IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (3) 2011 Calculate of the Rate Constant of Electron Transfer in TiO2 – Safranine Dye System H.J.M.Al-Agealy, M.A.Hassooni Departme nt of Physics, College of Education I bn-Al-Haitham, Unive rsity of Baghdad Received in : 28, September , 2009 Accepte d in : 13, March , 2011 Abstract A theoretical calculations of the rate constant of electron transfer (ET) in a dy e – semiconductor sy st em with variety solvent are applied on sy stem contains safranin eT dy e with TiO2 in many solvents like water, 1-p rop anol, Formamide, Ac etonitrile and Ethanol. A matlap p rogram has b een written to evaluate many p arameters such that, the solvent reorganization energy , effective free ener gy , activation free energy , coupling matrix element and the rate const ant of electron t ransfer. The results of the rate constant of electron transfer calculated theoretically are in a good agr eement with exp erimental and theoretical values of ot her research. Key Words: electron t ransfer, dye-semiconductor, quantum mechanical theory Introduction Electron transfer (ET) reactions rep resented a simp le p rocess which occurs in donor-acceptor system molecules. The transfer of a single electron from an atom or a molecule to another is considered to be the most elementary chemical and b iolo gical reaction. In general, reactions which involve the transfer of an electron are called r edox reactions. It should be noted that the p article that is actually transferred in redox reactions need not alway s be just a sin gle electron. Electron transfer forms t he basis of conventional color p hotography ; the absorp tion of light by an organic dy e p laced on a small silver halids semiconductor cryst al induces the transfer of an electron from the dy e to the crystal [1]. Electron transfer can be op tically or /and thermally activated and triggers p hotosy nthesis, metabolism, p olymerization reactions, electrochemical reaction, etc. Several theories for ET at differ ent levels of sop histication have been dev elop ed. The most generally useful theoretical fr ame work for thinkin g about electron transfer is M arcus theory [2]. The field of ET has grown enormously since both in the exp erimental and theoretical sp here. A substantial amount of work had been devoted to the p hotoinduced ET st ep in p hotosy nthetic reaction centra of several or ganisms. M any studies have also been conducted on IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (3) 2011 p hotoinduced ET in comp ounds that are much simpler than the active p art of biological reaction centra. A relatively new field in which ET p lays a role is molecular electronics . This subject has evolved during the 1980’s as scientists and technologists have become aware of the p otential applications of or ganic materials. One may think of electrically conducting wires, memories, electronic switches, rectifiers, light –sensitive detectors, electroluminescent device and p hotoconductors [1]. In our research we have calculated the rate constant of electron t ransfer in safranine dye with TiO2 semiconductor sy st em in variety solvent like water, 1-p rop anol, Formamide, Acetonitrile and Ethanol, by using a theoretical model that derived on this sy st em depending on quantum mechanical and golden rule exp ression model app lied theoretically sy st em with many solvents like water, 1-p rop anol, Formamide, Acetonitrile and Ethanol. Theoretical model The dy e should absorb light and up on excitation .This p hoto excitation of dy e leads to well defined ch ange in their r edox. Dye +h Dye * ………….. (1) Where h is p lank constant , is frequency Phot oexcitation of dy e molecules d isp ersed on the surface of band gap semiconductor, results in ejection