Gas adsorption and desorption effects on cylinders and their importance for long-term gas records

. It is well known that gases adsorb on many surfaces, in particular metal surfaces. There are two main forms responsible for these effects (i) physisorption and (ii) chemisorption. Physisorption is associated with lower binding energies in the order of 1–10 kJ mol − 1 , compared to chemisorption which ranges from 100 to 1000 kJ mol − 1 . Furthermore, chemisorption only forms monolayers, contrasting physisorption that can form multilayer adsorption. The reverse process is called desorption and follows similar mathematical laws; however, it can be inﬂuenced by hysteresis effects. In the present experiment, we investigated the adsorption/desorption phenomena on three steel and three aluminium cylinders containing compressed air in our laboratory and under controlled conditions in a climate chamber, respectively. Our observations from completely decant-ing one steel and two aluminium cylinders are in agreement with the pressure dependence of physisorption for CO 2 , CH 4 , and H 2 O. The CO 2 results for both cylinder types are in excellent agreement with the pressure dependence of a mono-layer adsorption model. However, mole fraction changes due to adsorption on aluminium (< 0.05 and 0 ppm for CO 2 and H 2 O) were signiﬁcantly lower than on steel (< 0.41 ppm and about < 2.5 ppm, respectively). The CO 2 amount adsorbed (5.8 × 10 19 CO 2 molecules) corresponds to about the ﬁve-fold monolayer adsorption, indicating that the effective surface exposed for adsorption is signiﬁcantly larger than the geometric surface area. Adsorption/desorption


Introduction
Precision and accuracy of trace gas mole fractions of ambient air composition depend among other factors on the stability of primary and secondary standards.Several studies in the past have documented instabilities of gas composition in high-pressure cylinders.These instabilities can either be viewed as temporal drifts of gas composition or as pressure-dependent composition changes along the lifetime of the cylinder gas.These drifts have been attributed to numerous diffusional fractionation processes such as ordinary diffusion (depending on molecular mass and molecular size), thermal diffusion, or effusion (Bender et al., 1994;Keeling et al., 1998Keeling et al., , 2007;;Langenfelds et al., 2005), or were related to surface interaction alterations (Yokohata et al., 1985).These latter processes, i.e. adsorption and desorption, have been investigated in more detail and play an important role regarding Published by Copernicus Publications on behalf of the European Geosciences Union.
gas composition stability, in particular for trace gas species.Besides the choice of the metal, surface condition, surface coating or finish, as well as the humidity, are also critical for the gas composition (Matsumoto et al., 2005).The presented work was motivated by the fact that adsorption/desorption effects have been observed to play an important role not only in the laboratory, but also in the field during different experimental setups (Berhanu et al., 2015;Schibig et al., 2015).
In sorption theory, one distinguishes several terms such as absorption, adsorption, sorption, desorption, physisorption, and chemisorption.Adsorption is a surface adhesion process of atoms, ions, or molecules from a gas, liquid, or dissolved solid (adsorbate), resulting in a layer on the adsorbent surface (main material).In contrast, absorption is a volume process in which permeation or dissolution of the absorbate in a liquid or solid material (absorbent) takes place.Sorption summarizes both processes, while desorption is the reverse process.
