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. 2001, 78, 1432. 0000005432 00000 n 0000044027 00000 n Phys. 0000010333 00000 n /Type Garland, C.; Nibler, J.; Shoemaker, D. Experiments in Physical Chemistry ; 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. For each dye, a 104 M stock dye solution was prepared in reagent grade methyl alcohol (Fisher, CAS# 67561). Phys. subscribers only). 0000006031 00000 n Schrdingers equation is used to calculate the energy levels, Equation (1). Be sure to read the questions raised in the texts3,4 as they may give you insight into the problem and suggest issues that you should address as part of your discussion. Three dyes will be used in this experiment: Dark Blue Blue Green Each dye is in methanol solution of with a concentration of approximately 1 x 10-4 M. Procedure Fill a cuvette with about 2 mL of sample (dye) solution. 10. 0 For the recalibration include a plot of the known wavelengths as a function of the measured wavelengths and the linear fit with your report. 1954, 22, 1448. a = (2j + 2)L, C: 1,1-Diethyl-2,2-dicarbocyanine Iodide, N = 2j + 2 = 2(4) + 2 = 10 pi electrons Make plots of the absorbance spectra for dyes A F. You may combine the plots in one or two page graphs. The literature max recorded in Sigma Aldrich is actually a range from 702 nm to 710 nm (4). 0 (3) 1= 2 (4) 2=+1 2 where N is the number of electrons. The particle-in-a-box (PIB) approximation is a theoretical model that calculates the absorption spectra of conjugated species. In the free electron model, represents a constant for a series of dyes of a given type. Worksheet for particle in a box; include with your report. Theobald, R. S. (1964). 0000004329 00000 n The experiment shows the impact chemical structure has on approximation models like the PIB. 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. Note: In the following work completely clean the cuvette between samples. Farrell, J. J. J. Chem. L = 1 x 10-10 m 0000040702 00000 n 720 0 2. The different in energy between these two levels is exactly equal to the energy a photon needs to excite the dye. Educ. Hb```f``c`e``ce@ ^yLPeP%-By:gTL9=\\.yJ[wO6>;2X2A8-,%%7RhhChX@9HK%X(^7\{S.T9]^VktH_gbf-[ty&lbt )\ endstream endobj 91 0 obj 281 endobj 63 0 obj << /Type /Page /Parent 60 0 R /Resources 64 0 R /Contents [ 69 0 R 73 0 R 78 0 R 80 0 R 82 0 R 84 0 R 86 0 R 88 0 R ] /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 64 0 obj << /ProcSet [ /PDF /Text ] /Font << /F2 74 0 R /TT2 66 0 R /TT4 70 0 R >> /ExtGState << /GS1 89 0 R >> /ColorSpace << /Cs5 67 0 R >> >> endobj 65 0 obj << /Type /FontDescriptor /Ascent 905 /CapHeight 0 /Descent -211 /Flags 32 /FontBBox [ -628 -376 2000 1010 ] /FontName /Arial-BoldMT /ItalicAngle 0 /StemV 133 >> endobj 66 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 150 /Widths [ 278 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 556 0 0 0 0 0 0 0 333 0 0 0 0 0 0 722 722 722 722 667 0 0 0 0 0 0 0 0 0 778 667 778 722 667 611 0 0 0 0 0 0 0 0 0 0 0 0 556 611 556 611 556 333 611 611 278 278 0 278 889 611 611 611 0 389 556 333 611 0 778 556 556 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 556 ] /Encoding /WinAnsiEncoding /BaseFont /Arial-BoldMT /FontDescriptor 65 0 R >> endobj 67 0 obj [ /CalRGB << /WhitePoint [ 0.9505 1 1.089 ] /Gamma [ 2.22221 2.22221 2.22221 ] /Matrix [ 0.4124 0.2126 0.0193 0.3576 0.71519 0.1192 0.1805 0.0722 0.9505 ] >> ] endobj 68 0 obj 764 endobj 69 0 obj << /Filter /FlateDecode /Length 68 0 R >> stream Below are the dyes which we will study \[-\frac{\hbar^{2} }{2m}\frac{\partial ^{2}\psi}{\partial x ^{2}}+ V\left ( x \right ) \psi = E \psi\] Molecules of a colored object absorb visible light photons when they are excited from their lowest-energy electronic state (called the ground state) to a higher-energy electronic state (called an excited state). 0000000967 00000 n 6 determine the wavelength of maximum absorbance (max) for each dye. Diluted solutions of each dye were analyzed using a UV/VIS spectrometer to determine the wavelength of maximum absorbance (max) for each dye. We will make the following assumptions: a = (2j + 2)L, j = 2 double bonds 0000002026 00000 n b) From the absorption spectrum of conjugated dye investigated, the wavelength of maximum absorption increases with increasing conjugation. >> 0000002439 00000 n /CS ( G o o g l e) Introduction: 1,1'-Diethyl-2,2'-carbocyanine iodide (Dye B) Figure 2 shows the potential energy of the conjugated pi-bonded systems for dyes A and B. 