Search

The limit of determination of an analytical procedure is defined as the smallest amount of substance or concentration that is to be determined quantitatively and discriminated significantly at a given statistic defined probability. In this definition the limit of detection is dependent upon the standard deviation of the measurement sdv(y), upon all parameters influencing to regression (number and position of datapoints), upon the sensitivity of the analytical method and upon the number of determinations of the analyses. In this paper it is discussed that the choice of datapoints can decrease the limit of determination dynamically. It is further possible to optimize the choice of datapoints in respect to a lowered limit of determination.

Programmable desk calculators and nowadays socalled personal computers are powerful computing systems with the advantage of sophisticated and flexible interfaces. Data transfer is therefore possible not only from the analytical equipment to the calculator but at the same time in the opposite direction to have a real computer control.

Titrations in respect to constant potential steps have advantages to titrations with constant steps in reagent volume, for there are more sufficient evaluation methods. A simple algorithm is described to calculate the next step of reagent addition. More precise results in the potential steps are obtained if the potential is controlled by computer during dosage.

Methods are discussed for linear calibration with an optimized number of data without loosing effective statistical information. Homoscedasticity is confirmed from, measurements at both limits of the chosen working range. The number of data used is given by the F-test borders. To confirm linearity a third series of measurements is taken near the mean of the working range and uniformity in sensitivity in both resulting parts is proven by t-statistics. If linearity is confirmed only data at the borders of the working range are taken as deducted from error propagation. If it is possible to recalibrate, this way is confirmed by means of the prediction interval. Furthermore, a method is discussed for finding out stochastic independence of data and systematic errors caused by memory effects.

Several types of optimization of wavelengths in multicomponent analyses are discussed. Usually the wavelengths of absorbance maxima are used. According to Kaiser the selectivity of any wavelength may be calculated and a set of wavelengths with highest selectivities is used in evaluation. In the case of two components the product of selectivities is introduced. Using all elements of the absorptivity-matrix in literature the determinant is described as criterion for selecting optimal wavelengths. From matrix operations it is shown, that the best results will be obtained if the condition of the matrix is used for optimization. Two examples are given to compare the results of optimization.

In 1954 Tubbs described a graphic method for locating the endpoint in recorded potentiometric titrations. Approximation of digital titration curves by hyperbolas and taking the curvature in the apex of each hyperbola leads to the centres of the smallest circles to be inscribed in the branches of the titration curve. The intersection of the straight line between these two points with the approximated titration curve gives the endpoint. This method is explained and discussed with non-symmetric redox titration curves and simultaneous titrations.

Fully computer controlled UV- and IR-photometers are described. Instead of the data transfer from the scanning photometer, the computer is able to set the monochromator to defined wavelengths or wave numbers. In order to avoid errors caused by time constants the data will be transferred to the computer a preset time after the monochromator has reached the real position. In quantitative analyses the signal to noise ratio may be improved by taking more data than only one at significant wavelengths.

Automated photometers for evaluating TLC plates by an optimized positioning of the spots in respect to the centre of the light beam are described. The evaluation can be performed by using the original measuring curve or a transformed one in respect to the Kubelka-Munk function. Two-wavelength techniques can be simulated, for the monochromator is controlled by the computer. This method has an advantage in measuring not well separated spots. In this case also an evaluation of the first derivative is often successful. The accuracy and reproducibility is given in respect to the different sources of errors: spotting, measurement, positioning and chromatography.

In a previous paper [1] a fully automated and computer-controlled polarographic equipment was described. The reproducibility of measurement is depending on the used range of amplification. If there is a current to be measured in the µA-range the relative standard deviation does not exceed 0.04% and reaches 0.5% in the nA-range. Only with the highest sensitivity of the used commercially available current to voltage converter the relative error will be about 1%. In order to determine the overall precision a cadmium sample with 11 µg/ml was used. In this case a relative standard deviation of 0.4% was found. The benzodiazepin-type drug clotiazepin was used to evaluate the accuracy. Calibration was run in the concentration range from 0.7 to 6.2 µg/ml. The overall accuracy was better than 1% using peak height.

