Technical Note: Determination Of Binary Gas Phase .
https://doi.org/10.5194/acp-2019-1050Preprint. Discussion started: 9 December 2019c Author(s) 2019. CC BY 4.0 License.Technical note: Determination of binary gas phase diffusioncoefficients of unstable and adsorbing atmospheric trace gases atlow temperature – Arrested Flow and Twin Tube methodStefan Langenberg1,a , Torsten Carstens1,2 , Dirk Hupperich1 , Silke Schweighoefer1,b , andUlrich Schurath31Institut für Physikalische und Theoretische Chemie, University of Bonn, Bonn, GermanyKarlsruher Institut für Technologie, Karlsruhe, Germany3Institut für Umweltphysik, University of Heidelberg, Heidelberg, Germanyanow at: Klinik und Poliklinik für Hals-Nasen-Ohrenheilkunde/Chirurgie, University of Bonn, Bonn, Germanybnow at: UP GmbH, Ibbenbüren, Germany2Correspondence: Stefan Langenberg (langenberg@uni-bonn.de)Abstract. Gas phase diffusion is the first step for all heterogeneous reactions under atmospheric conditions. Knowledge of binary diffusion coefficients is important for the interpretation of laboratory studies regarding heterogeneous trace gas uptake andreactions. Only for stable, nonreactive and non polar gases well-established models for the estimation of diffusion coefficientsfrom viscosity data do exist. Therefore, we have used two complementary methods for the measurement of binary diffusion5coefficients in the temperature range of 200 K to 300 K: the arrested flow method is best suited for unstable gases and thetwin tube method is best suited for stable but adsorbing trace gases. Both methods were validated by measurement of diffusioncoefficients of methane and ethane in helium and air and nitric oxide in helium. Using the arrested flow method the diffusioncoefficients of ozone in air, dinitrogen pentoxide and chlorine nitrate in helium and nitrogen were measured. The twin tubemethod was used for the measurement of the diffusion coefficient of nitrogen dioxide and dinitrogen tetroxide in helium and10nitrogen.Copyright statement. This work is distributed under the Creative Commons Attribution 4.0 License.1IntroductionThe critical role of heterogeneous reactions in atmospheric chemistry is widely accepted. The diffusion of gas moleculestowards the surface is the first step in a heterogeneous reaction, and it can influence and sometimes even control the overall rate15of the uptake of a trace gas onto the surface (Kolb et al., 2010; Tang et al., 2014a). Diffusion also plays a role in atmosphere– biosphere interactions: the incorporation of trace gases like ozone and nitrogen dioxide into leaves and isoprene out throughstomata is diffusion controlled (Laisk et al., 1989; Eller and Sparks, 2006; Fall and Monson, 1992).1
https://doi.org/10.5194/acp-2019-1050Preprint. Discussion started: 9 December 2019c Author(s) 2019. CC BY 4.0 License.Table 1. Lennard-Jones parameters of the species investigated in this studySpeciesFormulaM[g mol 1σ /k][Å][K]MethodSourceHeliumHe4.002.55110.2vPoling et al. (2004)NitrogenN228.013.79871.4vPoling et al. (2004)28.813.71178.6vPoling et al. (2004)AirMethaneCH416.043.758148.6vPoling et al. (2004)EtheneC2 H428.054.163224.7vPoling et al. (2004)Nitric oxideNO30.013.492116.7vPoling et al. (2004)Nitrogen dioxideNO246.013.765210.0vBrokaw and Svehla (1966)OzoneO348.003.875208.4bMassman (1998)Dinitrogen tetroxideN2 O492.014.621347.0vBrokaw and Svehla (1966)Chlorine nitrateClONO297.464.470364.7bPatrick and Golden (1983)Dinitrogen pentoxideN2 O5108.014.570450.0bPatrick and Golden (1983)v obtained from viscosity data, b obtained from Tb and Vb using Eqns. (4).Marrero and Mason (1972); Massman (1998); Tang et al. (2014a, 2015) and Gu et al. (2018) compiled and evaluated theavailable experimental data of diffusion coefficients of atmospheric trace gases. However, the existing compilations focus on20stable gases, experimental diffusion coefficients of ozone, nitrogen dioxide, chlorine nitrate and dinitrogen pentoxide are stillmissing. They cannot be predicted