A laboratory study on the uptake of gaseous molecular iodine by clay minerals at different relative humidities

Abstract

Dry deposition of iodine is a crucial parameter for estimating the public health risk of radioiodine released in the Fukushima Dai-ichi nuclear power plant accident. We measured the uptake of molecular iodine (I₂) by aqueous solutions and clay minerals in the laboratory to inform estimates of the ground surface resistance for I₂ in dry deposition which photolysis limited to nighttime. We injected rectangular pulses of humidified air including I₂ into a contactor holding samples of aqueous solutions and clay minerals and monitored I₂ concentrations in air leaving the contactor to distinguish I₂ loss from I₂ adsorption. Uptake of I₂ proceeded much more rapidly by aqueous ascorbic acid than by water; the former was limited by mass transfer in the gas-film layer. Uptake of I₂ by clay samples was confirmed under dry conditions (20–80% relative humidity), which suggested that it contributed to the dry deposition of I₂ onto soils as much as other processes such as reactions with organic matter. The surface resistance for I₂ increased with repeated experiments on the same clay samples, reaching 240–670 s m⁻¹, and its dependence on relative humidity differed from that for sulfur dioxide (SO₂), a commonly used proxy for I₂ in scaling methods. Reference values of surface resistance for SO₂ above soils remain useful for estimating the resistance for I₂ above vegetate surfaces at 80% RH in atmospheric transport and dispersion model calculations but may result in substantial errors at 20% RH unless organic matter in soils contributes to ground surface resistance for I₂.

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Environmental significance

Ground surface resistance for iodine is a crucial parameter in dry deposition for estimating the public health risk associated with accidental release of radioiodine from nuclear power plants. We conducted rectangular pulse experiments on the uptake of I₂ by clay samples and confirmed I₂ deposition on the clay samples. The deposition rates decreased with successive runs and remained finite through each set of experimental runs. The resultant ground surface resistances for I₂ were greater than the resistances adopted in atmospheric model calculations which considered no difference between I₂ and its photodegradation products. The relative-humidity dependence was different between these resistances. Radioiodine dry deposition processes therefore need to be estimated separately before and after sunrise when I₂ is released at night.

1. Introduction

Radioiodine-131 (¹³¹I), with a half-life of 8 days, is a major contributor to the public health risk associated with accidental release of radionuclides, because of its high short-term radiation levels and the tendency of iodine to concentrate in the thyroid gland.¹ The accident at the Fukushima Dai-ichi nuclear power plant following the 11 March 2011 Tohoku earthquake and tsunami released ¹³¹I into the atmosphere in several different forms, including molecular iodine (I₂), methyl iodine (CH₃I), and aerosol-form iodine such as cesium iodide (CsI),² which behave differently in the atmosphere. The atmospheric reaction and deposition processes of these species, in particular the deposition velocity, need to be known so that the emission source terms of radioiodine released in the accident and the inhaled internal dose of radioiodine in affected populations can be properly estimated by atmospheric transport and dispersion models^2,3 from limited field observations.^4–6

Dry deposition of ¹³¹I has been studied in both field releases^7–10 and wind tunnel experiments^11,12 to investigate the transfer from the atmosphere to grass and other surrogate surfaces. Deposition velocities of radioiodine have also been calculated from field observations after the Windscale nuclear accident in 1957¹³ and nuclear tests in the atmosphere.⁹ Reported deposition velocities of elemental iodine or I₂ onto various surfaces, however, vary from 0.02 to 26 cm s⁻¹.¹⁴ When dealing with atmospheric transport of radioiodine, the chemical form of iodine has to be considered explicitly. Because photolysis limits the lifetime of I₂ to about 10 seconds,^15,16 most field studies on the release of I₂ in daytime have reported the behavior of not I₂ itself, but a mixture of iodine species produced through atmospheric reactions initiated by photolysis of I₂.¹⁶ Similarly, in almost all models of the release of radioiodine from nuclear power plants, the species reported as I₂ include not only molecular iodine but also other potential iodine species, such as HOI, produced by atmospheric reactions; we refer to this mixture as I^model₂. In the models applied to the Fukushima accident, deposition velocities of I^model₂ over short vegetation are assumed to have constant values, such as 0.3 cm s⁻¹,¹⁷ or values similar to that of sulfur dioxide (SO₂).³ If dry deposition velocities of I₂ differ greatly from these values, the dry deposition process of I^model₂ needs to be estimated separately before and after sunrise when I₂ is released at night.

In numerical models, the dry deposition process is commonly treated as a resistance model, which consists of a series of resistances.¹⁸ The bulk surface resistance, which represents the transfer of substances at the level nearest to Earth's surface, is typically the most uncertain because it involves the atmospheric chemistry of each species over various surfaces, such as leaf cuticles and soils. The bulk surface resistance consists of stomatal resistance and non-stomatal resistance. For I₂, stomatal resistance is ignored because photolysis limits dry deposition of I₂ to nighttime, when most plants close their stomata.¹⁹ Non-stomatal resistance, R_ns, above vegetate surfaces is decomposed as

where R_ac is the in-canopy aerodynamic resistance, R_g is the subsequent ground resistance, and R_cut is the resistance to cuticle uptake.²⁰ For surfaces without canopies, such as bare soil and open water, R_ac and R_cut are not applicable. When information on R_g and R_cut is limited, models commonly estimate these resistances by a scaling method, relying on an effective Henry's law coefficient or a half-redox potential as an index.^20,21 For I₂, however, effective Henry's law coefficients cannot be defined unless the aqueous concentration of I⁻ in the following reaction is assumed to be constant.

I₂ + H₂O ⇄ I⁻ + HOI + H⁺ (R1)

Given these considerations, we conducted a laboratory study of I₂ uptake by various reactors, consisting of six different types of clay mineral particles and three different aqueous surfaces, to provide data for estimating R_g for I₂ above soils. We used a rectangular pulse method²² to distinguish loss of I₂ from adsorption onto the reactor. This method can be conducted under lower-atmospheric conditions such as humidified air at 1 atm. The pulse method is useful for determining the loss rates for the reactors which tend to deactivate with exposure to I₂ because it can control the exposure to I₂ precisely at low concentration levels of I₂. As a disadvantage, it needs an estimate of mass-transfer resistances in gas-film layers above the solid or the liquid reactors for determination of the surface resistance above the reactors. The clay samples consisted of five pure clay minerals and standard clay soil, and the aqueous surfaces were water, aqueous sulfuric acid, and aqueous ascorbic acid. In this paper we present surface resistances estimated from the experiment and resultant non-stomatal resistances and discuss their implications for calculations in atmospheric transport and dispersion models.

2. Methods

2.1 Materials

Molecular iodine (anhydrous, beads, 10 mesh, 99.999%) was purchased from Sigma-Aldrich. Sodium iodide (99.5%), 1/240 M standard aqueous potassium iodate (NaIO₃) solution, 0.5 M standard aqueous sulfuric acid (H₂SO₄) solution, L(+)-ascorbic acid (99.6%), and 1 M standard aqueous sodium hydroxide (NaOH) solution were purchased from FUJIFILM Wako Chemicals. These reagents were used without further purification. Water was purified with an EMD Millipore Milli-Q Gradient A10 system (>18 MΩ cm). Synthetic air (an O₂–N₂ mixture, 1 : 4 volume ratio) and carbon dioxide gas (CO₂, 1.02% in synthetic air) were purchased from Takachiho Chemical Industrial Co., Ltd.

