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J. Phys. Chem. C 2010, 114, 2208–2219
Interaction of Nitrous Acid with Polycrystalline Ice: Adsorption on the Surface and Diffusion into the Bulk Michael Kerbrat,† Thomas Huthwelker,† Heinz W. Ga¨ggeler,†,‡ and Markus Ammann*,† Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland, and UniVersity of Bern, CH-3012 Bern, Switzerland ReceiVed: October 5, 2009; ReVised Manuscript ReceiVed: December 1, 2009
The thermodynamic and kinetic constants needed to model the interactions of nitrous acid (HONO) with ice were measured. The experiments were done in a packed ice bed flow tube at temperatures between 213 and 253 K and at HONO gas phase concentrations between 0.4 and 137 ppbv. The experiments were performed using radioactively labeled HO13NO molecules. The use of the short-lived isotope 13N (t1/2 ≈ 10 min) enabled in situ monitoring of the migration of HO13NO in the flow tube. The measurements showed that the interactions do not only occur through adsorption but also via diffusion into polycrystalline ice. A method is suggested to disentangle the bulk and the surface processes. Using this method, the temperature dependence of the linear partition coefficient was found to be Klin,C,HONO ) 7.4 × 10-11 exp(5.4 × 103/T) in units of m. The 0 enthalpy and entropy of adsorption of HONO on ice were ∆Hads,HONO ) -45((20) kJ mol-1 and ∆Sads,HONO ) -17((89) J mol-1 K-1, respectively for the standard conditions Astd/Vstd ) 1.7 × 109 m-1. The time dependent uptake into the bulk was expressed using H*cc,HONO(Db,HONO)1/2, the product of the dimensionless effective Henry’s law constant and the square root of the effective diffusion constant in the bulk of the polycrystalline ice matrix. H*cc,HONO(Db,HONO)1/2 was evaluated to 1.6((69%) × 10-2 m s-1/2. The results are discussed in the context of HONO partitioning in snowpacks. Introduction Nitrous acid (HONO or HNO2) is an important atmospheric trace gas, as it can photodissociate to form hydroxyl radicals (•OH) and nitric oxide (NO). It therefore affects the HOx and NOx budgets, which are the two key groups of species when considering ozone formation and therefore the oxidative capacity of the atmosphere. Seasonal snowpacks may cover 40% of Earth’s landmass, and especially in Polar regions, they have recently attracted much attention due to their effect on regional atmospheric chemistry.1,2 At these latitudes, due to the low humidity and due to the lower actinic flux, the formation of (•OH) radicals through the photolysis of O3 in the presence of water is reduced. However, •OH concentrations at the South Pole may be as high as those in lower latitudes.1 Concentration gradients observed over the snowpack clearly suggest that HONO may be released from the snow3-5 under certain circumstances and could therefore account for the high •OH concentration measured at the South Pole. However, model calculations taking into account the measured HONO concentration lead to an overestimation of the HOx and NOx levels.6 This suggests missing sinks for HOx and NOx or artifacts associated with the HONO measurements.7 Understanding the mechanism of formation of HONO and its release out of the snowpack would enable a better evaluation of its role in the HOx and NOx budgets. Ice is also present in the upper troposphere in the form of cirrus clouds.8 Nitrous acid is also found in this region, where a significant fraction is due to direct emissions from aircrafts.9,10 Due to the importance of air/ice interactions in atmospheric chemistry, a significant body of literature of experimental and theoretical studies exist (for a review, see refs 11 and 12), but so far, only a few studies addressed the interaction of HONO † ‡
Paul Scherrer Institut. University of Bern.
with pure ice. Using a Knudsen cell coupled to a mass spectrometer, Fenter and Rossi13 derived an initial uptake coefficient, γ0, for temperatures between 180 and 200 K of 1 × 10-3. The behavior of the uptake curves at different gas phase concentrations indicated fully reversible adsorption. Chu et al.14 used a coated wall flow tube coupled to mass spectrometry (CWFT-MS) to determine γ0 and the surface coverage between 178 and 200 K. γ0 ranged between 6.4 × 10-4 (at 178 K) and 3.7 × 10-3 (at 200 K). The behavior of the uptake curves was interpreted in terms of a precursor mediated uptake process. From the temperature dependent coverage data, they derived an enthalpy of adsorption of ∆Hads,HONO ) -34 kJ mol-1. Finally, Bartels-Rausch et al.15 performed their experiments in a packed ice bed flow tube (PBFT), to which a steep temperature gradient from 250 or 218 to 77 K was applied. The deposition of radioactively labeled HO13NO molecules in the form of an adsorption peak was observed at temperatures between 180 and 200 K. Partitioning data were derived using the laws of linear gas chromatography. The adsorption enthalpy ∆Hads,HONO was estimated to be -32((2) kJ mol-1. Therefore, previous studies have only covered the temperature range below 210 K, and the details of the uptake process as observed for other acids have not been addressed so far. The aim of the present study is to obtain thermodynamic and kinetic data on the interaction of HONO with ice at high temperature that can be used to understand HONO release or deposition in snowpacks or partitioning to cirrus clouds. Experimental Methods The experiments were performed in a packed ice bed flow tube using HONO molecules containing both radioactive (13N) and stable (14N and15N) isotopes of nitrogen. The total pressure in the system ranged between 800 and 1000 mbar, the temperature ranged from 253 down to 213 K, and the HONO
10.1021/jp909535c 2010 American Chemical Society Published on Web 01/15/2010
Interaction of Nitrous Acid with Polycrystalline Ice
Figure 1. Schematic of the experimental setup. Flow directions are marked by arrows. The dashed lines represent electronic connections. The boxes labeled “Reactor” and “ABTS” represent the glass reactor where the oxidation of NO to NO2 takes place and the coated glass tube where HONO is produced, respectively (see text for details).