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). Educ. L = 1 x 10-10 m The goal of this exercise is to help students to think critically about their . /Parent Thus the percentage difference was approximately 40%. 3. 2000, 77, 637-639. Polymethine dyes 1,1-diethyl-2,2-cyanine iodide (Eastman, CAS# 977968), 1,1-diethyl-2,2-carbocyanine chloride (Eastman, CAS# 2768903), 1,1-diethyl-2,2-dicarbocyanine iodide (Eastman, CAS# 14187316), and 1,1-diethyl-44-carbocyanine iodide (Eastman, CAS# 4727508), corresponding to dyes 1, 2, 3, and 4, were used as received. subscribers only). 1. These electrons can be. 0000044295 00000 n 12. 1,1'-Diethyl-4,4'-dicarbocyanine iodide (Dye F) The experimental procedure that was followed can be found in the practical manual. Educ. For a molecule to absorb a photon, the energy of the 0000037547 00000 n 0000007549 00000 n ] the dye. All three dyes have a different max. Click here to view this article (Truman addresses and J. Chem. Using the spectra shown, the max is determined by observing for each dye where the absorbance was the highest. The majority of colors that we see result from transitions between electronic states that occur as a j = 3 double bonds %PDF-1.2 % Marketing-Management: Mrkte, Marktinformationen und Marktbearbeit (Matthias Sander), Handboek Caribisch Staatsrecht (Arie Bernardus Rijn), Big Data, Data Mining, and Machine Learning (Jared Dean), Junqueira's Basic Histology (Anthony L. Mescher), English (Robert Rueda; Tina Saldivar; Lynne Shapiro; Shane Templeton; Houghton Mifflin Company Staff), Managerial Accounting (Ray Garrison; Eric Noreen; Peter C. Brewer), Applied Statistics and Probability for Engineers (Douglas C. Montgomery; George C. Runger), Auditing and Assurance Services: an Applied Approach (Iris Stuart), Frysk Wurdboek: Hnwurdboek Fan'E Fryske Taal ; Mei Dryn Opnommen List Fan Fryske Plaknammen List Fan Fryske Gemeentenammen. Im in the Class of 2020, and a week ago I turned in my final lab report for college. Some references from the Journal of Chemical Education are included here to help you get started,5-12 and please discuss your ideas with the instructor. And the general solution for an equation of this form is: (x) = A \sin (kx) + B \cos (kx) (x) = Asin(kx)+ Bcos(kx) However, looking at the boundary conditions can help narrow this down. In this experiment, light absorption properties of a carefully chosen set of organic molecules The chemical structures are resonance structures; the positive charge can be equally well represented as residing on either nitrogen atom. Kuhn, H. J. Chem. } All three dyes have a different max. >> 0 >> Results calculation: IMPORTANT! For the dyes studied in this experiment the number of electrons (N) is an even number, p. There will be two electrons per energy level because of the Pauli Exclusion Principle. Carry out the necessary calculations and propagate the errors involved to the final answer. by treating the system as a 1-D particle in a box. The energy of the particle in the box is partly potential energy, which you might interpret as energy which is not yet ``realized'' as motion but could be. /Group Use the references 3 and 4 to develop an experimental procedure. subscribers only). /St 0000007528 00000 n 0000005322 00000 n In the case of electrons in the particle in a box there are two quantum numbers, n and spin. 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. While the particle in the box model1-4 can be used to rationalize the trend in lmax, it does not explain the other effects. ; Freeman: New York, 2006, p. 39-1-39-9. Calculate absorbance spectra for the dye solutions by taking the natural log of the ratio between the background spectra and the dye solutions. Since a linear trend between p and experimental max is shown in both plots, and the experimental and theoretical max match for each compound in each homologous series (Figure 3), our hypothesis that PIB is predictive only when applied to a homologous series is correct. Save your spectra as ASCII text files for importing into Excel. 