Pure clay minerals of kaolinite, halloysite, montmorillonite, allophane, and illite were purchased from Iwamoto Mineral. These were the same materials used in previous studies at our laboratory.^23–25 Clay powder of AgroMAT Clay Soil AG-1 (Lot No. S131024028, SCP Science) was purchased from GL Science Inc. The allophane and the illite samples were ground to reduce the particle size with a mortar machine. The other clay samples were used as purchased. The grain size of the samples ranged from several millimeters down to submillimeter sizes. Table 1 lists the Brunauer–Emmett–Teller (BET) surface areas of these samples. AgroMAT AG-1 contained organic matter by 3.7% in weight, based on the loss-on-ignition method.

Table 1 Properties of clay samples

	Kaolinite	Halloysite	Montmorillonite	Allophane	Illite	AgroMAT AG-1
a Standard clay samples from the American Petroleum Institute, no. 35 (Fithian, Ill).
Morphology	Thin sheets	Tubes	Thin sheets	Hollow spherules
Structure	Crystalline (1 : 1)	Crystalline (1 : 1)	Crystalline (2 : 1)	Amorphous	Crystalline (2 : 1)
Origin	Kawachi, Tochigi, Japan	New Zealand	Aterazawa, Yamagata, Japan	Kanuma, Tochigi, Japan	Fithian, Ill, USA
BET area (m^2 g^−1)	16	29	18	235	70	12
Others	Kanpaku kaolin	Metahalloysite	KUNIPIA-F, Na-type		API no. 35^a	200 mesh size

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2.2 Experimental setup

The experimental setup is shown schematically in Fig. 1. Each experimental run comprised preparation and injection of an I₂–air mixture of specified relative humidity (RH), passage of the mixture through a two-phase contact chamber (contactor), and analysis of the mixture leaving the contactor in an incoherent broad-band cavity-enhanced absorption spectroscopy (IBBCEAS) instrument.^26–28 The method for injecting and flowing the gas mixture through the contactor was essentially the same as that reported for volatile organic compounds by the authors.²² The gas flow was controlled with eight mass-flow controllers (d in Fig. 1) at rates listed in Table S1 in the ESI.† The gas mixtures flowed through perfluoroalkoxy alkane (PFA) tubes covered in black.

Fig. 1 Schematic diagram of the experimental setup: (a) bottle containing I₂ beads (b); (c) electronic dry bath; (d) mass-flow controllers; (e) four-port valve; (f) impinger with 20 mM NaOH; (g) syringe pump; (h) three-port ceramic valve; (i) humidifier; (j) temperature-controlled water circulator; (k) stainless-steal water bath; (l) four-port valve; (m) contactor; (n) turbine for stirring the gas phase; (o) dish to hold samples; (p) baffles; (q) light source; (r) optical bandpass filter; (s) IBBCEAS measurement cavity; (t) spectrometer.

2.2.1 Gas mixture preparation and injection. About 5 g of I₂ beads was placed in a PFA bottle (inner diameter, 25.4 mm) in the cavity of the aluminum block of an electronic dry bath (CTU-Mini, Taitec) set at 288.2 K (Fig. 1(a)–(c)). Synthetic air was introduced into the bottle to produce an I₂–air mixture that was further diluted with synthetic air to produce a mixture referred to hereafter as I₂–air(o). As shown in the ESI,† the partial pressure of I₂ in I₂–air(o), P_in-o, was determined by bubbling I₂–air(o) into 20 mL of 20 mM NaOH solution in an impinger (f) for a certain time period, followed by analysis of the solution with an ion chromatograph (Dionex ICS-2100, Thermo Fisher Scientific) for I⁻ and IO₃⁻ produced through

3I₂ + 3NaOH → 5I⁻ + IO₃⁻ + 3Na⁺ + 3H⁺ (R2)

I₂–air(o) was injected using a computer-controlled syringe pump (PSD/4, Hamilton Co.), comprising a 1.25 × 10⁻² dm³ glass gas-tight syringe (g) and a three-port ceramic valve (h), into the flow of a mixture of 400 ppmv CO₂ and humidified synthetic air (humidified at 283.2 K; (i) and (j)); the resulting I₂–CO₂–air mixture is hereafter referred to as I₂–air(s). The syringe pump was shaded with aluminum foil to protect I₂ from photolysis. The syringe pump introduced I₂–air(s) into the contactor as a rectangular pulse of I₂ (pulse width, 300 s; partial pressure, 4 × 10⁻⁷ or 2 × 10⁻⁷ atm).

2.2.2 Two-phase contactor. The contactor, a cylindrical PTFE vessel (Fig. 1(m): inner diameter, 81 mm; inner height, 80 mm), was almost fully submerged in a jacketed stainless-steel water bath (BT-80, SGI) (k) at 283.2 K; the temperature was maintained by circulating temperature-controlled water (NCB-2100, EYELA) through the jacket. Inside the contactor were a PTFE-coated stainless-steel turbine (n, Yamazaki Seisakusyo), a PTFE dish (80 mm in diameter and 5 mm high) with a central basin (o), and PTFE-coated stainless-steel baffles (p), leaving a remaining gas-phase volume of 0.390 dm³. The turbine consisted of two sets of three blades, arranged vertically and offset by 60°, with each blade containing 12 holes, and stirred the gas phase at 300 rpm. Synthetic air was slowly introduced into the contactor (ca. 2.4 × 10⁻⁵ dm³ s⁻¹) through the dead space between the contactor and the axis of the turbine using a mass-flow controller (MFC6 in Fig. 1) to prevent the sample gases from lingering there. The PTFE vessel, its PTFE lid, the support for the motor connected to the contactor, and the PTFE dishes were fabricated in our workshop. Fig. S1† shows the dimensions of the vessel, turbine, baffles, and dishes.

Aqueous solutions were set in dishes with deep basins (4 mm) of two different diameters (30 or 55 mm), and clay samples were set loosely in dishes with shallow (2 mm) basins with diameters of 35 or 55 mm. The ratios between the areas of the basin (S) and the floor of the contactor (S_c), S/S_c, were 0.137 or 0.461 for aqueous solutions and 0.187 or 0.461 for clay samples. The sample sizes depended on the S/S_c as follows: aqueous samples were 2.8 mL for S/S_c = 0.137 and 9.4 mL for S/S_c = 0.461, and clay samples were 0.73 g for S/S_c = 0.187 and 1.78 g for S/S_c = 0.461. Before I₂–air(s) was introduced into the contactor, the same gas mixtures without I₂ had flowed over each clay sample for >90 min under the same experimental conditions. A four-port PTFE valve (l) was used to direct I₂–air(s) into the contactor.

2.2.3 Detection and analysis. After passing through the contactor, the gas mixture entered a PTFE cell (Fig. 1(s); inner diameter, 20 mm) for measuring I₂ in the IBBCEAS instrument. The inlet and outlet of the cell were 0.203 m apart, and its ends were equipped with plano-concave mirrors 25 mm in diameter with a 1.0 m radius of curvature (quoted reflectivity > 0.999 at 515 nm; Article 142831, Layertec), forming a stable optical cavity ca. 0.5 m long. To protect the mirrors from I₂ and reduce the residence time of the sample gas in the cell, synthetic air was purged over the mirrors at a constant flow rate (MFC7 and MFC8 in Fig. 1; F7 and F8 in Table S1†).

Light from a laser-driven broadband xenon light source ((q) Model EQ-99-FC, ENERGETIQ) was directed into the cavity through a fiber-coupled output, using a bandpass filter ((r) FF03-525/50-25, Semrock) to exclude light outside the wavelength range of interest (500–550 nm). The light output from the cavity was directed into a spectrograph ((t) M25-GTM, Bunko Keiki) with a grating of 1200 grooves per mm equipped with a 1024 × 256 pixel CCD camera (DU420-OE, ANDOR). Full vertical binning was applied, providing 1024 superpixels. Spectra were recorded by averaging four spectra taken with exposure times of 1 s (total exposure time of 4 s).

