Dipoles linear-orientation

In all cases the dielectric constant used is that of the pure solvent. Neglect of the solute is usually justified by its low concentration and the assumption that any necessary correction would be additive. In at least a few cases where the first two expressions have been employed the linearity of the results is to some extent dependent on how closely the refractive index of the solute meets the conditions n2 = 2.0 or 2.5 a situation not always recognized by the investigators. In one instance attempts have been made to clarify the role of solvent reaction field by examining solutes with different dipole moment orientations relative to the bonds involving coupled atoms. 

Dipole forces or multi-pole forces, if the lattice components have dipoles or multipoles. Dipoles can be either intrinsic or induced. Depending on the orientation, the dipole-dipole interaction energy for linear-orientation (Figure 2.34a) is... 

Figure 2.34 Different dipole orientations, (a) Linear orientation and (b) parallel orientation.

A classic application of linear dichroism to study molecular orientations and motions in a complex biological system was R. Cone s study of induced dichroism in retinal rod outer segements [14]. Rhodopsin, the light-sensitive pigment-protein complex of the retina, contains 11-cw-retinal attached covalently to a protin (opsin) by a Schiff base linkage (Fig. 4.13A, B). Its transition dipole is oriented... 

We now discuss the use of fluorescence to study rotational motions of molecules on a finer scale. Suppose we have a sample of randomly oriented molecules that we illuminate with linearly polarized light. Let the polarizarimi be parallel to the laboratory s z-axis. The light will selectively excite molecules that have their transition dipole (/< a) oriented parallel to this same axis. However, molecules with off-axis orientations also will be excited with a probability that depends oti cos 0, where 0 is the angle from the z-axis (Eqs. 4.8a—4.8c). 

Dipolar interactions are very dependent on temperature since an increase in temperature promotes random motion in molecules, which makes the linear orientation of the dipoles less likely. The interaction between dipoles falls off with the fourth power of distance and thus acts over a... 

For linear moleeules, the vibrationally averaged dipole moment pave lies along the moleeular axis henee its orientation in the lab-fixed eoordinate system ean be speeified in terms of the same angles (0 and ([)) that are used to deseribe the rotational funetions Yl,m (0,(1)). Therefore, the three eomponents of the <(l)ir Pave I (1)6 integral ean be written as ... 

For molecules that are non-linear and whose rotational wavefunctions are given in terms of the spherical or symmetric top functions D l,m,K, the dipole moment Pave can have components along any or all three of the molecule s internal coordinates (e.g., the three molecule-fixed coordinates that describe the orientation of the principal axes of the moment of inertia tensor). For a spherical top molecule, Pavel vanishes, so El transitions do not occur. 

Steady-State Fluorescence Depolarization Spectroscopy. For steady state depolarization measurements, the sample is excited with linearly polarized lig t of constant intensity. Observed values of P depend on the angle between the absorption and emission dipole moment vectors. In equation 2 (9), Po is the limiting value of polarization for a dilute solution of fluorophores randomly oriented in a rigid medium that permits no rotation and no energy transfer to other fluorophores ... 

The geometrically optimized model of BD had a roughly linear conformation. This spontaneous ordering was unexpected given the general orientation of dipolar molecules. Azobenzenes that have permanent dipoles parallel to the molecular axis would intuitively be expected to tend to pair with their dipole oriented in the opposite direction. The linear geometry is probably due to the... 

The physical meaning of the g (ion) potential depends on the accepted model of an ionic double layer. The proposed models correspond to the Gouy-Chapman diffuse layer, with or without allowance for the Stem modification and/or the penetration of small counter-ions above the plane of the ionic heads of the adsorbed large ions. " The experimental data obtained for the adsorption of dodecyl trimethylammonium bromide and sodium dodecyl sulfate strongly support the Haydon and Taylor mode According to this model, there is a considerable space between the ionic heads and the surface boundary between, for instance, water and heptane. The presence in this space of small inorganic ions forms an additional diffuse layer that partly compensates for the diffuse layer potential between the ionic heads and the bulk solution. Thus, the Eq. (31) may be considered as a linear combination of two linear functions, one of which [A% - g (dip)] crosses the zero point of the coordinates (A% and 1/A are equal to zero), and the other has an intercept on the potential axis. This, of course, implies that the orientation of the apparent dipole moments of the long-chain ions is independent of A. 

Another important linear parameter is the excitation anisotropy function, which is used to determine the spectral positions of the optical transitions and the relative orientation of the transition dipole moments. These measurements can be provided in most commercially available spectrofluorometers and require the use of viscous solvents and low concentrations (cM 1 pM) to avoid depolarization of the fluorescence due to molecular reorientations and reabsorption. The anisotropy value for a given excitation wavelength 1 can be calculated as... 

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... 

Figure 4.9 illustrates time-gated imaging of rotational correlation time. Briefly, excitation by linearly polarized radiation will excite fluorophores with dipole components parallel to the excitation polarization axis and so the fluorescence emission will be anisotropically polarized immediately after excitation, with more emission polarized parallel than perpendicular to the polarization axis (r0). Subsequently, however, collisions with solvent molecules will tend to randomize the fluorophore orientations and the emission anistropy will decrease with time (r(t)). The characteristic timescale over which the fluorescence anisotropy decreases can be described (in the simplest case of a spherical molecule) by an exponential decay with a time constant, 6, which is the rotational correlation time and is approximately proportional to the local solvent viscosity and to the size of the fluorophore. Provided that... 

First, we treat the nuclear dynamics classically to clarify the quantum effects. For the harmonic generation, by using the steepest descent method, the induced dipole moment in a linear molecule whose axis is oriented at an angle of 0 with respect to the x axis of the laboratory system is given by... 

Considering that J 2 I 2 and that the ionization rates at R = Rq have little 9 dependence [35], the dominant difference should be due to the electron and nuclear dynamics in the steps 2 and 3. The observed single molecule responses are obtained by superposing the radiation from all the molecules with random orientation coherently. For linearly polarized laser field, whose direction is defined as x axis, the observed dipole moment is given by... 

The fact that linear CO species are observed at 0.05 V in the absence of C.H.CN (cf. spectrum a) indicates that H.O molecules at the inner Helmholtz plane are not able to displace CO out of its linear configuration at the same potential. This may be due to a re-orientation of the adsorbed HjO as a function of potential, with the positive end of the molecular dipole becoming attracted to the surface as the electrode potential is made more negative. This would reduce the ability of the H O molecule to donate electron density from its oxygen atom, and would also Increase the ability of its hydrogen atoms to compete for accepting electron density from the metal. 



---