Pore orifice

In order to reduce the size of bubbles formed by dispersion through filters, additional methods and devices are used, for example, rotating drums [8], horizontally situated filter pores, rotating cylinders causing solution movement [8], shock effects on the bubbles formed [25], round body devices placed over capillary or pore orifice outlet [26]. Very small bubbles can be formed from thin capillaries with diameter up to 10 - 20 im (sometimes up to 4 pm) or very fine filters. However, the rate of foam formation when such capillaries or filters are employed is very low. Simple injection type devices for generating highly dispersed foam... 

In order to describe the impedance of such electrodes, first a dc solution must be found. Two cases are considered here (1) porous electrodes in the absence of internal diffusion and (2) in the presence of axial diffusion. It is assumed that the electrical potential and concentration of electroactive species depend on the distance from the pore orifice only and there is always an excess of the supporting electrolyte (i.e., migration can be neglected). 

In this case it is assumed that the concentration of the electroactive species is independent of the distance along a pore. In the next section we will see when such an assumption is valid. The axially flowing dc current, /, which enters the pore, flows toward the walls and its value decreases with the distance x from the pore orifice (Fig. 34). This decrease in the current is proportional to the current flowing to the wall ... 

The important advantage of LC LC procedures that utilize controlled volume barriers lies in the high sample recovery. This is rather comprehensible because the pores of the colunm packing ate in a continuous equilibrium with the elution promoting mobile phase. The equihbrium is likely perturbed only within the pore orifices in the course of the brief contact of the colunm packing with the retention promoting barrier. 

Cdi is the specific capacitance (F cm ) of the pore walls. The ac potential phasor,, that enters the pore decreases from the initial value at the pore orifice, Eq, because of the ohmic drop in solution, and the ac charging current phasor, 7, decreases with... 

The amplitude of the ac signal decreases with x and reaches a constant value at X = /. Of course, such a graph is different at different frequencies. To determine the total impedance, the ratio of the phasors of the potential and current at the pore orifice must be calculated. The potential gradient at the pore orifice is... 

Fig. 9.22 Dependence of overpotential in pore as a fimction of distance fiom pore orifice for different exchange current densities and constant overpotential parameters r/ = 0.2 V, a = 0.5, / = 0.05 cm, r = 10 cm, = 10 cm the values of jo are displayed in the figure (From Ref. [72] with kind permission Irom Springer Seience and Business Media)...

Fig. 9.31 Dependence of dimensionless current as function of distance in pore for potentials from 0.1 V to —0.1 V, every 0.05 V arrow, direction of increase in negative potential) and dependence of current in pore divided by maximal current flowing at pore orifice on dimensionless distance (From Ref. [72] with kind permission from Springer Science and Business Media)...

The current flowing to the pore walls increases with increases in the negative potential (Fig. 9.31) however, the current divided by the maximal current flowing at the pore orifice / ,ax = /(z = 0) behaves differently the largest value is observed for = 0 and identical values are obtained for the positive and negative... 

The truncated conical-shaped glass nanopore electrode (for brevity, hereafter referred to as a glass nanopore electrode or GNE) comprises a Pt microdisk electrode sealed at the bottom of a conical-shaped pore in glass (1). The radius of the pore orifice can be varied between 5 nm and 1 pm. The GNE was developed as a structurally simple platform for nanopore-based sensors and for investigating molecular transport through orifices of nanoscale dimensions. 

Figure 6J.11.2 Flux as a function of position at a GNE. Note that the flux reaches a maximum value at the pore orifice, rather than at the electrode surface. This behavior is a result of the diffusion resistance being localized at the pore orifice (5).

A key prediction of equation (6.3.11.5) is that is independent of d, a consequence of the radial divergent flux within a conical-shaped pore. For typical values of d obtained in preparing GNEs (-10°), the current (equation (6.3.11.1)) asymptotically approaches the depth-independent value (equation (6.3.11.5)) when the pore depth is at least 20X greater than the radius of the pore orifice. For instance, for a pore with a 20-nm radius orifice, any pore depth greater than -400 nm will yield a similar value of the steady-state limiting current. Experimental measurements of as a function of d confirm the behavior predicted by the above set of equations (2). 

It is seen from Fig. 6.34, based on the results by scanning electron microscopy that part of ruthenium particles show aggregated status, large size and distributed unevenly when impregnation time is 3 h and 6 h, respectively. It can be seen from Fig. 6.34(c) that when impregnation time is 18 h, ruthenium is evenly distributed over surface of activated carbon and the pore orifice of support which is very clearly eyeable without obvious blocked objects. 

Consider, for example, a nanopore filled with and immersed in an aqueous KCl solution. The solution immediately adjacent to the pore orifice becomes enriched in K+ due to the presence of the EDL created by the negative surface charge on the pore surface. When a negative potential is applied inside the pore interior relative to the external solution, K+ are electrophoretically transported into the pore and Cl" move in the opposite direction. The EDL electrostatically rejects Cl and results in a buildup of ions inside the pore orifice. 

As noted previously, the resistance of a conical-shaped nanopore is highly localized at the pore orifice. With that in mind, it is no surprise that the buildup of ions in the orifice leads to a higher overall conductivity of the nanopore, as experimentally measured by an increase in the current recording. In contrast, when a positive potential is applied, the flux of Cl" from the external solution to the pore interior is rejected by the pore orifice, depleting Cl within the pore and resulting in a decrease in the nanopore conductivity and measured current. This qualitative description of the effect of EDL is consistent with the nonlinear i V behavior shown in Figure 2.16. 

FIGURE 2.24 Simulated (a) distributions of electric conductivity and (b) current-position (i-z) curves as a 160 nm radius nanoparticle translocates through a 215 nm radius nanopore in a 0.01 M KCl solution at an applied voltage of -0.4 V. z=0 corresponds to the location of the pore orifice. The surface charges at the pore wall and particle surface were set equal to -0.005 and -0.015 C/m, respectively. (Reprinted with permission from Lan, W.-J., Kubeil, C., Xiong, J.-W., Bund, A., and White, H.S., J. Phy. Chem. C, 2014,118, 2726-2734. Copyright 2014 American Chemical Society.)... 

The recessed nanopore electrode shown in Figure 2.2b comprises a Pt or Au microdisk electrode embedded at the bottom of a conical-shaped pore synthesized in a glass membrane. These electrodes are fabricated with pore orifice radii as small as a few nanometers. EDL gating refers to the ability to control the flux of redox-active molecules from the bulk solution to the electrode surface, through the orifice (Figure 2.25), by either chemical (e.g., pH) or external stimuli (e.g., photons) that... 

The interior surface is electrically neutral or positively charged due to functionalization with an aminosilane that may or may not be protonated depending on solution pH. The origin of the underlying coordinate system (r, z) used in the finite-element modeling is at the center of the pore orifice. (Reprinted with permission from White, H.S. and Bund, A., Langmuir, 2008, 24, 12062-12067. Copyright 2008 American Chemical Society.)... 

A geometry that is somewhat similar to a recessed ME is that of the nanopore electrode (Fig. 15.12). This electrode geometry is characterized by the small pore orifice, whose radius, a, can be varied between 5 nm and 1 pm the pore depth, d and the half-cone angle (f). An approximate analytical expression for the steady-state limiting current is given by equation T216 in Table 15.2. ... 

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