Thursday Feb. 12, 2009

We'll finish up the material on small ions today.

On Tuesday we looked at some of the sources of radiation that ionize air.  When neutral oxygen or nitrogen are ionized you are left with a positively charged N2 or O2 molecule and a free electron.  The electron subsequently attaches to neutral oxygen molecules (but not to nitrogen).

We can estimate how long it will be before the electron attaches to a neutral molecule.  In the case of attachment to oxygen we need to know the oxygen concentration in air, [O2],  and a rate constant k1.

We can use the ideal gas law equation to determine the oxygen concentration.  Electron attachment occurs very quickly, in a few or a few tens of nanoseconds.



The next step in small ion formation is clustering of a chemical species of some kind around the positively and negatively charged ions.  This occurs on a millisecond time scale.  In the figure above we show ionized nitrogen and oxygen molecules.  This is just one possibility.  CO4-  is apparently one of the more common ions found in the centers of these molecular clusters also.  And something other than water may envelope the central ion.

The mobilities of positively and negatively charged small ions are slightly different.  Typical values are shown above.  The positively charged small ions have a slightly higher mobility (slightly lower drift speed) than the negatively charged ions.

That's an ion balance equation at the bottom of the page above.  At this point the small ion concentration will depend on the ion production rate, q, and the rate at which ions recombine and neutralize each other.  The next figure gives the general and steady state solutions to the ion balance equation.


The small ion concentration reaches steady state pretty quickly.


Here is a table of typical electrical parameter values at different altitudes.

This information was compiled by Dr. Krider and was on a handout distributed in class.

The small ion balance equation has been modified by adding two loss terms.  The first involves small ion attachment to a neutral aerosol particle.  The second is small ion attachment to a charged aerosol particle of the opposite polarity.

The first balance equation is often simplified somewhat by lumping together the charged and uncharged aerosol particles.  Z above is the total aerosol concentration.

This next page is a copy of a handout with some properties of aerosols.

 The remaining notes were on a handout distributed in class.  We didn't really go through this material in detail, this is more "for your information" kind of stuff.

On the page above and the one below, a pretty good estimate of the attachment coefficient to neutral aerosol particles can be estimated using molecular diffusion.


The attachment to charged aerosol particles can also be estimated to within a factor of two using a relatively simple approach.

Small ion recombination is usually much smaller than loss by attachment to aerosol particles.  Here is the steady state solution when recombination is neglected.

On this next page we look at what fraction of the aerosol particles (total concentration = Z) are uncharged.  The calculated estimate is compared with measurements.  The agreement is not very good, especially for smaller particles.


On the next page, the uncharged fraction is computed using Boltzmann theory.


A couple of points to note: the uncharged fraction approaches 1 for the smaller particles.  The smaller particles that are charged only hold one electronic charge.