Article for the 26th Sensing Forum

Estimation of Uncertainty in Volume Measurement
Example of the gravimetric method using balances

Presented by: Naoto Izumo and Yuji Fukami
R&D Division 5, A&D Company, Limited
Organized by: The Society of Instrument and Control Engineers (SICE)

September 28 to 29, 2009
Ookayama Campus, Tokyo Institute of Technology
Tokyo, JAPANEstimation of uncertainty in volume measurement
Example of the gravimetric method using balances
Naoto Izumo, Yuji Fukami

A&D Company Limited

Higashi-Ikebukuro, Toshima-ku, Tokyo 170-0013 Japan

Abstract
Many kinds of volumetric meters, such as pipettes and dispensers, are used inresearch, clinical trials, industry, and so on.
Generally, the volume accuracy of such volumetric instruments is checked with thegravimetric method using a balance.
This report provides practical data and important points regarding volume
measurement using the gravimetric method.

Keyword
Piston pipettes, Z correction factors, Evaporation trap, Human error, Density ofliquid
1. Introduction
Pipettes are an example of a frequently used volumetric instrument. Pipettes areused in scientific experiments in fields ranging from medicine, pharmaceuticals, andbiotechnology to food products and in situations ranging from research to clinical andstudent science experiments. There are currently over 30 pipette manufacturers
worldwide. For micropipettes in particular, it is said that recent annual production
numbers are 1 to 2 million worldwide and usage has been increasing about 5% a year. In
fields ranging from food products, pharmaceuticals, and biotechnology to clinical testingin hospitals, individual locations and research departments use hundreds of pipettes. At
the laboratory level, there are about 10 pipettes per person on average. In university
chemical science departments, each department uses around 1,000 pipettes. Other thantechnical problems, they take up a substantial amount of time and money inadministrative work.
In production industries, dispensers are frequently used for automation. They arewidely used for the measurement of resist quantity in liquid crystal and LED
manufacturing equipment, for the control of liquid ejection in battery production lines,
and as important equipment in the application of cream solder, adhesives, grease, andoil. The performance of these products is maintained and quality is controlled.
Pipettes, dispensers, and other volumetric instruments used in liquid ejection work
are obviously valuable for volumetric ejection performance. Still, because of thedifficulty of introducing volumetric measurement technology to measure the liquid
ejection performance, it cannot be said that there are established volumetric detection
methods at locations using pipettes. Therefore, pipette experts typically have to arrange
measurement environments for pipette management. While management by an expert
is ideal, there exist differences with the actual usage environment and individual
differences in user skill. As a result, the differences between the managed performanceand actual ejection performance become a problem. This document presents aninvestigation of the gravimetric method, a standard method with a track record among
the volume measurement methods currently proposed. It identifies points of caution
during volumetric measurement with the gravimetric method and uses data obtained
through testing to show the reality of volumetric measurement.
2. Measurement principles of the gravimetric method
The gravimetric method involves measuring
volumeasmass.

Thisreflects

thatmass

measurement is cheap and easy compared to othermeasurements of physical values yet has a highresolution. For example, for a general analyticalbalance with a capacity of 200 g and a minimum
display of 0.1 mg has a resolution of 1/2,000,000,
there are low-priced balances available at aroundFig.1
A pipette volume tester using a 10μg balance(4)200,000 yen.
Meanwhile, among all pipettes, the micro-pipettes that are required formeasurement of minute amounts with a measurement capacity of 20 to 1000 μL sell
well. For example, testing of a pipette with a rated volume of 20 μL requiresdetermination level of 0.1 μL so measurement requires another decimal place, or 0.01
μL (10 nL). Using a standard of distilled water with a density of 1 g/mL, 10 nL equals 10μg. This means that a semi micro-balance is required as a weighing device. Since 10 μg
is 100,000th of a paper clip, measuring a volume of 10 nL is obviously not easy.
Density correction is required to actually determine volume by mass measurement.
Furthermore, the surrounding environment often increases measurement uncertainty
when measuring mass at a level finer than semi micro-balances. It is known that
control methods to reduce uncertainty require many technical cautions and can beexpensive due to environmental adjustments.
Fig.1 shows an example of a volumetric tester that uses the gravimetric methodwith a balance that can measure to a level of 10 nL (μg). From the left, it comprises anoperation section (display section), a weighing section, and a thermometer andcontainer to measure the liquid temperature. An evaporation trap is set on the weighing
section to minimize evaporation of liquid (distilled water). The evaporation trap limits
evaporation of liquid ejected from the pipette using vapor pressure. It reduces
uncertainty and ensures operability during weighing.
3. Factors for uncertainty with the gravimetric method
The main causes of uncertainty with the gravimetric method are as follows.
Correction coefficient: Z correction factor
In order to measure volume using mass, you must determine the mass of thesample you want to measure and then divide it by the density of the sample.
Volume: V=M/ρ

M: mass; ρ: density.