2.3 Quantification of I₂

In IBBCEAS measurements, the relationship between the spectra and the I₂ concentration in the cavity (Fig. 1(s)) is²⁶where n_I2 and σ_I2 are the number density and absorption cross section, respectively, of I₂; R_m is the mirror reflectivity; d_eff is the effective single-pass extinction path length of the I₂–air mixture in the cell; and I₀ and I are the intensity of transmitted light recorded with synthetic air and I₂–air(s), respectively, inside the cavity, with both gases containing CO₂ and water vapor. Letting P_out(t) be the partial pressure of I₂ in the I₂–air(s) leaving the contactor at time t, eqn (2) yieldswhere I_out(t) is the I value at time t for I₂–air(s) leaving the contactor, I_in(t) is the I value at time t for I₂–air(s) not passing through the contactor when the partial pressure of I₂ is P_in, and P_in is the partial pressure of I₂ in I₂–air(s) corresponding to the peak height of the rectangular input pulse. P_in is calculated from the partial pressure of I₂ in I₂–air(o), P_in-o, usingwhere F_s is the flow rate of I₂–air(o) from the syringe pump and F₃, F₄, and F₅ are the flow rates of CO₂–air, air, and humidified air, respectively, from the mass-flow controllers (Fig. 1; Table S1†). As shown in Section S1.2 in the ESI,†P_in-o was experimentally determined to be 7.1 ± 0.2 Pa on the basis of ion chromatography analysis of I⁻ and IO₃⁻ in 20 mM NaOH solutions that had captured I₂ from I₂–air(o). Letting P₀ be the value of P_in in our experiments, when 12.5 mL of I₂–air(o) was injected in 300 s at a flow rate F_s of 4.17 × 10⁻⁵ dm³ s⁻¹, P₀ was 41 mPa, yielding a concentration of 0.40 ppmv.

For the clay sample, eight measurements of I₂ in I₂–air(s) passing through the contactor were typically made for the same sample, when the value of P_in was set at P₀ for the first, third, fifth, and seventh measurements and at 0.5P₀ for the second, fourth, sixth, and eighth measurements. For the aqueous solutions, two measurements were made for the same sample with the value of P_in set at P₀. The input pulse width of I₂–air(s) was 300 s for all the measurements. In each measurement, the pulse was injected into the contactor at 89 s after the acquisitions on IBBCEAS started. The value of I₀ in eqn (2) and (3) was taken as the average of 10 spectra recorded 7–47 s before injecting I₂–air(s) into the contactor. Calibration pulses of I₂–air(s) not passing through the contactor were measured with the input pulse height set at P₀, 0.8P₀, 0.6P₀, or 0.5P₀ before each series and P₀ or 0.5P₀ after each series.

The absorption spectra of I₂ at the wavelength range of 500–550 nm had both gradual absorption and strongly varying absorption and the latter was used to determine P_out(t). The (I₀/I_in(t) − 1) spectrum was fitted by a polynomial of order 19.²⁸ This smooth function was subtracted to yield a strongly varying residual spectrum: an illustrative example is shown in Fig. S2.† After the spectra of both (I₀/I_in(t) − 1) and (I₀/I_out(t) − 1) had been given this treatment, a principal component regression was applied to the residual spectra from (I₀/I_out(t) − 1) to obtain a time series of I₂ concentrations while the residual spectra from (I₀/I_in(t) − 1) were used as calibration spectra. The regression was carried out, assuming one factor, by using the FACT chemometric toolbox in Scilab software.^29,30 No H₂O absorption features were detected around 505 nm as a 6ν polyad overtone,²⁸ and hence the influence of water vapor was expected to be negligible (Fig. S2c†).

Returning to eqn (2), let l_eff represent the effective pathlength in IBBCEAS, calculated from d_eff/(1 − R_m) (Fig. S2d†). Values of l_eff and R_m were approximately 600 m and 0.9997, respectively, in the wavelength range of 520–530 nm. The value of n_I2 was taken as 28 mPa (6.9 × 10¹² molecules per cm³) under the assumption that the additional flows over the mirrors (at flow rates of F7 + F8) diluted the I₂–air(s) in the detection cell, yielding a d_eff value of 0.20 m. The values of σ_I2 were interpolated by using previously reported values.^31,32 The partial pressure of I₂ observed at time t, P_m(t), is related to P_out(t) based on

where F_out is the total flow rate at 298.2 K of I₂–air(s); F_add is the flow rate of air added to the IBBCEAS cell (assumed equal to F7 + F8); τ_m is the residence time of I₂ in the cell fromwhere V_m is the partial volume of the cell (6.28 × 10⁻² dm³ with an effective length d_eff of 0.20 m). This yields a value of 6.1 s for τ_m.

2.4 Data analysis

2.4.1 residence ratios of I₂. The residence ratio x_out of I₂ at time t is defined as

The measured residence ratio x_m of I₂ at time t is given by

where P_0m is the partial pressure of I₂ for a pulse height when P_in is P₀:

Substituting eqn (8) and (9) into eqn (5), we get

Values of x_m(t) are approximately given by

Combining eqn (10) and (11) yields

2.4.2 Rectangular input pulse signals. Let f_m(t) represent x_m(t) observed in I₂–air(s) not passing through the contactor. The time series of f_m(t) were nonlinearly fitted usingwhere the parameters a_i (i = 1–4) and b_i (i = 1–9) determined from the experimental data by nonlinear regression are regulated to ensure continuity of f_m(t) at 300 s as follows:

If calculated values of f_m(t) are less than zero, f_m(t) is defined to be zero. Table S3† lists the values of a_i and b_i. As seen on the bottom row in Table S3,† the peak height of the rectangular input pulse (P_in) is a constant value (P₀ or 0.5P₀) within 1% and 3%, respectively, for P_in = P₀ and 0.5P₀ at 20–96% RH. Fig. 2 shows the time series of f_m(t) curves fitted to the experimental data obtained at each RH value (see Fig. S3† for plots of the underlying data).

Fig. 2 f _m(t) determined experimentally at four values of RH (a) when P_in is P₀ (4 × 10⁻⁷ atm) and (b) when P_in is 0.5P₀ (2 × 10⁻⁷ atm).

Unlike a previous study using the rectangular pulse method,²² the adsorption processes examined here had a nonlinear relationship between rates and concentrations; hence, f_m(t) could not be used as an input pulse in simulations to optimize parameters related to loss and adsorption of I₂ by clay samples in the contactor. Therefore, the input pulse signal in the simulation, f(t), was approximated on the basis of eqn (12) using

2.4.3 First-order rate constants with respect to the concentration of gaseous I₂ for uptake on surfaces. The loss rate of I₂ by uptake on surfaces such as clay samples, U(t), is calculated usingwhere P₀f(t) is the time series of I₂ in the input pulse, A_np is a unit conversion factor, and τ_c is the residence time of I₂–air(s) in the contactor:where V_c is the volume (3.90 × 10⁻¹ dm³) and T is the temperature (283.2 K) of the contactor; T₀ is 298.2 K. Eqn (17) is then rewritten as

From eqn (12), (16) and (19), U(t) can be expressed in terms of f_m(t) and x_m(t), as shown in the ESI,† using

Here, values of f_m(t) and df_m(t)/dt were calculated from eqn (13), and values of dx_m(t)/dt and d²x_m(t)/dt² were obtained for each value of x_m(t) by quadratic curve fitting of five data points from (t − 8) to (t + 8). The first-order rate constant for uptake of I₂ on the surface with respect to x_out(t) at time t, k_1-a(t), is given from eqn (12) using

If uptake of I₂ on the contactor is negligibly small, the deposition rate at time t, k_g-a(t) in cm s⁻¹, is then

where h_c is the height of the contactor (7.5 cm). Values of k_g-a(t) are related not only to loss but also to adsorption of I₂ on the samples. The apparent surface resistance for I₂ above the surface, R_g-a(t), is the reciprocal of k_g-a(t):

2.4.4 Parameter fitting by simulations to estimate surface resistance for I₂. The parameters related to I₂ uptake on surfaces were determined by a simulation in which the parameters were fitted to reproduce the time series of x_m(t) by using the parameter-fitting routine of FACSIMILE software (MCPA Software Ltd., UK).²² It is briefly described in Section 3.

