Electronic absorption spectra of symmetric cationic dye in constant electric field

Spectrochimica Acta Part A 61 (2005) 213–218

Electronic absorption spectra of symmetric cationic dye in constant electric field N.A. Davidenko a,∗ , M.A. Zabolotny a , A.A. Ishchenko b b

a Kiev National University, Vladimirskaya Street 64, Kiev 01033, Ukraine Institute of Organic Chemistry, National Academy of Sciences of Ukraine, Kiev 02094, Ukraine

Received 2 May 2003; accepted 12 April 2004

Abstract The electronic absorption coefficient of polymer films doped with symmetric cationic polymethine dye external electric field constant changes is researched. This effect is characterised by the short-wavelength band edge intensity increases and it decreases on the long-wavelength edge. The dye cation charge distribution in the model electric field 108 V m−1 of point charges was calculated by the method AM1. On the basis of the quantum chemical calculations the spectral regularities in electric field is interpreted by the cation electronic charge changes. The theoretical model, based on the eigenfrequencies value changes of the charged anharmonic oscillators under operation field is offered for the observed effects description. The experimental spectra well correlate with the theoretically calculated. © 2004 Elsevier B.V. All rights reserved. Keywords: Absorption coefficient; Anharmonic oscillators; Constant electric field; Electronic charge; Polymethine dyes

1. Introduction

2. Experimental

The photophysical properties of molecules external electric field influence researches is an actual problem, and gives a key to create new electrooptics materials. The long-wavelength bands of the organic dyes electronic absorption occurs on the external constant electric field intensities redistribution [1,2]. Such effects takes place both in the polymer matrices, and in the fluid solutions [1,2]. It should be noted, that they are not concerned to the known phenomena of the dyes molecules (ions) change orientation in the external electric field, for example by Freedericksz or the Kerr effect [3]. The E = 108 V m−1 electric fields strength were used in work [1,2]. Such fields are comparable with the intramolecular field values and do not cause the polymer matrix electrical breakdown. For the dyes with given electrooptics properties targeted synthesis it is necessary to develop the predictable and the dyes optical spectra changes quantitatively described under the electric field physical model. The engineering of such model is the aim of the present work.

We made the experiments of the electronic absorption spectra of symmetric cationic polymethine dyes 1,3,3,1 ,3 ,3 hexamethylindocarbocyanine tetrafluoroborate (HIC) [4], incorporated in polymer films based on photoconducting poly-N-epoxypropylcarbazole (PEPC) and non-photoconducting polyvinylethylal (PVE) under the E influence. The mass% concentration of the HIC in the polymers is 1.

∗ Corresponding author. Tel.: +380-44-419-8143; fax: +380-44-419-8143. E-mail address: [email protected] (N.A. Davidenko).

1386-1425/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.saa.2004.04.020

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Samples were prepared as a free surface structure: a quartz substrate—SnO2 —dye-doped polymer film. The absorption coefficient of such films and its change in the external electric field were measured. For this purpose in the beginning at the selected light wave length (λ) defines the absorption coefficient (κ0 ) of the dye-doped polymer film without the application of the external electric field. Then the electric field was created in this film. The absorption coefficient time changes, before its new quasistationary value, were registered and defined an absorption coefficient (κE ) in an external electric field. Then the value of the absorption coefficient κ changes were: κ = κE − κ0

(1)

under operation of this field. The electric field in the film was created in the corona discharge using the special electronic device [1,2]. The E value was 108 V m−1 . The E value was defined from the value of the SnO2 conductive free surface layer potential. The κ0 and κ values were defined for the light wavelengths in the range of 400–1000 nm, the long-wavelength absorption band of the HIC dye is arranged. The PEPC and PVE absorption in this region is absent. The quantum chemical calculations of the ground electronic state (S0 ) charge distribution (Table 1), total energy for the ground state, the electronic transition energy in the first singlet excited state (S0 –S1 transition) and oscillator strength (Table 2) in the HIC cation under a constant electric field and without it were carried out by the semi-empirical method AM1 [5]. The singly excited configurations stipulated by all possible electronic transitions with three HOMO on three LUMO interactions takes in to account. The geometry optimisation of the insulated molecules in the ground state was previously concerned with the same method using the restricted Hartree–Fock method and the Polak–Ribiere algorithm with the accuracy of 10−6 kcal A−1 mol−1 . The geometry optimised insulated molecule under the electric field was used in the calculations. The constant electric field was modelled by the two external point charges +Qj and −Qj with the opposite sign disposed on the distance l = 10 nm from each other. The +Qj and −Qj values are equalled correspondingly to 0 and 0 (j = a), +1 and −1 (j = b–e) of the electron charge. The external point charges values and the distance between them, the field in the region of the researched molecule can be considered as permanent with the 5% accuracy. The external electric field strength applied to the molecule is defined by the relation (2) E=