with the required accuracy because detailed kinetic theory requires intermolecular potentialswhich are not generally available for atmospherically relevant compounds.Chapman and Enskok derived the following equation from kinetic theory of gases for the molecular binary diffusion coefficient253D 16s2πkT (mA mB )mA mB kT2πσAB ΩD p (1)where m is the mass of the molecules, k is the Boltzmann constant, p the pressure and T is the absolute temperature. σAB isthe characteristic length of the intermolecular force law, ΩD is the dimensionless collision integral of diffusion. It depends onthe temperature and the characteristic energy AB of the Lennard-Jones potential describing the intermolecular force (Polinget al., 2004; Marrero and Mason, 1972). ΩD as function of temperature is expressed by the fit function30ΩD ACEG ΘB exp(DΘ) exp(F Θ) exp(HΘ)(2)where Θ kT / AB , A 1.06036, B 0.15610, C 0.19300, D 0.47635, E 1.03587, F 1.52996, G 1.76474,H 3.89411 (Neufeld et al., 1972; Poling et al., 2004). The equations AB A B ,σAB σA σB2(3)2
https://doi.org/10.5194/acp-2019-1050Preprint. Discussion started: 9 December 2019c Author(s) 2019. CC BY 4.0 License.are usually employed to relate the interaction parameters of the Lennard-Jones potential between components A and B to the35interaction potential parameters of the individual components. A tabulation of the potential parameters of the species consideredin this work is given in Table 1. The Lennard-Jones parameters σ and are generally not available for unstable atmospherictrace gases. Patrick and Golden (1983) estimated them by the equations1/3σ 1.18 Vb /k 1.21 Tb,(4)from Tb the normal boiling point temperature and Vb the molar volume at boiling point. In cases where Vb cannot be determined40experimentally, it is obtained from tables of atomic volumes using the LeBas method. Patrick and Golden (1983) assumed thesystematic errors of σ and obtained by this method to be 20%.The diffusion coefficient as function of pressure in a narrow temperature range close to the reference temperature T0 isusually expressed as bp0TD D0pT045(5)where T0 273.15 K are the standard temperature and p0 101325 Pa the standard pressure (STP). Close to the referencetemperature T0 , the temperature coefficient b can be calculated as follows (Poling et al., 2004) ln ΩD ln DT0 ΩD33 ,b ln T2 ln T2 ΩD Tb 50Θ3 2 ΩD ΩD Θ (6)(7)From Eq. (2) it is obtained by derivation ΩDABCDEFGH B 1 ΘΘexp(DΘ) exp(F Θ) exp(HΘ)(8)Fuller et al. (1966) developed a simple correlation equation for the estimation of gas phase diffusion coefficients usingadditive atomic volumes VA and VB for each species. With the molar masses MA and MB ([M ] g mol 1 ) of each speciesand [p] bar, the diffusion coefficient ([D] cm2 s 1 ) is given by55MAB 21/MA 1/MBD 0.00143 (9)T 1.751/3MAB (VA(10)1/3 V B )2 pTabulations of atomic volume increments are summarized by Poling et al. (2004) and Tang et al. (2014a).In the atmosphere, for typical submicron-sized aerosol particles, gas-phase diffusion does not usually limit uptake. Therefore,60for modelling atmospheric processes, it is sufficient to use diffusion coefficients obtained using the Fuller method. However,in many laboratory experiments for the measurement of mass accommodation coefficients, conditions are such that gas-phasediffusion limitations need to be taken into account (Kirchner et al., 1990; Müller and Heal, 2002; Davidovits et al., 2006).3