3. Results and discussion

3.1 Blank experiments

Blank experiments were run in which I₂–air(s) flowed through the contactor with no samples at each value of RH. These assumed perfect mixing of the gas phases and that no loss or adsorption of I₂ occurred in the contactor:

Here, f(t) is calculated from f_m(t) using eqn (16), and x_out(t) is related to x_m(t) by eqn (12).

The measured time series (Fig. 3) showed that x_m(t) before and after 300 s was smaller and larger, respectively, than the dashed curve representing the simulation results, which showed that I₂ was reversibly adsorbed on the inner wall of the contactor. This reversible adsorption of I₂ increased with increasing RH.

Fig. 3 Time series of x_m(t) for I₂ in blank experiments at four RH values. P_in was P₀ (4.0 × 10⁻⁷ atm; pink circles) or 0.5P₀ (2.0 × 10⁻⁷ atm; blue squares), the temperature was 283.2 K, and F_out was (a) 7.315 × 10⁻³, (b) 7.281 × 10⁻³, (c) 7.302 × 10⁻³, and (d) 7.369 × 10⁻³ dm³ s⁻¹. Dashed curves are the simulation results without loss or adsorption of I₂ (from eqn (24)) and solid curves are fitted to the experimental results using eqn (26)–(28).

The apparent uptake rates of I₂ by the contactor decreased with time, although the gas-phase concentrations of I₂ increased (Fig. S4†). This result suggests that the uptake occurred as an initial rapid stage followed by a slow stage, as documented for the sorption of volatile organic compounds on soil particles.³³ I₂ was readily adsorbed on the contactor walls, then transformed to internal surfaces, such as pores, at a slower rate. Thus our simulation assumed Freundlich-type adsorption of I₂ on the contactor walls (eqn (25)) and a reversible transformation of I₂ between the surface and internal sites:

y_b(t) = K_badsx_out(t)^1/N (25)

where y_b(t) is the amount of I₂ on the wall surface; K_bads and N are parameters of Freundlich adsorption equilibrium and N is 2 here, andwhere k_bm is the mass-transfer coefficient of I₂ between the gas phase and the wall surface; k_bf and k_bb are first-order forward and backward rate constants, respectively, for the transport of adsorbents between surface and internal sites in the wall; k_bl is a first-order rate constant for I₂ loss in the internal sites; z_b(t) is the amount of I₂ in the internal sites; and A_bpn is a unit conversion factor. Simulations using eqn (12) and eqn (26)–(28) were conducted to simultaneously reproduce the observed time series of x_m(t) with values of K_bads, k_bf, k_bb, and k_bl as common parameters for each value of RH while a value of k_bm is a common parameter for all data.

The solid curves in Fig. 3 show x_m(t) values from the simulation that minimized the residual sum of squares (RSS); the observed data were satisfactorily reproduced. The values determined for each parameter are listed in Table S4,† which also lists mole ratios of I₂ loss. In the blank experiments, the loss ratio of I₂ increased from 2.7% to 12.6% with increasing RH for P₀ as P_in and from 2.2% to 15.6% for 0.5P₀ as P_in. Langmuir-type adsorption of I₂ on the contactor also reproduced the x_m(t) time series (Table S5†), but the Freundlich-type equation fitted the data with a smaller RSS, as shown in the ESI.† The parameters determined at each RH value (Table S4†) were used to estimate k_1-a(t) and simulate x_m(t) in the other experiments.

3.2 Uptake of I₂ by aqueous solutions

In the time series of x_m(t) in I₂–air(s) after passage through the contactor with dishes holding 2.8 mL of water, 1 mM aqueous sulfuric acid, or 1 mM or 10 mM aqueous ascorbic acid in small basins (S/S_c, 0.138), maximum values of x_m(t) for water and sulfuric acid were both ∼5% smaller than those of the blank, and values for ascorbic acid were ∼40% smaller than those of the blank (Fig. 4). The similar time series for water and sulfuric acid suggests that the water surface was saturated with undissociated I₂ under the experimental conditions such that the uptake of I₂ was controlled by aqueous-phase diffusion of I₂. The dissociation ratio in reaction (R1) was estimated at 16% under the experimental conditions (283 K; pH, 5.6 for water in equilibrium with 400 ppmv CO₂; partial pressure of I₂, 3.2 × 10⁻⁷ atm) according towhere K_a is the dissociation constant of reaction (R1) at 283 K, K_H is the Henry's law constant of I₂ at 283 K, and P_I2 is the partial pressure of I₂ (see the ESI†). In contrast, in ascorbic acid, I₂ was reduced to I⁻ based on

I₂ + C₆H₈O₆ → 2H⁺ + 2I⁻ + C₆H₆O₆ (R3)

and I₂ uptake proceeded much faster than in water. With the reported rate constant for reaction (R3) of 1.2 × 10⁵ M⁻¹ s⁻¹ at 20 °C,³⁴ the lifetime of I₂ with respect to reaction (R3) in 10 mM ascorbic acid is estimated at about 10⁻³ s at 20 °C, which is two orders of magnitude shorter than that of I₂ with respect to hydrolysis in reaction (R1).³⁵ In this solution, I₂ thus reacts dominantly with ascorbic acid. However, the similar time series of x_m(t) for 1 mM and 10 mM ascorbic acid (Fig. 4c and d) suggests that the rate-limiting step is not the aqueous reaction but mass transfer in the gas-film layer, as described by two-film layer theory. We estimated the resistance for I₂ for mass transfer in the gas-film layer above ascorbic acid, or R_g-cont-w, under the experimental conditions from the k_1-a(t) values and simulations for 10 mM ascorbic acid, and as discussed below, we were able to compare them with the corresponding uptake coefficients (γ) of I₂ estimated from previously published data.

Fig. 4 Time series of x_m(t) in I₂–air(s) (P_in, 4.0 × 10⁻⁷ atm) after passage through the contactor over (a) water, (b) 1 mM aqueous sulfuric acid (H₂SO₄aq), (c) 1 mM aqueous ascorbic acid (ASCaq), and (d) 10 mM ASCaq. Blank runs are shown as dashed curves. Pink symbols are the results for 2.8 mL of solution in the small basin (S/S_c, 0.137) of the contactor dish, and blue symbols are the results for 9.4 mL of solution in the large basin (S/S_c, 0.461). The red and blue curves are the simulation results obtained by using eqn (S11)–(S13).†

Fig. 4 also shows the time series of x_m(t) for experiments with 9.4 mL of liquid in the contactor dish with a large basin (S/S_c, 0.461). Loss rates of I₂ through uptake on the surface, U(t), were calculated during the injection period (13–289 s) using eqn (20). After 50 s, these values decreased with time for water and the blank but were almost constant for 10 mM ascorbic acid (Fig. 5a). Because the gas-phase concentration of I₂ increased with time, the rate constants k_1-a(t) calculated using eqn (21) decreased with time (Fig. 5b). The k_1-a(t) value for uptake by the contactor (Table S6†) was subtracted from the rate constants, and the remainders were used to calculate deposition rates, k_g-a(t), using eqn (22) (Fig. 5c).

