Solvent Effect on the Electronic Polarizability of Benzonitrile Y. J. Alvarado, P. H. Labarca, N. Cubill´an, E. Osorio, and A. Karam a Laboratorio de Electr´onica Molecular, Departamento de Qu´ımica, Fac. Exp. de Ciencias, La Universidad del Zulia, Ap. 526, Grano de Oro, M´odulo No. 2, Maracaibo, Venezuela a Laboratorio de Pol´ımeros, Centro de Qu´ımica, IVIC, Caracas, Venezuela Reprint requests to Dr. Y. J. A.; E-mail: [email protected] Z. Naturforsch. 58a, 68 – 74 (2003); received September 16, 2002 In this study, the static and dynamic electronic polarizability of benzonitrile is reported. This prop- erty was determined using refraction index measurements of neat benzonitrile and CCl4, THF, C6H12 and CH3CN diluted solutions. The real refractive index of pure benzonitrile was obtained by refrac- tometry, FTIR transmission spectroscopy and Kramers-Kr¨onig transform. These results indicate that the vibrational contribution to the visible refraction is very small, and the electronic polarizabili- ties calculated with these values agree with reported values. In binary mixtures, the polarizability of benzonitrile was obtained with the refractometric method proposed by Singer and Garito at five frequencies to obtain the dispersion curve. The local field effects were tested within the Onsager and Lorentz local field approach. The static properties in each solvent was obtained by extrapolation of the Cauchy-type dispersion curve to zero frequency, which gave a monotonic increased as a func- tion of the squared frequency. The polarizabilities obtained in this work agree well with theoretical and experimental data, reported by other authors. The static and dynamic electronic polarizability of benzonitrile was found to be little affected by the dielectric nature of the solvent, and the electric deformability is similar to that of the benzene molecule. The effect of the replacement of the C—H group by N in 4-cyano-pyridine and benzonitrile molecules is discussed. Key words: Benzonitrile; Polarizability; Solvent Effect. 1. Introduction The dynamic and static polarizability of pure ben- zonitrile, obtained by refractometric measurements, is The importance of cyano-substituted aromatic com- reported in the literature. Unfortunately, these values in pounds in molecular electronic devices and new kinds different solvents are scarce for this reason, the role of of mesogenic materials has renewed the interest in intermolecular interactions and the frequency depen- their chemical and electronic properties [1, 2]. For ex- dence of the polarizability of benzonitrile in solution ample, the benzonitrile (BZCN) moiety is a relevant are unknown [6, 16 – 20]. Based in this, and continuing polar group in molecules present in calamitic and lin- with our interest in this field, we report in this work a ear and nonlinear optical materials [1, 3 – 5]. Several detailed evaluation of the solvent effect in dynamic and molecular properties, such dipole moment, polarizabil- static electronic polarizability of benzonitrile. ity (dynamic and static), polarizability anisotropies, and nonlinear optical properties are currently explored 2. Theory in benzonitrile, cyano-biphenyl, and azulene deriva- tives by both experimental and theoretical methods [3, 2.1. Electric Dipole Polarizability 4, 6, 7]. However, intermolecular forces and solvent The molecular dipole polarizability α is the lin- effects can have a large influences on these properties, ear response of a molecular electronic distribution to and their evaluation is important to allow an adequate the action of an external electric field ℑ that induces comparison of the optical susceptibilities of molecules changes in the permanent molecular dipole moment µ and their crystals [8 – 13]. In this context we have re- e according to equation (1) [14, 15, 21]. cently reported the determination and theoretical cal- culation of solvent effects on the static and dynamic µe(ℑ)=µe(ℑ = 0)+α · ℑ dipole polarizability of highly polarizable heteroaro- (1) matic compounds [14, 15]. +(1/2!)β · ℑ2 +(1/3!)γ · ℑ3 + ···. 