Intermediate order

They have demonstrated that the Smoluchowski approach could indeed be derived rigorously as a cut-off of the set of rigorous kinetic equations discussed in Chapter 4. However, the accuracy of this approximation and the range of applicability of the Smoluchowski approach remained unclear until recently [16]. 

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In a comparative study of the crystallinity of isomeric aliphatic polyamides by NMR, DSC and X-ray, the NMR-based crystallinity was obtained by a two component fit of the proton broad-line spectra and their associated mobilities by Tip determination. Compared to the crystallinity estimates from DSC and WAXS, the content of rigid material obtained from NMR is significantly higher, but comparable to the crystallinity determined by SAXS. The difference with the DSC value was associated with a fraction of intermediate order within the crystalline phase [193]. 

Peptide E n.a. 25 SDS Two beta-turns, intermediate order parameters 102... 

One may consider a series of physical states ranging from the crystalline, where molecular aggregation and orientation are large, to the dilute gaseous state, where there are no significant orientational limits. States of intermediate order are represented by micelles, liquid crystals, monolayers, ion pairs, and dipole-dipole complexes. In the crystalline state, the differences between pure enantiomers, racemic modifications, and diastereomeric complexes are clearly defined both structurally and energetically (32,33). At the other extreme, stereospecific interactions between diastereomerically related solvents and solutes, ion pairs, and other partially oriented systems are much less clearly resolved. 

If the desired reaction is of intermediate order then some intermediate will give the best product distribution. 

Detonation High-, Low-, and Intermediate Order, Velocities of. It has been known since the end of the last century that some liquid expls (such as NG or NGc) and some gelatinous expls (such as Gelatin Dynamites) are capable of detonating at either low (1000-2000 m/sec) or high velocity (up to 8000 m/sec), depending on method of initiation. More recently it was found that the same phenomenon can occur, under certain conditions, with crystalline secondary, or even primary, expls... 

In TNT pellets the initial Type II low-order detonation does not lead immediately to the final high order but to an intermediate level, of almost normal rate but of very low shock luminosity. A luminous strip due to the collision of the shock waves of two low-ordet detonations in TNT is observed in the simple dark space in some still photographs. Initiation at slightly below the limit, in all of the expls studied, produces low-order detons that fade after traversing-a short distance and the wave fronts show a strong shock effect. In TNT pellets the intermediate-order may also fade... 

Detonation, Intermediate Order Velocities of. See under Detonation, High-, Low-, and Intermediate Order Velocities of... 

Fig. 35. Magnetic-field-vs.-temperature magnetic phase diagram for TbNi2B2C proposed by Cho et al. (1996a). AF antiferromagnetic WF weakly ferromagnetic. The nature of the intermediate ordered state is not yet...

Detonation, high-, low- and intermediate order, velocities of 4 D384... 

If the value used for k6 is correct (a slight change in the activation energy used could markedly offset the value), NO and/or HI is about 300 times as efficient as the chaperones used in other studies. Thus, the observed intermediate order of the reaction is entirely reasonable. 

Fig. 1.16. The intermediate order in ideal gas (i) ideal classical gas (full line) (ii) ideal Fermi gas (broken line) (iii) ideal Bose gas (dotted line).

Fig. 1.17. The intermediate order in a dense system of rigid balls.

The use of more realistic potentials, including both repulsive and attractive contributions, results in the more smooth intermediate order curves G(r). As previously, they reveal oscillations thus reflecting the specific law of mutual particle distribution in dense systems. 

Let us consider now behaviour of the gas-liquid system near the critical point. It reveals rather interesting effect called the critical opalescence, that is strong increase of the light scattering. Its analogs are known also in other physical systems in the vicinity of phase transitions. In the beginning of our century Einstein and Smoluchowski expressed an idea, that the opalescence phenomenon is related to the density (order parameter) fluctuations in the system. More consistent theory was presented later by Omstein and Zemike [23], who for the first time introduced a concept of the intermediate order as the spatial correlation in the density fluctuations. Later Zemike [24] has applied this idea to the lattice systems. 

How could we take into account the fluctuations of the order parameter Let us return to the well-studied example of the gas-liquid system. A general equation of the state of gases and liquids proved in statistical physics [9] has a form p = nk T - n2G(x) where G(x) is some integral containing the interaction potential of particles and the joint correlation function x(r). Therefore, the equation for the long-range order parameter n contains in itself the functional of the intermediate-order parameter x r)-... 

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