Jean-Louis Déjardin

Quantum theory of the spectral density of the hydrogen bond in solution Part 1. A closed autocorrelation function

Abstract A novel formulation of the quantum theory of the spectral density of the hydrogen bond in solution is proposed. It leads to a compact form for the autocorrelation function to be Fourier transformed in order to get the spectral density. An approximation concerning the modelization of the damping that was performed in our initial approach is avoided, leading to an autocorrelation function that is more physical. The compact form of the autocorrelation function provides an understanding of how our model reduces to that of Witkowski and Marechal in the absence of relaxation and what the differences are between our model and the classical model of Robertson which involves damping. It is also shown that it is not possible to find an equivalent formulation of the spectral density in terms of the density operator formalism, which eliminates the possibility of treating more complex hydrogen bonds with the aid of the perturbation theory using the density operator formalism. Finally, we underline the importance of the recent work of Witkowski on the coupling between slow and fast movements which gives a physical basis for understanding the unexplained coupling between the slow and fast modes of hydrogen bonds, which is at the basis of all the explanations of the features of hydrogen bonds.

Temperature behavior of the electric field-induced entropy increment within a homologous series of nematogenic compounds.

Based on the temperature behavior of the entropy increment induced by the probing electric field in the isotropic phase of mesogenic compounds belonging to the homologous series C(n)H(2n+1)PhCOOPhCN ( n = 4-10), it is found that an ability to the dipolar aggregation of the molecules depends on the alkyl tail length, and, in particular, the ability is strongly reinforced when the number n changes from 7 to 8. The role of the molecular structure in the self-assembling process is discussed.

Nonlinear response in dielectric relaxation including the induced polarization of polar molecules

The steady‐state nonlinear dielectric response is calculated where the applied electric field consists of an alternating field superimposed on a constant field. Both permanent and induced dipolar moments are considered. This gives rise to three harmonic terms in ω, 2ω, and 3ω which are time‐dependent and to a stationary frequency‐dependent term, if we restrict ourselves to the third‐order response. These results are obtained from the Smoluchowski equation by using a perturbation method and are therefore complementary to those previously derived in Kerr effect relaxation. Some analytic expressions are presented which could be checked experimentally.

Steady state response of the nonlinear dielectric relaxation and birefringence in strong superimposed ac and dc bias electric fields: Polar and polarizable molecules

Both nonlinear dielectric relaxation and dynamic Kerr effect responses of an assembly of polar and anisotropically polarizable molecules acted on by strong superimposed external dc E0 and ac E1(t)=E1 cos ωt electric fields are evaluated in the context of the rotational diffusion model in the noninertial limit. The relaxation functions fn(t) (the expectation value of the Legendre polynomials Pn), which are appropriate to describe these nonlinear relaxation phenomena, are calculated by expanding them as a Fourier series in the time domain. An infinite hierarchy of recurrence relations for these Fourier amplitudes of fn(t) is obtained, the solution of which is expressed in terms of an infinite matrix continued fraction, so allowing us to evaluate the dynamic characteristics of the electric polarization and birefringence. For a weak ac field, the results predicted by the theory are in complete agreement with previous solutions obtained by perturbation methods. The solutions for the particular cases, where onl...

Analytical Solutions for the Dynamic Kerr-Effect - Linear-Response of Polar and Polarizable Molecules to a Weak AC Electric-Field Superimposed on a Strong DC Bias Field

The infinite hierarchy of differential-recurrence relations for ensemble averages of the spherical harmonics pertaining to the noninertial rotational Brownian motion of an ensemble of polar and anisotropically polarizable molecules in a strong external dc electric field is derived by averaging the underlying Langevin equation. This procedure avoids recourse to the Fokker–Planck equation, the solution of which involves complicated mathematical manipulations. By calculating the Laplace transforms of the relaxation functions for the dynamic Kerr effect of symmetric top molecules, two equilibrium correlation functions are established, thus allowing one to express the corresponding birefringence ac responses by using linear response theory. Exact analytic solutions for the spectra of these correlation functions and relaxation times are first calculated for two limiting cases, namely, pure induced dipole moments and pure permanent moments, using the continued fraction method. The general case where both types o...