0932–0784 / 03 / 0100–0068 $ 06.00 c 2003 Verlag der Zeitschrift f¨ur Naturforschung, T¨ubingen · http://znaturforsch.com Y. J. Alvarado et al. · Solvent Effect On The Electronic Polarizability Of Benzonitrile 69 Here, µe(ℑ = 0) is the permanent dipole moment where η and κ are the real and imaginary compo- in the absence of an electric field, α is a second rank nents of the refractive index, respectively. In liquids, tensor that represent the dipole polarizability, and the the κ spectrum is obtained from transmission or at- higher order terms are the first and second hyperpolar- tenuated total reflection spectra. The η spectrum is izabilities, respectively. obtained from the κ spectrum through the Kramers- In polarizability studies, the components αii(i = Kr¨onig transform as [22, 23] x,y,z) of the diagonalized α tensor and the associated 2 ∞ νκ˜ (ν˜ ) average polarizability η(ν˜ )=η(0)+ P dν˜, (9) i π ν2 − ν2 0 ˜ ˜i 1 where the second term can be split in an infrared and a α = α = (α + α + α ) (2) ave 3 ii jj kk UV-Visible contribution. For colorless compounds (not and anisotropy absorbing in the visible region) this equation is simpli- fied to 1 2 2 ∆α = { [(αii − α jj) +(αii − αkk) 2 νκ(ν) (3) 2 4 2 ˜ ˜ 2 1 η(ν˜i)=η(0)+A1ν˜ + A2ν˜ + P dν˜ , +(α jj− αkk) ]} 2 i i π ν2 − ν2 IR ˜ ˜i are of great experimental interest. (10) The average dipole polarizability can be determined where η(0) and the coefficients A and A are obtained experimentally by means of the refractive index η of a 1 2 by a linear least squares fit of the refractive index at vis- gas according to the equation ible frequencies. The evaluation of the integral in the 2πασ infrared region represents the contribution of infrared- η = 1 + , (4) kBT active vibrational modes to the visible refractive index. where σ is the pressure. Equation (4) holds if the For a binary mixture, such as solvent and solute, the molecules do not interact with each other. In the con- refractometric equation of Singer and Garito can be de- rived from (7), [6, 24]. densed phase, each molecule is polarized by the ex- ternal field and the field produced by surrounding 4π 3M ∂η2(ν) N αe(ν)= 2 (11) molecules. The total local field F is expressed in terms A 2 ρ (η2(ν)+ )2 ∂ 3 1 1 2 w 0 of the dielectric polarization P as 1 ∂V η2(ν) − 1 F = E + 4πLP, (5) + M + 1 . 2 ρ ∂ η2(ν)+ 1 w 0 1 2 where L is the dimensionless Lorentz factor, which de- Another refractometric expression can be obtained pends on the structure of the phase and equals 1/3 for by employing the Onsager [25] local field factors cubic and isotropic phases, giving the Lorentz local within the Garito and Singer approximation. This field equation at the infinite dilution limit becomes [24] 4π F = E + P. (6) η2(ν)(η2(ν)+ ) ∂η2(ν) 3 NA αe(ν) 1 2 2 = 1 2 η2(ν)+η2(ν) πρ ∂ The Lorenz-Lorentz equation can be derived from (6): M2 2 1 2 4 1 w 0 η2 − 1 4πNα η2(ν) − 1 ∂V η2(ν) − 1 = , (7) + 1 + 1 η2 + 2 3V 4π ∂w 4πρ1 0 where N is the number of molecules in the volume V. η2(ν) − 1 1 ∂η2(ν) − 1 , (12) Equation (7) allows to determine polarizabilities α by πρ η2(ν) ∂ 4 1 3 1 w 0 measurements of the refraction index η in the off-re- where w is the solute weight fraction and η(ν), η (ν) sonance regime, and the density ρ = N/V in pure com- 1 and η (ν) are the solution, solvent and solute real re- pounds [14, 15]. In the resonance region the refractive 2 fraction indices at the optical frequency (ν), respec- index is a complex quantity defined as [22, 23] tively; ρ1 is the solution density, M2 the solute molec- ηˆ (ν˜ )=η(ν˜ )+iκ(ν˜), (8) ular weight, V the specific volume of the solution, NA 70 Y. J. Alvarado et al. · Solvent Effect On The Electronic Polarizability Of Benzonitrile α e(ν) Avogadro’s number, and 2 the electronic contribu- in this work from extrapolation to zero-frequency of tion from the mean dynamic polarizability of a solute the experimental refractometric dynamic refractive in- molecule. dex [22]. In (11) and (12) it is assumed that the solute and The dynamical refractive index of benzonitrile in the solvent are not interacting and that the molecular po- visible regime obtained by this method does not take in larizations are additive. The electronic dynamic po- account the infrared contribution. In other words, these larizability, obtained from (11) and (12), is treated as values represent the contribution of electronic absorp- a frequency-dependent quantity and calculated at dif- tion only. These results were used in the determination ferent wavelengths. The long-wavelength limit is ob- of the electronic polarizability of pure benzonitrile and tained by an extrapolation to zero frequency of the dy- binary solutions. namic mean polarizability α e(ν). This relationship is 2 3.2. Benzonitrile in Solution referred to as the Cauchy-type dispersion curve, and it gives the behavior of the dispersion of the polariz- The average electronic polarizability dispersion ability in field frequency terms. This curve allows to curves of benzonitrile were experimentally determined extrapolate the electronic part only, and the limit value using refractometric techniques. The refractive index, corresponds to the static dipole polarizability. Contri- η, of both, solvent and solutions, were measured with butions from infrared-active vibrational modes (vibra- Bellingham and Stanley high resolution ABBE refrac- tional polarizability) are not considered here [26, 27]. tometers 60/LR and 60/LR with CCD camera at 20 ◦C (±0.1 ◦C).