Using commercially available parts computer-controlled titration systems may be built up. Depending on the problems to be solved one computer is able to control two systems with probe transport and two burettes each. In this case also more sophisticated types of titration are performed under computer control. The reagent addition is highly flexible and the size of the volume steps to be delivered are calculated from the slope and type of the titration curve.

Calibration of ion-sensitive electrodes using nonlinear regression analysis is combined with an increase of the working range to lower concentrations. It is possible to have statistically reliable results lower than the so-called limit of determination according to IUPAC. From these items the critical level, the limit of detection and the limit of determination are derived by the calibration function, its inverse (the function of analysis) and the confidence interval. The limit of detection is defined by the smallest detectable signal and the calibration function. The limit of determination is defined by the smallest concentration of an analysis that will be statistically significant with a preset probability of error differentiated from the concentration zero and the blind value of the potentiometric measurement. The limit of determination is therefore the smallest concentration of analysis that may be quantitatively determined.

Contrary to IR spectra there are only very few or no maxima in most UV spectra. Therefore library search based on peak tables will not be successful. The use of derivatives seems insufficient for there are too less data points for numerical derivatives and in case of trace analysis the signal-to-noise ratio is too bad.

The straight forward determination of concentrations by means of ion-sensitive electrodes is based on calibration procedures. In the case that the working range is within Nernstian response linear regression with ordinary least square calculation is sufficient. Caused by blanks there are deviations from linearity and calibration has to be done by a non-linear regression technique. Confidence intervals are discussed for both methods of calibration, for the calibration function as well as for the inverse function from the viewpoint of statistics. Furtheron, the expected relative error in the analytical result is taken into consideration as a very useful tool of comparing both methods. The influences of data distances and number of data are discussed. In many cases non-linear calibration has advantages compared to linear calibration eliminating the influence of a blank value. The possible working range is extended even below the socalled blank value.

The mathematical derivation is given by two different statements: differential equation and hyperbolic-trigonometric functions. It is shown that measurement of absolute values of remission is inapplicable. The signal is easily to be linearized. The evaluation is given by the maximum peak value obtained by the zig-zag scan technique (Shimadzu CS 900). To get similar scatter values sample and reference wave-length should be tuned as close as possible. Caffeine is measured from 0.25 to 20 µg. In this range the linearizer works unobjectionably and the error as relative standard deviation is in the order of 1.9% (4–20 µg,n=15) and 2.7% (0.25–2 µg,n=22), respectively.

For making use of the whole working range of ion-sensitive electrodes, it is often preferred to measure the potentials at various concentrations in order to get a straight line of potentials versus logarithm of concentration. The numerical evaluation of the electrode parameters yields furthermore the statistical errors of these parameters. Using error propagation, it is possible to calculate the error in analysis caused by errors in calculation and measurement. Experimental details and results are given.

Die theoretischen Grundlagen von Orthogonalfunktionen werden vollständig erklärt und auf Mehrkomponentenanalysen übertragen. Die Methode wird anhand der Bestimmung von Benzoesäure, p-Hydroxybenzoesäure und Sorbinsäure illustriert; die Auswertung erfolgt über die Methode der minimalen Summe der Fehlerquadrate. Die erhaltenen Ergebnisse lassen erkennen, daß die Methode auch dann auf Gemische von drei oder mehr absorbierenden Verbindungen anwendbar ist, wenn irrelevante Absorption zu erwarten ist. Letztere führt dann zu fehlerhaften Ergebnissen, wenn bei der Bestimmung von einzelnen Verbindungen die Extinktionen direkt zur Anwendung gelangen.

A method for determination of thermodynamic acidity constants is described. The potentiometric titration curve will be linearised with an iterative procedure for activity coefficients and an assumption for acidity constant calculated without activity coefficients. From the straight line given by least square analysis the acidity constant is computed. The described method is also useful in mixed solvents if the dielectric constant is large enough to prevent ion association. The precision is in the order of 0.01 pK-units (standard deviation).

