1,1'-Diethyl-4,4'-cyanine iodide (Dye D) 7 Note that although your spectra are experimentally determined (and so one would think that they should be shown as individual points), it is common practice to show spectra as solid lines, unless there is good reason to do otherwise. 1 R $('document').ready(function() { To verify our hypothesis, we plot the literature and theoretical max against p for dye 4 along with 1,1-diethyl-4,4-cyanine iodide (dye 5) and 1,1-diethyl-4,4-dicarbocyanine iodide (dye 6), two dyes that fall within the homologous series containing dye 4 (8). 5 Evaluate and tabulate the difference between the length of the box calculated from Equation (11) and the length estimated from the number of bonds for each dye. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. /Page Figure 2 shows that there is a potential energy barrier at the nitrogen atoms and there are wells at each atom; however to a reasonable degree of accuracy the potential energy of the conjugated pi-bonded system can be approximated by a particle in a box potential. The number of -electron pairs equals k + 3. I got a 89%, which is close to being the bottom of my class :( But I worked hard for it, and thought I did well, so Im posting it here for you to see. Particle in a Box is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts. We will make the following assumptions: endobj HTMo0vnY?;vkZpH=z(YYPD:*?oi6A6oR0%J*e,uD|.j'NZ1NlD'Z{ ]^>IlrcN" YGHI4Hr4&y Ls43)i3 ef=:(+K)U\2%=+MQ5~P4zihve1\^v'M( 7v.OFz`\71+k(MmM]u36vU[q%pZ%qJf{7*`#u& sqJbY=rB1+C7R'rKyM^]L*HVZ4qcKs. Figure 1: The absorption spectra of each conjugated dye. You will measure the absorption spectra of a series of conjugated dyes and then use the Particle-In-A-Box (theoretical model) to explain the observed spectra. state of the molecule. Simple Point Charge (SPC) water molecules were employed to fill with the box. Then we use the number of pi electrons to determine the energy level of the highest occupied molecular orbital and the lowest unoccupied molecule orbital. All six dyes: 1,1'-Diethyl-4,4'-cyanine iodide, 1,1'-Diethyl-4,4'-carbocyanine iodide, 1,1'-Diethyl4,4'-dicarbocyanine iodide, 1,1'-Diethyl-2,2'-cyanine iodide, 1,1'-Diethyl-2,2'-carbocyanine iodide and 1,1'-Diethyl-2,2'-dicarbocyanine iodide and methanol are considered highly toxic and irritate the skin. % So in this case was, 1, 1 Diethyl -2, 2 dicarboncyanine iodide for it has ranged with 700nm. 9. 8 For example, your hypothesis might be that the dyes large second hyperpolarizability is the source of dependence of lmax on number of carbon atoms in the dye, which could be measured by light scattering. Im in the Class of 2020, and a week ago I turned in my final lab report for college. Three things need to be considered to calculate the energy changes from Equation 5. IMPORTANT! The one-dimensional version of this solution, the "particle-on-a-line" is attractively simple. The experiment shows the impact chemical structure has on approximation models like the PIB. In the case of electrons in the particle in a box there are two quantum numbers, n and spin. In (B-F), the horizontal axis is position, and the vertical axis is the real part (blue) and imaginary part (red) of the wavefunction.The states (B,C,D) are energy eigenstates, but (E,F) are not. This spectrum will be your background spectrum (Io) for this dye. >> /D subscribers only). Schrdingers equation is used to calculate the energy levels, Equation (1). Equations (6 - 9) 0000001782 00000 n j = 3 double bonds Furthermore, when we calculate the theoretical max using a lengthening parameter, gamma, the chemical connectivity of dye 4, being different from that of dyes 1, 2, and 3, may contribute to a less-than-accurate gamma. >> An increase in major peak wavelength is observed as the carbon number increases from dyes 1 to 3. 4 (an appropriate eigenfunction for eq. Ephoton = h v = Emolecule = Eupper state Elower State (1) In this experiment, light absorption properties of a carefully chosen set of organic molecules The literature and experimental major wavelengths (max) absorbed for dyes 1, 2, and 3 agree within the experimental absolute uncertainty; however, the literature max absorbed for dye 4 falls outside the experimental absolute uncertainty (Table 1). m"^}U%SzjFmV[luPym}jc^mvV;G;u4Xt4\VIZiYV+_;k|/l"#[bG EuL qf>Y#tLbJ( ]WIkrF'd kHP|o9ra+3Igeu * w[VI[fSQ13M4/V# UMVyTp?8f34M3)0w^p2/&xX:~ q*j BI{J9LCL'u"/|&46W'LJUuW~Fb>L /S These dyes are typically $100-$300 per gram and so it is important not to waste the materials. If the theoretical max for dye 4 yields a smaller absolute percent error when it is run with dyes 5 and 6 rather than dyes 1, 2, and 3, our hypothesis that structural difference contributes to a less-than-accurate is correct. /MediaBox Click here to view this article (Truman addresses and J. Chem. 0000037547 00000 n Results calculation: It is possible to obtain