Dipole Correlations

That is, a(co) can be expressed in terms of the dipole correlation function form. 

Correlations between molecular orientations, that is, between terms with different X, are disregarded (except in EFISH where the dipole correlation factor g is employed in the ji v term (40) - a practice which assumes the tensorial behavior of the vector components of to show the same intermolecular correlations as the permanent dipole) single terms for each molecular type are adopted. 

Without the external field, the Stockmayer fluid near the wall exhibits symmetric density oscillations that die out as they reach the middle of the film. Near the surface, the fluid dipoles are oriented parallel to the walls. Upon turning on the electric field, the density profile of the Stockmayer fluid exhibits pronounced oscillations throughout the film. The amplitude of these oscillations increases with increasing field strength until a saturation point is reached at which all the fluid dipoles are oriented parallel to the field (perpendicular to the walls). The density profile remains symmetric. The dipole-dipole correlation function and its transverse [] and longitudinal [] com-... 

Fig. 4.1 a Typical time evolution of a given correlation function in a glass-forming system for different temperatures (T >T2>...>T ), b Molecular dynamics simulation results [105] for the time decay of different correlation functions in polyisoprene at 363 K normalized dynamic structure factor at the first static structure factor maximum solid thick line)y intermediate incoherent scattering function of the hydrogens solid thin line), dipole-dipole correlation function dashed line) and second order orientational correlation function of three different C-H bonds measurable by NMR dashed-dotted lines)... 

Y. Kakitani, Y. Koyama, Y. Shimoikeda, T. Nakai, H. Utsumi, T. Shimizu and H. Nagae, Stacking of bacteriochlorophyll c macrocycles in chlorosome from CMorobium limicola as revealed by intermolecular magnetic-dipole correlation. X-ray diffraction, and quadrupole coupling in Mg NMR. Biochemistry, 2009,48, 74—86. 

The authors finish by exploring the transferability of their force field parameters to a different zeolite, namely, silicalite. In this instance, a Fourier transform of the total dipole correlation function provides another model infrared (IR) spectrum for comparison to experiment, and again excellent agreement is obtained. Dominant computed bands appear at 1099, 806, 545, and464 cm while experimental bands are observed at 1100, 800,550, and 420 cm A Some errors in band intensity are observed in the lower energy region of tlie spectrum. 

In Fig. 2 we show the IR spectrum in the O-H/D stretching region of our 7D model. The data have been obtained by a Fourier-transform of the dipole-dipole correlation function, where the... 

The classical dipole correlation function is symmetric in time, C(—t) = C(f), as may be seen from Eq. 5.59 by replacing x by x — t the classical scalar product in Eq. 5.59 is, of course, commutative. Classical line shapes are, therefore, symmetric, J(—. Furthermore, classical dipole autocorrelation functions are real. 

To the extent that the dipole induced in a cluster of atoms may be represented by a sum of pair dipoles induced in dissimilar atoms, i and i, fiu, = ft(Rw), we may write for the total dipole ft = Xw Mu - The summation is over all atoms i and all atoms i. The dipole correlation function can then be written as a sum of three parts (Poll 1980),... 

Using the standard expression of the dipole-dipole correlation function the CC absorption cross section can be derived as [9,42] ... 

Interestingly enough, one sees differences between the various variants of Markovian and non-Markovian theories already in static linear absorption spectra. In the regime of second-order perturbation theory in the coupling to the electromagnetic field the linear absorption line-shape / (ui) can be calculated from the Fourier transform of the dipole-dipole correlation function as... 

In order to explain the interactions between silica surfaces, the polarization model is adapted to poorly-organized surfaces. To account for the disorder induced in water by the rough surfaces of silica, the dipole correlation length Am, which is the main parameter of the polarization model, is allowed to decrease from Am=14.9A obtained for water perfectly organized in ice-like layers in the vicinity of a surface to smaller values. For Am=4A, good agreement with experiment is obtained for reasonable values of the parameters involved (such as surface dipole and charge densities) [7.9],... 

It should be emphasized that the assumption of an icelike structure of water in the vicinity of the surface is only an approximation used to calculate the dipole correlation length A, (Eq. (TO)). In feet, if the water would be organized in perfect ice-like layers parallel to the planar surface, the model would predict an oscillatory behaviour of the polarization in the vicinity of the surface [35],... 

An important issue is whether or not this increase in the decay length occurs for any colloidal system. The derivation of the value tor A ,=14.9 A assumed an ice-like order for the clusters around each water molecule [30], When this order is lowered, the value of the dipole correlation length is expected to decrease. A phenomenological model for the decrease of A, with the decrease of the average dipolar moment of water molecules is proposed in Section 2.3. In... 

In summary, when the Debye-Huckel Adh largely exceeds the dipole correlation length A , (eitho because of low ionic strength, or because of disordo), the polarization model predicts, at large separations, results similar to those obtained from the DLVO theory (with suitably adjusted... 

The polarization model is extended to account for the ion-ion and ion-surface interactions, not included in the mean field electrical potential. The role of the disorder on the dipole correlation length A, is modeled through an empirical relation, and it is shown that the polarization model reduces to the traditional Poisson Boltzmann formalism (modified to account for additional interactions) when X, becomes sufficiently small. 

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