Hyperpolarizabilities for the one-dimensional infinite single-electron periodic systems. I. Analytical solutions under dipole-dipole correlations

The analytical solutions for the general-four-wave-mixing hyperpolarizabilities chi(3)[-(omega1 + omega2 + omega3);omega1,omega2,omega3] on infinite chains under both Su-Shrieffer-Heeger and Takayama-Lin-Liu-Maki models of trans-polyacetylene are obtained through the scheme of dipole-dipole correlation. Analytical expressions of dc Kerr effect chi(3)(-omega;0,0,omega), dc-induced second-harmonic generation chi(3)(-2omega;0,omega,omega), optical Kerr effect chi(3)(-omega;omega,-omega,omega), and dc electric-field-induced optical rectification chi(3)(0;omega,-omega,0) are derived. By including or excluding nabla(k) terms in the calculations, comparisons show that the intraband contributions dominate the hyperpolarizabilities if they are included. nabla(k) term or intraband transition leads to the break of the overall permutation symmetry in chi(3) even for the low-frequency and nonresonant regions. Hence it breaks the Kleinman [Phys. Rev. 126, 1977 (1962)] symmetry that is directly based on the overall permutation symmetry. Our calculations provide a clear understanding of the Kleinman symmetry breaks that are widely observed in many experiments. We also suggest a feasible experiment on chi(3) to test the validity of overall permutation symmetry and our theoretical prediction. Finally, our calculations show the following trends for the various third-order nonlinear optical processes in the low-frequency and nonresonant region: chi(nonres)(3)(-3omega;omega,omega,omega)>chi(nonres)(3)(-2omega;0,omega,omega)>chi(nonres)(3)(-omega;omega,-omega,omega)>chi(nonres)(3)(-omega;0,0,omega) > or = chi(nonres)(3)(0;omega,-omega,0), and in the resonant region: chi(res)(3)(-omega;0,0,omega)>chi(res)(3)(-omega;omega,-omega,omega)>chi(res)(3)(-2omega;0,omega,omega)>chi(res)(3)(0;omega,-omega,0)>chi(res)(3)(-3omega;omega,omega,omega).     

Brillouin scattering and optical Kerr effect study of dimethacrylates: temperature effects

In this paper we report a temperature study of Brillouin scattering and optical Kerr effect in the ethane-1,2-diol dimethacrylate, pentane-1,5-diol dimethacrylate and hexane-1,6-diol dimethacrylate belonging to the series of dimethacrylate homologues. Using these methods we have studied the temperature behaviour of the hypersonic velocity, adiabatic compressibility and optical Kerr constant in the temperature range from 283 to 323 K.

The obtained results are compared to those obtained earlier from Brillouin scattering and optical Kerr effect experiments for butane-1,4-diol dimethacrylate and 2,2′-thiodiethyl dimethacrylate (a sulfur-containing monomer). The results are also discussed in terms of changes in the intermolecular interactions and arrangement in the liquid compounds under study.     

Shape and electrostatic effects in optical Kerr effect spectroscopy of aromatic liquids

We present a detailed, temperature-dependent, optical Kerr effect (OKE) study of pyridine, pyridine-d(5), 2,4,6-trifluoropyridine, 2,4,6-trimethylpyridine, and 1,3,5-tris(trifluoromethyl)benzene. By combining these data with those for other aromatic liquids that we have studied previously (Loughnane, B. J.; Scodinu, A.; Fourkas J. T. J. Phys. Chem. B, 2006, 110, 5708), we are able to assess the relative importance of molecular shape and electrostatic forces in determining the form of the OKE reduced spectral density for such liquids.     

Structural relaxation in complex liquids: non-Markovian dynamics in a bistable potential

The time correlation function C(t) identical with of the distance fluctuations of a particle moving in a bistable potential under the action of fractional Gaussian noise (fGn) is calculated from a Smoluchowski-type equation derived from a generalized Langevin equation (GLE). The time derivative of this function, dC(t)dt, is compared with data from optical Kerr effect measurements of liquid crystal dynamics in the vicinity of the isotropic-to-nematic transition, which are related to the time derivative of an orientational correlation function. A number of characteristic features of the experimental decay curves, including short and intermediate time power law behavior and long time exponential relaxation, are qualitatively reproduced by the analytical calculations, even though the latter do not explicitly treat orientational degrees of freedom. The GLE formalism with fGn was, in fact, originally proposed as a model of protein conformational fluctuations, so the present results suggest that it may also serve more generally as a model of structural relaxation in complex condensed phase media.     