gas phase concentrations were between 0.4 and 137 ppbv. A schematic of the experimental setup is shown in Figure 1. In the following paragraphs, we described the three different units of the system, namely, the nitrous acid source, the packed ice bed, and the detection systems. Nitrous Acid Source. Most commonly, in laboratory experiments, HONO is produced in the reaction of sodium nitrite (NaNO2) with sulfuric acid (H2SO4) in solution13,14,16 or in the reaction of hydrochloric acid (HCl) with solid (NaNO2).17 Vecˇerˇa and Dasgupta18 passed N2 over NH4NO2(s) to generate NH3(g) and HONO(g) in the exit stream. The disadvantage of these production schemes for ice uptake experiments mainly resided in the fact that they delivered HONO in a carrier gas at high humidity and in the presence of other precursor or product gases, such as HCl or NH3. Moreover, using radioactively labeled HONO molecules required that an online HONO production starting from nitrogen monoxide (NO) was used (see below). For this reason, Ammann19 and Bartels-Rausch et al.15 synthesized HONO by reacting gaseous NO2 with solid N-(1naphthyl)ethylenediamine dihydrochloride (NDA) at 30% relative humidity. However, because of the still significant humidity required and because NDA also has an appreciable vapor pressure, we developed a new scheme via the reaction of NO2 with 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) diammonium salt (ABTS) purchased from Sigma Aldrich. ABTS was chosen for being a well established one-electron reductant.20 An aqueous solution of 3% ABTS was used to obtain a coating of ∼30 mg of ABTS on a 400 mm long, 8 mm i.d. quartz tube. A 100 mL min-1 humid N2 flow was added to a flow of 300 or 400 mL min-1 containing NO2 before entering the ABTS coated tube. All flows are given for the standard conditions of temperature and pressure and were controlled by mass flow controllers. The minimum humidity for reasonable performance was ∼5.5% humidity at room temperature. NO2 was obtained by reacting NO with ozone in a 0.95 L flow reactor. The residence time in the reactor was adjusted to 2.4-3.2 min to allow total conversion of NO to NO2. Ozone was obtained by irradiating an oxygen/nitrogen mixture with a mercury penray UV lamp (λ ) 185 nm). The amount of ozone formed was adjusted by varying both oxygen mixing ratio and the residence time in the UV lamp. The possibly remaining excess of ozone was removed by reaction on ABTS. The conversion of NO2 to HONO ranged between 30 and 100% depending on the quality of the ABTS coating and the humidity. We operated this source
J. Phys. Chem. C, Vol. 114, No. 5, 2010 2209
Figure 2. Typical performance test of the HONO source. The red dashed, the blue dashed-dotted, and the green solid lines represent NO as measured by the chemiluminescence detector (CLD), NO2 or HONO as measured by the CLD, and the HONO concentration as measured by the long path absorption photometer (LOPAP), respectively.
