ABSTRACT
Water (H2O) molecule is polar and electron-attaching, and it has 10 electrons The electronic polarizability is 161 × 10−40 F m2, the dipole moment is 1845 D, and the ionization potential is 12621 eV The molecule has three vibrational modes as shown in Table 371 (Shimanouchi, 1972)
See Table 372
Table 373 shows the recommended total scattering cross sections for water vaporFigure 371 shows these and measured data The main points to note are
1 A minimum in the total cross section at ~4 eV and a maximum at ~10 eV, the latter phenomenon being attributed to attachment processes
2 A decrease in the total cross section for energies >10 eV, a feature common to many gases
3 A trend toward increasing cross section as the energy decreases below 1 eV It is noted that the dipole moment of water molecule exceeds the minimum value of 167 D for the formation of parent negative ion (Crawford, 1967)
Figure 372 shows the differential scattering cross sections for elastic scattering in the low-energy range 22-20 eV
371 Selected References for Data 247 372 Total Scattering Cross Sections 247 373 Differential Scattering Cross Sections 247 374 Elastic and Momentum Transfer Cross Sections 249 375 Vibrational Excitation Cross Sections 250 376 Ion Appearance Potentials 250 377 Ionization Cross Sections 250 378 Attachment Cross Sections 251 379 Dissociation Cross Section 253 3710 Electron Drift Velocity 253 3711 Diffusion Coefficients 253 3712 Ionization Coefficients 253 3713 Gas Constants 254 3714 Attachment Coefficients 255 3715 Attachment Rate Constant 256 3716 Positive Ion Mobility 256 3717 Addendum 256 References 256
TABLE 37.1 Vibrational Modes and Energies
Designation Motion Energy (meV)
ν1 Symmetrical stretching 4534 ν2 Bending 1978 ν3 Asymmetical stretching 4657
Source:Adapted from Shimanouchi, T, Tables of Molecular Vibrational Frequencies Consolidated Volume I, NSRDS-NBS 39, US Department of Commerce, Washington (DC), 1972
Selected References for DH2O
Quantity Range: eV, (Td) Reference
Total scattering cross section
15-10,000 Champion et al (2002)
Dissociation cross section
10-300 Harb et al. (2001)
Vibrational excitation cross section
6-20 El-Zein et al. (2000)
Ionization cross section 135-1000 Straub et al. (1998) Ionization cross section 126-5000 Hwang et al (1996)
Vibrational excitation cross section
4-10 Cvejanovic´ et al (1993)
Elastic scattering 6-50 Johnstone and Newell (1991)
Total scattering cross section
25-300 Sagˇlam and Aktekin (1990)
Ionization cross section 15-400 Orient and Srivastava (1987)
Elastic scattering cross section
22-20 Shyn and Cho (1987)
Total scattering cross section
813-3000 Zecca et al. (1987)
Ionization cross section 50-2000 Bolorizadeh and Rudd (1986)
Elastic scattering cross section
100-1000 Katase et al. (1986)
Total scattering cross section
1-400 Sueoka et al. (1986)
Elastic scattering cross section
3-200 Nishimura (1985)
Ro-vibrational cross section
05-60 Jung et al. (1982)
Ionization coefficients (30-3000) Risbud and Naidu (1979)
Attachment coefficients (40-180) Risbud and Naidu (1979)
Vibrational excitation 05-30 Rohr (1977) Vibrational excitation cross section
05-10 Seng and Linder (1976)
Transport coefficients (1-25) Wilson et al. (1975) Attachment cross sections
0-13 Melton (1972)