of electrons from the excited dy e (Dy e * ) to the conduction band or ener getically accessible surface electronic state of semiconductor. Dye + + (semiconductor) KET Dye ………….. (2) Where the represents the electron ejected from the exited dy e molecu le to the conduction band. In addition, the dy e should be located close to the semiconductor, otherwise luminesc ence or nonr adiative d ecay takes p lace instead of electron injection from the excited molecu le [3]. A dy e couple to semiconductor is an excellent model for p rocesses that occur in the ET fields. The dye should absorb l ight p romotes an electron from the ground st ate of the dye located in the semiconductor ener gy gap into an excited st ate that is in resonance with the conduction band (CB). Typically, the dye excited state is well inside the conduction band [4]. Light excites the dy e molecules from the ground st ate, which is located energetically in the semiconductor band gap, to an excited state resonant with t he conduction band, Figure (1) shows the energy level Jobloniske diagram [4]. We have app lied the theoretical model that suggested for ET on the dy e and metal oxide which are the main fo cus in this research. Under this discussion the Hamiltonian of the acceptor /donor sy stem is given by [5] Ĥ = ĤD +ĤA +ĤDA ……………………………………….. (3) IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (3) 2011 This op erator obeys the Schrodinger equation [6] Ĥ …….………… (4) The probability of transfer is [7] ……… (5) Where is the p robability of ET, t is the time , is the Coup ling coeff icient of ET , is the density of state . We consider a donor ( ) or acceptor ( ) are a continuum levels t he rate constant for ET can then be written as [8] …(6) where, h is Planck constant, is reorganization ener gy , is the effective fr ee ener gy , is Boltz man constant, T is the absolute temp erature, is Coup ling coefficient, is Fermi energy , is the decay constant, is volume of un it cell. The reor ganization ener gy can be derived by treating the solvent as a dielectric continuum and given by [9]. λout ……..(7) Where is the vacuum p ermitt ivity , is the st atic dielectric constant of solvent, is the refractive index of the solvent, is the refractive index of the semiconductor, dielectric constant of the semiconductor, is the radius of the molecular dy e, and R is the distance between the comp lex and the semiconductor , and q is the charge of electron. The radius of the dy e molecule can be evaluated from the app arent molar volumes using sp herical app roach [10]. ……………….. (8) Where M is the molecular weight, is Avogadro numb er, and is the density. Where ( ) is an averaged couplin g electronic matrix elements square [11] ………… (9) IBN AL- HAITHAM J . FO R PURE & APPL. SC I. VOL.24 (3) 2011 ……………… (10) Where effective free ener gy is given by [7] ...................... (11) The volume of unit cell for semiconductor is given by [12] …………… (12) Where a, b, and c are latt ice const ant of semiconductor. The coup ling electronic matrix elements can be evaluated by the exp ression [13]: …………. (13) Where is the effective coupling length, is the density of the atom that contributes to the density of st ates in the bond of concern, and is the electronic parameter. The average of the square of the coup ling whi ch is t hen multip lied by the volume to y ield the total coupling coefficient t hat’s mean. …………… (14) Results The ET rate constant is determined theoretically , using quantum mechanical theory and the Golden Rule by many p arameters; the valu e of the reorganization ener gy of the electron donor (D) and accep tor (A) required up on ET, activation free ener gy , the effective free ener gy , and the coupling coeff icient matri x element of ET, between two sites donor