https://doi.org/10.5194/acp-2019-1050Preprint. Discussion started: 9 December 2019c Author(s) 2019. CC BY 4.0 License.Figure 1. Arrested flow method: a pulse of trace gas is introduced into the column by simultaneously switching valves V3 and V4 for a shorttime. After the peak has reached the middle of the column, the carrier gas is bypassed by switching V1 and V2 for arrest times ta between 0and 200 s. After each arrest time ta the corresponding peak shape is recorded by the detector D. The gas flow is controlled by flow controllerFC.2Methods2.165Arrested flow methodThe arrested flow (AF) method was first described by Knox and McLaren (1964) and McCoy and Moffat (1986): the diffusioncoefficient of a given trace gas is derived from the broadening of width ςt of trace gas plugs arrested for different times ina long void gas chromatography glass column (length l 2.8 m, radius r 0.189 cm). A plug is generated by injecting asmall amount of dilute trace gas into a steady flow of carrier gas by means of computer controlled solenoid valves. The flowis arrested when the plug has travelled halfway down the tube, see Fig. 1. In the absence of turbulence, the initial plug profile70spreads out along the tube by molecular diffusion only. Until the flow is arrested, the box profile of the trace gas has reshapedto Gaussian by Taylor diffusion (Taylor, 1953, 1954), if the conditionlV̇πD(11)is fulfilled, where V̇ is the carrier gas flow rate. After a given arrest time ta , the trace gas is eluted with 20 sccm (1 sccm 1 ml min 1 at 273.15 K and 1013 hPa) and the concentration profile is measured with a suitable gas chromatography detector.75This procedure is repeated for different arrest times ta . The experimental peak profiles are fitted to Gaussians to determine thepeak variance ςt2 . According to theory based on Fick’s second law of diffusion 2 c c D t z z 2 t(12)a plot of ςt2 versus arrest time ta should be linear. The slope of the plot of ςz vs. ta is given by ςz2 2D ta(13)4
https://doi.org/10.5194/acp-2019-1050Preprint. Discussion started: 9 December 2019c Author(s) 2019. CC BY 4.0 License.80Since the variance is measured in units of time, it has to be converted to units of length using the gas flow speed v in the column ςz2 v 2 ςt2 .(14)From the carrier gas mass flow ṅ, temperature T and pressure p in the column which approximately equals atmosphericpressure, the flow speed can be determined by85v ṅRTπr2 p(15)The column is embedded in an aluminum block which is cooled by a recirculating cryostat (Lauda RLS6). The aluminumblock is mounted in a plastic box insulated by Styrodur. The column temperature homogeneity is monitored with 2 Pt-100sensors connected to the upper and lower parts of the column coil. The solenoid valves are connected by 1/16" Teflon tubes andcontrolled by computer using the software Asyst 3.1 (Keithley). At each temperature, 12 to 20 peaks are recorded at different90arrest times.The systematic error of the determined diffusion coefficients using this method primarily depends on the systematic error ofmeasuring the inner diameter of the column and the systematic error of the mass flow rate. A Teflon tube pushed through thecolumn was used to determine the length of the column. The void volume of the column was determined by filling the columnwith water and measuring the weight of the water. From volume and length, the cross-sectional area and radius are calculated,95yielding a mean radius with a systematic error of 0.5%. After the experiments, the column was cut into small fragments.The inner diameter of these fragments was measured using a caliper gauge. We found that the inner diameter synchronouslychanges with column winding with a variability of 1%. When using Eq. (14) to transform ςt to ςz , not the mean velocitybut the actual velocity v and radius r at the location where the peak is arrested are relevant. Therefore, the actual systematicerror of the radius is about 1%. The mass flow controllers were calibrated using a soap bubble flow meter. Thus, the systematic100error of the mass flow rate is about 1.5%. This sums up to a total theoretical systematic error of the AF method to about 7%.The random error of the method is about 0.4%, twice the repeatability 0.2% of the flow rate.2.2Twin tube methodThe twin tube (TT) method is a steady state technique for diffusion coefficient measurements over a wide temperature rangeusing a diffusion bridge (Marrero and Mason, 1972). It is insensitive to wall adsorption effects which may invalidate AF105measurements at low temperature. Our apparatus