Diffusion-based passive samplers are increasingly used for water quality monitoring. While the overall method robustness and reproducibility for passive samplers in water are widely reported, there has been a lack of a detailed description of uncertainty sources. In this paper an uncertainty budget for the determination of fully labile Cu in water using a DGT passive sampler is presented. Uncertainty from the estimation of effective cross-sectional diffusion area and the instrumental determination of accumulated mass of analyte are the most significant sources of uncertainty, while uncertainties from contamination and the estimation of diffusion coefficient are negligible. The results presented highlight issues with passive samplers which are important to address if overall method uncertainty is to be reduced and effective strategies to reduce overall method uncertainty are presented.
The overall goal of environmental management programs is to provide a framework for assessing environmental status, identifying problem areas, and to continuously assess quality indicators to ensure that those are within established acceptable limits which ensure a “good and nondeteriorating status.” One of the indicators of environmental quality outlined by the Water Framework Directive of the European Union is heavy metal concentration in water bodies, including Cu, Pb, Cd, and Ni [
A passive sampler is a device used to collect a target analyte
A passive sampler for metal sampling is typically composed of a membrane filter, a diffusion layer gel, and a receiving phase placed in a sampler housing, like the DGT (diffusive gradients in thin films) technique (Figure
A schematic rendering of a DGT passive sampler showing its principal components.
In (
Although there has been some consideration of overall uncertainty in passive sampler measurements [
For the purpose of this study, a simple case was assumed; a DGT passive sampler with characteristics listed in Table
Predefined passive sampler characteristics and environmental conditions used as a basis in the uncertainty calculations.
Parameter | Property/Value |
---|---|
Passive sampler | |
Diameter | 2 cm |
Diffusion layer | Acrylamide gel with APA cross-linker (APA2) [ |
Cellulose nitrate membrane | 135 |
Receiving phase | Resin-gel containing Chelex resin |
Environmental conditions | |
pH | 7.5 |
Water temperature | 25°C/298 K |
Turbulence | Estimated |
The uncertainty budget presented here was estimated for a generic passive sampler under predefined environmental conditions (Table
Uncertainty in passive sampling is expected from all steps in the analytical process, including preparation of the samplers, deployment, analyte extraction, analysis, and estimation of diffusion rates and pathways. Overall, the estimation of uncertainties and the propagation of uncertainties were based on standard methodology [
Parameters for which uncertainty is determined and respective units.
Parameter | Unit | Definition |
---|---|---|
|
m2 | Effective area of diffusional cross-section |
|
m2 s−1 | Diffusion coefficient of the Cu2+ ion in the MDL |
|
m2 s−1 | Diffusion coefficient of the Cu2+ ion in water |
|
g | Accumulated amount of Cu2+ determined from sample |
|
g | Contamination determined from field blank |
|
Recovery during the extraction phase | |
|
K | Temperature in bulk water phase |
|
hours | Exposure time |
|
m | Diffusional boundary layer thickness |
|
m | Diffusional pathway thickness of the MDL |
Cause and effect diagram describing the uncertainties associated with the determination of bulk concentration
When deploying a prepared passive sampler, the fully labile metal ion (Cu2+) accumulates on the receiving phase and the accumulation rate is governed by diffusion across a diffusion boundary layer (DBL, see Figure
Schematic representation of the concentration gradient that forms over the diffusional pathway.
The DBL is the water layer closest to the passive sampler-water interface that is not affected by the mixing conditions in the bulk water phase. This measure is a representation of the effective DBL as this is neither evenly distributed layer across the surface nor a true unmixed layer but rather a velocity gradient. The effective thickness of the DBL is subject to uncertainty. The uncertainty can be reduced by deploying several devices with varying
The diffusion coefficients
The diffusion coefficient
The uncertainty introduced from variability of
The effective area of the section through which diffusion occurs has been reported to be somehow larger than the nominal area due to lateral diffusion; that is, diffusion occurs in three dimensions [
Summation in quadrature was used to combine the uncertainties from the determination of effective radius and the estimation of the shrinkage in order to calculate the total uncertainty associated with the effective area [
The combined uncertainty of the effective radius was calculated to be 0.0449 cm, making the effective radius of the sampler
During preparation, transport, storage, and handling of the passive sampler devices there is a risk of contamination. The best assessment of the uncertainty from these sources comes from the use of field blanks [
The analyte (Cu2+) is subsequently extracted from the receiving phase using a small volume of nitric acid. The recovery factor,
The resulting extract is diluted to a suitable volume concentration before analysis by a selected analytical technique. Inductively coupled plasma-mass spectrometry (ICP-MS) is widely used for the determination of trace metal concentrations in environmental samples and therefore, we estimate uncertainty for ICP-MS analysis in this paper. The ICP-MS instrument is calibrated using calibration standards prepared from certified standard solutions.
