Questions to "Answer" in Your Report.

Please do not write your report as a set of answers to these questions. Instead, use these questions for guidance of what important points should not be missed in presenting your results and discussion

Section A

• Submit the graphs of absorbance against l for Dyes A through F. You can combine them into one or two Figures. Note l_max for each dye.
• Use Eq. (5) to compute an effective box length L for each of the dyes. Then compare each length with the geometric box length qb based on a uniform spacing of b = 1.39 Å = 0.139 nm for each of the q bonds in the conjugate system. Evaluate and tabulate the difference (L - qb) for each dye. This difference is usually positive and can be ascribed to an increased of the effective free-electron box length due to potential energy rising not as abruptly (to infinity) right at each terminal nitrogen atom. In other words, the effective free-electron box length is expected to exceed the geometric distance.

Molecule	lmax(nm)	Color	Experimental box length, Le (nm)	Predicted box length, Lth (nm)
Dye A	__________	__________	______________	______________
Dye B	__________	__________	______________	______________
Dye C	__________	__________	______________	______________
Dye D	__________	__________	______________	______________
Dye E	__________	__________	______________	______________
Dye F	__________	__________	______________	______________

You can also present these data as a graph of l_max vs. L_th for both series of dyes.

• Is the difference (L - qb) the same throughout each series of A-C and D-F? Why? Is it the same within series? Why?
• At high concentrations, absorption spectra change because of dye complexation (section B), but for absorbances below 1 (in a 1 cm cuvette) in ethanol, further concentration decrease makes no difference. Nevertheless, the spectra show one or two shoulders to the blue. Why? What is the origin of those shoulders? It would be nice if you supported your idea with numbers. You can use any software of your choice (such as Origin on the lab computer) to deconvolve the spectra into the two or three gaussian lines to emphasize your statement.

Extra credit

• (up to 5 points) The extinction coefficient, e, is proportional to the transition dipole moment squared:

, i.e. e ~ |m_mn|², where x is the operator of coordinate and y_n ,y_m are the wavefunctions of the states n and m, respectively. One can obtain |m_mn|² from the experimental absorption spectra A(l), first by normalizing it by concentration and getting e(l)=A(l)/[C]l, and then using the equation:    

(9)

where e is in cm^-1M^-1 and m - in D (Debye). This parameter, |m²|, is often call the dipole strength. The integral can be crudely estimated using only the extinction coefficient at the wavelength of maximum and the width at half maximum: e(l_max)(Dl/l_max)

1. Calculate m_mn for the lowest energy transition f or the particle in the box problem and show that m_mn is nonzero only when m - n is an odd number
2. Compare experimental m_mn values, estimated for the dyes using Eq.(9), with those of the particle in the box problem

Section B

• Submit the graphs of absorbance against l for the compounds you studied and show maxima for the monomers and aggregates.  You can combine a few graphs on the same Figure. 
• Identify which dye forms H-aggregates and which  - J-aggregates. You can speculate, using their molecular structure, on why that is such.
• Explain why the aggregation is affected by the ionic strength and dye concentration
•  

Extra credit

• (5 points) Presuming that aggregates are dimers and transition dipole moments of the molecules are parallel, estimate the angle, q, between the dipole moments, m, and the axis connecting them using point dipole approximation of Eq.(7). Use Eq. (9) to calculate m and presume that r =3.5 Å (see Figure on the right) 
• (6 points) From the concentration dependence of the ratio A₂/A₁ obtain the equilibrium constant for each of the four cases. You should derive yourself all the appropriate equations.

______________________________________________________________________________

Last updated 01/19/05..