Microscopic order-macroscopic disorder

Rotational motion can be isotropic or anisotropic (e.g., when spin labels are attached to larger polymer molecules) and analysis of CW EPR spectra most often is quantified by spectral simulations assuming a rotational model of some sort (e.g., isotropic Brownian or uni-axial motion or more complicated models like microscopic order, macroscopic disorder, or MOMD see [19, 21]). 

While slow tumbling spectra are best simulated to extract rotational correlation times, fast tumbling spectra can be quantified via relative fine widths T2,r or amplitudes hi of the three fines using Kivelson fine width theory. As three lines define two independent amplitude ratios, the imderlying assumption of isotropic Brownian rotational diffusion can be tested. For spin labels in polymers or sirrfactant spin probes nitroxide motion is usually not isotropic In favorable cases, more detailed models of the motion can be obtained by the microscopic order macroscopic disorder (MOMD) or slowly relaxing local stracture (SRLS) models. ... 

When analyzing experimental EPR spectra of spin probes in micellar phase of complexes we used the model "Microscopic Order and Macroscopic Disorder" (MOMD) [33], This model is often used for description of EPR spectra of spin probes in micelles, dispersions, vesicles and other microscopically ordered but macroscopically disordered systems [34, 35],... 

Carpenter, M.A. (1985) Order-disorder transformations in mineral solid solutions. In Keiffer, S.W., Navrotsky, A. (eds) Microscopic to Macroscopic Atomic Enviromnents to Mineral Thermodynamics. Rev Mineral 14 187-223... 

Electrons residing in molecular clusters can be viewed as microscopic probes of both the local liquid structure and the molecular dynamics of liquids, and as such their transitory existence becomes a theoretical and experimental metaphor for one of the major fundamental and contemporary problems in chemical and molecular physics, that is, how to describe the transition between the microscopic and macroscopic realms of physical laws in the condensed phase. Since this chapter was completed in the Spring of 1979, several new and important observations have been made on the dynamics and structure of e, which, as a fundamental particle interacting with atoms and molecules in a fundamental way, serves to assist that transformation for electronic states in disordered systems. In a sense, disorder has become order on the subpicosecond time-scale, as we study events whose time duration is shorter than, or comparable to, the period during which the atoms or molecules retain some memory of the initial quantum state, or of the velocity or phase space correlations of the microscopic system. This approach anticipated the new wave of theoretical and experimental interest in developing microscopic theories of... 

Fig. 4.10 a V/Vq plot for BagSi4 as a function of pressure (points) along with a third-order Birch-Mumaghan equation of state (line). The macroscopic order parameter corresponds to spontaneous i c., the Variation of the volume cmrected from the compressibility, b Aspo ,a eous as a function of pressure fits with the theoretical analysis based on the Landau theory of phase transition null before the transition pressure, a jump at the transition and a square-root evolution after the transition. Such a behaviOT is also observed for Si atomic displacement parameters that can be used as microscopic order parameter [82]. The correlation between these physical quantities underlines the relationships between the isostructural transition and disordering of the Si sub-lattice... 

Basic to the thermodynamic description is the heat capacity which is defined as the partial differential Cp = (dH/dT)n,p, where H is the enthalpy and T the temperature. The partial differential is taken at constant pressure and composition, as indicated by the subscripts p and n, respectively A close link between microscopic and macroscopic description is possible for this fundamental property. The integral thermodynamic functions include enthalpy H entropy S, and free enthalpy G (Gibbs function). In addition, information on pressure p, volume V, and temperature T is of importance (PVT properties). The transition parameters of pure, one-component systems are seen as first-order and glass transitions. Mesophase transitions, in general, were reviewed (12) and the effect of specific interest to polymers, the conformational disorder, was described in more detail (13). The broad field of multicomponent systems is particularly troubled by nonequilibrium behavior. Polymerization thermodynamics relies on the properties of the monomers and does not have as many problems with nonequilibrium. 

Figure 1. Deuteron NMR line shapes. Top static powder pattern for a macroscopically disordered sample in the absence of molecular motions (77 = 0 case). Middle , motionally narrowed powder pattern for a macroscopically disordered mesophase with axially symmetric molecular motions (( ]) = 0). The ratio of the peak splittings in the top and middle spectra defines the microscopic order parameter. Bottom , doublet spectrum of a macroscopically aligned mesophase. If the microscopic order parameter is known, the angle between the director and the magnetic field can be obtained from the splitting.

Self-organization seems to be counterintuitive, since the order that is generated challenges the paradigm of increasing disorder based on the second law of thermodynamics. In statistical thermodynamics, entropy is the number of possible microstates for a macroscopic state. Since, in an ordered state, the number of possible microstates is smaller than for a more disordered state, it follows that a self-organized system has a lower entropy. However, the two need not contradict each other it is possible to reduce the entropy in a part of a system while it increases in another. A few of the system s macroscopic degrees of freedom can become more ordered at the expense of microscopic disorder. This is valid even for isolated, closed systems. Eurthermore, in an open system, the entropy production can be transferred to the environment, so that here even the overall entropy in the entire system can be reduced. 

At the macroscopic level, a solid is a substance that has both a definite volume and a definite shape. At the microscopic level, solids may be one of two types amorphous or crystalline. Amorphous solids lack extensive ordering of the particles. There is a lack of regularity of the structure. There may be small regions of order separated by large areas of disordered particles. They resemble liquids more than solids in this characteristic. Amorphous solids have no distinct melting point. They simply become softer and softer as the temperature rises. Glass, rubber, and charcoal are examples of amorphous solids. 

As its name suggests, a liquid crystal is a fluid (liquid) with some long-range order (crystal) and therefore has properties of both states mobility as a liquid, self-assembly, anisotropism (refractive index, electric permittivity, magnetic susceptibility, mechanical properties, depend on the direction in which they are measured) as a solid crystal. Therefore, the liquid crystalline phase is an intermediate phase between solid and liquid. In other words, macroscopically the liquid crystalline phase behaves as a liquid, but, microscopically, it resembles the solid phase. Sometimes it may be helpful to see it as an ordered liquid or a disordered solid. The liquid crystal behavior depends on the intermolecular forces, that is, if the latter are too strong or too weak the mesophase is lost. Driving forces for the formation of a mesophase are dipole-dipole, van der Waals interactions, 71—71 stacking and so on. 

As it is known [5], the intensity of the scattered light gives us an information about the system s disorder, e.g., presence therein of pores, impurities etc. Since macroscopically liquid is homogeneous, critical opalescence arises due to local microscopic inhomogeneities - an appearance of small domains with different local densities. In other words, liquid is ordered inside these domains but still disorded on the whole since domains are randomly distributed in size and space, they appear and disappear by chance. Fluctuations of the order parameter have large amplitude and involve a wide spectrum of the wavelengths (which results in the milk colour of the scattered light). 

Using the methods of classical statistical physics one may more or less rigorously solve problems where the system on a microscopic level is either in a state of complete chaos (perfect gas) or total order (solid perfectly crystalline bodies). In contrast, disordered media and processes in which there is neither crystalline order nor complete chaos on the microscopic level have not yet had an adequate description. This problem is connected with the condition that the macroscopic variables must considerably exceed the correlation scales of microscopic variables, a condition which is not met by disordered media. Consequently in order to describe such systems, fractal models and phased averaging on different scale levels (meso-levels) should be effective. 

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