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NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 394800, 12052]*) (*NotebookOutlinePosition[ 395589, 12079]*) (* CellTagsIndexPosition[ 395545, 12075]*) (*WindowFrame->Normal*) Notebook[{ Cell["Attachment-detachment in dry air", "Subtitle", TextAlignment->Center], Cell["\<\ A.V. Phelps, JILA, University of Colorado and National Institute of Standards \ and Technology, \ \>", "Subsubtitle"], Cell["\<\ This is a very preliminary review and evaluation of published data. 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FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[CellGroupData[{ Cell[BoxData[ \(now\ = \ StringForm["\<``/``/`` ``:``:``\>", \(Date[]\)[\([2]\)], \ \(Date[]\)[\([3]\)], \(Date[]\)[\([1]\)], \(Date[]\)[\([4]\)], \ \(Date[]\)[\([5]\)], \(Date[]\)[\([6]\)]]\)], "Input", ExportPostScriptOptions->{"IncludeCellLabels"->False}, ExportNativeGraphicsOptions->{"IncludeCellTags"->False}, ExportTypesetOptions->{"IncludeCellTags"->False}, ExportQuickTimeOptions->{"IncludeCellLabels"->False}, FindSettings->{"Wraparound"->True, "DisplayedSearchList"->"Styles"}, GridCreationSettings->{"DrawRowLines"->False, "DrawFrame"->False, "Fill"->False, "DiagonalFill"->False}, NotebookStatisticsSettings->{"Domain"->Selection}, MessageOptions->{"StartupHelp"->False, "ExplainBeepHelp"->True, "IgnoreTagBoxDeletionWarning"->True, "AllowDisablingWarnings"->True}], Cell[BoxData[ InterpretationBox["\<\"\\!\\(1\\)/\\!\\(15\\)/\\!\\(2002\\) \ \\!\\(20\\):\\!\\(16\\):\\!\\(25\\)\"\>", StringForm[ "``/``/`` ``:``:``", 1, 15, 2002, 20, 16, 25], Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SetDirectory["\"]\)], "Input"], Cell[BoxData[ \("c:\\AllProjects\\AirAttDetachment"\)], "Output"] }, Open ]] }, Closed]], Cell["\<\ The objective of this notebook is to review the available data and mechanisms \ for electron attachment and detachment and ion stabilization for dry air at \ E/n near the cross over between net attachment and ionization.\ \>", "Subsubtitle"], Cell["\<\ Graphs comparing the various results are at the end of this notebook. To \ open the various sections double click on the arrows at the right hand \ border.\ \>", "Subsubtitle"], Cell["Swarm experiments and models", "Section"], Cell["Geballe and Harrison, Phys. Rev. 85, 372 (1952)", "Subsection"], Cell["Harrison and Geballe, Phys. Rev. 91, 1 (1953)", "Subsection"], Cell[CellGroupData[{ Cell["Burch and Geballe, Phys. Rev. 106, 183 and 188 (1957)", "Subsection"], Cell["\<\ Conditions: 9 < E/p 50 V/cm Torr, 7 < pd < 26 Torr cm, 4 cm dia Measured mobilities of three ions from rather indistinct structure in current \ following a photon induced electron pulse. Presents arguments for \ identifying them as O- at low and moderate E/p, O3- at low and moderate E/p, \ and O2- at moderate and high E/p.\ \>", "SmallText"] }, Open ]], Cell["Prasad and Graggs, Proc. Phys. Soc. (London) 77, 385 (1961)", \ "Subsection"], Cell[CellGroupData[{ Cell["Eiber, Z. Angew. Phys. 15, 103 (1962)", "Subsection"], Cell["\<\ Determined mobilities of three negative ions and one positive ion from time \ dependence of current and from frequency dependence of current in synchronous \ multiple shuttered drift tube. The scatter in the data was rather large. \ Negative ions are identified as O-, O3- and O2-. Discusses processes \ responsible for loss of O2- and production of O3-.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Dutton, Harris, and Llewellyn-Jones, Proc. Phys. Soc. (London) 81, 52 \ (1963)\ \>", "Subsection"], Cell["\<\ Determine spatial ionization and attachment coefficients for electrons in air \ from spatial growth of ionization for 90 < E/n < 115 Td and 100 < p < 300 \ Torr. Do not consider detachment. While net ionization coefficients agree \ with previous values, the attachment coefficients are much smaller.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["Frommhold, Fortschr. Phys. 12, 597 (1964)", "Subsection"], Cell["\<\ Discharge parameters: 100 < E/n < 150 Td, 3 < p < 30 Torr, d = 1 cm (?). The time-integrated total currents on the time scale of a few electron \ transit times were analyzed in terms of spatially independent ionization, \ attachment, and detachment coefficients. Ion stabilization by ion-molecule \ reactions was not considered in the analysis.\ \>", "SmallText"], Cell["Electron drift velocity", "Subsubsection"], Cell["\<\ Because of the neglect of the delayed electron detachment form the negative \ ions one expects the apparent drift velocities to be too small. Some E/p and \ drift velocities in m/s are:\ \>", "SmallText"], Cell["\<\ fromholdElDrift = Map[#*{1/0.33,1}&, \ {{35,1.2*10^5},{50,1.45*10^5},{65,2.*10^5},{89,2.5*10^5}}];\ \>", "Input"], Cell["\<\ frommholdVelPlot = LogLogListPlot[fromholdElDrift,PlotRange -> \ {{1.,1000},{10^3,10^6}}, PlotStyle -> {Hue[0.5],PointSize[0.02]}, \ DisplayFunction->Identity];\ \>", "Input"], Cell["Attachment", "Subsubsection"], Cell["\<\ From digitization of Fig. 14, the apparent attachment coefficient is \ \>", "SmallText"], Cell["!! c:\\AllProjects\\AirAttDetachmentfrommhold2.dat", "Input", PageWidth->Infinity, Evaluatable->False], Cell["Read in the data from this file and prepare plots.", "Text"], Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\frommhold2.dat\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; frommholdAttPlot = ListPlot[data1,PlotRange -> \ {{0.,250},{0.,10^-17}}, PlotStyle -> {Hue[0.5],PointSize[0.02]}, DisplayFunction->Identity];\ \ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["Detachment from O- in dry air", "Subsubsection"], Cell["\<\ Frommhold obtains an effective detachment coefficient 1/tau p20 which we fit \ with the expression 5.9*10^-15*Exp[-1.015*10^-20/eon] m^3/s where eon is in \ V/cm Torr or for E/n in Td (eontd) \ \>", "SmallText"], Cell["deltadeton = 5.9*10^-15*Exp[-1015/eontd]; (*m^3/s*)", "Input"], Cell["The digitized data from Fig. 15 is ", "SmallText"], Cell["!! c:\\AllProjects\\AirAttDetachmentfrommholddet.txt", "Input", PageWidth->Infinity, Evaluatable->False], Cell["Read in the data from this file and prepare plots.", "Text"], Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\frommholddet.txt\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; data2 = Transpose[data1]; frommholdDetTable = Transpose[{data2[[3]],data2[[4]]}]; frommholdDetPlot = LinearLogListPlot[frommholdDetTable,PlotRange \ -> {{0.,250},{10^-19,10^-16}}, PlotStyle -> \ {Hue[0.5],PointSize[0.02]}, DisplayFunction->Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ He interprets this as the rate coefficient for the reaction O- + O2 -> e + O \ + O2 with a treshhold of 2.25 eV. The peak rate coefficient is close to the \ Langevin value. (Note that Rebentrost (1973) and Parkes (1974) use a \ different model for the high energy part of the ion energy distribution and \ get only 1.5 eV activation enrgy.)\ \>", "SmallText"], Cell["\<\ frommholdDetPlot2 = LinearLogPlot[deltadeton, {eontd,60,250}, PlotRange -> \ {{0.,250},{10^-18,1.0*10^-16}}, DisplayFunction->Identity];\ \>", "Input"], Cell["Detachment from O- pure O2", "Subsubsection"], Cell["\<\ Frommhold finds that the detachment coefficient for an ion assumed to be O- \ in pure O2 is about 20% greater than for O- in dry air over a very wide range \ of E/n. This suggests that the same detachment process, i.e., O- + O2 -> e + \ O + O2, dominates in dry air as in O2. The nearly equal rate coefficient for \ dry air in spite of the low O2 fraction would require that the O- drift \ velocity in air be significantly larger, e.g., a factor of 2, than for O- in \ O2. If the drift velocities are roughly equal then one must invoke O- + N2 \ -> e + ?? with a very similar detachment energy for dry air.