2|Qj | πε0 l2

(2)

where ε0 = 8.85 × 10−12 F m−1 the vacuum permittivity. In the case when j = a and j = b–e the ε0 value is equal to 0 and 1.15 × 108 V m−1 correspondingly. The limiting orientations of dye cation relative to external point charges at identical value of a field (1.15 × 108 V m−1 ) are construed: parallel (j = b, Fig. 2, case A) and perpendicular

Table 1 The data of the quantum chemical calculations of electronic charge distribution in HIC cation by a semi-empirical method AM1 in the absence of (j = a) and in the presence of a constant electric field created by the point charges (j = b − e) Atom Electronic charge, j number a b 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

−0.202606 −0.202606 0.003983 −0.118656 −0.095848 −0.077023 −0.117598 0.008298 −0.116488 0.191620 −0.145775 −0.336510 0.121888 −0.336510 0.191620 −0.145775 0.003983 −0.117598 0.008299 −0.077023 −0.118657 −0.095848 −0.116488 −0.202606 −0.202606 −0.092879 −0.092879 0.105127 0.101099 0.078781 0.101099 0.105127 0.078781 0.155856 0.156339 0.151493 0.152965 0.152233 0.133436 0.152233 0.151493 0.155856 0.156339 0.152965 0.101099 0.105127 0.078781 0.105127 0.101099 0.078781 0.121894 0.106815 0.106815 0.121894 0.106815 0.106815

−0.202630 −0.202630 0.003780 −0.117298 −0.095352 −0.077294 −0.117589 0.006299 −0.115136 0.192108 −0.143008 −0.336151 0.121825 −0.336749 0.191033 −0.148504 0.004199 −0.117599 0.010295 −0.076753 −0.120012 −0.096344 −0.117843 −0.202582 −0.202582 −0.093784 −0.091980 0.105563 0.101344 0.078220 0.101344 0.105563 0.078221 0.156870 0.157631 0.151611 0.153565 0.152327 0.133439 0.152131 0.151376 0.154842 0.155046 0.152365 0.100853 0.104688 0.079343 0.104687 0.100853 0.079344 0.122965 0.107114 0.107114 0.120826 0.106518 0.106518

c

d

e

−0.202436 −0.202775 0.003983 −0.118659 −0.095848 −0.077025 −0.117599 0.008301 −0.116487 0.191619 −0.145774 −0.336508 0.121887 −0.336508 0.191619 −0.145773 0.003983 −0.117599 0.008301 −0.077025 −0.118659 −0.095848 −0.116487 −0.202436 −0.202775 −0.092880 −0.092880 0.104964 0.100349 0.078676 0.101851 0.105284 0.078885 0.155854 0.156340 0.151490 0.152968 0.152236 0.133433 0.152236 0.151490 0.155854 0.156340 0.152968 0.100349 0.104964 0.078676 0.105284 0.101851 0.078886 0.121896 0.107457 0.106176 0.121896 0.106176 0.107457

−0.202436 −0.202435 0.003891 −0.119259 −0.095620 −0.077532 −0.117886 0.008847 −0.116027 0.191321 −0.145450 −0.336048 0.121550 −0.336048 0.191321 −0.145449 0.003891 −0.117886 0.008847 −0.077532 −0.119259 −0.095620 −0.116027 −0.202436 −0.202435 −0.093338 −0.093338 0.104359 0.101319 0.078668 0.101312 0.104358 0.078668 0.155172 0.156481 0.150729 0.153699 0.152945 0.132837 0.152945 0.150729 0.155172 0.156481 0.153699 0.101318 0.104359 0.078669 0.104358 0.101312 0.078668 0.122304 0.107378 0.107383 0.122304 0.107383 0.107378

−0.202776 −0.202777 0.004076 −0.118056 −0.096075 −0.076511 −0.117312 0.007751 −0.116951 0.191919 −0.146099 −0.336971 0.122226 −0.336971 0.191919 −0.146099 0.004076 −0.117312 0.007751 −0.076511 −0.118056 −0.096075 −0.116951 −0.202776 −0.202777 −0.092421 −0.092421 0.105894 0.100880 0.078894 0.100886 0.105895 0.078895 0.156540 0.156197 0.152256 0.152231 0.151520 0.134034 0.151520 0.152256 0.156540 0.156197 0.152231 0.100880 0.105894 0.078894 0.105895 0.100886 0.078895 0.121485 0.106252 0.106247 0.121485 0.106247 0.106252

