Orientational structure factor

Figure 2.24 Temporal evolution of the compositional structure factor (a) and the orientational structure factor Ss (b) for the temperature quench into lu region...

Figure 2.24 shows the temporal evolution of the compositional structure factor S<(, (a) and the orientational structure factor Ss (b) for the temperature quench into the lu region (T/Tn, = 0.6, (f)Q = 0.55) in Figure 2.22. The structure factor for concentration has a maximum at q, which corresponds to the peak wavenumber of coi(q). With time the corresponding mode grows exponentially and the peak position qm is invariant. Then the time evolution of the structure faaor S<, is lhe same as that of the Cahn-Hilliard theory for isotropic SD [102]. The amplitude of the peak at q = 0 decreases with time because s > 0 and another peak appears at q. In this quench, the concentration fluctuation initially induces the SD and the orientational ordering within the domain subsequently takes place due to the coupling between the two order parameters concentration-induced SD.

Figure 2.25 shows the temporal evolution of the compositional structure factor S,)) (a) and of the orientational structure factor Ss (b) for the temperature quench into Nu region (T/Tni = 0.6, ( )o = 0.85) in Figure 2.22. In the very early stages, the concentration fluctuation becomes weak with time because> 0. However, the orientational fluctuations grow exponentially with time because s < 0. On further increasing time, a peak in S,), appears and shifts to lower wavenumbers. There is no longer any time stage in which the peak position in S( ) is invariant. The instability of the orientation fluctuation induces the SD and the concentration fluctuation is induced by the coupling between two order parameters orientation-induced SD. The time dependence of the average domain size is given by ...

Here Pyj is the structure factor for the (hkl) diffiaction peak and is related to the atomic arrangements in the material. Specifically, Fjjj is the Fourier transform of the positions of the atoms in one unit cell. Each atom is weighted by its form factor, which is equal to its atomic number Z for small 26, but which decreases as 2d increases. Thus, XRD is more sensitive to high-Z materials, and for low-Z materials, neutron or electron diffraction may be more suitable. The faaor e (called the Debye-Waller factor) accounts for the reduction in intensity due to the disorder in the crystal, and the diffracting volume V depends on p and on the film thickness. For epitaxial thin films and films with preferred orientations, the integrated intensity depends on the orientation of the specimen. 

Various structural factors have been considered in interpreting this result The most generally satisfactory approach is based on a transition>state model, advanced by Felkin and co-woricers, in which the largest group is oriented perpendiculariy to the carbonyl group. Nucleophilic addition to the carbonyl groi occurs from the opposite side. ... 

The diffraction lines due to the crystalline phases in the samples are modeled using the unit cell symmetry and size, in order to determine the Bragg peak positions 0q. Peak intensities (peak areas) are calculated according to the structure factors Fo (which depend on the unit cell composition, the atomic positions and the thermal factors). Peak shapes are described by some profile functions 0(2fi—2fio) (usually pseudo-Voigt and Pearson VII). Effects due to instrumental aberrations, uniform strain and preferred orientations and anisotropic broadening can be taken into account. 

The used S5mbols are K, scale factor n, number of Bragg peaks A, correction factor for absorption P, polarization factor Jk, multiplicity factor Lk, Lorentz factor Ok, preferred orientation correction Fk squared structure factor for the kth reflection, including the Debye-Waller factor profile function describing the profile of the k h reflection. 

In order to determine the structural factors maximizing 2PA cross section values, we analyze (8) from Sect. 1.2.1. For all cyanine-like molecules, symmetrical and asymmetrical, several distinct 2PA bands can be measured. First, the less intensive 2PA band is always connected with two-photon excitation into the main absorption band. The character of this 2PA band involves at least two dipole moments, /

symmetry forbidden for centro-symmetrical molecules, such as squaraines with C, symmetry due to A/t = 0, and only slightly allowed for polymethine dyes with C2V symmetry (A/t is small and oriented nearly perpendicular to /t01). It is important to note that a change in the permanent dipole moment under two-photon excitation into the linear absorption peak, even for asymmetrical D-a-A molecules, typically does not lead to the appearance of a 2PA band. 2PA bands under the main absorption peak are typically observed only for strongly asymmetrical molecules, for example, Styryl 1 [83], whose S0 —> Si transitions are considerably different from the corresponding transitions in symmetrical dyes and represent much broader, less intense, and blue-shifted bands. Thus, for typical cyanine-like molecules, both symmetrical and asymmetrical, with strong and relatively narrow, S (I > S) transitions, we observe... 

The question now arises of what simplification is possible in the treatment of orientationally structured adsorbates and what general model can be involved to rationalize, within a single framework, a diversity of their properties. Intermolecular interactions should include Coulomb, dispersion, and repulsive contributions, and the adsorption potential should depend on the substrate constitution and the nature of adsorbed molecules. However difficult it may seem, all these factors can be taken into account if we follow the description pattern put forward in this book. Its fundamentals are briefly sketched below. 

A series of aggregation structures of bilayer forming azobenzene amphiphiles, CnAzoCmN+Br, both in single crystals and cast films was determined by the X-ray diffraction method and uv-visible absorption spectroscopy. From the relationship between chemical structures and their two-dimensional supramolecular structure, factors determining the molecular orientation in bilayer structure were discussed. Some unique properties based on two-dimensional molecular ordering were also discussed. 

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)... 

Another structural factor that influences the sign and magnitude of the n-7t and n-n Cotton effects is the presence of an allylic axial substituent56 57 (Table 3). The 6/7-substituent in steroidal 4-en-3-ones 3-8 is ideally oriented for an effective overlap with the 7r-orbital, left-handed helicity of the R-C-C = C system giving rise to the strong negative contribution to the 7T-7t Cotton effect and, relatively smaller, positive contribution to the n-7i Cotton effect. The effect is not observed with epimeric 4-en-3-ones substituted in the equatorial 6a-position. 

The major mechanistic and structural aspect of the acetalation process is its orientation toward derivatives obtained either under thermodynamically controlled conditions or under kinetically controlled conditions. We will not discuss here all structural factors concerning the relative stabilities of acyclic and cyclic acetals of polyols and monosaccharides, because such a discussion has been extensively reviewed and adequately commented on [8,10,12 -14]. However, it is important to focus here on the main consequences of these relative stabilities in relation to the various experimental conditions to orientate the choice of specific conditions, particularly for the most important monosaccharides (D-glucose, D-mannose, and D-galactose). 

The calculation of the monodomain structure factor requires several averaging procedures to account for all possible molecular conformations and orientation configurations. For reasons of clarity we have labelled each of these averaging procedures according to Table 2. 



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