Manejo del poder y autoridad dentro de la dinámica familiar en el abuso

> 0.8 - -

0 .4 - -

0.2 - -

0.0

6 3 9 1 0 11 1 2 13 1 4 15

Energy Loss (eV)

Figure 5.20 A differential oscillator strength spectrum for 1-butene obtained in the present electron impact work for the energy range, 6 e V < E < 15 eV.

The DOS spectrum measured for 1-butene in the present electron impact work is shown in figure 5.20. Nine broad features are observed at 7.1 eV, 8.3 eV, 9.2 eV, 9.8 eV, 10.7 eV, 11.5 eV, 12.3 eV, 13.1 eV and 14.5 eV. The energies of some of these broad features are compared with similar broad features observed in the spectra of ethylene and propylene and are presented in table 5.11. The mean energies of the broad features in propylene are approximately 0.5 eV lower than similar features in ethylene and about 0.2 eV higher than similar features in 1-butene. These values are similar to the differences of 0.5 eV and 0.3 eV between the ionisation potentials of ethylene ( — 10.4 eV), propylene ( — 9.9 eV) and 1-butene ( — 9.6 eV).

Table 5.11 The mean energy positions of similar broad features observed in the

present spectra for ethylene, propylene and 1-butene.

Ethylene Propylene 1-butene Ee - Ep Ep - Eg

îrgy Ee (eV) Energy Ep (eV) Energy Ep (eV) (eV) (eV)

7.6 7.2 7.1 0.4 0 . 1 9.2 8.5 8.3 0.7 0 . 2 9.9 9.5 9.2 0.4 0.3 1 0 . 1 9.8 0.3 1 1 . 2 10.9 10.7 0.3 0. 2 1 2 . 2 11.7 11.5 0.5 0 . 2 12.7 12.3 0.4 13.3 13.1 0 . 2

Upon comparison of the fine structure indicated by vertical lines in the 1-butene spectrum with the peaks observed in the ethylene and propylene spectra (figure 5.2), designations have been attempted and are presented in table 5.12. The difference

between the transition energies of propylene and 1-butene for the same transition

varies from 0.14 eV to 0.35 eV, giving an average of —0.3 eV which is comparable

Table 5.12 The designations of similar peaks observed in the present ethylene,

propylene and 1-butene spectra, a, ô and e are unassigned features.

Ethylene Propylene 1-butene

Designation Energy Energy Energy Energy dit

Ee (eV) Ep(eV) Eg (eV) Ep - Eg

N -* 2 R 7.12 6.57 6.40 0.17 a 7.08 6.84 0.24 7.23 7.05 0.18 Ô 7.58 7.26 0.32 N -^ 3 R ' 8.26 7.75 7.43 0.32 N 3R" 8.58 7.97, 8.11 7.62, 7.79 0.35, N -> 3R 8.93 8.31 8 . 1 0 0. 21 N ^ 4R" 9.09 8.50 8.30 0 . 2 0 e 9.23 8.65 8.51 0.14 N -a. 4R" 9.51 8.84 0.33 N ^ 5 R 9.95 9.36 9.10 0.26 N - >6R 1 0 . 1 1 9.50 9.25 0.25

Alternative designations of the fine structure in the 1-butene spectrum are also suggested by consideration of possible vibrational progressions observed in the DOS spectrum. The first possible vibrational series contains peaks at 6.40 eV, 6.62 eV, 6.84 eV, 7.05 eV and 7.26 eV with an average spacing of 0.21 eV. This could be designated as a vibrational progression in the N ^ 2R system, similar to that observed

in ethylene. A vibrational progression for the N 3R' system is suggested for the

peaks at 7.43 eV, 7.62 eV and 7.79 eV with a vibrational spacing of 0.18 eV. Another vibrational series is suggested for the three peaks observed on feature 2 with energies, 8.10 eV, 8.30 eV and 8.51 eV. This series has an average vibrational spacing of 0.21 eV and may be associated with the N ^ 3R system. Finally a fourth vibrational progression is suggested for the peaks at 9.10 eV, 9.25 eV and 9.39 eV observed on feature 3 with an average vibrational spacing of 0.14 eV.

1 . 2 - - 1.D - - > <u % O 0 . 6 -- û 0 .4 - - 0.2 - - 0.0 15 13 7 8 9 1 0 11 1 2 1 4 6

Energy Loss (eV)

Figure 5.21 Differential oscillator strength spectra for 1-butene. — Present work, - - Samson et al. (1961), ... Koizumi et al. (1985).

In figure 5.21 the present DOS spectrum for 1-butene is compared with the DOS

spectra obtained in the optical work of Samson et al. (1961) and the synchrotron work

of Koizumi et al. (1985). Agreement with the spectrum of Samson is extremely good

up to an energy of 11 eV, although the DOS values of Samson are a little higher than the present work in the energy regions, 6 .8 e V < E < 7 .4 e V and 7 .9 e V < E < 8 .8 e V . Above 11 eV Samson’s DOS values become gradually smaller than the present data as the limit of the LiF window is approached. The shape of Koizumi’s spectrum is in good agreement with the present results apart from (1) the energy region, 11.5 e V < E < 12.5 eV, which suffers from large errors of up to 40% due to second order light and (2) the energy region, 12.5 e V < E < 14.0 eV, in which the broad feature observed in Koizumi’s spectrum is not seen in the present work. In general, the DOS values of Koizumi are about 10% lower than the present DOS results for reasons similar to those suggested for propylene.

5.12 Summary

In this chapter, DOS spectra are presented for the four smallest linear alkanes; methane, ethane, propane and n-butane, and the three smallest alkenes; ethylene, propylene and 1-butene. For each hydrocarbon there is good agreement with the chosen sources of DOS data obtained from previous electron impact, optical and synchrotron experiments. Where possible, the observed features in each spectrum have been assigned or designated using various sources of theoretical and experimental data for all of the hydrocarbons apart from 1-butene. In this work

tentative designations of many of the features observed in the 1-butene spectrum have

been made by comparison with the other alkenes. These new designations are presented in table 5.12.

Several trends are observed in the DOS spectra for the small alkanes shown in figure 5.1. As the size of the molecule increases, the threshold energy for electronic excitation decreases and the maximum DOS value observed in the energy region, 7 e V < E < 1 7 eV, increases. These trends are also observed for the small alkenes (figure 5.2). Also the spectra become smoother and less structured as the molecular size increases. The shapes of the DOS spectra for propane and n-butane are very similar although there is less agreement with the other alkanes (methane and ethane) since their structure is complicated by Jahn-Teller splitting. The very close similarities between the spectral features in the alkene series have been essential to the designation of the peaks observed in the 1-butene spectrum (tables 5.11 and 5.12).

CHAPTER 6