Absorption Spectrum of a Conjugated Dye

1. Absorption Spectrum of a Conjugated Dye

2. Dye Characteristics • Absorption occurs in the visible region of the spectrum • Absorption intensities are very high • Usually organic molecules • Absorption frequencies are dependent on the length of the conjugated system

3. Characteristics of Spectra • Transition energy • Bohr frequency condition: • Hυ = E2 – E1 • Transition intensity • Transition moment • (μx)mn = < Ψn| ex | Ψm > • Transition length • (x)mn = < Ψn| x | Ψm >

4. Typical Dyes CH3— ( CH == CH)n — CH3

5. Conjugation in Cyanine Dyes

6. Transition Strength Dnm= < Ψn| x2 + y2 + z2 | Ψm > Where the dimensions of D are cm2 and the frequency is in wavenumbers. The above equation is for a solution. A symmetric Gaussian-shaped band allows the integral to be estimated by: Where h is the half-width of the band at its half-height (in wavenumbers).

9. The dye molecule’s conjugated system of length L may be represented by the Particle in a Box model potential with solution: Where the absorption excites the molecule from the energy state E1 to the excited energy state E2. According to the Bohr Frequency Condition then:

10. Where the quantum numbers for the two half-occupied orbitals involved with the transition are n2 and n1 for the excited and ground state half-occupied orbitals, respectively. This gives a transition energy of: There are N electrons in the π system so now the energy is:

11. Spectrophotometer spectra are usually produced as a function of wavelength so since: We can write: The number of carbon atoms in the box is p = N – 3 which affords an easy expression for the conjugation length, L, in terms of the bond length, l:

12. So the wavelength of the absorption may now be expressed as: And with substitution of the appropriate values for the constants: Different dyes have different end groups of different polarizability, and this leads to the final expression:

13. Quantum Dots

15. Instrumentation for Spectroscopy

17. Photomultiplier Tube

18. I I I - dI I Experimental Procedure • Lambert-Beer Law I I Sample of concentration c and cell of pathlength d

19. Double-beam Spectrophotometer

20. Safety • Dyes can be toxic and some have been associated with carcinogenicity. • Wear gloves in handling the dyes and their solutions. • Immediately wash any contact with the dyes or their solutions with soap and water.

21. Prepare a 10 ml sample of your assigned dye(s) with an approximate concentration of 1.0 x 10-3 M by dissolving 3-5 mg of the dye in methanol. Some solutions may already be prepared. • Use the spectrophotometer to obtain a solution spectrum over the visible range (400-800 nm). • You may need to dilute the solution to insure that the absorbance reading at the maximum wave-length does not exceed 1.0 (10% transmittance). • At high concentrations of dye, dimerization may occur which could alter the spectrum. For sufficiently dilute solutions, dimerization does not contribute to the spectrum.

22. Calculations • Plot spectra and decompose bands to obtain the peak wavelength of absorption for each dye. • Using the appropriate equation, calculate the peak wavelength of absorption for each dye. • 1. Using the longest λmax calculate ΔEexp for each dye and the 95% confidence limits. (Note: The 95% confidence limits of λmax may be taken as ± 1 nm.) • 2. Use PIB equation to calculate ΔEtheo for each compound. Compare the result to the experimental value. • 3. For each set of dyes use an iterative method to calculate the best-fit. Recalculate ΔEtheo for each dye, and compare the results to the experimental values.

23. The sum                         should be minimized for obtaining the best-fit in a regression analysis. • Choose the best value of α ( how can you use a least squares fit of the data?). • Use the Hückel Approximation to calculate the best value of the exchange integral for the dye series. Again, a regression analysis should be considered.