Deformation molecular description

Stress and strain or deformation can be useful in microscopic or molecular descriptions of how the observed phenomena come about. They have directional properties that distinguish an elongation from a shear, for example. When the stress and strain may depend on time, it can be either the unchanging equilibrium state or a steady... 

The simulations revealed a picture of ion permeation that is in sharp contrast with the continuum dielectric model. As the ion moves across the water-membrane interface into the bilayer, the membrane surface does not remain approximately planar. Instead, a local deformation is formed in which water molecules and polar head groups (normally restricted to the surface of the membrane) follow the ion into the nonpolar interior of the bilayer. Once the ion crosses the midplane of the membrane, the deformation on the incoming side relaxes and simultaneously, a similar deformation forms on the outgoing side. Thus, during the entire transfer process, the ion remains partially solvated by both the polar head groups and water molecules. The key feature of this molecular description of the ion transfer process is that the ion is never fully solvated by the nonpolar hydrocarbon tails. Thus, the calculated is markedly lower than the barrier predicted from the continuum model. For Na", was estimated at... 

A kinetic theory of fracture intends to interrelate the motion and response of molecules to the ultimate properties of a stressed sample. A kinetic theory, therefore, entails a molecular description of the deformation of the microscopically heterogeneous and anisotropic aggregates of chains to such an extent that critical deformation processes can be identified. The macroscopic deformation of any aggregate potentially involves the deformation, displacement, and/or reorientation of so different substructural elements as bond vectors, chain segments or crystal lamellae. 

As mentioned in the introduction, a kinetic theory of fracture deals with and particularly considers the existence and discrete size, the motion, and the response of molecules or their parts in a stressed sample. It thus requires a molecular description of polymer structure and deformation. Such a description is available in the cited books [1—12], [20] or papers [15, 38]. In Chapter 2 only a very brief summary is offered which is not meant to be self-supporting or complete. 

The kinetic nature of the glass transition should be clear from the last chapter, where we first identified this transition by a change in the mechanical properties of a sample in very rapid deformations. In that chapter we concluded that molecular motion could simply not keep up with these high-frequency deformations. The complementarity between time and temperature enters the picture in this way. At lower temperatures the motion of molecules becomes more sluggish and equivalent effects on mechanical properties are produced by cooling as by frequency variations. We shall return to an examination of this time-temperature equivalency in Sec. 4.10. First, however, it will be profitable to consider the possibility of a thermodynamic description of the transition which occurs at Tg. 

The above description refers to a Lagrangian frame of reference in which the movement of the particle is followed along its trajectory. Instead of having a steady flow, it is possible to modulate the flow, for example sinusoidally as a function of time. At sufficiently high frequency, the molecular coil deformation will be dephased from the strain rate and the flow becomes transient even with a stagnant flow geometry. Oscillatory flow birefringence has been measured in simple shear and corresponds to some kind of frequency analysis of the flow... 

Interest in thermotropic liquid crystals has focussed mainly on macroscopic properties studies relating these properties to the microscopic molecular order are new. Lyotropic liquid crystals, e.g. lipid-water systems, however, are better known from a microscopic point of view. We detail the descriptions of chain flexibility that were obtained from recent DMR experiments on deuterated soap molecules. Models were developed, and most chain deformations appear to result from intramolecular isomeric rotations that are compatible with intermodular steric hindrance. The characteristic times of chain motions can be estimated from earlier proton resonance experiments. There is a possibility of collective motions in the bilayer. The biological relevance of these findings is considered briefly. Recent similar DMR studies of thermotropic liquid crystals also suggest some molecular flexibility. 

Because dipolar interaction is related to the intemuclear vector, which is the direct description of the molecular framework, the relation between the orientation distribution function obtained from a dipolar-DECODER spectrum and the molecular frame distribution is simpler than that from CSA-DECODER and quadrupolar-DECODER spectrum. One example of the 2D dipolar-DECODER experimental spectrum is shown in Fig. 19. The change of the orientation distribution caused by the deformation can be measured by the difference of the spectra before and after deformation. Of course, since the dipolar interaction tensor is always axially symmetric, the information content of a dipolar-DECODER spectrum is decreased. 

---