper the issue of evaluation of secondary pH standards measured with reference to a primary standard in a differential cell with free diffusion type liquid junctions is considered. Relatively high uncertainty, U=0.015, has been assigned to such standards in the recent IUPAC Recommendations on pH (2001), because of a specific residual liquid-junction potential treated statistically as a contribution to the combined uncertainty. Close inspection of the problem leads to the conclusion that a correction for the residual liquid-junction potential should be applied to the measured value of a secondary pH standard. This can be considered as a correction for a known systematic effect on the traceability route. With available experimental data it is demonstrated that such a correction can reasonably be made for well-studied standard buffer systems. In this way the uncertainty associated with secondary pH standards is kept to a low level, and, what is more, the problem of two pH scales, a multi-standard scale and a single-standard scale, gains a proper solution. The need for different treatment of residual liquid-junction potentials at different levels in the measurement hierarchy is noted. Much attention is also given to rational categorization of pH standards in the hierarchy.     

The history and development of a rigorous metrological basis for pH measurements

This paper discusses the basis and historical development of the traceability chain for pH. The quantity pH, first introduced in 1909, is among the most frequently measured analytical quantities. The practical measurement of the pH value of a sample is inexpensive, easy to perform, and yields a rapid result. However, the problems posed by the traceability of pH are not easy to solve. Most pH measurements are performed by potentiometry, using a glass electrode as the pH sensor. Such pH electrodes must be calibrated at regular intervals. Confidence in the reliability of pH measurements requires establishment of a metrological hierarchy including an uncertainty budget for calibration that links the pH measured in the sample to an internationally agreed and stated reference. For pH, this reference is the primary measurement of pH. A traceability chain can be established that links field measurements of pH to primary buffer solutions that are certified using this primary method. This allows the user in the field to estimate the measurement uncertainty of the measured pH data. As the realization of the primary measurement is sophisticated and time-consuming, primary standards are generally realized at national metrology institutes. A number of potentiometric methods are suitable for the determination of the pH of reference buffer solutions by comparison with the primary standard buffers. The choice between the methods should be made according to the uncertainty required for the application. For reference buffer solutions that have the same nominal composition as the primary standard, the differential potentiometric cell, often called the Baucke cell, is recommended.     

Estimation of uncertainty in routine pH measurement

A procedure for estimation of measurement uncertainty of routine pH measurement (pH meter with two-point calibration, with or without automatic temperature compensation, combination glass electrode) based on the ISO method is presented. It is based on a mathematical model of pH measurement that involves nine input parameters. Altogether 14 components of uncertainty are identified and quantified. No single uncertainty estimate can be ascribed to a pH measurement procedure: the uncertainty of pH strongly depends on changes in experimental details and on the pH value itself. The uncertainty is the lowest near the isopotential point and in the center of the calibration line and can increase by a factor of 2 (depending on the details of the measurement procedure) when moving from around pH 7 to around pH 2 or 11. Therefore it is necessary to estimate the uncertainty separately for each measurement. For routine pH measurement the uncertainty cannot be significantly reduced by using more accurate standard solutions than ±0.02 pH units – the uncertainty improvement is small. A major problem in estimating the uncertainty of pH is the residual junction potential, which is almost impossible to take rigorously into account in the framework of a routine pH measurement.¹ Received: 11 August 2001 Accepted: 22 February 2002     

Experimental design and measurement uncertainty in ligand binding studies by affinity capillary electrophoresis