10 drops of each stock dye solution were transferred to a cuvette followed by dilution with methyl alcohol. Physical Chemistry Laboratory The majority of colors that we see result from transitions between electronic states that occur as a result of selective photon absorption. This, however, also depends on the literature value referenced. The Pauli exclusion principle and the energy levels establish the electron distribution. << McRae, E.G. New Mexico State University, Department of Chemistry 100 East Normal Avenue Using the spectra shown, the max is determined by 0000037568 00000 n 0000010740 00000 n We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. If the particle in a box is used to represent these molecules then the pi electrons need to be distributed into the box. 0000007892 00000 n 0000002998 00000 n >> In the free electron model, represents a constant for a series of dyes of a given type.1 In this lab, represents the penetration distance which lies between 0-1. Figure 3. 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 Molecules of a colored object absorb visible light photons when they are excited from their This spectrum will be your background spectrum (Io) for this dye. A higher level means a higher potential energy. Part A Click here to view this article (Truman addresses and J. Chem. The dyes are light sensitive, and so if it is necessary to store the dye solutions, protect them from light. Horng, M.-L. and Quitevis, E. L. J. Chem. /Outlines Our experimental max for dyes 1, 2, and 3 agree with their respective literature values within their uncertainties. 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. 0 Donot put all 11 spectra on a single graph as this will be a big mess! observing for each dye where the absorbance was the highest. electron model. The spectrum of each dye was shown above. /FlateDecode Please turn in your lab writeup as a printed copy. Figure 2. Abstract. Particle in a Box : Absorption Spectrum of Conjugated Dyes Part A - Recording the Spectra and Theoretical determination of max Theory Absorption bands in the visible region of the spectrum (350 - 700 nm) correspond to transitions from the ground state of a molecule to an excited electronic state which is 160 to 280 kJ above the ground state. 0000002694 00000 n dyes. Remembering that: You MUST bring a completed pre-lab before you will be allowed to start the lab. Conjugated pi-bonded system for dyes A and B. 0 CAUTION! [CDATA[*/ Provide a sample calculation in your report. Discuss the difference between the length of the box calculated from Equation (11) and the length estimated from the number of bonds. We can read off the potential energy of the particle at any point in the box by looking at the level of the floor of the box at that point. 0000009509 00000 n % Educ. Report the final absorption spectra for each dye you studied. 3) we can obtain their energy levels (the eigenvalues of this eigenfunction): where n is any integer > 0. 0000040920 00000 n Image 3. 9. Kirksville, Missouri 63501 Assignment of electrons into particle in a box model for dyes A and B. 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. The calculated length of 1, 1 Diethyl -2, 2 dicarboncyanine was 1 x 10-10 m. The 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). The absolute percent error between theoretical and experimental max absorbed for dye 4 is much larger than that of dyes 1, 2, and 3. Elsevier. Identify the wavelength of the maximum absorbance, max, for each dye. Dye A Dye B. Reviewing Principles of UV-Vis Spectroscopy a. Accessibility StatementFor more information contact us atinfo@libretexts.org. Oxford Press: UK. In all four dyes we are forcing the conjugation through the chain. %PDF-1.4 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%). The spectra of other types of cyanine dyes, which have been discussed ex-tensively in the literature (9-11), can be represented by the simplified general formula An example is the family of thiacarbocyanine dyes Cyanine Dyes: Unmodified PB .