consists of two parallel horizontal flow tubes (length 2 m, inner diameter10 mm) which are connected by a bunch of n 220 carefully thermostatted fused silica capillaries of radius r (39.2 0.4) µmand length l (20.8 0.3) mm, see Fig. 2. The capillaries are embedded in a block made of brass. The cooling liquid of acryostat (Lauda RLS6) circulates through the brass block, thereby covering the range from ambient temperature down to 198 K.Close to the diffusion bridge, the temperature in the block is measured with two Pt-100 sensors. The capillaries are pasted into110two parallel slits in a short section of the parallel flow tubes that is made of stainless steel. Up and downstream of the brassblock, the flow tubes consist of glass. The entire apparatus consisting of the flow tubes and the diffusion bridge are housed5
https://doi.org/10.5194/acp-2019-1050Preprint. Discussion started: 9 December 2019c Author(s) 2019. CC BY 4.0 License.Figure 2. Schematic diagram of the twin tube experiment (false to scale): a diffusion bridge is connecting two flow tubes. Downstream thediffusion bridge some gas is continuously sampled for analysis to determine the trace gas concentrations c0 and c.Figure 3. Twin tube method, continuous mode: a partial current is sucked through the detector D by a mass flow controller FC. A second4-port valve enables to switch the detector to pure carrier gas to record the baseline.6
https://doi.org/10.5194/acp-2019-1050Preprint. Discussion started: 9 December 2019c Author(s) 2019. CC BY 4.0 License.Figure 4. Twin tube method, peak mode: the carrier gas is admitted first through the sample loop V1 or V2 of a six-port valve. Then thecontent of the sample loop is pushed into the detector as peak after switching the six-port valve.Figure 5. Twin tube method with internal standard as used for NO2 in N2 : the species under investigation is monitored in continuous mode,the internal standard is sampled by a 6-port valve and detected by a flame ionization detector.in a large insulated box which can be cooled down to 260 K. After changing the setting of the recirculating thermostat by anincrement of 10 K it takes about 1 h until the temperature of the diffusion bridge has equilibrated.Pure carrier gas is flown through one of the flow tubes, while a constant trace gas concentration c0 is maintained in the115other. A concentration gradient is established along the capillaries. This gives rise to a constant flux JD by molecular diffusionthrough the diffusion bridge described by Fick’s first law of diffusion cc0 c DJD D z tl(16)where c is the trace gas concentration at the low concentration end. Pressure differences between the flow tubes are carefullyeliminated to suppress trace gas transport by viscous flow through the capillaries. This requires that both flow tubes are totally120symmetric. The difference pressure is monitored using a differential high accuracy pressure transducer (MKS model 398,measuring range 10 4 Torr to 1 Torr). By measuring the concentration ratio in both flow tubes, downstream the diffusion7
https://doi.org/10.5194/acp-2019-1050Preprint. Discussion started: 9 December 2019c Author(s) 2019. CC BY 4.0 License.bridge the diffusion coefficient is obtained byD 125V̇ l cnπr2 c0(17)when c c0 where V̇ is the volume flow rate of the carrier gas. The ratio of mass transport by viscous flow to diffusion flowthrough the capillaries is given by (viscosity η)JVr2 p .JD16ηD(18)Therefore, the ratio of interfering viscous trace gas to mass flow by diffusion was minimized by using narrow capillaries. Forthe diffusion of NO2 in N2 at standard pressure and temperature, the fraction of viscous flow can be held 1% when keeping130the differential pressure p 2 10 4 Torr. During the TT-experiments the differential pressure was maintained low so thatthe fraction of viscous flow was less than 0.3%.A trace gas detector is required which is linear over a wide concentration range and stable over time. Depending on the tracegas and