Surface atoms of the bulk material, specified by the fact that they are not fully surrounded by other adsorbent atoms, can therefore attract adsorbates.Adsorption itself splits into physisorption and chemisorption.The former is a general phenomenon forming mono-or multilayers, whereas the latter depends on the chemical feature of both the adsorbate and adsorbent, and forms only monolayers.Similar to surface tension, adsorption is a consequence of surface energy.
Physical adsorption, also known as physisorption, is a process governed by low electrostatic interactions between the electron configuration of the adsorbate and the adsorbent, in particular van der Waals forces.The involved energy is weak (10-100 meV corresponding to 1-10 kJ mol −1 ) and therefore barely influences the electron structure of the substances involved, and it mainly appears under low temperature conditions (room energy).The upper energy limit involves the interaction with permanent electric dipoles of polar surfaces (salts) or with the image charges as present in electrically conductible surfaces such as metals.For these processes the energies can reach those of chemisorption.
Chemisorption in contrast involves much higher energies in the range of 1 to 10 eV (100 to 1000 kJ mol −1 ) and often requires an activation energy, finally resulting in a structure that is similar to a chemical bond of either ionic or covalent type.Sorption and desorption can differ; in this case we deal with hysteresis; i.e. the quantity adsorbed differs from the corresponding quantity desorbed.
Several mathematical models have been presented for adsorption.Equation (1) expresses the pressure dependence by adjusting the empirical constants k and n. x denotes the quantity adsorbed, m the mass of absorbent, and P the pressure (Freundlich, 1906).
Irving Langmuir (Langmuir, 1916(Langmuir, , 1918) ) was the first to derive a scientifically based adsorption isotherm.It is based on four assumptions.(i) All of the adsorption sites are equivalent and each site can only accommodate one molecule.
(ii) The surface is energetically homogeneous and adsorbed molecules do not interact.(iii) There are no phase transitions.(iv) At the maximum adsorption, only a monolayer is formed.Adsorption only occurs on localized sites on the surface, not with other adsorbates.His final result expresses the fraction of the adsorption sites occupied, , as given in Eq. ( 2): where K is the ratio of the direct (adsorption) and reverse rate (desorption) constants (k, k −1 ), and P is the pressure.For low pressures, corresponds to KP , and for high pressure it approaches unity.The four assumptions listed by Langmuir are often not fulfilled, in particular, assumption (iv); but an in depth discussion of these issues would exceed the scope of this publication.However, in our experiments we found a good agreement with this simplified adsorption theory.Besides the pressure or gas (particle) density dependence, there is also a temperature dependence of adsorption/desorption processes.According to the Polanyi-Wigner equation given in Eq. ( 3), the desorption rate (k −1 ) is dependent on time, t, on a frequency term, υ( ), a coverage-order term, n , and an Arrhenius factor containing the activation energy, E = E( ), for desorption.
A similar equation can be written for adsorption; however the adsorption energy is significantly lower, such that the equilibrium conditions are characterized by the desorption energy.Following the van't Hoff equation, different equilibrium conditions, K(T ) and K(T 0 ), can be represented by In this work we mainly investigate the adsorption and its reverse process.In particular we present results for the pressure-and temperature-dependent adsorption process of trace gases (CO 2 , CO, CH 4 ) as well as H 2 O on two metal surfaces, namely steel and aluminium, using the cylinders tabulated in Table 1.