\ \>", "SmallText"], Cell["\<\ Stabilization of negative ion by ion-molecule reaction for pure O2 and dry \ air.\ \>", "Subsubsection"], Cell["\<\ Frommhold (1964) does not invoke this process. Note that Frommhold, Corbin, \ and Goodson (1973) do find evidence for stabilization in pure O2.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["Prasad and Graggs, Electronics Lett. ???? (1965)", "Subsection"], Cell["\<\ A reexamination of measurements from Prasad and Graggs (1961) and Harrison \ and Geballe (1953) of current growth in uniform electric field in O2. Claim \ that for 34 < E/p <37 V/Torr cm detachment is barely detectable or absent for \ pressures above 100 Torr, but is measurable at lower pressures.\ \>", "SmallText"] }, Open ]], Cell["Feshenfeld et al, J. Chem. Phys. 45, 1844 (1966)", "Subsection"], Cell[CellGroupData[{ Cell["Moruzzi and Phelps, J. Chem. Phys. 45, 4617 (1966)", "Subsection"], Cell["\<\ Mass spectrometer measurements of unnormalized fluxes of [O3-]/[O-] show the \ three-body behavior of the O- + 2 O2 -> O3- + O2 reaction at E/n = 16 Td and \ pressures of 1 - 3 Torr. The [O2-]/[O-] ratio is consistent with a two-body \ behavior of the O- + O2 -> O2- + O reaction at E/n = 83 Td at pressures of \ 0.9 to 2 Torr. At 90 Td the [O2-]/[O-] ratio is significantly larger and the \ pressure dependence is somewhat faster at pressures of 0.9 to 2 Torr.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["Ryzko, H and Astrom E., J. Appl. Phys. 38, 328 (1967)", "Subsection"], Cell["\<\ Discharge parameters: 100 < E/n < 160 Td, 4.4 < p20 < 60 Torr, 4.5 < d < 6 \ cm. The experiments used the integrated current following a 40 ns uv pulse to \ produce photoelectrons. He did not consider negarive ion stabilization. \ Note that the scatter in Ryzko's data is rather large, e.g., a factor of two.\ \ \>", "SmallText"], Cell["Attachment coefficients", "Subsubsection"], Cell["\<\ Says attachment coefficients are increase from 0.007 and 0.016 cm^-1Torr^-1 \ for 100 and 160 Td and are roughly equal to those of Frommhold (1964), but \ incease wth increasing E/p. The electron drift velocities wFit used to \ convert the spatial attachment coefficients to rate coefficients are from \ Phelps (1987).\ \>", "SmallText"], Cell["wFit = 7.*10^3*eontd^0.45*(1+(eontd/13)^2)^0.18;", "Input"], Cell["\<\ nuonAttRyzko = {0.007,0.0160}*100/(3.3*10^22)*(wFit /. eontd -> {110,160}); \ (*cm^-1T0rr^-1*)\ \>", "Input"], Cell[CellGroupData[{ Cell["nuonAttRyzkoTable = Transpose[{{110,160},nuonAttRyzko}]", "Input"], Cell[BoxData[ \({{110, 2.6624097289284275`*^-18}, {160, 8.232581332479596`*^-18}}\)], "Output"] }, Open ]], Cell["\<\ ryzkoAttPlot = ListPlot[nuonAttRyzkoTable, PlotRange -> \ {{0.,250},{0.,1.01*10^-17}}, PlotStyle -> {Hue[0.1],PointSize[0.02]}, \ DisplayFunction->Identity];\ \>", "Input"], Cell["Detachment coefficients", "Subsubsection"], Cell["\<\ Derived negative ion lifetimes times pressure vary from 30 to 1.8 us torr for \ E/n of 100 and 160 Td. These values are somewhat smaller than those of \ Frommhold (1964).\ \>", "SmallText"], Cell["\<\ nuonDetRyzko = {1/30.,1/1.8}/10^-6/(3.3*10^22); (*cm^-1T0rr^-1*)\ \>", "Input"], Cell[CellGroupData[{ Cell["nuonDetRyzkoTable = Transpose[{{110,160},nuonDetRyzko}]", "Input"], Cell[BoxData[ \({{110, 1.0101010101010103`*^-18}, {160, 1.6835016835016838`*^-17}}\)], "Output"] }, Open ]], Cell["\<\ ryzkoDetPlot = LinearLogListPlot[nuonDetRyzkoTable, PlotRange -> \ {{0.,250},{10^-19,1.*10^-16}}, PlotStyle -> {Hue[0.1],PointSize[0.02]}, \ DisplayFunction->Identity];\ \>", "Input"] }, Open ]], Cell["Hessenauer, H., Z. Phys. 204, 143 (1967)", "Subsection"], Cell[CellGroupData[{ Cell["\<\ Sukhum, Prasad, and Graggs, Brit. J. Appl. Phys. 18, 785 (1967)\ \>", "Subsection"], Cell["\<\ Measurements of current growth in uniform electric field in O2. Say \ detachment is negligible for pressures above 50 Torr. They give detachment \ coefficients for lower pressures. The detachment coefficients vary from 4e-4 \ cm^-1 Torr^-1 at 35 V/cm Torr to 3e-3 cm^-1 Torr^-1 at 40 V/cm Torr, while \ the ionization and attachment coefficients are nearly constant at 0.1 cm^-1 \ Torr^-1.\ \>", "SmallText"], Cell[CellGroupData[{ Cell["\<\ sukumDet = Map[#*{1/0.33,100/(3.3*10^22)}&,{{35,4.*10^-4},{40,3.*10^-3}}] \ (*Td,m^2*)\ \>", "Input"], Cell[BoxData[ \({{106.06060606060606`, 1.2121212121212123`*^-24}, {121.21212121212122`, 9.090909090909091`*^-24}}\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Dutton and Howells, J. Phys. B 1, 1160 (1968)", "Subsection"], Cell["\<\ Determine mobilities for three negative ions and two positive ions using \ four-gause electrical shutter drift tube. Also, determined D/mu values for \ two positive ions. Identify positive ions as O2+ and O4+ and discuss \ equiliblrium amomg these ions.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["Moruzzi, Ekin, and Phelps, J. Chem. Phys. 48, 3070 (1968)", "Subsection"], Cell["\<\ These are measurements of detachment in O2 - H2 mixtures. Although not \ mentioned in this paper, the data of Fig. 2 yields an upper limit to the rate \ coefficient for detachment in O2- + O2 collisions of 7.5e-10 * 2e-4 = 1.5e-13 \ cm^/s = 1.5e-19 m^3/s at E/p = 5 V/cm Torr = 15 Td. Pack and Phelps, J. \ Chem. Phys. 44, 1870, (1966) give values as low as 1e-16 cm^3/s = 1e-22 m^3/s \ at 0.1 Td and 375 K and 2.3e-21 m^3/s at E/n = 1 Td and 477 K.\ \>", "SmallText"] }, Open ]], Cell["Naidu and Prasad, J. Phys. B 3, 957 (1970)", "Subsection"], Cell["\<\ Kinsman and Rees, Int. J. Mass Spectrometry and Ion Phys. 5, 71 (1970)\ \>", "Subsection"], Cell["McKnight, Phys. Rev. A 2, 762 (1970)", "Subsection"], Cell[CellGroupData[{ Cell["Eccles, O'Neill, and Craggs, J. Phys. B 3, 1724 (1970)", "Subsection"], Cell["\<\ Conditions: 135 < E/p < 150 V/cm Torr, 20 < pd < 60 Torr cm, 4 cm dia A drift tube is divided into two sections by a grid. Section 1( E/p = 1 V/cm \ Tott and d1 = 3 cm) is used to produce oxygen negative ions. Section 2 (d2 = \ 0.5 to 1cm) is used to look for electron production by collisional detachment \ and subsequent ionization. Using other sources of ionization and attachment \ coefficient data they determine the detachment coefficient. The results are \ summarized by a detacment coefficient of ~ 0.01 cm^-1Torr^-1 at E/p ~ 140 \ V/cm Torr.\ \>", "SmallText"] }, Open ]], Cell["Snuggs et al, Phys. Rev. A 3, 487 (1971)", "Subsection"], Cell["\<\ Measure rate coefficients for reactions of O- with O2 for 5 < E/n < 30 Td, \ 0.1 < p < 0.6 Torr using a drift-tube using mass spectrometer identification.\ \ \>", "SmallText"], Cell[CellGroupData[{ Cell["Wagner, K. H., Z. Phys. 241, 258 (1971)", "Subsection"], Cell["\<\ Discharge parameters: 110 < E/n < 130 Td, 150 < p20 < 244 Torr, 4.5 < d < 6 \ cm. Gives relative mass spectrometer fluxes for O- and O2-. Apparently the time-integrated total currents on the time scale of a few \ electron transit times were analyzed in terms of spatially independent \ ionization, attachment, detachment, and ion stabilization coefficients. Says \ longer drift distance gave better relative time resolution.