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# Thermal Desorption Technical Support Note 2: Prediction of Uptake Rates for Diffusive Tubes
Acknowledgement Markes International Limited would like to acknowledge the work and help of Nico van den Hoed and co-workers (Shell BV, Amsterdam), Mike Wright and Richard Brown (UK Health and Safety Executive) and Jan Kristensson and Erik Nordstrand (University of Stockholm) in preparing this Application Note. 

### Introduction Diffusive (passive) monitoring provides a cost effective and 'wearer friendly' approach to monitoring atmospheric concentrations of volatile organic air pollutants. The standard sorbent tube-type diffusive monitor, reported by Brown and co-workers in 1981 1 , overcame the air speed restrictions of early badge-type diffusive samples and is now widely used for both workplace and ambient air measurements. Diffusive monitoring can only be used for quantitative measurements however, if an uptake rate constant (U) is known for the particular analyte-sorbent combination in use. Uptake rates have already been determined for many compounds on standard tubes 2 (See also TD Technical Support Note 1) and international protocols 3,4,5 now also exist for validating new methods. However, the experimental procedures demanded by such official validation protocols can be time consuming and expensive to carry out. To overcome this limitation, several researchers have investigated techniques for accurately predicting uptake rates. 

### Prediction of uptake rates The ideal uptake rate (U id ) of an analyte on a diffusive tube is independent of the sorbent and can be calculated using the appropriate diffusion coefficient. U id may be used for quantitative measurements in some cases, particularly for strongly retained analytes , however, the actual or effective uptake rate (U eff ) which applies in practice will differ considerably from U id for more volatile, less well retained components. There is therefore a requirement for some simple method of calculating U eff . Coutant et al 6 and Posner and Moore 7 proposed simple linear-isotherm models for thin-bed samplers, but for tube-type (thick-bed) diffusive samplers, this model cannot be strictly applied. Work carried out by van den Hoed et al 8 ,9 , on the application of Freundlich isotherms to the prediction of diffusive tube sampler behaviour, led to the development of a FORTRAN computer program for predicting U eff from U

id using an iterative process. Further work by Kristensson and Nordstrand 10 ,11 facilitated translation of the original program into PC compatible software and simplified several operational aspects. Using the PC program, U id is calculated and combined with isotherm data to derive U eff . This work has advanced the cause of accurate prediction of U eff , but the method still requires Freundlich isotherms to be determined for the sorbent-sorbate combination concerned. The determination of Freundlich isotherms requires the generation of standard atmospheres at a range of concentrations. These atmospheres are then sampled to determine the breakthrough volume at each concentration. This relatively complex procedure limits the usefulness of the approach. Recent work sponsored by the European Commission Measurement and Testing Program (MPT formerly known as BCR 12 ), has shown that, under certain conditions, U eff for the standard tube can be predicted to ± 10% from the specific retention volume (V g ) alone. Broadly, these conditons are:TDTS02_2 5-11-02 2

MARKES International Ltd

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• Exposure time between 2 and 8 hours

• When the specific retention volume (V g ) falls within the range 100L/g < V g < 10,000+ L/g The following empirical relationship (Equation 1) between U eff and V

g was derived from sampling intercomparisons with analytes of wide-ranging volatility and polarity on both Tenax TM and Chromosorb 106 TM . It should be independent of sorbent type. Equation 1: U eff = (0.154 log 10 V g +4) x U id 

### Determining V g and U id The factors V

g and U

id must be obtained before Equation 1 can be used to calculate U eff . The determination of V g does require some limited experimental work and the following stepwise procedure is recommended:

• Inject 0.5 mg of analyte into a stoppered ~1L volume glass flask fitted with a septum. Check that all the analyte has evaporated.

• Buy or prepare a standard sample tube with the maximum 6 cm bed length of sorbent. Condition the tube carefully.

• Connect the sample tube to the injection port of a GC. Use 530 mm, uncoated fused silica capillary tubing, or other appropriate narrow bore tubing, to connect the other end of the sample tube to a FID detector. Use 1⁄4-inch fittings with graphite ferrules to connect to the sample tube itself. [N.B. Metal ferrules damage the tube and result in leak test failures on UNITYTM and other thermal desorbers.]

• Set a nitrogen carrier gas flow of 50 mL/min through the tube.

• Inject a 0 .1 mL sample of the vapor phase standard onto the tube using a gas syringe. Adjust the GC oven temperature so that the analyte peak elutes on the FID between 1 and 20 minutes.

• Repeat the experiment 4 or 5 times using different GC oven temperatures within a 30 or 40°C range. The retention time of the peak will vary considerably with temperature. Try to ensure that at each of the GC temperatures selected, the peak elutes within 1-20 minutes. [Note :Use the time from injection to peak crest as the retention time. This may have to be measured manually, depending on the type of integrator available. Strictly speaking, the mass median or 'centre of gravity' of a peak is the more rigorous measure of retention time, but the error can be usually ignored.]