Comparative study of temperature dependent orientational relaxation in a model thermotropic liquid crystal and in a model supercooled liquid

Recent optical Kerr effect experiments have revealed a power law decay of the measured signal with a temperature independent exponent at short-to-intermediate times for a number of liquid crystals in the isotropic phase near the isotropic-nematic transition and supercooled molecular liquids above the mode coupling theory critical temperature. In this work, the authors investigate the temperature dependence of short-to-intermediate time orientational relaxation in a model thermotropic liquid crystal across the isotropic-nematic transition and in a binary mixture across the supercooled liquid regime in molecular dynamics simulations. The measure of the experimentally observable optical Kerr effect signal is found to follow a power law decay at short-to-intermediate times for both systems in agreement with recent experiments. In addition, the temperature dependence of the power law exponent is found to be rather weak. As the model liquid crystalline system settles into the nematic phase upon cooling, the decay of the single-particle second-rank orientational time correlation function exhibits a pattern that is similar to what has been observed for supercooled liquids.     

The calculation of frequency-dependent hyperpolarizabilities including electron correlation effects

The theory for the calculation of the frequency-dependent hyperpolarizabilities β(?2ω; 0, ω), β(?ω; 0, ω), and β(0; ω, ?ω) is discussed. New relations between these tensors are derived for those wave functions that obey the time-dependent Hellmann–Feynman theorem (e.g., the self-consistent field [SCF] or the exact wave function). Using second-order Møller–Plesset perturbation theory (MP2), expressions are obtained for the hyperpolarizabilities in terms of derivatives of appropriately defined linear polarizability tensors with respect to a static electric field. Results are presented for ammonia and formaldehyde for the optical Kerr effect and for secondharmonic generation. These results indicate that it is desirable to determine the frequency-dependent contribution to the hyperopolarizability at the MP2 rather than the SCF level of theory, in cases where the static hyperpolarizability has a large contribution from electron correlation and/or where the frequency-dependent contribution may be more significant, such as for secondharmonic generation.     

Nonlinear optical properties of ferrocene- and porphyrin-[60]fullerene dyads.

A series of novel [60]fullerene-ferrocene and [60]fullerene-porphyrin dyads, in which a fullerene and an electron donating moiety are attached through a flexible triethylene glycol linker are synthesized and their nonlinear optical (NLO) response studied. Specifically, the third-order susceptibility chi(3) of all fullerene derivatives are measured in toluene solutions by the optical Kerr effect (OKE) technique using 532 nm, 35 ps laser pulses and their second hyperpolarizability gamma are determined. All fullerene dyads studied exhibit enhancement of their NLO response compared to pristine fullerenes which has been attributed to the formation of a charge separated state. All experimentally measured hyperpolarizability gamma values are also calculated by the semiempirical methods AM1 and PM3. A good correlation is found between the theoretical and experimental values, suggesting that simple semiempirical methods can be employed for the designing and optimization of the fullerene-containing dyads displaying improved nonlinear responses.     

Depolarized light scattering versus optical Kerr effect. II. Insight into the dynamic susceptibility of molecular liquids

We have previously discussed [J. Chem. Phys. 125, 114502 (2006)] that optical Kerr effect (OKE) and depolarized light scattering (DLS) data of molecular liquids reveal, each in their native domain, the same characteristic signatures of the glass transition dynamics; in particular, the intermediate power law of OKE is equivalent with the excess wing of the frequency-domain data, long since known in dielectric spectroscopy. We now extend the discussion to show that the excess wing is an equally common feature in DLS. We further discuss the time-temperature superposition property of OKE data in relation to our DLS and literature dielectric-spectroscopic results, and the merits of their mode coupling theory analyses. Spectroscopic signatures of a liquid-crystal-forming system (nematogen) are discussed in the same frame.     

Molecular dynamics investigation with the time resolved optical Kerr effect on the CS2-C6H6 mixtures

An investigation of the molecular dynamics in pure liquids and in mixtures through the technique of time resolved optical Kerr effect is performed. The samples studied were the mixtures of carbon disulfide (CS(2)) with benzene (C(6)H(6)). The molecular dynamics of the pure liquids is briefly discussed while the main results are obtained for the mixtures. A slow dynamics component is observed for the optical heterodyne detected optical Kerr effect transient decaying exponentially with time constants on picosecond time scale. The fast subpicosend time relaxations are analyzed in terms of the nondiffusive component of the spectral response that is associated with the molecular dynamics. The modifications of the spectrum are quantified, and the explanation of the observed changes is given in terms of the structural interaction configurations that produced changes in the intermolecular potential within which the molecules execute librational motions.     