\ \>", "SmallText"], Cell["\<\ Claims that O- + 2 O2 -> O3- + O2 and O- + O2 + N2 -> O3- + N2 are not \ important at pressures used. \ \>", "SmallText"], Cell["Ionization coefficients", "Subsubsection"], Cell["\<\ Says ionization coefficients differ insignificantly from those of Harrison \ and Geballe (1953) and Frommhold (1964).\ \>", "SmallText"], Cell["Attachment coefficients", "Subsubsection"], Cell["\<\ Says attachment coefficients are close to 21% of the O2 values, actual values \ are constant at 0.017 cm^-1Torr^-1 for 110 < E/n < 130 Td. Points out that \ these values are about twice those of Frommhold (1964) and of Rysko (1967), \ where ion stabilization by charge transfer was neglected. The electron drift velocities wFit used to convert the spatial attachment \ coefficients to rate coefficients are from Phelps (1987).\ \>", "SmallText"], Cell[CellGroupData[{ Cell["\<\ nuonAttWagner = 0.017*100/(3.3*10^22)*wFit /. eontd -> {110,130} \ (*cm^-1T0rr^-1*)\ \>", "Input"], Cell[BoxData[ \({6.465852198826182`*^-18, 7.397506872985046`*^-18}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["nuonAttWagnerTable = Transpose[{{110,130},nuonAttWagner}]", "Input"], Cell[BoxData[ \({{110, 6.465852198826182`*^-18}, {130, 7.397506872985046`*^-18}}\)], "Output"] }, Open ]], Cell["\<\ wagnerAttPlot = ListPlot[nuonAttWagnerTable, PlotRange -> \ {{0.,250},{0.,1.01*10^-17}}, PlotStyle -> {Hue[0.3],PointSize[0.02]}, \ DisplayFunction->Identity];\ \>", "Input"], Cell["Detachment coefficients", "Subsubsection"], Cell["\<\ Derived detachment coefficients are roughly a factor of two larger than for \ pure O2 , actual values are 0.25, 0.5, and 0.8 cm^-1Torr^-1 for E/n of 110, \ 120, and 130 Td. He points out that these values are more than an order of \ magnitude larger than corresponding attachment coefficients. \ \>", "SmallText"], Cell["\<\ Note that the detachment and charge transfer coefficients are defined in \ terms of the ion drift velocity, not the electron drift velocity. The \ detachment rate coefficients are evaluated under Davies (1983).\ \>", "Subsubtitle"], Cell["\<\ He assumes that the normalized negative ion mobility is 3.4 cm^2/V s at 760 \ Torr and 20 deg or .\ \>", "SmallText"], Cell[CellGroupData[{ Cell["\<\ 3.4*2.75*10^19*eontd*10^-17/100 /. eontd -> {110.,120.,130.} \ (*m/s*)\ \>", "Input"], Cell[BoxData[ \({1028.5`, 1122.`, 1215.5`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ nuonDetWagner = \ {0.25,0.5,0.8}*100/(3.22*10^22)*(3.4*2.75*10^19*eontd*10^-17/100 /. eontd -> \ {110.,120.,130.})\ \>", "Input"], Cell[BoxData[ \({7.985248447204969`*^-19, 1.7422360248447205`*^-18, 3.0198757763975156`*^-18}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ nuonDetWagnerTable = Transpose[{{110.,120.,130.},nuonDetWagner}]\ \>", "Input"], Cell[BoxData[ \({{110.`, 7.985248447204969`*^-19}, {120.`, 1.7422360248447205`*^-18}, {130.`, 3.0198757763975156`*^-18}}\)], "Output"] }, Open ]], Cell["\<\ wagnerDetPlot1 = LinearLogListPlot[nuonDetWagnerTable, PlotRange -> \ {{0.,250},{10^-19,1.*10^-16}}, PlotStyle -> {PointSize[0.02]}, \ DisplayFunction->Identity];\ \>", "Input"], Cell["Ion stabilization", "Subsubsection"], Cell["\<\ Derived negative ion stabilization coefficients, presumably by the charge \ transfer reaction O- + O2 -> e + O + O2, vary from 0.09, 0.12, and 0.15 \ cm^-1Torr^-1 for E/n of 110, 120, and 130 Td. He claims that these values \ are 21% of pure O2 values. although the graph shows ~ 16%.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["Parkes, Trans. Faraday Soc. 67, 711 (1971)", "Subsection"], Cell["\<\ Mass spectrometer studies of negative ions from an O2 drift tube. Conditions: \ 0.1 < E/n < 60 Td, 0.5 < p < 10 Torr, 8 cm length, 4.8 cm dia.\ \>", "SmallText"], Cell["\<\ Looks at the [O3-]/[O-] and [O4-]/[O2-] ratios at the anode. I found the \ pressure dependencies of the results of this paper very confusing and suspect \ that the model used is over simplified. See Parkes, Vacuum 24, 561 (1974) for \ possible interpretation of these results.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["Price, Lucas, and Moruzzi, J. Phys. D 5, 98 (1972)", "Subsection"], Cell["\<\ Measurements of steady-state ionization growth are in O2-H2 mixtures are used \ to get spatialionization coefficients for pure O2 in the absence of \ attatchment, i.e., it is assumed that all O- formed by dissociative \ attachment quickly undergoes detachment in O- + H2 collisions. Their \ ionization coefficients for O2 are lower than most, but not all, previous \ values.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["Frommhold, Goodson and Corbin, Phys. Lett. 45A, 51 (1973)", "Subsection"], Cell["\<\ Use measurements of the ratio of the charge collected in one electron transit \ time to the total charge collected to obtain the spatial inization \ coefficient for 14 < E/p < 160 V/cm Torr. A set of rate equations including \ attachmant, detachment, in conversion, and charge transfer were used to \ analyze the data. Details are not given.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["Frommhold, Corbin, and Goodson, Phys. Rev. A 8, 1403 (1973)", \ "Subsection"], Cell["\<\ Here they consider various analytic models of attachment, detachment and ion \ conversion. For me, this paper is best read after Goodson, Corbin, and \ Fromhold, Phys. Rev. A 9, 2049 (1974).\ \>", "SmallText"] }, Open ]], Cell["Skullerud, J. Phys. B 6, 728 (1973)", "Subsection"], Cell[CellGroupData[{ Cell["Lucas, Price, and Moruzzi, J. Phys. D 6, 1503 (1973)", "Subsection"], Cell["\<\ Boltzmann calculation of electron transport and reaction coefficients for O2.\ \ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["Price, Lucas, and Moruzzi, J. Phys. D 6, 1514 (1973)", "Subsection"], Cell["\<\ Determine spatial ionization, apparent attachment coefficient from spatial \ growth of ionization in O2 for 90 < E/n < 150 Td and 10 < p < 100 Torr. \ Detachment coefficients are inferred from the difference between calculated \ and apparent attachment coefficients. Cite evidence that detachment also \ occurs from another negative ion.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["O'Neill, and Graggs, J. Phys. D 6, 2625 (1973)", "Subsection"], Cell["\<\ Using a drift tube and mass spectrometer at pressures of 20-60 Torr and E/n \ of 124 to 155 Td, they measured current growth and relative negative ion \ signals. A two section drift tube is used to vary the ion injected into the \ drift region that is sampled by the mass spectromenter. Claim negligible \ collisional dissociation of O3- to O-. Give tables of detachment and ion \ conversion coefficients.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Rebentrost, Chem. Phys. Lett. 21, 368 (1973) and Int. J. Mass Spectrom. and \ Ion Phys. 1, 475 (1973)\ \>", "Subsection"], Cell["\<\ In the first paper he applies his model of ion-induced endothermic reactions \ - Chem. Phys. Lett. 17, 486 and 489 (1972) - to O- + O2 -> O2- + O and finds \ a threshold energy of 0.95 eV in center of mass.