Methods
We ran two experiments in order to determine the pressure and temperature dependencies of gas adsorption on two different metal cylinder surfaces (steel and aluminium).We used 50 L tempered steel (34CrMo4) cylinders equipped with a standard brass valve K44-8 from VTI with PEEK as spindle-sealing material.The regulator connection type is G 5/8 RH (right-handed) female thread from Carbagas, Switzerland, sealed with a PA (nylon) disk.Gas wetted materials for these cylinders are steel, brass, and PEEK.The aluminium cylinders are new 30 L Scott-Marrin Luxfer (AA 6061 T6) cylinders equipped with a brass valve D 202 from Rotarex with PA as spindle material.The regulator connection type is CGA-590.Gas-wetted materials are aluminium, stainless steel, brass, and PA.No additional pre-treatment of the inner surfaces was applied, except that applied by the supplier and producer that we do not know in detail, as well as that given above.The steel cylinders were filled by Carbogas according to their protocol.We do not know the filling history of these cylinders except that they are used for compressed air fillings only.The aluminium cylinders were pumped three times to roughly 10 mbar and then flushed and pressurized to 10 to 15 bar using dry compressed air with ambient mole fractions, and then filled with dry compressed air from another cylinder again at ambient mole fractions.CB09877 was prepared similarly at Empa and was additionally blended by a second compressed air cylinder.CA03901 was prepared at Boulder by NOAA/CMDL according to their protocol.In the first experiment we decanted 5 L min −1 from both steel and aluminium cylinders.The cylinder's mole fractions of CO 2 , CH 4 , and H 2 O were monitored by a Picarro G2311f and G2401, in which case CO was measured in addition.Attached to the vertically standing cylinders were pressure regulators from Tescom (type: 64-3441KA412 dual stage).The starting pressures were about 110 and 95 bar for the steel and aluminium cylinder, respectively.Due to the large gas flow which was maintained by the detector itself in the case of G2311f and by an external flow controller for the G2401, it took only about 14 h (steel) and 8 h (aluminium), respectively, to empty the cylinders.The mole fractions were monitored on a 0.1 s level with the G2311f instru- ment, whereas they were monitored on a 5 s level with the G2401.In parallel, we recorded the pressure continuously.This experiment was performed at the University of Bern under normal laboratory conditions (room temperature was 22 • C; room pressure was about 950 mbar).
The second experiment was performed in the climate chamber at the Swiss Federal Institute of Metrology (METAS).The purpose of this experiment was to determine the temperature dependence of the adsorption/desorption process.Gas usage in experiment 2 was designed to be far less than that in experiment 1.Eight cylinders (five steel and three aluminium) were tested over a temperature range from −10 to +50 • C as documented in Fig. 1.The temperature was set to a fixed temperature for 2 h at each level.Within every 2 h sequence, we switched between the six cylinders which were placed horizontally on  a wooden tray (Table 1), and an additional reference cylinder (CA03901) outside the climate chamber, using a 10port VICI AG valve (type: EMT2CSD12MWE).Due to a leak, cylinder LK548528 had to be exchanged for cylinder LK535353 during the experiment.Unfortunately, the electronics of the VICI valve were malfunctioning after the first night (remained in the same position) and therefore we had to replace it.This sequence was neglected in the evaluation.
The experiment was extended in order to obtain two full temperature cycles for data evaluation.The temperature in the climate chamber was measured directly on the cylinders using 80PK-1-type sensors with a range of −40 to +260 • C and was logged by a GMH3250 unit from Greisinger.The pressure transducers used were PTU-S-AC160-31AC for high pressures and PTU-S-AC6-31AC for low pressures, from Swagelok.Measurements were displayed by a homemade LCD device and logged by a Labjack U12 from Meilhaus Electronic GmbH.Both cavity ring-down spectroscopy instruments are frequently calibrated with known standard gas admissions, i.e. in the case of experiment 1 before and after the experiment, and in the case of experiment 2, during the complete experiment; though the repeatability and drift rates are of more importance for these experiments that are designed to be short-term measurements.The repeatability can be accessed by the short-term measurement variability and corresponds to < 0.01 ppm (averaged over 5 min), whereas the drift rate was estimated from the standard cylinder CA03901 to be 0.0041 ppm day −1 (see also Sect.3).