In all life sciences ligand binding assays (LBAs) play a crucial role. Unfortunately these are very error prone. One part of this uncertainty results from the unavoidable random measurement uncertainty, another part can be attributed to the experimental design. To investigate the latter, uncertainty propagation was evaluated as a function of the given experimental design. A design space including the normalized maximum response range (nMRR), the data point position (DPP), the data point range (DPR) and the number of data points (NoDP) was defined. Based on ten measured ms ACE source data sets 20 specific parameter sets were selected by Design of Experiments. Monte Carlo simulations using 100 000 repeats for every parameter set were employed. The resulting measurement uncertainty propagation factors (measurement uncertainty multiplier: MUM) were used to describe the whole design space by polynomial regression. The resulting 5‐dimensional response surface was investigated to evaluate the design parameter's influence and to find the minimal uncertainty propagation. It could be shown, that the nMRR is of highest importance, followed by DPP and DPR. Interestingly, the NoDP is less relevant. However, the interactions of the four parameters need to be carefully considered during design optimization. Using at least five data points which cover over 40% of the upper part of the binding hyperbola (DPP > 0.57) the MUM will be minimized (MUM approximately 1.5) when the nMRR is appropriate. It is possible to reduce the measurement uncertainty propagation more than one order of magnitude.     

Implementing combined uncertainty according to GUM into a commercial gamma spectrometric software

Measurement uncertainty is an important part of a measurement result that still often is neglected. A complete combined uncertainty budget can be calculated for non-routine measurements. However, for routine measurements, this work becomes time-consuming since every measurement result requires an uncertainty analysis. By analysing the uncertainty on a measurement system level in e.g. high resolution gamma spectrometry, the uncertainty analysis will be universal for a particular measurement geometry. The problem is then reduced to implementing the combined uncertainty into measurement software. This work shows how this analysis can be done and implemented into a commercial software for gamma spectrometric measurements.     

原子吸收光谱法测定载金碳中金含量的不确定度评定

介绍了原子吸收光谱法(AAS)测定载金碳中金含量的不确定度评定方法。建立了不确定度评定的数学模型,对不确定度来源进行分析,并对不确定度分量进行量化。测量不确定度的主要来源为测量重复性引入的标准不确定度、样品称量引入的标准不确定度、样品溶液中金含量测定值的标准不确定度、样品溶解后定容体积的不确定度,其中测量重复性引入的标准不确定度和样品溶液中金含量测定值引入的标准不确定度为不确定度主要来源。当载金碳中金含量为0.56 g/kg时,其扩展不确定度为0.02 g/kg(k=2)。     

Approaching target uncertainty in proficiency testing schemes: experience in the field of water measurement

Good correspondence between evaluations of the proficiency testing data for water measurements according to different scoring schemes was found as a result of implementation of the measurement quality according to the target uncertainty defined in the Drinking Water Directive. The accuracy of the evaluation is determined by the uncertainty of the assigned value, and this uncertainty should be in correspondence with the target uncertainty. Modification of the zeta-score by the thorough application of the target uncertainty is presented. It is convenient for generalised presentation of the proficiency testing data. The allowed bias is included as a linear term on the measured value scale, as it is treated in uncertainty analysis. The importance of implementation of the target measurement uncertainty in other fields of the routine measurements is indicated.     

Estimation of uncertainty in p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> values determined by potentiometric titration

A procedure is presented for estimation of uncertainty in measurement of the pK(a) of a weak acid by potentiometric titration. The procedure is based on the ISO GUM. The core of the procedure is a mathematical model that involves 40 input parameters. A novel approach is used for taking into account the purity of the acid, the impurities are not treated as inert compounds only, their possible acidic dissociation is also taken into account. Application to an example of practical pK(a) determination is presented. Altogether 67 different sources of uncertainty are identified and quantified within the example. The relative importance of different uncertainty sources is discussed. The most important source of uncertainty (with the experimental set-up of the example) is the uncertainty of pH measurement followed by the accuracy of the burette and the uncertainty of weighing. The procedure gives uncertainty separately for each point of the titration curve. The uncertainty depends on the amount of titrant added, being lowest in the central part of the titration curve. The possibilities of reducing the uncertainty and interpreting the drift of the pK(a) values obtained from the same curve are discussed.     