Fig. 5 Time series of (a) loss rates of I₂ by uptake on surfaces, U(t), (b) their apparent first-order rate constants, k_1-a(t), and (c) their apparent deposition rates, k_g-a(t) in blanks and the first experimental run for 10 mM ascorbic acid and water in small basins (S/S_c, = 0.138, closed symbols) and large basins (S/S_c = 0.461; open symbols). Red square symbols represent the results for ascorbic acid, blue triangle symbols represent the results for water, and gray circle symbols represent the results for blank (open circles, P₀ as P_in at 96% RH; closed circles, 0.5P₀ as P_in at 96% RH; the former was taken as the blank to obtain k_g-a(t) values here).

The rate constant k_1-a and the deposition rate k_g-a were defined as the average of 10 data points of k_1-a(t) and k_g-a(t), respectively, from 253–289 s and the surface resistance R_g-a was determined to be the reciprocal of k_g-a. When the k_1-a(t) value for the blank with P₀ as P_in was subtracted from the rate constants in the first experimental run, the k_g-a values in 10 mM ascorbic acid were 0.91 ± 0.03 cm s⁻¹ for the small basin and 0.85 ± 0.01 cm s⁻¹ for the large basin, yielding R_g-a values of 109 s m⁻¹ and 118 s m⁻¹, respectively. Values of k_1-a, k_g-a, and R_g-a were estimated similarly for all of the aqueous solutions (Table S6†).

Simulations were carried out to distinguish the uptake of I₂ by ascorbic acid and the contactor (Section S6-3 in the ESI†). Letting k_m be the mass-transfer coefficient of I₂ in the gas-film layer above ascorbic acid, values of k_m are thus estimated to be 0.91 ± 0.01 cm s⁻¹ and 0.78 ± 0.01 cm s⁻¹ for the small and large basins, respectively (errors at 90% confidence level). These values are approximately equal to the estimated values of k_g-a. Overall, R_g is estimated to be 120 ± 5 s m⁻¹ from 16 data of R_g-a for 1 mM and 10 mM ascorbic acid (Table S6†). Errors represent the standard deviation.

Referring to the reported physicochemical properties of I₂,^34,36–38 we estimate the uptake coefficients (γ) of I₂ at 2.6 × 10⁻³ for 10 mM ascorbic acid and 1.0 × 10⁻³ for 1 mM ascorbic acid (Section S6.4. in the ESI†). In this estimate, 10⁻² was adopted as the accommodation coefficient of I₂.³⁶ In the absence of the gas-film transfer limitation, the R_g values for I₂ above ascorbic acid would be 10 s m⁻¹ and 26 s m⁻¹, respectively (the ESI†). These values are much smaller than the R_g values obtained here; this supports our experimental finding that the R_g value of 120 s m⁻¹ is the resistance for mass transfer of I₂ in the gas-film layer above aqueous surfaces (R_g-cont-w). This value of R_g-cont-w was used as the resistance for mass transfer of I₂ in the gas-film layer above clay samples in Section 3.3.

Fig. 4 and 5 suggest that uptake of I₂ by water differed with basin size, probably because of a difference in aqueous-phase turbulence between them. We did not obtain surface resistance for I₂ above water. As seen in eqn (29), dissociation of I₂ in water occurs much more strongly in the atmosphere than that observed here because the partial pressure of I₂ is very low, and I₂ uptake on aqueous surfaces in the atmosphere is determined not only by turbulence near surface water but also by hydrolysis in reaction (R1).³⁶ For ascorbic acid, because the leaf apoplast contains ascorbic acid, reaction (R3) is expected to proceed in the leaf interior, where O₃ is taken up by ascorbic acid.³⁹ However, this will happen only in the small number of plants that open their stomata at night.¹⁹

3.3 Uptake by clay samples

3.3.1 Loss and adsorption ratios of I₂. The first of our experiments with a flow of I₂–air(s) over the clay samples was conducted at 80% RH and yielded x_m(t) values that were definitely smaller than those of the blank experiment (Fig. 6). For each clay sample, x_m(t) was smaller in the large basins than in the small basins. These results showed that I₂ was deposited on the clay samples and removed from the gas phase. Uptake of I₂ by clay samples probably involved irreversible adsorption of I₂ in micropores of clay minerals because of the relatively large size of I₂, as reported for I₂ uptake by active carbons.⁴⁰ This decrease of x_m(t) varied among the clay samples, but the variation was small compared to that of the BET surface areas of the samples (Table 1). Fig. S5 and S6† show the results for 20% RH and 50% RH, respectively.

Fig. 6 Time series of x_m(t) in I₂–air(s) (P_in, 4.0 × 10⁻⁷ atm) after passage through a contactor containing (a) illite, (b) allophane, (c) montmorillonite, (d) kaolinite, (e) halloysite, or (f) AgroMAT AG-1 in run 1 at 80% RH in small basins (S/S_c, 0.187; sample, 0.73 g; green closed symbols) and large basins (S/S_c, 0.461; sample, 1.78 g; blue open symbols). Dashed curves show time series of x_m(t) in blank experiments at 80% RH.

Loss ratios of I₂ were defined as ΔQ_loss/Q_in, where ΔQ_loss = Q_in − Q_out, Q_in was the amount of I₂ entering the contactor, and Q_out was the integrated amount of I₂ observed at 0–1709 s in I₂–air(s) leaving the contactor. Loss ratios of I₂ decreased over successive runs for every clay sample. The decrease was greatest after run 1 (Fig. 7). Loss ratios decreased with increasing RH from 20% RH to 80% RH for all runs of allophane and for runs 3–7 of illite and kaolinite. This dependence on RH tended to strengthen as runs were repeated. Loss ratios for montmorillonite, halloysite, and AgroMAT AG-1 decreased between 20% RH and 50% RH and increased between 50% RH and 80% RH. However, the latter increase was also evident in the blank experiments. This relative-humidity dependence is discussed in Section 3.3.3 (see eqn (40)).

Fig. 7 Loss ratios of I₂, ΔQ_loss/Q_inversus RH for I₂–air(s) mixtures flowing over large basins of (a) illite, (b) allophane, (c) montmorillonite, (d) kaolinite, (e) halloysite, and (f) AgroMAT AG-1 samples in odd-numbered runs (P_in, 4.0 × 10⁻⁷ atm). Gray squares show ΔQ_loss/Q_in in blank experiments with P₀ as P_in.

Fig. 8 shows the time series of x_m(t) in odd-numbered runs for kaolinite at 80% RH along with the same profiles normalized to the maximum (x_m-max) in each run to bring out changes in the profile shape with successive runs. The monotonic decrease with successive runs of the ratios of the integrated amount of I₂ during the injection period (0–300 s) to that after 300 s meant that there was an increase in the ratio of I₂ adsorption to I₂ loss. Fig. 9 shows stacked column charts of ΔQ_loss/Q_in and ΔQ_ads/Q_in for odd-numbered runs with each clay sample at 80% RH. ΔQ_ads is the amount of I₂ reversibly adsorbed on the clay samples and was defined as ΔQ_ads = Q_aft − Q₃₀₀ − Q_saft where Q_aft is the integrated amount of I₂ observed at 301–1709 s in I₂–air(s) leaving the contactor, Q₃₀₀ is the amount of gaseous I₂ in the contactor at 300 s, and Q_saft is the integrated amount of I₂ in I₂–air(s) entering the contactor at 301–1709 s (Fig. 2). ΔQ_loss decreased and ΔQ_ads increased with successive runs; the sum of ΔQ_loss and ΔQ_ads, which represented the amount of I₂ accommodated by clay samples, remained almost constant or decreased more slowly than ΔQ_loss with successive runs. This behavior could be explained by using a two-stage model with two kinds of active sites on the surface and in the interior for loss of I₂. One kind was consumed on the surface, and the other retained its activity in the interior for uptake of I₂, as shown in Section 3.3.3. Similar behavior of ΔQ_loss/Q_in and ΔQ_ads/Q_in over successive runs was observed at 20% RH and 50% RH and for even-numbered runs (Fig. S7–S11†).