the detector properties, the trace gas can either be detected by continuous mode (Fig. 3) or by peak mode (Fig. 4).The low concentration is determined with a random error of about 1%. The signal of the trace gas detector is fed into aA/D-converter with 16-bit resolution (Data Translation DT2705/5715A).135The supplier of the capillary columns used in this work as raw material for assembling the diffusion bridge reports theinner diameter with a systematic error of 10%. This is too much for the measurement of diffusion coefficients. Therefore, twosegments of the column were used to determine the inner diameter by weighing an empty and a water filled section of thecapillary column. Thereby the radius of the diffusion bridge capillaries was determined with a systematic error of 1%. We triedto validate the result by electron micrography of two cross sections of the column material. However, the systematic error of140the inner diameter measured by electron micrography is about 5%. When assuming a systematic error of the flow rate of 1.5%,this results in a total systematic error of the method of 4%. The random error of the method depends on the random error ofabout 1% of the determination of the lower concentration c.Later on during the experiments it was found that some capillaries of the diffusion bridge became blocked by dust or condensed matter. Fortunately, the TT method can be utilized to measure diffusion coefficients of several species simultaneously145when using the peak mode and a gas chromatograph as detector. If the diffusion coefficient of one of the trace gases has beendetermined with another reliable technique at one temperature, this diffusion coefficient can be used as internal standard, seeFig. 5. It is assumed that the effective area of the capillaries is independent of temperature.3 Results and discussionTo determine D0 and b, the diffusion coefficients obtained at different temperatures were fitted by nonlinear regression to150Eq. (5). They were weighted by the inverse of their statistical error where available. The results are summarized in Table 3together with the diffusion coefficients calculated by the Chapman-Enskok theory using Eq. (1) and the Fuller method usingEq. (10). The input parameters used are summarized in Table 1.8
rint. Discussion started: 9 December 2019c Author(s) 2019. CC BY 4.0 License. (b) 0.60.6 0.4 0.5D / [cm2s 1]0.5 0.4D / [cm2s 1] 220240 arrested flowtwin tubeDunlop & Bignell (1987)McCoy & Moffat (1986)260280300 0.30.3 200 320200220T / [K]240arrested flowtwin tubeDunlop & Bignell (1990)260280300320T / [K]Figure 6. Comparison of diffusion coefficients obtained by the AF and TT method: (a) diffusion coefficient of methane in helium, comparedto data of Dunlop and Bignell (1987) (fit D0 0.582 cm2 s 1 , b 1.66) and D 0.614 cm2 s 1 at 297 K of McCoy and Moffat (1986). (b)Diffusion coefficient of ethene in helium compared to data of Dunlop and Bignell (1990) (fit D0 0.508 cm2 s 1 , b 1.68). The dashedline is calculated by the Lennard-Jones model.Table 2. Measured diffusion coefficients D0 at the reference temperature T and reference data of diffusion coefficients Dr . With 298 K asreference temperature, the measured diffusion coefficients were extrapolated to this temperature using Eq. (5).SpeciesCarrierD0 /Dr 1TDr[K][cm2 s 1 ]AFTTNOHe2730.624a6%7%CH4He2730.582b6%5%C2 H4He2730.508c-2%-8%CH4air2980.221d8%0%C2 H4air2980.163d8%-4%Source: a Dunlop and Bignell (1992), b Dunlop and Bignell (1987), cDunlop and Bignell (1990), d Tang et al. (2015)9
