AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus GmbHGöttingen, Germany10.5194/amt-8-5289-2015Gas adsorption and desorption effects on cylinders and their importance for
long-term gas recordsLeuenbergerM. C.leuenberger@climate.unibe.chhttps://orcid.org/0000-0003-4299-6793SchibigM. F.NyfelerP.Climate and Environmental Physics, Physics Institute and Oeschger Centre for
Climate Change Research, University of Bern, SwitzerlandM. C. Leuenberger (leuenberger@climate.unibe.ch)18December20158125289529911May20154August201527November201527November2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://amt.copernicus.org/articles/8/5289/2015/amt-8-5289-2015.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/8/5289/2015/amt-8-5289-2015.pdf
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 decanting one steel and two aluminium
cylinders are in agreement with the pressure dependence of
physisorption for CO2, CH4, and H2O. The CO2 results for
both cylinder types are in excellent agreement with the pressure dependence
of a monolayer adsorption model. However, mole fraction changes due to
adsorption on aluminium (< 0.05 and 0 ppm for CO2 and
H2O) were significantly lower than on steel (< 0.41 ppm and
about < 2.5 ppm, respectively). The CO2 amount adsorbed
(5.8 × 1019 CO2 molecules) corresponds to about the fivefold monolayer
adsorption, indicating that the effective surface exposed for adsorption is
significantly larger than the geometric surface area. Adsorption/desorption
effects were minimal for CH4 and for CO but require further attention
since they were only studied on one aluminium cylinder with a very low mole
fraction. In the climate chamber, the cylinders were exposed to temperatures
between -10 and +50 ∘C to determine the corresponding
temperature coefficients of adsorption. Again, we found distinctly different
values for CO2, ranging from 0.0014 to 0.0184 ppm ∘C-1 for
steel cylinders and -0.0002 to -0.0003 ppm ∘C-1 for aluminium
cylinders. The reversed temperature dependence for aluminium cylinders points
to significantly lower desorption energies than for steel cylinders and due
to the small values, they might at least partly be influenced by temperature,
permeation from/to sealing materials, and gas-consumption-induced pressure
changes. Temperature coefficients for CH4, CO, and H2O adsorption
were, within their error bands, insignificant. These results do indicate the
need for careful selection and usage of gas cylinders for high-precision
calibration purposes such as requested in trace gas applications.
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., 1998, 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 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).
xm=kP1/n
Irving Langmuir (Langmuir, 1916, 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,
Θ, as given in Eq. (2):
Θ=KP1+KP,
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, Θ 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(Θ), a coverage-order term, Θn, and an Arrhenius factor containing the activation energy, E=E(Θ), for desorption.
k-1ΘT(t)=-dΘdt=υ(Θ)⋅Θn⋅e-E(Θ)R⋅Tt
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(T0), can be represented by
K(T)=k(T)k-1(T)=K(T0)⋅eER⋅1T-1T0.
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 (CO2, CO, CH4) as well as
H2O on two metal surfaces, namely steel and aluminium, using the
cylinders tabulated in 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
H2O 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.
a Due to a leak, cylinder LK548528 had to be exchanged
for cylinder LK535353 during the experiment. b The pressure reading was made at 45 ∘C; the pressure comparable to the other pressure
readings taken at 22 ∘C will be lower.
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 CO2,
CH4, and H2O 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 instrument, 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).
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).
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
10-port 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).
Emptying experiment within 14 h: CO2 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 (CO2,ad= 0.41 ppm, K= 0.0436 bar-1).
Emptying experiment within 14 h: H2O even shows a 5-times stronger desorption effect documented by the linear correlation with
the CO2 mole fraction.
