Edwards order parameter

Here is the Edwards order parameter, such that is the local... 

It should be also noted that the dynamic NMR line width Avayn = is always small (Fig. 11a) as compared to the static glassy line width induced by the inhomogeneous nature of the spectrum. Therefore the nanocluster dynamics can be locally seen only by T2 measurements, and not by ID line shape data which reflect the static glassy nature of the relaxor state characterized by the Edwards-Anderson order parameter. 

For a ferromagnet the order parameter is the magnetization, while for antiferromagnets it is the sublattice magnetization. For spin glasses the magnetization is zero at all temperatures, and an appropriate order parameter was proposed by Edwards and Anderson [78] as the average value of the autocorrelation function... 

Key Words Dipolar glasses, Ferroelectric relaxors, Conducting polymers, NMR line shape, Disorder, Local polarization related to the line shape, Symmetric/asymmetric quadrupole-perturbed NMR, H-bonded systems, Spin-lattice relaxation, Edwards-Anderson order parameter, Dimensionality of conduction, Proton, Deuteron tunnelling. 

NMR measurements in these systems have allowed for the following. A determination of the local-polarization distribution function W(p) and the Edwards-Anderson order parameter qEA in the weak substitutional disorder limit (x=0.5) ongoing through Tc. The results showed that W(p) is asymmetric below Tc and symmetric above Tc and that qEA makes a discontinuous jump on going through Tc in view of first-order nature of this transition. 

Dimensional (ID) NMR, using line shape, estimating the Edwards-Anderson parameter ijEA, is applicable to systems, on the time scale of the order 10 3-10 8 s and this method fails for the direct determination of gEA on longer time scales. 

Line shape studies of 7Rb and deuteron NMR lines have thrown more light on the frustration in the system. Blinc et al.5 have shown clearly the measurement of second moment can be related to the Edwards-Anderson spin-glass order parameter in the glass phase. 

Blinc et al.4 in a classic paper on the NMR line shapes in PGs have presented the relation between the RF distribution and the quadrupole-perturbed NMR line shape for both first-order and second-order quadrupole effects. Static as well as time fluctuating RFs have been considered. By evaluating the local RF distribution, Blinc et al.4 have evaluated the Edwards-Anderson (qEA) order parameter. 

The Edwards-Anderson spin-glass order parameter is defined as32... 

It is not clear, whether the experimentally observed random local freezing of the deuterons in the O-D—O bonds in deuteron glasses corresponds to a true thermodynamic phase transition or whether one deals with a dynamic phenomenon which only seems static because of the finite observation time of the experimental techniques. The recently observed42 splitting between the field-cooled and zero-field dielectric susceptibilities below an instability temperature Tf seems to speak for the occurrence of an Almeida-Thouless-like thermodynamic phase transition in deuteron glasses. It is well known that ID NMR and EPR allow a direct measurement of the Edwards-Anderson order parameter qEA only on time scales of 10 3-10 8 s and 2D exchange NMR possibly seems to be a better technique for such slow motions. 

The detail of the Doi theory can be refered to in the book by Doi and Edwards The Theory of Polymer Dynamics (1986) in which the Leslie coefficients are related to the order parameter and the isotropic viscosity fj as follows... 

Figure 6.12. Miesowicz coefficients of liquid crystalline polymers against order parameter. (From Doi and Edwards, 1986.)...

The relations are shown in Figure 6.12 where the Miesowicz viscous coefficients are plotted as a function of the order parameter of long rods in solution. The Doi and Edwards theory gives the order parameter vs. the concentration shown in Figure 6.13, in which the order parameter starts at... 

Although the Swain equation made a very important contribution, it led to some confusion because it was originally applied to all types of reactions including alkylation, acylation, and sulfonylation. The nucleophilic order is highly dependent on the nature of the substrate, and the equation was modified in the Swain-Edwards four-parameter equation (7). 

