Liquid-liquid extraction and solid-phase extraction aim to take all of the analyte out of the sample. SPME does not. The fibre takes up a fraction, set by how strongly the coating holds the analyte compared with the sample, and by how long and how hard the sample is mixed.
That is why SPME results stand or fall on calibration. A 2015 review calls quantitation in complex food and environmental matrices “one of the major challenges of SPME procedures” (Merkle et al. 2015, section 3.5). A large part of my Ph.D. work in Janusz Pawliszyn’s lab at Waterloo was on exactly this: modelling how analytes move into the coating, so that the calibration can be chosen on purpose.
This piece explains the main options and when each one fits.
The uptake curve
Plot the extracted amount against extraction time and you get three zones: a linear zone at the start, a curved zone, and a plateau at equilibrium. Our 2018 review in Analytical Chemistry shows this for four compounds, and points out something useful: in the early linear zone, analytes with similar diffusion coefficients extract at almost the same rate, whatever their affinity for the coating (Reyes-Garcés et al. 2018, Fundamentals, Figure 1C).
Each calibration approach uses a different part of that curve.
Equilibrium calibration
Leave the fibre in until the plateau. For a sample much larger than the coating, the extracted amount is:
n = Kes × Ve × C
where Kes is the coating-sample distribution constant, Ve the coating volume, and C the sample concentration (Reyes-Garcés et al. 2018, equation 6).
Two things follow. The amount does not depend on sample volume, so the fibre can sample air, water or a process stream directly. And if Kes is known, the concentration can be calculated without an external calibration (same section).
The cost is time. Equilibrium can take a long time for some analytes, and in that case pre-equilibrium extraction is preferred, as Merkle and co-workers note (Merkle et al. 2015, section 3.5.1).
Pre-equilibrium: time and agitation become part of the method
Pull the fibre before the plateau and the amount extracted depends on how long it was in and how the sample was mixed. Merkle and co-workers put it simply: in pre-equilibrium calibration the amount is related to the extraction time, and the agitation must be constant (section 3.5.1).
Agitation matters more than people expect. In my simulations of the boundary layer around the fibre, flow compresses the diffusion layer on the upstream side and stretches it on the downstream side, and the layer thins as flow speeds up. That is why our review recommends vortex-type agitation, which keeps changing direction (Reyes-Garcés et al. 2018, Figure 1B). If two samples are agitated differently, they are not extracted the same way.
Diffusion-based calibration
In the linear zone, uptake follows Fick’s first law: the rate depends on the analyte’s diffusion coefficient, the coating area and the boundary-layer thickness, which together give a sampling rate. If the sampling rate is known, the concentration follows from the amount extracted and the time, without a calibrant (Reyes-Garcés et al. 2018, equations 7–20). This is the basis of passive time-weighted-average samplers.
The catch is that the diffusion coefficients and the physical properties of the sample must be known, which “might limit their applicability” (same section). In our 2017 paper we argued that calibrant-free sampling is often underestimated because people do not understand how the extraction parameters affect the result, and built a model to identify the parameters that matter, including in samples with binding components (Alam et al. 2017).
Kinetic calibration: a standard that leaves as the analyte arrives
Chen and Pawliszyn introduced a neat idea: load a standard onto the coating before sampling. During extraction the standard leaves the coating while the analyte enters, and both are governed by the same mass transfer. So the loss of the standard tells you how efficient the extraction was, and corrects for variations in time, agitation and temperature (Reyes-Garcés et al. 2018, Kinetic calibration).
In our 2016 Analytical Chemistry paper we modelled this calibrant-loaded extraction phase approach and tested it against experiment, varying sample volume, flow velocity, temperature and the presence of a binding matrix. The approach held up as those conditions changed. And it can give free or total concentration from a single experiment, depending on whether the distribution constant is measured in a matrix-free or a matrix-matched sample (Alam & Pawliszyn 2016).
Traditional calibration still works
External standards, internal standards and standard addition are all used with SPME. External standards need blank matrix and a very stable procedure. Standard addition suits heterogeneous samples. Internal standards, preferably isotope-labelled, compensate for matrix effects and for variation in sample preparation (Merkle et al. 2015, section 3.5.1 and Table 2).
For routine quantitation in a regulated or contract lab, the isotope-labelled internal standard is the one I would start with. EPA Method 8272 is built on it, and I explain why in SPME without an isotope-labelled internal standard is a guess.
Choosing
| Situation | Approach |
|---|---|
| Lab samples, isotope-labelled standards available | Internal standard (isotope dilution), fixed time and agitation |
| Equilibrium reached in a practical time, Kes known | Equilibrium calibration |
| On-site or in vivo, no way to add a standard to the sample | Kinetic calibration with a pre-loaded standard |
| Long-term air or water monitoring | Diffusion-based (time-weighted average) sampling |
| Heterogeneous samples without labelled standards | Standard addition |
Sources
- Reyes-Garcés N, Gionfriddo E, Gómez-Ríos GA, Alam MN, et al., Pawliszyn J. Advances in solid phase microextraction and perspective on future directions. Anal Chem 2018; 90:302–360. Fundamentals section.
- Alam MN, Pawliszyn J. Numerical simulation and experimental validation of calibrant-loaded extraction phase standardization approach. Anal Chem 2016; 88:8632–8639.
- Alam MN, Ricardez-Sandoval L, Pawliszyn J. Calibrant free sampling and enrichment with solid-phase microextraction: computational simulation and experimental verification. Ind Eng Chem Res 2017; 56:3679–3686.
- Merkle S, Kleeberg KK, Fritsche J. Recent developments and applications of SPME in food and environmental analysis. Chromatography 2015; 2:293–381. A review; its calibration table draws on Ouyang and Pawliszyn.
If you are setting up an SPME method and are not sure which calibration fits your samples, tell me the matrix and the analytes on LinkedIn and I will tell you which I would choose.
Common questions
- Why does SPME need careful calibration?
- SPME is non-exhaustive: only a fraction of the analyte moves into the coating. The amount extracted depends on the coating-sample distribution constant, the coating volume, and, before equilibrium, on extraction time and agitation. A 2015 review calls quantitation in complex matrices one of the major challenges of SPME.
- What is equilibrium calibration in SPME?
- The fibre is left in the sample until the analyte concentrations in the coating and sample reach equilibrium. For a large sample volume, the extracted amount equals the distribution constant Kes times the coating volume times the sample concentration, so if Kes is known the concentration can be calculated without external calibration.
- What is pre-equilibrium calibration?
- The fibre is removed before equilibrium. The extracted amount then depends on extraction time and on agitation, so both must be held constant between samples and standards, or a model must account for them.
- What is kinetic calibration in SPME?
- A standard is pre-loaded onto the extraction phase before sampling. Its loss from the coating during sampling tracks the conditions that control analyte uptake, so it corrects for variations in time, agitation or temperature. The approach was introduced by Chen and Pawliszyn and is also called the calibrant-loaded extraction phase method.
- Can SPME measure free and total concentration?
- Yes, in principle. In our 2016 Analytical Chemistry paper on the calibrant-loaded extraction phase, total or free concentration could be obtained from one experiment, depending on whether the distribution constant was measured in a matrix-matched or a matrix-free sample.