Re: [Phys-L] Infinite square well experimental data?

[Jim Diamond <jiminoregon@gmail.com>]

There is a classic physical chemistry experiment which measures the
absorption spectrum of a few members of a series of organic dyes with
conjugated (a chain of alternating double- and single-bonded) carbon atoms.
The conventional experiment uses merocyanine dyes, which are toxix. This is
experiment #34 in the well-known physical chemistry textbook
  Experiments in Physical Chemistry
  8th Edition
  By Carl Garland and Joseph Nibler and David Shoemaker
http://www.mheducation.com/highered/product.M0072828420.html

These molecules are based on the sequence
H2C=CH2 (ethylene) with the 'carbon-only' structure //
H2C=CH-HC=CH2 (butadiene) with the  structure // \ //
H2C=CH-HC=CH-HC=CH2 (hexatriene) with the  structure // \ // \ //

which have 1, 2, and 3 double bonds, respectively (these double bonds
correspond to electron pairs in π molecular orbitals, if that means
something to you). The infinite square-well AKA particle-in-a-box model can
be used successfully to determine the C=C bond length, through the
approximate result that the wavelength of maximum absorption is roughly
proportional to the number of double bonds (which suggests why carrots are
orange as well as a primitive explanation for stealth technology).

Butadiene, hexatriene, and longer polyenes tend to polymerize, but chemical
modifications (such as sticking benzene group at each each of the polyene
chain) can stabilize these compounds.

I prefer the "alpha,omega diphenyl" polyenes to the cyanine dyes because
they are relatively inexpensive and safe to work with and cheap to dispose
of by comparison.

25 grams of trans-stilbene (the one double-bond diphenylpolyene) costs $39
from Aldrich,
http://www.sigmaaldrich.com/catalog/product/aldrich/139939?lang=en&region=US

with similar prices for all-trans diphenyl-butadiene
http://www.sigmaaldrich.com/catalog/product/aldrich/d206008?lang=en&region=US
and the hexatriene analog.
http://www.sigmaaldrich.com/catalog/product/aldrich/d208000?lang=en&region=US

The octatetraene analog s pricey
http://www.sigmaaldrich.com/catalog/product/aldrich/r751774?lang=en&region=US
but students need only a few mg at a time, so 50 mg will last.

These are all soluble in hexane.

The diphenyl polyenes also fluoresce, and the same particle-in-a-box model
can be applied to the fluorescence spectrum. Solutions of these polyenes
should be purged with N2 to remove O2 prior to measuring the fluorescence. Use
spectroscopy grade hexane
http://www.sigmaaldrich.com/catalog/product/sial/248878?lang=en&region=US
that won't interfere with the fluorescence spectrum.

Low resolution (5 nm is fine) devices are all that are required to do the
spectroscopy

And these molecules are small enough so that students can model these using
conventional density functional-based molecular structure packages such as
Spartan or Gaussian to determine approximate structures including C=C bond
lengths for each compound.

It is a bit surprising to find that such crude methods can successfully
predict the C=C bond length with an accuracy of about 30%. It is for this
reason that this is one of my favorite experiments.

These ideas go back to Hans Kuhn, a Swiss physical chemist.
https://en.wikipedia.org/wiki/Hans_Kuhn

Bruce Hudson (my thesis advisor), now at Syracuse, and Ron Christensen,
emeritus professor at Bowdoin, studied the spectroscopy of the fluorescing
states in these species for many years.

I hope this helps.

Jim Diamond
Professor of Chemistry
Linfield College, McMinnville OR

On Mon, Dec 28, 2015 at 9:00 AM, <phys-l-request@www.phys-l.org> wrote:

> From: "Daniel V. Schroeder" <dschroeder@weber.edu>
> To: "phys-l@phys-l.org" <phys-l@phys-l.org>
> Cc:
> Date: Mon, 28 Dec 2015 07:42:58 -0700
> Subject: [Phys-L] Infinite square well experimental data?
> For many years it has bugged me that we never show students any
> experimental data to compare to the calculated energy levels of a
> one-dimensional infinite square well.  Does anyone know of such data?
> Obviously the 1-D infinite well involves many idealizations that will hold
> only approximately for actual physical systems, natural or fabricated.  But
> the essential result, it seems to me, is a quantum ladder of energy levels
> that get farther apart as you go up.  Can anyone point me to an
> experimental energy level diagram that has this property?
>
> Dan Schroeder
> Physics Department
> Weber State University
> Ogden, Utah