0.16 int. Discussion started: 9 December 2019c Author(s) 2019. CC BY 4.0 License.(b)0.14 0.12 0.10D / [cm2s 1]0.15D / [cm2s 1]0.20(a) 0.10 2002202400.08 arrested flowtwin tubeTang (2015)Cowie & Watts (1971)260280 300200T / [K] 220240260arrested flowtwin tubeTang (2015)280300T / [K]Figure 7. (a) Diffusion coefficient of methane in air, recommended value of D 0.221 cm2 s 1 at 298 K of Tang et al. (2015) and D 0.217cm2 s 1 of Cowie and Watts (1971) at 298.2 K. For the TT method only the fit function is shown. (b) Diffusion coefficient of ethene in airas function of temperature, recommended value of Tang et al. (2015) D 0.163 cm2 s 1 at 298 K. The dashed line is calculated using theLennard-Jones model.3.13.1.1155Method validationDiffusion of methane (CH4 ) and ethene (C2 H4 ) in helium and airThese gases were investigated with both methods for validation purposes. They are stable and non adsorbing, reference literature data of diffusion coefficients do exist. The diffusion coefficients in helium have been measured previously over a widertemperature range with high precision and accuracy by Dunlop and Bignell (1987) for methane and Dunlop and Bignell (1990)and ethene. Evaluated diffusion coefficients of hydrocarbons in air at 298 K are reported in the review of Tang et al. (2015).In addition, the diffusion coefficients can be calculated using the Lennard-Jones model and the Chapman-Enskok theory using160Eq. (1).We have used a flame ionization detector (Carlo Erba FID 40 with EL980 control unit) which is fast, sensitive and linear overa wide concentration range to measure the hydrocarbons. For the AF experiments, 0.1% of methane or ethane in helium or airwere injected as a 300 ms pulse. About 20–26 sccm were used as flow rate. The arrest time was varied from 0 to 200 s. For theTT experiments 0.5% and 1% methane in air, 0.4% methane in He, 0.4% ethene in He and 0.5% ethene in air were admitted in165the flow tube. Downstream of the diffusion bridge, the trace gas was analyzed using the peak mode setup, see Fig. 4.10
0.60.50.4D / [cm2s int. Discussion started: 9 December 2019c Author(s) 2019. CC BY 4.0 License. 200220240arrested flowtwin tubeDunlop & Bignell (1992)260280300T / [K]Figure 8. Diffusion coefficient of NO in He measured by AF and TT method as function of temperature. For the TT method only the fitfunction is shown. Experimental results of Dunlop and Bignell (1992) and a fit to Eq. (5) with D0 0.624 and b 1.64 are displayed asreference. The dashed line is calculated using the Lennard-Jones model.The results are summarized in Table 2 and Table 3, in Fig. 6 and Fig. 7. Higher diffusion coefficients were found for the AFmethod compared to the TT-method.3.1.2Diffusion of nitric oxide (NO) in heliumNO was monitored by a chemiluminescence detector (Marić et al., 1989) which was adapted to the lower flow rates of the diffu170sion experiments. In the detector, NO reacts with O3 in a low pressure reaction chamber (0.9–2 mbar) in a chemiluminescencereaction:NO O3 NO2 O2 hν(R1)The emitted photons were detected using a Hamamatsu R562 photomultiplier tube.For the AF experiment 100 ppm NO were injected as 300 ms pulse into the flow tube with a flow rate of 22.5 sccm. The175valves were connected using stainless steel tubes. For the TT experiment 30–70 ppm NO in He were admitted into the diffusionbridge. The setup displayed in Fig 3 was used to monitor NO in the continuous mode. It was found that after measuring thehigh concentration c0 , it needs several hours until the baseline has stabilized when measuring clean carrier gas. Therefore, itis not possible to measure c and c0 in succession. Thus, first c0 was measured at room temperature. Then the detector wasswitched to clean carrier gas until the baseline has stabilized. Then c was measured after lowering the temperature until the11
https://doi.org/10.5194/acp-2019-1050Preprint. Discussion started: 9 December 2019c Author(s) 2019. CC BY 4.0 License.0.18 0.16 0.12D / [cm2s 1]0.14 0.10 0.08 200220240260280300T / [K]Figure 9. Diffusion coefficient of O3 in air as function of temperature. The shaded area shows the diffusion coefficient expected by theLennard-Jones model. The upper border is calculated with D(T, 0.8σAB , 0.8 AB ), the lower border with D(T, 1.2σAB , 1.2 AB ) usingEq. (1) corresponding to a 20% uncertainty of σAB and AB . The dotted line is calculated by Fuller’s model.180signal has stabilized. After arriving at 200 K, c0 was