Curie spin

The Curie spin relaxation is also called magnetic susceptibility relaxation. Vega and Fiat (52) have also considered the Curie spin relaxation originating from anisotropic magnetic susceptibility, rather than an isotropic one as assumed in Eqs. (21-23). 

Fig. 3.13. Field dependence of the Curie spin relaxation contributions to R u and R2M (arbitrary scale) zr = 2 x 10 9 s.

Once R m and Rim have been measured, it is useful to try to understand the relative weight of dipolar, contact, and Curie spin contributions to the overall relaxation effect. Indeed, each of the three contributions is independently capable of providing valuable information whereas the whole value may not. The dipolar and Curie relaxation mechanisms — Eqs. (3.16), (3.17), (3.29) and (3.30) —... 

Under these conditions the Curie spin contribution is always negligible (see Section 3.6). If rcdip = rccon it is only necessary to compare the following two expressions ... 

No explicit temperature dependence is included in the equations for R m and Rim, except for cases where Curie spin relaxation is the dominant term (Section 3.6). In the latter case, Curie paramagnetism has a T x dependence and therefore relaxation depends on T 2. The effect of temperature on linewidths determined by Curie relaxation is dramatic also because of the xr dependence on temperature, as shown in Eq. (3.8). All the correlation times modulating the electron-nucleus coupling, either contact or dipolar, are generally temperature dependent, although in different ways, and their variation will therefore be reflected in the values of Rim and Rim-... 

When tr is unknown, it can be adjusted together with re and r by using non-linear least-squares fits of eqs. (15), (16) as similarly described for the treatment of NMRD profiles (Bertini et al., 1995 Ruloff et al., 1998 Toth et al., 1998), but a much simpler approach considers that both dipolar and Curie-spin contribution depend on r 6. When a nucleus for which the / -nucleus distance rref can be estimated either from crystal structure or gas-phase modeling is used as a reference, eq. (15) reduces to its simplest form (eq. (18)) and relative /Gnucleus i distances are accessible without estimations of re and rr (Barry et al., 1971 ... 

Isostructurality along the complete lanthanide series has been ultimately confirmed by relaxation measurements. For the bimetallic complexes [B2(L14-2H)3], each nucleus undergoes the sum of two dipolar and two Curie-spin paramagnetic contributions to their longitudinal relaxation rate. Thus eq. (18) is no longer valid and must be replaced with eq. (70) which takes into account the effect of the two paramagnetic centres (fig. 54, Elhabiri et al. (1999)),... 

A development in the theory of nuclear relaxation in macromolecules by paramagnetic ions has been suggested by Gueron. (675) In the case of heme proteins there is a net polarization of the iron electronic spin magnetic moment which is oriented along the direction of the magnetic field. Modulation of this dipolar field due to the spin polarization (Curie spin) by rotational diffusion introduces an additional term into the expression for transverse relaxation [equation (18)] giving ... 

The first term is the Curie spin term and the second term the usual dipolar expression. It follows that the Curie spin linewidth contribution should exhibit a field dependence of Bq and a temperature dependence of Since for Brownian diffusion ... 

In trat)s-VA, the Curie spins attributable to the neutral soliton rapidly decrease upon doping through conversion of the netural solitons to the charge solitons [168,206,211,214-216], whereas the Pauli susceptibility remains very small for values up to several % of the dopant concentration and then abruptly increases to approach about )(p 3 x 10 emu/molc C or N( i ) 0.1 states/eV C as found in Figure 6.42 for a variety of dopants AsFe [167,168,217] [206] ... 

In the case of c/T-PA. the number of Curie spins shows a peak around 1 mole % of doping due to the sum of increasing and decreasing contributions [232]. The increase results from doping induced cix-to-trans isomerization that produces the neutral solitons and the decrease results ftom the conversion of the neutral solitons to the charged solitons. 

It is known that water molecules in PANl enhance the electrical conductivity several-fold [312]. Kahol el al. demonstrated that magnetic properties of PANl and its derivatives protonaled by HCI are affected by heat treatment to remove water molecules from the sample [2,313-315]. They found a conversion of the Pauli-like spins to the Curie spins upon heating below 100°C, causing removal of the water molecule from the polymer, and de-doping of HCI well above 100 C, resulting in a steep decrease in both the Pauli and Curie spins [313,314]. 

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