at HONO concentrations between 2 and 760 ppbv of HONO at ∼5.5% humidity. Depending on the NO2 to HONO conversion, NOx represented between 9 and 86% of total nitrogen oxides. Figure 2 presents the evolution of the NOx and HONO concentrations during a performance check of this HONO source. At t ) 4 min, the UV lamp for ozone production was switched on, which induced the conversion of NO to NO2. At t ) 19 min, the gas flow was passed over the ABTS, and HONO production started. Depending on the NO2 concentration, stable HONO delivery was achieved after a time lasting from 10 min up to a few hours. In Figure 2, the HONO concentration was measured using a commercial long path absorption photometer (LOPAP-O3),21,22 whereas on routine experiments, in order to simplify the experimental setup and the experimental procedure, HONO was measured using a chemiluminescence detector (see also below). Although this new HONO source allowed a lower humidity than that previously used, the ∼5.5% still represented a dew point of ∼257 K, i.e., much higher than the vapor pressure of ice at the lowest temperature intended for our experiments. Therefore, a flow of N2 was added for further dilution to exactly match the vapor pressure of ice in the flow tube. This was checked with a dew point sensor after the ice flow tube by comparing the signals with the ice in line or bypassed. After this dilution, the HONO concentration was between 0.3 and 137 ppbv. The production of 13N (t1/2 ) 10 min) used for the radioactively labeled HO13NO molecules has been described in detail elsewhere.19 In brief, the 13N isotopes were produced via the reaction 16O(p,R)13N in a gas target, which was set up as a flow cell, through which 10% O2(5.5) in He(6.0) passed at 1 L min-1 and 2 atm. The gas target was continuously irradiated by 11 MeV protons provided by the accelerator facilities at Paul Scherrer Institut, Switzerland. The radiation chemistry in the target cell also led to the production of nonlabeled nitrogen oxides at around 30 ppbv from nitrogen impurities in the carrier gas supplies. The primary 13N molecules and radicals, along with their nonlabeled counterparts, were reduced to nitrogen monoxide over a molybdenum catalyst at 380 °C, immediately after the target cell. The resulting gas was continuously transported to the laboratory through a 580 m long capillary, from where it was delivered to our flow system. Packed Ice Beds. The ice spheres, used to fill the flow tube, were produced by spraying ultrapure water (Milli-Q) into liquid nitrogen. After 2-3 days of annealing at -20 °C, the ice balls were sieved in a walk-in cold room. For most of the experiments, the fraction 500-600 µm was extracted to fill 12-58 cm long,
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6 mm i.d. PFA tubes. For a subset of experiments, the fractions 400-500 and 800-1000 µm were used. After another 2-3 days of sintering at -20 °C, the packed ice bed could be used in an experiment. The packing of the flow tube was very reproducible, and the density was measured to be 580((60 at 2σ) kg m-3 for the fraction 500-600 µm. The volumetric density was therefore 0.63 ((0.06 at 2σ), which is close to an ideal closed packed structure of spheres, which has a volumetric density of 0.74 (the density of ice was taken as 917 kg m-3). The specific surface area (SSA) of the packed beds was calculated from the geometric surface area of the ice spheres to be 12 m2 kg-1. SSA of seven samples produced in the same way as for the uptake experiments was measured by X-ray tomography to be 11((1 at 2σ) m2 kg-1, which is in very good agreement with the calculated specific surface area for spheres of the same size. On the basis of these measurements, the error on the specific surface area was set to 15%. Although the tomograph used had a spatial resolution of only 10 µm, the SSA optically measured is equal to the one accessible to gases for such ice samples.23 The packed beds were mounted by inserting the filled PFA tubes into a doubly jacketed glass reactor to enable the system to be operated at temperatures between 253 and 213 K. The cooling fluid was circulated in the inner jacket, while the vacuum was maintained in the outer jacket for additional thermal insulation. Detection System. The use of short-lived 13N isotopes enabled the in situ monitoring of the HO13NO distribution along the flow tube. This was achieved by a coincident γ-counter system, which continuously scanned the flow tube and which was described in detail by Ammann19 and Bartels-Rausch et al.15 In brief, two bismuth-germanate-detector heads, 3 cm in diameter, were mounted face to face with a gap of 80 mm. The annihilation of the positron emitted in the decay of 13N leads to emission of two coincident γ rays in opposite directions. Therefore, the output of each detector is wired to a timing filter amplifier and constant fraction discriminator, and combined to a coincident counting unit with a logical “and” unit. This allowed the determination of the spatial distribution of HO13NO along the flow tube with very low background count rate (less than 1 count s-1). The detectors were moved continuously by a step motor along the flow tube, in intervals of 1-2 min, with a resolution of 7 mm. This resolution was determined by the width of lead collimators mounted on the detectors. For most of the experiments, parallel to the radioactive measurements, the gas phase concentration at the end of the packed ice bed was monitored using a commercial chemiluminescence detector (Monitor Lab ML8841). It directly measures NO and indirectly also NO2 and HONO by passing the sample gas over a built-in molybdenum converter held at 380 °C, which converted these species to NO. A sodium carbonate (Na2CO3) trap was used to differentiate between NO2 and HONO.19,24 Therefore, NO2 was measured with this trap in line, while the sum of NO2 and HONO was measured with the trap bypassed. Results A contour plot of the raw coincident γ-counter data, recorded during a typical experiment at 253 K, is shown in Figure 3a. From the color code, it can be seen that as soon as the HO13NO was injected (at t ) 0 s) it accumulated at the entrance of the packed ice bed (marked by the green vertical line) and then slowly migrated along the packed ice bed. The migration front, which is defined as the position at a given time, at which the first HO13NO molecules reach a still unexposed section of the ice, can be seen from the white to dark blue transition. While the molecules were migrating
Kerbrat et al.