Generally, the analytical procedure using ICP-MS is subject to known and unknown interferences of which some can be compensated for, while others may persist, depending on specific instrument capabilities [
The estimated accumulated mass and mass on blank samples was determined using ICP-MS and then corrected for by the recovery factor according to
Using the rule for uncertainty propagation in quotients the estimate for
Uncertainty budget for
Symbol | Source of uncertainty | Type* | Standard uncertainty |
Distribution | Divisor | Relative uncertainty |
---|---|---|---|---|---|---|
|
Estimated mass from ICP-MS analysis | A |
|
Normal | 1 | 0.008 |
|
Recovery factor | B | 0.0293 | Rectangular |
|
0.064 |
Uc (M) | Combined standard uncertainty | A |
|
Normal | 0.038 |
To estimate the combined standard uncertainty of the bulk concentration
This means that the combined uncertainty is equal to the root square sum of the partial derivatives of the variables. However, it is also possible to derive a numerical solution as suggested by Kragten [
A summary of the quantities and the associated standard uncertainties is presented in Table
Quantities, nominal values, and their associated uncertainty used in this work.
Quantity | Value | Standard uncertainty | Comment |
---|---|---|---|
|
3.66 cm2 | 0.30 cm2 | See previous section and [ |
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|
Empirical value [ |
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Empirical value [ |
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|
|
Observation |
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|
|
Observation |
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0.793 | 0.051 | Observation [ |
|
168 h | 0.3 h | Covers the time it takes to deploy and retrieves 5 passive samplers |
|
25°C/298 K | 4 K | Standard deviation of the measured temperature |
|
|
|
Estimate [ |
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|
|
Estimate |
During calculations values were not rounded to avoid the introduction of additional uncertainty. The output of the numerical treatment of combined uncertainties can be seen in Table
Uncertainty budget for determination of time weighted average concentration of Cu2+ in water using a DGT passive sampler.
Symbol | Source of uncertainty | Type | Standard uncertainty |
Distribution | Divisor |
|
---|---|---|---|---|---|---|
|
Determination of accumulated mass | A |
|
Normal | 1 | 0.49 |
|
Determination of contamination | A |
|
Normal | 1 | 0.02 |
|
Diffusion coefficient in water | A |
|
Normal | 1 | 0.16 |
|
Thickness of material diffusion layer (MDL) | B |
|
Rectangular |
|
0.33 |
|
Diffusion coefficient in MDL | A |
|
Normal | 1 | 0.16 |
|
Diffusion boundary layer | B |
|
Rectangular |
|
0.29 |
|
Time | B | 624 s | Rectangular |
|
0.01 |
|
Effective area | A |
|
normal | 1 | 0.69 |
Uc ( |
Combined standard uncertainty | Normal | 0.98 | |||
Uc ( |
Expanded standard uncertainty | Normal ( |
1.95 |
When plotting the relative standard uncertainties of the components graphically (Figure
Relative standard uncertainty (a) and percentage of total uncertainty (b) for the variables in the model equation.
A sensitivity analysis shows that halving the uncertainty for the effective radius and shrinkage in the determination of
Results from sensitivity analysis, showing the effect on total uncertainty of the passive sampler measurement from reductions in uncertainty of selected parameters.
Parameter | Change in uncertainty | Result on total uncertainty |
---|---|---|
Effective area, |
50% reduction | Reduction from 7.6% to 6.1% in overall relative uncertainty |
Recovery factor, |
50% reduction | Reduction from 7.6% to 6.9% in overall relative uncertainty |
Diffusion boundary layer, |
From 0.05 mm to 0.014 mm standard uncertainty | Reduction from 7.6% to 7.3% in overall relative uncertainty |
Diffusion pathway thickness | 50% reduction | Reduction from 7.6% to 7.3% in overall relative uncertainty |
Diffusion pathway thickness | 4 times increase | Increase from 7.6% to 12.2% in overall relative uncertainty |
The sensitivity analysis shows that overall method uncertainty can be significantly reduced by addressing the proper sources of uncertainties and also that deterioration in diffusion layer consistency can have significant negative effects on overall method uncertainty.
An uncertainty analysis was performed for passive sampling of a metal ion in water to highlight critical steps in the method and to identify key factors for potential improvement. In the analysis performed here the uncertainty of the effective cross-sectional diffusion area
The authors declare that there is no conflict of interests regarding the publication of this paper.