Transverse correlation length

T — Tmf, while the expansion of this energy in terms of q — x determines4) the longitudinal and transverse correlation length, f0 and f ox, respectively. 

The symmetric limit corresponds very probably to the BCS superconductivity in the conducting polymer24 (SN)X. It seems that there the ratio of the longitudinal and transverse correlation lengths is temperature independent, as in Equ. (45). 

Depending on the strength of the interchain couplings, we have to distinguish the situations in which the unrenormalized transverse correlation lengths are either larger or smaller than the corresponding interchain distances. 

A new transversal correlation length is established at about 37 % strain. By shearing the lamellar blocks break down to a size which later represents the dimensions of the fibrils. According to the relatively low internal mobility the aligned chains are not able to form new crystallites. Their mean dimension in transversal direction is with 8.4 nm clearly below the lamellar thickness. This correlates with the WAXS results, which also indicate the final disappearance of the lamellar transversal order during cold drawing. Ultimately, at high strains, this transversal correlation dominates the whole CDF. 

The transverse correlation length, has also been measured for HAB by fitting the equatorial intensity profile of the wide-angle intermolecular peak I(Q) to a Lorentzian lineshape [21] ... 

FIGURE 8 Transverse correlation length as a function of temperature fw HAB obtained from the equatorial peak profile of X-ray (filled circles) and neutron (filled squares) scattering. From [21] with permission. 

Figure 7. Isometric map of iujectant cor centratiou tor a case with large correlation lengths and no diffusioii. The longitudinal direction (parallel to flow) is x the transverse direction (perpendicular to flow) is y. Concentration gives the appearance of layering even though there are none present. (Reproduced from Refo. )...

The situation in TTF-TCNQ is potentially much richer than that in KCP. Transverse correlations in this material are probably considerably, stronger in one than in the other of the two transverse directions. This can lead to a complicated 3—2 — 1 dimensional cross-over for n — 2. Empirically2 , however, the fluctuation tails do not seem to be as large in this material as they are in KCP. It might well be that the structural transition in TTF-TCNQ falls into the symmetric limit, with only the fluctuations enhanced. It would be interesting therefore to have more data about the temperature behaviour of all three, or at least of two correlation lengths. 

Correlation length, longitudinal (parallel to n) (Jn = transverse (perpendicular to n) ... 

Li and Olsen [14] were the first to perform such calculations. They calculated spatial correlations from ensembles of instantaneous velocities fields for flows in square microchannels and defined turbulent length scales in the streamwise and transverse directimis as the distance it takes normalized spatial correlations of streamwise velocity correlations to drop to 0.5. These correlation lengths in the streamwise and transverse directions were called Lxuu and Lyu , respectively. A comparison of these microchaimel correlation lengths normalized by microchannel width, W, and correlation lengths for macroscale chaimels [15] are shown in Table 1. Excellent agreement was observed between the microscale... 

Figure 4. Longitudinal ( n) and transverse (ijj correlation lengths as a function of the reduced temperature for 8CB (n-octylcyanobiphenyl). The solid lines are least-squares fits to single power laws corresponding to V =0.67 0.02 and Vj =0.51 0.04 (after [39]).

Boundary layer similarity solution treatments have been used extensively to develop analytical models for CVD processes (2fl.). These have been useful In correlating experimental observations (e.g. fi.). However, because of the oversimplified fiow description they cannot be used to extrapolate to new process conditions or for reactor design. Moreover, they cannot predict transverse variations In film thickness which may occur even In the absence of secondary fiows because of the presence of side walls. Two-dimensional fully parabolized transport equations have been used to predict velocity, concentration and temperature profiles along the length of horizontal reactors for SI CVD (17,30- 32). Although these models are detailed, they can neither capture the effect of buoyancy driven secondary fiows or transverse thickness variations caused by the side walls. Thus, large scale simulation of 3D models are needed to obtain a realistic picture of horizontal reactor performance. 

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