Results
Figure 2 displays the CO 2 mole fraction change for experiment 1 (emptying gas cylinders) for a steel cylinder.A significant CO 2 and H 2 O (Fig. 3) mole fraction increase of 6 ppm (30 ppm for H 2 O) is observed towards lower cylinder pressure in contrast to CH 4 which does not exhibit any change (not shown).One could argue, as detailed in Langenfelds et al. (2005), that ordinary diffusion is at play.Diffusion coefficients for CO 2 in air have been known for a long time (Kestin et al., 1984;Marrero and Mason, 1972;1973).However, if one calculates the diffusion length, i.e. twice the square root of the product of the diffusion coefficient (≈ 0.16 cm 2 s −1 for 20 • C and 1 bar (Massman, 1998)) and time (60 s), of CO 2 diffusion in air in a cylinder at high pressure (100 bar) corresponding to 6 mm and compares it to the radius of the gas volume at high pressure (5 L min −1 ) that is decanted from the cylinder during our experiment 1, i.e. 27.7 mm, it has to be strongly questioned whether ordinary diffusion is responsible for the observed CO 2 increase.It is worthwhile mentioning that a comparison of the diffusion length with the radius of cylinders (100 mm) used for our experiments requires a diffusion time of 4 or 5 h, i.e. correspondent observation time is needed.Similar arguments can be used to exclude ordinary diffusion on the low pressure side, though with slightly lower confidence since the diffusion length is only half of the decanting volume.Furthermore, the diffusion fractionation should decrease with increasing gas flow, just opposite to what has been observed in Langenfelds et al. (2005), thermal diffusion induced by the Joule-Thomson cooling effect might only play a role for the low-flow decanting experiment, as shown below.Therefore, we follow the adsorption theory.According to Eq. ( 2), the initial CO 2 mole fraction (CO 2, initial ) can be calculated from the measured mole fraction (CO 2, meas ) through the following formula (see Appendix): •ln where CO 2, ad corresponds to the adsorbed CO 2 molecules on the wall, expressed as CO 2 mole fraction multiplied by the occupied adsorption sites at pressure P 0 .CO 2, ad and K can be determined experimentally from a fit of the measured CO 2 mole fraction.Note that K is temperature-dependent on the form as given in Eq. ( 5).For P = P 0 , the measured CO 2 mole fraction corresponds to the initial CO 2 mole fraction minus the adsorbed CO 2 amount.In our experiment this results in an adsorbed CO 2, ad mole fraction of 0.41 ppm, corresponding to about 2.15 mL STP (standard temperature and pressure) (P 0 = 105 bar) or 96 micromoles of CO 2 or 5.8 × 10 19 CO 2 molecules and 0.0436 bar −1 for K by minimization of the squared differences of Eq. ( 5) to the measured values.These values can be compared with a monomolecular layer of CO 2 molecules on the inner cylinder wall area.Our steel cylinders have an outer diameter of 0.24 m, an inner diameter of 0.2 m, and a length of 1.5 m.Therefore, the inner area corresponds roughly to 1 m 2 , which is about 5 times lower than a monolayer of the adsorbed CO 2 molecules, corresponding to 5.25 m 2 when assuming a molecule diameter of 3.4 Å.It is interesting to note that the adsorbed water amount is about 5 times bigger (< 2.5 ppm) as shown by an equal pressure behaviour of desorption (Fig. 3) than for CO 2 (0.41 ppm).
Considering the smaller molecule size for water would correspond to an even higher ratio to a monomolecular layer.
The observed pressure dependence of both mole fractions shows only slightly increasing values in the range of 100 to 50 bar, contrasting the nature of a multiple layer adsorption isotherm (Brunauer et al., 1938).Hence, it seems plausible to question the validity of our assumption that the exposed adsorption surface corresponds to the geometric surface.Due to surface roughness, the adsorption surface might be significantly larger than the geometric measure.This is known in literature as rugosity.Values may range from 1 to more than 10 in the case of a sponge.For metals, surface roughness is more often expressed as Ra; i.e. the arithmetic mean of the surface height changes.These considerations justify using the Langmuir model.Similar considerations can be made for the aluminium cylinder which results in empirically derived values of 0.047 ppm for CO 2, ad and 0.001 bar −1 for K (Fig. 4).The effect of adsorption is significantly less on aluminium than on the steel surface; only about 35 % of the adsorption sites are occupied.This further supports our approach to use the Langmuir model for a monomolecular layer in contrast to a multi-layer coverage.