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Table 2 The data of the quantum chemical calculations of the total energy, S0 –S1 transition energy, oscillator strength and r0 and rπ0 values in the HIC cation using the semi-empirical method AM1 without (j = a) and with the constant electric field created by the point charges (j = b–e) Value (j)

Total energy (kcal mol−1 )

S0 –S1 transition energy (cm−1 )

Oscillator strength

r0 (nm)

r0π (nm)

a b c d e

−92374.5506 −92374.5629 −92374.5512 −92374.3843 −92374.7245

20996.0 21000.1 20995.9 20977.5 21014.4

1.2844 1.2999 1.2844 1.2868 1.2820

0 0.010271 0.001981 0.003281 0.003147

0 0.030174 0.000000 0.001103 0.001094

Fig. 1. Atom numbers of HIC cation.

(j = c–e, Fig. 2, cases B–D). In the (j = b–e) cases the cation positioned in the field of charges, then the central carbon atom (atom number 19, Fig. 1) of the polymethine chain is arranged precisely in the central point of the connecting charges +Qj and −Qj straight line (Fig. 2, cases A–D). It can allow shunning the symmetry distortion of the charge distribution in the dye cation as a dimensional effect sense. Actually, under zero field (j = a) the symmetry in the charge distribution is saved, and its numerical values co-

Fig. 2. Orientations of the external point electric charges +Qj and −Qj relative to the HIC cation. Case A has field produced by charges 1(+1) and 1 (−1); case B has field produced by charges 2(+1) and 2 (−1); case C has field produced by charges 3(+1) and 3 (−1); case D has field produced by charges 3(−1) and 3 (+1). Distance between values +Qj and −Qj is diminished in 10 times.

incide with the data of the charges values calculation of the HIC molecule without field.

3. Results and discussion The E influence on the dye-doped films based on PEPC and PVE electronic absorption spectra is revealed. This influence appears after application of the E in accordance of the positive and negative maximums of the dependence κ(λ). Under the E operation in the HIC films with the intensity of absorption in short-wavelength area of the band increases (κ > 0) and in the long-wavelength area decreases (κ < 0) (Fig. 3). After application of E the absorption coefficient value varies with the speed of film surface charging in time is not more than 0.2 s. After turn-off the E absorption spectrum is reduced. In a researched range of the E the position of positive and negative maxima of the κ(λ) dependence does not depend on the E and thickness of the polymer film, but the |κ| increase with the E propagation, this increase is proportional to E2 . The κ absolute values does not depend on the peculiar polarisation and the transited light through the sample. Consequently, the observed effects in the spectra under the electric field operation are not concerned with the orientation phenomena. Also they are not concerned with the processes of the electron transfer in the polymer–dye system, as take place both in the photoconducting PEPC, and in the non-photoconducting PVE. The exception of these factors gives the basis to assume, that the spectral effects are caused by the dyes electronic structure changes under the electric field operation. It is confirmed by the quantum chem-

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Fig. 3. A experimental spectrum of an absorption coefficient (1) and change of the absorption coefficient (2) in an external constant electric field of films PEPC + 1 mass.% HIC as well as corresponding to them calculated an spectra (3 and 4). The field strength is E = 1.15 × 108 V m−1 .

ical calculation data of HIC cation. The electronic charge changes on the atoms of the cation in the all cases (j = b–e), as seen from Table 1 in the field of the point charges +Qj and −Qj which corresponds to the value of strength were used in our experiments. The atomic charges changes are small, but they are larger for the case (j = b). It leads to the induced electronic asymmetry in the HIC symmetric dyes. For the quantitative characteristic of the electronic charge distribution integral changes inside the molecule under the field operation the center coordinates of this distribution are calculated, from the formula (3)
rcj = qjn · rn (3) n

where qjn is the probability of the molecule optical electron presence without field (j = a) and under the external electric field (j = b–e) created by external charges +Qj and −Qj in a point of the atom n with coordinate rn presence. The summation (3) is made for all the atoms of the molecule. If the elementary charge is equal to 1 and under the field operation vary only the electronic coordinates and the nuclear remain stationary, we receive from the relation (3) the formula (4) for change of the position of the optical electron center r0 r0 = rca − rcj