For normalization of spectra in spectral libraries in UV/VIS range the maximum of absorbance, the area under the spectrum or a linear regression technique may be used. Using the error propagation law the best method should be the linear regression followed by area normalization. In practical work the area normalization has no advantages compared to a modified point normalization, where the mean of the maximum and the two next data points are taken. Therefore, in an automated comparison of UV spectra the modified point normalization is used for searching for similar spectra. The final comparison is done after linear regression normalization. This has advantages in calculation of error propagation and significance levels of two spectra. The reference spectrum is used as independent, the spectrum of the sample as dependent variable.

The measured potential using ion-sensitive electrodes in multiple standard addition procedures or in direct-potentiometry is characterized by the response/time-curve, by the noise and by the remaining drift of the electrode. Different algorithms are compared for use in data-acquisition with a computer-controlled equipment. The mean of a given number of measurements, moving average and a statistical trend test according to von Neumann are discussed. The best way seems to be a moving linear regression technique with suitable algorithms that can be used in realtime measurement independent of the number of single measurements.

TLC and HPTLC as chromatographic separation procedures differ in data processing: TLC is a discontinuous process in the local domaine using off-line data processing while HPLC as a continuous process in times domaine needs on-line data processing. In HPLC fully automated (in the sense of fully mechanized) systems are state of the art, in TLC only spotting and evaluation are fields of interest in automatization. As there is a need of real positioning in the x/y-coordinates a computer controlled way has advantages compared to automated scanning equipments. In order to have low limits of determination a signal-to-noise enhancement may be used, but there are different ways in TLC or HPLC. The determination of non-separated peaks may be done in both methods by the same procedures as derivative or double wavelength techniques. In HPLC, using photodiodearray detectors, there are further possibilities as derivative spectroscopy or convoluting techniques by orthogonal polynominals in the spectral domaine. Calibration in TLC is restricted by the non-linear relationship between reflectance and mass of substance per spot. Non-linear regression techniques for instance using the Michaelis-Menten function are more reliable than the often used linearization methods.

Sources of error in automatic spectroscopic analyses in the UV or visible range are the transmission Tref and Tanal and the wavelength error. Using instruments equipped with flow-cells, errors in positioning the cell and the pathlength are eliminated. An error equation is given and verified by experimental results. Modern UV-photometers having only small straylight can be used in the range of 0.3 to 1.6 absorbance units for precise quantitative analyses.

The possibility of computerizing polarography is pointed out. Programmable desk-top computers may be used for data transfer and also for controlling the instrument. The equipment and some details of the switching unit are explained and are given as main diagrams. New methods of evaluation in polarography are mentioned.

Computer controlled equipments have the advantage to automize an analytical procedure. In most cases it is very important to know the sources of errors, because in automatic systems errors may have a higher influence on the result than in manual work. Furthermore, new methods of evaluation have to be used in automatic systems with digital data handling. The possibilities of controlling automatic systems by programmable desk top-computers will be given in the following analytical procedures: potentiometric titrations, coulometric titrations, quantitativ analysis by UV or IR-spectrometry, scanning TLC plates in reflectance or fluorimetric mode.

The evaluation of titration curves in acid/base titrations with electrolytically generated reagents by the method described by Keller and Richter is discussed from theoretical aspects. Experimental data agree with these considerations. The reproducibility of digital-coulometric titrations is in the order of 0.4–0.8%. In case of strong acids and weak acids with pK-values smaller than 7 the error is smaller than 1% and increases with the pK-value, if weaker acids are titrated.