Cross sections Compilation Olivero et al (1972)
Attachment coefficients (40-80) Parr and Moruzzi (1972)
Attachment cross section 0-15 Compton and Christophorou (1967)
Ionization cross section 100-20,000 Schutten et al. (1966) Drift velocity (170-265) Ryz˙ko (1965) Drift velocity (006-60) Pack et al. (1962) Ionization and attachment coefficients
(75-150) Prasad and Craggs (1960)
Attachment coefficients (50-80) Kuffel (1959) Attachment processes – Mann et al. (1940)
Note:Bold font indicates experimental study
Total Scattering Cross Sections for Water Vapor
Energy (eV) QT (10-20 m2) Energy (eV) QT (10-20 m2)
10 292 200 113
12 243 220 110
14 207 250 102
16 179 300 95
18 171 350 90
20 158 400 85
22 150 500 75
25 139 600 71
28 130 700 67
31 122 800 63
34 120 900 60
37 117 100 56
40 122 120 52
45 117 150 46
50 119 200 40
55 120 250 35
60 125 300 32
65 123 350 29
70 126 400 26
75 130 500 25
80 130 600 21
85 133 700 19
90 132 800 17
95 127 900 16
100 127 1000 14
110 130 1250 12
120 128 1500 100
130 127 1750 087
140 125 2000 075
150 123 2250 069
160 120 2500 060
170 118 2750 054
180 117 3000 049
190 116
Zecca (1987)
Recommended Saglam (1990) Saglam (1991) Sueoka (1986)
Q T (1
m 2 )
1.0
0.1 100 101 102
Total scattering (H2O)
Energy (eV) 103 104
tinues up to ~50 eV (not shown) (Johnstone and Newell, 1991) The minimum tends to flatten out at energies >100 eV as shown in Figure 373 (Katase et al, 1986) Note the increased forward scattering at higher energies
Table 374 and Figures 374 and 375 show the suggested integral elastic and momentum transfer cross sections
10-15
10-16
dσ /d Ω
(c m
2 / sr
)
10-17 0 30 60 90 120
H2O Elastic cross section
θ (°) 150 180
101 0 40 80
Scattering angle
Di ffe
re nt
ial cr
os ss
ec tio
n (1
m 2 /
sr )
(deg)120 160
TABLE 37.4 Suggested Integral Elastic and Momentum Transfer Cross Sections
Energy (eV) Qel (10-20 m2) QM (10-20 m2)
2 1170 623
3 1283 687
5 1405 799
7 1445 874
10 1532 882
15 1454 912
20 1340 804
30 1104 664
40 953 508
50 814 422
60 684 325
70 599 227
80 514 184
90 467 146
100 427 116
125 335 081
150 288 060
175 249 051
200 217 041
300 169 026
400 125 019
500 106 015
600 091 011
700 084 010
800 076 007
900 071 007
1000 059 006
0.1 1 10 100
Energy (eV)
Elastic scattering (H2O)
Q e l(
10 –2
0 m 2 )
The bending mode is designated as (010), symmetric stretch as (100), and asymmetric stretch as (001)In view of the proximity of the quanta of energies for the latter two excitations modes (Table 371), excitation cross sections for (100 + 001) are measured togetherThese are shown in Table 375 (Brunger et al, 2003) and Figure 376
processes for ion formation (Mann et al, 1940)Process 1 is direct ionization, 2-6 are dissociative ionization, 7-9 dissociative attachment, and 10-11 ion pair formation
Table 377 shows the total ionization cross sections (Straub et al, 1998; Schutten et al, 1966) with good agreement between the two sets up to 1000 eV For higher energies the cross sections of Schutten et al (1966) are the only available data Figure 377 shows comparison with selected data Figure 378 shows partial ionization cross sections of selected fragments
Q M (1
m 2 )
0.1 1 10 100
Energy (eV)
Momentum transfer (H2O)
0.6
0.4
0.2Q v (1
m 2 )
0 1 10
Energy (eV)
B
A
TABLE 37.6 Ion Appearance Potentials and Probable Processes
