Transport frequency response technique

More recently, essentially the same technique as proposed by Hermann et al. [944,945], viz. FTIR microscopy (Fourier transform micro-IR spectroscopy on single crystals), and by Mirth and Lercher [815], was successfully employed by Zhobolenko and Dwyer [949], who determined the transport diffusivities of a number of hydrocarbons (benzene, toluene, p-xylene, cyclohexane) in sili-calite-1 in different crystallographic directions. No significant differences of the diffusivities in the straight and sinusoidal channels of the structure were found (cf. Fig. 54), at remarkable variance to results reported by Rees et al., who used the frequency response technique [950] and found significant differences for the diffusion coefficients in both types of channels, viz. one order of magnitude smaller ones for the sinusoidal than for the straight channels. 

Figure 13 displays the self-diffusivities of n-hexane and 2-methylpentane in silicalite-1 and H-ZSM-5 as a function of the ratio of the hydrocarbons. The self-diffusivities of both hexanes linearly decrease with increasing gas-phase fraction of the branched hexane in the gas phase for the non-acidic and acidic zeolite. In H-ZSM-5, the mobility of alkanes is approximately two times slower than in silicalite-1. Obviously, the presence of acid sites strongly affects the molecular transport due to stronger interactions with the n-hexane molecules. A similar effect of Bronsted sites on the single component diffusion of aromatics was observed in MFI zeolites with different concentration of acid sites [63-65]. The frequency response (FR) technique provided similar results... 

Spectral spin diffusion in the solid state involves simultaneous flipflop transitions of dipolar-coupled spins with different resonance frequencies 11,39,63-76], whereas spatial spin diffusion transports spin polarization between spatially separated equivalent spins. In this review we deal only with the first case. The interaction of spins undergoing spin diffusion with the proton reservoir provides compensation for the energy imbalance (extraneous spins mechanism) [68,70,73,74]. Spin diffusion results in an exchange of magnetization between the nuclei responsible for resolved NMR signals, which can be conveniently detected by observing the relevant cross-peaks in the 2D spin-diffusion spectrum [63-65]. This technique, formally analogous to the NOESY experiment in liquids, is already well established for solids and can also be applied to the study of catalysts. 

Here we refer to a class of techniques where the response of a system to small, periodic modulations of the driving force is studied as a function of the frequency of the disturbance. These give the same information as time-domain studies but without the need for large amplitude disturbances. This is particularly useful for dye-sensitized - and for a wide range of complex systems - because the optical and electronic response is nonlinear in n, and therefore diffusion coefficient and recombination times are not constants. The use of small modulations permit linearization of the transport problem, and yields effective diffusion and recombination parameters, which can be related to the injection level through the underlying steady state driving force. 

We will distinguish various modes. The techniques most widely used in DSSCs are intensity modulated photocurrent spectroscopy (IMPS) which is, like IPCE, concerned with electron transport under short circuit conditions Intensity modulated photovoltage spectroscopy IMVS, which probes the competition between transport and recombination at open circuit and electrical impedance spectroscopy (EIS), which probes the bias-dependent electrical response, analogous to dark-current transients. Other variants, such as frequency-resolved transmittance, the frequency domain analogs of transient absorption, have been developed [50]. The techniques and... 

There are in fact two slightly different types of non-steady state technique. In the first an instantaneous perturbation of the electrode potential, or current, is applied, and the system is monitored as it relaxes towards its new steady state chronoamperometry and chronopotentiometry are typical examples of such techniques. In the second class of experiment a periodically varying perturbation of current or potential is applied to the system, and its response is measured as a function of the frequency of the perturbation cyclic and a.c. voltammetry are examples of this type of approach. In both cases the rate of mass transport varies with the time (or frequency), and by obtaining data over a wide range of these variables and by using curve fitting procedures, kinetic parameters are obtainable. Pulse techniques will be discussed later in this chapter, whilst sweep methods are described in Chapter 6 and a.c. methods in Chapter 8. 

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