\ \>", "SmallText"], Cell["\<\ In the second paper he applies his model of ion-induced endothermic reactions \ to O- + O2 -> e + O + O2 and O- + N2 -> e + N2 + O and find threshold \ energies of about 1.4 eV. He neglects associative detachment - O- + O2 -> e \ + O3 - on the basis of Feshenfeld et la (1966)\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["Goodson, Corbin, and Fromhold, Phys. Rev. A 9, 2049 (1974)", \ "Subsection"], Cell["\<\ The discharge parameters are: 100 < E/n < 350 Td, 1 < p < 30 Torr, d = 2.54 \ cm. The principle result, shown in Fig. 3, is the frequency of electron \ detachment events in O2- + O2 collisions. Their argument is that the time \ scale of the decay of O- flux is so short that they essentially start with a \ cloud of O2- ions that collide with O2 to detach and to form stable O3-. \ They appear to assume that the O2- -> e -> O- -> O3- is so fast that they \ cannot detect the steps. The O4- ion is essentially neglected, as justified \ in part by mass spectrometer studies.\ \>", "SmallText"], Cell["O- + O2 -> e + ? from Fig. 3", "Subsubsection"], Cell["The digitized data from Fig. 3 is ", "SmallText"], Cell["!! c:\\AllProjects\\AirAttDetachment\\Goodson74.dat", "Input", PageWidth->Infinity, Evaluatable->False], Cell["Read in the data from this file and prepare plots.", "Text"], Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\Goodson74.dat\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; goodsonDetPlot = LinearLogListPlot[data1,PlotRange -> \ {{0.,250},{10^-19,10^-16}}, PlotStyle -> {Hue[0.7],PointSize[0.02]}, DisplayFunction->Identity];\ \ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ Formation of O2- and O3- by electron \"attachment\" from Figs. 5 and 6\ \>", "Subsubsection"], Cell[TextData[{ "These authors describe the formation of O2- and O3- by effective \ \"attachment\" coefficients, i.e., the rate equation terms are proportional \ to the electron density rather than the O- density. This leads to strong \ pressure dependences of the coefficients because of competition between the \ two body processes of detachment and of charge transfer and the three body \ process of O3- formation. They attempt to include the effects of the \ competition between energy relaxation of the O- and its reactions with O2, \ i.e., the fact that the O- reactions can occur while the O- \"remembers\" its \ initial kinetic energy resuting from dissociative attachment. We note that \ his means that one should not use the Wannier or Rebentrost expressions for \ the O- energy distribution. ", StyleBox["See Parkes (1974) for other proposals.", FontColor->RGBColor[1, 0, 0]] }], "SmallText"], Cell["Summary of this paper", "Subsubsection"], Cell["\<\ In summary, the authors say that following the initial electron pulse, with \ its associated O- detachment and charge transfer reactions, there are delayed \ electrons resulting from detachment from O2- O2 collisions. They also say \ the data requires a stabilization process that fits O2- -> e -> O- -> O3-. \ They consider the fact that the O- energy distribution is not an equilibrium \ distribution. The estimated relative magnitudes of the detachment \ coefficients shown in their Fig. 4 is very useful for understanding the \ overall model.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["Corbin and Frommhold, Phys. Rev. A 10, 2273 (1974)", "Subsection"], Cell["\<\ In the third paper, electron growth measurements in O2-H2 mixtures yields an \ ionization coefficient for electrons in pure O2 of\ \>", "SmallText"], Cell["2.5*Exp[-170/eop] (*cm^-1Torr^-1 for V/cm Torr*);", "Input"], Cell[CellGroupData[{ Cell["alphaion = %/(3.3*10^22) /. eop -> 0.33*eontd (*m^2*)", "Input"], Cell[BoxData[ \(7.575757575757577`*^-23\ \ \[ExponentialE]\^\(\(-515.1515151515151`\)/eontd\)\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Parkes, Vacuum 24, 561 (1974)", "Subsection"], Cell["\<\ This is a rather thorough review and analysis of experiments and models \ concerned with negative ion reactions in O2.\ \>", "SmallText"], Cell["\<\ A major point of this paper is to question the use of a Maxwellian ion energy \ distribution with the temperature given by the Wannier relation. Parks \ advocates the Rebentrost model that gives a pronounced forward peak to the \ energy distribution caused by ions that travel several mean-free-paths \ without collision. The result of this is a reduction of the threshold energy \ for detachment from 2.2 eV as found by Frommhold (1964) to 1.5 eV.\ \>", "SmallText"], Cell["O- + 2 O2 -> O3- + O2 ", "Subsubsection"], Cell["\<\ Parkes compares numerous sets of data in Fig. 10. We take a fit to the data \ to be\ \>", "SmallText"], Cell[CellGroupData[{ Cell["kOn3body = 1.*10^-30/(1+(eontd/65)^4) (*cm^6/s*)", "Input"], Cell[BoxData[ \(9.999999999999999`*^-31\/\(1 + eontd\^4\/17850625\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["% /. eontd -> {1,10,80,100,150}", "Input"], Cell[BoxData[ \({9.999999439795557`*^-31, 9.9944010917871`*^-31, 3.0352721128197494`*^-31, 1.5146822513669314`*^-31, 3.405953770804986`*^-32}\)], "Output"] }, Open ]], Cell["\<\ Parkes attributes this surprisingly fast decrease with increasing E/n to the \ inclusion of the back reaction, O3- + O2 -> O- + 2 O2, to give a net rate \ coefficient. We now make a plot of the effective 2-body reaction rate \ coefficient appropriate to atmospheric pressure so as to show the maximum \ effect of this process.\ \>", "SmallText"], Cell["\<\ parkes3bodyPlot = LinearLogPlot[(kOn3body/10^12n /. n ->2.45*10^25), \ {eontd,1,250}, PlotRange -> \ {{0.,250},{10^-19,1.0*10^-16}}, PlotStyle -> {Hue[0.8],Thickness[0.007]}, \ DisplayFunction->Identity];\ \>", "Input"], Cell[TextData[{ "Parkes estimates of the back reaction, i.e., the O3- dissociation rate \ coefficient, give values that are too small. He proposes other O3- \ destruction processes, i.e., O2- formation and detachment. ", StyleBox["This is an unsatisfactory situation.", FontColor->RGBColor[1, 0, 0]] }], "SmallText"], Cell["O- + O2 -> O2- +O", "Subsubsection"], Cell["\<\ Parkes compares numerous sets of data in Fig. 11. We take a fit to the data \ to be\ \>", "SmallText"], Cell[CellGroupData[{ Cell["kOn2body = 1.*10^-8*Exp[-900/eontd]/10^6 (*m^3/s*)", "Input"], Cell[BoxData[ \(1.`*^-14\ \[ExponentialE]\^\(\(-900\)/eontd\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["% /. eontd -> {60,80,100,150,200}", "Input"], Cell[BoxData[ \({3.0590232050182596`*^-21, 1.300729765406763`*^-19, 1.234098040866796`*^-18, 2.4787521766663594`*^-17, 1.1108996538242308`*^-16}\)], "Output"] }, Open ]], Cell["\<\ This looks like a reasonable fit at the E/n of Fig. 11, but extrapolates to \ unreasonably large values at higher energies.\ \>", "Subsubtitle"], Cell["\<\ parkes2bodyPlot = LinearLogPlot[kOn2body, {eontd,10,250}, PlotRange -> \ {{0.,250},{10^-19,1.0*10^-16}}, \ PlotStyle -> {Hue[0.5],Thickness[0.007]}, DisplayFunction->Identity];\ \>", "Input"], Cell["O2- + O2", "Subsubsection"], Cell["\<\ Parkes points out that the endothermic reactions of O2-, such as dissociation \ to form O-, are inhibited by the large cross section of O2- with O2 which \ keeps the energy of the O2- small. He claims Frommhold's detachment rates \ for O2- + O2 are high.