It was also tested whether the decanting rate has an influence, by performing tests with 5 and 0.25 L min −1 .The results are displayed in Fig. 4 and show similar increases towards lower pressures but there are obvious trends superimposed that cannot be explained by the adsorption theory.In particular the slightly decreasing mole fractions in the lowflow (0.25 L min −1 , Fig. 4, lower panel) decanting experiment on the aluminium cylinder is most probably a result of the Joule-Thomson effect; though instrumental drifts may play a role.However, our observation of drift rates under laboratory conditions using the instruments does not strongly support this.The Joule-Thomson effect leads to a significant temperature decrease of the gas and its surroundings at the regulator where the pressure decreases suddenly from high to ambient pressure (60 to 1 bar).The temperature decrease The Langmuir monomolecular layer desorption model is shown in blue (CO 2, ad = 0.047 ppm, K = 0.001 bar −1 ) for a decanting rate of 5 L min −1 in the upper panel and for 0.25 L min −1 in the lower panel (CO 2, ad = 0.028 ppm, K = 0.001 bar −1 ).Temperature evolution corresponding to the pressure evolution is displayed for the aluminium cylinder (green line) and for the pressure regulator (in violet).Note that the decreasing trend can be explained by the Joule-Thompson cooling effect and has nothing to do with the adsorption theory.The desorption energies could not be determined with confidence during these decanting experiments.can be estimated using the Joule-Thomson coefficient for air, i.e. +0.27 K bar −1 .For 100 bar pressure change, a temperature decrease of 27 K is estimated.The gas exposed to this temperature gradient suffers from thermal diffusion as the heavier gas constituents tend to move to the colder end and hence are enriched in the gas measured by the detector.However, the regulator temperature decrease by the gas cooling effect is partly compensated by the heat exchange with the surroundings.We used a symmetrically built two-stage Tescom regulator; therefore two-step cooling was induced.However, only the first cooling stage is important because this connects to the large gas volume in the cylinder, whereas from there on, fractionation cannot develop under quantitative transport of the gas into the analyser.It is difficult to determine the temperature distribution at the location where thermal fractionation due to the Joule-Thomson effect occurs.What we observe is exactly the opposite to our expectations, i.e. a CO 2 decrease pointing to a warmer temperature at the inter-stage compared to the high-pressure side.This requires further dedicated experiments.Unlike the steel cylinder, the aluminium cylinder did not show any desorption effects for H 2 O and CO, and it showed a hardly visible effect for CH 4 , as displayed in Fig. 5.However, it has to be stressed that the H 2 O and CO mole fractions were very low and further experiments should be done in particular for CO, including steel and aluminium cylinders.
The second experiment conducted in a climate chamber followed expectations in that the temperature dependence of CO 2 adsorption is considerable for steel surfaces but again significantly smaller for aluminium (Fig. 6).For the latter case it even changed sign to a slightly negative correlation with temperature, though this is statistically less robust than for steel.The temperature dependencies vary between 0.0014 to 0.0184 ppm • C −1 for steel and −0.0002 to −0.0003 ppm • C −1 for aluminium cylinders.The different sign of the dependencies for steel and aluminium cylinders is a first hint that these dependencies do not originate from instrument drift.This is supported by the measurements of cylinder CA03901, which acted as a reference that was not exposed to the temperature variations but was placed just beside the instrument in an anteroom.These measurements done throughout the experiment showed rather constant values with a standard deviation of 0.009 ppm on 5 min averages.There is only a small trend of +0.0041 ppm day −1 (not corrected in displays).Excluding the trend, the standard deviation reduces to 0.006 ppm.Furthermore, even with this small constant drift of the analyser, only the scatter of the data, but not the temperature dependence itself, would be affected.Actually, large instrument drifts could potentially be estimated from the scatter of the data.Therefore, the temperature dependencies seen for steel and aluminium cylinders are most certainly not due to drifts of the analyser.The pressure drop for gas consumption throughout this experiment was in the order of 14 and 24 bar, with initial pressures around 150 and 120 bar for the steel and aluminium cylinders, respectively (Table 1).The induced desorption changes are moderate and amount to about 0.01 ppm for both steel and aluminium cylinders according to Eq. ( 6).Also, the temperature-induced pressure changes amounting to about 30 bar (150 bar × T /T ) are only twice as large.The relative influence on the temperature dependency observed for steel cylinders is expected to be minor.For the aluminium cylinders though, these influences are most probably the reason for the observed reversed temperature behaviour.Furthermore, we investigated whether the sealing material in use at the cylinder valve as well as at the connection to the pressure regulator (PEEK, PA) has an influence on our findings.An aluminium cylinder, not listed in Table 2, equipped with a VTI K44-8 (PEEK as spindle-sealing material) and with PA sealing at the regulator connection (G 5/8 RH female thread), as used for the steel cylinders, showed similar Table 2. Temperature dependencies of gas adsorption on steel and aluminium surfaces for CO 2 and H 2 O applying a temperature range from −10 to +50 • C. NA when r 2 < 0.02.Temperature dependencies for CO and CH 4 could not be detected within experimental uncertainties.

