Bulk Transient Measurements

In the bulk analog of a stress relaxation experiment, the sample is suddenly compressed to a smaller volume and the pressure required to hold it at constant volume is recorded as a function of time. Apparatus for this purpose has been described by Matsuoka and Maxwell. In practice, it is more often used to obtain pressure-volume curves at a constant rate of volume decrease, from which the bulk relaxation modulus can be obtained by differentiation equation 59 of Chapter 3 

Alternatively, in the bulk analog of a creep experiment, the pressure is maintained constant and the decrease in volume is followed with time. Apparatus for very precise measurements at moderate pressures has been described by Goldbach and Rehage the volume change is measured by. motion of mercury in a capillary. Other devices, suitable for higher pressures, have been used by Mandelkern and by Findley, who measured voluminal deformation by strain gauges. 

Closely related information can be obtained without actually changing the external pressure, in an experiment which involves an abrupt temperature change followed by precise measurements of change in volume. If the final temperature is near the glass transition, the volume change is time dependent with a time scale which may extend over many hours. Though this experiment does not correspond exactly to either creep or stress relaxation, it yields essentially equivalent information, as discussed in Chapter 18. Its applicability is, however, restricted to the immediate vicinity of the glass transition temperature. 

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A simple criterion whether the observed reaction rate in solid catalysts is not limited by mass transport has been derived by Weisz 61). If this criterion is not fulfilled, one can obtain the dimensiordess moduli 0 and 99 from the observed rate and known or estimated values of the respective diffusion coefficient, as described in the literature (57, 59, 60). In the case of a pelleted zeolite, these methods have first to be applied to the bulk pellet and subsequently to the individual crystals. The procedure requires that the concentration (ca)o at the phase boundary of the zeolite crystals and the binary diffusivity at steady state are known must be estimated from transient measurements in the same... 

For an electrostatically activated micromembrane pump fabricated by bulk micro-machining transient measurements of the pump chamber pressure and the inlet and outlet pressures were made. From these values also the time dependent flow rate can be deduced. A complex dynamic behaviour can be observed, with a low frequency oscillation of the maximum pressure. Measurements can be compared and predicted with the results of an simulation tool PUSI for micropumps connected to a peripheral fluid system. 

To distinguish bulk dissociation and electrode processes, one must carry out transient measurements by the voltage step technique. The surface process initially gives an increase in current with time, whereas for bulk dissociation the current decreases monotonically (Fig. 

The classical electrochemical methods are based on the simultaneous measurement of current and electrode potential. In simple cases the measured current is proportional to the rate of an electrochemical reaction. However, generally the concentrations of the reacting species at the interface are different from those in the bulk, since they are depleted or accumulated during the course of the reaction. So one must determine the interfacial concentrations. There axe two principal ways of doing this. In the first class of methods one of the two variables, either the potential or the current, is kept constant or varied in a simple manner, the other variable is measured, and the surface concentrations are calculated by solving the transport equations under the conditions applied. In the simplest variant the overpotential or the current is stepped from zero to a constant value the transient of the other variable is recorded and extrapolated back to the time at which the step was applied, when the interfacial concentrations were not yet depleted. In the other class of method the transport of the reacting species is enhanced by convection. If the geometry of the system is sufficiently simple, the mass transport equations can be solved, and the surface concentrations calculated. 

Figure 17 Transient current induced in SOI pn junction diode by 15-MeV C-ion irradiation (solid line). The result obtained for bulk Si pn diode is also shown as a dotted line in the figure for comparison. The reverse bias of 10 V was applied to pn diodes during measurements.

We now discuss some of the experimental aspects of temperature spectroscopy. Lang (1974) called his original method deep level transient spectroscopy (DLTS), and he measured capacitance transients produced by voltage pulses in diodes made from conductive materials. However, in SI materials, this method is not feasible and an alternate method, involving current transients produced by light pulses in bulk material (or Schottky structures), was... 

The total transient Stokes shift (v(O)-v(oo)) observed in our time resolved experiments of coumarin in bulk water was 820 cm"1. In the case of C343 adsorbed on Z1O2 it is 340 cm 1. From measurements of the time-zero spectrum, i.e. the emission spectrum of C343 before solvent relaxation, Maroncelli et al. estimated the Stokes shift from solvation to be 1953 cm 1 for C343 in water [8]. Thus the time resolution of our experiments allows to observe about 42% of the total solvation process. Especially the very initial part, containing the inertial response is missed. 

Although both SH transients in Fig. 5.21 fall to a minimum at about the same time, their form is quite different and qualitative comparisons are useful. The isotropic contribution, /pp(/), decays as a single exponential, in agreement with previous measurements of submonolayer thallium deposition on polycrystalline electrodes [54]. The solid line in Fig. 5.21 a is an exponential fit with r = 10.7 msec. The exponential form suggests that the deposition occurs by an absorption, rather than a nucleation, mechanism [154]. The transient anisotropic response is not as simple. In fact, the initial fall in /ps( ) in Fig. 5.21 b is not a simple decaying exponential. The differing time dependencies for the isotropic and anisotropic responses suggests that f, the bulk anisotropic susceptibility element which is the only common element, is not the main source of the nonlinear response in either case. 

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