\ \>", "SmallText"], Cell["O3-+O2", "Subsubsection"], Cell["\<\ Models for this problem are the data and analyses of O- + O2 -> O2- + O \ measurements by Lin, Bardsley, Dotan, Fehsenfeld, and Albriton, Int. J. Mass. \ Spectrom. and Ion Physics 34, 113 (1980) and the analysis of measurements for \ O- + N2 by Lindinger et al, J. Chem. Phys. 63, 3238 (1975) versus Comer and \ Schulz, Phys. Rev. A 10, 2100 (1974). These experiments were done in a \ helium buffer and require theory to convert to reaction coefficient data for \ O2 or air.\ \>", "Text"], Cell["\<\ Parkes discusses the reactions leading to O-, O2-, and free electrons.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["Lindinger et al, J. Chem. Phys. 63, 3238 (1975)", "Subsection"], Cell["\<\ A flowing afterglow combined with a drift tube is used to show that the rate \ coefficient for O- + N2 -> e +? in an He buffer gas is less than 1e-12 cm^3/s \ for mean relative energies up to 2 eV. This is said to be much smaller than \ that calculated from the cross section reported by Comer and Schulz, Phys. \ Rev. A 10, 2100 (1974) ,i.e., <7e-12 cm^3/s for of 0.5 to 1 eV. We \ will plot the Langevin cross section divided by 1000.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(qLindingerLimit\ = \ \(\(\(2. *Pi* ao^2. *\((\(alphaauN2/2. \)/\((enrel/27.211)\))\)^0.5\ / 1000. \ /. alphaauN2\ -> \ 1.76*10^\(-30\)/ao^3\)\ /. ao -> 0.529*10^\(-10\)\)\(\ \)\(//\)\(\ \)\(PowerExpand\)\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\( (*m^2\ and\ eV*) \)\)\)], "Input"], Cell[BoxData[ \(2.236254830114636`*^-22\/enrel\^0.5`\)], "Output"] }, Open ]], Cell["\<\ LindingerLimitPlot = LinearLogPlot[qLindingerLimit, {enrel, 0.01,10}, \ PlotRange -> {{0.,10},{3.*10^-22.,3.*10^-19}}, PlotStyle -> \ {Hue[0.3],Thickness[0.007]}, DisplayFunction->Identity];\ \>", "Input"], Cell[CellGroupData[{ Cell["\<\ Rayment and Moruzzi, Int. J. Mass Spectrometry and Ion Phys. 26, 321 (1978)\ \>", "Subsection"], Cell["\<\ Discharge parameters: 3 < E/n < 120 Td, 0.25 < p < 2 Torr, d ~ 5 cm. The experiments used a cross flow drift tube and measured the relative O- \ signal reaching the anode with a differentially pumped mass spectrometer. \ From the dependence of the O- signal on N2 presure they obtain the loss of O- \ in collisions with N2.\ \>", "SmallText"], Cell["The digitized data from Fig. 15 is ", "SmallText"], Cell["!! c:\\AllProjects\\AirAttDetachmentRayment78.dat", "Input", PageWidth->Infinity, Evaluatable->False], Cell["Read in the data from this file and prepare plots.", "Text"], Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\Rayment78.dat\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; raymentDetPlot = LinearLogListPlot[data1,PlotRange -> \ {{0.,250},{10^-19,10^-16}}, PlotStyle -> {Hue[0.4],PointSize[0.02]}, DisplayFunction->Identity];\ \ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ They interpret this data as the rate coefficient for the reaction O- + N2 -> \ e + N2O with a treshhold of ~ 0.2 eV. \ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Okada, Sakai, Tagashira, and Sakamoto, J. Phys. D 11, 1107 (1978)\ \>", "Subsection"], Cell["\<\ A very graphic MC calculation showing the details of relaxation and charge \ transfer for O- in O2 following dissociative attachment. They calculate the \ drift velocities and diffusion coefficients for O- and O2- in O2. They \ present calculated detachment and charge transfer spatial coefficients for \ E/n from 80 to 200 Td. Unfortunately, they make no comparisons with \ coefficients calculated using the Wannier energy distributions. It would \ therfore be desirable to compare with other calculations.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Lin, Bardsley, Dotan, Fehsenfeld, and Albriton, Int. J. Mass. Spectrom. and \ Ion Physics 34, 113 (1980)\ \>", "Subsection"], Cell["\<\ An analysis of O- + O2 -> O2- + O data from a flow-drift tube with an \ attached mass spectrometer for to obtain the charge transfer cross section \ for 1.0 < Ecm < 5 eV. The authors state that because of the lack of rate \ coefficient data to very low values, they cannot determine the threshold \ energy but must assume it and show consistency with the assumed value. These \ results for the near threshold cross section should be good.\ \>", "SmallText"] }, Open ]], Cell["!!c:\\AllProjects\\AirAttDetachment\\Lin80Fig4.dat", "Input", PageWidth->Infinity, Evaluatable->False], Cell["\<\ Read in the data from this file and prepare plots of O- charge transfer in \ collisions with O2\ \>", "Text"], Cell[CellGroupData[{ Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\Lin80Fig4.dat\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; lin80Fig4Plot =LinearLogListPlot[data1,PlotRange -> \ {{0.,10},{3.*10^-22,3.*10^-19}}, PlotStyle -> {Hue[0.3],PointSize[0.02]}(*, DisplayFunction->Identity*)]\ ;\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix 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"Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Doussot, Bastien, Marode, and Moruzzi, J. Phys. D 16, 2451 (1982)\ \>", "Subsection"], Cell["\<\ A variable-length, drift-tube with an attached mass spectrometer. \ Apparently, the objective was to determine the loss coefficients for O- by \ comparing the spatial and temporal dependences of the O- signal. It appears \ to me that this experimant was unsuccessful.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Davies, Theoretical Note No. 346, Westinghouse Research Laboratories, May \ 1983\ \>", "Subsection"], Cell["\<\ A long abstract with figures covering this material appeared in Proc. XVIII \ Int. Conf. on Ionization Phenomena in Gases, Ed by Williams Swansea 1987 p. 2\ \ \>", "SmallText"], Cell["\<\ Discharge parameters: 0.6 < E/n < 225 Td, 30 < p0 = 100 Torr, 0.07 < d < 5.2 \ cm. There are two modes of operation: 1) a 20 ns pulsed spark discharge was used \ to measure electron drift velocities and 2) a ~100 us pulsed discharge lamp \ was used to measure positive and negative ion currents to get ion mobilities \ and effective attachment coefficients for dry and moist air. One concern is \ the distortion of the electron pulse caused by delayed detachment and the \ resultant underestimate of the electron drift velocities. These experiments \ do not separate the effects of attachment, detachment, and ion conversion.\ \>", "SmallText"], Cell["Effective attachment coefficient", "Subsubsection"], Cell["!! c:\\AllProjects\\AirAttDetachmentdaviesatt.txt", "Input", PageWidth->Infinity, Evaluatable->False], Cell["Read in the data from this file and prepare plots.", "Text"], Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\daviesatt.txt\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; data2 = Transpose[data1]; attachmentData= Transpose[{data2[[2]],data2[[5]]*10^-18}]; daviesAttPlot = ListPlot[attachmentData,PlotRange -> \ {{0.,250},{0.,10^-17}}, PlotStyle -> {Hue[1],PointSize[0.02]}, DisplayFunction->Identity];\ \ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["Electron drift velocity", "Subsubsection"], Cell["!! c:\\AllProjects\\AirAttDetachmentdavieselectron.txt", "Input", PageWidth->Infinity, Evaluatable->False], Cell["Read in the data from this file and prepare plots.", "Text"], Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\davieselectron.txt\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; data2 = Transpose[data1]; driftVelData= Transpose[{data2[[1]],data2[[5]]}]; daviesElectronVelPlot = LogLogListPlot[driftVelData,PlotRange -> \ {{0.1,1000.},{1000.,1000000.