Cylinder
CO 2 H 2 O surface (ppm • C −1 ) (ppm behaviour in an independent temperature sensitivity test to the aluminium cylinders used in this study, equipped with Rotarex D 202 valves (PA as spindle-sealing material) with gold rings as sealing material at the CGA 590 connections.All other measured gas species, i.e.CO, CH 4 , and H 2 O showed no temperature dependence as documented in Table 2, except for H 2 O of the steel cylinder LK548528 that had to be replaced due to a leak.It is surprising that the leak obviously had no or at least not a strong effect on the derived thermal dependence, though the value for CO 2 is the highest observed.A reason for this behaviour might be that there is no fractionation associated with the leak (less plausible) or it remains constant and led only to a common shift of the mole fraction values but would not alter the temperature dependence.
According to Eq. ( 3), the coverage of the adsorption sites is temperature-dependent.The desorption and adsorption rates depend on whether we increase or decrease the temperature from a mean value.During the temperature increase (decrease) the adsorption rate will be lower (higher) than the desorption rate; and therefore the coverage of adsorption sites decreases (increases), while the gas mole fraction increases (decreases).A derivation of this temperature dependence is given in the Appendix that leads to Eq. ( 6): Hence, during a temperature increase or decrease, we will determine the desorption energy, E = E( ), of the process when plotting the logarithm of 1 minus the temperaturescaled relative CO 2 mole fraction changes (CO 2 (T )−CO 2 (T 0 )) to the adsorbed CO 2 vs. the difference of inverse temperatures.For steel cylinder 1, the values are plotted  6).Open red symbols correspond to decreasing temperature; and filled red symbols correspond to increasing temperature shown in Fig. 1.The correlation is excellent (r 2 = 1), therefore the slopes correspond to the negative desorption energy (Eq.6) as we have changed the x axis with a minus sign due to visibility reasons.The desorption energies do slightly differ from 14.74 to 15.10 kJ mol −1 for increasing and decreasing temperature, respectively, with a mean of 14.88 kJ mol −1 for the overall correlation using a CO 2, ad value of 1.2 ppm and 0.0168 bar −1 for K 0 .Open and filled blue symbols correspond to the CO 2 mole fractions vs. temperature, whereas the blue line corresponds to the estimated CO 2 mole fractions according to Eq. (A25).
in Fig. 7. From this graph or through Eq. ( 6), we now can estimate CO 2, ad , K(T 0 ), and E by minimizing the squared differences of using Eq. ( 6) iteratively with initial values obtained from experiment 1 for steel and aluminium cylinders, respectively.The slopes corresponding to the desorption energies for positive and negative temperature gradients do only slightly differ and vary between 14.74 ± 0.17 and 15.10 ± 0.25 kJ mol −1 , with an average value of 14.88 ± 0.14 kJ mol −1 for all measurements using a value of 1.2 ppm for CO 2, ad and 0.0168 bar −1 for K 0 .For the aluminium cylinders it looks very different with very low and even reversed temperature dependencies, which indicates lower desorption based on the dependence given in Eq. ( 6).This equation shows a sign change for desorption energies around 2.43 kJ mol −1 when setting T 0 to 20 • C.This sign change moves towards zero when T 0 approaches absolute zero (see Appendix, Eqs.A25-A27).Indeed, the optimized desorption energy (1.58 kJ mol) for aluminium cylinder 2 is below this threshold of 2.43 kJ mol −1 using a value of 0.45 ppm for CO 2, ad and 0.001 bar −1 for K 0 .The significantly lower correlation (r 2 < 0.75) than for the steel cylinder (Fig. 7) can only partly be explained by the very small effects observed for the aluminium cylinders ( CO 2 < 0.04 ppm) since the measurement repeatability is below 0.006 ppm as documented by the reference cylinder (CA03901).This calls for additional influences.The fact that there are small offsets observed for the CO 2 mole fraction for positive and negative temperature gradients (dotted red lines in Fig. 8) may indicate a temperature-driven influence.A small contribution of  6).Open red symbols correspond to decreasing and filled red symbols to increasing temperature in Fig. 1 together with their corresponding correlation lines (dotted red lines).The red line corresponds to all values.The slopes correspond to the negative desorption energy (Eq.6) as we have changed the x axis as in Fig. 7.The correlation is rather weak (r 2 = 0.6).Part of the variability might be due to temperature-induced effects that are independent of adsorption/desorption phenomena.Hence care has to be taken with desorption energies of 1.53 kJ mol −1 increasing to 1.68 kJ mol −1 for decreasing temperature with a mean of 1.58 kJ mol −1 .Open and filled blue symbols correspond to the CO 2 mole fractions vs. temperature, whereas the blue line corresponds to the estimated CO 2 mole fractions according to Eq. (A25).
thermal diffusion to the measured CO 2 mole fraction (Keeling et al., 2007) as discussed above can therefore not be excluded and requires further attention, e.g.regarding temperature distribution on regulators.Therefore the determination of the desorption energy for aluminium cylinders is difficult due to the very small, hardly measurable CO 2 change.Hence care should be taken with those values that are lower than for steel cylinders.