Anomalous rotational diffusion in the vicinity of the isotropic to nematic phase transition

Dielectric relaxation measurements are performed with very high accuracy on a liquid crystalline compound n-octylcyanobiphenyl (8CB) in the isotropic (I), nematic (N) and smectic A (SA) phases. The data obtained display an essential difference in the rotational diffusion process in the vicinity of the I–N phase transition in comparison to that taking place in the vicinity of the N–SA phase transition. Thus, for the I–N transition, anomalously slow diffusion (subdiffusion), characterized by an anomalous coefficient α<1, is observed, while normal Brownian rotational diffusion with is found for the N–SA transition. It is also shown how the fractal parameter α is temperature dependent with an extremely sharp variation at the I–N transition point in the form of a lambda-like profile.

Anomalous dielectric relaxation in strong ac external fields.

Dielectric relaxation of complex polar fluids is considered in the context of the anomalous diffusion characterized by a fractional parameter alpha < or = 1 (subdiffusion). An infinite hierarchy of three-term differential-recurrence equations governing the time evolution of the electric polarization is established by following a purely phenomenological procedure. The matrix-continued fraction method is used to derive the exact numerical solution of the stationary regime for an assembly of nonelectrically interacting, polar symmetric-top molecules in presence of a strong ac electric field. The results so obtained are valid to any order in the field strength parameter gamma1, thus extending previous theories applicable to fields of very small amplitudes only. This is illustrated by Cole-Cole diagrams and three-dimensional relaxation spectra for the first- and third-harmonic components of the electric polarization as a function of alpha, gamma1, and the angular frequency.

Nonlinear electro-optical response. I. Steady state Kerr effect relaxation arising from a weak ac electric field superimposed on a strong dc bias field

The dynamic Kerr effect (excluding inertial effects) of an assembly of both polar and anisotropically polarizable molecules acted on by a strong external dc electric field superimposed on a weak ac electric field is evaluated by starting from the Smoluchowski equation valid in the noninertial limit. The calculation proceeds by expanding the expectation value of the second Legendre polynomial which describes the Kerr effect relaxation, as a power series up to the second order in the small ac field strength, so that frequency components in ω and 2ω exist. This is accomplished using the matrix continued fraction method which allows one to express exactly the solution of the infinite hierarchy of differential-recurrence relations for the first and second order ac responses of ensemble averages of the Legendre polynomials (relaxation functions). In order to illustrate these results, diagrams showing the behavior of the real and imaginary parts of the complex birefringence functions are presented. In particular...

Anomalous Kerr effect relaxation in an alternating field

Perturbation theory is used to derive the complex harmonic components (stationary regime) arising in Kerr effect relaxation for an assembly of nonelectrically interacting, polar, and polarizable symmetric-top molecules acted on by a strong dc bias electric field superimposed on a weak ac electric field. The approach starts from a fractional kinetic equation written in configuration space and represents an extension of the Smoluchowski equation to fractional dynamics. This equation is solved in the context of a subdiffusive process characterized by an anomalous exponent alpha ranging from 0 to 1, the Brownian limit. By using a perturbation procedure restricted to the second order in the ac field strength, analytic expressions for the electric birefringence spectra representing the frequency dependence of the first (in omega) and the second (in 2omega) harmonic components are obtained. Various Cole-Cole-like diagrams are presented in order to illustrate the results so obtained and to emphasize the role played by the fractal parameter alpha in the anomalous diffusion collision process. A comparison of our theoretical model with experimental measurements of the ac Kerr effect response of a dilute polymer solution [poly(3-hexylthiophene)] appears to be quite satisfactory.

On the nonlinear behavior of dielectric relaxation in alternating fields. II: Analytic expressions of the nonlinear susceptibilities

Starting from the rotational diffusion equation of Smoluchowski, the ensemble average of the first Legendre polynomial appropriate to dielectric relaxation is calculated. The corresponding response is given up to the third order in the applied electric field by considering a constant field on which is superimposed an alternating field. Moreover, the polar molecules are assumed to be anisotropically polarizable. Thus, we obtain three harmonic components of the electric susceptibility where nonlinear coupling effects appear between the unidirectional field and the alternating field together with permanent and induced dipole moments. Dispersion plots are presented for some values of the parameter P which measures the ratio between induced and permanent moments. Also, for some values of this parameter P, the variations of phase angles with frequency are considered and it is shown how they are interesting in the treatment of experimental data by application of Kramers–Kronig relations.