Isotropic state

Liquid Glassy LC structure crystalline state Isotropic melt... 

Position Chemical Shift (ppm) Experimental Theoretical Two-State Isotropic Motion Internal Motion ... 

Fe—2 S] center Characteristic U.V./visible and very intense CD spectra. EPR variable from narrow (putidaredoxin) to broad and rhombic (plant ferredoxin), g < 2 signal in the reduced state, observable at 77 K. No signal in the oxidized state. Isotropic EPR signal observed below 77 K in 80% DMSO in reducing conditions. Extrusion and displacement reaction give characteristic products. 

Solid-state Hg NMR can clearly resolve several issues raised by solution NMR studies. If the solid-state isotropic shift is equal to the solution shift, then the solution chemical shift does not represent an average of several species in rapid exchange. As has been shown with Cd NMR (186), correspondence between solution and solid-state chemical shifts greatly increases the ability of the inorganic chemist to use solution spectra to classify molecular structure and bonding. Equally important, analysis of the solid-state chemical shift and the shielding tensor components can provide information about coordination number and asymmetry at the metal center in solids, even when other structural information is lacking. 

For the two four-coordinate complexes we have measured by Hg CP MAS NMR, Hg(S-t-Bu)2 and [Hg(SC6H4Cl)4], the solid-state isotropic chemical shifts (Table XIII) do not agree with those obtained in solution (Table XII). The discrepancy arises because Hg(S-r-Bu)2 is a polymer in the solid state but is two coordinate in solution. The chemical shift of Hg(S-r-Bu)2 in solution more closely corresponds to those measured for other two-coordinate complexes (202). In the case of [Hg(SC6H4Cl)4] , the complex dissolved in DMSO has a chemical shift of -569 ppm and titration with RS" leads to a deshielding that approaches the solid-state value (- 485 ppm) (136). This finding illustrates the importance of dynamic processes and ligand-dissociated states in solution and is a graphic demonstration of the value of solid state Hg NMR (136). 

Fig. 4.12 Comparison of solution state and solid state NMR spectra of paracetamol (A) the C H solution state spectrum recorded on a ISmgmL solution of paracetamol in DMSO-d 125 MHz, (B) the solid state spectrum obtained on pure paracetamtd at 90.5 MHz, and (C) the solid state spectrum (90.5 MHz) of a crushed tablet of a paracetamol formulation. The solution state assignments are readily available from inverse corelation methods described in Section 4.2.4.1. The solid state isotropic chemical shifts are very similar to those obtained in the solution state, but note that the inequivalence of the chemically equivalent carbons e.g. 2,2 and 3, 3 in the solid state spectrum. The dmg resonances can easily be diffterentiated from those of the excipients in spectrum (C). The resonances between 60 and lOOppm in spectrum (Q originate from the cellulosic formulation ingredients. 

The peptide cvclo(Glv-Pro-GlvK presents a quite different situation. The analysis of its NMR spectrum leads to the conclusion that it adopts a Cp-symmetric conformation in solution, at least on NMR timescales. The solution NMR spectrum (Figure 2B) shows the minimum number of resonances expected (one per carbon in the repeating trlpeptlde unit). By contrast, in the solid-state spectrum there Is clear indication of asymmetry since there are two Pro Cg resonances in Figure 2A, X-ray diffraction analysis has revealed an asymmetric molecular conformation for the crystalline peptide (17), with two different types of 3-turns, only one of which is intramolecularly hydrogen-bonded. Analysis of the solid state isotropic chemical shifts in terms of local conformation yields a picture of the molecule which is consistent with the X-ray data,... 

There are a number of assumptions implicit in this equation, such as that the refractive index of the solvent in the visible-region wavelengths is the same as at zero frequency. This is reasonable for solvents other than water, but for water there is quite a large difference between the values at zero and visible-region frequencies. The ground-state isotropic polarizability of the solute is assumed to be a jl. 

Isotropic Spectra. Numerous computer programs have been written for the simulation of solution state (isotropic) ESR spectra. Often these include the facility to simulate spectra from mixtures of radicals and to allow for contributions from satellite lines arising from the presence of low-abundance magnetic nuclei such as C, N, and S. 

Solid Phase. There exists in the literature a wide range of isotropic and anisotropic hf coupling constants which were determined from electron spin resonance (ESR) spectra of NH2 in the solid state. Isotropic g factors and hf coupling constants (in MHz) are compiled in the following table ... 

L. The liquid-expanded, L phase is a two-dimensionally isotropic arrangement of amphiphiles. This is in the smectic A class of liquidlike in-plane structure. There is a continuing debate on how best to formulate an equation of state of the liquid-expanded monolayer. Such monolayers are fluid and coherent, yet the average intermolecular distance is much greater than for bulk liquids. A typical bulk liquid is perhaps 10% less dense than its corresponding solid state. 

Perturbation theory yields a siim-over-states fomnila for each of the dispersion coefficients. For example, the isotropic coefficient for the interaction between molecules A and B is given by... 

