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Self dynamic

As mentioned before, due to the coupling between different modes of the solvent, all solvent dynamic quantities are interdependent and need to be calculated self-consistently. An additional self-consistency is present in the calculation of friction, since the self-dynamic structure factor itself depends on the friction. [Pg.96]

From the above discussion, it is obvious that the mode coupling theory calculations are quite involved and numerically formidable. Balucani et al. [16] have made some simple approximations to incorporate the self-consistency between the self-dynamic structure factor and the friction. This required the knowledge of only the zero frequency friction. The full self-consistent calculation is more elaborate and will be discussed later in this chapter. [Pg.96]

The solute dynamic variables required to calculate the density and current contribution are the self-dynamic structure factor, Fs(q, t) and inertial part of the self-intermediate structure factor, Fs0(q, t). Fs0(q, f) is given by... [Pg.114]

The other dynamic variables required to calculate Rpp(t) and Rrr(t) are the dynamic structure factor of the solvent, F(q, t), the inertial part of the dynamic structure factor, Fo(q, t), the transverse current autocorrelation function of the solvent, C (q,t), the inertial part of the same, Ctf0(q, t), the self-dynamic structure factor of the solute, Fs(q, t), and the inertial part of the self-dynamic structure factor of the solute, Fs0(q,t). The expressions for all the above-mentioned dynamic quantities are similar to that given in Section IX but in two dimensions. [Pg.197]

The inconsistency in this approach and all other mode coupling theoretical approaches [9, 37, 57, 176] is that a finite diffusion coefficient has been assumed to define the diffusive behaviour of the self-dynamic structure factor, and then it has been concluded that this diffusion coefficient itself diverges. [Pg.198]

In the present theoretical approach this inconsistency is avoided by not assuming any diffusion coefficient in defining the self-dynamic structure factor. [Pg.198]

The self-dynamic structure factor of the solute at all time is calculated from the mean square displacement (MSD) using the following definition ... [Pg.198]

Calculational procedure of all the dynamic variables appearing in the above expressions—namely, the dynamic structure factor F(q,t) and its inertial part, Fo(q,t), and the self-dynamic structure factor Fs(q,t) and its inertial part, Fq (q, t) —is similar to that in three-dimensional systems, simply because the expressions for these quantities remains the same except for the terms that include the dimensionality. Cv(t) is calculated so that it is fully consistent with the frequency-dependent friction. In order to calculate either VACF or diffusion coefficient, we need the two-particle direct correlation function, c(x), and the radial distribution function, g(x). Here x denotes the separation between the centers of two LJ rods. In order to make the calculations robust, we have used the g(x) obtained from simulations. [Pg.206]

If one returns to u space by Fourier transforming, one obtains the self-dynamical form factor S,(k, < >), the real part of. which is... [Pg.305]

Figure 12. The half-widths of the Lorentzian lines contributing to the real part of the self- dynamical form factor... Figure 12. The half-widths of the Lorentzian lines contributing to the real part of the self- dynamical form factor...
Another quantity that can be obtained is the density of states of mobile protons, in particular the translational and librational modes for water of hydration as compared to those of bulk water. This method has been used with success for studying the self-dynamics of bulk water as a function of the temperature [62] as previously reported. [Pg.66]

A very complete study of the self-dynamics of water close to some well-defined hydrophilic surface as the Vycor surface has been performed by quasi-elastic and inelastic neutron scattering it has been done for levels of hydration ranging from full hydration down to the lowest one (25%), corresponding to one monolayer coverage of water molecules and as a function of temperature [69]. We report here the main results. [Pg.67]

Brodeck et al., 2010). In the Gaussian approximation for displacements, the segmental self-correlation function relates directly to (r (r)), resulting in the intermediate self-dynamic structure factor having the Gaussian form (Niedzwiedz et al., 2007),... [Pg.236]

Inelastic neutron scattering is a technique that has been widely used both in the liquid and in the solid states to measure the stmcture and dynamics at small (that is, molecular) length scales. In an incoherent inelastic neutron-scattering experiment, the measured quantity is the self-dynamic structure factor Ss(Q, (o), which gives information, as in the liquid state, of the self-diSiision coefficient of the water molecules. Ss(Q, (o) is the Fourier transform of the intermediate self-scattering function Fg(Q, t), which is defined by... [Pg.127]

This method has been used with success for studying the self-dynamics of bulk water as a function of temperature [72] as previously reported. [Pg.70]

Incoherent neutron scattering by the sample atoms provides information the self-dynamics such as mean square displacements and the onset of anharmonic motions of these atoms... [Pg.456]

Figure 4 is a comparison of the behaviour of these functions, along with W( ) for a particle moving through a typical liquid. Fourier transforming the Fs(Q, )s gives the corresponding forms for the (self) dynamic structure factors ... [Pg.916]

A substantially similar process beginning with the self-dynamic structure factor, Eq. 4.7, leads to... [Pg.85]

In summary, for short times the self-dynamics of PEO follows the Rouse expectation, however, with a significant larger friction coefficient compared to pure PEO. The collective chain dynamics at longer times are further retarded and... [Pg.357]


See other pages where Self dynamic is mentioned: [Pg.96]    [Pg.314]    [Pg.312]    [Pg.66]    [Pg.237]    [Pg.225]    [Pg.918]    [Pg.72]   
See also in sourсe #XX -- [ Pg.239 ]




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