Results
Figure 2 displays the CO2 mole fraction change for experiment 1
(emptying gas cylinders) for a steel cylinder. A significant CO2 and
H2O (Fig. 3) mole fraction increase of 6 ppm (30 ppm for H2O) is
observed towards lower cylinder pressure in contrast to CH4 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 CO2 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 cm2 s-1 for 20 ∘C and 1 bar
(Massman, 1998)) and time (60 s), of CO2 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 CO2 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 CO2 mole fraction (CO2,initial) can be calculated from the measured mole fraction (CO2,meas) through the following formula (see Appendix):
CO2,meas=CO2,ad⋅K⋅P-P01+K⋅P+1+K⋅P0⋅lnP0⋅1+K⋅PP⋅1+K⋅P0-1+CO2,initial,
where CO2,ad corresponds to the adsorbed CO2 molecules on the
wall, expressed as CO2 mole fraction multiplied by the occupied adsorption
sites at pressure P0. CO2,ad and K can be determined
experimentally from a fit of the measured CO2 mole fraction. Note that K
is temperature-dependent on the form as given in Eq. (5). For P=P0,
the measured CO2 mole fraction corresponds to the initial CO2 mole
fraction minus the adsorbed CO2 amount. In our experiment this results
in an adsorbed CO2,ad mole fraction of 0.41 ppm, corresponding to
about 2.15 mL STP (standard temperature and pressure) (P0= 105 bar) or 96 micromoles of CO2 or
5.8 × 1019 CO2 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 CO2
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 m2, which is about 5
times lower than a monolayer of the adsorbed CO2 molecules,
corresponding to 5.25 m2 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 CO2 (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 CO2,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.
Fast- and slow-emptying experiment within 8 h (upper panel) and 120 h
(lower panel), respectively: CO2 mole fraction of an aluminium
cylinder vs. its pressure in red (5 s resolution). The Langmuir
monomolecular layer desorption model is shown in blue (CO2,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 (CO2,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.
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 low-flow (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 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 CO2 decrease pointing to a warmer temperature at
the inter-stage compared to the high-pressure side. This requires further
dedicated experiments.
Decanting experiment within 8 h: no effect of CO and H2O
can be detected given the limitations of the analyser's signal-to-noise ratio at
that level on the aluminium cylinder compared to the CO2 mole
fraction.
Temperature dependence for the CO2 mole fraction deviations from
their corresponding value at 20 ∘C (T0) 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.
Unlike the steel cylinder, the aluminium cylinder did not show any desorption
effects for H2O and CO, and it showed a hardly visible effect for CH4, as
displayed in Fig. 5. However, it has to be stressed that the H2O 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 CO2 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 ×ΔT/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
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, CH4, and
H2O showed no temperature dependence as documented in Table 2, except
for H2O 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
CO2 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.
Temperature dependencies of gas adsorption on steel and aluminium
surfaces for CO2 and H2O applying a temperature range from -10
to +50 ∘C. NA when r2 < 0.02. Temperature
dependencies for CO and CH4 could not be detected within experimental
uncertainties.
a Due to a leak, cylinder LK548528 had to be exchanged
for cylinder LK535353 during the experiment.
Dependence of scaled CO2 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
(r2= 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 CO2,ad value
of 1.2 ppm and 0.0168 bar-1 for K0. Open and filled blue symbols
correspond to the CO2 mole fractions vs. temperature, whereas the
blue line corresponds to the estimated CO2 mole fractions according to
Eq. (A25).
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):
R⋅ln1-CO2T0,T-CO2T0CO2,ad=E⋅1T-1T0-R⋅lnT0T+P0⋅KT0⋅eER⋅1T-1T01+P0⋅K(T0).
Hence, during a temperature increase or decrease, we will determine the
desorption energy, E=E(Θ), of the process when plotting the logarithm of 1 minus the
temperature-scaled relative CO2 mole fraction changes (CO2(T)-CO2
(T0)) to the adsorbed CO2 vs. the difference of inverse
temperatures. For steel cylinder 1, the values are plotted in Fig. 7. From
this graph or through Eq. (6), we now can estimate CO2,ad, K(T0), 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 CO2,ad and 0.0168 bar-1 for K0. 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 T0 to 20 ∘C. This
sign change moves towards zero when T0 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 CO2,ad and 0.001 bar-1 for
K0. The significantly lower correlation (r2 < 0.75) than
for the steel cylinder (Fig. 7) can only partly be explained by the very
small effects observed for the aluminium cylinders (ΔCO2 < 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 CO2
mole fraction for positive and negative temperature gradients (dotted red
lines in Fig. 8) may indicate a temperature-driven influence. A small
contribution of thermal diffusion to the measured CO2 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
CO2 change. Hence care should be taken with those values that are lower than for steel cylinders.