Fig. 8 (a) Time series of x_m(t) in I₂–air(s) for odd-numbered runs with kaolinite in the small basin at 80% RH (P_in, 4.0 × 10⁻⁷ atm). (b) Normalized time series from (a).

Fig. 9 Loss ratios (ΔQ_loss/Q_in, grey columns) and adsorption ratios (ΔQ_ads/Q_in, white columns) of I₂ for blank and odd-numbered runs with each clay sample, (a) in small basins (S/S_c, 0.187) and (b) in large basins (S/S_c, 0.461), at 80% RH (P_in, 4.0 × 10⁻⁷ atm). Green circles represent loss ratios, ΔQ_loss/Q_in, calculated from R_g-a (Tables S8–S13†) with eqn (S21).†

3.3.2 Apparent surface resistance for I₂. We calculated I₂ loss rates through surface uptake U(t), the rate constants k_1-a(t), and the deposition rates k_g-a(t) during the injection period (13–289 s) for each run of the clay experiments at the two basin sizes. Fig. 10 shows the results of runs 1 and 5 with illite at 80% RH. We then used a procedure analogous to our procedure for the aqueous solutions (Section 3.2) to obtain the apparent surface resistance, R_g-a, above the clay samples (Tables S8–S13) as described in Section S7.3 in the ESI.†

Fig. 10 Plots calculated from the experimental results during I₂ injection over illite at 80% RH showing (a) loss rates of I₂ by surface uptake, U(t), (b) the apparent first-order rate constants k_1-a(t), and (c) the apparent deposition rates k_g-a(t) in blank experiments and in runs 1 and 5 with small basins (S/S_c, 0.187; closed symbols) and large basins (S/S_c, 0.461; open symbols). Green squares indicate the results in run 1, blue triangles indicate the results in run 5, and grey circles indicate the results for the blank run (open circles, P_in = P₀; closed circles, P_in = 0.5P₀). The k_1-a(t) value for the blank with P_in = 0.5P₀ was subtracted from each value of k_1-a(t), and the difference was used to calculate the k_g-a(t) value.

If R_g-cont is the resistance for mass transfer of I₂ in the gas-film layer above clay samples in the contactor, the surface resistance for I₂ above clay samples, R_g-a-clay, is given by

R_g-a-clay = R_g-a − R_g-cont (30)

The R_g-cont-w value above ascorbic acid (120 ± 5 s m⁻¹; Section 3.2) was taken as the value of R_g-cont in eqn (30). Fig. 11 shows the R_g-a-clay values thus calculated from the average of R_g-a values for each clay sample with the R_g-cont-w value.

Fig. 11 Resistance for I₂ above clay samples of R_g-a-clay, R_g-clay-0, and R_g-clay at 20% RH, 50% RH, and 80% RH. The R_g-a-clay values (open symbols) were calculated with eqn (30) by subtracting the R_g-cont-w value (120 s m⁻¹) from the average of the R_g-a values with small and large basins for each clay sample in run 1 (red squares) and run 5 (blue circles) (Tables S8–S13†). Values of R_g-clay-0 (red closed squares) and R_g-clay (blue closed circles) were calculated with eqn (38) and eqn (40), respectively, using the values of parameters obtained in the simulation (Table S14†). Error bars are standard deviations of the two values: one is calculated for the results with the small basins and the other is calculated for the results with the large basins.

However, as is apparent in Tables S8–S13,† the values of R_g-a for all clay samples in even-numbered runs (P_in, 0.5P₀) are apparently smaller than the R_g-a values in odd-numbered runs (P_in, P₀), except for run 1. This pattern suggests that there was a systematic error in the determination of R_g-a. This error was probably caused by the fact that the degree of decrease in k_1-a(t) with time differed between even-numbered and odd-numbered runs because the values of P_in differed and because the differences varied between each run and blank. To reduce these errors, the mass-transfer processes of I₂ in a gas-film layer above clay samples need to be formulated and then taken into account in a simulated calculation to reproduce the decrease of I₂ uptake rates with time and to distinguish between I₂ uptake on clay samples and uptake on the wall surfaces of the contactor (blank). The parameters obtained in the simulation were used to estimate I₂ uptake rates at the low concentrations of I₂ that might be found in the atmosphere.

3.3.3 Simulation of I₂ uptake by clay samples. The simulation was conducted on the basis of a two-stage model in which the uptake of I₂ by clay samples occurred via an initial stage of rapid sorption onto surface sites followed by a stage of slow sorption onto interior sites such as the mesopores and the micropores of clay samples. Such a two-stage process has been documented for the sorption of volatile organic compounds on soil particles.³³ Kinetics of adsorption on porous solids such as clay particles in the gas phase and in liquid phase has been investigated on the basis of intraparticle diffusion models or surface reaction models.^33,41,42 Statistical rate theory also approached adsorption/desorption kinetics for homogeneous and heterogeneous solid surfaces.⁴¹ We used a surface reaction model assuming homogeneous surfaces. This model was simple but could reproduce the time series of x_m(t) in consecutive runs as shown below.

For the first stage, as mentioned in the previous section, we assumed that the mass-transfer rates of the I₂ in the gas-film layer above the clay samples were represented by a time-dependent function of k_m(t) that took positive values for the mass transfer from the gas to surfaces and negative values for the reverse transfer. This scenario is analogous to a model for gas-film layer diffusion followed by Langmuir-type adsorption (see the ESI†) and takes the form

where K_ads is the equilibrium coefficient for the adsorption of I₂ onto clay samples, and k_ma is a parameter needed to determine k_m(t); it is noteworthy that k_ma may take larger values than the actual mass-transfer rates of I₂ in the gas-film layer. Here, θ(t) is the fractional coverage on the surface, that is, q_t/q_∞, where q_t and q_∞ denote the amount of I₂ adsorbed at time t and when the clay surface is fully saturated, respectively.