Estimating measurement uncertainty in high-performance liquid chromatography methods

In every measurement procedure, it is important to know the components of measurement uncertainty affecting the quality of measured result and reliability of quantified result. The procedure for recognizing measurement uncertainty is not universal but depends on the method and sample type. It has to be made according to good laboratory practice. This paper aims at showing the comparison of measurement uncertainty component estimations for three methods using the high-performance liquid chromatography techniques: determination of the type and content of aromatic hydrocarbons in diesel fuels and petroleum distillates by normal phase high-performance liquid chromatography, determination of nitrates in water samples by ion chromatography, and determination of molecular weights of polystyrene by size exclusion chromatography technique. Both similarity and differences were found during the measurement uncertainty component estimation, and conclusions about influences of certain components on the result uncertainty were made.     

尿素法合成高结晶度类水滑石

尿素的高温分解特性被用于控制层状化合物合成过程中的pH值。室温下尿素可与硝酸盐形成均一溶液，当其高温分解时可以保证溶液内部各点的pH值始终一致，因而可获得高结晶度的水滑石样品。利用该法可合成出Mg-Al、Zn-Al及Ni-Al类水滑石，但难以合成出Co-Al，Mn-Al及Co-Cr类水滑石，相信这与不同金属离子发生沉淀时所需的pH值有关。     

Planning and combining of isochronous stability studies of CRMs

The first part of this paper discusses some critical factors in planning and evaluation of isochronous stability studies. Recommendations on the number of time-points, number of items, and number of replicates to be measured on each unit are given. In general, more than two time-points should be used. The effect of batch heterogeneity can be eliminated by spreading the results over more units. An approach for combining two or more isochronous stability studies is developed in the second part. This approach includes a potential correction of the earlier stability study, pooling of data of the stability studies, and an uncertainty evaluation taking into consideration the uncertainty of the initial correction. The statistical basis for this approach is developed and equations for evaluation of the uncertainty of stability of the combined study are given.     

Intrinsic charge and Donnan potentials of grafted polyelectrolyte layers determined by surface conductivity data

In order to characterize grafted polyelectrolyte layers based on electrokinetic measurements a theory of the surface conductivity Ksigma was developed, starting from the model of thick polyelectrolyte layers with uniform segment distribution and dissociable groups with an unknown pK value. According to this model the inner part of the polyelectrolyte layer adjacent to the substrate is considered to be isopotential while the potential decay occurs in a zone near the solution side of the layer. A simple equation for the Donnan potential psiD as a function of pH, pK, electrolyte concentration C0, and volume charge density rho was obtained. In the derived equation Ksigma is directly related to psiD while the other terms have less influence on the magnitude of Ksigma and can be accounted for in a second approximation using psiD as determined from the measured Ksigma. Evaluation of the suggested model indicates that Ksigma measurements provide an effective method to characterize polyelectrolyte layers by analyzing the dependence of psiD on pH and C0: The magnitude of Ksigma yields information about the surface charge at complete dissociation of the ionizable groups. The dependence of Ksigma on pH and C0 can be used for the determination of the pK value of the dissociating functions and the segment volume fraction of the polyelectrolyte can be estimated using the measured value of rho.     

Uncertainty-based measurement quality control

According to a simple acceptance decision rule for measurement quality control, a measured value will be accepted if the expanded uncertainty of the measurements is not greater than a preset maximum permissible uncertainty. Otherwise, the measured value will be rejected. The expanded uncertainty may be calculated as the z-based uncertainty (the half-width of the z-interval) when the measurement population standard deviation σ is known or the sample size is large (30 or greater), or by a sample-based uncertainty estimator when σ is unknown and the sample size is small. The decision made based on the z-based uncertainty will be deterministic and may be assumed to be correct. However, the decision made based on a sample-based uncertainty estimator will be uncertain. This paper develops the mathematical formulations for computing the probability of acceptance for two sample-based uncertainty estimators: the t-based uncertainty (the half-width of the t-interval) and an unbiased uncertainty estimator. The risk of incorrect decision-making, in terms of the false acceptance probability and false rejection probability, is derived from the probability of acceptance. The theoretical analyses indicate that the t-based uncertainty may result in significantly high false rejection probability when the sample size is very small (especially for samples of size 2). For some applications, the unbiased uncertainty estimator may be superior to the t-based uncertainty for measurement quality control. Several examples from acoustic Doppler current profiler streamflow measurements are presented to demonstrate the performance of the t-based uncertainty and the unbiased uncertainty estimator.     