Effect of high electric fields on the isotropic phase of a lyotropic liquid‐crystalline system

The effect of high (>1000 V/mm) electric fields on solutions of a lyotropic liquid‐crystalline polymer, poly(n‐hexyl isocyanate) in p‐xylene, is presented. The concentrations are adjusted such that the solutions are strictly within the isotropic phase domain region, thus exhibiting no spontaneous liquid crystallinity. The effects of field strength, frequency, and concentration are varied and the morphological changes are noted. The results are analyzed with birefringence measurements via comparison with the optical Kerr effect. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4116–4125, 2004     

Searching for voids in liquids with optical Kerr effect spectroscopy

It has recently been shown [J. Chem. Phys. 2005, 122, 134506; J. Am. Chem. Soc. 2006, 128, 5119] that liquid tetrahydrofuran has an unusual structure that features voids of significant dimension. Such voids should affect other observable properties of this liquid. Here we present temperature-dependent, optical Kerr effect data for tetrahydrofuran and a number of related liquids (furan, cyclopentane, tetrahydropyran, cyclohexane, diethyl ether, and n-pentane) as well as hexamethylphosphoramide to test whether this technique can be used to reveal the presence of sizable voids in liquids.     

Short time dynamics in the isotropic phase of liquid crystals: the aspect ratio and the power law decay

Optical heterodyne detected optical Kerr effect (OHD-OKE) experiments are used to study the orientational dynamics of the liquid crystal 4^′-octyl-4-biphenylcarbonitrile (8CB) in the isotropic phase near the isotropic to nematic phase transition. The results are compared to those for three other liquid crystals. The 8CB data display a short time scale temperature independent power law decay and a long time scale exponential decay with a temperature dependence described by Landau–de Gennes theory. The power law exponent is −0.56. Combining this result with previous results for three other liquid crystals [J. Chem. Phys. 116 (2002) 6339; J. Chem. Phys. 116 (2002) 360], it is found that the power law exponent depends linearly on the aspect ratio of the liquid crystal.     

Laser-induced Kerr constants for alkanoic acids at 532 and 1064 nm inducing wavelengths

The nanosecond optical Kerr constants of a series of alkanoic acids from formic acid to nonanoic acid have been measured at the two inducing wavelengths of 532 and 1064 nm. Results indicate that the values are of similar magnitude to a previous study of the 1-alkyne series and exhibit a similar behaviour of relatively invariant values amongst the higher members of the series. This effect is attributed to the dominant contribution of the carbonyl group to the observed optical Kerr constant.     

Large third-order optical nonlinearity of self-assembled porphyrin oligomers.

Third-order nonlinear optical properties of two series of self-assembled porphyrin wires, one being terminated by zinc porphyrin and the other by free base porphyrin, were measured by femtosecond time-resolved optical Kerr effect. The hyperpolarizability values of the latter series were extremely large ranging from 10-30 to 10-29 esu, 10 times larger than the former. The behavior is accounted for by the contribution of terminal free base porphyrin to enhance the molecular polarization by acceptor nature toward central metalloporphyrin array.     

飞秒光学外差光学克尔效应和低频拉曼光谱技术研究离子液体[bmim][PF6]的低频光谱

利用飞秒光学外差光学克尔效应技术获得了咪唑类离子液体1-丁基-3-甲基咪唑六氟磷酸盐([bmim][PF6])体系中反映分子间相互作用的低频光谱. 结果分析中, 利用Brownian振子时间相关函数的精确表达式对光学克尔效应动力学数据中的核振动部分进行模拟, 在时域上获得各个振动组分的时间演化行为, 并进而通过快速Fourier变换获得各个振动组分的频域光谱和总加和光谱. 此外还利用低频拉曼光谱技术测量了离子液体[bmim][PF6]的低频光谱, 并和飞秒光学外差光学克尔效应实验的结果进行对比, 发现两种方法获得的低频光谱相近. 实验结果表明Brownian振子时间相关函数的精确表达式可用来解析离子液体体系中低频振动的时间演化行为.     

Ultrafast dynamics of liquid poly(ethylene glycol)s and crown ethers studied by femtosecond Raman-induced Kerr effect spectroscopy

