Collective orientational

Ea of 0.01 V/ftm is then applied. This is required for two reasons to induce directional charge transport along the wavevector axis, and due to the collective orientational response that produces the index of refraction change. In other words, the applied field, which is greater in magnitude than the internal space-charge field, is required to keep the modulation of the internal electric field... 

Figure 46. A unified molecular mechanism of protein hydration dynamics and coupled water-protein fluctuations. The initial ultrafast dynamics in a few picoseconds (ii) represents local collective orientation or small translation motions, which mainly depend on local electrostatic interactions. On the longer time (12), the water networks undergo structural rearrangements in the layer, which are strongly coupled with both protein fluctuations and bulk-water dynamic exchange.

The orientational diffusion observed by intermolecular Raman techniques is not the diffusion of single molecules, but rather arises from collective effects. For symmetric tops, the collective orientational correlation time rcon is related to the single-molecule orientational correlation time rsm via... 

Figure 5 Natural logarithm of the room-temperature OHD-RIKES data for benzene. Note that the tail of the decay is linear, implying that the collective orientational diffusion of benzene is described well by a single-exponential decay, as would be expected for a symmetric-top liquid.

Figure 7 Single-molecule orientational correlation times (circles) from NMR data (57) and collective orientational correlation times (triangles) from OHD-RIKES data (56) as a function of rj/T and estimated static orientational correlation parameter (squares) as a function of temperature for acetonitrile-d3.

Since the collective orientational correlation time depends on the structure of a liquid, it is plausible that the rate of structural evolution of the liquid is proportional to this quantity. Thus, at lower temperatures rcon is longer and therefore the structural fluctuations are slower. As a result, motional narrowing is less effective as the temperature is lowered. While less motional narrowing would normally lead to a slower decay in the time domain, in this case the spectral density goes down to zero frequency. Thus, motional narrowing can reduce the spectral density at low frequencies and thereby decrease the intermediate relaxation time. 

In contrast to diamagnetism, where all valence electrons of each atom are spin paired, paramagnetism is found in solids where the constituent atoms contain an unpaired valence electron(s). In a simple paramagnetic substance, the unpaired electrons spins are randomly oriented within the solid. Upon exposure to an external magnetic field, the spins become collectively oriented in a parallel direction to the applied field. However, the dipoles re-randomize when the field is removed. 

The dynamics of molecular motion in simple (i.e., nonviscous) liquids have long been of interest in their own right and because of their importance in mediating liquid state chemical reactions. Collective orientational relaxation times, which measure the return of partially aligned liquids to their isotropic equilibrium states and are usually in the 5-100-ps range, have been determined in many fluids from Rayleigh linewidths or optical Kerr... 

Figure 7.8 log-log plot (solid lines) of the collective orientational correlation functions Qoii for water confined in pores of different diameters (inserted number) and power-law fits (dashed lines). Lower and upper traces are for hydrophilic and hydrophobic pores, respectively [16],... 

Gottke et al. [5] offered a theoretical treatment of collective motions of mesogens in the isotropic phase at short to intermediate time scales within the framework of the Mode coupling theory (MCT). The wavenumber-dependent collective orientational time correlation function C/m(, t) is defined as... 

Despite extensive investigation of phase behavior of liquid crystals in computer simulation studies [97-99], the literature on computational studies of their dynamics is somewhat limited. The focal point of the latter studies has often been the single-particle and collective orientational correlation functions. The Zth rank single-particle orientational time correlation function (OTCF) is defined by... 

The growth of orientational correlations and the slow down of collective orientational dynamics were subsequently investigated using a soft potential [106]. Allen and Warren (AW) studied a system consisting of N = 8000 particles of ellipsoids of revolution, interacting with a version of the Gay-Beme potential, GB (3, 5, 1, 3), originally proposed by Berardi et al. [107]. AW computed the direct correlation function, c( 1, 2), in the isotropic phase near the I-N transition. The direct correlation function is defined through the Omstein-Zemike equation [108]... 

Dt and Z)r are the rotational and translational difiusion coefficients, respectively. The analogy between translational and rotational motion can be extended further. We can define not only position (r) dependent isotropic collective number density, p(r,t) but also position (r) and orientation (fi) dependent collective orientational density, p r,il,f). These collective quantities are different from tagged (single) particle densities, as they count not just the tagged but all the molecules in the system present in a volume element arovmd r and ft. 

A. Chandra and B. Bagchi, Molecular theory of solvation and solvation dynamics in a binary dipolar liquid. J. Chem. Phys. 94, 8367-8377. A. Chandra and B. Bagchi, A molecular theory of collective orientational relaxation in pure and binary dipolar liquids. J. Chem. Phys., 91 (1989), 1829. 

In condensed matter one is not interested in the state of each single molecule on the microscopic level but in the collective state and behaviour of the system as a whole, which is reflected in its macroscopic appearance. In the isotropic phase LC the medium possesses full symmetry. On the contrary, in the nematic phase the symmetry is lowered because the molecules exhibit collective orientational order. The two phases are schematically depicted in Fig. 8.1. To express the order of the system quantitatively, we need to define the order parameter. This has to vanish in the isotropic phase and has to become nonzero in the ordered nematic phase. 

On the molecular level, we see that certain crystaUine surfaces induce collective orientational and positional order in the first layer of liquid crystalline molecules. We observe, that there are several energetically degenerate domains that coexist at the interface. This is a clear signature of the orientational rigidity of an ensemble of hquid crystalhne molecules that collectively adopt certain spatial orientation via the molecule-molecule interactions. 

Ubuntic inclusion is more than a set of leadership behaviors, organizational practices, or rules. It is a paradigm. To create, niulau e, and sustain Ubuntic inclusion in an organization (and reap its benefits), a fundamental paradigm shift from rampant individualism to a more collective orientation such as Ubuntu is necessary. Once that shift has been made, true inclusion becomes possible. 

The first term on the right hand side of equation (18) contains the collective orientational correlation function <0 2(0) weighted by the (generally un-... 

According to Keyes and Kivelson 22 the collective orientational correlation function in the diffusion limit is given by equations (21) and (22). It has been argued 22 and to a certain extent verified experimentally 131, that the angular velocity correlation factor j2 is close to unity for ordinary liquids. 

The far infra-red and Rayleigh spectra are related to the correlation function of the collective orientation density fluctuations... 

Figure 10, The collective orientational correlation at 244K calculated from (47), The functions are averaged over five values of m. The number indicates the index of +++ i = 1, i = 2, i = 3.

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