Linear dichroism orientational averaging

Here is the angle between the transition moment and the director n. Using to denote the orientationally averaged quantity (P2(cos /8J), the reduced linear dichroism [Eq. (4)] becomes... 

Orientational order of LCPs is conveniently described in terms of two differoit order parameters, characterizing the average orientation of the mesogenic units within a molecular domain (microorder) and the macroscopic alignment of the domains (see Fig. 3) [10,35]. The measurement of these parameters is important for relating macroscopic physical properties of LCPs to their molecular structure. Various methods have been used to measure order parameters in these systems, including the use of X-ray diffraction [128-130], birefringence [103, 104], and linear dichroism [104,131], but these methods can not essentially separate the two types of orientational order. 

Rusling and his collaborators have obtained reversible voltammetric responses of cyt. P-450cam. hemoglobin, Mb, cyt. c, and chlorella ferredoxin cast in bquid crystal films or composites of liquid crystal and Nafion [79-81] on gold electrodes. The structure of the cast films was characterized by low angle x-ray diffraction. The structures of Mb and cyt. P-450cam hi the cast film were characterized by UV-vis. Electron Spin Resonance (ESR), and reflectance Fourier Transform Infrared (FT-IR) spectroscopic techniques, and are shown to be similar to the native conformations. Visible linear dichroism and ESR anisotropy showed that Mb is specifically oriented in the static films. The orientation of the heme plane of Mb averaged 60° with respect to the normal to the film plane, and distributions are rather broad. 

The optical anisotropy, as characterized by the difference between the absorption of IR light polarized in the directions parallel and perpendicular to the reference axis (i.e., the direction of applied strain), is known as the IR linear dichroism of the system. For a uniaxially oriented polymer system [10, 28-30], the dichroic difference, A/4(v) = y4 (v) - Ax v), is proportional to the average orientation, i.e., the second moment of the orientation distribution function, of transition dipoles (or electric-dipole transition moments) associated with the molecular vibration occurring at frequency v. If the average orientation of the transition dipoles absorbing light at frequency is in the direction parallel to the applied strain, the dichroic difference AA takes a positive value on the other hand, the IR dichroism becomes negative if the transition dipoles are perpendicularly oriented. 

IV.6 Linear Dichroism A number a linear dichroism (LD) experiments have recently been performed in order to measure the average molecular stretching (or orientation) predicted by the reptation models of DNA gel electrophoresis.43-46 These LD measurements give the orientation factor... 

Although intra-tube effects may be expected to play a larger role in pulsed field techniques and transient effects, the form of the model which averages over these effects offers a good framework to discuss the experimental results even in these cases. The orientation overshoot observed with linear dichroism is a transient effect that occurs at a time which is smaller than the tube-renewal time we thus conclude... 

As discussed above. X-ray diffraction and linear dichroism infrared studies have clearly shown that the guest molecules present well-defined average locations and orientations into co-crystalline phases. Moreover, solid-state H-NMR studies have shown that the mobility of the solute molecules is heavily reduced when they are guests of the crystalline host phase, rather than simply absorbed in the amorphous phase [124-126]. 

Systems involving two centers with fixed mutual orientation have been shown to exhibit other circular differential effects with a similar linear dependence on the separation. Examples include circular differential Rayleigh and Raman scattering (Barron and Buckingham 1974 Andrews and Thirunamachandran 1978), optical rotation (Barron 1975) and two-photon circular dichroism in which only one chromophore is excited (Andrews 1976). As might be expected, on performing subsequent rotational averages for the case where A and B are randomly oriented, the odd-j terms in the rate equations vanish and consequently no circular dichroism is displayed. 

The molecular anisotropy also manifests itself in a variety of spectroscopic techniques. Dichroism, the difference in absorption coefficients of linearly polarized light measured in orthogonal directions, is another phenomenon wherein one can extract average molecular orientational order present in the nematic phase. The dichroic ratio D = A Ax (see Chapter 7), the ratio of the intensities of the absorption band of a characteristic transition measured with the polarized incident radiation parallel to n, A, relative to that with it perpendicular to n. Ax, is given by... 

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