and accep tor.One initial we have been evaluated the reorganization energy for the safranineT dy e with TiO2 syst em by using equation(7)with values of [14] , [15], , R=5.4782 , and , from table (1),the results t abulated in table(1) The driving force, that is p rovided by the absorp tion of light in Dy e– Semiconductor interface sy st em that is shown from equation (11). The values of the free energy can be calculated for safranin e T, TiO2 sy stem by taking the difference between the reorganization energy ( ) and the absorption energy , where is the absorp tion energy were IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (3) 2011 taken from the absorption sp ectral of safranine T [16], h, Plank constant (h= , is the frequency that equals (= velocity of light / wave length ), wave len gth of safranine -T is taken from absorption sp ectra (400–800) nm [14], The results obtained are summarized in table (2). The electron is t ransfer occurs when its energy is sufficient to excessed the potential barrier represented by the activation free energy that is evaluated by insertin g the data of the reorganization from table (1)[17] , and the effective fr ee energy from table (2), in to equation (10), one immediately obtains t he values of t he activation fr ee energy , the values ar e list ed in table (3), for safranine T– TiO2sy stem with variety solvent. Anot her imp ortant quantity that can be calculated theoretically is the electronic couplin g term, , which describes t he overlap integral of the donor and the acceptor state [18]. For the semiconductor –dy e sy stem the coup ling matrix element coefficient can be calculated by using equation (14). Inserting the valu es of [13], [13], and atyp ical values of ( =5, 10, 15, 20 ) that assumes in equations (13)and (14), y ou can evaluate the value of the coup ling coeff icient, the results are list ed in table (4). The rate constant of ET is dep ending on the volume of the unit cell through depending on the number of electron density that is p rop ortional with volume by relation [17]. The volume of unit cell is evaluated from equation (12) for any semiconductor with a= b=4.570 and c=2.989 [19]for TiO2 semiconductor. The results of the volume of unit cell for TiO2 is substitution of these p arameters as data into a design ed program to c alculate the rate constant of ET through the solution of the theoretical model equation. These p arameters have been calcu lated theoretically with distance is taken (1 ). A matlab program is writt en to compute the p arameters that’s leading to the evaluation of the rate constant of ET in ST– TiO2 using equation (10), the results are tabulated in tables (4) t o (8). Discussion The electron transp ort mechanism in dy e –semiconductor has been described in term of a quantum mechanical model to transfer across the tunneling region between dy e and semiconductor that is created when the semiconductor is brought to contact with dy e. In this region /tunneling, the tail of the wave functions for dy e and semiconductor over lap . In ord er for electron tunneling between dy e and semiconductor to occur, the initial and final electronic st ates should have approximated equal energies that happ en when consider the dy e–semiconductor system interfaces involves the continuum of electronic states. IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (3) 2011 Accordin g to a fundamental post ulate of ET theory, these two states are brought into resonance by fluctuations of p olar medium surroundin g dy e and semiconductor sy st em. This resonance is the transition state of ET reaction. The transfer matrix element (couplin g coeff icient) , hence controls the dy namics of transition between the donor and accep tor or dy e–semiconductor system and