Dependence of scaled CO2 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. 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 (r2= 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 CO2
mole fractions vs. temperature, whereas the blue line corresponds to the
estimated CO2 mole fractions according to Eq. (A25).
Conclusion
The experiments performed clearly demonstrate that the aluminium cylinders
are significantly more robust against adsorption/desorption processes for
CO2, CO, CH4, and H2O than steel cylinders. The CO2
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 CO2,ad, K0, 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.
Derivation of Eqs. (5) and (6)
During experiment 1, gas is decanted from a cylinder with a fixed volume, V,
and at a constant temperature, T, after air with an initial CO2 mole
fraction, CO2,initial, i.e. nCO2,initial/nair, is
compressed into a cylinder to a pressure, P0. After reaching adsorption
equilibrium, the CO2 mole fraction in the cylinder is reduced by
CO2,ad. The CO2 amount, nCO2, in the gas phase of the
cylinder at any pressure, P, is expressed using the ideal gas law by
nCO2=nair⋅CO2=P⋅VR⋅T⋅CO2,
where R is the ideal gas constant and CO2 is the mole fraction of CO2.
Assuming that CO2 adsorption/desorption follows Eqs. (2) and (3), the
Langmuir's adsorption isotherm, the amount adsorbed at pressure P, nad,
is expressed in relation to the inversely scaled adsorbed amount at pressure
P0, a, according to
nad(P)=a⋅KP1+KPnadP0=a⋅KP01+KP0=P0⋅VR⋅T⋅CO2,ad.
This results in
a=P0⋅VR⋅T⋅CO2,ad⋅1+KP0KP0=1+KP0K⋅VR⋅T⋅CO2,ad,
which results in
nadP=1+KP0⋅VR⋅T⋅CO2,ad⋅P1+KP,
where K represents the equilibrium constant at constant temperature, T (K=k/k-1). In the case of experiment 2, the temperature dependence of K
needs to be taken into account.
Thus the change in the CO2 amount in the gas phase of the cylinder
according to pressure change is expressed by the following differential
equation:
dnCO2dP=nCO2P-dnaddP.
The first term on the right-hand side corresponds to the change in the
CO2 amount due to the gas pressure change during gas decanting. The
second term describes the effect of the CO2 desorption from the inner
cylinder walls that can be derived from the derivative of Eq. (A5):
dnCO2dP=nCO2P-1+KP0⋅VR⋅T⋅CO2,ad1+KP2.
Solving the differential Eq. (A6) yields
nCO2=c⋅P-1+KP0⋅VR⋅T⋅CO2,ad⋅P⋅11+KP+lnKP-ln(1+KP).
With
nCO2P0=P0⋅VR⋅T⋅CO2,initial-CO2,ad,
it follows
c=VR⋅T⋅CO2,initial+1+KP0⋅VR⋅T⋅CO2,ad⋅lnKP01+KP0,
and therefore
nCO2=P⋅VR⋅TCO2,ad⋅KP-P01+KP+1+KP0⋅lnP0⋅1+KPP⋅1+KP0-1+CO2,initial.
Therefore, the measured CO2 mole fraction of the cylinder according to
Eq. (A1), can be expressed as
CO2,meas=CO2,ad⋅KP-P01+KP+1+KP0⋅lnP0⋅1+KPP⋅1+KP0-1+CO2,initial,
which corresponds to Eq. (5) in the main text.