}}, PlotStyle -> \ {Hue[1],PointSize[0.02]}, DisplayFunction->Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["Ion drift velocities", "Subsubsection"], Cell["!! c:\\AllProjects\\AirAttDetachmentdaviesmobility.txt", "Input", PageWidth->Infinity, Evaluatable->False], Cell["Read in the data from this file and prepare plots.", "Text"], Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\daviesmobility.txt\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; data2 = Transpose[data1]; ionMobilityData= Transpose[{data2[[1]],data2[[5]]}]; daviesIonMobilityPlot = LogLogListPlot[ionMobilityData,PlotRange \ -> {{0.1,1000},{1.,10000.}}, PlotStyle -> {Hue[1], PointSize[0.02]}, \ DisplayFunction->Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["\<\ In the following we limit the fitting to the last 9 points, i.e., the values \ that appear to give the O- mobility in dry air. The lower E/n points appear \ to apply to O2- in dry air.\ \>", "SmallText"], Cell[CellGroupData[{ Cell["daviesOnMobility = Interpolation[Take[ionMobilityData,-9]]", "Input"], Cell[BoxData[ TagBox[\(InterpolatingFunction[{{60.`, 175.`}}, "<>"]\), False, Editable->False]], "Output"] }, Open ]], Cell["Evaluation of Wagner's detachment frequencies", "Subsubsection"], Cell["\<\ Derived detachment coefficients are roughly a factor of two larger than for \ pure O2 , actual values are 0.25, 0.5, and 0.8 cm^-1Torr^-1 for E/n of 110, \ 120, and 130 Td. He points out that these values are more than an order of \ magnitude larger than corresponding attachment coefficients. \ \>", "SmallText"], Cell[CellGroupData[{ Cell["\<\ nuonDetWagner2 = {0.25,0.5,0.8}*100/(3.22*10^22)*(daviesOnMobility[eontd] /. \ eontd -> {110.,120.,130.})\ \>", "Input"], Cell[BoxData[ \({7.533865720201123`*^-19, 1.6132870219025825`*^-18, 2.719701863354038`*^-18}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ nuonDetWagnerTable2 = Transpose[{{110.,120.,130.},nuonDetWagner2}]\ \>", "Input"], Cell[BoxData[ \({{110.`, 7.533865720201123`*^-19}, {120.`, 1.6132870219025825`*^-18}, {130.`, 2.719701863354038`*^-18}}\)], "Output"] }, Open ]], Cell["\<\ wagnerDetPlot2 = LinearLogListPlot[nuonDetWagnerTable2, PlotRange -> \ {{0.,250},{10^-18,1.01*10^-15}}, PlotStyle -> {PointSize[0.02]}, \ DisplayFunction->Identity];\ \>", "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Verhaart and van der Laan, J. Appl. Phys. 55, 3286 (1984)", "Subsection"], Cell["\<\ These authors measure the short time current pulse followint pulsed laser \ induced electron emission. Extrapolation of their moist air data to zero \ moisture yields data in agreement with the data of Wen and Wetzer (1988).\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Phelps, Gaseous Dielectrics V, ed by Christophorou and Bouldin (Pergamon, \ New York, 1987), p. 1. and \ ftp://jila.colorado.edu/collision_data/electron.txt\ \>", "Subsection"], Cell["\<\ This calculation is based on cross sections for O2 from Lawton and Phelps, J. \ Chem Phys. 69, 1055 (1978) and for N2 from Phelps and Pitchford, Phys. Rev. \ 31, 2932 (1985).\ \>", "SmallText"], Cell["!! c:\\AllProjects\\AirAttDetachmentdryair.txt", "Input", PageWidth->Infinity, Evaluatable->False], Cell["Read in the data from this file and prepare plots.", "Text"], Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\dryair.txt\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; data2 = Transpose[data1]; attachmentData= Transpose[{data2[[1]],data2[[8]]/10^6}]; driftVelData= Transpose[{data2[[1]],data2[[2]]/100}]; phelpsAttPlot = ListPlot[attachmentData,PlotRange -> \ {{0.,250},{0.,10^-17}}, PlotStyle -> {Hue[0.7],Thickness[0.007]}, PlotJoined -> True, \ DisplayFunction->Identity]; phelpsVelPlot = LogLogListPlot[driftVelData,PlotRange -> \ {{1.,1000},{10^3,10^6}}, PlotStyle -> {Hue[0.7],Thickness[0.01]}, PlotJoined -> True, \ DisplayFunction->Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["phelpsAttInt = Interpolation[attachmentData];", "Input"], Cell["From a fit to the drift velocity data of this file we get", "SmallText"], Cell["wFit = 7.*10^3*eontd^0.45*(1+(eontd/13)^2)^0.18;", "Input"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Wen and Wetzer, IEEE Trans. on Electrical Insulation 23, 999 (1988)\ \>", "Subsection"], Cell["\<\ Discharge parameters: 100 < E/n < 110 Td, p20 = 750 Torr, d < 1 cm. These authors measure the short time current pulse following pulsed laser \ induced electron emission for dry air. They find the total negative ion loss \ rate coefficient of <(delta + beta)/p> = 4.8E-3 cm^-1Torr^-1 and the product \ of the detachment and attachment coefficients of = 13E-6 \ cm^-2Torr^-2. Note that the all of the corresponding rate coefficients are \ obtained by multiplying by the electron drift velocity.\ \>", "SmallText"], Cell["The sum of their O- loss coefficients is ", "SmallText"], Cell[CellGroupData[{ Cell["wenOnLoss = {0.0055,0.0051} (*cm^-1Torr^-1*)", "Input"], Cell[BoxData[ \({0.0055`, 0.0051`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["daviesOnMobility[eontd] /. eontd -> {100,110}", "Input"], Cell[BoxData[ \({888.6031746031746`, 970.3619047619047`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ wenOnLoss2 = wenOnLoss*100/(3.3*10^22)*(wFit /. eontd -> {100,110}) \ (*cm^3s-1*)\ \>", "Input"], Cell[BoxData[ \({1.9374801749014887`*^-18, 1.9397556596478543`*^-18}\)], "Output"] }, Open ]], Cell["\<\ For comparison we add our fits to Frommhold's (1964) detachment coefficient \ and Parkes' (1974) charge transfer coefficient\ \>", "SmallText"], Cell[CellGroupData[{ Cell["(deltadeton + kOn2body) /. eontd -> {100,110} ", "Input"], Cell[BoxData[ \({1.464646922753474`*^-18, 3.377023462083785`*^-18}\)], "Output"] }, Open ]], Cell["\<\ This is rough agreement in magnitude, but the experimental variation with E/n \ is much too small.\ \>", "Subsubtitle"], Cell["\<\ The product of their attachment and detachment coefficients is\ \>", "SmallText"], Cell[CellGroupData[{ Cell["wenOnProduct = {12.*10^-6, 15.*10^-6} (*cm^-2Torr^-2*)", "Input"], Cell[BoxData[ \({0.000012`, 0.000015`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ wenOnProduct2 = wenOnProduct*(100/(3.3*10^22))^2*(wFit /. eontd -> \ {100,110})^2 (*cm^6s-2*)\ \>", "Input"], Cell[BoxData[ \({1.489122417773079`*^-36, 2.169926193273288`*^-36}\)], "Output"] }, Open ]], Cell["\<\ For comparison we add our fits to Phelps' (1987) attachment coefficient and \ Frommhold's (1964) detachment coefficient\ \>", "SmallText"], Cell[CellGroupData[{ Cell["(deltadeton /. eontd -> {100,110}) *phelpsAttInt[{100,110}]", "Input"], Cell[BoxData[ \({8.622528182561755`*^-37, 2.6336268185428758`*^-36}\)], "Output"] }, Open ]], Cell["The agreement is not good, but not too bad.", "Subsubtitle"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Teich, Gaseous Dielectrics VI, ed by Christophorou and Sauers (Plenum, New \ York, 1991), p. 215\ \>", "Subsection"], Cell["\<\ Formulation and example of theoretical flux and density waveforms for oxygen \ at low and at high E/n. No new experimental results.\ \>", "SmallText"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Pasko, Inan, Bell, and Taranko, J. Geophys. Res. 102, 4529 (1997)\ \>", "Subsection"], Cell["\<\ In Fig. 29c the present results for ionization and attachment coefficients \ that essesntially repeats Phelps (1987). 