电极/溶液界面pH值的现场测量

一般认为阴极表面功能陶瓷电沉积层的形成是由于基底 /溶液界面化学环境变化造成的 [1,2 ] ,但目前还没有直接的实验数据加以证明 .原位测量电极 /溶液界面 p H的变化存在两方面的困难 :(1 )传统方法是采用玻璃 p H计 ,由于其体积较大、强度脆弱等原因 ,使其在测量固 /液界面化学环境变化的应用方面受到一定限制 [3 ] ;(2 )将 p H微探针置于电极表面 ,将会影响功能陶瓷在电极表面的沉积 ,从而使测定的界面 p H值不能真实反映电沉积过程中固 /液界面化学环境的变化 .本文基于功能陶瓷电沉积过程不受影响的情况下现场直接测量电极 /溶液界面…     

Extended traceability of pH: an evaluation of the role of Pitzer's equations

The 2002 IUPAC recommendation on pH (provisional) has taken its own philosophy to provide a basis for comparable and traceable assignment of a value, from a measurement, to the quantity pH. Whereas the substituted 1983 IUPAC recommendation relied heavily on precisely prescribed experimental techniques and procedures, the current recommendation defines a hierarchical relationship between references for comparison (primary and secondary standards) and objective criteria on the comparison of measurements with these standards. The recommendation aims at a traceability chain from the national metrological institution (NMI) level down to field and laboratory measurements. Currently, however, the traceability chain is developed to the level of certified reference materials (CRM), namely the above mentioned primary and secondary standards. To complete the traceability chain, several theoretical and practical aspects have to be pondered. In part, the methods for comparative assessment of different options have yet to be developed. As an illustrating example of the complexity of issues to be considered in a further extension of the traceability chain is estimation of the doubt associated with Pitzer coefficients. The Pitzer equations for activity coefficient modelling are explicitly mentioned in the 2002 IUPAC recommendation on pH (provisional) as enabling possible improvement in the ionic strength extrapolations to zero ionic strength. An assessment of uncertainty of ternary Pitzer coefficients is given for the first time.     

pH buffer assessment and Pitzer��s equations

Traceable measurement of the quantity pH in media outside the limits of the recent IUPAC recommendation requires an alternative to the Bates?CGuggenheim convention. The Pitzer??s approach to ion interactions is widely appraised and offers a suitable approach to the estimation of single-ion activity coefficients. For this purpose, the underlying electrolyte data need to be consistent and the uncertainty in existing Pitzer??s data needs to be assessed. Such an assessment is attempted in this study for pH in potassium acetate buffer medium. The re-evaluation of Pitzer??s data from potassium nitrate data revealed inconsistencies and wide uncertainty margins. The uncertainty contribution from binary Pitzer??s parameters to an assessment of pH in seawater resulted in an uncertainty in pH of about 0.03 (95% confidence interval). This contribution has to be taken into account in the overall uncertainty budget. Lack of appropriate data for other pH buffer systems (e.g., phosphate buffers) is noted.     