Accordingly, the uncertainty of the volume is determined by the uncertainty of themass measurement and the uncertainty of the density determination, meaning that thefactors constituting the uncertainty accrue at the time of each physical quantity
measurement.
In volume measurements of distilled water ejected from a pipette, the factor related
to density correction is called Z correction factor, which is defined as the coefficient for
conversion from mass to volume.1, 2
Volume: V=M x Z

M:mass;Z:

Z

correction

factor(conversioncoefficient)
The main factors of the Z correction factor are the density changes of water that
accompany temperature changes and buoyancy changes from temperature andatmospheric changes.
If water at 20 ℃ changes 1 ℃, the density of water changes about 0.02%.
Changes in the mass value due to the evaporation of liquid
It is known that after liquid is ejected from the pipette to the container on the panof the balance the vaporization and evaporation of the liquid create uncertainty in themass measurement, which decreases the value.
Uncertainty from pipette usage
The main causes of uncertainty caused by the user are excessive or insufficientsuctioning, residual water on the tip of the pipette when water is suctioned and ejected,
and convective flow caused by temperature changes when the user holds themeasurement container.
Of these causes, density changes and evaporation volume are mainly theuncertainty due to the measurement system. Uncertainty caused by water suction andresidual water, as well as body heat, depends on the knowledge and experience of theuser. Since density changes can be simply corrected after calculating the water and air
density changes, our testing is focused on the remaining two items: the evaporation ofliquid and user-created uncertainty.
4. Measurement results
4-1. Evaporation amount of liquid
When using the gravimetric method, the medium is generally distilled water, which
has a fixed density in relation to temperature. Since water has a large specific heat anda high boiling temperature, it does not evaporate easily. Nevertheless, water starts toevaporate after it is ejected from the pipette. Table 1 shows the measurement results forthe amount of evaporation from the container.
When water is left in a 30 mL container at a room temperature of 30 ˚C and ahumidity of 50%, the amount of evaporation reaches about 0.3 mg per minute (0.3 μL(300 nL) per minute). This amount will be problematic in determining the results when
testing 20 μL, or 10% of a pipette with a rated capacity of 200 μL.
To improve the volume measurement environment, an evaporation trap like the one
shown in Fig. 2 was introduced. The trap reduced evaporation to 0.07 mg per minute(0.07 μL (70 nL) per minute), which is a reduction of about 75%. If a measurement iscompleted in 10 seconds or less, evaporation is further reduced to about 10 nL. This
indicates that an evaporation trap can reduce the effect of evaporation to about 0.05%,
even when measuring 20 μL.

80% RH area

Evaporation of water per unit time
Container
5 mL

pipette tip

Evaporation trap
NoYes
Liquid measurement

0.14 mg per 0.05 mg per(Inner diameter: 13 minutecontainerminutemm)
30 mL

Opening for

Water

0.26 mg per 0.07 mg per(Inner diameter: 30 minuteJigbalance panminutemm)
T30℃
H idit 50%(Rh)
Table 1. Amount of evaporation

placedFig. 2. Evaporation trapon

4-2. Convection flow caused by user holding container
It has been proposed that a cover should be usedwith the container to reduce the effect of evaporation,
particularly with regard to measurement of small
volumes.1, 3 However, if the user holds the container
for a certain amount of time under some conditions,body heat is transferred to the container and its
temperature is raised. It was confirmed that thisFig. 3. Thermograph immediately after thecontainer was held by handtemperature change caused convection around thecontainer and changed the weighing value.
Fig. 3 shows temperature measurement resultsfrom a thermograph immediately after the container
was held by hand for a period of time (about 10seconds). The thermograph shows the analyticalbalance from the side. The operation section anddisplay section are on the left and the white section in
the middle is the container on the weighing pan(diameter: 53 mm, length: 100 mm, material: steel).