The coil conformation in a good solvent is characterized by a low density of segments, and fluctuations of segment density (as the order parameter of the system) must play a large role. Indeed, in the self-consistent field approximation, Edwards, actually, has arrived at results similar to Flory s approximation (see Equation 3.1-216). 

A similar difficulty occurs when we compare polymer solutions with magnets. In a formal sense, the order parameter is the magnetization of a spin system with a number of spin components n = 0. This does not help very much. A more concrete statement, based on ideas of S. F. Edwards, is the following the ordv parameter r) for a polynto- solution is similar to a quantum mechanical creation (or destruction) operator." A factor if[Pg.288]

In conclusion these measurements again have indirectly shown the presence of a wide spectrum of relaxation times near the spin-glass temperature (Murani 1981). The elastic magnetic scattering in the cross-section, eq. 57, of neutron scattering is formally related to the Edwards-Anderson order parameter... 

In spin glasses critical behavior near Tj is not expected in the linear term of the susceptibility M/H, but in the nonlinear susceptibility This is known from mean-field theory of spin glasses (Suzuki 1977) where the order parameter is not the magnetization but the quantity = S, [(5,) ] as suggested by Edwards and Anderson in 1975 (see sec. 4). Then, the field conjugate to the order parameter q is in spin glasses (instead of H which is coupled to the order parameter A/ in a... 

About the same time Beutier and Renon (11) also proposed a similar model for the representation of the equilibria in aqueous solutions of weak electrolytes. The vapor was assumed to be an ideal gas and < >a was set equal to unity. Pitzer s method was used for the estimation of the activity coefficients, but, in contrast to Edwards et al. (j)), two ternary parameters in the activity coefficient expression were employed. These were obtained from data on the two-solute systems It was found that the equilibria in the systems NH3+ H2S+H20, NH3+C02+H20 and NH3+S02+H20 could be represented very well up to high concentrations of the ionic species. However, the model was unreliable at high concentrations of undissociated ammonia. Edwards et al. (1 2) have recently proposed a new expression for the representation of the activity coefficients in the NH3+H20 system, over the complete concentration range from pure water to pure NH3. it appears that this area will assume increasing importance and that one must be able to represent activity coefficients in the region of high concentrations of molecular species as well as in dilute solutions. Cruz and Renon (13) have proposed an expression which combines the equations for electrolytes with the non-random two-liquid (NRTL) model for non-electrolytes in order to represent the complete composition range. In a later publication, Cruz and Renon (J4J, this model was applied to the acetic acid-water system. 

Second-order rate constants for the reactions of phenacyl bromide with a number of anionic or neutral nucleophiles in 3 2 (v/v) acetone-water have been measured at several temperatures.141 Correlation analysis with the Bronsted equation or Swain-Scott equation is not satisfactory. Better results were obtained with the two-parameter Edwards equation. 

Arrhenius parameters for the Ist-order step (1) were reported as A = 2.3 x 10 sec", = 51.4 kcal.mole the activation energy for step (2) was estimated to be 15 kcal.mole" ( 3 0). In a similar study at 533-750 °C Edwards and Small , however, reported somewhat different parameters for steps (1) and (2), viz., Ai = 6.9 X 10 sec , 1 = 55.79 kcal.mole and A2 = 2.2x 10 l.mole. sec , 2 = 6.21 kcal.mole . Edwards and Small also estimated Arrhenius parameters for the dissociation of perfluoroethylene to difluorocarbene these were = 4.6x 10 sec", = 70.36 kcal.mole". Panshin examined the decomposition of difluorochloromethane in a flow system at 598-702 °C using a surface conditioned quartz vessel and obtained Arrhenius parameters for step (1) in substantial agreement with those of Edwards and Small 4 = 1.8 x 10 sec", = 55 kcal.mole". Carrier gases used were helium, toluene and carbon tetrachloride. The rate of decomposition was found to be similar to that for chloro-... 

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