Index decoupling

A method of characterising transport mechanisms in solid ionic conductors has been proposed which involves a comparison of a structural relaxation time, t, and a conductivity relaxation time, t . This differentiates between the amorphous glass electrolyte and the amorphous polymer electrolyte, the latter being a very poor conductor below the 7. A decoupling index has been defined where... 

In this case it is the silver cation that can slip through the channels set up by the alkali halide sublattice [35]. These systems can retain their high conductivity in the glassy state, as illustrated in the case of the silver-alkaU halide system in Figure 2.4b. For such systems a decoupling index has been defined from the ratio of the conductivity and fluidity relaxation times [32, 36], which can equally well be defined from the exponent a in the fractional Walden rule. 

Figure 6.12. Dependence on lithium mole fraction of (a) conductivity and activation energy, (b) glass transition temperature and (c) decoupling index in LiF-Pbp2-A1(P04)3 glasses. (After Kulkami and Angell, 1988)...

Decoupling index is thus a dimensionless measure of the looseness of the glassy ionic conductor. 

CdO and smaller amounts of CdCU, YF3 and LaFs). The modulus relaxation spectrum has been fitted to stretched exponential function and it has been found that p has a roughly constant value in the glassy state and above Tg, it decreases rapidly. Since decoupling index also decreases rapidly above the glass transition temperature, it is suggestive of an implicit relation between and / . It is also noted that Rr Tg itself is inversely correlated to the corresponding p values and P decreases linearly with log at Tg (also see Hunt, 1994)... 

Further, as noted in chapter 6, (FIC glasses) Rt is very high and of the order of lO -lO " since ojc is very high. The decoupling index therefore is directly related to the differences in the behaviour of shear and conductivity relaxation times. Since both shear viscosity and conductivity obey the VTF equation, of the form,... 

Figure 7.12. Correlation of nonexponentiality parameter P of Kohlrausch function with decoupling index R, for a variety of ionic glasses (After Angcll, 1990).

Glassy and polymer electrolytes may be considered as liquids and AngelF has defined a decoupling index J , as the ratio of mechanical (viscosity tf) and electrical relaxation time i , = For some ionic... 

Equation [3.7] correlates conductivity with ionic diffusion and electrolyte viscosity. Since the Nernst-Einstein equation [3.8] gives the relationship between conductivity and diffusion and since the right-hand side of equation [3.7] is obtained by combining equations [3.6] and [3.8], the decoupling index R, is basically a measure of the effect of viscosity on conductivity. 

Angell [50] proposed the so called decoupling index model by introducing an index defined as the ratio of two relaxafion times ... 

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