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\>", "SmallText"], Cell["Beam experiments", "Section"], Cell[CellGroupData[{ Cell["Langevin cross section", "Subsection"], Cell["\<\ In this section we consider only the dipole polarizability and neglect the \ higher multipole polarizabilities.\ \>", "SmallText"], Cell["\<\ The value of the mean dipole polarizability for O2 is given by McDaniel and \ Mason (1980) p. 344 as 1.60 Ang^3 so that in atomic units the polarizability \ and the Langevin cross section are \ \>", "SmallText"], Cell[" ao = 0.529*10^-10; (*m^2*)", "Input"], Cell[BoxData[ \(\(\(alphaauO2\ = \ 1.60*10^\(-30\)/ ao^3\ \ ;\)\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\( (*au*) \)\)\)], \ "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(qLangevinO2\ = \ \(\(2*Pi* ao^2*\((\(alphaauO2/ 2\)/\((enrel/ 27.211)\))\)^0.5\)\(\ \ \)\(//\)\(\ \)\(PowerExpand\)\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\( (*m^2\ and\ eV*) \)\)\)], "Input"], Cell[BoxData[ \(2.1321853205340628`*^-19\/enrel\^0.5`\)], "Output"] }, Open ]], Cell["\<\ langevinO2Plot = LinearLogPlot[qLangevinO2, {enrel, 0.01,10}, PlotRange -> \ {{0.,10}, {3.*10^-22,3.*10^-19}}, PlotStyle -> {Hue[0.5],Thickness[0.007]}, \ DisplayFunction->Identity];\ \>", "Input"], Cell["\<\ The corresponding ion mobility at NTP from McDaniel (1964), p. 446, is \ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(muLangevinO2\ = \ 35.9/\(\(\((alphaauO2*32. *16. /\((32. + 16. )\))\)^0.5\)\(\ \ \)\( (*cm^2/V - s*) \)\)\)], "Input"], Cell[BoxData[ \(3.3435175220184408`\)], "Output"] }, Open ]], Cell["or when normalized to unit density", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(muNLangevinO2\ = \ 2.69*10^19*35.9/\((alphaauO2*32. *16. /\((32. + 16. )\))\)^0.5\)], "Input"], Cell[BoxData[ \(8.994062134229605`*^19\)], "Output"] }, Open ]], Cell["The Langevin collision frequency is ", "SmallText"], Cell[CellGroupData[{ Cell["\<\ nuonLangevinO2 = \ 1.602*10^-19/(1.660*10^-27*16.*32./(16.+32.))/(muNLangevinO2*100) (*m^3/s*)\ \ \>", "Input"], Cell[BoxData[ \(1.0059347627367836`*^-15\)], "Output"] }, Open ]], Cell["\<\ The value of the mean dipole polarizability for N2 is given by McDaniel and \ Mason (1980) p. 344 as 1.76 Ang^3 so that in atomic units the polarizability \ and the Langevin cross section are \ \>", "SmallText"], Cell[BoxData[ \(\(\(alphaauN2\ = \ 1.76*10^\(-30\)/ ao^3\ ;\)\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\( (*au*) \)\)\)], \ "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(qLangevinN2\ = \ \(\(2*Pi* ao^2*\((\(alphaauN2/ 2\)/\((enrel/ 27.211)\))\)^0.5\)\(\ \ \)\(//\)\(\ \)\(PowerExpand\)\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\( (*m^2\ and\ eV*) \)\)\)], "Input"], Cell[BoxData[ \(2.2362548301146357`*^-19\/enrel\^0.5`\)], "Output"] }, Open ]], Cell["\<\ langevinN2Plot = LinearLogPlot[qLangevinN2, {enrel, 0.01,10}, PlotRange -> \ {{0.,10},{3.*10^-22.,3.*10^-19}}, PlotStyle -> {Hue[0.5],Thickness[0.007]}, \ DisplayFunction->Identity];\ \>", "Input"], Cell["\<\ The corresponding ion mobility at NTP from McDaniel (1964), p. 446, is \ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(muLangevinN2\ = \ 35.9/\(\(\((alphaauN2*32. *16. /\((32. + 16. )\))\)^0.5\)\(\ \ \)\( (*cm^2/V - s*) \)\)\)], "Input"], Cell[BoxData[ \(3.1879188737317095`\)], "Output"] }, Open ]], Cell["or when normalized to unit density", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(muNLangevinN2\ = \ 2.69*10^19*35.9/\(\(\((alphaauN2*32. *16. /\((32. + 16. )\))\)^0.5\)\(\ \ \ \)\( (*cm^\(-1\)\ V^\(-1\)\ \ s^\(-1\)*) \)\)\)], "Input"], Cell[BoxData[ \(8.575501770338299`*^19\)], "Output"] }, Open ]], Cell["The Langevin collision frequency is ", "SmallText"], Cell[CellGroupData[{ Cell["\<\ nuonLangevinN2 = \ 1.602*10^-19/(1.660*10^-27*16.*32./(16.+32.))/(muNLangevinN2*100) \ (*m^3/s*)\ \>", "Input"], Cell[BoxData[ \(1.0550332798402806`*^-15\)], "Output"] }, Open ]] }, Open ]], Cell["Hasted and Smith, Proc. Roy. Soc. (London) A235, 349 (1956)", \ "Subsection"], Cell["10 to 2500 eV", "Text"], Cell[CellGroupData[{ Cell["\<\ Muschlitz, IV Int. Conf. Ionization Phenomena in Gases, Uppsula (North \ Holland, Ammsterdam, 1960) p 52\ \>", "Subsection"], Cell["O- + O2 inelastic cross section", "Subsubsection"], Cell["!!Muschlitz59Inelastic.dat", "Input", PageWidth->Infinity, Evaluatable->False], Cell["\<\ Read in the data from this file and prepare plots of O- detachment in \ collisions with N2\ \>", "Text"], Cell["\<\ inputfile := \"Muschlitz59Inelastic.dat\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; muschlitz59InelasticPlot =LinearLogListPlot[data1,PlotRange -> \ {{0.,10},{3.*10^-22,3.*10^-19}}, PlotStyle -> \ {Hue[0.1],PointSize[0.02]},DisplayFunction->Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["O- + O2 total cross section", "Subsubsection"], Cell["!!Muschlitz59Total.dat", "Input", PageWidth->Infinity, Evaluatable->False], Cell["\<\ Read in the data from this file and prepare plots of O- detachment in \ collisions with N2\ \>", "Text"], Cell["\<\ inputfile := \"Muschlitz59Total.dat\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; muschlitz59TotalPlot =LinearLogListPlot[data1,PlotRange -> \ {{0.,10},{3.*10^-22,3.*10^-19}}, PlotStyle -> \ {Hue[0.1],PointSize[0.02]},DisplayFunction->Identity];\ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Open ]], Cell["Doering, J. Chem. Phys. 41, 1164 (1964)", "Subsection"], Cell[CellGroupData[{ Cell["Chantry and Schulz, Phys. Rev. 156, 134 (1967)", "Subsection"], Cell["\<\ Measure energy distribution of O- formed by dissociative attachment of \ electrons to O2 for various incident electron energies.\ \>", "SmallText"] }, Open ]], Cell["Snow, Rundel, and Geballe, Phys. Rev. 178, 228 (1969)", "Subsection"], Cell["From 150 to 3000 eV.", "Text"], Cell["Roche and Goodyear, J. Phys. B 2, 191 (1969)", "Subsection"], Cell[CellGroupData[{ Cell["Bailey and Mahadavan, J. Chem. Phys. 52, 179 (1970)", "Subsection"], Cell["O- + O2 plot", "Subsubsection"], Cell["!!c:\\AllProjects\\AirAttDetachmentBailey70Fig10.dat", "Input", PageWidth->Infinity, Evaluatable->False], Cell["\<\ Read in the data from this file and prepare plots of O- detachment in \ collisions with O2\ \>", "Text"], Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\Bailey70Fig10.dat\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; bailey70DetOnPlot =LinearLogListPlot[data1,PlotRange -> \ {{0.,10},{3.*10^-22,3.*10^-19}}, PlotStyle -> {Hue[0.7],PointSize[0.02]}, DisplayFunction->Identity];\ \ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["O2- + O2 -> e plot", "Subsubsection"], Cell["!!c:\\AllProjects\\AirAttDetachmentBailey70Fig11.dat", "Input", PageWidth->Infinity, Evaluatable->False], Cell["\<\ Read in the data from this file and prepare plots of O2- detachment in \ collisions with O2\ \>", "Text"], Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\Bailey70Fig11.dat\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; bailey70DetO2nPlot =LinearLogListPlot[data1,PlotRange -> \ {{0.,10},{3.*10^-22,3.*10^-19}}, PlotStyle -> {Hue[0.3],PointSize[0.02]}, DisplayFunction->Identity];\ \ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["O- + O2 -> O2- + O plot", "Subsubsection"], Cell["!!c:\\AllProjects\\AirAttDetachmentBailey70Fig08.dat", "Input", PageWidth->Infinity, Evaluatable->False], Cell["\<\ Read in the data from this file and prepare plots of O2- charge transfer in \ collisions with O2\ \>", "Text"], Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\Bailey70Fig08.dat\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; bailey70O2nCTPlot =LinearLogListPlot[data1,PlotRange -> \ {{0.,10},{3.