Ion Appearance
Potential (eV) Process
1 H2O+ 130 H2O + e → H2O+
2 OH+ 187 H2O + e → H + OH+
3 O+ 188 H2O + e → H2 + O+
4 281 H2O + e → 2H + O+
5 H+ 195 H2O + e → OH + H+
6 H2+ 230 H2O + e → O + H2+
7 H− 56 H2O + e → OH + H−
8 H2O + e → O + H + H−
9 O− 015 H2O + e → 2H + O−
10 H2O + e → H + H+ + O−
11 H2O + e → H+ + H+ + O−
12 OH− 43a H2O + H− → OH− + H2 69a
88a
Source: Adapted from Mann, M V, A Hustrulid, and J T Tate, Phys. Rev, 58, 340, 1940
a Indicates Melton (1972)
TABLE 37.5 Vibrational Excitation Cross Sections
Energy (eV)
Qex (10-20 m2)
Mode: (000→001)
Mode: (000→100+001)
1 0370 0500
2 0200
21 0320
22 0190
3 0160 0310
4 0150 0385
5 0157 0430
6 0163 0489
7 0520
75 0317 0529
8 0495
875 0227
8875 0413
10 0180 0325
15 0130 0190
20 0100 0080
Source:Adapted from Brunger, M, SBuckman, and MElford, Excitation cross sections, in Interactions of Photons and Electrons with Molecules, Vol17, Springer-Verlag, New York, NY, 2003, Chapter 64, pp 118-201
The negative ion species detected are H−, O−, and OH− with decreasing abundance in that order (Itikawa, 2003)Data for the production of H− and O− ions are shown in Table 378
Tables 379 through 3712 show the attachment cross sections for the formation of negative ions from H2O (Itikawa,
Total Ionization Cross S
Straub et al. (1998) Schutten et al. (1966)
Energy (eV) Qi (10-20 m2) Energy (eV) Qi (10-20 m2)
135 00340 20 046 15 0133 30 097 175 0292 50 157 20 0460 80 198 225 0638 90 201 25 0801 100 198 30 1087 120 196 35 1322 160 183 40 1529 200 171 45 1677 300 146 50 1802 400 126 60 1992 500 112 70 2097 600 100 80 2187 1000 0622 90 2224 2000 0375 100 2252 3000 0261 110 2252 4000 0220 125 2216 5000 0183 150 2152 6000 0160 175 2076 8000 0123 200 2008 10,000 0101 250 1821 12,000 0088 300 1647 14,000 0078 400 1417 16,000 0064 500 1205 18,000 0058 600 1062 20,000 0054 700 0932 800 0848 900 0776 1000 0707
1Q i (1
m 2 )
0 10 100 1000
Energy (eV) 10,000
Ionization (H2O)
(b)
(c)
Q i (1
0 10 100
Ionization (H2O)
Total H2O+ + OH+ + O+
Q i (1
m 2 )
0 10 100
H+ (×0.1)
Q i (1
m 2 )
0 10 100
Energy (eV)
H2+ (×0.001)
TABLE 37.8 Data for Dissociative Attachment Cross Section
Ion Onset Energy
(eV) Peak Energy
(eV) Peak Cross
Section (m2) Reference
H− 55 64 66 × 10−22 Melton (1972) 73 86 16 × 10−22
O− 44 66 13 × 10−23
70 84 32 × 10−23
85 112 57 × 10−23
OH− 43 64 12 × 10−25
69 84 85 × 10−26
88 112 85 × 10−26
H− 57 65 69 × 10−22 Compton and Christophorou (1967)
73 86 13 × 10−22
O− 49 69
78 89 114
H− 67 Dorman (1966)
88
O− 66
89 114
H− 56 65 Schulz (1960)
85
continued
TABLE 37.9 Attachment Cross Sections for Formation of H-/H2O
Energy (eV) Qa (10-22 m2) Energy (eV) Qa (10-22 m2)
550 0020 769 0877
574 0160 789 0740
590 0985 800 0790
601 4300 809 0995
617 6220 814 1090
629 6317 854 1166
640 6370 840 1040
652 6250 879 0760
665 5790 901 0620
681 4890 957 0280
700 3560 980 0170
747 1290 1000 0098
Source:Adapted from Itikawa, Y, Interactions of Photons and Electrons with Molecules, Vol17, Springer-Verlag, New York, NY, 2003, Chapter 52, pp 78-114
Data for Dissociative ACross Section
Ion Onset Energy
(eV) Peak Energy
(eV) Peak Cross
Section (m2) Reference
O− ~12
H− 48 60 Cottin (1959)
80
O− 74 915
1125
H− 56 71 Mann et al (1940)
89
O− 75 82
111
128
H− 68 Lozier (1930)
88
