Sigma and pi Orbitals

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Return to Molecular Orbitals Menu | Next Topic Polarization is an important concept in designing electro optical materials.

If you have any mechanism to apply an external electrical field this may lead to polarization of the molecules. In electronic polarization the field pulls electrons more than it repells the nucleus because electrons are far lighter than the protons and neutrons. The timescale for polarization of a atom due to a field is 10 -15 seconds. This is about as fast as you can do things.

If two atoms with unequal electronegavity are bonded the molecule will have a dipole moment. A vibration of the atoms results in a change in the position of the nuclei and the electrons follow the nuclei. This happens on a timescale of picoseconds. Infrared leads to vibrations of molecules. The reciprocal of the frequency of IR has a time constant of 100 femptoseconds.

You can have molecules that already have a dipole moment and place them in an electronic field the molecules will align. This time constant for this rotation is in the area of 10s of nanoseconds. Microwave radiation can be used to cause rotations in molecules.

If there are ions in the presence of an electric field there will be a bulk motion. If there is an oscillating electronic field it needs to be matched to the timescale of the polarization mechanism. Only those components that react as fast or faster than the frequency will make a contribution to the bulk polarization of the material. The following animation demonstrates these four types.

<swf width="500" height="400">http://depts.washington.edu/cmditr/media/01 Polarization Mechanisms.swf</swf>

Here is an hydrogen atom in an oscillating electric field. The atom is is oscillating as the electrons are being displaced and the energy levels are changing.

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In an atom with π orbitals there is more polarizability in the π orbitals than in the σ orbitals. Dyes are typically π conjugated compounds because π orbitals are more polarizable in the visible spectrum.

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Molecules that have a dipole moment will orient in an electric field. These are known as second order non-linear material. The force that is on the system is a torque that is related to angle between dipole and the electric field, and upon the magnitude of the field and the dipole. If the molecule is aligned with the field it will not feel a torque. If it oriented at 90 degrees it will feel a substanstial torque.

Dipole is vector quantity, it has a magnitude and a direction. An opposite field will induce a dipole in the opposite direction.

If you plot dipole moment against the electric field you get a straight line. The slope (α) of the line for the function is the linear polarizability. A higher α means a greater amount of polarization for the same amount of applied field.

<math>\mu = \alpha |Epsilon\,\!</math>

Dipole align.jpg