Measurement uncertainty of selenium determination in the reference material Seronorm Trace Elements Serum by hydride generation atomic fluorescence spectrometry

 An analytical result is not considered to be complete without a statement of the measurement uncertainty associated with it. Evaluation of measurement uncertainty is therefore an essential part of every determination. In the present study the measurement uncertainty of the result of determination of selenium in the reference material Seronorm Trace Elements Serum was studied. The combination of a digestion procedure using sulfuric acid, V₂O₅ in H₂SO₄ and hydrogen peroxide and the continuous flow approach of hydride generation atomic fluorescence spectrometry (HG-AFS) detection was used for selenium determination. The total uncertainty budget was calculated with the help of the GUM Workbench program, in which computations follow the rules of the ’ISO guide to the expression of uncertainty in measurement’. The major sources of uncertainty were found to be due to the recovery of the procedure, measurement of peak heights and the purity of Na₂SeO₃. A selenium mass fraction of 77.1±4.8 ng/g (with a coverage factor of 2.1, 95% probability) was determined, which is comparable with the recommended value of 80 ng/g. Received: 13 September 2002 Accepted: 23 December 2002 Acknowledgements We would like to thank Tinkara Buˇcar, B.Sc. for useful discussions and the IAEA Vienna, for financial support of the project 11553/RO. Presented at CERMM-3, Central European Reference Materials and Measurements Conference: The function of reference materials in the measurement process, May 30–June 1, 2002, Rogaška Slatina, Slovenia Correspondence to V. Stibilj     

Gel speciation studies-II An extension of earlier studies of the protonation equilibria of cross-linked carboxymethyldextran

The potentiometric properties of the rigidly cross-linked Sephadex gel CM-25 have been studied. The gel was equilibrated in sodium perchlorate at fixed concentration levels (0.010 and 0.0010M) and with variable concentration levels of NaClO(4) (from 0.0010 to 0.10M). The volume of the gel was measured for every equilibrated sample simultaneously with the solution pH and pNa. The pK computed after correction for a Donnan potential term was found to be independent of alpha, the degree of neutralization, and ionic strength; its value of 3.35 +/-0.15 was in excellent agreement with the intrinsic pK measured earlier for the flexible CM-50 Sephadex gel and reported for its linear polyelectrolyte analogue, carboxymethyldextran. An interesting observation from these studies is the efficient screening of the charged surface by the counter-ions in the presence of a three-dimensional charged network.     

Uranium assay determination using Davies and Gray titration: an overview and implementation of GUM for uncertainty evaluation

The International Organization for Standardization (ISO) Guide to the expression of Uncertainty in Measurement (GUM) was developed to meet the demand for a standardized way of evaluating and expressing uncertainties. The Davies and Gray (D&G) titrimetry method is routinely used in nuclear safeguards for uranium accountability measurement and a statement of the uncertainty that can reasonably be attributed to the measured assay value is therefore of importance. A mathematical model for an uncertainty evaluation of D&G measurements in compliance with ISO GUM is presented. This is illustrated by a numerical example and the utilization of the uncertainty budget is explored.     

Influence of buffer quality on pH measurement uncertainty: prediction and experimental evaluation

Dependence of the uncertainty of a pH measurement result on the quality of buffers (i.e. the uncertainty of their certified pH values) at different levels of instrumental uncertainty (pH-meter, etc.) was simulated using the Monte Carlo method and regression analysis. The contribution of the instrumental standard uncertainty (in the studied range from 0.1 to 1 mV) to the uncertainty of the pH measurement result is negligible, if the standard uncertainties of the pH buffers exceed 0.04 pH (e. g. for in-house buffers). It is shown how the choice of pH-meter and buffers should be correlated in order to meet the required uncertainty of a pH measurement result in a sample under analysis. The results of the simulation were compared with experimental data obtained from calibrations of a pH/ion-meter with a hydrogen working electrode (Radiometer PHM-240) and with a glass electrode (Metrohm 744). Buffers of different quality (National Institute for Standards and Technology standard reference materials, certified Radiometer buffers and Merck CertiPUR buffers) were used for the calibrations. The uncertainties of the experimental results are close to the predicted ones obtained by the simulation. Received: 16 June 2002 Accepted: 19 July 2002 Presented at the 14^th International Conference of the Israel Society for Quality, 18–21 November 2002, Jerusalem, Israel Correspondence to I. Kuselman