is therefore of our interest, it is this matrix element that inters into the exp ression for the rate of non adiabatic ET reactions. Hence, the typ ical of the square v alues of the coupling coefficient (m atrix element) can be exp ected to be in the range for such sy stem. ET rates were determined by electronic couplin g matrix element between the dy e molecu le and conduction band (CB) of the semiconductor, the driving force ener gy (effective free ener gy , activation free ener gy , volume of the unit cell , and the solvent reorganization ener gy ). The rate of ET values that calculated theoretically is list ed in tables (4) to (8) for ST– TiO2/ sy stem with variety solvent like Water, 1– Prop anol, Formamide, Acetonitrile, and Ethanol. From these results ET occurs in sy stem with most p olar solvents like water and Acetonitrile. The solvent reorganization ener gy are lar ge for more p olar solvents and small values for less p olar solvents, this indicates that the reorganization ener gy is dependent on the p olarity of the solvents. The values of the solvent reorganization ener gy that were calculated theoretically were fitt ing the exp erimental value [18], and [20]. The rate constant value that is calcu lated shows lar ge v alues for dy e –semiconductor sy st em with most p olar solvent and high valu e for safranine T–semiconductor sy stem, this indicates that the ST dy e is more reactive towards semiconductor than coumarin dy e and ET occurs activity with p olar solvents. Table (9) shows the results of rate constant which are in a good agreement with the exp erimental valu e rate const ant . Conclusion In summary , it can be concluded from the present results that. I– theoretical model was suggested for ET in dye –semiconductor interface p rovides an excellent model for st udy ing the transfer of electron through the results of this model as fitting with exp erimental value. II–The reactions of ET st rongly dep ends on the solvent p olarity . For more p olar solvents, the reorganization ener gies are lar ge and small v alues for less p olar solvents, this indicates that, t he reorganization energy dependent on p olarity of the solvent. III– The rate constant of ET is lar ge in (dy e –semiconductor) sy st em with solvent more p olar than less p olar. IV– The rate const ant of ET is lar ge in safranin e T– semicondu ctor ,t his indicates the safranine T dy e is more reactive towards semiconductor . IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (3) 2011 Re ference 1- Wibren,Du.,W.and Gispen.W . H. (2002), Electron transfer in donor–bridg e– acceptor system and derived materials, Ph. D. thesis , Debye Institute and university of Utrecht. 2- Franzen , S.; Golds tein, R. F. and Boxer , S. G. (1993), Distance dependence of ET reactions in organized systems: the role of superchange and non-Condon effects in photosynthetic reaction centers ” J. Phys. Chem. 97, 3040-3053. 3- Karin,W . (2001), Dye /s emiconductor interface ,Ph. D. thesis, Acta un iversity, Uppsala. 4- Walter, R.; Duncan, and Oleg, V. P., (2007), Theoretical Studies of Photoinduced Electron Transfer in Dye-Sensitized TiO2, Annu. Rev. Phys. Chem. 58:143–84. 5- Natalya, A.Z.( 2000) Low temperature electronic transport through macro molecules and characteristics of intramolecular electron transfer Department of physics city co llege of Cuny , New Yor k. 6- Lewiss ,G., (1999), quantum mechanics ”, Boo k,wiley. 7- Mohsin ,A. H.(2010) A Quantum Mechanical Model for Electron Transfer at Semiconductor / Dye Interface at Solvent , Thesis, College of Education Ibn AL– Haithem of Baghd ad University. 8- Shachi, S. Gosavi. (2003), Electron Trans fer at Metal Surfaces , Ph.D Thesis, California Ins titute of Technology Pasadena, California. 