Fig. 4. Changes of container temperature and weighing values

Fig. 4 shows the measurement results for the container temperature and weighing
values at this time. The results of a test in which the container was held for a certain
amount of time and then left at room temperature confirmed that the temperature of
the container dropped about 0.7 ˚C per minute and the weighing value increased about
0.7 mg per minute after one minute at room temperature.
This change in value was about double that of the evaporation amount in 4-1 (inwhich no evaporation trap was used). While the actual container used is smaller andmade of plastic, repeatedly holding it by hand can lead to increased temperatures. The
difference of the room temperature and the container temperature causes convection on
the surface of the container, which in turn leads to changes in weighing values. This
indicates that directly holding the container by hand for long periods can be major
disturbance.
4-3. The effect of pipette usage proficiency
Next, we will report on measurement results when three new engineers (EngineerA, B, and C) at our company used pipettes. The three engineers received a pipette witha rated capacity of 200 μL and measured a volume of 100 μL under the following threeconditions: 1. No instructions 2. Brief instructions about suction and ejection procedures
3. Instructions about all aspects of stable measurement, including tip exchange,
pre-rinsing, suction angle, tip submergence depth, and procedure speed. Table 2 shows
the results. While an extreme case, Engineer B improved in accuracy/repeatability from
5.8%/22% to 0.20%/0.15% and then to 0.11%/0.18%. Even Engineer C, who had
experience using pipettes in experiments as a student, showed improvement in accuracy
from 0.36 to 0.34 and then to 0.04%.

A (novice)

Training level

B (novice)

C (experienced)

Accuracy

Repeatability

Accuracy

Repeatability

Accuracy

Repeatability

1. No training

-3.9%

0.46%

5.8%

22%

-0.36%

0.13%

2. Instruction about-0.26%

0.24%

0.20%

0.15%

-0.34%

0.22%-0.15%

0.25%

0.11%

0.18%

-0.04%

0.10%

pipette procedures
3. Instruction about stablemeasurement procedures
Accuracy: Deviation of the mean value from a set volume; Repeatability: Coefficient of variation (standarddeviation/mean); measurement repeated 10 times

Table 2. Improvement by training level

5. Conclusion and summary○Introducing an evaporation trap effectively limits the evaporation of water ejectedfrom a pipette. When a trap is used, data shows that it is possible to perform volume
measurements in which evaporation is limited to around 10 nL for each measurement(10 second period), even when there is an opening for the tip of the pipette. It has beenshown that this method can improve the inefficiencies caused by handling containers
and uncertainty caused by the body temperature of the user (the trouble caused by themethod of covering the container before measurement as proposed for measurement ofsmall volumes in JIS K0970-1989 and ISO8655-6).
○In volumetric measurement using the gravimetric method, measurement system

uncertainty includes (1) uncertainty of mass measurement by a balance, and (2)uncertainty caused by the environment measurement (temperature, atmosphericpressure) required for conversion from mass to volume. The standard uncertainty ofmass measurement was investigated based on the specifications of the balance used in
the test in 4-3, considering the following as the main causes of uncertainty with massmeasurement by balance: repeatability, linearity, rounding error, and sensitivity drift.

The results showed that when the temperature change at measurement is assumed tobe 1 ˚C, the uncertainty when measuring 100 μL (100 mg) is 0.058 μL. Furthermore, themain cause of the uncertainty in environment measurement was the temperaturechange of the distilled water. When the uncertainty of temperature measurement wasassumed to be 1 ˚C, from the relation of the temperature and density of distilled water(deviation of 0.02 for each 1 ˚C), the uncertainty related to conversion from mass tovolume when measuring a volume of 100 μL is 0.012 μL. Accordingly, the standard
uncertainty of measurement in the weighing system is 0.059 μL and the extended
uncertainty is 0.118 μL (coverage factor k=2). For a measurement volume of 100 μL, thevalues are 0.06% and 0.12%, respectively.
○It was learned that the repeatability depends on user handling when the effects ofevaporation are controlled. As shown by the test results of 4-3, repeatability whenmeasurement is performed by a novice without training was 0.46% (Engineer A) and22% (Engineer B). The estimated standard uncertainty obtained by dividing these by
the square root of the number of measurements (10) for 100 μL were 0.15% (Engineer A)
and 6.9% (Engineer B) respectively. This is more than double the standard uncertaintyof the measurement system, and further training improved the repeatability.
○The results proved that operator skill causes individual differences when

determining volumes using pipettes. In addition, training (even with novice users) andthe addition of measuring instruments that can numerically demonstrate training
results reduce uncertainty (accuracy, repeatability), which makes it possible to measure
volumes with better stability. A method must be established to confirm andacknowledge these effects to follow the cycle of “plan-do-check-action” in volume
measurement, and the results here clearly demonstrate that introducing measurement
devices based on the gravimetric method is effective in this regard.
○As an example of future work, we would like to propose methods to make procedures

easier, such as a method to reduce residual liquid on the tip during ejection, and further
the development of instruments that can help reduce uncertainty in a wide range ofvolume measurements.

References[1] ISO8655 1-6: 2002(E) Piston-operated volumetric apparatus[2] ISO/TR20461: 2000(E) Determination of uncertainty for volume measurements
made using the gravimetric method[3] JIS K 0970-1989
Piston operated micro-volumetric apparatus[4] A&D http://www.aandd.co.jp