Dielectric relaxation mechanisms model

It was thought for some time that central peaks were due to impurities, defects and other such extrinsic or intrinsic factors. A number of models and mechanisms based on entropy fluctuations, phonon density fluctuations, dielectric relaxation, molecular... 

Attempts have been made to identify primitive motions from measurements of mechanical and dielectric relaxation (89) and to model the short time end of the relaxation spectrum (90). Methods have been developed recently for calculating the complete dynamical behavior of chains with idealized local structure (91,92). An apparent internal chain viscosity has been observed at high frequencies in dilute polymer solutions which is proportional to solvent viscosity (93) and which presumably appears when the external driving frequency is comparable to the frequency of the primitive rotations (94,95). The beginnings of an analysis of dynamics in the rotational isomeric model have been made (96). However, no general solution applicable for all frequency ranges has been found for chains with realistic local structure. 

Without using any motional model, the temperature positions of T and Tip minima can be assigned an appropriate frequency 90 MHz at 120 °C from Ti and 43 kHz at - 34 °C from T r These two results fit quite well on the relaxation map of BPA-PC obtained from dynamic mechanical and dielectric relaxation. They support the fact that phenyl ring motions are involved in the /3 relaxation of BPA-PC. Furthermore, the Ti and T f> data can be simulated by considering the Williams-Watts fractional correlation function [33] ... 

It is worth noticing that a molecular modelling approach is used to complement the experimental techniques of dynamic mechanical analysis, dielectric relaxation, solid-state 13C and 2H NMR. 

The quasi-static modelling of the dynamics of the ester group flip in an amorphous cell of atactic PMMA has yielded information complementary to that derived from dynamic mechanical analysis, dielectric relaxation and, mainly, multidimensional 13C and 2H solid-state NMR. The main results are ... 

The approach developed in this paper, combining on the one side experimental techniques (dynamic mechanical analysis, dielectric relaxation, solid-state 1H, 2H and 13C NMR on nuclei at natural abundance or through specific labelling), and on the other side atomistic modelling, allows one to reach quite a detailed description of the motions involved in the solid-state transitions of amorphous polymers. Bisphenol A polycarbonate, poly(methyl methacrylate) and its maleimide and glutarimide copolymers give perfect illustrations of the level of detail that can be achieved. 

In another paper in this issue [1], the molecular motions involved in secondary transitions of many amorphous polymers of quite different chemical structures have been analysed in detail by using a large set of experimental techniques (dynamic mechanical measurements, dielectric relaxation, H, 2H and 13C solid state NMR), as well as atomistic modelling. 

Figure 41. The scheme pertaining to the composite hat-curved—harmonic oscillator model the contributions of various mechanisms of dielectric relaxation to broadband spectra arising in liquid water. Frequency v is given in cm-1.

F. Ingrosso, B. Mennucci and J. Tomasi, Quantum mechanical calculations coupled with a dynamical continuum model for the description of dielectric relaxation time dependent Stokes shift of coumarin Cl53 in polar solvents, J. Mol. Liq., 108 (2003) 21 -6. 

The models (26) and (27), used to explain the kinetics of chemical reaction rates, were also found to be very useful for other applications. Taking into account the relationship x 1 ik, these equations can describe the temperature dependence of the relaxation time x for dielectric or mechanical relaxations provided by the transition between the initial and final states separated by an energy barrier. 

The conversion of the initially formed Si np state to the Si ct state by intramolecular electron transfer is very fast and varies in a way that parallels but does not exactly correspond to the dielectric relaxation time for the solvent used. This is because the local environment around the excited-state molecule is different from that surrounding a solvent molecule [120, 340]. That is, the ICT process is to a large extent determined by the dielectric relaxation processes of the solvent surrounding the ANS molecule. Thus, solvent motion seems to be the controlling factor in the formation and decay of the ICT excited state of ANS and other organic fluorophores [120, 340]. A detailed mechanism for fast intramolecular electron-transfer reactions of ANS and 4-(dimethylamino)benzonitrile, using two simplified molecular-microscopic models for the role of the solvent molecules, has been given by Kosower [340] see also reference [116]. 

Our purpose is to demonstrate how it is possible to describe the anomalous dielectric relaxation from microscopic models of the underlying processes. Moreover, we shall illustrate how the effects of the inertia of the molecules and an external potential arising from crystalline anisotropy or indeed any other mechanism could be included. 

The dynamics of the so-called biological water molecules in the immediate vicinity of a protein have been studied using dielectric relaxation [18], proton and O NMR relaxation [19], reaction path calculation [20], and analytical statistical mechanical models [21]. While the dielectric relaxation time of ordinary water molecules is 10 ps [16], both the dielectric [18] and nuclear magnetic resonance (NMR) relaxation studies [19], indicate that near the protein surface the relaxation dynamics are bimodal with two components in the 10-ns and 10-ps time scale, respectively. The 10-ns relaxation time cannot be due to the motion of the peptide chains, which occurs in the 100-ns time scale. From the study of NMR relaxation times of " O at the protein surface, Halle et al. [19c,d] suggested dynamic exchange between the slowly rotating internal and the fast external water molecules. 

The dielectric di persion of DNA solutions was measured with various samples. The dielectric increment and the relaxation time of helical DNA are proportional to the square of the length of the molecule, hut values for coil DNA are distinctly smaller than for helical DNA. The rotary diffusion constant is measured simultaneously with the dielectric measurement. The agreement of both relaxation times is fair in a region of low molecular weight, hut the disparity becomes pronounced when DNA is larger. Theories on the mechanism of ionic electric polarization are reviewed. Currently, counter ion polarization for a cylindrical model seems to account most reasonably for the dielectric relaxation of DNA. 

Special models have been developed for the crystallization of these and related stiff-chain aromatic copolymersThe basic crystal was suggested to be of the condis crystal type with rotational disorder based on conformational mobility, proven by mechanical and dielectric relaxation The morphology of the superimposed crystals was proposed to be based on a matching of order between adjacent molecules similar to cold crystallization originally proposed for the crystallization of PET-copolymers from the glassy state... 

In Debye s model of dielectric relaxation, the polarisation process has a single relaxation time. The model has both electrical circuit and viscoelastic model analogues (Fig. 12.14). The electrical circuit is the dual of the mechanical model, because the voltages across the capacitor and resistor... 

Maxwell model A mechanical model for simple linear viscoelastic behavior that consists of a spring of Young s modulus E) in series with a dashpot of coefficient of viscosity (ri). It is an isostress model (with stress 8), the strain (e) being the sum of the individual strains in the spring and dashpot. This leads to a differential representation of linear viscoelasticity as stress relaxation and creep with Newtonian flow analysis. Also called Maxwell fluid model. See stress relaxation viscoelasticity. Maxwell-Wagner efifect See dielectric, Maxwell-Wagner effect. 

Description of the mechanics of elastin requires the understanding of two interlinked but distinct physical processes the development of entropic elastic force and the occurrence of hydrophobic association. Elementary statistical-mechanical analysis of AFM single-chain force-extension data of elastin model molecules identifies damping of internal chain dynamics on extension as a fundamental source of entropic elastic force and eliminates the requirement of random chain networks. For elastin and its models, this simple analysis is substantiated experimentally by the observation of mechanical resonances in the dielectric relaxation and acoustic absorption spectra, and theoretically by the dependence of entropy on frequency of torsion-angle oscillations, and by classical molecular-mechanics and dynamics calculations of relaxed and extended states of the P-spiral description of the elastin repeat, (GVGVP) . The role of hydrophobic hydration in the mechanics of elastin becomes apparent under conditions of isometric contraction. 

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