FABOX.RU                   
дипломы,курсовые,рефераты,контрольные,диссертации на заказ
Рефераты Химия

Просмотр реферата - Dissociation of Benzene Molecule in a Strong Laser Field

Dissociation of Benzene Molecule in a Strong Laser Field


Скачать реферат Dissociation of Benzene Molecule in a Strong Laser Field в zip архиве





Dissociation of benzene molecule in a strong low-frequency linearly polarized laser field is considered theoretically under the conditions of recent experiments. Analogy with the dissociation of diatomic molecules has been found. The dissociation probability of benzene molecule has been derived as a function of time. The three-photon dissociate process is shown to be realized in experiments.

1. Introduction.
The number of articles devoted to the interaction of molecules with a strong laser field increased considerably in recent years. The main features of interaction between diatomic molecules and a laser radiation were considered in a great number of experimental [1-5] and theoretical [6-9] papers. Classical and quantum investigations of spatial alignment of diatomic molecules and their molecular ions in a strong laser field, as well as ionization and dissociation of these molecules and their molecular ions account for physical pictures of all processes.
However, when considering complex organic molecules, we observe physical phenomena to be richer, and they are not thoroughly investigated. Most of results obtained for diatomic molecules can be generalized to the multi-atomic molecules. This short paper contains the results of theoretical derivations for dissociation of benzene molecule C6H6 in the field of linearly polarized Ti:Sapphire laser. Data were taken from experimental results by Chin’s group, Ref. [4]. We use the atomic system of units throughout the paper.

2. Theoretical approach.
Let us consider the benzene molecule C6H6 in the field of Ti:Sapphire laser with the wavelength ?=400 nm, pulse length ?=300 fs and maximum intensity Imax=2?1014 W/cm2. According to Ref. [4] first electron is ejected from this neutral molecule and then the dissociation of C6H6+-ion occurs.
The most probable channel for decay of this ion is the separation into the equal parts :

Of course, there is another channel for decay of C6H6+-ion which includes the ejection of the second electron and subsequent Coulomb explosion of the C6H6++-ion. We do not consider the latter process.
The channel (1) is seen to be similar to the dissociation of the hydrogen molecular ion considered in Ref. [2]. Indeed, the model scheme of energy levels for C6H6+-ion (see Ref. [4]) reminds the model scheme of energy levels for H2+ [2] containing only two low-lying electronic levels: 1?g (even) and 1?u (odd).
Therefore we consider the dissociation process of C6H6+-ion analogously to that for H2+-ion (see Fig. 1). The benzene molecular ion has the large reduced mass with respect to division into equal parts. Hence, its wave function is well localized in space (see Fig. 2) and therefore we can apply classical mechanics for description of the dissociation process (1). However, the solution of Newton equation with the effective potential (see below) does not produce any dissociation, since laser pulse length is too small for such large inertial system. In addition to, effective potential barrier exists during the whole laser pulse and tunneling of the molecular fragment is impossible due to its large mass ( see Fig. 2). Thus, we should solve the dissociation problem in the frames of quantum mechanics.
The ground even electronic term of C6H6+-ion is presented here in the form of the well-known Morse potential with parameters ?=2k and De=6.2 эВ, where k is approximated by the elastic constant of C-C coupling in the C6H6-molecule and De is the dissociation potential for the C2-molecule. The interaction of the molecular ion with the laser field is given by expression (see. Ref. [9])
Where the strength envelope of the laser radiation is chosen in the simple Gaussian form F(t)=F0exp(-t2/2?2) and R internuclear separation between the fragments C3H3+ and C3H3, ? is the laser frequency and ? is the laser pulse length. The value?sin?t? takes into account the repulsion between the involved ground even electronic term and the first excited odd repulsive electronic term.

Thus, the Hamiltonian of the concerned system is

The kinetic energy operator being of the form

Where Re is the equilibrium internuclear separation. When calculating we make use of Re=1.39 A.
The time dependent Schrodinger equation with Hamiltonian (3) has been solved numerically by the split-operator method. The wave function has been derived by the iteration procedure according to formula

The initial wave function ?(R,0) was chosen as the solution of the unperturbed problem for a particle in the ground state of Morse potential.
The dissociation probability has been derived as a function of time according to formula W(t)=?



Обзор других работ по химии



Ректификация

да из формул (13) и (14) следует


Подставив результаты в (11) и (12) получаем:



2.2 Скорость пара и диаметр колонны

На этой стадии необходимо выбрать тип тарелки. Поскольку предполагается, что жидкость не содержит взвешенных частиц выберем используем ситчатые тарелки.

Допустимая скорость в верхней и нижней части колонны определяется по формуле:
(15)
Поскольку плотности бензола и толуола близки, то плотность жидкой фазы может быть приближенно определена как 796 кг/м3.
Средняя плотность пара для нижней и для верхней части колонны может быть определена по формуле:
(16)
где t - температура для верхней или для нижней части колонны.
Температура в колонне, в свою очередь, определяется по диаграмме t - x,y, которую можно увидеть на рисунке 2.

Рисунок 2
Диаграмма t - x,y
По средним сост   Читать       

Теплопроводность в сплошных средах и двухфазных, продуваемых и непродуваемых телах (слоях).

дится в некоторых случаях отказываться, например, при движении потока теплоты навстречу потоку газа и при нестационарном нагревании или охлаждении слоя потоком газа (подробнее эти случаи будут рассмотрены ниже).
В соответствии с аналогией тепло- и массопереноса, перенос теплоты в движущейся через зернистый слой среде подчиняется тем же закономерностям, что и транспорт вещества. Однако то обстоятельство, что теплота в зернистом слое в отличие от вещества распространяется как через жидкую, так и через твердую фазу, приводит к существенному нарушению подобия коэффициентов диффузии и теплопроводности в области малых критериев Рейнольдса. Так, при Reэ
Общая зависимость для коэффициента теплопроводности выражается в виде следующего уравнения:
Величина ?0 представляет собой сумму всех компонентов теплопереноса, не зависящих от u (скорости потока). Существенным составляющим в нее входит теплоперенос при неподвижной среде в слое ?оэ. При возникновении естес   Читать

  
© 2000 — 2017, Все права защищены