Conductance fluctuations

These quantum effects, though they do not generally affect significantly the magnitude of the resistivity, introduce new features in the low temperature transport effects [8]. So, in addition to the semiclassical ideal and residual resistivities discussed above, we must take into account the contributions due to quantum localisation and interaction effects. These localisation effects were found to confirm the 2D character of conduction in MWCNT. In the same way, experiments performed at the mesoscopic scale revealed quantum oscillations of the electrical conductance as a function of magnetic field, the so-called universal conductance fluctuations (Sec. 5.2). 

Typical magnetoconductance data for the individual MWCNT are shown in Fig. 4. At low temperature, reproducible aperiodic fluctuations appear in the magnetoconduclance. The positions of the peaks and the valleys with respect to magnetic field are temperature independent. In Fig. 5, we present the temperature dependence of the peak-to-peak amplitude of the conductance fluctuations for three selected peaks (see Fig. 4) as well as the rms amplitude of the fluctuations, rms[AG]. It may be seen that the fiuctuations have constant amplitudes at low temperature, which decrease slowly with increasing temperature following a weak power law at higher temperature. The turnover in the temperature dependence of the conductance fluctuations occurs at a critical temperature Tc = 0.3 K which, in contrast to the values discussed above, is independent of the magnetic field. This behaviour was found to be consistent with a quantum transport effect of universal character, the universal conductance fluctuations (UCF) [25,26]. UCFs were previously observed in mesoscopic weakly disordered... 

So, despite the very small diameter of the MWCNT with respeet to the de Broglie wavelengths of the charge carriers, the cylindrical structure of the honeycomb lattice gives rise to a 2D electron gas for both weak localisation and UCF effects. Indeed, both the amplitude and the temperature dependence of the conductance fluctuations were found to be consistent with the universal conductance fluctuations models for mesoscopic 2D systems applied to the particular cylindrical structure of MWCNTs [10]. 

In conclusion, wc have shown the interesting information which one can get from electrical resistivity measurements on SWCNT and MWCNT and the exciting applications which can be derived. MWCNTs behave as an ultimate carbon fibre revealing specific 2D quantum transport features at low temperatures weak localisation and universal conductance fluctuations. SWCNTs behave as pure quantum wires which, if limited in length, reduce to quantum dots. Thus, each type of CNT has its own features which are strongly dependent on the dimensionality of the electronic gas. We have also briefly discussed the very recent experimental results obtained on the thermopower of SWCNT bundles and the effect of intercalation on the electrical resistivity of these systems. 

Gibson, C. H. and W. H. Schwarz (1963a). Detection of conductivity fluctuations in a turbulent flow field. Journal of Fluid Mechanics 16, 357-364. 

The transformations (286) allow one [118,119] to calculate the effective galvanomagnetic properties of a 2D inhomogeneous medium when conductivity fluctuates only, and the Hall factors of the components are equal that is, cti / c>2, Pi = p2. If we apply complementarity—that is, in the first phase (cr. p ) we have cr = cr2. p = — p2, and in the second phase (a2, p2) we have a a. p = — pj—then we shall obtain the following results for the effective Hall properties ... 

A noise that has a clearly distinct origin from noise discussed in previous sections is the electric noise that originates in modulation of ion transport by fluctuations in system conductance. These temporal fluctuations can be measured, at least in principle, even in systems at equilibrium. Such a measurement was conducted by Voss and Clark in continuous metal films (44). The idea of the Voss and Clark experiment was to measure low-frequency fluctuations of the mean-square Johnson noise of the object. In accordance with the Nyquist formula, fluctuations in the system conductance result in fluctuations in the spectral density of its equilibrium noise. Measurement of these fluctuations (that is, measurement of the noise of noise) yields information on conductance fluctuations of the system without the application of any external perturbations. The samples used in these experiments require rather large amplitude conductance fluctuations to be distinguished from Johnson noise fluctuations because of the intrinsic limitation of statistics. Voss and... 

Clark (44) reported successful measurements for a InSb bridge with relative fluctuations as large as SG(f)/(G)2 = 10 1 Hz-1 at 10 2-Hz frequency. Here G is conductance of the sample and Sc(f) is spectral density of conductance fluctuations. 

In biological ionic systems, conductance noise is induced by membrane structures such as ion channels and fluctuations in electrolyte conductance. Noise that originates from the switching of ion channels between different conductance states has been reviewed extensively (3-9). Therefore, we limit ourselves to a discussion of conductance fluctuations in electrolyte solutions (45) and new noise sources that have been identified recently for currents through open ion channels (46, 47). 

An excellent review of the early history of noise studies of different ionic systems, such as single pores in thin dielectric films, microelectrodes, and synthetic membranes, is reference 3. The review by Weissman (48) describes several state-of-the-art fluctuation spectroscopy methods that include (1) determination of chemical kinetics from conductivity fluctuations in salt solutions, (2) observation of conductivity noise that arises from enthalpy fluctuations in the electrolyte with high temperature coefficient of resistivity, and (3) detection of large conductivity fluctuations in a binary mixture near its critical point. 

Fluctuation phenomena in ionic solutions are a subject of growing interest (49-51). However, for several reasons (48), experimental approaches to studies of conductance fluctuations in liquid phase samples are not as well established as those in the solid state. Strong electric fields that are used to measure conductance fluctuations (to produce noise in excess of the Johnson noise) cause pronounced electroosmotic and electrophoretic complications. As a result, the measurements of conductance fluctuations are usually made with a significant uncertainty factor (cited as 0.4 in reference 52). 

