A: In most situations where DGT is deployed in water that is flowing or subject to convection currents the standard DGT equation is appropriate.
cDGT (nmol or ng mL-1) is the concentration of analyte in the deployment medium measured by DGT.
M (nmol or ng) is the mass of analyte accumulated in the binding layer.
Δg (also known as δg) (cm) is the total thickness of the materials that comprise the diffusion layer (gel and filter membrane).
Dmdl (cm2 s-1) is the diffusion coefficient of analyte in the material diffusion layer.
Ap (cm2) is the physical area of the exposed filter membrane.
t (s) is the deployment time.
Δg and Ap are known properties for the supplied DGT device. The time of deployment, t, is known by the operator. DMDL is also available provided the deployment temperature is known. The accumulated mass, M, is measured in the laboratory. Usually it is obtained by eluting the analyte and calculating the mass from the measured concentration in the known volume of eluate. Recommended units to facilitate easy calculation are shown.
This standard DGT equation incorporates an automatic correction for a modest diffusive boundary layer (DBL) at the surface of the device. Such a modest DBL thickness will apply when there is good solution flow over the surface of the DGT device. In this case cDGT is likely to be accurate to ±5%. More generally when DGT devices are deployed in natural waters with unknown hrdrodynamics, because of uncertainties in the thickness of the DBL due to the local hydrodynamics and deployment configuration, cDGT should be regarded as accurate to ±20%.
If greater accuracy is required the DBL thickness should be measured in situ using 3 or more DGT devices with different values of Δg. Then a fuller equation is required. Detailed accounts of the most appropriate calculation procedure for different circumstances are available in W. Davison and H. Zhang, Principles of measurements in simple solutions, Chapter 2, in: Diffusive Gradients in Thin-films (DGT) for Environmental Measurements, Editor: William Davison, Cambridge University Press, 2016 and in W. Davison and H. Zhang, Progress in understanding the use of diffusive gradients in thin-films – back to basics, Environ. Chem. 9: (2012), 1-13. These articles also consider when the necessary requirement that the time taken to reach a steady state transfer of analyte to the DGT device is negligible compared to the deployment time.
The most commonly used equation for multiple devices is
AE is the effective area which has a value of 3.8 cm2 for standard solution devices. δmdl is the combined thickness of diffusive gel and filter membrane and δdbl is the thickness of the diffusive boundary layer. Concentration, in this case denoted by cDGTe, and δdbl can be obtained from linear plots of 1/M versus δmdl.
The above treatments assume that there are no competition effects or limitations to the capacity of the binding layer, which will generally be true. Calculations can still be made if these situations apply, using the approaches and equations provided in M. Jimenez-Piedrahita, A. Altier, J. Cecilia et al., Extending the use of diffusive gradients in thin films (DGT) to solutions where competition, saturation, and kinetic effects are not negligible, Anal. Chem, 89: (2017), 6567-6574.