Diffusion times

We can imagine measuring experimental curves equivalent to those in Fig. 9.11 by, say, scanning the length of the diffusion apparatus by some optical method for analysis after a known diffusion time. Such results are then interpreted by rewriting Eq. (9.85) in the form of the normal distribution function, P(z) dz. This is accomplished by defining a parameter z such that... 

Thus, during solute transfer between the phases, (t) is now the average diffusion time (to) and (o) is the mean distance through which the solute diffuses, Le., the depth or thickness of the film of stationary phase (df). Thus,... 

Gas density Propellant density Boltzmann constant A factor to account for temperature oscillations ignition delay time Diffusion time... 

The recombination of fragments stemming from one macromolecule, at times shorter than the diffusion time, prevents the linear increase in RD with the absorbed dose per pulse, as not all main-chain scissions result in the formation of fragments. The effect of molecular oxygen on RD in the case of PBS can be interpreted by formation of peroxyl radicals, e.g. 

The drops should be on the order of 0.1 mm to obtain a diffusion time r = 2.5 s, which is less than the settling time. 

Diffusion time constant (s) Acceleration time constant (s)... 

Another important factor in diffusion measurements that is often encountered in NMR experiments is the effect of time on diffusion coefficients. For example, Kinsey et al. [195] found water diffusion coefficients in muscles to be time dependent. The effects of diffusion time can be described by transient closure problems within the framework of the volume averaging method [195,285]. Other methods also account for time effects [204,247,341]. 

The ideal packing should be relatively large in diameter, 80-100 nm, and be available with a pore size range from 500 to 10,000 A. The ores should be uniform in size distribution and shallow to reduce diffusion times. Improvements of this type will lead to the use of size exclusion chromatography for particle size determinations in the routine manner in which it is now employed for molecular weight determinations. 

Under the condition that the Stokes-Einstein model holds, the translational diffusion coefficient, D, can be represented by Eq. (8.3). the diffusion time, Xd, obtained through the analysis is given by Eq. (8.4). 

Figure 8.14 (a) Values of as a function of corresponding diffusion times (observation times) for each CdTe quantum dot. Four sets of measurements for one sample were conducted with diferent sized pinholes and different solvent as follows (1) 25 Xm pinhole, in water (2) 25 Xm pinhole, in deuterated water (3) 50 Xm pinhole. 

D is the diffusion coefficient and t the diffusion time (ii) a coarsening regime (occurring at longer annealing times) with a radius scaling as The two equations that... 

The drying time for the solid can be characterised by L /D, a diffusion time. Verify this by simulation by varying D and L separately. 

The relative pressure of disilane increases as a function of total pressure, due to the increased production of radicals, which is a result of increased dissociation of silane, as well as to the shorter gas volume reaction times and longer diffusion times to the walls, which result from increasing the pressure. 

Fig. 2.9.3 Proton spin density diffusometry in a two-dimensional percolation model object [31]. The object was initially filled with heavy water and then brought into contact with an H2O gel reservoir, (a) Schematic drawing ofthe experimental set-up. The pore space is represented in white, (b) Maps ofthe proton spin density that were recorded after diffusion times t varying from 1.5 to 116 h. Projections of the...

Since it was proposed in the early 1980s [6, 7], spin-relaxation has been extensively used to determine the surface-to-volume ratio of porous materials [8-10]. Pore structure has been probed by the effect on the diffusion coefficient [11, 12] and the diffusion propagator [13,14], Self-diffusion coefficient measurements as a function of diffusion time provide surface-to-volume ratio information for the early times, and tortuosity for the long times. Recent techniques of two-dimensional NMR of relaxation and diffusion [15-21] have proven particularly interesting for several applications. The development of portable NMR sensors (e.g., NMR logging devices [22] and NMR-MOUSE [23]) and novel concepts for ex situ NMR [24, 25] demonstrate the potential to extend the NMR technology to a broad application of field material testing. 

The essence of the DDIF method is to first establish a spin magnetization modulation that follows the spatial variation of the internal magnetic field within the individual pore. Such modulation is created by allowing spins to precess in the internal magnetic field. Then the diffusion-driven time-evolution (often decay) of such a modulation is monitored through a series of signal measurements at various evolution times tD. The time constant of this decay corresponds to the diffusion time of a molecule (or spin) across the pore and thus is a direct measure of the pore size. 

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