A method of large-scale conductance fluctuation measurements in flowing ionic solutions was developed (21) recently to measure the space average squared value of these fluctuations with an accuracy of several percent. This... 

This ideal gas behavior" of conductance fluctuations appears to be rather unaccountable. First, electrolyte solutions are systems with pronounced interactions that are attributable to a slow decrease of Coulomb forces between ions this brings about substantial correlation between mutual positions of ions in space. Second, even in the hypothetical case of weakly interacting charge carriers, the conductance fluctuation level is expected to be equal to the value calculated from the total number of carriers only when the mobilities of different carriers are identical. Indeed, substantial difference in mobilities, say for a 1 1 electrolyte, forces lower mobility carriers to be electrically invisible and, thus, the conductance fluctuations must be normalized only to ion species with higher mobility that is, to the total number of dissolved molecules. Figure 3 shows that this conclusion contradicts the HCl electrolyte experiments in which the mobility of cations is almost five times as large as that of anions. Nevertheless, the level of... 

Figure 3. Large-scale conductance fluctuations in aqueous solutions of several strong electrolytes measured by the laminar flow method vs. electrolyte concentration (45). The upper solid line shows the inverse total number of dissolved electrolyte molecules in the sample (that is, in solution volume confined by a fused quartz capillary channel of 13-pm radius and 0.4-mm length). The middle and lower lines correspond to inverse total numbers of ions for 1 1 and 2 1 electrolytes. At small electrolyte concentrations the fluctuation level is within several percent of the inverse number of ions independent of...

A generalization of the classical result of Lax and Mengert (53) to the case of multicharge ions and combined systems demonstrates that just because of the long-range Coulomb forces between ions, the conductance fluctuation level in dilute simple electrolytes must be normalized to the total number of ions regardless of the electrolyte type and ion mobility difference (45). However, this condition does not hold for complex electrolytes or electrolyte mixtures that contain more than one type of cation or anion. If the mobilities of different types of ions of the same sign are not equal, the fluctuation level would increase so that normalization to the total number of ions in the sample would fail. 

Figure 4. Mixtures of NaCl and HCl electrolytes show higher conductance fluctuations than individual electrolytes (45). The sample composition changes from pure NaCl solution (Kh = 0.0J to pure HCl solution (KH = 1.0) the total number of ions is held constant. Experimental points for pure electrolytes are in good agreement with the inverse number of ions in the capillary.

Indeed, much higher levels of conductance fluctuations were reported for electrolytes that contain polystyrene latex suspensions (21) or micellar colloids (22). Fluctuations were shown to depend on concentration, characteristic size, and the charge of colloid particles. For uncharged nonconductive spherical particles that occupy volume fraction F of the total sample volume... 

V, excess conductance fluctuations were in agreement with the expression... 

The effect of added foreign-phase dispersions on the excess noise in electrolytes was studied (21, 22). From relation 15 of Bezrukov et al. (21), it follows that the mean-square value of the relative conductance fluctuations that originate from nonconducting contaminants does not depend on the electrolyte concentration. Hence, to present the results of the excess noise measurements in the form of Hooge s formula, with the samples equally contaminated on the average, the parameter a must be taken to be proportional to the electrolyte concentration. 

Flicker noise has long been a nuisance in measurements of the spectral density of conductance fluctuations in experiments with biological membranes. In 1973, Fishman measured the differential voltage noise spectra of a native membrane and a membrane whose potassium conductance has been blocked with tetraethylammonium. The differential spectrum he obtained fitted well... 

Note that at fixed current values the voltage fluctuations are substantially equivalent to conductance fluctuations. For potassium channels similar measurements showed that the potassium conductance spectrum can be represented as a sum of the flicker and Lorentzian conponents. However, the fcidifferent systems and techniques involved. 

EIM, prepared from bacterially desugared egg-white, when incorporated in lipid bilayers, produces membranes which show complex voltage-dependent conductance changes, the so-called bilayer action potentials [30]. Furthermore, discrete conductance fluctuations can be observed with appropriate conditions [31]. 

Analysis of melittin-induced conductance fluctuations suggests perturbations of the lipid bilayer structure, and formation of structural channels. Addition of pronase to the trans-side in the presence of a trans-negatiwe membrane potential abolished the conductance as it did when added to the cis side. This implies that the conducting state of melittin requires a trans-membrane configuration. In a non-conducting absorbed state a hydrophobic loop, with the region from threonine-9 to proline-13 as the likely site of the turn, penetrates the lipid but does not extend across the membrane. In the conducting state the turn becomes extended as the peptide assumes a rra w-bilayer position. 

F. Conti, B. Neumcke, W. Nonner, and R. Stampfli, Conductance Fluctuations from the Inactivation Process of Sodium Channels in Myelinated Nerve Fibres, J. Physiol 308, 217-239 (1980). 

The root. i simply indicates that infinite distances are correlated with infinite time, S2 is the reciprocal of the Debye relaxation time, and 3 is the kinetic relaxation frequency of the system. Depending on the kinetic parameters of the chemical process, the kinetic relaxation frequency can be faster or slower than the Debye frequency of the system. If the kinetic relaxation frequency is much smaller than the Debye mode, it can be determined experimentally by conductance fluctuation analysis. 

Neher, E. Stevens, C. F. (1977). Conductance fluctuations and ionic poses in membranes. Ann. Rev. Biophys. Bioeng., 6, 345-81. 

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