9- Kuciunskas , et al . (2001),J. Phys.Chem. B, 105, 2. 10- René .M., W., (1996)”introduction to electron trans fer” PhD Thesis, Amsterdam . 11- Lewis, N. S. (1998), Prog ress in Understanding Electron-Transfer Reactions at semiconductor liqu id interface". J.phys . chem.B. 102(23): 4843. 12- Charles . K. (2005) Introdu ction to solid s tate physics″ . 8 TH , Wiley and Sons INC, 13- Dennis,A;Gaal. Ja mes ,E.M. Fang , L.; Janie, E.C., and Joseph.T.H., (2004), Nonadiabatic electron transfer at the nanoscale tin-oxide semicondu ctor/aqueous solution interface , Photochem.photo boil. Sc il, 3, 240-245. 14- Pradyot, P. ( 2003,) Handb ook of inorganic chemicals, 938-944, New York. 15- Zhiyong, F. and Jia, G. (2005), Zinc Oxide Nanostructures: Synthesis and Properties″ University of California, Irv ine, CA 92697, USA, 1-25. 16- Narjes s, Z.; Amor, H. and Mahmou d ,D. (2008), Remov al of the dy e safranineT in the wastewater using mi cellar enh anced ultrafiltration. " Desalination, 222: 348–356. 17- Shafiqu l, D.M. I.; Mamoru, F. an d Osamu, I.; (1999)," Photochemical reaction s of triplet state of safranine-T studied by transient absorption spectroscopy in visible/near-IR regions" Phys. Chem. 1 : 3737–3742. 18- Gao,Y.B. and Marcus,R. A. (2000), On the theory of electron transfer at semiconductor/liqu id interfaces II: a free electron model, Y. Q. Gao and R. A . Marcus, J. Chem. Phys. 113, 6351 (2000). J. Chem. 113( 15). 19- ZHAO, J. WANG, G.; LIANG, Y.; (2008),CHIN.PHYS.LETT 25(12): 4356– 4359 IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (3) 2011 20- Gao,Y. Q.; Georgievs kii, Y.; and Marcus, R. A.;( 2000) on the theory of electron transfers reaction at semiconductor electrode/ liquid interface" J. chem. Phys., 112( 7). 21- Fajardo,A.M. and Lewis,N.S. ( 1997), Free-energy dependence of electron-transfer rate constants at Si/liqu id interfaces ,J.Phys.Chem. B 101: 11136. 22- Pomykal, K.E. and Lewis., N.S. (1997), Meas urement of Interfacial Charge- Trans fer Rate Constants at n-Type InP/CH3OH Junctions" J.Phys.Chem..B, 101, 2476. Table (1): the reorganization energies value for donor S T dye and acceptor se miconductor TiO2 Solvent Chemical Formula [14] n [14] (Our resoult )λ(eV) for TiO2 Water H2O 80 1.333 0.6798942561 1-p rop anol C3H8O 20.33 1.3856 0.5795911754 Formamide HCONH2 111 1.4475 0.5978483206 Acetonitrile C2H3N 37.5 1.3441 0.6480338344 Ethanol C2H6O 24.5 1.3614 0.6116580688 IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (3) 2011 Table (2): the effective free energy for safranine T–TiO2 system with varie ty sol vent at wave length ( ) (400–800)nm Table (3): The activation free energy for safranine T–TiO2 system with varie ty sol vents at wave length ( ) (400–800)nm SOLVENT for for for f or for Water -2.4221656689 -1.8017536839 -1.3881456939 -1.0927114153 - 0.8711357064 1-propanol -2.5224687496 -1.9020567645 -1.4884487745 -1.1930144959 - 0.9714387870 Formamide -2.5042116044 -1.8837996194 -1.4701916294 -1.174757350 - 0.9531816419 Acetonitrile -2.4540260906 -1.8336141056 -1.4200061156 -1.1245718370 - 0.9029961281 Ethanol -2.4904018562 -1.8699898712 -1.4563818812 -1.1609476026 - 0.9393718937 SOLVENT for f or f or f or f or water 1.11616977517 0.46278100030 0.18444783679 0.0 62663423547 0.0 13448154614 1-propanol 1.62820511577 0.75437450925 0.35629516559 0.1 62307582500 0.0 66229679289 Formamide 1.51970861371 0.69150932018 0.31821735641 0.1 39175781600 0.0 52798412612 Acetonitrile 1.258270732310 0.54225586105 0.22990358346 0.0 87606717384 0.0 25078077622 Ethanol 1.442668052168 0.64717487014 0.29164918917 0.1 23320122540 0.0 43895583380 IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (3) 2011 Table (4): The coupling coefficient value that is calculated for semiconductor dye system ( ) ( ) 3.25244 4.032421511* 5 V1=3. 