1 Introduction

The pipetting of small volumes in the range of microlitres is widely used in various research laboratories. A piston-operated pipette (popularly known as micropipette) is a simple instrument which is used to deliver small amount of liquid in the range of microlitre. They are extensively used in analytical laboratories, biological applications, pathological laboratories, medicinal research laboratories and various other fields. Therefore, it is important to calibrate the micropipettes to know the correct volume with known uncertainty [1, 2]. Mostly, these instruments are used in extremely sensitive research and manufacturing laboratories like medicines and biological testing; therefore, even a small unknown error in pipetting could cause critical and sometimes life-threatening end results. Hence, it is of paramount importance that the micropipettes are well calibrated either by the National Metrology Institute (NMI) of the country (CSIR-National Physical Laboratory in case of India, internationally known as “NPLI”) or by accredited laboratories traceable to the “National Standards” maintained by the NMI through an unbroken chain [3, 4].

There have been several approaches followed by researchers around the world to analyse the micropipette calibrations [5,6,7,8,9]. The researchers have focused on improving various parts of the sources of error or on establishing an entirely different technique. The current study is to analyse the various types of gravimetric techniques using wide array of experiments. This paper is the article on the volume calibrations using the micropipette explaining the techniques used and a fine comparison between the various combinations of techniques used by the NMI of India (NPLI). Further the uncertainty evaluation is also discussed considering the parameters having significant contribution [10, 11].

2 Experimental Methodology

2.1 Instruments Used

We used a single channel micropipette at nominal value of 5 µl capacity. The distilled water used for the aspiration was kept in the experiment room for 48 h prior to the observations for thermal stabilization. The experiment room was under controlled environmental conditions, and to avoid air drafts, double doors with sufficient spacing were used. The weighing balance used was of 0.001 mg resolution and a maximum capacity of 5 g. Balance was in-house calibrated using mass standards. The stopwatch utilized for the measurements get calibrated from the Time and Frequency Section and the thermometer used to measure the water temperature was of 0.1 °C resolution which was get calibrated from the Temperature and Humidity Section of the NPLI. Calibrations of all the equipment used in the measurements are traceable to “National Standards” of measurements [12]. As per the standards [9], for volumes below 50 μl, errors due to evaporation of the test liquid during weighing shall be taken into consideration. Since the nominal value is low, therefore, to minimize the evaporation effect, an evaporation trap mechanism was used inside the balance.

2.2 Standard Documents Followed

The international standard document named ISO Piston-operated volumetric apparatus - Part 6: Gravimetric methods for the determination of measurement error [13] is followed for the detailed calibration of the micropipette.

2.3 Principle of Operation

The single channel micropipette is an easy to operate and commonly used instrument in the laboratories. The electronic variant used in this study is a microprocessor-controlled battery-operated piston-stroke pipette. After setting the volume to the required nominal value (5 µl in this case), the tip is securely attached. Standard ISO 8655 [13] prescribes rinsing the pipette well before starting the operation. The pipette is held vertically, and the tip is immersed (2-3) mm into the distilled water. The pipetting key is pressed to aspirate the liquid into the tip. Next the liquid is discharged into an empty beaker on the balance tared. The discharge angle is 30°–45° (visual observation), and the tip is placed against the vessel wall. Finally, the distilled water is completely discharged into the empty vessel.

2.4 Calibration Techniques Used

The calibration of the micropipette was carried out using the gravimetric method with various combinations based on the ISO standard [13]. A suitable weighing balance is required for accurate measurement of the mass of water delivered by the micropipette into the vessel [14]. The following formula is used for conversion of the mass of liquid of the micropipette into volume at 27 °C [11, 15]:

$$V_{27} = \left( {I_{L} - I_{E} } \right) \cdot \frac{1}{{\rho_{W} - \rho_{A} }} \cdot \left( {1 - \frac{{\rho_{A} }}{{\rho_{B} }}} \right) \cdot [1 - \gamma \cdot (t - 27)]$$
(1)

where V27 = volume of water (= micropipette) at 27 °C in µl; \({I}_{L}\) = indication of weighing balance after pipetting the distilled water (empty beaker on the balance), in mg; \({I}_{E}\) = indication of weighing balance before pipetting the distilled water (beaker with distilled water), in mg; \({\rho }_{W}\) = density of water at the calibration temperature calculated with the “Tanaka” formula, in kg/m3 [16]; \({\rho }_{A}\) = density of air during measurement calculated using approximation formula, in kg/m3 [13]; \({\rho }_{B}\) = density of the mass standard used during calibration of balance, in kg/m3; \(\gamma\) = cubical coefficient of thermal expansion of the piston pipette material, in /°C; t = water temperature, in °C.

The experiments are conducted in India; therefore, the standard reference temperature is adopted at 27 °C. Nevertheless, for non-tropical countries the standard reference temperature used in the formula is 20 °C.