Figure 3. Migration of HO13NO along the packed ice bed. Upper panel: Contour plot of coincident counts measured along the flow tube at 253 K. The vertical lines indicate the extent of the packed ice bed. The horizontal dashed lines indicate the averaging interval to obtain the steady state migration profiles shown in the lower panel. Yellow symbols are iso-activity points which represent the migration front, fitted by a linear model (red dashed-dotted line, see text for details). Lower panel: Averaged normalized steady state migration profiles (SSMPs) at 253 (red circles), 233 (gray diamonds), and 213 K (light gray squares). For clarity, the initial increase is not shown for 233 and 213 K. The dashed line indicates a single exponential fit to the data according to eq 14 (see text for details).
further and further, the signal near the entrance of the ice bed also continued to increase. A steady state was reached after about 2 × 103 s of exposure of HO13NO, corresponding to about three halflives of the 13N isotope. An average, normalized steady state profile is shown in Figure 3b, which represents the normalized sum of all scans taken between the times indicated by the horizontal lines shown in Figure 3a. The width of the initial increase, spreading over 20 mm, is likely due to inhomogeneity of the ice packing and increased advection. Two centimeters into the ice, the packing was homogeneous, and from that point, the filled red circles represent what we call the steady state migration profile (SSMP hereafter). As will be explained quantitatively below, the slope of the SSMP can be used to calculate the effective migration velocity of HONO through the packed ice bed, using the decay rate of 13N as a stopwatch. The slope of the SSMPs depends on the strength of the interaction of HO13NO with the ice. It increases with decreasing temperature, as demonstrated by the corresponding profiles at 233 and 213 K in Figure 3b. Therefore, at lower temperatures, when the strength of the uptake increases, HO13NO did not necessarily reach the end of the ice bed. The measured signals upstream and downstream of the ice bed are due to the very weak adsorption of HO13NO and 13NO2 on the walls of the PFA tube. An example of the evolution of the HONO concentration as measured by the chemiluminescence detector (CLD) at the end of the flow tube at 243 K is shown in Figure 4. Such a measurement is referred to as a breakthrough curve. At t ) 0, the gas flow was directed to the packed bed which led to the total removal of HONO from the gas phase. After 1.8 × 103 s,
Interaction of Nitrous Acid with Polycrystalline Ice
J. Phys. Chem. C, Vol. 114, No. 5, 2010 2211 ng,HONO(x, t) )
{ (
n0 exp -
Figure 4. Breakthrough curve observed for HONO at the end of a packed ice bed flow tube at 243 K (black solid line) and for acetic acid (gray dashed line) obtained under similar conditions (see Table 1). In both cases, the ice was exposed to the trace gases at t ) 0. For the HONO case, the ice was bypassed at t ≈ 1 × 104s. For the acetic acid case, CH3COOH has recovered back to its initial concentration before the ice was bypassed. The blue dashed-dotted line represents the result of the asymptotic fit made to retrieve H*cc,HONO(Db,HONO)1/2.
TABLE 1: Comparison of the Experimental Conditions Used for the Breakthrough Curve Measurements Presented in Figure 4 quantities
HONO
CH3COOH
temperature (K) gas phase concentration (ppbv) length of the packed ice bed (cm) gas flow (mL min-1) total surface area (m2) mass of ice (g)
243 137 46.0 710 7.6 × 10-2 6.4
243 20 47.5 1 000 7.5 × 10-2 6.3
HONO started breaking through the ice. This is the time when the migration front observed with the labeled molecules reached the end of the packed bed. After this, the HONO concentration increased very slowly. The HONO concentration did not reach the value measured with the packed ice bed bypassed within a reasonable experimental time. This behavior is in considerable contrast to similar experiments performed with other gases. In Figure 4, we show an acetic acid (CH3COOH) breakthrough curve (gray dashed line), which was obtained under similar experimental conditions (see Table 1). The only significant difference is the gas phase concentration, which was 137 ppbv for the HONO experiment and only 20 ppbv for the CH3COOH experiment. This difference will play a role for the total uptake but should not influence the shape of the curves. At t ≈ 2 × 103 s, CH3COOH started breaking through the packed ice bed andsunlike for the HONO casesrecovered to its initial concentration within a few minutes. As will be shown below, the behavior of the uptake curve for HONO at long interaction times can be interpreted in terms of uptake limited by slow diffusion in a bulk phase and is referred to as