18586082 1.626042324 6.50486 8.064824289* 10 V2=6. 371721642 6.504139082 9.75730 1.209723643* 15 V3=9. 557582465 1.463431293 13 1.612964833* 20 V4=1. 274344329 2.601655551 Table (5): The rate constant of electron transfe r at S afranine T–TiO2 system with varie ty sol vents at coupling coefficient 4.032421511* Solven t/ Wate r 1-propanol Formamide Ac et onitr ile Ethanol 400 8.542250641 1.17833068 8.898357073 2.974730921 1.917267125 500 1.914687409 1.78344521 2.170726702 1.264196539 600 1.30990681 1.46759453 6.627515407 2.177784004 1.896392603 700 1.709433055 3.42944051 8.54321766 6.45601581 1.59958876 800 1.224077414 1.60531287 2.704892721 7.866342259 3.818116749 8.16394338*10 -3 1 IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (3) 2011 Table (6): The rate constant of electron transfe r at S afranine T–TiO2 system with varie ty sol vents at coupling coefficient 8.064824289* Table (7): The rate c onstant of electron transfer at Safranine T–TiO2 system wit h variety solvents at coupling coefficient 1.209723643* Table (8): The rate c onstant of electron transfer at Safranine T–TiO2 system wit h variety solvents at c oupling coefficient 1.612964833* Solvent / Wate r 1-propanol Formamide Ac et onitrile Ethanol 400 3.416884384 4.713300824 3.55932646 1.189886841 7.669038875 500 7.658714059 7.133744944 8.682866877 3.265562184 5.056762667 600 5.239599985 5.870350983 2.650993971 8.71109555 7.585538172 700 6.837700122 1.371769844 3.417271311 2.58237568 6.370325446 800 4.896286913 6.421221659 1.081952113 3.146522287 1.527239605 Solvent/ Wate r 1-propanol Formamide Ac et onitrile Ethanol 400 7.68989861 1.06492685 8.008484413 2.677245391 1.725532397 500 1.757168651 1.605092612 1.953645018 7.347514911 1.1377716 600 1.178909996 1.32082891 5.964736343 1.959996498 1.706745414 700 1.538482602 3.086482148 7.688860331 5.8103868 1.433323225 800 1.101664555 1.444774873 2.434392216 7.079675143 3.436289111 Solvent/ Wate r 1-propanol Formamide Ac et onitrile Ethanol 400 1.366753711 1.8853271 1.423730539 4.759547215 3.067613054 500 3.063485527 2.853497888 3.473146642 1.306224833 2.022705003 600 2.095839928 2.348140319 1.060397555 3.484438111 3.03443974 700 2.735508000 5.487079205 1.366908481 1.032957582 2.548130099 800 1.958514703 2.568488583 4.327808314 1.258608897 6.108958229 IBN AL- HAITHAM J. FOR PURE & APPL. S CI. VOL.24 (3) 2011 Table (9): compared between our results and experimental and theoretical research for dye -semiconductor Sy st em Theoretical Exp erimental Si/v iolo gen dye 1.3-1.6 [20] 0.6 [21] InP/M e2Fe 0.084-0.086 [20] 1-2 [22] Si/v iolo gen dy e 1.2-1.9 [18] 0.6 [18] Si/ M e2Fe 0.024-1.7 [18] 1 [18] InP/M e2Fe 0.017-1.1 [18] ST– TiO2 1.2 -3.4 (our result) ST– TiO2 1.10166 (our result) ST– TiO2 1.53848 (our result) ST– TiO2 1.43332 (our result) ST– TiO2 3.08648 (our result) ST– TiO2 1.9599 (our result) ST– TiO2 3.0344 (our result) Fig. (1): The energy level Jobloniske diagram [4]. 2011) 3( 24مجلة ابن الھیثم للعلوم الصرفة والتطبیقیة المجلد صبغة السافرانین حساب معدل االنتقال االلكتروني في نظام ، محسن عنید حسونيالعكیلي ھادي جبار مجبل كلیة التربیة ابن الھیثم ،جامعة بغداد ،قسم الفیزیاء 2009لول، ،ای 28:استلم البحث في 2011، اذار، 13: قبل البحث في لخالصةا ام یحتوي ظطبقت على ن،مختلفة شبة الموصل لمذیبات -الحسابات النظریة لمعدل االنتقال االلكتروني في نظام صبغة اسیتونترایل والفورمامید، وبروبانول،- 1 ولماء ،ا :مثل ولمذیبات مختلفة و شبة موصل (ST)على صبغة السافراناین .،واالیثانول الطاقة الحرة الفعالة، و الطاقة الحرة المؤثرة، وطاقة اعادة االنتظام ، :مثل ،كتب برنامج ماتالب لحساب معامالت مختلفة .مصفوفةالعوامل المرتبطة، و معدل االنتقال االلكترونيو .مع نتائج حسابات البحوث العملیة والنظریة ریا كانت ذا تطابق جیدالنتائج لمعدل االنتقال االلكتروني المحسوبة نظ شبة موصل ، نظریة المیكانیك الكمي-االنتقال االلكتروني ، صبغة: الكلمات المفتاحیة