TABLE 37.10 Attachment Cross Sections for Formation of O-/H2O
Energy (eV) Qa (10-22 m2) Energy (eV) Qa (10-22 m2)
459 0004 664 0100
471 0011 700 0079
500 0025 719 0031
529 0050 730 0029
572 0091 743 0036
600 0116 756 0062
619 0128 770 0133
632 0133 800 0230
645 0122 821 0286
TABLE 37.11 Attachment Cross Sections for Formation of OH-/H2O
Energy (eV) Qa (10-22 m2) Energy (eV) Qa (10-22 m2)
451 00009 819 00780
475 00019 831 00820
500 00040 839 00830
521 00066 853 00810
539 00109 864 00756
556 00165 885 00570
569 00246 900 00436
584 00379 923 00304
600 00537 936 00244
610 00757 949 00201
627 01048 957 00194
636 01140 965 00202
644 01160 978 00229
654 01154 1001 00358
663 01105 1026 00530
677 00950 1052 00669
687 00763 1083 00775
702 00624 1100 00824
715 00489 1113 00847
732 00376 1130 00830
741 00356 1145 00795
749 00345 1160 00699
760 00360 1187 00482
773 00417 1200 00402
783 00480 1219 00311
802 00670 1247 00184
Source:Adapted from Itikawa, Y, Interactions of Photons and Electrons with Molecules, Vol17, Springer-Verlag, New York, NY, 2003, Chapter 52, pp 78-114
Cross Sections for Formation of O-/H2O
Energy (eV) Qa (10-22 m2) Energy (eV) Qa (10-22 m2)
835 0310 1066 0550
844 0316 1080 0570
860 0310 1090 0576
876 0285 1100 0576
900 0244 1118 0553
922 0213 1150 0466
940 0208 1200 0327
956 0214 1250 0200
967 0226 1300 0108
989 0256 1328 0069
1000 0285 1363 0038
1014 0337 1380 0026
1046 0493 1400 0023
Source:Adapted from Itikawa, Y, Interactions of Photons and Electrons with Molecules, Vol17, Springer-Verlag, New York, NY, 2003, Chapter 52, pp 78-114
energy, a process involving considerable computation
Dissociation cross sections due to electron impact with production of ground-state OH molecule have been measured by Harb et al (2001) as shown in Table 3713 and Figure 3710
See Tables 3914 and 3915
See Tables 3916 (Crompton, 1965) and 3917 Figure 3713 shows the number density-normalized diffu-
sion coefficient (ND) for water vapor
Density-reduced ionization coefficients have been measured by Risbud and Naidu (1979) as shown in Table 3718 and Figure 3714
10-1
10-2
Q a (1
m 2 )
10-3 4 8 12
Energy (eV)
Cross Section
Energy (eV) Qa (10-22 m2) Energy (eV) Qa (10-22 m2)
11 001 80 206
13 003 90 204
15 038 100 203
17 051 120 202
20 076 140 201
25 117 160 194
30 128 180 183
35 156 200 178
40 166 220 167
45 170 240 160
50 181 260 154
60 202 280 150
70 207 300 150
Source:Digitized and interpolated from Harb, T, WKedzierski, and JW McConkey, J. Chem. Phys, 115, 5507, 2001
(1 0-
2 )
0 0 50 100 150
Energy (eV)
Dissociation (H2O)
Halb et al. (2001)
200 250 300
TABLE 37.12 Total Attachment Cross Sections for H2O
Energy (eV) Qa (10-22 m2) Energy (eV) Qa (10-22 m2)
45 00009 900 0910
475 0015 925 0738
500 0029 950 0554
525 0054 975 0447
550 0104 1000 0418
575 0223 1025 0443
600 4191 1050 0574
625 6548 1075 0640
650 6522 1100 0658
675 5459 1125 0621
700 3703 1150 0543
725 2170 1175 0452
750 1280 1200 0367
800 1085 1250 0217
825 1479 1300 0108
850 1545 1350 0048
875 1186 1400 0023
TABLE 37.15 Drift Velocities of Electron in Water Vapor
E/N (Td) W (105 m/s) E/N (Td) W (105 m/s)
170 229 220 270
180 237 230 278
190 245 240 287
200 254 250 295
210 262 220 270
Source:Adapted from Ryz˙ko, H, J. Phys. B: At. Mol. Phys., 85, 1283, 1965
TABLE 37.17 Ratio of Longitudinal Diffusion Coefficient to Mobility