This paper describes a reliable working station for the in line-process control in chemical plants. Essential parts of the equipment (pump, column) are in duplicates and may be combined by computer control in different lines. One pump and column is in working position, the other is held in ready to work position by conditioning. While one column is in working position, the system is able to calibrate the other column and to switch to this column in the case of breakdown of the other column. By means of chromatographic data (as retention time, peak height of standards, data of separation) the working column is under control and the switching to the other column is down before a real breakdown. The status of the detector is followed by number and distance in time of the necessary auto-zero operations and by the noise of the lamp.

A fully automated and computer-controlled working station for use in routine polarographic analysis with the possibility of connecting to a computer network is described. Change of samples and transfer from the degassing vessel to the measuring cell including all steps of rinsing are controlled by the computer. The system is designed for use with the dropping mercury electrode. By means of flow charts the timings are described. Details of the necessary interface between computer and working station with sample transport and polarograph are given.

An incremental titration system with coulometric generation of the reagent is described. The constant current delivered by a coulostat is switched to the working electrode for a definable time. Between these current periods the system controls the electrochemical equilibrium of the measuring electrode. A programmable desk calculator controls the whole system, the current periods, the potential of the measuring electrode and calculates the endpoint of the titration. The analyses are performed automatically. The evaluation can be done by the approximation method published by Keller and Richter or by a slighty modified Gran function.

Summary: Ion-sensitive electrodes are commonly calibrated by means of standard solutions. In this paper a computer controlled method is described. The standard solution is added to the blank in the way of geometric series starting from 0.02 ml up to 25 ml. From this follows a concentration range in the order of three decades. The calibration points are situated nearly equidistant, caused by the logarithmic behaviour of the Nernstian law. If the working range is in between the linear response of the electrode, evaluation is done by mean in linear least square routines. If the working and calibration range is near the limit of detection, a non-linear regression technique has advantages compared with the commonly used blank correction.

Multiple standard addition techniques are commonly used with equidistant volume increments of standard addition. The disadvantage of this method is discussed in respect to data intervals in the measured potentials and to the extrapolation using Liberti-Mascini's method of evaluation. With computer-controlled instruments the standard addition is done in such a way that equidistant intervals of the potential steps to be measured are achieved. Using this method a greater working range will be obtained and the results will be more reliable because of the smaller extrapolation range and better error propagation.

In the computer controlled evaluation in polarography one problem is to find mathematical criteria to approximate the baseline. Two modell functions are described in this paper: a three-parametric exponential function and the third-degree polynomial. It is possible to give some conditions for using the polynomial. The advantages are in this case the shorter timer required for all calculations and the higher stability towards numerical problems. Some examples are given to discuss the proposed method.

A method for evaluating the endpoint of non-symmetric digital titration curves is described. An approximative value for the endpoint is calculated from two potential steps in the outer region of the titration curve. After that, it is possible to calculate the heterovalence part of the greatest potential step. At last, the endpoint of the titration is evaluated by the numerical version of the Hahn-Fortuin nomograms given by Keller and Richter.

For the evaluation of digital-potentiometric titrations two principles are known: methods based on the mathematics of titration curves and methods using only three points near the equivalence point of the titration reaction. The paper describes the systematic errors of the latter methods by the example of acid/base titrations. Percentage errors are given as diagrams with respect to the relative location of the endpoint of the titration curve to the points where the potentials have been measured. Also other parameters of the titration are discussed (initial concentration, acidity constants, electrode parameters and errors caused by kinetics). Most useful is the method published by Keller and Richter, which is based on nomograms given by Hahn and Fortuin.

The paper describes the principles of a programm for numerical peak detection and numerical integration for area determination by digital computers with respect to thin-layer chromatography. Integrating analog to digital conversion and digital smoothing will improve the signal to noise ratio. The first derivative will be found by smoothed numerical differentiation and is used for peak detection. The actual base line is corrected by eomparision of the tangents between the minima of the peaks.

The orthogonal function method is applied to the determination of dihydrocodeine bitartrate as a minor component (5 mg) in presence of noscapine hydrochloride (25 mg) without separation. Another method based upon precipitating noscapine by a saturated solution of sodium acetate is also presented. Dihydrocodeine is determined in the filtrate using the orthogonal function method to correct for the unprecipitated fraction of noscapine. Standard deviation is 1.56 and 0.66 for direct and precipitation methods, respectively.

