4.3: Proceedure and Treatment of Data

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

Determine Experimental  \(\lambda_{max}\) from Absorption Spectra:

1. Perform instrument diagnostics tests using the Validate program. (See Operation Instructions for Agilent Cary Spectrophotometers)
2. Fill four standard glass cuvettes approximately 4/5 full with methanol (about 2.5 - 3 mL). Then add 3-15 drops of one dye to each cuvette. 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.

Use Particle in the Box model to calculate theoretical \( \lambda_{max} \)

1. Determine \(\gamma\) for the series of homologous dyes.

   Use the 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.

2. 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.)

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Thinking about the Data

Be sure to address all of the following in your ELN.

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. Enter your data with appropriate certainty in a data table in your ELN.
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.
   Record the calculated value of \(\gamma\) in your ELN.
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 and record them in your notebook.
7. Tabulate your data in the format shown below.

   		WAVELENGTH (nm)
   Dye #	Name of Data file	\( \lambda_{max} \) 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 the table above as the basis for a discussion of your results as follows:
   1. Compare your experimental \( \lambda_{max} \) values (from your spectra) with literature \( \lambda_{max} \) values. In your discussion, include a comparison of these \( \lambda_{max} \) values in the context of their absolute errors (the absolute error between your experimental result and the literature) and how that compares to the uncertainty (± value) of the measured and reported \( \lambda_{max} \) values.
   2. Compare the results of the Particle in the Box (PIB) model calculations of \( \lambda_{max} \) to the values derived from experiment.
      • As part of this comparison, discuss the agreement of computational to measured values in terms of the absolute error between computational and experimental values. 
      • Also describe the relationship between \( \lambda_{max} \) and \(p\) for the measured \( \lambda_{max} \) values, and compare this trend with that of the computational results. 
   3. Discuss how well the dyes fit into the trend described in part 8b. If they do not all fit the trend identified for a homologous series, explain why in the context of the PIB model and the structure of each dye.
   4. 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?