*10^-22,3.*10^-19}}, PlotStyle -> {Hue[0.7],PointSize[0.02]}, DisplayFunction->Identity];\ \ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Open ]], Cell["Compton and Bailey, J. Chem. Phys. 53, 454 (1970)", "Subsection"], Cell["\<\ Tiernan, Hughes, and Lifshitz, J. Chem. Phys. 55, 5692 (1971)\ \>", "Subsection"], Cell["O- + O2 -> O2- + O for 0.3 < Ecm < 5 eV ", "Text"], Cell["\<\ Rutherford, Turner, and Vroom, J. Chem. Phys. 58, 5267 (1973)\ \>", "Subsection"], Cell["\<\ O-+O3\[Rule]O3-+O for 1 Elab < 500 eV\ \>", "Text"], Cell["Ranjan and Goodyear, J. Phys. B 6, 1070 (1973)", "Subsection"], Cell[CellGroupData[{ Cell["Comer and Schulz, Phys. Rev. A 10, 2100 (1974)", "Subsection"], Cell["O- + O2 plot", "Subsubsection"], Cell["!!c:\\AllProjects\\AirAttDetachmentComer74.dat", "Input", PageWidth->Infinity, Evaluatable->False], Cell["\<\ Read in the data from this file and prepare plots of O- detachment in \ collisions with N2\ \>", "Text"], Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\Comer74.dat\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; comerN2DetPlot =LinearLogListPlot[data1,PlotRange -> \ {{0.,10},{3.*10^-22,3.*10^-19}}, PlotStyle -> {Hue[0.7],PointSize[0.02]}, DisplayFunction->Identity];\ \ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell["O- + N2 plot", "Subsubsection"], Cell["!!c:\\AllProjects\\AirAttDetachmentComer74O2.dat", "Input", PageWidth->Infinity, Evaluatable->False], Cell["\<\ Read in the data from this file and prepare plots of O- detachment in \ collisions with N2\ \>", "Text"], Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\Comer74O2.dat\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; comerO2DetPlot =LinearLogListPlot[data1,PlotRange -> \ {{0.,10},{3.*10^-22,3.*10^-19}}, PlotStyle -> {Hue[0.8],PointSize[0.02]}, DisplayFunction->Identity];\ \ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Open ]], Cell["Mathis and Snow, J. Chem. Phys. 61, 4274 (1974)", "Subsection"], Cell["\<\ O-+O2\[Rule]O2-+O for 10 Elab < 10,000 eV\ \>", "Text"], Cell["Vogt and Opiela, Phys. Lett. 54A, 331 (1975)", "Subsection"], Cell["\<\ Isotopic studies of O-+O2\[Rule]O2-+O preliminary data \ \>", "Text"], Cell[CellGroupData[{ Cell["Vogt, Dreves, and Mischke, Z. Naturforsch. 32a, 13 (1977)", "Subsection"], Cell["!!c:\\AllProjects\\AirAttDetachmentVogt77.dat", "Input", PageWidth->Infinity, Evaluatable->False], Cell["\<\ Read in the data from this file and prepare plots of O- + O2 -> O2- + O\ \>", "Text"], Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\Vogt77.dat\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; vogtCTPlot = LinearLogListPlot[data1,PlotRange -> \ {{0.,10},{3.*10^-22.,3.*10^-19}}, PlotStyle -> {Hue[0.8],PointSize[0.02]}, DisplayFunction->Identity];\ \ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Open ]], Cell["\<\ Note that Lin et al (1980) appear to assume that the cross sections shown by \ Vogt et al are plotted a factor of ten too small.\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell["Penent et al, J. Phys. B 20, 6065 (1987) O- + N2 -> e + ?", \ "Subsection"], Cell["!!c:\\AllProjects\\AirAttDetachment\\Penent87.dat", "Input", PageWidth->Infinity, Evaluatable->False], Cell["\<\ Read in the data from this file and prepare plots of O- detachment in \ collisions with N2\ \>", "Text"], Cell["\<\ inputfile := \ \"c:\\\\AllProjects\\\\AirAttDetachment\\\\Penent87.dat\"; stream = OpenRead[inputfile]; Find[stream,\"%\"]; Find[stream,\"%\"]; data1 = ReadList[stream, Number,RecordLists ->True]; Close[stream]; penentDetPlot =LinearLogListPlot[data1,PlotRange -> \ {{0.,10},{3.*10^-22,3.*10^-19}}, PlotStyle -> {Hue[1.],PointSize[0.02]}, DisplayFunction->Identity];\ \ \>", "Input", PageWidth->Infinity, FontFamily->"Arial", FontSize->11, FontWeight->"Bold", FontColor->GrayLevel[0], Background->GrayLevel[1]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Champion, in Gaseous Dielectrics ed by Christophorou and Sauers (Plenum, New \ York, 1991) Fig. 3. 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The O- formed by \ dissociative attachment of an electron with O2 is subject to several possible \ ion-molecule reactions as it relaxes in energy toward a steady-state energy \ distribution and as it is destroyed by collisions. These reactions include \ electron detachment in collisions with O2 and N2, charge transfer collisions \ with O2, and three-body reactions with an O2 and with a third body, i.e., O2 \ or N2, to form O3-. On a longer time scale, one may have to include O- \ production by collisional dissociation of O3-, etc. Frommhold and coworkers (1974) discuss a model in which one regards the \ initial attachment and ion reaction sequence as an effective attachment \ process leading to the formation of O2- and O3-. Such a model is \ appropriate when the O- reactions occur on a time scale comparable with the \ O- energy relaxation time. A disadvantage of this approach is that one ends \ up with very odd pressure dependencies for the effective attachment \ coefficients, especially when three-body formation of O3- is included. The initial attachment and ion collision processes in O2 have been modeled \ using Monte Carlo techniques by Okada et al (1978). They neglect the \ three-body formation of O3-. They find that for E/n = 141 Td about 6 \ collisions are required for the O- to reach a steady-state energy \ distribution, i.e., about 6/(6e-10*N) sec (~300 ns at 1 Torr and ~0.4 ns at 1 \ atm pressure), while the e-folding decay of O- number requires about 50 \ collisions (~ 2 us at 1 Torr). I conclude that, this relative long decay \ time for the O- population would seem to show that the rate equation approach \ should work. (Okada et al (1978) do not make a recommendation). This result \ is dependent on the relatively low ratio of the cross sections for O- + O2 \ reactions to the elastic (Langevin) cross section at the energies of the O- \ ions formed by dissociative attachment, i.e., at ~ 1.5 eV Lab or \ = ~1 eV,. Note that this large ratio of elastic to reaction cross sections \ does not hold for higher energy O- collisions, e.g., > 10 eV in center of \ mass. The situation is less clear for the modeling of electron and negative ion \ behavior in air. Depending on which experiment one accepts for O- detachment \ in collisions with N2, the cross section ratio may be less favorable for the \ rate equation approach for air than for O2. See Comer and Schulz (1974) \ versus Lindinger et al (1975).\ \>", "SmallText"], Cell[BoxData[ \(HTMLSave["\"]\)], "Input", Evaluatable->False], Cell[BoxData[ \(TeXSave["\", "\"]\)], "Input", Evaluatable->False], Cell[CellGroupData[{ Cell["runtime = SessionTime[] - startclock", "Input", PageWidth->Infinity], Cell[BoxData[ \(4.`\)], "Output"] }, Open ]] }, FrontEndVersion->"4.1 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 695}}, CellGrouping->Manual, WindowSize->{838, 537}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, CellLabelAutoDelete->True, StyleDefinitions -> "AvpStyle.nb" ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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