The paper describes the coupling of TLC-photometer, electronic integrator and desk calculator for the determination of phthalic acid by measurement of the remission at 280.3 nm. The average of integrator counts by scanning in and against development of the plate avoids errors caused by base line-drifts. From standards on the plate results a straight line by least squares using the quadratic proportionality of peak area to concentration. From this straight line the concentrations will be determined. The error of this method is in the range of 2–2.5% (relative standard deviation).

The paper describes the coupling TLC photometer-electronic integratordesk calculator for determination of quinine as standard compound of fluorimetry. The average of integrator counts by scanning in and against development of the plate avoids errors causing in base line-drifts. From the standards on the plate results a straight line by least squares, from which the concentration of the analyses will be determined. The error of this method is in the magnitude of 1.5% (standard deviation). The method is compared with others.

The paper describes a method for determining acidity and basicity constants from potentiometric titration curves. The method is based on the solvation of the system of equations that are the mathematic foundation of titration curves. The results are thermodynamic constants, for there is included the mean Debye-Hückel activity coefficient by an iterative approximation. The reproducibility is in the magnitude of 0.01 to 0.03 logarithmic pK-units, the reproducibility in the same titration curve at 0.004 pK-units. The limitations are pK-constants of about 2.5 and 10.5.

Gran-plots are well suitable for analysing potentiometric titrations by digital computers. Straight lines however do not result in the case of weak acids. Therefore linear regression analyses are subjected to rather great errors. Better results can be obtained by polynomial approximations. Orthogonal polynomials are preferred in order to avoid numerical problems.

The paper describes the—as far as possible—automatic determination of carbon, hydrogen and nitrogen in the ultramicorange. The method is based on the Hewlett-Packard CHN-Analyzer. An electronic desk-calculator controlls the determination from weighing the substance, integrating the areas of the gaschromatographic separation of CO2, H2O and N2 to printing the results by alphanumeric output.

In the case of titrations of strong acids the influence of the mean activity coefficient, the slope and zero point of the glass electrode on the computed end point is discussed. For exact computations only the slope of the electrode is to be known, while zero point of potential and activity coefficient are calculated by the computer itself upon the given data of titration.

In previous papers a fully automated and computer-controlled polarographic equipment [6] and its precision and accuracy [5] was reported. Automated development of methods can be done by computer-controlled dosage of the substance to be determined to various buffers. From 3D-plots optimum conditions can be easily seen. Calibration is done by computer-controlled dosage of the substance to be determined to different electrolyte solutions, repeated measurements and repeated dosage. Change of samples and transfer to degassing vessel and measuring cell are controlled by the computer.

An explicit equation can be derived for acidity constants from the basic equations of the titration-curves of weak acids. Furthermore, an iterative optimization procedure for the initial concentration of the substance can be derived from the systematically deviation of calculated pK-values. Thus, the determination of acidity constants is possible also without exactly known weight of substances, within the precision of the method (standard deviation 0.01 pK-units).

A TLC method for the determination of phenacetin and caffeine in pharmaceutical preparations using a densitometer in line with an integrator and electronic desk calculator is described. The calibration curves of each compound were prepared where the higher and lower tolerance concentration levels were defined. The accuracy of the method is 1.51% (phenacetin) and 2.56% (caffeine) for two experiments carried out on each plate; 1.50% (phenacetin) and 2.64% (caffeine) for four experiments for each plate (relative standard deviation, n=18 and n=36, respectively).

For the determination of absolute pH-values by combined glass electrodes the parameters of the electrode are determined by a straight-line calibration curve after measurement of some NBS-buffers. The numerical evaluation of the electrode parameters yields furthermore the statistical errors of these parameters. Using error propagation, it is possible to calculate the error in the pH-values caused by errors in calibration of the electrode. Experimental details and results are given.