Liquid crystals represent a state of matter with physical properties normally associated with both soHds and Hquids. Liquid crystals are fluid in that the molecules are free to diffuse about, endowing the substance with the flow properties of a fluid. As the molecules diffuse, however, a small degree of long-range orientational and sometimes positional order is maintained, causing the substance to be anisotropic as is typical of soflds. Therefore, Hquid crystals are anisotropic fluids and thus a fourth phase of matter. There are many Hquid crystal phases, each exhibiting different forms of orientational and positional order, but in most cases these phases are thermodynamically stable for temperature ranges between the soHd and isotropic Hquid phases. Liquid crystallinity is also referred to as mesomorphism. 

Fig. 17. Polymer dispersed Hquid crystal display (PDLC). (a) U < clear state, where U) is the threshold voltage of the ceU. and rij represent the indexes of refraction for light polarized parallel and perpendicular to the director of the Hquid crystal represents the index of refraction of the isotropic...

Fibers produced from pitch precursors can be manufactured by heat treating isotropic pitch at 400 to 450°C in an inert environment to transform it into a hquid crystalline state. The pitch is then spun into fibers and allowed to thermoset at 300°C for short periods of time. The fibers are subsequendy carbonized and graphitized at temperatures similar to those used in the manufacture of PAN-based fibers. The isotropic pitch precursor has not proved attractive to industry. However, a process based on anisotropic mesophase pitch (30), in which commercial pitch is spun and polymerized to form the mesophase, which is then melt spun, stabilized in air at about 300°C, carbonized at 1300°C, and graphitized at 3000°C, produces ultrahigh modulus (UHM) carbon fibers. In this process tension is not requited in the stabilization and graphitization stages. 

In an ideal fluid, the stresses are isotropic. There is no strength, so there are no shear stresses the normal stress and lateral stresses are equal and are identical to the pressure. On the other hand, a solid with strength can support shear stresses. However, when the applied stress greatly exceeds the yield stress of a solid, its behavior can be approximated by that of a fluid because the fractional deviations from stress isotropy are small. Under these conditions, the solid is considered to be hydrodynamic. In the absence of rate-dependent behavior such as viscous relaxation or heat conduction, the equation of state of an isotropic fluid or hydrodynamic solid can be expressed in terms of specific internal energy as a function of pressure and specific volume E(P, V). A familiar equation of state is that for an ideal gas... 

In the case of most nonporous minerals at sufficiently low-shock stresses, two shock fronts form. The first wave is the elastic shock, a finite-amplitude essentially elastic wave as indicated in Fig. 4.11. The amplitude of this shock is often called the Hugoniot elastic limit Phel- This would correspond to state 1 of Fig. 4.10(a). The Hugoniot elastic limit is defined as the maximum stress sustainable by a solid in one-dimensional shock compression without irreversible deformation taking place at the shock front. The particle velocity associated with a Hugoniot elastic limit shock is often measured by observing the free-surface velocity profile as, for example, in Fig. 4.16. In the case of a polycrystalline and/or isotropic material at shock stresses at or below HEL> the lateral compressive stress in a plane perpendicular to the shock front... 

In this section, the general inelastic theory of Section 5.2 will be specialized to a simple phenomenological theory of plasticity. The inelastic strain rate tensor e may be identified with the plastic strain rate tensor e . In order to include isotropic and kinematic hardening, the set of internal state variables, denoted collectively by k in the previous theory, is reduced to the set (k, a) where k is a scalar representing isotropic hardening and a is a symmetric second-order tensor representing kinematic hardening. The elastic limit condition in stress space (5.25), now called a yield condition, becomes... 

This result comes from the idea of a variational rate theory for a diffusive dynamics. If the dynamics of the reactive system is overdamped and the effective friction is spatially isotropic, the time required to pass from the reactant to the product state is expected to be proportional to the integral over the path of the inverse Boltzmann probability. 

Infrared ellipsometry is typically performed in the mid-infrared range of 400 to 5000 cm , but also in the near- and far-infrared. The resonances of molecular vibrations or phonons in the solid state generate typical features in the tanT and A spectra in the form of relative minima or maxima and dispersion-like structures. For the isotropic bulk calculation of optical constants - refractive index n and extinction coefficient k - is straightforward. For all other applications (thin films and anisotropic materials) iteration procedures are used. In ellipsometry only angles are measured. The results are also absolute values, obtained without the use of a standard. 

The shock-compression pulse carries a solid into a state of homogeneous, isotropic compression whose properties can be described in terms of perfect-crystal lattices in thermodynamic equilibrium. Influences of anisotropic stress on solid materials behaviors can be treated as a perturbation to the isotropic equilibrium state. ... 

In solids of cubic symmetry or in isotropic, homogeneous polycrystalline solids, the lateral component of stress is related to the longitudinal component of stress through appropriate elastic constants. A representation of these uniaxial strain, hydrostatic (isotropic) and shear stress states is depicted in Fig. 2.4. Such relationships are thought to apply to many solids, but exceptions are certainly possible as in the case of vitreous silica [88C02]. 

Perhaps the most dramatic exception to the perfectly elastic, perfectly plastic materials response is encountered in several brittle, refractory materials that show behaviors indicative of an isotropic compression state above their Hugoniot elastic limits. Upon yielding, these materials exhibit a loss of shear strength. Such behavior was first observed from piezoelectric response measurements of quartz by Neilson and Benedick [62N01]. The electrical response observations were later confirmed in mechanical response measurements of Waekerle [62W01] and Fowles [61F01]. 

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