Interface pore wall

A common feature of all electrochemical pore formation processes in solid-state electrodes of a homogeneous chemical composition is the remarkable difference in dissolution rate between pore tip and pore wall. This is usually discussed in terms of an active-passive transition between the pore tip interface and the pore wall interface. But this still leaves the question open as to what quality of the pores makes their tips active and the remaining surface passive. On a basic level the active-passive transition has been ascribed to three distinct causes [Le31] ... 

When a liquid is placed in contact with a surface of a porous solid the question arises as to whether it will penetrate into the pores. The answer must be pursued in the realm of capillarity which deals with the equilibrium geometries of liquid-solid interfaces and the angle of contact between the liquid and the pore wall. 

The main difference between the two approaches, as indicated in Figure 3.9, is that the first route leads to hybrid materials in which the main fraction of the organic components protmde into the pores, that is, a modification of the pore wall interface is achieved, while in the second route the organic moieties are incorporated directly into the framework. 

Another criterion could be whether the organic functions are only incorporated into the framework or only the pore wall interface is functionalized. However, how then should a co-condensation reaction between a silsesquioxane precursor and a terminal organotrialkoxysilane be classified ... 

An alternative method to synthesize organically functionalized mesoporous silica phases is the co-condensation method (also called one-pot synthesis or direct synthesis). It is possible to prepare mesostmctured silica phases by the co-condensation of tetraalkoxysilanes [(RO Si (predominantly TEOS or TMOS)], either (1) with terminal organotrialkoxysilanes of the type (R 0)3Si-R or (2) with bis- or multi-sily-lated precursors of the type [(R 0)3Si]m, m > 2 in the presence of structure-directing agents (see Fig. 3.9). As also ternary mixtures were applied, that is, functionalization of both the pore wall interface and the framework were carried out simultaneously, we will not explicitly subdivide this section according to these two routes. 

Increase of the electronic state density in the carbon pore walls with the voltage. Hahn et al. [52] have measured double-layer capacitance and electronic conductance of an activated carbon electrode in an aprotic electrolyte solution, 1 mol/dm3 (C2H5)4NBF4 in acetonitrile. Both quantities show a similar dependency on the electrode potential with distinct minima near the potential of zero charge. This correlation suggests that the capacitance, like the conductance, is governed substantially by the electronic properties of the solid, rather than by the ionic properties of the solution in the interface of the double layer. 

One of the potential applications of these ABC triblock copolymers was explored by Hillmyer and coworkers in 2005 [118]. They have prepared nanoporous membranes of polystyrene with controlled pore wall functionality from the selective degradation of ordered ABC triblock copolymers. By using a combination of controlled ring-opening and free-radical polymerizations, a triblock copolymer polylactide-/j-poly(A,/V-dimethylacrylamide)-ib-polystyrene (PLA-h-PDMA-h-PS) has been prepared. Following the self-assembly in bulk, cylinders of PLA are dispersed into a matrix of PS and the central PDMA block localized at the PS-PLA interface. After a selective etching of the PLA cylinders, a nanoporous PS monolith is formed with pore walls coated with hydrophilic PDMA. 

In mesopores a multilayer film will be adsorbed at the pore wall as the saturation pressure is approached. The stability of this film is determined by the interaction with the wall, e.g. long-range Van der Waals Interaction, and by the surface tension and curvature of the liquid-vapour interface. Saam and Cole -have advanced a theory, showing how the curved film becomes unstable at a certain critical thickness t = a-r. The adsorption process is shown schematically in fig. 1.32a (1) (3). During desorption (4) -> (6) an asymmetrical state... 

The essence of the technique is that the size of the transformed solid (from the condensate) which is confined by the pore walls is inversely proportional to the degree of undercooling (ST), Thus the finely dispersed transformed solid present in the membrane pores melts at temperatures l low its ambient melting point when the liquid behaves as a bulk liquid outside the membrane pores. The change in the freezing (or melting) point of the capillary condensate. AT allows the determination of the pore radius provided it is univocally related to the radius of curvature of the interface. The value of /AT is linear with respect to the pore radius (r) with the following relationship ... 

Kinetically, the overall dissolution process consists of carrier transport in the semiconductor, electrochemical reactions at the interface, and mass transport of the reactants and reaction products in the electrolyte. Also, toe are a number of reactions involved at the interface and these reactions consist of several steps and subreactions. At any given time the dissolution kinetics can be controlled by any one or several of these steps. The distribution of reactions along a pore bottom under a steady-state condition during pore propagation must be such that pore walls are relatively less active than the pore tip. Then, the dissolution reactions are concentrated at the pore tip resulting in the preferential dissolution and formation of pores. The formation of pores is the consequence of spatially and temporally distributed reactions. 

The classical model for describing adsorption in simple geometric pores is based on the Kelvin equation [125], which is derived from the condition of mechanical equilibrium for a curved interface between coexisting vapor and liquid phases in a pore. If the adsorbed liquid completely wets the pore walls, as shown in Fig. 17a, and the vapor phase is assumed to be an ideal gas, then mechanical equilibrium requires that... 

For the sake of concreteness of the following developments, we consider a fluid confined to a slit-pore such that the solid surfaces representing the pore walls are planar, parallel to one another, and perpendicular to the 2-axis of a Cartesian coordinate system. The separation between the pore walls will be denoted s. In addition, the two solid surfaces can be manipulated by external agents normal to the fluid-solid interface sucli that s, may be altered. EventuaJl), these planar surfaces will come to rest at some equilibrium separation Sj,. As we shall see later in Section 5.3.1, the situation just described is akin to laboratory experiments in which the rheology of confined fluids is investigated by means of the so-called surface forces apparatus (SFA). 

This extends the previous work (I ) In which the Lennard-Jones type surface potential function and the frictional function representing the Interfaclal forces working on the solute molecule from the membrane pore wall were combined with solute and solvent transport through a pore to calculate data on membrane performance such as those on solute separation and the ratio of product rate to pure water permeation rate in reverse osmosis. In the previous work (1 ) parameters Involved in the Lennard-Jones type and frictional functions were determined by a trial and error method so that the solutions in terms of solute separation and (product rate/pure water permeation rate) ratio fit the experimental data. In this paper the potential function is generated by using the experimental high performance liquid chromatography (HPLC) data in which the retention time represents the adsorption and desorption equilibrium of the solute at the solvent-polymer interface. 

The third distance, perhaps the most relevant to reactions on surfaces, is the actual distance traversed by a diffusing molecule. This is a very complex issue which we only begin to understand. The diffusional distance reflects not only the geometric considerations made above, but also the facts that the surface is energetically heterogeneous, and that the diffusion is some combination of movements which follow closely the surface features, and of jumps from pore-wall to pore-wall and from one tip to the next. Obviously this diffusional distance is also a function of the temperature and of the solvent interfaced with the solid. Furthermore, since different types of connectedness can yield the same D value, this textural characteristic is an additional parameter to be considered (the fracton or spectral dimension (IS)). In view of this complex picture, what is then the practical advise Under the current state of art, the best one can do is to get a preliminary estimate of d from eq s [4]-[6] the direct observation of actual diffusional process in disordered systems, is still in its infancy. For some recent studies see ref. 16,17. 

---