a “diffusion-like” tailing.12,25 This type of behavior has not been observed for CH3COOH (e.g., ref 26), nor for acetone (e.g., ref 27) or other oxygenated organics (e.g., ref 28), but for strong acids, such as HCl25,29-31 or HNO332 (see also ref 12 and references therein). The occurrence of a “diffusion-like” tailing significantly complicates data analysis. In order to extrapolate partitioning of HONO to ice to other conditions, the two processes, namely, adsorption and diffusion, must be separated, as shown below. Transport of HONO along Packed Ice Beds The Flow Tube Equation. In this section, we will suggest a method to analyze the uptake experiments. This will be based on the flow tube equation (e.g., ref 12), which is given by
x ωHONOγHONO(t) aexp + kg,HONO ugas 4 Vexp
)}
(1)
A complete list of symbols and their meaning is given in Tables 4 and 5. Equation 1 models the gas phase concentration, ng,HONO, of the trace gas considered at a distance x from the entrance of the packed ice bed and at a time t after the beginning of the exposure. It can be used to model experimental data under two conditions. (i) Radial concentration gradients perpendicular to the gas flow must not exist. In our porous packed ice bed, the radii of the air channels are smaller than 200 µm. At this spatial scale, diffusion is fast enough to ensure thorough mixing of the gas flow. (ii) The system must be in a quasi-stationary state, which means that the temporal change of the gas phase concentration closely follows to any changes of the uptake coefficient.12 Equation 1 was slightly modified from the original flow tube equation to take into account a first order gas phase reaction having a rate constant kg,HONO. This modification is described in detail in the Appendix. The Uptake Coefficient. Following Po¨schl et al.,33 Ammann and Po¨schl,34 and Hanson,35 the uptake coefficientsγHONO in eq 1slumps together all of the independent processes during uptake of HONO on ice. It is defined as the net probability that a gas kinetic collision with a surface leads to a loss of HONO and can be expressed as γHONO(x, t) )
jads,HONO(x, t) - jdes,HONO(x, t) jcoll,HONO(x, t)
(2)
where the flux density of adsorption and desorption are represented by jads,HONO and jdes,HONO, respectively, and jcoll,HONO is the total flux density of HONO molecules hitting the surface. The uptake coefficient can be expressed by performing a mass balance at the ice surface dns,HONO(x, t) dt
) jads,HONO(x, t) - jdes,HONO(x, t) ls,HONO(x, t) - js,b,net,HONO(x, t)
(3)
where the term js,b,net,HONO gathers all of the processes taking place in the bulk of the ice matrix such as transfer surface f bulk and bulk diffusion in and out, as well as a first order bulk reaction which would lead to an irreversible loss of HONO from the system (in our case due to radioactive decay of labeled molecules). It represents the net uptake of HONO into the bulk of the ice matrix. The term ls,HONO represents the loss due to a first order surface reaction. The exact expression for each term is given in the Appendix. Equation 3 can only be solved analytically when assuming a quasi-stationary state, where the HONO surface concentration is almost constant with time, i.e., dns,HONO(x, t)/dt ≈ 0. Under this assumption, γHONO reads
γQSA,HONO(t) )
{
Vstd 4 k K0 + ωHONO s,HONO p Astd
(
H*cc,HONO
)}
Db,HONO + √Db,HONOkb,HONO πt
See the Appendix for a step by step derivation.
(4)
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TABLE 2: Values of Kp0 Plotted in Figure 5 (Red Circles), Their Corresponding Klin,C,HONO, the HONO Gas Phase Concentration (ng,HONO) during the Experiment and the Calculated Coverage (ns,HONO) temperature (K)
K0p (×107)
Klin,C,HONO (m)
ng,HONO (ppbv)
ns,HONO (×1016 molecules m-2)
213 223 223 223 233 233 233 243 243 243 243 243 246 253
1110((510) 860((330) 411((62) 350((190) 170((110) 120((110) 75((72) 74((99) 69((84) 60((83) 42((65) 40((59) 44((71) 15((66)
6.6((3.1) 5.1((2.0) 2.46((0.37) 2.1((1.1) 1.02((0.66) 0.72((0.66) 0.45((0.43) 0.44((0.59) 0.41((0.50) 0.36((0.50) 0.25((0.39) 0.24((0.35) 0.26((0.43) 0.09((0.40)
8((1) 8.3((0.4) 2.1((0.2) 11.4((0.6) 5.6((0.3) 7.2((0.4) 6.1((0.3) 0.38((0.02) 2.1((0.2) 9.5((0.5) 9.0((0.4) 6.1((0.3) 15((1) 9.5((0.5)
123((73) 105((45) 12.5((3.1) 59((35) 14((10) 13((12) 6.7((6.8) 0.42((0.58) 2.1((2.8) 10((12) 5.5((8.9) 3.6((5.5) 10((16) 2.1((9.3)
TABLE 3: H*cc,HONO(Db,HONO)1/2 Values Derived for Different pH Valuesa H*cc,HONO(Db,HONO)1/2 (m2 s-1) pH
temperature (K)
minimum
maximum
average ((2σ)
at minimum
at maximum
0.31 0.89 6.7 65 650
0.95 1.6 9.1 85 840
0.65((66%) 1.3((36%) 8.2((17%) 77((16%) 770((16%)
260 260 260 260 260
221 226 234 235 235
3 4 5 6 7
a Calculations were made for the temperature range plotted in Figure 8 and with 1 point per degree.