(4)

where j = b–e. The value r0 was received in view of all valence electrons. As the main contribution to optical transition of the ␲-electrons in this paper the values of the ␲-electrons center r0π position changes were also defined. The calculations by the formula (4) shows, that from the case (j = a) to (j = b–e) the value of center shift of the optical electron r0 and r0π undergoes maximal changes as effect of the unlike

point charges +Qj and −Qj on the asymmetrical parts of the dye cation (Table 2): the case j = d top part corresponds to the positively charged field, and low one to the negatively charged (Fig. 2, case C), and in the case j = e (Fig. 2, case D) quite contrary. It is accompanied by the change, from the following results of the quantum chemical calculations, of the total energy values, the S0 –S1 transition energy state and its oscillator strength of the HIC molecule (Table 2). Depending on the position of charges polarity (top or bottom) these values vary in the opposite directions. The external charges effect by the cation symmetric parts (Fig. 2, cases A and B) as one can see from Table 2 is stronger at its orientation along a straight line connecting the point charges (j = b) than at the cation orientation perpendicularly power lines of the field (j = c). It is because the greater sensitivity of ␲-electrons of the conjugate system to external effects in a direction from a charge −Qj to a charge +Qj as seen from the values r0π (Table 2), than perpendicularly to it. The ␲–␲∗ electronic transition is polarised, along the chromophore answers for the long-wavelength absorption band. Therefore, the contribution of the external electric field to the intensities in an absorption spectrum redistribution in the case (j = b) must be maximal. Actually, the greatest increase of the oscillator strength characterising the electronic transition (intensity of absorption) probability is achieved in this case. Consequently, the orientation of the cation along the point charges connecting line the greatest change under the external electric field operation undergone the ␲-electronic density of the dye. The slight change of the oscillator strength in spite of the maximal values r0 and r0π take place in the cases (j = d, e) in contrast to the cases (j = b, c). From here it is possible to conclude that the field mainly influences the σ-electrons.

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It is expedient to find the connection between the values r0 (r0π ) and κ(λ), λ. Then it will be possible to prognosticate theoretically the tendencies in change not only the position but also the absorption bands contour, based on quantum chemical calculations of the charge distribution in a molecule. The long-wavelength absorption bands contour of the polymethine dyes without the strong intermolecular interactions is defined by the vibronic interactions [6–10]. The main contribution to these interactions provide the valence full symmetric vibration of the chromophore atoms in the excited state, which split the pure electronic transition and cause appearance of the vibronic progression in the spectrum [6–10]. Length and intensity of progression, and consequently, the absorption band contour is defined by the value of the internuclear equilibrium distances change of the chromophore bands at the excitation. The degree of their change is pledged in the features of the ground state structure. According, to the principle of Franck–Condon, the light absorption by the molecule is realised at this state geometry. The dye charge distribution changes under the field operations, play a dominating role in the change of the experimental bands contour in the ground state also. It follows that the value κ in our experiments does not depend on time of the application of a field, simultaneously with the sample irradiation by the light or before starting its irradiation and measuring the κ and κ. Therefore, it is possible to consider that spectral effects in the electric field are mainly connected to the charge distribution in ground state changes of the dye ion, as the first approximation. It allows to use a simple model of anharmonic oscillators, placed in the electric field and interacting with a light wave as the description of the process of light absorption by molecules of the dye [11]. Each of the oscillators, which interact with the light wave, is described in Eq. (5) [11]. ∂2 r ∂r eE eE0 + 2β + ω02 r + αr 2 = + exp(iωt) (5) 2 ∂t m m ∂t Here r is the deviation of the optical electron from the equilibrium position, β the damping coefficient, ω0 the frequency of the free vibrations of an oscillator, E0 the amplitude value of the electric field intensity of the light wave, m the electron mass, α the anharmonicity oscillator coefficient, ω the light frequency. The origin of coordinates is disposed by the location of an electron without the external field. The amplitude r, as follows from (5), is a complex value. It defines electrical dipole moment of the modelled molecule and modulus the polarisation P vector (6): P = Ner

(6)

where N is the volume concentration of the dye molecules. The parameter P, is connected with the complex permittivity ε by the relation (7) [12]: P ε=1+ (7) ε0 E0

217

The imaginary part looks like (8): Im ε = −

2Ne2 ωβ mε0 [(ω02 − ω2 )2 + 4β2 ω2 ]

(8)

and it is connected with the absorption coefficient of the medium κ(λ) by a relation (9) [12]: κ(λ) =

2π Im ε nr λ

(9)

where nr is the refracting coefficient of the medium. After the substitution of Eq. (8) in Eq. (9) and usage of the expression ω = 2πc/λ we can receive Eq. (10): κ(λ) =

