Dynamic mobility frequency dependence

Once the instrument has been calibrated, it can be used for the determination of the dynamic mobility from the ESA measurements. The dynamic mobility clearly depends on the zeta potential, and from the above discussion about particle inertia it can be seen that the dynamic mobility also depends on particle size. This is illustrated by the measured mobility spectra for four different silica sols (Figure 4.3) The 1-micron silica particles have large phase lags and a pronounced drop in magnitude with increasing frequency, while the nanopartides show almost no frequency dependence over this frequency range. 

The electrochemical quartz crystal microbalance is a versatile technique for studying several aspects of electroactive polymer film dynamics. For rigid films, it is a sensitive probe of mobile species (ion and solvent) population changes within the film in response to redox switching. For non-rigid films, it can be used to determine film shear moduli. In the former case, one simply follows changes in crystal resonant frequency. In the latter case, the frequency dependence of resonator admittance in the... 

Transient terahertz spectroscopy Time-resolved terahertz (THz) spectroscopy (TRTS) has been used to measure the transient photoconductivity of injected electrons in dye-sensitised titanium oxide with subpicosecond time resolution (Beard et al, 2002 Turner et al, 2002). Terahertz probes cover the far-infrared (10-600 cm or 0.3-20 THz) region of the spectrum and measure frequency-dependent photoconductivity. The sample is excited by an ultrafast optical pulse to initiate electron injection and subsequently probed with a THz pulse. In many THz detection schemes, the time-dependent electric field 6 f) of the THz probe pulse is measured by free-space electro-optic sampling (Beard et al, 2002). Both the amplitude and the phase of the electric field can be determined, from which the complex conductivity of the injected electrons can be obtained. Fitting the complex conductivity allows the determination of carrier concentration and mobility. The time evolution of these quantities can be determined by varying the delay time between the optical pump and THz probe pulses. The advantage of this technique is that it provides detailed information on the dynamics of the injected electrons in the semiconductor and complements the time-resolved fluorescence and transient absorption techniques, which often focus on the dynamics of the adsorbates. A similar technique, time-resolved microwave conductivity, has been used to study injection kinetics in dye-sensitised nanocrystalline thin films (Fessenden and Kamat, 1995). However, its time resolution is limited to longer than 1 ns. 

Second, the positions and llneshapes of resonances arising from potentially mobile parts of the peptide (e,g, side chains) have revealed dynamical aspects of the solid-state structures of peptides. The analysis of molecular motions is simplified In the solid state by the absence of overall molecular tumbling, which modulates spin interactions and leads to complex frequency -dependent spectral responses. In particular, signals arising from aromatic ring side chains are well separated from other resonances, and may be interpreted in terms of reorientation models of these side chains. Such ring dynamics are of great importance in protein structures, and studies with model peptides can help elucidate fundamental aspects of these processes. 

The factor (1 in Eq. (2) measures the tangential electric field at the particle siuface. It is this component which generates the electrophoretic or electroacoustic motion. For a fixed frequency, it can be seen from Eq. (4) that (1 +J) depends on the permittivity of the particles and on die function X - Kg/K a, where Ks is the surface conductance of the double layer X measures the enhanced conductivity due to the charge at the particle surface. It is usually small unless the zeta potential is very high, so for most emulsions with large ka, X has a negligible effect. The ratio fp/f is also small for oil-in-water emulsions. Equation (4) can then be reduced to/= 0.5 and hence the dynamic mobility becomes ... 

Assuming (as it is reasonable) that for conditions in which the approximation ko 5> 1 is valid, the dynamic mobility also contains the (1 — Cq) dependence displayed by the static mobility (Equation (3.37)), one can expect a qualitative dependence of the dynamic mobility on the frequency of the field as shown in Figure 3.14. The first relaxation (the one at lowest frequency) in the modulus of u can be expected at the a-relaxation frequency (Equation (3.55)) as the dipole coefficient increases at such frequency, the mobility should decrease. If the frequency is increased, one finds the Maxwell-Wagner relaxation (Equation (3.54)), where the situation is reversed Re(Cg) decreases and the mobility increases. In addition, it can be shown [19,82] that at frequencies of the order of (rj/o Pp) the inertia of the particle hinders its motion, and the mobility decreases in a monotonic fashion. Depending on the particle size and the conductivity of the medium, the two latter relaxations might superimpose on each other and be impossible to distinguish. 

Dynamics of Mobile Ions in Materials with Disordered Structures - the Case of Silver Iodide and the Two Universalities, Fig. 3 Second universality (Nearly Constant Loss) low-temperature conductivity isotherms displaying a linear frequency dependence and essentially no temperature dependence (Data from 0.3 Na20 0.7 B2O3 glass [11])... 

Impedance spectroscopy (IS) is a versatile and powerfiil characteization technique for the investigation of frequency dependent electrical properties of materials and interfaces. It can be used to investigate the dynamics of boimd or mobile charge, both in the bulk and in interfacial regions of any kind of soUd or Uquid material with electronic, ionic, semiconducting, mixed electronic-ionic conductivity or even dielectric properties (Macdonald, 1987a). 

LFM is another widely used AFM technique to laterally probe the polymer surface, sometimes referred to as friction force microscopy (FFM). In this mode of operation, the AFM tip slides aaoss the polymer surface at a range of scanning speeds. The friction and adhesion force with the surface cause the cantilever to twist, and the friction force is measured from the torsion of the sliding cantilever. The frictional behavior of polymeric solids is closely related to their dynamic viscoelastic properties.The friction force depends on both the temperature and the scanning speed. The scanning rate dependence of the lateral force corresponds to the frequency dependence of the loss modulus ". Master curves can be constmcted with measurement at different temperatures and scanning speeds. The results based on this technique reflea the controversies commonly seen in the field of polymer dynamics in thin films and confined geometries. There are multiple observations of polymer surfaces and thin films with either bulk-like behavior or enhanced mobility. " " " ... 

Equation (5.1) described the vibrational response of a single particle to an applied forceF(t). In a (crystalline) system of many mobile particles (ensemble), the problem is analogous but the question now is how the whole system responds to an external force or perturbation Let us define the system s state (a) as a particular configuration of its particles and the probability of this state as pa. In a thermodynamic system, transitions from an a to a p configuration occur as thermally activated events. If the transition frequency a- /5 is copa and depends only on a and / (Markovian), the time evolution of the system is given by a master equation which links atomic and macroscopic parameters (dynamics and kinetics)... 

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