measured again. Then the measurement was repeated by stepwise raisingthe temperature. Therefore, the complete measurement extended over several days.The diffusion coefficients for NO obtained by the two methods are in fair agreement with the reference data of Dunlop andBignell (1992), see Fig. 8 and Table 2. In contrast to diffusion coefficients of methane and ethane, the diffusion coefficientsobtained by the TT method are slightly larger than the diffusion coefficients obtained by the AF method.185Comparing all diffusion coefficients obtained for stable gases to reference data, it is found that the deviation of the AF andTT method is less than 8% compared to the reference data. However, for the TT method this is a little more, as expected astheoretical systematic error, which can be explained by decreasing effective areas of the diffusion capillaries.3.23.2.1190Diffusion of atmospheric trace gasesDiffusion of ozone (O3 ) in airThe diffusion coefficient of ozone in air has never been measured before. Ivanov et al. (2007) reported D (0.53 0.03) cm2 s 1for the diffusion of O3 in He at 298 K. Since ozone is an unstable but non-adsorbing species, only the AF method was usedfor the determination of the diffusion coefficient. A fast and sensitive ozone detector is required to record the ozone peaksleaving the column. A suitable detection technique is chemiluminescence arising from the reaction of ozone with Coumarin12
https://doi.org/10.5194/acp-2019-1050Preprint. Discussion started: 9 December 2019c Author(s) 2019. CC BY 4.0 License.47 (Lambda Physik, 7-diethylamino-4-methylcoumarin), adsorbed on silica-gel plates (Schurath et al., 1991). Chemilumines195cence is emitted in the range λ 440 550 nm which is detected by photomultiplier (Hamamatsu 931 B). The anode currentwas admitted through a 100 kΩ resistor and measured as voltage by a microvoltmeter (Keithley model 155).Ozone containing air was generated in an aluminum block enclosing an elliptically shaped polished chamber. A rod-shapedlow-pressure Hg UV-lamp and a quartz tube with air running through are mounted parallel in the focal lines of the ellipticallyshaped chamber. Thereby, the UV radiation is focused to the air flowing through the quartz tube (Becker et al., 1975). 5 blocks200arranged in series were used yielding an ozone concentration of about 40 ppm.The injection time was varied from 250 ms to 500 ms and the arrest time was varied from 0 s to 360 s. It was found that themaxima of the eluted peaks did not coincide: peaks arrested longer were eluted later. Later it was found that this was causedby leaking sealings of the solenoid valves, which were made of neoprene. Therefore, at some temperatures only arrest times ofless than 100 s were included in the fit of ςz2 vs. ta . The statistical error of the slope of ςz2 vs. ta was up to 3.7%.205With regard to the systematic error of 7% of the AF method for the diffusion coefficients (Section 3.1.1), the obtained valuewith error ranges is D0 0.15 0.01 cm2 s 1 . This value is in accordance with the value of D0 0.1444 cm2 s 1 estimatedby Massman (1998) from critical constants using the model of Chen and Othmer (1962).3.2.2Diffusion of nitrogen dioxide (NO2 ) and dinitrogen tetroxide (N2 O4 ) in helium and nitrogenNO2 is in equilibrium with its dimer2102 NO2N2 O 4(R2)Therefore, a pure sample of NO2 for determinations of D is not available. Chambers and Sherwood (1937) assumed thatthe ratio of D(NO2 )/D(N2 O4 ) 1.43 yielding D0 (NO2 ) 0.121 cm2 s 1 in nitrogen from their value of D0 (N2 O4 ) (0.0845 0.0005) cm2 s 1 . Massman (1998) estimated D0 (NO2 ) 0.146 cm2 s 1 from D0 (N2 O4 ) 0.101 cm2 s 1 in nitrogen reported by Sviridenko et al. (1973). Since NO2 is an adsorbing species, the diffusion coefficient can only be measured215using the TT method. The total flux of the pseudo species NIV NO2 2 N2 O4 though the capillaries is given byJ(NIV ) D(NO2 )c0 (NO2 ) 2D(N2 O4 )c0 (N2 O4 ).l(19)At higher temperatures and when keeping the concentration of NO2 low, diffusion of N2 O4 can be neglected. The degree ofdissociationα 220p(NO2 )p(NIV )(20)can be calculated from the equilibrium constantK p2 (NO2 )p(NIV ) 2α2 p p(N2 O4 )p1 α(21)where p 1 bar. The equilibrium constant close to 250 K is estimated from JANAF Thermochemical Tables (NIST, 1998)ln K 21.16 6878.1 K/T.(22)13