the absorption spectrum of all the dyes in Table 1 (all in the same solvent), and generate only 100 mL of waste. The Pauli exclusion principle and the energy levels establish the electron distribution. Fill out the worksheet given below as you do the following. Report the final absorption spectra for each dye you studied. /Annots N = 2j + 2 = 2(3) + 2 = 8 pi electrons How spectroscopic measurements may be used to derive some molecular properties (in this case the length of a conjugated pi-bonded system in dye molecules). For dyes 1 and 3, the absolute percent errors are 8.79% and 3.64%, respectively, while the absolute percent error is the greatest for dye 4 (21.7%). conjugated dyes. Derive equation 2, which shows the relationship between the energy of the absorbed photon lmax and the quantum states of molecules. signifies that light or any electromagnetic radiation can penetrate a significant distance into the 1,1'-Diethyl-4,4'carbocyanine iodide (Dye E) \[\psi \left ( q_{1}, q_{2}, q_{3}, q_{4}, \right ) = - \psi \left ( q_{2}, q_{1}, q_{3}, q_{4}, \right ) \] Looking at the individual dyes, the theoretical max agree with our experimental max within their absolute errors only for dye 2, with an absolute percent error of 0.05%. R the sides of the box or the walls of the well, the wave function has to go to zero. 0000007413 00000 n 0000011917 00000 n http://www.chemistry.nmsu.edu/studntres/chem435/Lab5/ >> 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. The goal of this exercise is to help students to think critically about their . $('#widget-tabs').css('display', 'none'); 3. /Outlines Be sure to select solvents that do not absorb light in the same wavelength region as your dyes. The wavelength of maximum absorbance (lmax) for the cyanine family of conjugated dyes, representative members of which are shown in Table 1, has a marked dependence on the number of conjugated carbons,1,2 while some also exhibit changes in lmax with solvent polarity, dye concentration and other factors. The experiment showed that finding the wavelength of maximum absorbance of a conjugated dye can be used to find the empirical parameter and the length of a conjugated system within the dye. 0000008957 00000 n We can describe this concept using the equation. As p gets larger, the experimental max gets larger. Using the spectra shown, the max is determined by Physical Chemistry 10th ed. The dyes are light sensitive, and so if it is necessary to store the dye solutions, protect them from light. Thus the percentage difference was approximately 40%. The "particles" in this particle in a box model are, of course, the p electrons of this conjugated system, and solving eq. subscribers only). The dyes can be run in any order. 0000006938 00000 n However, our new gamma calculated using only dyes 1, 2, and 3 is 1.2400, which is the same as the one calculated using dyes 1, 2, 3, and 4. The chemical structures are resonance structures; the positive charge can be equally well represented as residing on either nitrogen atom. \[\psi \left ( q_{1}, q_{1}, q_{3}, q_{4}, \right ) = - \psi \left ( q_{1}, q_{1}, q_{3}, q_{4}, \right ) \] For the recalibration include a plot of the known wavelengths as a function of the measured wavelengths and the linear fit with your report. 7 The absorption spectrum of each dye solution was taken at room temperature with a CARY 1G UV-Vis Spectrophotometer (Varian) at a 1 nm step size, 2 nm spectral bandwidth, 1 nm data interval, 600 nm/min scan rate, and 0.02 mm slit width. trailer <<3068649AEBAF11DF80810026B0D9EA12>]>> startxref 0 %%EOF 106 0 obj<>stream Our experimental max for dyes 1, 2, and 3 agree with their respective literature values within their uncertainties. Phys. %PDF-1.3 % Figure 1. Oxford Press: UK. To test the robustness of the PIB model against four . 0 0000008795 00000 n [ 0000005032 00000 n a Molar absorption coefficient in methanol at the absorption maximum (from reference 2).. P = # of carbon atoms in chain of conjugation. All of the conjugated dyes used have the largest You MUST fill out the cover sheet fully and correctly to receive credit. 9 /FlateDecode Educ. accepted length of was 1 x 10-10. determine the wavelength of maximum absorbance (max) for each dye. 2010 Five-membered heterocyclic compounds with two nitrogen atoms in the ring. If the particle in a box is used to represent these molecules then the pi electrons need to be distributed into the box. &P?ED Hp*^hZ{6@Lb"cx:+R+. If you are using the Varian it is suggested that you set it to record data every 1 nm and that the scan speed be set to no more 300 nm/min. The calculated length of 1, 1 Diethyl -2, 2 dicarboncyanine was 1.727 x 10-10 m. The accepted length of was 1.23 x 10-10. E = 1.196 10 5 nm kJ 700nm mol = 171.kJ/mol b. %PDF-1.3 In the experiment the length of the conjugated pi-system will be calculated for each dye from measurements of abs and Equation (11). The Particle-In-A-Box approximation Electrons in the -electron system of a conjugated aromatic compound are not restricted to specific nuclei but are free to move throughout the system. Kirksville, Missouri 63501 Below are the dyes which we will study conjugated bonds between the nitrogen atoms of the dye molecules. Educ. 8. 