Ultrafast molecular dynamics of liquid poly(ethylene glycol)s, tetra(ethylene glycol), penta(ethylene glycol), and poly(ethylene glycol) with the molecular weight of 600, and crown ethers, 12-crown-4 and 15-crown-5, have been investigated by means of femtosecond optical heterodyne-detected Raman-induced Kerr effect spectroscopy. Picosecond Kerr transients of poly(ethylene glycol)s and crown ethers are characterized by a biexponential function with the time constants of about 2 and 20 ps. Both the faster and slower time constants do not vary much among the five oligo(ethylene oxide)s. Femtosecond dynamics is discussed based on the Kerr (depolarized Raman) spectra obtained by Fourier transform deconvolution analysis of the high time resolution Kerr transients. The broad low-frequency band (0-200 cm(-1)) in the Kerr spectrum is analyzed by two Brownian oscillators. The spectral shapes of linear poly(ethylene glycol) and cyclic crown ether are very different. Both the low- and high-frequency Brownian oscillators for crown ethers show lower frequency and broader spectral features than those for poly(ethylene glycol)s. The comparison of the low-frequency spectra of poly(ethylene glycol)s and crown ethers shows that the low-frequency spectrum of 15-crown-5 is closer to that of poly(ethylene glycol)s than that of 12-crown-4 is. The difference of the low-frequency spectra between poly(ethylene glycol) and crown ether is discussed with the concepts of molecular conformation and liquid density. The features of the observed intramolecular vibrational bands are also correlated with the molecular conformations.     

Ultrafast molecular dynamics of liquid aromatic molecules and the mixtures with CCl4

The ultrafast molecular dynamics of liquid aromatic molecules, benzene, toluene, ethylbenzene, cumene, and 1,3-diphenylpropane, and the mixtures with CCl(4) have been investigated by means of femtosecond optical heterodyne-detected Raman-induced Kerr effect spectroscopy. The picosecond Kerr transients of benzene, toluene, ethylbenzene, and cumene and the mixtures with CCl(4) show a biexponential feature. 1,3-Diphenylpropane and the mixtures with CCl(4) show triexponential picosecond Kerr transients. The slow relaxation time constants of the aromatic molecules and the mixtures with CCl(4) are qualitatively described by the Stoke-Einstein-Debye hydrodynamic model. The ultrafast dynamics have been discussed based on the Kerr spectra in the frequency range of 0-800 cm(-1) obtained by the Fourier transform analysis of the Kerr transients. The line shapes of the low-frequency intermolecular spectra located at 0-180 cm(-1) frequency range have been analyzed by two Brownian oscillators ( approximately 11 cm(-1) and approximately 45 cm(-1) peaks) and an antisymmetric Gaussian function ( approximately 65 cm(-1) peak). The spectrum shape of 1,3-diphenylpropane is quite different from the spectrum shapes of the other aromatic molecules for the low magnitude of the low-frequency mode of 1,3-diphenylpropane and/or an intramolecular vibration. Although the concentration dependences of the low- and intermediate-frequency intermolecular modes (Brownian oscillators) do not show a significant trend, the width of high-frequency intermolecular mode (antisymmetric Gaussian) becomes narrower with the higher CCl(4) concentration for all the aromatics mixtures with CCl(4). The result indicates that the inhomogeneity of the intermolecular vibrational mode in aromatics/CCl(4) mixtures is decreasing with the lower concentration of aromatics. The intramolecular vibrational modes of the aromatic molecules observed in the Kerr spectra are also shown with the calculation results based on the density functional theory.     

The electro-optic properties of fluorinated polydialkoxyphosphazenes with different lengths of side substituents

Polydialkoxyphosphazenes with partially fluorinated side substituents of different lengths in dioxane and ethyl acetate are studied via the methods of the equilibrium electro-optic Kerr effect, isothermal translational diffusion, and viscosimetry. It is experimentally found that the magnitude and sign of the Kerr constant depend on the length of the side substituents. The observed dependence is explained by the changes in the optical polarizability tensor and the angle between the direction of the permanent dipole moment and the primary axis of optical polarizability of the monomer unit of these macromolecules with an increase in the number of carbon atoms in the chains of alkoxy substituents attached to phosphorus. It is shown that fluorinated polydialkoxyphosphazenes are comblike polymers with high equilibrium skeletal rigidity and non-coincident principal directions of the optical polarizability and dielectric polarizability of the monomer unit.     

New polyamides with main-chain cyanine chromophores

Polyamides containing main-chain cyanine chromophores are synthesized, and their molecular, nonlinear optical, and mechanical properties are studied. It is shown that the Kerr electro-optical effect in polymer solutions is determined by the rigidity of polymer chains and that the nonlinear optical properties are dependent only on the chromophore content.     

Relaxation of the optical Kerr effect of anisotropic molecules in mixed liquids

The relaxation time of the Kerr effect of nitrobenzene and m-nitrotoluene in various mixtures with carbon tetrachloride and various alcohols was determined by measuring the kinetics of the Kerr effect using picosecond laser techniques. These measurements yield information on the rotational motion of molecules in liquids. The relaxation time data are interpreted in terms of an effective local viscosity effect, pair correlation, and coupling of rotational motion with shear modes.