Soliton diffusion

Finally H NMR 77h in (mni -NT-PA is mentioned briefly. The anisotropy pattern of H NMR T h in (roti.s-S-PA has been reported to be basically understandable with neutral soliton diffusion [62]. Does it hold even for (ro .f-NT-PA The angular dependence of 7]]j is shown in Figure 6.14 [24]. It is noteworthy that the depression around > = 90° is deeper than that in b-atu-S-PA and the origin of such a depression cannot be expected firom the diffusion mechanism of the neutral solitons as depicted by the solid curve B in Figure 6.14. To account for such a depression by another mechanism, spectral diffusion and localized. spins as described in (6.18) (see, [8] p. 379) [8,83] it is... 

Figure 6.14. The H NMR 7]]) in trans-NT-PA as a function of the angle / at 50 MHz ]24]. The solid curve A is a total of the three parts, B, C and the isotropic one. B is the neutral soliton diffusion mechanism via modulation of the dipolar, the hyperfine and their cross-couplings. C is the localized spin -E spectral difrusion mechanism [8,83], The straight line is the isotropic contribution.

Problem (2) is that the spin-lattice relaxation rate of C NMR, 77c. should obey (6.14) as H NMR 77,j does, if the neutral soliton diffuses whole the sample. To investigate a role of spin flip/flop diffusion through H and C Scott and Clarke have measured 77] and 77c ll samples enriched by various ratios of C to D ( ) 98 0 (2) 90 98 and (3) 20 98 [152]. They observed ... 

Finally, they proposed a model to account for together with T h that only 1/30 of the chains carry one neutral soliton and that the nuclear magnetization flows to a cylindrical relaxation core due to a soliton diffusion, through the nuclear flip/flop diffusion. An interpretation of the above observations with this model is as follows. On H NMR T]]] it is reasonable that the non-deuterated sample (l)(98/0) shows /y/w dependence due to the soliton diffusion, but not for the fully deuterated samples (2)(90/98) and (3)(20/98) in which the flip/flop diffusion rate of H is slower than a sink rate of the relaxation cores. On C NMR a situation is more complicated. In the samples (l)(98/0) and (3)(20/98), the observed frequency independency... 

Fig. 5. Temperature dependence of effective spin-lattice Tj and spin-spin Ti relaxation times calculated from Eqs. 8 as well as of intrachain and interchain diffusion rates calculated from Eq. 10 for neutral solitons diffusing in trans-PA along and between randomly oriented chains and chains oriented with their c-axis with respect to an external magnetic field by / = 90°, 60°, 30°, and 0°. [From Refs. 12(b) and 61 with permission.]...

Fig. 5 displays the temperature dependencies of the Did and coefficients calculated for the soliton diffusion in trans-PA with randomly oriented and partly stretch-oriented chains. This figure shows that, as in the case of relaxation parameters, both the ID and 3D diffusion rates are sensitive to the orientation of the polymer chains in an external magnetic field due to soliton diffusion in this QID system. The DiD(t /) function for an oriented sample is opposite to the D3d( /) one. Since the main c-axes are arbitrarily oriented in an initial trans-PA, these values are averaged over angle /. Moreover, the averaged Did value is well described by the equation = D d cosV + Djd sinV. where Dj -q and D"d are the extremes of the Did(i /) function. Thus, D] -d D]d inequality displays spin delocalization over soliton sites equal to VDid / analysis of the data presented in Fig. 5 gives Ns(T) oc r °... 

Figure 6 exhibits the conductivity due to intra- and interchain soliton diffusion in slightly iodine-doped trans-PA. The intrachain charge transfer was analyzed in terms of phonon-assisted spin hopping between soliton sites, in the framework of the Kivelson phenomenological model, with predicted conductivity... 

As single crystals are not available in conducting polymers, the use of the spin echo technique is more complicated and interpretation of the data is quite model-dependent. However, electron spin echo studies of spin dynamics in polyacetylene were reported in the early 1980s [30]. The results on the soliton diffusion rate, which were not consistent with those obtained by the other methods, gave rise to a long controversy. They were recently carefully discussed and invalidated [31]. 

It is noteworthy that these spin dynamics studies, leading to fully convergent results, were performed independently in Grenoble and in Tokyo. Let us mention that a controversy concerning the value of the soliton diffusion coefficient took place in the 1980s. In contrast to the high value found by the Grenoble and Tokyo... 