HONO Gas Phase Concentration in the Flow Tube. After inserting eq 4 into eq 1, we obtain
(
H*cc,HONO
{ [
Vstd 1 aexp k K0 + ugas Vexp s,HONO p Astd
)]
Db,HONO + √Db,HONOkb,HONO πt
}
+ kg,HONO
(5)
Equation 5 simulates the gas phase concentration (ng,QSA,HONO) of a trace gas along the flow tube at a time t under quasistationary conditions. In the case of the labeled molecules, radioactive decay will lead to a loss of HONO from all of the phases it is present in. We will therefore have kg,HONO ) ks,HONO ) kb,HONO ) λ13N, where λ13N ) 0.00116 s-1 is the decay rate constant of 13N. The function f(t) hence becomes
f(t) )
1 ugas
{ [
aexp Vstd λ13NK0p + H*cc,HONO Vexp Astd
√Db,HONOλ
( )] }
13N
+ λ13N
1 aexp H* ugas Vexp cc,HONO
Db,HONO πt
ng,SS,HONO(x) aexp ωHONO γSS,HONO λ13N Vice 4
A(x) ) εng,SS,HONO(x) + (1 - ε)nice,SS,HONO(x)
{ [ (
A(x) ) A0 exp -x
λ13N aexp Vstd K0 + ugas Vexp Astd p
√
N
) ]}
(10)
The full expression of A0 is given in the Appendix. Equation 10 could be used to fit the steady state migration profiles shown in Figure 3b, but it still contains two unknowns, namely, Kp0 and H*cc,HONO(Db,HONO)1/2. They can however be gathered into a term we denote by the 13N-steady state partition coefficient, defined as
13
(7)
(9)
where ε is the porosity of the packed bed. After substitution, we obtain
H*cc,HONO√Db,HONO Astd +1 Vstd λ13
(6)
(8)
See the Appendix for a detailed derivation of eq 8. The activity along the flow tube under steady state conditions is then given by
Db,HONO + πt
In the case of nonlabeled molecules, no reaction is occurring to remove molecules from the system and therefore kg,HONO ) ks,HONO ) kb,HONO ) 0 and f(t) becomes
f(t) )
In Figure 3a, it can be seen that, after about 2 × 103 s of HONO exposure, the color distribution, i.e., the HONO distribution along the packed ice bed, stays constant with time. This means that the system has reached a steady state. From that time on, the assumption made to derive eq 4 is therefore satisfied and eq 6 can be used to simulate the evolution of the gas phase concentration. At this time also (λ13N)1/2 . 1/(πt)1/2 so that the time dependent term, [Db,HONO/(πt)]1/2, becomes negligible. Under steady state conditions, the gas phase concentration and the uptake coefficient will be denoted as ng,SS,HONO and γSS,HONO, respectively. In the radioactive experiments, measured activities originate from both the gas phase and the ice. Under steady state conditions, the HO13NO ice phase concentration, nice,SS,HONO, is given by nice,SS,HONO(x) )
ng,QSA,HONO(x, t) ) n0 exp{-xf(t)} where f(t) )
Data Analysis
Kp N,SS ) K0p +
H*cc,HONO√Db,HONO Astd Vstd λ13
√
N
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TABLE 4: List of Latin Symbols Used in the Text in Alphabetical Ordera symbols
meaning
units 2
experimental ice surface area standard quantity for an adsorbed molecule diffusion constant of HONO in ice effective diffusion constant of HONO in snow effective Henry’s law constant flux of molecules adsorbing onto the surface flux of molecules hitting the ice surface flux of molecules desorbing from the surface flux of gaseous HONO molecules flux of HONO molecules onto the ice surface net flux of molecules into the bulk of ice rate constant of reaction in the ice phase rate constant of reaction in the gas phase rate constant of reaction on the surface linear partition coefficient standard partition coefficient 13 N-steady state partition coefficient partition coefficient from the breakthrough curves partition coefficient from the migration front partition coefficient for the total uptake after a time (t) length of the packed bed loss of HO13NO in the gas phase due to decay loss of HO13NO on the surface due to decay HONO concentration in the ice phase HONO concentration in the gas phase HONO concentration on the ice surface gas constant HO13NO sink into the ice temperature time gas velocity in the packed bed HO13NO velocity in the packed bed experimental gas volume experimental ice volume standard quantity for a gaseous molecule distance along the flow tube
aexp Astd Db,HONO D*g,eff,s,HONO H*cc,HONO jads,HONO jcoll,HONO jdes,HONO Jg,HONO dJice,HONO js,b,net,HONO kb,HONO kg,HONO ks,HONO Klin,C,HONO K0p 13 Kp N,SS BC Kp KMF p Ktot p Lice dLg,HONO ls,HONO nice,HONO ng,HONO ns,HONO R sice,HONO T t ugas uHONO Vexp Vice Vstd x
m m2 molecule-1 m2 s-1 m2 s-1 molecules m-2 molecules m-2 molecules m-2 molecules s-1 molecules s-1 molecules m-2 s-1 s-1 s-1 m m molecules s-1 molecules m-2 molecules m-3 molecules m-3 molecules m-2 J mol-1 K-1 molecules m-3 K s m s-1 m s-1 m3 m3 m3 molecule-1 m
s-1 s-1 s-1 s-1
s-1
s-1
a If the subscripts “SS” and “QSA” are added to the listed symbols, they indicate that this quantity is given under steady state and quasi-stationary approximation conditions, respectively. The symbol “-” denotes dimensionless.