2βNe2 1/λ2 2 2 (2πc) cε0 mnr ((1/λ0 ) − (1/λ2 ))2 + (β/πcλ)2 (10)

where c is the light velocity. At this expression (10) it is necessary to take into account the existence possibility of oscillators of various types interacting with a light wave, that should give in appearance of appropriate summation in (10) on sorts of oscillators. However, the contribution of each sort of oscillator must be added to the absorption coefficient. Therefore, with the purpose of the record simplification of the sign and the summation indexes in the expression (10) do not show. Within the framework of the anharmonic oscillators model a shift of the equilibrium position of the electronic density (oscillator) on the value r0 under the external electric field operation takes place according to Eq. (11) [12]:  −ω02 ± ω04 + (4αeE/m) r0 = 2α eE e2 E2 α 2e3 E3 α2 ≈ − + ··· (11) mω02 m3 ω010 m2 ω06 where value ω0 corresponds to the S0 –S1 transition frequency. This shift at the presence of anharmonicity causes the eigenfrequency (eigenwavelength) changes of the oscillator, modelling an optical electron, on the valueω0 (λ0 ): αr0 ω0 = (12) ω0 λ0 = −

ω0 αr0 2πc

(13)

The eigenfrequency (eigenwavelength) changes of the oscillator causes the absorption coefficient changes (12). The wavelength changes in a maximum point (12, 13) under the electric field can be presented as (14):   2πcα eE e2 αE2 2e3 α2 E3 λ0 = − 3 − + ··· (14) mω02 ω0 m3 ω010 m2 ω06 To estimate the absorption coefficient κE (λ) changes under the external electric field operation must replace in Eq. (10)

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the λ0 to λ0 + λ0 values and substitute it to expression (14). Let us receive Eq. (15): 2βNe2 (2πc)2 cε0 mnr

κE (λ) =

·

λ−2 (15) [((λ0 + λ0 )−2 − λ−2 )2 + (4β2 /(2πcλ)2 )]

The change of this coefficient in practically realised cases λ0  λ0 can be presented as (16): κ(λ) =

2 2 λ−2 λ−3 βNe2 0 (λ0 − λ ) λ0 −2 2 2 2 2 (πc)2 cε0 mnr [(λ−2 0 − λ ) + (β /(πcλ) )] (16)

With consideration for relation (13) these equations are conversed to Eq. (17): κ(λ) = −

2 2 λ−2 λ−4 βαNe2 0 (λ0 − λ ) r0 −2 2 2 2 2 (πc)2 cε0 mnr [(λ−2 0 − λ ) + (β /(πcλ) )] (17)

The representation (17) allows within the framework of the offered model to install the interrelation between the change of the absorption coefficient of the sample in the external electric field and the value of the center shift of the optical electron of the molecule (molecule electrical dipole moment changes) which is calculated by the quantum chemical methods. It is necessary to take into account the various orientations of the molecule axes relatively to the external electric field, as the dopants molecules distribution in the amorphous polymer matrices and liquids is isotropic. In this connection we receive Eq. (18): eff kE = 21 (kE (λ) − k(λ)) + 21 (kE (λ) − k(λ)) ∼ E2

(18)

The graphs of the experimental and theoretical dependencies k(␭) (curves 1 and 3) and k(␭) (curves 2 and 4) in films PEPC + 1 mass.% of HIC are presented in Fig. 3. The curves (3 and 4) in an electric field calculated for the case (j = b) is characterised by the greatest value of the oscillator strength of S0 –S1 transition. Using for this purpose the value r0π and ω0 of the HIC cation is defined based on the quantum chemical calculation. Then on the basis of expres-

eff was calcusions (10), (17) and (18) the dependence kE lated. The parameters α and β at constancy of the value N varied, so that the difference between the experimental and theoretically calculated values of the absorption coefficients will be minimal. The minimum difference between these coefficients is reached at α = 1.103 × 1030 s−2 m−1 and β = 0.732 × 1015 s−1 . eff from the The experimental dependence of the kE E well correlate with values calculated theoretically (Fig. 3).

4. Conclusion Therefore, the offered model which can be used for the theoretical prediction of the organic dyes absorption spectra changes under the external electric field is connected with the redistribution of the electronic density (charge) in molecules. The results of such calculations are in accordance with the experiment. The offered model can be applied not only for the purposes of a spectroscopy, but also for other problems, connected with the conversion of the light energy in the dye-doped polymer materials.

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