Asymmetric states

Figure 1. The vacuum or coherent states are denoted by V, C the n-photon or thermalized states by N, T the asymmetric states by A the squeezed states by S, PS.

Microscopic, Semiclassical, and Cluster Treatments of Low-Lying Reflection Asymmetric States in the Light Actinides... 

A molecule whose geometrical structure is not identical to its mirror image possesses chirality. For example, enantiomers are mirror-image structures of a chiral molecule. Two mirror-image molecules are identified as l- and D-enantiomers. Amino acids and deoxyribose in DNA are chiral molecules. Asy mmetry in biochemistry requires the constant catalytic production of the preferred enantiomer in the reactions between enantiomers, a process known as racemization. In systems with appropriate chiral autocatalysis, instability may appear. Due to random fluctuations, the instability occurs accompanying the bifurcation of asymmetric states in which one enantiomer dominates. These states of broken symmetry can be observed in the following simple model reaction scheme with chiral autocatalysis (Kondepudi and Prigogine, 1999)... 

With the following parameters, the symmetric and asymmetric states may become more explicit... 

In mesopores a multilayer film will be adsorbed at the pore wall as the saturation pressure is approached. The stability of this film is determined by the interaction with the wall, e.g. long-range Van der Waals Interaction, and by the surface tension and curvature of the liquid-vapour interface. Saam and Cole -have advanced a theory, showing how the curved film becomes unstable at a certain critical thickness t = a-r. The adsorption process is shown schematically in fig. 1.32a (1) (3). During desorption (4) -> (6) an asymmetrical state... 

Figure 1 shows the model of the adsorption state in a cylindrical mesopore whose pore width is R. The symmetrical state in Figure 1 (a) expresses multilayer adsorption, whereas Figure 1(b) shows the asymmetrical state due to a partial capillary condensation. The chemical potential change A/j of the adsorbed molecules in the cylindrical pore is generally described by the summation of... 

The Saam-Cole approach has several approximations, among which are the neglect of the sohd-adsorbate interaction and curvature effects on the adsorbate chemical potential, and curvature effects on surface tension in symmetrical and asymmetrical states, while modeling the multilayer region. Here, a more accurate version of the above approach has been introduced and tested for explaining the reversibihty of adsorption in MCM-41. For fluid molecules inside a cyhndrical pore of radius R, the incremental potential function has been expressed as [4,6,7]... 

Sheintuch (1981) analyzed an oscillatory kinetic mechanism with surface oxide and gas phase reactant as variables, and showed that depending on operating conditions an asymmetric state of surface oxide is reached. The asymmetric state was found to be stable, except near the bifurcation point where it might be oscillatory. A mathematical model was developed. Sheintuch and Pismen (1981) investigated the existence of inhomogeneous surface states for three oscillatory kinetic models, i.e. autocatalytic gas-phase variable, autocatalytic surface variable and two surface variables. Sheintuch (1982) also analyzed an oscillatory kinetic mechanism by employing two surface concentrations as variables and the mechanism was simulated by the proposed model and discussed. 

However, for very high frequencies of the external field, such as 10 Hz, the time for one oscillation is 10 s and this is comparable to or even smaller than the relaxation time. Under these conditions the ion is impelled backwards and forwards so rapidly that the build up of the ionic atmosphere to the asymmetric state cannot occur fast enough, and the asymmetric ionic atmosphere will not be fiiUy set up. At even higher frequencies the ionic atmosphere never has time to reach the asymmetric state and the relaxation effect totally disappears. The retarding effect of the asymmetry on the movement of the ions under the influence of the external field is removed. In consequence, the velocity of the ions and their individual ionic molar conductivities are significantly higher than for ordinary frequencies and are much nearer what would they would be expected to be if there were no retarding effect of the ionic atmosphere. 

Biochemistry s hidden asymmetry was discovered by Louis Pasteur in 1857. Nearly 150 years later, its true origin remains an unsolved problem, but we can see how such a state might be realized in the framework of dissipative structures. First, we note that such an asymmetry can arise only under far-from-equilibrium conditions at equilibrium the concentrations of the two enantiomers will be equal. The maintenance of this asymmetry requires constant catalytic production of the preferred enantiomer in the face of interconversion between enantiomers, called racemization. (Racemization drives the system to the equilibrium state in which the concentrations of the two enantiomers will become equal.) Second, following the paradigm of order through fluctuations, we will presently see how, in systems with appropriate chiral autocatalysis, the thermodynamic branch, which contains equal amounts of L- and D-enantiomers, can become unstable. The instability is accompanied by the bifurcation of asymmetric states, or states of broken symmetry, in which one enantiomer dominates. Driven by random fluctuations, the system makes, a transition to one of the two possible states. 

To make the symmetric and asymmetric states explicit, it is convenient to define the following variables ... 

So, super lattice is a transformation of one disordered or asymmetric state to one ordered or symmetric state of this alloy and the order-disorder transformation around a temperature establish that the symmetry and asymmetry may be viewed as the two sides of the same coin. 

There are only 32 possible combinations of the above-mentioned elements of symmetry (including the asymmetric state), and these are called the 32 classes or point groups. For convenience these 32 classes are grouped into 7 systems characterized by the angles between their x, y and z axes. Crystals of course, can exhibit combination forms of the crystal systems. 

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