• Inject a sample of methane to measure the delay time of the system and subtract this from the analyte retention times determined in step 6.

• Use the flow of nitrogen carrier gas and corrected retention times to calculate the analyte retention volumes at different sorbent temperatures.

• Plot a graph of log 10 retention vol. v. 1/ temp(k). It should produce a straight line plot which can be readily extrapolated to ambient temperatures. Use this to obtain V g .

• Check your technique, if possible, with a compound that has a known literature value. This procedure should take no longer than 1⁄2 a day per analyte. The ideal uptake rate (U id ) is calculated using the PC program described above. The software required can be obtained from Dr. J. Kristensson, Chemik Lab, AB, PL. 10840, Gribby 76172 Norrtalje, SWEDEN. Fax No. (46) 2 27307. The program calculates U id using a procedure related to atomic volumes 13 . The information required by the software includes the chemical formula of the analyte of interest and whether or not the substance is aromatic. Once these details have been entered U

id will be predicted. 

### Calculation of the effective uptake rate U eff
. Once V g and U id have been determined as described above, U eff can be calculated using Equation 1. For example:

• A U id of 2.6 ng/ppm/min and a V g of 1000 L/g analyte would give a U eff of 2.24

• A U id of 3.3 ng/ppm/min and a V g of 250l L/g analyte would give a U eff of 2.54TDTS02_2 5-11-02 3

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### Summary Provided a relatively strong sorbent-sorbate combination is selected with V g >100 L/g, this method should apply to all routine industrial hygiene and ambient air monitoring applications i.e. to all atmospheres with analyte concentrations below ~10ppm. The U eff values predicted using Equation 1 are reported 12 to be accurate within 10%. This is well within international standards for method performance criteria 14 . A simple, parallel pumped and diffusive monitoring exercise may be used to confirm U eff if required. By facilitating accurate prediction of U eff for tube-type diffusive samplers in almost every practical monitoring situation, this procedure will allow the cost and labor saving benefits of diffusive monitoring to be realized for an even wider range of air pollution applications.


### Trademarks UNITY is a trademark of Markes International Ltd., U.K.


### References 1 The development of an improved diffusive sampler, Brown R.H., Charlton J and Saunders K.J., Am.Ind.Hyg.Assoc.J.(42) pp 865-869 12/81
2 Methods for the Determination of Hazardous Substances No. 80 - Volatile organic compounds in air. Laboratory method using diffusive solid sorbent tubes, thermal desorption and GC. A UK Health and Safety Executive Procedure. Publ.: HMSO Books, PO Box 276, London, SW8 5DT, UK.
3 Protocol for assessing the performance of a diffusive sampler. UK Health and Safety Executive, Method for the Determination of Hazardous Substances No.27.
4 CEN Pr EN 838: Workplace atmospheres - requirements and test methods for diffusive samplers for the determination of gases and vapours.
5 Protocol for the evaluation of passive monitors. Kennedy E.R. et al, US National Institute for Occupational Safety and Health (NIOSH). Published in: "Diffusive sampling; An alternative approach to workplace air monitoring" CEC Pub.No .: 10555EN (1986).
6 Passive sampling devices with reversible adsorption. Coutant R.W., Lewis R.G. and Mulik J. ,Anal. Chem. (57), 219-223, 1985
7 A thermodynamic treatment of passive monitors. Posner J.C. and Moore G., Am. Ind. Hyg. Assoc. J. (46), 227-285, 1985
8 Sampling and thermal desorption efficiency of tube type diffusive samplers: Selection and performance of adsorbents. Van den Hoed N. and Halmans M.T.H., Am.Ind.Hyg.Assoc.J.(48), pp364-373, 1987
9 A computer model for calculating effective uptake rates of tube-type diffusive air samplers

.. Van den Hoed N. and van Asselen O.L.J. , Ann.Occup.Hyg. (35) pp 273-285, 1991.
10 A computer program for prediction of uptake rates for diffusive sampling. Nordstrand E, Kristensson J., Clean Air At Work- New Trends in Assessment and Measurement for the 1990s. Eds: Brown RH, Curtis M, Saunders KJ ., Vandendriessche S, ISBN 0-85186- 217-9, 1992.
11 A computer program for simulating the function of thick bed diffusive samplers - ideal and effective uptake rates and a theoretical model for reverse diffusion. Nordstrand E, Kristensson J., Am.Ind. Hyg. Assoc. J., Vol. 55, No. 10, pp 935-941, (1994)
12 Diffusive uptake rates for the Perkin-Elmer tube - BCR air sampling intercomparisons at VITO (Mol, Belguim) February 1991-April 1992. Wright MD ., UK Health and Safety Executive Report No. IR/L/IA/93/3.
13 A new method for prediction of binary gas phase diffusion coefficients. Fuller E. N., Schettler P.D. and Giddings J.C. Ind. Eng. Chem., 58, pp 19-27, 1966
14 EN 482: General requirements for the performance of procedures for workplace measurements