Pore population

This function effectively assigns the variation in the volumetric uptake in a radius interval to differences in the pore lengths and assumes constancy of pore population in each interval. 

When a volume AF is intruded into a narrow pore radius range of Ar, centered about a unit radius r, one can write 

For equal small pore radius intervals, assuming equal pore lengths, equation (11.28) can be used to obtain relative pore populations, namely  

In this manner it is possible to obtain relative throughout the entire range of measurable pores. pore populations 

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Figure 6 shows calibration curves for three other two column combinations, each representing 30,000 to 40,000 plates per set. The 10 A° plus 10 A° curve can be interpreted to show a deficiency in relative pore population in the range equivalent to about 50,000 to 600,000 molecular weight. The other two, properly calibrated, can conceivably be used for determination of molecular weight distributions. However, utility for resolution of specific polymodal mixtures is too difficult to assess from calibration curve alone. How much curvature of a calibration curve translates into utility or non-utility Calibration curves indicating pore size populations all have the same shape for given column combinations whether the plate count level is 5000 plates or 20,000 plates or 80,000 plates. 

The equation provides the corresponding pore radius for a given relative pressure, p/po. At the beginning of an adsorption process when the relative pressures is low, only a monolayer of the vapor molecules is adsorbed to the pore wall. This is followed by multilayer adsorption which is restricted to the so-called t-layer (adsorbed layer) with a maximum thickness on the order of a few molecules. As the relative pressure is increased, capillary condensation (i.e., the condensation of a vapor) occurs first in the smallest pores. Then progressively larger pores are filled according to Eq. (4-5). This continues until the saturation pressure is reached when the entire pore population is filled with the condensate. 

Changes in the transmembrane voltage, U(t), cause changes in the pore population... 

Transient behavior is determined by calculating how the pore population changes... 

Feedback between 17(f) and G(f) involves both the pore population and external... 

Pore density function that describes a wide range of pore sizes Dynamic behavior of the heterogeneous pore population Bom energy-modified conductivity within pores Hindered transport through pores [Renkin equation (37)] Local transmembrane voltage reduced by the spreading resistance... 

Figure IB. Corresponding computed pore population distribution (probability density), n(r, t) (16). Each curve is labeled by the corresponding value of the injected charge Q. For Q = 25 and 20 nC (cases for which REB occurs), N increases to about 108 in less than 0.5 pus and then decays exponentially with a time constant of 4.5 pus. For Q — 15 nC, N increases rapidly to about 105 and remains almost constant for about 4 pus before the exponential decrease. For Q — 10 nC, N increases to about 2 X 103 in about 5 pus and remains almost constant for about 30 pus before the decay phase. The membrane in this case ruptures. For Q = 5 nC, N increases to about 40 in 80 pus. N will return to its initial value as the membrane discharges with a time constant of about 2 s.

A combination of physical forces and diffusion governs pore evolution. As a result, pores with a wide range of sizes appear in the membrane. This distribution of sizes is described by a pore population function that is, a probability density function, n(r, t) At any time t, there are n(r, t) Ar pores with radii between r and r +Ar. 

The kinetics of the pore population are quantitatively described by Smoluchowskfs equation (14, 42) ... 

Our initial estimates of molecular transport based on electrical drift should be extended by including convection [e.g., electroosmosis (31)] and diffusion (52). The same general strategy is reasonable A dynamic pore population will be computed, in which electrical interactions are the dominant source of pore creation and expansion. In the case of a pl nar membrane with no osmotic or hydrostatic pressure gradient, the final stages of pore population expansion and collapse should also be governed by purely electrical interactions. By following the pore population over its development, the contribution of each transport mechanism can be estimated. For cell membranes, a nonzero pressure difference will usually exist. In this case, pores of... 

Figure 6.—Continued. C, Predicted electrical drift contribution to molecular transport across one of the two cubic cell membranes. (Weaver, J. C. Barnett, A. Wang, M. W. B/iss, J. G., unpublished). A hypothetical series of molecules, a// with unit charge (zs = l) was used to test the relative importance of different size pores in the pore population. More realistic predictions would use estimates of the size (radius rs), shape (a form factor), and the Bom energy repulsion (zs>eff — zm, where m is a number in the range 1 < m < 2).

Much faster diffusion In-pore populations change Ions displaced... 

Regarding the shapes of the pore size distribution plots, figure 3 shows that in all samples, with the exception of the pure titania sample, exist a small population of pores of around 40 A in diameter and a main pore population of around 130 A in diameter. The pore size distribution curve of the pure titania sample showed in contrast, the first maximum at 60 A and the indication of larger pores with the maximum beyond 300 A. 

Fleury (2002) proposed a trimodal pore-size model for carbonates with three pore populations (micro, meso, macro). The electrical network comprises a series of mesopores and macropores micropores are in parallel. 

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