Normal Molecular origin

The phenomenological approach does not preclude a consideration of the molecular origins of the characteristic timescales within the material. It is these timescales that determine whether the observation you make is one which sees the material as elastic, viscous or viscoelastic. There are great differences between timescales and length scales for atomic, molecular and macromolecular materials. When an instantaneous deformation is applied to a body the particles forming the body are displaced from their normal positions. They diffuse from these positions with time and gradually dissipate the stress. The diffusion coefficient relates the distance diffused to the timescale characteristic of this motion. The form of the diffusion coefficient depends on the extent of ordering within the material. 

The minus sign in this equation is a matter of convention t(n) is considered positive when it acts inward on a surface whereas n is the outwardly directed normal, andp is taken as always positive. The fact that the magnitude of the pressure (or surface force) is independent of n is self-evident from its molecular origin but also can be proven on purely continuum mechanical grounds, because otherwise the principle of stress equilibrium, (2 25), cannot be satisfied for an arbitrary material volume element in the fluid. The form for the stress tensor T in a stationary fluid follows immediately from (2 59) and the general relationship (2-29) between the stress vector and the stress tensor ... 

The molecular origin of ferroelectricity in FLCs is attributed to a pronounced anisotropy of the angular orientations of the lateral dipole moments, induced by the tilt of the molecular long axes with respect to the normal of the smectic layers. This is supported by the results of broadband dielectric spectroscopy performed on a low molecu-... 

Thus, the restoring force is proportional to the extension and the onedimensional chain behaves as a Hookean spring. This important result simplifies the analysis of the normal modes of motion of a polymer. Polymer chain models can be treated mathematically by the much simpler linear differential equations because second order effects are absent. (It should be noted diat, while the elastic equation for a polymer chain is identical in form with Hooke s law, the molecular origin of the restoring force is very different). 

Several steps are necessary before heat capacity can be linked to its various molecular origins. First, one finds that linear macromolecules do not normally crystallize completely, they are semicrystaUine. The restriction to partial crystallization is caused by kinetic hindrance to full extension of the molecular chains which, in the amorphous phase, are randomly coiled and entangled. Furthermore, in cases where the molecular structure is not sufficiently regular, the crystallinity may be further reduced, or even completely absent so that the molecules remain amorphous at all temperatures. 

The Mossbauer spectra of powdered samples of the clathrate are shown in Fig. 1. The statistics of the spectra is very poor at high temperature due to a low Debye-Waller factor (the absorption is 0.4 % at 320 K) and a relaxation phenomenon(absorption becomes broad in the region of the releixation time of 120 ns. The accumulated counts are more than a million counts above 250 K. The low temperature spectra of this clathrate are quite normal The efg for ferrocene derivatives is known to be essentially of molecular origin and the QS values do not... 

Ma, A., Stratt, R.M. (2002). The molecular origins of the two-dimensional Raman spectrum of an atomic liquid. II. Instantaneous-normal-mode theory. 7. Chem. Phys. 116 4972 984. 

Normal ions (M+, Fj+,. .., F +) in a spectrum can provide a molecular structure for substance M if the fragments can be theoretically reassembled. The problem is rather like deducing an original jigsaw puzzle by putting the pieces together correctly. For most molecules containing more than a few atoms, this reassembly exercise is difficult and often problematic. 

By measuring a mass spectrum of normal ions and then finding the links between ions from the metastable ions, it becomes easier to deduce the molecular structure of the substance that was ionized originally. 

In SEC, universal calibration is often utilized to characterize a molecular weight distribution. For a universal calibration curve, one must determine the product of log(intrinsic viscosity molecular weight), or log([7j] M). The universal calibration method originally described by Benoit et al. (9) employs the hydro-dynamic radius or volume, the product of [tj] M as the separation parameter. The calibration curves for a variety of polymers will converge toward a single curve when plotted as log([7j] M) versus elution volume (VJ, rather than plotted the conventional way as log(M) versus V, (5). Universal calibration behavior is highly dependent on the absence of any secondary separation effects. Most failures of universal calibration are normally due to the absence of a pure size exclusion mechanism. 

The sphere radii were deduced from Slater s (1965) table based on crystal data. The basic molecular HF-Xa equations were originally derived on the basis that the spheres did not overlap (Schwarz and Connolly, 1971). But the equations remain valid when the spheres are allowed to overlap, provided that each sphere does not contain more than one nucleus and that none of the nuclei lie outside the outer sphere. A 10% overlap seems to be normal practice, and our results are given in Table 12.2. 

Surface force apparatus has been applied successfully over the past years for measuring normal surface forces as a function of surface gap or film thickness. The results reveal, for example, that the normal forces acting on confined liquid composed of linear-chain molecules exhibit a periodic oscillation between the attractive and repulsive interactions as one surface continuously approaches to another, which is schematically shown in Fig. 19. The period of the oscillation corresponds precisely to the thickness of a molecular chain, and the oscillation amplitude increases exponentially as the film thickness decreases. This oscillatory solvation force originates from the formation of the layering structure in thin liquid films and the change of the ordered structure with the film thickness. The result provides a convincing example that the SFA can be an effective experimental tool to detect fundamental interactions between the surfaces when the gap decreases to nanometre scale. 

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