Particle in a Box Experiment

The visible absorption bands or conjugated dye arise from electron transitions involving the electrons in the conjugated and they are free to move along the chain and are not attached to any atom. An example of such a dye is 3,3-diethyl-thiacyanine iodide. The cation has two resonance forms causing each of the bonds in the conjugated chain to have an order of 1. 5 and have a length similar to the C–? C bond length in benzene. We will assume that the potential energy is constant along the chain and sharply rises to infinity at the ends.Therefore, we can replace the electron system by free electrons moving in a one dimensional box of length . Objective: The purpose of this experiment is to obtain the visible spectra of several cyanine dyes and then interpret them to a simple model of the electronic structure of the ? system: the Particle in a Box. Theoretical Model “Particle in a Box” In the Particle in a Box model, all potential energy interactions are assumed to be zero (constant) along the chain except at ends of the chain where the potential energy abruptly goes to +?. If a particle moving freely along the length of the box the energy an be calculated as : E = n2h28mL2 + V n = 1, 2, 3 … (1) where n is an integer positive quantum number, h is Planck’s constant, m is the mass of the particle and L is the length of the box. If we assume that the most intense band in the experimentally observed spectrum can be interpreted as absorption of electromagnetic radiation by an electron as it is promoted from the HOMO to the LUMO, we can derive the following expression for the energy absorption ? E. ????????????????????????????? E =h2 [2ni+ 1]/ (8mL? ) (2) he absorption wavelength for the HOMO _ LUMO transition is given by: ? = 8mcL? /h (2ni + 1) ni = p p = #e/2 (3) Therefore, the Particle in a Box model predicts that the wavelength of the absorption maximum is a function of chain length (L) and number of p-electrons (N). The adjustable parameter Lmax can be calculated as: ? = 8mc/h(2p+1)[(2p-1)Lb + Lext]2 (4) ?max h/8mc=[2p-1Lb + Lext ]2/ (2p +1) (5) Procedure: In this experiment, we used the following dyes. Dye #1: 3,3-diethyl-thiacyanine iodide (yellow) Dye #2: 3,3′-diethylthiacarbocyanine iodide (Pink)Dye #3: 3,3′-diethylthiadicarbocyanine iodide (Blue) Dye #4: 3,3′-diethylthiatricarbocyanine iodide (Olive) We placed 0. 3 ml of dye solution in the 1- cm cuvette and added 3. 00 ml of water and mixed well. Using the nano drop spectrometer, first cuvette with water was used as a blank and later second Cuvette with dye solution was inserted and measured the absorbance of the sample. Once our absorbance of the highest peak was less than 0. 5 and the absorption spectrum of each dye was between 400-800 we collected the data. Notes On Wavelength:If only changes in electronic energy accompany absorption of light, a very sharp maximum in absorption should be observed at the characteristic wavelength. Although sharp lines are observed for isolated atoms, broad absorption bands are observed for substances in liquid phases (due to the accompanying vibrational and rotational transitions). In the experiment, we shall assume that the wavelength ? max, the wavelength at which the dyes absorb most strongly, is the wavelength to use in the equation (5). Data/Result: A UV-Vis absorbance spectrum (Fig 1) was obtained and used to calculate experimental ? ax values for each of the studied cyanine dyes. Fig 1: UV Absorbance Spectrum for Dye 5d, Dye 6, Dye7 and Dye 8b Collected from Nanodrop Based on the data: Dye | Emprical formula | ? max /nm | Lit ? max| 3,3′-Diethylthiacyanine Iodide| C19H19IN2S2| 417| 423| 3,3′-Diethylthiacarbocyanine Iodide| C21H21IN2S2| 549| 556| 3,3′-Diethylthiadicarbocyanine Iodide| C23H23IN2S2| 564| 652| 3,3′-Diethylthiatricarbocyanine Iodide| C25H25IN2S2| 744| 757| In order to experimentally to calculate the Lext a plot of h ? 8mc experimental bond length, and P the number of the c atoms in conjugated system (N / 2) was constructed. Dye| ? (m)| N| h (j. s)| m(Kg)| C (m/s)| h? /8mc| p| 5d| 0. 000000417| 6| 6. 62E-34| 9E-31| 3*10^8| 1. 27803E-19| 3| 6| 0. 000000549| 8| 6. 62E-34| 9E-31| 3*10^8| 1. 68258E-19| 4| 7| 0. 000000564| 10| 6. 62E-34| 9E-31| 3*10^8| 1. 72856E-19| 5| 8b| 0. 000000744| 12| 6. 62E-34| 9E-31| 3*10^8| 2. 28022E-19| 6| Using Regression Wizard: | | | | | y = (((2*x -1)*(0. 139*10^-9) + L)^2) /(2*x+1)| | | | |  | | reduced Chi-square| SDR| sum of squared errors| r^2| | | 4. 6915E-10| 6. 6031E-19| 0. 636| | | Covariance Matrix|  | | |  | | | L|Parameters| Initial Value| Optimized Value| Standard Deviation| | L| 3. 2614E-4| L =| 1. E+0| 6. 1243E-5| 1. 8059E-2| | | | | | | | | | | | x| y| y_calc| error| | 3| 1. 27803E-19| 5. 35822E-10| -5. 3582E-10| | 4| 1. 68258E-19| 4. 16754E-10| -4. 1675E-10| | 5| 1. 72856E-19| 3. 40984E-10| -3. 4098E-10| | 6| 2. 28022E-19| 2. 88527E-10| -2. 8853E-10| | | | | | | | | | | | | | | | | | | | | | | | | | | Lb= 1. 39E-10 Calculation of Lext based on equation (5) Dye| P| ? (m)| ((2p-1)*0. 139*10^-9 +Lx)^2/(2p+1)| 5d| 3| 4. 17E-07| 2. 51*10^-10| 6| 4| 5. 9E-07| 2. 56*10^-10| 7| 5| 5. 64E-07| 1. 72*10^-10| 8b| 6| 7. 44E-07| 1. 92*10^-10| Uncertainties in ? max: See the attachment Conclusion: The spectrum obtained from Nanodrop revealed that 3,3′-Diethylthiacyanine Iodide and 3,3′-Diethylthiacarbocyanine Iodide have fairly broad spectral band compare to, 3,3′-Diethylthiadicarbocyanine Iodide and 3,3′-Diethylthiatricarbocyanine Iodide. This can be due to the electronic transitions from state to state which occur within a time interval much shorter than that of a molecular vibration and also experimental error was responsible for the lack of resolution.The collected electrically spectra were useful in comparison of experimentally and theoretically predicted ? max values and it shows that the experimentally determined values are close to the predicted value. Extracting Lext from equation (5) for each dye doesn’t follow the observed trend in the absorption maxima. For 3,3′-Diethylthiacyanine Iodide and 3,3′-Diethylthiacarbocyanine Iodide dyes as ni increases Lext and ? max increases and in 3,3′-Diethylthiadicarbocyanine Iodide and 3,3′-Diethylthiatricarbocyanine Iodide, Lext decreases as ni increases. The experimentally calculated Lext for compounds 1-4 was determined to be 6. 2E-5 m which doesn’t seem sensible. Large differences existed difference between the calculated effective box length compare to lb. From the experimental evidence and analysis, we don’t except the particle in a box model to be an appropriate one to describe the spectra of cyanine dyes. Since the errors in the ? max are not normally distributed experimental errors.Work Citedhttp://homepages. gac. edu/~anienow/CHE-372/Labs/Example. pdf http://homepages. gac. edu/~anienow/CHE-372a/Labs/Conjugated%20Dyesa. pdf

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