For the second stage, some of the adsorbed I₂ is assumed to transfer between the surface and the interior sites and some is lost. As described in Section 3.3.1, the loss ratios of I₂ decreased over successive runs for every clay sample. The decrease was greatest after run 1 and remained finite through each set of experimental runs. This pattern suggests different kinds of active sites for loss of I₂. We hence assumed that there were two kinds of active sites: one kind was consumed on the surface, and the other retained its activity in the interior for uptake of I₂ as follows:

where k_f is the first-order rate constant for the transfer of adsorbents from the surface to the interior sites of the clay samples, K_pads is the equilibrium constant of I₂ between the surface and the interior, φ(t) is the number of the interior sites into which I₂ has been transformed as a fraction of q_∞, B_pn is a conversion factor used to convert units, k_loss-p is the first-order rate constant for loss of I₂ in the interior sites that retain their activity regardless of I₂ loss. Here, k_loss-s(t) is the time-dependent, first-order rate constant for loss of I₂ in the surface sites and is represented bywhere k_ls0 is the first-order rate constant for I₂ loss for fresh clay samples at the active sites that are lost per loss of I₂, and N_ls0 and n_ls(t) are the numbers of these active sites as a fraction of q_∞ for fresh clay samples and for clay samples exposed to I₂–air(s) during time t, respectively. Assuming that the decrease of n_ls(t) is equal to the loss of I₂, it follows that

Simulations using eqn (31)–(36) together with eqn (12), (27) and (28) were conducted to simultaneously reproduce the time series of x_m(t) for runs 1–5 for the same clay sample in two experimental sets, one set with small basins and another with large basins for each clay sample (Fig. S12–S17†). The simulation was conducted with common values of the parameters k_ma, K_ads, k_f, k_loss-p, k_ls0, and N_ls0 for both experimental sets and with a parameter q_∞ that varied between the sets. Fig. 12 shows the result for montmorillonite samples at 80% RH. The observed time-series of x_m(t) were reproduced by the simulation. The active sites for I₂ loss on the surface decreased with successive runs and almost all sites were lost at the end of run 5. The observed data were similarly reproduced by the simulation for all clay samples (Fig. S12–S17†). The values of the parameters obtained in the simulation are listed in Table S14.† The residual sums of squares, RSS, for allophane and kaolinite samples at 20% RH were larger than those for the other samples. Values of k_f decreased with increasing relative humidity for all clay samples (Table S14†). This decrease was consistent with the scenario that a water film formed in the interior, which increased with relative humidity and decreased surface areas in shale clay,⁴³ reduced rates for the transfer of I₂ between the surface and the interior of clay samples.

Fig. 12 Time series of x_m(t) in I₂–air(s) observed (pink circles) and simulated (grey curves) in runs 1–5 with each montmorillonite sample at 80% RH in (a) small basins (S/S_c, 0.187) and (b) large basins (S/S_c, 0.461). Green dashed curves indicate the time series of residence ratios of active sites for I₂ loss, n_ls(t)/N_ls0. Temporal duration of each run was about 1700 s and there were several minutes between runs; however, each panel shows plots of all data from runs 1–5 in consecutive 1800 s intervals for convenience.

The corresponding equilibrium constant, K_pads, decreased with increasing RH between 50% and 80% for illite, allophane, and kaolinite samples while it increased or remained almost constant for montmorillonite, halloysite, and AgroMAT AG-1 samples. It suggested that the water film might destabilize I₂ on the surface and in the interior to almost the same extent for the latter three clay samples since K_pads was the equilibrium constant of I₂ between the surface and the interior of clay samples. This equal destabilization might be the reason that the loss ratios for the latter three clay samples increased with RH between 50% and 80% (Fig. 7 and 11) as discussed below (see eqn (40)).

When uptake of I₂ proceeded at a constant rate at low concentrations of I₂ such as the concentrations in the atmosphere, we calculated the uptake rate k_g0 of I₂ by fresh clays with eqn (37) (see the ESI†)

Because the term k_ma⁻¹ on the right side of eqn (37) corresponds to mass transfer in a gas-film layer, the surface resistance above fresh clays, R_g-clay-0, is represented by

We assumed that k_loss-s(t) = 0 for clays in the environment because surface active sites might be consumed by exposure to naturally-occurring I₂ and other species. For clays with k_loss-s(t) = 0, the uptake rate k_g of I₂ by the clays and the surface resistance for I₂ above the clays, R_g-clay, are given by eqn (39) and (40), respectively, from eqn (37) and (38).

Values of k_g0, R_g-clay-0, k_g, and R_g-clay were calculated from the values of the parameters obtained in the simulation (Table S14†). The calculated values of R_g-clay-0 and R_g-clay are plotted in Fig. 11. The R_g-clay-0 values were greater than the R_g-a-clay values for run 1 and the difference was about 100 s m⁻¹ for illite and AgroMAT-AG-1 samples. The implication is that the value of R_g-cont in eqn (30) was overestimated. It is possible that the value of R_g-cont was smaller than the value of R_g-cont-w because the surface roughness of clay samples decreased resistance to mass transfer in the gas-film layer. For the same reason, the R_g-clay values were greater than the R_g-a-clay values for run 5. This also resulted from the fact that, even at the end of the injection period in run 5, k_1-a(t) did not decrease to a constant value which corresponded to the value expressed using eqn (40).

Fig. S18 and S19† show the plots of B_nq/q_∞/K_ads, r₁, and r₂ against RH for each clay sample in small basins (Fig. S18†) and large basins (Fig. S19†) where r₁ and r₂ are the first term and the second term, respectively, in the right of eqn (40). Fig. S18 and S19† show that values of B_pn/q_∞/K_ads decreased with RH between 50% and 80% for all clay samples. It meant that the adsorption of I₂ on the surfaces of clay samples increased with increasing RH. Hence if k_f, K_pads, and k_loss-p were constant, values of r₁ and r₂ would decrease with increasing RH and the loss ratios would increase for all clay samples. However, r₁ or r₂ or both increased with increasing RH for illite, allophane, and kaolinite samples because K_pads decreased with increasing RH. In contrast, values of K_pads increased or remained almost constant and the loss ratios increased with increasing RH between 50% and 80% for montmorillonite, halloysite, and AgroMAT AG-1. It suggested that relative humidity might destabilize I₂ in the interior more than on the surface for the former three clay samples and to almost the same extent as on the surface for the latter three clay samples. This difference might come from the difference in pH values of the water film in the interiors and buffering capacity against absorption of CO₂ among the clay samples.

Values of R_g-clay for all samples reached 241–402 s m⁻¹ at 20% RH, 288–666 s m⁻¹ at 50% RH, and 260–608 s m⁻¹ at 80% RH. These values were equal to a value of 330 s m⁻¹, which corresponded to a deposition velocity of 0.3 cm s⁻¹ in atmospheric model calculations for I^model₂, within a factor of two. However, if the clay content in soils, such as 10–20% in weight,^44,45 was taken into account, the surface resistance for I₂ with respect to uptake by clay minerals further exceeded the values used in the atmospheric models. We used the R_g-clay values calculated from eqn (40) to estimate non-stomatal bulk surface resistance in dry deposition (Section 3.4).

3.4 Influence of I₂ uptake by clay minerals on non-stomatal resistance for I₂ above ground surfaces

We estimated non-stomatal resistance for I₂ above ground surfaces (R_ns) with eqn (1) using the R_g values for I₂ above the clay minerals that we examined. The values of R_ac and R_cut in eqn (1) have been expressed as functions of friction velocity (u_*) and the leaf area index (LAI), both of which have been specified for each land use category (LUC) for dry and wet conditions.²⁰ Because the RH range in this study (20–80% RH) fell within the range of dry conditions, we calculated R_ac and R_cut values under dry conditions with eqn (41) and (42), respectively:where R_ac0 is the reference value for in-canopy aerodynamic resistance specific to each LUC and R_cut0 is the reference value for cuticle resistance under dry conditions specific to both depositing species and the LUC. Table S16† lists reference values of R_ac0, R_cut0 for SO₂, R_g for SO₂, and LAI for three LUCs (short grass and forbs, evergreen broadleaf trees, and deciduous broadleaf trees).²⁰

For soils in each LUC, we calculated R_ns values (1) using the reference value of R_g for SO₂ as the ground surface resistance (R_ns-SO2) and (2) using the R_g-clay values for I₂ above the clay samples as ground surface resistance (R_ns-RgI2). Fig. 13 shows plots of these resistances against u_* at 20% RH and 80% RH. The R_ns-RgI2 values were calculated from the minimum and maximum R_g-clay values for I₂ for all the clay samples. Values of R_ns-RgI2 consistently exceeded those of R_ns-SO2; the difference between them was smaller at 80% RH than at 20% RH because the R_cut values for SO₂ decreased with increasing RH, as seen in eqn (42), and R_ns was thereby more strongly controlled by R_cut than by R_g (eqn (1)).