Conclusion
The experiments performed clearly demonstrate that the aluminium cylinders are significantly more robust against adsorption/desorption processes for CO 2 , CO, CH 4 , and H 2 O than steel cylinders.The CO 2 desorption rate behaviour follows a pressure-driven monomolecular layer desorption as described by the Langmuir equation nicely and is about 10 times larger for steel than for aluminium surfaces.Also, the adsorbed amount is about 10 times higher for steel (0.41 ppm) than for aluminium (0.028 and 0.047 ppm).The mole fractions close to atmospheric pressure are strongly influenced and reach values of about 100 times larger than the World Meteorological Organization (WMO) target value of 0.1 ppm for steel and values still significantly above that for aluminium.Therefore, special attention has to be paid to which end pressure the cylinders should be used for calibration purposes.The community is generally aware of this influence that has been investigated by Chen et al. (2013), but it has not yet been properly quantified.It is noteworthy that desorption starts already close to 100 bar (1450 per square inch gauge).At 30 bar it can already reach 0.5 ppm for steel cylinders.The WMO target value of 0.1 ppm might already be reached at 60 bar compared to the value at 100 bar.
The temperature dependence that was observed for three steel and aluminium cylinders ranged from 0.0014 to 0.0184 ppm • C −1 and from −0.0002 to −0.0003 ppm • C −1 , respectively.This might have an influence on the precision when facing large temperature fluctuations in the laboratories or when measuring in the field with large ambient temperature variations -but only for steel and not for aluminium cylinders.A robust estimate of the desorption energy was possible only for steel (14.9 kJ mol −1 ) but not for aluminium, due to the low temperature dependence and temperature range investigated.The determined energy value underpins that the observed adsorption mechanism is physisorption only.
The two experiments are qualitatively in agreement in the present study; however, they were carried out on different cylinders.Similar experiments are required using exactly the same cylinders, i.e. first determining the temperature dependence following by the decanting experiment.This would allow the consistency of the estimated parameters CO 2, ad , K 0 , and E to be checked.
The recommendation for high-precision trace gas determination is to use aluminium cylinders and to minimize temperature fluctuations in order to limit desorption and thermal diffusion effects, and that the usage should be restricted to pressure above 30 bar to remain within the WMO target.which results in n ad (P , T) = CO 2, ad (P , T ) = R • T P • V • n ad (P , T ) (A20) CO 2, ad (P , T ) = R • T P • V • Since the amount of air does not change during experiment 2, we follow CO 2, ad (P , T ) = CO 2, ad • 1 + P 0 • K(T 0 ) P 0 • K(T 0 ) With Eq. (A23), Eq. (A14) can be rearranged to CO 2 (T 0 , T ) − CO 2 (T 0 ) = CO 2, ad − CO 2, ad • 1 + P 0 • K(T 0 ) P 0 • K(T 0 ) CO 2 (T 0 , T ) − CO 2 (T 0 ) = CO 2, ad It is noteworthy that Eq. (A25) has a root at energies around 2430 J mol 1 for T 0 at 293.15 • C. A general dependence of E 0 (T , T 0 ) corresponds to above which Eq. ( A25) is increasing and below which it is decreasing.E 0 approaches zero when T 0 is close to a temperature of absolute zero.This is important for the different adsorption/desorption behaviour on steel and aluminium cylinders (see main text).
This equation allows us to estimate CO 2, ad , K(T 0 ), and E by minimizing the squared differences of using Eq. ( A27) with initial values obtained from experiment 1 for steel and aluminium cylinders, respectively.This yields a CO 2, ad of 1.2 ppm, K(T 0 ) of 0.0168 bar −1 , and a desorption energy of 14 882 ± 176 J mol −1 for cylinder 1 (steel, robust estimate).
The estimates for aluminium cylinders are significantly less robust due to much smaller adsorption/desorption effects.