E/N (Td) DL/µ (V) E/N (Td) DL/µ (V)
45 00260 35 00264
6 00255 375 013
75 00261 40 037
9 00280 45 102
105 00269 50 220
12 00284 55 332
15 00292 60 419
18 00287 65 434
21 00311 70 407
24 00350 75 335
27 00414 775 364
30 00425
Source:Adapted from Wilson, J F et al, J. Chem. Phys, 62, 4204, 1975 Note:See Figure 3712 for graphical presentation
Ratio of Radial Diffusion Coefficients to Mobility (D/µ) E/N (Td) Dr/µ (V) E/N (Td) Dr/µ (V)
60 18 825 285
6775 203 90 296
75 26
Source:Adapted from Crompton, RW, JARees, and R L Jory, Aust. J. Phys, 18, 541, 1965
Note:See Figure 3712 for graphical presentation
TABLE 37.14 Drift Velocities of Electron in Water Vapor
E/N (Td) W (m/s) E/N (Td) W (m/s)
150 277 × 102 330 806 × 103
225 502 × 102 360 884 × 103
300 653 × 102 390 103 × 104
450 990 × 102 420 118 × 104
600 133 × 103 450 139 × 104
750 167 × 103 480 168 × 104
100 222 × 103 510 210 × 104
120 267 × 103 540 234 × 104
135 302 × 103 570 295 × 104
150 337 × 103 600 356 × 104
165 370 × 103 630 425 × 104
180 404 × 103 660 518 × 104
210 479 × 103 690 591 × 104
240 559 × 103 720 695 × 104
270 635 × 103 750 770 × 104
Source: Adapted from Wilson, J F et al, J. Chem. Phys, 62, 4204, 1975 Note:See Figure 3711
W (m
/s )
102 100 101 102
E/N (Td)
Drift velocity (H2O)
0.1
0.01 0 20 40 60
Diffusion coeff./mobility (H2O)
D/ μ
(V )
E/N (Td) 80 100
α N
F GN E
= −
exp (371)
are F = 125 × 10−20 m2 and G = 3854 Td−1 See inset of Figure 3714
Table 3719 and Figure 3715 show density-reduced attachment coefficients
TABLE 37.19 Density-Reduced Attachment Coefficients for Water Vapor
E/N (Td) η/N (10-22 m2) E/N (Td) η/N (10-22 m2)
70 390 115 616
75 454 120 613
80 499 125 600
85 538 130 582
90 571 140 560
95 589 150 517
100 599 160 476
105 606 170 428
110 613
Source:Adapted from Risbud, AVand MSNaidu, J. Physique Colloque, c7, Supplément au n°7, 40, c7-77, 1979
η/ N
(1 0-
2 )
0 40 80 120
Attachment coeffient (H2O)
E/N (Td) 160
10-1
10-2N D
(1 02
s1 )
10-3 0 50 100 150
E/N (Td)
Diffusion coeffient (H2O)
200 250
E/N (Td)
10-3
10-2α /N
(1 0-
2 )
2 )10-1
100 Ionization coeffient
TABLE 37.18 Density-Reduced Ionization Coefficients for Water Vapor
E/N (Td) α/N (10-20 m2) E/N (Td) α/N (10-20 m2)
500 00007 160 012
550 0002 170 014
600 0002 200 018
650 0003 225 023
700 0003 250 029
750 0005 275 033
800 0007 300 035
850 0011 400 053
900 0015 500 071
950 0018 600 089
100 0022 700 112
105 0027 800 132
110 0035 900 149
115 0043 1000 167
120 0051 1500 257
125 0061 2000 340
130 0073 2500 416
140 0091 3000 480
150 010
Source:Adapted from Risbud, AVand MSNaidu, J. Physique Colloque, c7, Supplément au n°7, 40, c7-77, 1979
Table 3720 shows the attachment rate constants as function of E/N under swarm conditions (Compton and Christophorou, 1967)
The mobility of positive ions, 0061 m2/V s is constant over the range of 150-270 Td at N = 322 × 1022 m−3 (Ryz˙ko, 1965)
A more complete set of vibrational excitation cross sections has been provided by Olivero et al (1972)
Attachment Rate CWater Vapor
E/N (Td) ka (m3/s) E/N (Td) ka (m3/s)
120 23 × 10−18 195 439 × 10−17
135 57 × 10−18 210 583 × 10−17
150 123 × 10−17 225 726 × 10−17
165 211 × 10−17 24 879 × 10−17
180 321 × 10−17
Source: Adapted from Compton, R N and L G Christophorou, Phys. Rev, 154, 110, 1967
