4.3: Procedure for Collecting Absorption Spectra and Applying the PIB model

The ELN Template for this part of the experiment is here: ELN01_dyes2024

Materials

• Equipment:
  • UV/Vis spectrometer (you will use either an Agilent Cary 60 Spectrometer or an Agilent Cary 100 Spectrometer)
  • Cuvettes (you will use glass cuvettes, which are optically transparent to visible (but not to UV) light)
• Reagents:
  • Reagent grade methyl alcohol (methanol)
  • Stock solutions of four polymethine dyes dissolved in methanol (solutions are approximately 10^–4 M):
    • 1,1'-diethyl-2,2'-cyanine iodide
    • 1,1'-diethyl-2,2'-carbocyanine chloride (also known as pinacyanol chloride)
    • 1,1'-diethyl-2,2'- dicarbocyanine iodide
    • 1,1'-diethyl-4,4'-carbocyanine iodide (also known as cryptocyanine)

Note

The cyanine dyes used in this experiment are toxic irritants. Solutions of these dyes in methanol must be handled wearing gloves at all times. Perform all dilutions in a fume hood. Read the safety data sheets for these dyes (http://www.sigmaaldrich.com) prior to the lab.

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Procedure

1. Perform instrument diagnostics tests using the Validate program. (See Operation Instructions for Agilent Cary Spectrophotometers)
2. Fill four glass cuvettes approximately 4/5 full with methanol (about 2.5 - 3 mL). Then add about 5-15 drops of each dye to a series of glass cuvettes. Add enough dye that you can see a light color for each solution. 
3. Use the UV-vis to record the spectrum of each dye. If needed, adjust the solution concentration of one or more of the dye samples until the peak maximum absorbance reading is approximately 0.2 to 1.0 absorbance units.
4. Annotate the resulting overlay display of all four dyes, noting which dye is associated with each trace and the associated \( \lambda_{max} \) value.

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Treatment of Data: Calculations and Discussion Questions

1. What is the experimental maximum wavelength for each dye solution?
   Carefully examine all spectra (absorbance versus \( \lambda \)) and determine the wavelength of maximum absorbance (\( \lambda_{max} \)), for each dye.
2. What is the uncertainty in your experimental peak wavelength determinations?
   Estimate error in each assignment of (\( \lambda_{max} \)) considering both the instrument tolerance indicated by the validation procedure (the wavelength accuracy test) and the data interval that was used during data collection.
3. How do your results compare to literature values?
   Compare your experimental results for \( \lambda_{max} \) with literature values for \( \lambda_{max} \) that you found as part of the pre-lab assignment.^10-12,14
4. What is the energy of electronic transition (absorption)?
   For each dye, calculate the energy (eV and kJ/mol) of the experimentally observed \( \lambda_{max} \).
5. Determine \(\gamma\) for the series of homologous dyes.
   Use a Matlab script called dye_v3 to determine the "best" value of \( \gamma \) This script will prompt you for information about the four dyes, and the experimentally measured values of \( \lambda_{max} \). It will solve the particle in a box equation for \( \lambda \), separately for each dye, over the range of \( \gamma \) from 0.00 to 2.00 in steps of 0.01. It will sum the absolute deviation between the calculated \( \lambda \) and your experimentally measured \( \lambda_{max} \) for each value of \( \gamma \), for each dye. It will output the one value of \( \gamma \) that produces the smallest summed deviation over the series of the four dyes. That is, the script will calculate the value of gamma which gives the best fit between peak wavelengths calculated using the free electron model and peak wavelengths measured experimentally. To use this script, start up a Matlab session and type the dye_v3 command:

   dye_v3

   Then simply enter the information as prompted by the script. 
   
   Use the output value of \( \gamma \) to calculate a value for \( \lambda_{max} \) for each of the four dyes using the equation \[ \lambda=\frac{8mca^2}{h} \frac{\left ( p+3+\gamma \right )^2}{p+4} \]
   (Remember that the value of the average bond length of a carbon-carbon bond, a, is 1.39 x 10^–8 cm the mass of the electron, m, is 9.1 x 10^–31 kg.)
6. Calculate the absolute error between your experimental (from the spectrum) values and the literature values. Calculate both the absolute error and the percent deviation between your experimental (from the spectrum) and your calculated theoretical (Particle-in-a-box Model) \( \lambda_{max} \) results.
7. Tabulate your data in the format shown below.

   	WAVELENGTH (nm)
   Dye #	# drops used	\( \lambda_{max} \) Literature*	\( \lambda_{max} \) Experimental		\( \lambda_{max} \) Particle in a Box
   			Value (nm)	Absolute Error (nm)	Value (nm)	Absolute Error (nm)	% Error
   1			±
   2			±
   3			±
   4			±
   * reference for your literature values goes here

8. Use this table as the basis for discussion of your results as follows.
   1. How well do your \( \lambda_{max} \) values from your spectra agree with literature \( \lambda_{max} \)? When thinking about this look to see if the absolute error between your experimental result and the literature is equal to or less than the uncertainty (± value) of the measurement.
   2. How well does the Particle in the Box (PIB) model reproduce the experimental results? When thinking about this look first at your experimental result to see how varies as a function of p. Does the PIB result give the same trend? Looking at the individual dyes, do your PIB results agree with your experimental results within their absolute errors?
   3. Are the results for each dye equally satisfactory? If your answer is no, explain why you think this is so. How is the PIB model useful and what might be done to improve the results?
9. Calculate the wavelength (in nm) and minimum energy (eV) of the molecule 1,3,5,7-octatetrene (\(\ce{CH2=CHCH=CHCH=CHCH=CH2}\)) using the particle-in-a-box model. What color does the molecule absorb from white light? What color does it then appear to the eye?