Figure 1 .
Figure 1.Temperature exposed to the cylinders in the climate chamber.Every 2 h, the temperature changed by 10 • C. The actual temperature (red line) follows the set temperature (light blue) with a delay of 2.75 h (the bold blue line accounts for the time shift).

Figure 2 .
Figure 2. Emptying experiment within 14 h: CO 2 mole fraction of a steel cylinder vs. its pressure is shown in red (only every 100 point of 0.1 s resolution data is shown).The Langmuir monomolecular layer desorption model is shown in blue (CO 2, ad = 0.41 ppm, K = 0.0436 bar −1 ).

Figure 3 .
Figure 3. Emptying experiment within 14 h: H 2 O even shows a 5times stronger desorption effect documented by the linear correlation with the CO 2 mole fraction.

Figure 4 .
Figure 4. Fast-and slow-emptying experiment within 8 h (upper panel) and 120 h (lower panel), respectively: CO 2 mole fraction of an aluminium cylinder vs. its pressure in red (5 s resolution).The Langmuir monomolecular layer desorption model is shown in blue (CO 2, ad = 0.047 ppm, K = 0.001 bar −1 ) for a decanting rate of 5 L min −1 in the upper panel and for 0.25 L min −1 in the lower panel (CO 2, ad = 0.028 ppm, K = 0.001 bar −1 ).Temperature evolution corresponding to the pressure evolution is displayed for the aluminium cylinder (green line) and for the pressure regulator (in violet).Note that the decreasing trend can be explained by the Joule-Thompson cooling effect and has nothing to do with the adsorption theory.The desorption energies could not be determined with confidence during these decanting experiments.

Figure 5 .
Figure 5. Decanting experiment within 8 h: no effect of CO and H 2 O can be detected given the limitations of the analyser's signalto-noise ratio at that level on the aluminium cylinder compared to the CO 2 mole fraction.

Figure 6 .
Figure 6.Temperature dependence for the CO 2 mole fraction deviations from their corresponding value at 20 • C (T 0 ) for the steel cylinders 1, 3, 5, 5 * (increasing values, left y axis), as well as for aluminium cylinders 2, 4, 6 (decreasing values, right y axis).The y axes are different by a factor of 40.For clarity, measurements are only given for cylinder 1 (measurements for cylinder 2 are displayed in Fig.8), together with its linear correlation line, whereas for the other cylinders, only linear correlations lines are given.The temperature dependencies vary between 0.0014 and 0.0184 ppm • C −1 for steel and −0.0002 and −0.0003 ppm • C −1 for aluminium cylinders.

Figure 7 .
Figure 7. Dependence of scaled CO 2 mole fraction difference plus offset b on the difference of inverse temperature for the steel cylinder 1 according to Eq. (6).Open red symbols correspond to decreasing temperature; and filled red symbols correspond to increasing temperature shown in Fig. 1.The correlation is excellent (r 2= 1), therefore the slopes correspond to the negative desorption energy (Eq.6) as we have changed the x axis with a minus sign due to visibility reasons.The desorption energies do slightly differ from 14.74 to 15.10 kJ mol −1 for increasing and decreasing temperature, respectively, with a mean of 14.88 kJ mol −1 for the overall correlation using a CO 2, ad value of 1.2 ppm and 0.0168 bar −1 for K 0 .Open and filled blue symbols correspond to the CO 2 mole fractions vs. temperature, whereas the blue line corresponds to the estimated CO 2 mole fractions according to Eq. (A25).

Figure 8 .
Figure 8. Dependence of scaled CO 2 mole fraction difference plus offset b on the difference of inverse temperature for the aluminium cylinder 2 according to Eq. (6).Open red symbols correspond to decreasing and filled red symbols to increasing temperature in Fig.1together with their corresponding correlation lines (dotted red lines).The red line corresponds to all values.The slopes correspond to the negative desorption energy (Eq.6) as we have changed the x axis as in Fig.7.The correlation is rather weak (r 2 = 0.6).Part of the variability might be due to temperature-induced effects that are independent of adsorption/desorption phenomena.Hence care has to be taken with desorption energies of 1.53 kJ mol −1 increasing to 1.68 kJ mol −1 for decreasing temperature with a mean of 1.58 kJ mol −1 .Open and filled blue symbols correspond to the CO 2 mole fractions vs. temperature, whereas the blue line corresponds to the estimated CO 2 mole fractions according to Eq. (A25).

Table 1 .
Cylinders used for the two experiments with their identification and trace gas mole fractions.Note that the absolute values of both CO and H 2 O are of lower quality due to values close to the lower end of the measurement range.Note that no pretreatment of cylinders has been applied by us, i.e. no steam cleaning, surface conditioning, or finishing, except that applied by the supplier (see main text).Values displayed in figures are non-calibrated values.Due to a leak, cylinder LK548528 had to be exchanged for cylinder LK535353 during the experiment.bThe pressure reading was made at 45 • C; the pressure comparable to the other pressure readings taken at 22 • C will be lower. a