Not only are the solitons highly mobile, but in addition the motion is highly one-dimensional. Since Ti" throughout the experimental frequency range, the cutoff frequency is smaller than the smaller frequency used, that is, < 6 x 10 rad/s. Estimates of Wc have been obtained from Tip measurements (wc 4.5 x 10 rad/s), from the residual (diffusive) ESR linewidth (Wf 3 X 10 rad/s) [25], and from the data of AH versus (o [o>c (6-8) X 10 rad/s] [57]. The cutoff frequency (i)c is an upper limit for the transverse diffusion rate D , but that may be due to another process more efficient than transverse soliton diffusion. The interchain electronic dipole-dipole interactions are large enough to account for the observed o)c- In fact, owing to the actual nature of the soliton-like species, namely (CH), seg-... 

Fig. 5.10 Temperature dependence of the soliton diffusion coefficient in /roAj -polyacetylene from NMR data obtained in Grenoble ( ) and ESR data obtained in Tokyo (O). Theoretical results (by Jeyadev and Conwell [67]) for phonon scattering only (dashed line) and for phonon scattering plus barriers of 0.01 eV (solid line).

The linear and nonlinear optical properties of the conjugated polymeric crystals are reviewed. It is shown that the dimensionality of the rr-electron distribution and electron-phonon interaction drastically influence the order of magnitude and time response of these properties. The one-dimensional conjugated crystals show the strongest nonlinearities their response time is determined by the diffusion time of the intrinsic conjugation defects whose dynamics are described within the soliton picture. 

It is conceivable that diffusion of kinks, or overdamped solitons, along the DNA could act to relax the FPA with a time dependence similar to that predicted for torsional deformation/31 32) High levels of intercalated dyes would be expected to alter both the equilibrium population of kinks and their mobility along the DNA. Hence, this question is addressed by examining the effect of intercalating dyes on the torsional dynamics. 

Measurements of diffusion of neutral solitons have been made using the electron spin resonance (ESR) and the nuclear magnetic resonance (NMR). An unambiguous interpre-... 

Fig. 2.7. Intrachain diffusion coefficient of solitons in the t-PA versus temperature. The closed circles are the data from Ref. [24] and the open circles from Ref. [26], The dashed curve shows the results of theoretical calculations including only the phonon scattering and the solid curve shows the calculated value including 0.01 eV barriers [23].

Fig. 2.8. Intrachain mobility of solitons in the t-PA calculated using the values of the diffusion coefficient given in Fig. 2.7 and the Einstein relation given in Eq. (2.10). Labeling of the curves and the symbols are the same as in Fig. 2.7 [25],...

Furthermore, quantitative characterizations of the spin motion in trans-(CH) have been performed by measurements of the proton NMR relaxation time 7 and analysis of the ESR line width [70,71]. The spin motion can be described in terms of highly one-dimensional diffusion. The diffusion rate along the chains is very fast D[ 1013 rad/s (i.e., a diffusion coefficient of ca. 5 x 10 3 cm2/s), and the anisotropy is extremely high Z>j /Z>x > 105. The very high anisotropy is also an argument for the soliton picture neutral... 

This is not sufficient, however. In several cases of practical interest, charge transport has the characteristics of a thermally activated hopping process the importance of the diffusion of localized (soliton or polaron) states is elusive and band conduction seems to be an idealization. The description of transport phenomena in polymer materials will therefore require a thorough characterization of the structure in both crystalline and disordered ( amorphous ) regions, and a detailed picture of how these are dispersed and interconnected. 

On the dynamics of the neutral soliton, in 1980 Nechtschein and co-workers have demonstrated the evidence for the rapid diffusion of the neutral soliton along a one-dimensional chain from the observation of the pure Overhauser effect (OE) in trans-PA using a dynamic nuclear polarization (DNP) experiment and from the l/v frequency dependence of the H NMR spin-lattice relaxation rate 7Yil [143]. These observations give quantitative estimations that the pure OE implies the condition T (iJc 10" rad/s for the... 

Good evidence for the rapid motion and trapping of the soliton is demonstrated by a DNP experiment as shown in Figure 6.30 [146,173]. The dynamic nuclear polarization (DNP) experiments are carried out at 9 GHz between 1.5 and 300 K in cis [143,174] and irons PA [143,145,146,173,174]. At room temperature the pure Overhauser effect (OE) was observed in a -irans-PA without air or oxygen but a mixed solid state effect (SSE) together with OE was found in c/s-rich PA without air [143,174] and al -lrans-PA with air [146]. In particular, below 150 K, the mixed effect was observed, even in a -trans-PA without air [145,173], The OE is characteristic of dynamic interaction between nuclear spins and electron spins, with rapid motion, On the other hand, the SSE is of the static interaction between them. In other words, observation of the pure OE is clear evidence for the electron spin for motion with an inverse of the correlation time comparable with or larger than Wj,. At 300 K, the pure OE observed in all-/ra s-PA, is consistent with the conclusions for the neutral soliton to diffuse rapidly compared with 1/We as concluded from the ESR linewidth narrowed by motion [53] and the proton NMR 7Y ] [143] as a function of frequency over a broad range. 

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