https://doi.org/10.5194/acp-2019-1050Preprint. Discussion started: 9 December 2019c Author(s) 2019. CC BY 4.0 License.Table 3. Results of fit of Eq. (5) to the measured data. The errors listed are the errors obtained by the fit. Diffusion coefficients calculated bythe Lennard-Jones and Fuller method are displayed for comparison. D0 (N2 O4 ) is estimated by nonlinear regression of Eq. (23) arbitrarilysetting b 1.75. For N2 O5 the fit parameters of Eq. (24) are rTT199–293C2 H4HeAF197–284C2 H4HeTT218–294C2 H4airAF197–295C2 eTT251–299NO2N2TT251–319O3airAF196–303N2 O4HeTT202–299N2 298N2 O5HeAF245–298N2 O5N2AF246–298D02 1[cm sLennard-Jones modelb2 1]0.618 0.0020.610 0.0010.205 0.0010.188 0.0030.497 0.0020.468 0.0040.150 0.0000.133 0.0010.662 0.0010.667 0.0130.520 0.0010.145 0.0010.153 0.0010.221 0.0140.084 0.0040.310 0.0040.085 0.0010.300 0.0120.081 0.005D0[cm sbFuller et al. (1966)D0[cm2 s 1 ]]1.68 0.020.5961.680.549"""1.75 0.020.1881.800.180"""1.66 0.030.4841.700.418"""1.81 0.010.1351.840.128"""1.71 0.02
Table 1. Lennard-Jones parameters of the species investigated in this study Species Formula M k Method Source [gmol 1]
Binary prices Binary prices rautmann (2013 Binary no price Epstein (2002 Binary prices al. (2014 Binary maximis- seek- er- t al. (2010 Binary individ- price al. 2014 Binary prices Binary sset prices Halevy (2019 Auction y Binary diffi- sig- nals Liang (2019 sm y Binary erreac- news al. (2012 Auction y Binary under- signals et y Gaussian erreac .
Binary compounds are those that are composed of only two elements. There are three types of binary compounds: binary covalent compounds, binary ionic compounds and binary acids. Examples of binary covalent compounds include water (H 2O), carbon monoxide (CO), and carbon dioxide CO 2. The naming convention for bina
And there are also only two options of the outcome that is: right or wrong. Hence, Binary Options are also known as Binary Bets or Binary Transactions. This simplicity, the simple two-way choice, is one of the main reasons why Binary Options have been so successful since their beginning. Binary Options exist since 2008 and in 2012 it became .
Lecture #1: Bits, Bytes, and Binary CS106E Spring 2018, Young The binary number system underlies all modern computers. In this lecture we'll take a look at the binary number system and some of the implications of using binary numbers. Having a solid grounding in binary will set us up to explore digital images and digital music in the next two .
Computer devices (Machine) can understand two state 0 or 1, this binary language is also known as a machine language, and the o and 1 known as bit. Computer can perform operation on binary data so It accept binary data and output in binary format, it store data on disk or in chips also in binary so we can
Reinforcing sequencing in binary number systems Codes for letters using binary representation Evaluation: Students can be challenged to take the binary math “magic” trick home with them to show off their number devising skills with their families. You could give them binary
Binary Relations A binary relation over a set A is a predicate R that can be applied to pairs of elements drawn from A. If R is a binary relation over A and it holds for the pair (a, b), we write aRb.3 3 5 7 Ø ℕ If R is a binary relation over A and it does not hold
Index 3 Top Reasons to Trade Binary Options 4 Binary Options: A History 5 How to Execute a Classic Trade with Binary Options 7 Advanced Binary Trading Tools 7 RollOver Tool 8 Double Up Tool 9 An Overview of One-Touch Trading 12 Option Builder: The Basics 13 Open Platform: The Basics 14 Asset Types 14 My Acount 14 U