Fig. 13 Plots of non-stomatal surface resistance, R_ns, against friction velocity, u_*, at 20% RH (red) and 80% RH (blue) if R_g is the reference value for SO₂ (solid curves, R_ns-SO2) or the R_g-clay value for I₂ (dashed curves, R_ns-RgI2) for (a) short grass and forbs, (b) evergreen broadleaf trees, and (c) deciduous broadleaf trees. For the deciduous broadleaf tree LUC, LAI is 0.5, the reference value of LAI in March (see the ESI†).

Fig. 14 shows the ratio of these two resistances (R_ns-RgI2/R_ns-SO2) for each LUC at 20% RH, 50% RH, and 80% RH against wind velocity at a height of 10 m (u₁₀), which was calculated by relating u₁₀ to u_* with eqn (S37).† For the short grass and forb LUCs, the R_ns-RgI2/R_ns-SO2 ratios at u₁₀ = 5 m s⁻¹ were approximately 1.1–1.4 at 20% RH, 1.1–1.6 at 50% RH, and 1.1–1.3 at 80% RH, whereas the values of R_g-clay were approximately 1.2–3.3 times the reference value of R_g for SO₂ above soils in this LUC (200 s m⁻¹). For the evergreen broadleaf tree LUC, the dependence of the R_ns-RgI2/R_ns-SO2 ratios on wind velocity was greater than for the short grass and forb LUCs because the roughness length was longer in the former than in the latter. The R_ns-RgI2/R_ns-SO2 ratios at u₁₀ = 10 m s⁻¹ were approximately 1.5–1.8 at 20% RH, 1.3–1.6 at 50% RH, and 1.1–1.2 at 80% RH whereas the values of R_g-clay were approximately 2.4–6.6 times the reference value of R_g for SO₂ above soils in this LUC (100 s m⁻¹). For the deciduous broadleaf tree LUC, the R_ns-RgI2/R_ns-SO2 ratios at u₁₀ = 10 m s⁻¹ were approximately 1.1–1.6 at 20% RH, 1.2–1.8 at 50% RH, and 1.1–1.4 at 80% RH. Fig. 14 also shows the R_ns-RgI2/R_ns-SO2 ratios calculated from the R_g-clay values above the AgroMAT AG-1 sample (dashed curves). Values of this ratio at 80% RH were as much as 1.2 for all LUCs. Values of this ratio became greater at lower relative humidity and the values at 20% RH were as much as 1.6 for the evergreen broadleaf tree LUC and as much as 1.3 for the other LUCs. The change in R_ns by switching the R_g values between I₂ and SO₂ in the scaling method could thus be appreciable at 20% RH.

Fig. 14 R _ns-RgI2/R_ns-SO2versus wind velocity at 10 m of height at (1) 20% RH, (2) 50% RH, and (3) 80% RH for (a) short grass and forbs, (b) evergreen broadleaf trees, and (c) deciduous broadleaf trees. Red regions indicate values calculated from the range of the R_g-clay values. Dashed curves indicate values calculated from the R_g-clay values above the AgroMAT AG-1 sample. The reference values of R_g for SO₂ are 100 s m⁻¹ for evergreen broadleaf tree LUCs and 200 s m⁻¹ for the other LUCs. For deciduous broadleaf tree LUCs, roughness length, z₀, is set at 0.4 m and LAI is 0.5, the reference value of LAI in March (see the ESI†).

4. Conclusion

We used the rectangular pulse method with an IBBCEAS instrument to determine uptake rates of I₂ by aqueous solutions and clay particles in a gas mixture of 400 ppmv CO₂ and humidified air at 283 K. Uptake of I₂ proceeded much more rapidly by aqueous ascorbic acid than by water; the former was limited by mass transfer in the gas-film layer. Reactions of I₂ with ascorbic acid were expected to proceed in the leaf interior. However, this would happen only in the small number of plants that open their stomata at night.

Uptake of I₂ by clay particles was confirmed at 20–80% RH. Uptake rates of I₂ varied among the clay samples, but the variation was small compared to that of the BET surface areas of the samples. Uptake rates of I₂ decreased with successive runs and remained finite through each set of experimental runs. These finite rates decreased with increasing relative humidity from 20% RH to 80% RH for illite, allophane, and kaolinite samples. This dependence on relative humidity was different from that for SO₂, a commonly used proxy for I₂ in scaling methods. Ratios of I₂ loss and adsorption decreased and increased, respectively, with the exposure time of clay samples to I₂ and their changes were largest during the initial periods after exposure to I₂. Confirmation of the uptake of I₂ by clay minerals at 20–80% RH suggested that it contributed to the dry deposition of I₂ on soils as much as other processes such as reactions of I₂ with organic matter. Uptake of I₂ by clay samples probably proceeded through irreversible adsorption of I₂ in micropores of clay minerals, as reported for I₂ uptake by active carbons.⁴⁰

The time-series of I₂ were reproduced in the simulation by assuming a two-stage process. The parameters obtained in the simulation were used to estimate I₂ uptake rates at low concentrations of I₂ that might be found in the atmosphere. For fresh clay samples, the surface resistance for I₂ above them was smaller than that for I^model₂ above soils applied to atmospheric model calculations, such as 200 s m⁻¹. For clay samples having been exposed to a gas mixture of I₂, the surface resistance, however, exceeded the values used in atmospheric models. Further excess was expected by taking into account the clay content in soils. For vegetated surfaces such as those near the Fukushima Dai-ichi nuclear power plant, the change in R_ns by switching the R_g values between I₂ and SO₂ in the scaling method was smaller at 80% RH than at 20% RH, and it could be appreciable at 20% RH. For vegetated surfaces, switching the R_g values between I₂ and SO₂ in the scaling method thus remained useful for estimating the dry deposition velocity of I₂ at 80% RH, but it might result in substantial errors for the surface resistance at 20% RH, unless surface resistance for I₂ above soils is controlled by other processes such as reactions of I₂ with organic matter in soils. This suggested that the dry deposition processes of I₂ or I^model₂ needed to be estimated separately before and after sunrise when I₂ was released at night.

In the blank experiments (Section 3.1), the loss and adsorption of I₂ on inert surfaces (PTFE wall surfaces) increased with increasing RH. This pattern was similar to the pattern of R_cut for SO₂, as expected from eqn (42). As seen in Fig. 13, R_ns values above vegetated surfaces at 80% RH were determined mostly by R_cut rather than by R_g. The estimate of R_cut for I₂ was thus important for evaluating the dry deposition velocity of I₂ at night. A study on R_cut was, however, beyond the scope of this work. Although we did not explicitly drive dry deposition velocities in this study, the surface resistance data we obtained can be used in series-resistance models of dry deposition embedded in atmospheric transport and dispersion models to assess the human risk of radioiodine.

Author contributions

The laboratory experiments and simulated calculations were performed by SK. The manuscript was written through the contributions of all authors. All authors have given approval to the final version of the manuscript.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

We thank Dr Zheng-Ming Wang (AIST) for providing data on the BET surface area of AgroMAT Clay Soil AG-1. This work was supported by the Japan Society for the Promotion of Science (grant number JP18K11633).

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Footnote

† Electronic supplementary information (ESI) available. See https://doi.org/10.1039/d2ea00039c

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