Senftleben-Beenakker effect
Encyclopedia
The Senftleben-Beenakker effect is the dependence on a magnetic or electric field of transport properties (such as viscosity
and heat conductivity) of polyatomic gases. The effect is caused by the precession
of the (magnetic or electric) dipole
of the gas molecules between collisions. The resulting rotation of the molecule averages out the nonspherical part of the collision cross-section
, if the field is large enough that the precession time is short compared to the time between collisions (this requires a very dilute gas). The change in the collision cross-section, in turn, can be measured as a change in the transport properties.
The magnetic field dependence of the transport properties can also include a transverse component; for example, a heat flow perpendicular to both temperature gradient and magnetic field. This is the molecular analogue of the Hall effect
and Righi-Leduc effect for electrons. A key difference is that the gas molecules are neutral, unlike the electrons, so the magnetic field exerts no Lorentz force
. An analogous magnetotransverse heat conductivity has been discovered for photons and phonons.
The Senftleben-Beenakker effect owes its name to the physicists Hermann Senftleben (Münster University, Germany) and Jan Beenakker (Leiden University, The Netherlands), who discovered it, respectively, for paramagnetic gases (such as NO and O2) and diamagnetic gases (such as N2 and CO). The change in the transport properties is smaller in a diamagnetic gas, because the magnetic moment is not intrinsic (as it is in a paramagnetic gas), but induced by the rotation of a nonspherical molecule. The importance of the effect is that it provides information on the angular dependence of the intermolecular potential. The theory to extract that information from transport measurements is based on the Waldmann-Snider equation (a quantum mechanical version of the Boltzmann equation
for gases with rotating molecules). The entire field is reviewed in a two-volume monograph.
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
and heat conductivity) of polyatomic gases. The effect is caused by the precession
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...
of the (magnetic or electric) dipole
Dipole
In physics, there are several kinds of dipoles:*An electric dipole is a separation of positive and negative charges. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some distance. A permanent electric dipole is called an electret.*A...
of the gas molecules between collisions. The resulting rotation of the molecule averages out the nonspherical part of the collision cross-section
Cross section (physics)
A cross section is the effective area which governs the probability of some scattering or absorption event. Together with particle density and path length, it can be used to predict the total scattering probability via the Beer-Lambert law....
, if the field is large enough that the precession time is short compared to the time between collisions (this requires a very dilute gas). The change in the collision cross-section, in turn, can be measured as a change in the transport properties.
The magnetic field dependence of the transport properties can also include a transverse component; for example, a heat flow perpendicular to both temperature gradient and magnetic field. This is the molecular analogue of the Hall effect
Hall effect
The Hall effect is the production of a voltage difference across an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current...
and Righi-Leduc effect for electrons. A key difference is that the gas molecules are neutral, unlike the electrons, so the magnetic field exerts no Lorentz force
Lorentz force
In physics, the Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:...
. An analogous magnetotransverse heat conductivity has been discovered for photons and phonons.
The Senftleben-Beenakker effect owes its name to the physicists Hermann Senftleben (Münster University, Germany) and Jan Beenakker (Leiden University, The Netherlands), who discovered it, respectively, for paramagnetic gases (such as NO and O2) and diamagnetic gases (such as N2 and CO). The change in the transport properties is smaller in a diamagnetic gas, because the magnetic moment is not intrinsic (as it is in a paramagnetic gas), but induced by the rotation of a nonspherical molecule. The importance of the effect is that it provides information on the angular dependence of the intermolecular potential. The theory to extract that information from transport measurements is based on the Waldmann-Snider equation (a quantum mechanical version of the Boltzmann equation
Boltzmann equation
The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in rarefied gas...
for gases with rotating molecules). The entire field is reviewed in a two-volume monograph.
External links
- Historical remarks on the experiment by Jan Beenakker.
- Historical remarks on the theory by Siegried Hess (a student of Ludwig WaldmannLudwig WaldmannLudwig Waldmann was a German physicist who specialized in transport phenomena in gases. He derived the Waldmann-Snider equation.-Career:...
).