This partition coefficient represents the total HO13NO uptake both on the surface and in the bulk under steady state conditions. It is inherent to 13N because the amount of HO13NO taken up in the bulk depends on its lifetime. When eq 11 is plugged into 13 eq 10, Kp N,SS can be retrieved by fitting the resulting equation to the SSMPs. 13 The temperature dependence of Kp N,SS is shown in Figure 5 (green stars). It ranges from 3.7 ( 10-8 to 1.2 × 1010 and has a negative temperature dependence. No effect of the size of the ice spheres was observed. The analysis of the breakthrough curves can be done using ng,QSA,HONO(t) ) n0 exp{f(t)} when f(t) is given by eq 7. It results in
(
ng,QSA,HONO(t) ) n0 exp -
Lice aexp H* ugas Vexp cc,HONO
)
Db,HONO πt (12)
where x was substituted by Lice, which is the length of the packed bed, because the gas phase measurements were made at the end of the flow tube. The leveling-off observed in Figure 4 is due to a slow saturation, which is described by an uptake coefficient with a 1/t dependence in time. Hence, for infinitely long times, the quasi-stationarity can be expected and eq 12 can then be used to fit experimental data. To be as close as possible to these
TABLE 5: List of Greek Symbols Used in the Text in Alphabetical Ordera symbols
meaning
units
γHONO ∆Hads,HONO ∆Hsol,HONO 0 ∆Sads,HONO 0 ∆Ssol,HONO ε η λ13N ωHONO
uptake coefficient enthalpy of adsorption enthalpy of solvation entropy of adsorption entropy of solvation porosity of the packed ice bed viscosity rate constant of decay of 13N thermal velocity
J mol-1 J mol-1 J mol-1 K-1 J mol-1 K-1 cP s-1 m s-1
a If the subscripts “SS” and “QSA” are added to the listed symbols, they indicate that this quantity is given under steady state and quasi-stationary approximation conditions, respectively. The symbol “-” denotes dimensionless.
conditions, we used eq 12 to fit asymptotically the late data points taken before bypassing the flow tube. An example of such a fit is shown in Figure 4. The data points used for the fit are shown in red. The values retrieved for H*cc,HONO(Db,HONO)1/2 from our data set are presented in Figure 6. Within uncertainty apparent from the significant scatter, H*cc,HONO(Db,HONO)1/2 does not depend on temperature nor on HONO concentration. We will therefore consider that H*cc,HONO(Db,HONO)1/2 is constant and equal to 1.6 × 10-2 m s-1/2 within the experimental conditions used here. The relative error inherent to this value was calculated using
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Kerbrat et al.
Figure 5. Van’t Hoff plot of the adsorption partition coefficient K0p (red circles) as calculated from eq 11. The K0p values are compared to 13 MF Kp N,SS (green stars), Ktot p (for t ) 1 h, red solid line), Kp (open blue 0 (open black squares), and the K values published by triangles), KBC p p Chu et al.14 (yellow diamonds). The shaded area represents the 13 contribution of H*cc,HONO(Db,HONO)1/2 to Kp N,SS for the same 1/2 H*cc,HONO(Db,HONO) confidence interval range as the ones shown in Figure 6. The blue dashed-dotted line represents the result of the linear regression made on the K0p data. For clarity, errors are only shown for the K0p values. These were calculated from error propagation but are mainly due to the uncertainty on H*cc,HONO(Db,HONO)1/2. Individual values for K0p are given in Table 2.
the Student’s distribution law to reach (85 and (69% at a confidence level of 95 and 90%, respectively. This corresponds to 2.3σ and 1.9σ, respectively. Separation of the Surface and the Bulk Process. A separation of the surface (Kp0) and the bulk (H*cc,HONO(Db,HONO)1/2) processes can now be achieved by substituting the measured H*cc,HONO(Db,HONO)1/2 value in eq 11. The adsorption partition coefficient, Kp0, is obtained by subtracting the bulk contribution 13 from Kp N,SS. Note that, in some cases at temperatures above 250 K, the subtraction led to negative results. These values were discarded. The remaining Kp0 values range between 1.5((0.4) × 10-8 and 1.1((0.1) × 1010 and are plotted in Figure 5 (red circles). The errors on Kp0 are mainly due to the uncertainty on H*cc,HONO(Db,HONO)1/2 and were calculated for a confidence level on H*cc,HONO(Db,HONO)1/2 of 90% (see previous section). The adsorption partition coefficient can also be expressed as Klin,C,HONO ) ns,HONO/ng,HONO ) Kp0 × (Vstd/Astd), which is independent of the chosen standard state.36 It ranges between 9.0 × 10-2 and 6.7 m and can be parametrized as Klin,C,HONO ) 7.4 × 10-11 exp(5.4 × 103/T), where Klin,C,HONO is in meters and T in kelvins. Measured Klin,C,HONO values are given in Table 2. HONO coverage was calculated for each experiment using Kp0 and ng,HONO. Results are given in Table 2. In Figure 5, we show how H*cc,HONO(Db,HONO)1/2 influences 13N,SS 13 . This was done by calculating Kp N,SS (gray dashed line) Kp according to eq 11. The error on H*cc,HONO(Db,HONO)1/2 is represented by the gray shaded area (see Figure 6 for the color code). It can be seen that, due to the fact that H*cc,HONO(Db,HONO)1/2 13 is temperature independent, it has more of an effect on Kp N,SS 0 at high temperature where Kp is low than at low temperature where Kp0 is high. Total Partition Coefficient. To calculate the total partition coefficient of nonradioactive molecules, the total number of molecules taken up into the bulk after a time t has to be calculated. This can be done by integrating js,b,net,HONO (eq 22b) for 0 < τ < t. After normalization using Astd/Vstd, it leads to 0 Ktot p (t) ) Kp + 2H* cc,HONO
Db,HONOt Astd π Vstd
(13)
Figure 6. Result of the asymptotic fit (red circles) of the breakthrough curves (see eq 12 and Figure 4). The confidence interval at a confidence level of 90% is represented by the light gray area. The dark gray area represents the confidence interval at a confidence level of 95%. The open blue triangles represent the H*cc,HONO(Db,HONO)1/2 values as retrieved from the migration front measurements (see text for details).
