Relaxation - Localization Model

This paper is devoted to the presentation of a brief overview of a recently-developed "relaxation-localization" model of localized molecular-ion and exciton states in polymers and molecular glasses. This model was proposed initially to interpret photoemission measurements from two pgn ant-group polymers polystyrene and p ly(2-vinyl pyridine.) It ext was utilized in the prediction and subsequent observation of surface states of molecular solids as well as of the temperature dependence of photoe iss on and UV absorption linewidths of molecular films. Having proven successful in describing the spectroscopic properties of typical pendant-group polymers and molecular glasses, the model most recently has been extended to provide a description of electron-transfer processes in both these materials and molecularly-doped polymers. Therefore it affords a unified and experimentally-verified microscopic description of electron ionization, excitation and transfer processes in a variety of molecular and polymeric materials. 

The basic concepts o hich the relaxation-localization model is based are simple. The molecular character of the solid state leads to weak interactions between the molecular entities and hence to a high degree of disorder. Contributions to the disorder are both static (e.g., local variations in composition and/or structure) and dynamic (e.g., thermally induced vibrations) in nature. The static disorder localizes both injected charges as molecular ions and injected excitations as molecular excitons. Once localized, these entities interact strongly with the (dynamic) charges which they induce in the surrounding dielectric medium. The induced charges in turn can be described... 

The relaxation-localization model of charge motion in molecular media incorporates the interaction of each of these polarization-... 

In this section the major results obtained by applying the relaxation-localization model to interpret photoemission, UV absorption, and transport experiments are indicated. The analysis of photoemission measurements is emphasized because the model has been tested most extensively in this case. 

The analysis of intramolecular UV absorption using the relaxation-localization model is completely analogous to that of valence-electron photoemission. The major change is that charge densities appropriate for molecular excitons rather than molecular ions 2 27 model expressions for the... 

The relaxation-localization model recently has been applied to derive explicit expressions for electron (hole) transfer probabilities between two molecular sites in pendant-group and molecularly-doped polymers. These probabilities are the input data used in multiple-hopping models of measured transport properties, e.g., drift mobilities and photoconductivity. ... 

In this paper the development and major applications of a new relaxation-localization model of electronic states in molecular solids have been briefly outlined. This model affords a detailed description of valence-electron photoemission spectra which, moreover, have been utilized to verify explicitly several of its important predictions. It provides a similar description of DV absorption spectra and electron-transfer processes. Inadequate experimental data are available in these cases, however, to test the model critically. Finally a phenomenological version of the model has been shown to provide a quantitative description of steady-state contact charge exchange in polymers and to constitute a link between this charge exchange and the molecular architecture of pendant group polymers. 

A simple composite model of slow motions and molecular reorientations is the so-called slowly relaxing local structure model by Freed.156,157 This... 

Another difference between the predictions of the two models is as follows. The classical model yields a finite value for the critical current when the relaxation parameter k tends to infinity (Ic = 0(1), k — oo). In contrast to this, the local model predicts... 

Liang, Z., et al. (2000). An electron spin resonance study of DNA dynamics using the slowly relaxing local structure model. J. Phys. Chem. 104, 5372-5381. 

Static imaging experiments conducted on fluid-saturated samples are used to determine porosity distributions. Carr-Purcell-Meiboom-Gill (CPMG) imaging is used to evaluate the spin density. The local relaxation is modeled in order to estimate the intrinsic magnetization intensity, which is proportional to the amount of saturating fluid. 

Elliott (1987, 1988 and 1989) approached the relaxation problem differently. In his diffusion controlled relaxation (DCR) model, Elliott, like Charles (1961) considers ionic motion to occur by an interstitialcy mechanism. There is a local motion of cations (for example Li ion in a silicate glass) among equivalent positions located around a NBO ion. Motions of cations among these positions causes the primary relaxational event and it occurs with a characteristic microscopic relaxation time t. The process gives rise to a polarization current. However, when another Li ion hops into one of the nearby equivalent positions with a probability P(/), a double occupancy results around the anion and this makes the relaxation instantaneous. Since the latter process involves the diffusion of a Li ion, the process as a whole involves both polarization and diffusion currents. Thus the relaxation function can be written as [l-P(/)]exp(-t/r). [1-P(0] is a function of the jump distance and the diffusion constant. Making use of the Glarum-Bordewijk relation (Glarum, 1960 Bordewijk, 1975) for [1-/ (/)] Elliott (1987) has shown that... 

E. Two-Body Kramers Model Slowly Relaxing Local Structure... 

This is a two-body AFPE that is fully equivalent to those described by Stillman and Freed, including both a fluctuating torque effect (matrix f) and a slowly relaxing local structure (interaction potential V) the equivalence of the two approaches will be further investigated in the next section for the case of a planar model. 

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