The three methods used for the comparative analysis are as follows:

  1. (a)

    Conventional method

  2. (b)

    With evaporation loss correction

  3. (c)

    Without evaporation loss correction

The "conventional method" is signified by cleaning the beaker after each cycle. The micropipette is wetted a few times to adjust to the humidity inside the pipette. The empty beaker is kept inside the weighing balance to determine the mass of empty beaker (balance may be tared with empty beaker). Next the liquid is aspirated from the reservoir beaker and discharged into the beaker on the balance to note down the mass of the beaker with the liquid. The stopwatch is used to measure the time elapsed in the observation, since as per standard, each cycle should be completed within 60 s to minimize the evaporation loss. Two distinct sets of readings with ten cycles of operations each are performed. The liquid temperature is measured during each cycle using the thermometer and so are the environmental conditions, i.e. temperature, relative humidity and pressure.

The second method is the "with evaporation loss correction" method. The beaker is kept inside the mass comparator with a small amount of the liquid (\({m}_{0}\)). Next the liquid is aspirated from the reservoir beaker and discharged into the beaker and the mass of the liquid is \({m}_{1}.\) Similarly, subsequent readings are taken, and the beaker is not cleaned (liquid is added on in each cycle) between the readings unlike the conventional method. The stopwatch is used to measure the time elapsed during each cycle (tc). The mass obtained by difference (\({m}_{1}\) − \({m}_{0}\)), (\({m}_{2}\) − \({m}_{1}\)), etc., is converted to volume of the micropipette using Eq. (1). After ten readings, the liquid is left for 10 times the time elapsed for each set (10tc) and the final reading is taken as \({m}_{11}.\) The adjustment due to evaporation loss is [\(\frac{\left({m}_{11}-{m}_{10}\right)}{10}]\). The value determined due to evaporation loss is then added to each cycle measurement.

The third method is the "without evaporation loss correction" method. It is the same as the second method and does not involve cleaning the beaker after each cycle unlike the conventional method, but here the evaporation loss is not considered. Rest all technique is the same as the "with evaporation loss correction" method. This method is used to know the effect of evaporation loss in volume measurement with respect to associated uncertainty.

Two distinct sets of readings with ten cycles of operations each are performed for the micropipette set at 5 µl.

2.5 Uncertainty Evaluation

The uncertainty factors are determined from the formula (1) used for the evaluation of the volume. The formula (1) can be divided into components each contributing to the uncertainty in the measurement. Figure 1 shows the detailed breakdown of the formula into various factors contributing to the measurement errors and subsequent sources of uncertainty.

Fig. 1
figure 1

Structure of the volume calibration model

Full size image

3 Results and Discussion

This paper is a detailed study to evaluate the volume of the micropipette using the various methods and analysis on the obtained results. The results are shown in Fig. 2. The prescribed limit (shown in bold black line) for the range of systematic error has been taken from the standard prescribed value of ± 0.125 µl for 5 µl nominal value [15]. As it can be seen, in all the three techniques, the obtained volume of the micropipette is within the range of the systematic error value. Although for conventional technique, the variation is the maximum from the nominal value of 5 µl and the one without evaporation loss shows the volume nearest to 5 µl. Further, the associated uncertainty for conventional technique is the highest (0.075 µl, k = 2 rounded up as 0.08 µl), whereas the lowest uncertainty is obtained for the without evaporation loss correction technique (0.058 µl, k = 2 rounded up as 0.06 µl).

Fig. 2
figure 2

Calibration of a 5-µl micropipette using three different techniques

Full size image

The above experiment is a preliminary comparative analysis and shows that the most repeatable method with the lowest uncertainty is the one "without evaporation loss correction". It is a reliable method without any cleaning requirements in between the observations. Moreover, this technique does not involve volume corrections due to evaporation loss to be added.

On the other hand, the conventional technique is the most tedious one that requires longer time owing to the cleaning of the weighing beaker. The non-uniform time gap may result in change in the environmental stability inside the beaker and thereby affect the result. Further the volume correction being measured manually and added uniformly at the end may have reduced the reliability of the method. Moreover, the major evaporation part occurs in between the readings rather than during it. Therefore, it is concluded with plausible explanations that apparently the method without evaporation loss correction is the most efficient one among the three techniques considered in this preliminary study. However, to conclude strongly, we need to conduct such analysis at several other nominal values and using different instruments. With a wider range of data sets, it can be determined perfectly which technique will provide the most accurate results. Such analysis for other nominal values is under the future scope of metrological research.

Table 1 presents a sample calculation for the uncertainty estimation of a 5 µl micropipette. The standard deviation of the mean from the repeated measurements is taken as “Type A” contribution and all other components are contributing to “Type B” uncertainty [1, 17].

Table 1 Sample uncertainty budget for a 5 µl micropipette calibration
Full size table

4 Conclusion

This is a first report on the micropipette calibration techniques from the NPLI. Several tests were conducted based on the ISO standards to obtain the method with the least uncertainty and good repeatability. After preliminary set of experiments and evaluation of the obtained results and analysis of the uncertainty, it is concluded that the "without evaporation loss correction" method is the apparently most efficient technique for this nominal value, however, for any concrete decision, need more data in same and different nominal values. The structure of the volume model with the factors for uncertainty appropriate for the techniques was discussed. Although the conventional method had the maximum uncertainty, there is a lot of scope to develop a more advanced mechanism to measure the evaporation loss accurately which does not make the process slow and does not affect the final results. Similar analysis can also be done on other volumetric glassware calibration techniques which are now under future scope.