Rigid-dipole model

Second, an alternative hat-curved-cosine-squared potential (HC-CS) model is also considered, which, as it seems, is more adeuate than the HC-HO model. The CS potential is assumed to govern angular deflections of H-bonded rigid dipole from equilibrium H-bond direction. The HC-CS model agrees very well with the experimental spectra of water. 

This section presents the continuation of Section V. In the latter a new model [10] termed the hat-curved model was described, where a rigid dipole reorients in a hat-like intermolecular potential well having a rounded bottom. This well differs considerably from the rectangular one, which is extensively applied to polar fluids. Now the theory of the hat-curved model will be generalized, taking into account the non-rigidity of a dipole that is, a simplified polarization model of water is described here. 

Figure 35. Frequency dependence in the submillimeter wavelength region of the real (a, b) and imaginary (c, d) parts of the complex permittivity. Solid lines Calculation for the composite HC-HO model. Dashed lines Experimental data [51]. Dashed-and-dotted lines show the contributions to the calculated quantities due to stretching vibrations of an effective non-rigid dipole. The vertical lines are pertinent to the estimated frequency v b of the second stochastic process. Parts (a) and (c) refer to ordinary water, and parts (b) and (d) refer to heavy water. Temperature 22.2°C.

We shall remove an important drawback of the polarization model described in Section VI by considering another variant of a composite model than that described in previous Section VILA. We use again a linear-response theory to find the contribution of a vibrating dipole to the total permittivity . We split the total concentration N of polar molecules into the sum Nm and Nv b, where each term refers to rotation of a like rigid dipole (viz. with the same electric moment p) but characterized by different law of motion ... 

Figure 4.34. Time-independent part of the orientation parameter as a function of the field frequency for different values of the internal magnetic anisotropy of the particles. The ratio e = TdAb = 1CT4 curves correspond to a = 100 (1), a = 10 (2), o = 5 (3), a = 2 (4), a = 0.1 (5). Thin lines a and b resemble the limiting behavior predicted by the rigid and soft dipole models, respectively. Note that at this graph the lines a and 1 visually coincide.

Pure rotary diffusion of rigid dipoles in two or three dimensions, then, gives exponential decay of polarization with a single relaxation time, provided the sites are uniformly distributed and D is constant. The description of the motion in terms of D alone breaks down, as we shall see, for very short times. A three-dimensional rigid body in any case executes a more complex motion. Even an internally uniform model of rectilinear charge-carrier difiurion automatically shows multiple relaxation. More realistic models must take account of the dynamic s of molecular motion. 

Onsager model—reaction field effects. In the simplest form of this model a chosen molecule is represented by a spherical cavity of suitable volume filled with fluid of relative permittivity c , containing a rigid dipole of value fi. This p, is chosen so that if py is the measured vacuum dipole moment of the molecule, = (c , + 2)py/3. Correct calculation of the orienting couple on the dipole due to a given external field leads to the Onsager relation... 

Computations of minimum-energy configurations for some off-centre systems were first carried out on the basis of polarizable rigid-ion models, mainly devoted to KChLi" " [95,167-169]. Van Winsum et al. [170] computed potential wells using a polarizable point-ion model and a simple shell model. Catlow et al. used a shell model with newly derived interionic potentials [171-174]. Hess used a deformation-dipole model with single-ion parameters [175]. At the best of our knowledge, only very limited ab initio calculations (mainly Hartree-Fock or pair potential) have been performed on these systems [176,177]. 

In the fixed axis rotation model of dielectric relaxation of polar molecules a typical member of the assembly is a rigid dipole of moment p rotating about a fixed axis through its center. The dipole is specified by the angular coordinate < ) (the azimuth) so that it constitutes a system of 1 (rotational) degree of freedom. The fractional diffusion equation for the time evolution of the probability density function W(4>, t) in configuration space is given by Eq. (52) which we write here as... 

In order to understand the overall orientation of the chromophores within guest-host systems under differing external electric fields, we examine the orientational alignment of the dipole moment of the chromophores with respect to the direction of the external electric field. In the non-interacting rigid gas model, the intermolecular electrostatic interactions are ignored and one can describe a general order parameter of... 

Weakly bound complexes display unusual structural and dynamical properties resulting from the shape of their intermolecular potential energy surfaces. They show large amplitude internal motions, and do not conform to the dynamics and selection rules based on the harmonic oscillator/rigid rotor models (4). Consequently, conventional models used in the analysis of the spectroscopic data fail, and the knowledge of the full intermolecular potential and dipole/polarizability surfaces is essential to determine the assignments of the observed transitions. 

The simple rigid dipole theory is not truly applicable to a molecule, because the polarisation is altered by the presence of the additional electron, i.e. we have a combination of the two mechanisms. Jordan and Luken [76] have set up a more elaborate ab initio model using a Hartree-Fock scheme, which accounts satisfactorily for molecular relaxation. 

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