Derivation of Eq. (6)
During experiment 2, cylinders are exposed to temperature changes and only a
small amount of gas is decanted from a cylinder for analysis. Therefore, we
assume that the changes in CO2 mole fraction in the gas phase are only
due to adsorption changes associated with direct temperature and pressure changes that are induced by it.
dnCO2dT=-dnaddTnCO2T=C-nad(T)nCO2T0=C-nadT0=ninitial-nadT0nCO2T-nCO2T0=nadT0-nad(T)
According to Eq. (4) in the main text the temperature dependence of K can
be written as
K(T)=kk-1=K(T0)⋅eER⋅1T-1T0.
We can generalize Eq. (A2) with Eq. (A15) to Eq. (A16) and Eq. (A17):
nad(PT)=a⋅P⋅K(T0)⋅eER⋅1T-1T01+P⋅K(T0)⋅eER⋅1T-1T0nadP0,T0=a⋅1+P0⋅K(T0)P0⋅K(T0)=P0⋅VR⋅T0⋅CO2,ad.
This results in
a=P0⋅VR⋅T0⋅CO2,ad⋅1+P0⋅K(T0)P0⋅K(T0),
which results in
nadP,T=P0⋅VR⋅T0⋅CO2,ad⋅1+P0⋅K(T0)P0⋅K(T0)⋅P⋅K(T0)⋅eER⋅1T-1T01+P⋅K(T0)⋅eER⋅1T-1T0CO2,adP,T=R⋅TP⋅V⋅nadP,TCO2,adP,T=R⋅TP⋅V⋅P0⋅VR⋅T0⋅CO2,ad⋅1+P0⋅K(T0)P0⋅K(T0)⋅P⋅K(T0)⋅eER⋅1T-1T01+P⋅K(T0)⋅eER⋅1T-1T0.
Since the amount of air does not change during experiment 2, we follow
R⋅TP⋅V⋅P0⋅VR⋅T0=P0P⋅TT0=1CO2,adP,T=CO2,ad⋅1+P0⋅K(T0)P0⋅K(T0)⋅P⋅K(T0)⋅eER⋅1T-1T01+P⋅K(T0)⋅eER⋅1T-1T0.
With Eq. (A23), Eq. (A14) can be rearranged to
CO2T0,T-CO2T0=CO2,ad-CO2,ad⋅1+P0⋅K(T0)P0⋅K(T0)⋅P⋅K(T0)⋅eER⋅1T-1T01+P⋅K(T0)⋅eER⋅1T-1T0CO2T0,T-CO2T0=CO2,ad⋅1-1+P0⋅K(T0)P0⋅K(T0)⋅P⋅K(T0)⋅eER⋅1T-1T01+P⋅K(T0)⋅eER⋅1T-1T0.
It is noteworthy that Eq. (A25) has a root at energies around 2430 J mol1 for
T0 at 293.15 ∘C. A general dependence of E0(T,T0)
corresponds to
E0T,T0=R1T-1T0⋅lnT0T=R⋅T⋅T0T0-T⋅lnT0T
above which Eq. (A25) is increasing and below which it is decreasing. E0 approaches
zero when T0 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).
R⋅ln1-CO2T0,T-CO2T0CO2,ad=E⋅1T-1T0-R⋅lnT0T+P0⋅KT0⋅eER⋅1T-1T01+P0⋅K(T0)
This equation allows us to estimate CO2,ad, K(T0), 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 CO2,ad of 1.2 ppm, K(T0) 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.
Acknowledgements
This is a contribution to the CarboCount CH Sinergia project financed by the
Swiss National Science Foundation (CRSII2_136273). We thank Rüdiger Schanda for helping us with the measuring device. We are also
grateful to the national and international intercomparison initiatives, such
as Round Robins organized by WMO/IAEA, the Cucumber program organized by UEA,
and others that were helpful in leading to these investigations. We are very
grateful for the comments of three anonymous reviewers that significantly
improved the ACPD manuscript and additionally to a reviewer of the primarily
revised manuscript for ACP, furthermore for two additional reviewers of
AMTD.