0000002720 00000 n length of the box and is one of the two requirements to use the . When applying the PIB model to conjugated systems, the following assumptions are made: All the carbon-carbon bonds in a conjugated system have equivalent bond lengths Each carbon atom forms 3 sigma bonds. Fill a cuvette with methanol and record a spectrum. Gerkin, R. E. J. Chem. Bring a floppy disk to record your data. electron model. 0000002119 00000 n xb```f``b`c`sb`@ V( k,b'220gXDl .g;s&IvBV 5_ndny6Z|QTf] To calculate the length of the box, assume that the molecule is linear and use 154 pm and 135 pm for C-C and C = C bond lengths respectively. subscribers only). Abstract The particle in a box model can be used to predict the location of the lowest electronic transition in dye molecules. 0000009530 00000 n [CDATA[*/ Using this wavelength, 3 (an eigenvalue equation) by substituting eq. Further, the theoretical linear regression line shows a positive linear association between the number of carbons framed by nitrogen atoms (p) and wavelength absorbed, while for experimental, the linear association breaks down when dye 4 is added (Figure 2). Using this wavelength, the best fit is determined to be equal to 1 and the length of the box of , 1, 1 Diethyl -2, 2 dicarboncyanine is 1.727 x 10-10 m. The purpose of this experiment is to determine the value of the empirical parameter and determine the length of a conjugated carbon chain for a set series of dyes by a UV/VIS spectrometer. The theoretical max also shows a similar trend. 0000007549 00000 n << carbon atoms. The general approach to this experiment is adapted from D. P. Shoemaker, C. W. Garland, and J. W. Nibler, Experiments in Physical Chemistry, 6th edition, McGraw Hill Co. Inc, NY, 1996, p378. The potential energy of a system needs to be defined to calculate the energy levels. Representative members of the cyanine family of conjugated dyes. 0 0000010333 00000 n 0 0000001720 00000 n Make plots of the absorbance spectra for dyes A F. You may combine the plots in one or two page graphs. Educ. R You only need to turn in your work (with enough context to understand what you are answering), and not the entire Mathcad file. Learning more about how organic compounds absorb radiation. >> Mathematically: %PDF-1.2 % 2000, 77, 637-639. $('#commentText').css('display', 'none'); 1 Kuhn, H. J. Chem. The molar absorptivities (extinction coefficients) of these dyes are quite high, so plan your dilutions to minimize the use of the solutes and solvent. \[ A = \ln \left ( \frac{I_{o}}{I} \right ) \]. 0000047672 00000 n Click here to view this article (Truman addresses and J. Chem. /Type Thus the percentage difference was approximately 40%. Repeat steps 3 5 until spectra have been recorded for all the dye solutions. If we look at their structures carefully, we see that only dye 4 has a para- substituted ring, with the carbon chain and the nitrogen atom para- to each other, while dyes 1, 2, and 3 have an ortho-substituted ring, with the carbon chain and the nitrogen atom ortho- to each other (7). 4 /Transparency 0 2 Soltzberg, L. J. J. Chem. Add a drop or two dye A solution. 28, 721. /Nums Particle in a one dimensional box laboratory experiments have traditionally used chemicals like polyenes or cyanine dyes as model systems. Swenberg, Electronic Processes in Organic Crystals, (Oxford University Press, New York, 1982), Chapter 1D. 0000033368 00000 n 0000008638 00000 n the dotted lines. Image 1. Electrons change energy levels when radiation is absorbed. This weeks dry lab will consist of a single Mathcad module to work through. 0000001838 00000 n It was also seen that the lengths of the box calculated increase with the number of carbon atoms. We can describe this concept using the equation. Halpern, A. M. and McBane, G. C. Experimental Physical Chemistry: A Laboratory Text book, 3rdEd. A ( pinacynol In conclusion, we find that PIB is predictive as long as we apply it to a homologous series. Use the references 3 and 4 to develop an experimental procedure. In conclusion, my results suggest that PIB is predictive of the experimental only when it is applied to compounds in a homologous series. Elsevier. 1954, 22, 1448. Educ. 0000002699 00000 n Olsson, L. F. (1986). 0000047792 00000 n where: \( E \) represents the possible energy levels \( h \) is Plancks constant, \( m \) is the particles mass and \( L \) is the length of the box. An in-house MATLAB subroutine was used to determine the optimum gamma value and calculate the PIB or theoretical wavelengths of the series of four dyes.