To evaluate the contribution of diffusion-like uptake during the time scale of a laboratory experiment, the total partition coefficient for an exposure time of 1 h is shown in Figure 5 (solid red line). Enthalpy and Entropy of Adsorption. The enthalpy 0 (J mol-1 K-1) of ∆Hads,HONO (J mol-1) and entropy ∆Sads,HONO adsorption of HONO on ice can be calculated using a form of the van’t Hoff equation
ln(K0p) )
(
1 -∆Hads,HONO 0 + ∆Sads,HONO R T
)
(14)
From the slope and the intercept of the linear regression made on the K0p data (blue dashed-dotted line in Figure 5), ∆Hads,HONO was evaluated to be -45((20) kJ mol-1 and ∆S0ads,HONO reached -17((88) J mol-1 K-1. Uncertainties on Kp0 were taken into account by assigning each data point a weight equal to 1/∆Kp0, where ∆Kp0 is the error on Kp0. Large errors are due to the large uncertainty on H*cc,HONO(Db,HONO)1/2, which is propagating to Kp0 0 and therefore to ∆Hads,HONO and ∆Sads,HONO . The magnitude of the uncertainty is related to the data at the highest temperatures. Migration Front and Integrated Uptake. In Figure 3a, the migration front of HO13NO, which was defined above, represents the velocity of migration of HO13NO, uHONO (m s-1). It can be retrieved by fitting an iso-activity level (yellow points in Figure 3a) to a linear model. Iso-activity lines are computed from the coincident γ-counter data using the algorithm provided in the software PV-Wave 9.01 (National Numerics, Inc.). Using the ratio of the velocity of the HONO molecules, uHONO, over the velocity of the carrier gas, ugas, a migration front partition coefficient can be calculated:
KMF p )
ugas Astd Vexp uHONO Vstd aexp
(15)
0 Interestingly, KMF p well agrees with Kp. This can be seen in Figure MF 5 where the Kp values are plotted as blue open triangles. Similarly, breakthrough curves were integrated from the time the ice was first exposed to the time the gas phase concentration at the end of the packed ice bed started recovering, i.e., for 0 s e t e 2000 s in the case presented in Figure 4. The integrated amount of HONO taken up (in molecules m-2) during the time slot was then divided by the HONO gas phase concentration.
Interaction of Nitrous Acid with Polycrystalline Ice The obtained partition coefficient was finally normalized using Astd and Vstd.36 The hence obtained normalized partition coefficients, KpBC, are shown in Figure 5 (open black squares). Here again, the values of KpBC well agree with the Kp0 values. These observations show that molecules in the migration front and similarly the first molecules reaching the end of the packed ice bed do not significantly diffuse into the liquid-like reservoirs, so that the effective migration velocity of the foremost HONO molecules is mostly driven by the reversible adsorption equilibrium only. It is however difficult to rationalize this observation on a more quantitative basis, because they take place in the transient regime, which could only be addressed through a more detailed 2-D numerical model, rather than the analytical approach presented above. Because the system can only be solved analytically when it has reached a steady or a quasi-stationary state, it is also difficult to interpret the total uptake measured in the breakthrough curves. Whereas it can be easily calculated from numerical integration, it is to date not possible to normalize the results to the surface area and the bulk volume into which uptake takes place. Indeed, during the transient regime, the ratio of bulk uptake to surface uptake is not known and might change with time. 1/2 When the KMF p values are used to calculate H* cc,HONO(Db,HONO) 13N,SS from Kp , we obtain similar values to those retrieved from the asymptotical fit. This is shown in Figure 6 where it can be seen that the H*cc,HONO(Db,HONO)1/2 retrieved only from the scanner data falls within the uncertainty range of H*cc,HONO(Db,HONO)1/2. This is a notable observation, as it indicates that measuring the SSMPs and the evolution until they are reached provides similar information as retrieved from the much longer lasting measurements of breakthrough curves. Discussion The “Diffusion-Like” Parameter. To our knowledge, we observed “diffusion-like” uptake of HONO in polycrystalline ice for the first time. Previous studies on the interactions of HONO with ice were made at temperatures where bulk diffusion may not have been detectable. As already mentioned in the Introduction, Fenter and Rossi13 did their experiments at temperatures between 180 and 200 K, Chu et al.14 between 174 and 205 K, and Bartels-Rausch et al.15 detected adsorbed HONO at temperatures