Edited by: T. von Clarmann
ReferencesBender, M. L., Tans, P. P., Ellis, J. T., Orchardo, J., and Habfast, K.: A
high-precision isotope ratio mass-spectrometry method for measuring the O2
N2 ratio of air, Geochim. Cosmochim. Ac., 58, 4751–4758, 1994.Berhanu, T. A., Satar, E., Schanda, R., Nyfeler, P., Moret, H., Brunner, D.,
Oney, B., and Leuenberger, M.: Measurements of greenhouse gases at
Beromünster tall tower station in Switzerland, Atmos. Meas. Tech. Discuss.,
8, 10793–10822, 10.5194/amtd-8-10793-2015, 2015.
Brunauer, S., Emmett, P. H., and Teller, E.: Adsorption of Gases in
Multimolecular Layers, J. Am. Chem. Soc., 60, 309–319, 1938.Chen, H.: Long-term stability of calibration gases in cylinders for
CO2, CH4, CO, N2O, and SF6, in 17th WMO(IAEA meeting on Carbon Dioxide , other greenhouse gases and related measurement techniques (GGMT-2013), edited
by: WMO/IAEA, Chinese Meterological Administration, Beijing, China, 2013.
Freundlich, H. M. F.: Über die Adsorption in Lösungen., Z. Phys. Chem., 57, 385–470, 1906.Keeling, R. F., Manning, A. C., McEvoy, E. M., and Shertz, S. R.: Methods for
measuring changes in atmospheric O2 concentration and their application in
southern hemisphere air, J. Geophys. Res.-Atmos., 103, 3381–3397,
1998.Keeling, R. F., Manning, A. C., Paplawsky, W. J., and Cox, A. C.: On the long-term
stability of reference gases for atmospheric O2/N2 and CO2 measurements,
Tellus B, 59, 3–14, 2007.
Kestin, J., Knierim, K., Mason, E. A., Najafi, B., Ro, S. T., and Waldman,
M.: Equilibrium and transport-properties of the noble-gases and their mixtures
at low-density, J. Phys. Chem. Ref. Data, 13, 229–303, 1984.Langenfelds, R. L., van der Schoot, M. V., Francey, R. J., Steele, L. P.,
Schmidt, M., and Mukai, H.: Modification of air standard composition by diffusive
and surface processes, J. Geophys. Res.-Atmos., 110, D13307, 10.1029/2004JD005482, 2005.
Langmuir, I.: The constitution and fundamental properties of solids and
liquids, J. Am. Chem. Soc., 38, 2221–2295, 1916.
Langmuir, I.: The adsorption of gases on plane surfaces of glass, mica and
platinum, J. Am. Chem. Soc., 40, 1361–1403, 1918.
Marrero, T. R. and Mason, E. A.: Gaseous Diffusion Coefficients, J. Phys. Chem. Ref. Data, 1,
3–118, 1972.
Marrero, T. R. and Mason, E. A.: Correlation and prediction of gaseous
diffusion-coefficients, Aiche J., 19, 498–503, 1973.Massman, W. J.: A review of the molecular diffusivities of H2O, CO2, CH4, CO,
O3, SO2, NH3, N2O, NO, and NO2 in air, O2 and N2 near STP, Atmos. Environ., 32,
1111–1127, 1998.
Matsumoto, N., Watanabe, T., and Kato, K.: Effect of moisture
adsorption/desorption on external cylinder surfaces: influence on
gravimetric preparation of reference gas mixtures, Accredit. Qual. Assur., 10, 382–385, 2005.Schibig, M. F., Steinbacher, M., Buchmann, B., van der Laan-Luijkx, I. T., van der Laan, S., Ranjan, S.,
and Leuenberger, M. C.: Comparison of continuous in situ CO2 observations at Jungfraujoch
using two different measurement techniques, Atmos. Meas. Tech., 8, 57–68, 10.5194/amt-8-57-2015,
2015.
Yokohata, A., Makide, Y., and Tominaga, T.: A new calibration method for the
measurement of CCL4 concentration at 10-10 V/V level and the behavior of
CCL4 in the atmosphere, B. Chem. Soc. JPN, 58, 1308–1314, 1985.