Pore filling

U, - meaning of linear relaxation coefficient for i - element tomogram s, Vi - volume of object, appropriate i -clement tomogram s, po - meaning of linear relaxation coefficient of a matrix material, (p/p)mei - mass relaxation coefficient of metal, wo - faaor of a pore filling material... 

Adsorption isotherms in the micropore region may start off looking like one of the high BET c-value curves of Fig. XVII-10, but will then level off much like a Langmuir isotherm (Fig. XVII-3) as the pores fill and the surface area available for further adsorption greatly diminishes. The BET-type equation for adsorption limited to n layers (Eq. XVII-65) will sometimes fit this type of behavior. Currently, however, more use is made of the Dubinin-Raduschkevich or DR equation. Tliis is Eq. XVII-75, but now put in the form... 

These various considerations led Pierce, Wiley and Smith in 1949, and independently, Dubinin, to postulate that in very fine pores the mechanism of adsorption is pore filling rather than surface coverage. Thus the plateau of the Type 1 isotherm represents the filling up of the pores with adsorbate by a process similar to but not identical with capillary condensation, rather than a layer-by-layer building up of a film on the pore walls. 

In very small pores the molecules never escape from the force field of the pore wall even at the center of the pore. In this situation the concepts of monolayer and multilayer sorption become blurred and it is more useful to consider adsorption simply as pore filling. The molecular volume in the adsorbed phase is similar to that of the saturated Hquid sorbate, so a rough estimate of the saturation capacity can be obtained simply from the quotient of the specific micropore volume and the molar volume of the saturated Hquid. 

An adsorbent can be visualized as a porous soHd having certain characteristics. When the soHd is immersed in a Hquid mixture, the pores fill with Hquid, which at equilibrium differs in composition from that of the Hquid surrounding the particles. These compositions can then be related to each other by enrichment factors that are analogous to relative volatiHty in distillation. The adsorbent is selective for the component that is more concentrated in the pores than in the surrounding Hquid. 

During the adsorption or occlusion of various molecules, the micropores fill and empty reversibly. Adsorption in zeoHtes is a matter of pore filling, and the usual surface area concepts are not appHcable. The pore volume of a dehydrated zeoHte and other microporous soHds which have type 1 isotherms may be related by the Gurvitch rule, ie, the quantity of material adsorbed is assumed to fill the micropores as a Hquid having its normal density. The total pore volume D is given by... 

Admixtures are sometimes used to reduce permeabiUty of concrete (80—82). These iaclude pore-filling materials such as chalk. Fuller s earth, or talc water repellents such as mineral oil, asphalt, or wax emulsions organic polymers (acryflc latexes, epoxies) and salts of fatty acids, especially stearates. 

Because of their ordered stmcture, molecular sieves have high capacity at low water concentrations and do not exhibit a capiHary condensation pore-filling mechanism at high water concentrations. The desiccating properties of the material are stiU good at elevated temperatures (Fig. 10). A dew point of —75° C can be obtained in a gas dried at 90°C with a molecular sieve that adsorbs water to the level of 1 wt %. In normal operations at ambient temperature, dew points of < — 100° C have been measured. 

Chemical Potential. Equilibrium calculations are based on the equaHty of individual chemical potentials (and fiigacities) between phases in contact (10). In gas—soHd adsorption, the equiHbrium state can be defined in terms of an adsorption potential, which is an extension of the chemical potential concept to pore-filling (physisorption) onto microporous soHds (11—16). 

Flat Surface Isotherm Equations The classification of isotherm equations into two broad categories for flat surfaces and pore filling reflec ts their origin. It does not restrict equations developed for flat surfaces from being apphed successfully to describe data for porous adsorbents. 

Transport in a homogeneously dissolved state, as for a neutral molecule inside a sorbent gel or in a pore filled with a liquid which is immiscible with the external fluid... 

Fig. 19.2. The microscopic mechanism of sintering. Atoms leave the grain boundary in the neck between two particles and diffuse into the pore, filling it up.

Now, we would like to investigate adsorption of another fluid of species / in the pore filled by the matrix. The fluid/ outside the pore has the chemical potential at equilibrium the adsorbed fluid / reaches the density distribution pf z). The pair distribution of / particles is characterized by the inhomogeneous correlation function /z (l,2). The matrix and fluid species are denoted by 0 and 1. We assume the simplest form of the interactions between particles and between particles and pore walls, choosing both species as hard spheres of unit diameter... 

Recently, many experiments have been performed on the structure and dynamics of liquids in porous glasses [175-190]. These studies are difficult to interpret because of the inhomogeneity of the sample. Simulations of water in a cylindrical cavity inside a block of hydrophilic Vycor glass have recently been performed [24,191,192] to facilitate the analysis of experimental results. Water molecules interact with Vycor atoms, using an empirical potential model which consists of (12-6) Lennard-Jones and Coulomb interactions. All atoms in the Vycor block are immobile. For details see Ref. 191. We have simulated samples at room temperature, which are filled with water to between 19 and 96 percent of the maximum possible amount. Because of the hydrophilicity of the glass, water molecules cover the surface already in nearly empty pores no molecules are found in the pore center in this case, although the density distribution is rather wide. When the amount of water increases, the center of the pore fills. Only in the case of 96 percent filling, a continuous aqueous phase without a cavity in the center of the pore is observed. 

Porenanteil, m. proportion of voids, poren-frei, a. free from pores, -fiillend, a. pore-filling. 

In contrast, D films followed the resistance of the solution in which they were immersed, and this behaviour was originally explained by assuming that D films contained holes, or pores, filled with solution that controlled the resistance of the film. Thus a typical value for the resistance of a ) film in 3-5 N potassium chloride is 10 Qcm and if this resistance was due to a pore, then it would have a radius of about 500 A. In order to test this... 

In the as-synthesized MFI-crystals the tetrapropylammonium (TPA) ions are occupying the intersections between the straight (parallel) and the sinusoidal channels of the zeolite, thus providing an efficient pore filling. The detailed structure of as-synthesized MFI-TPA has been elucidated by X-ray single crystal analysis (ref. 3). Also the combination tetrabutyl-Ztetraethylammonium can be applied as template in MFI-synthesis. A 1 1 build-in is found then (Fig. 1). When only tetrabutylammonium is available as template, the MEL (ZSM-11) lattice is formed with another distance between the channel intersections. 

Step 7 pre-treatment of porous wash-coals evacuation pore filling with CO,I... 

The tortuosity for pore-filling liquids is ideally a purely geometric factor but can, in principle, depend on the fluid-surface interaction and the molecular size if very small pores are present such as in zeolites (see Chapter 3.1). To obtain a measure for a realistic situation, we have used n-heptane as a typical liquid and have computed x... 

The conductivity of membranes that do not contain dissolved ionophores or lipophilic ions is often affected by cracking and impurities. The value for a completely compact membrane under reproducible conditions excluding these effects varies from 10-8 to 10 10 Q 1 cm-2. The conductivity of these simple unmodified membranes is probably statistical in nature (as a result of thermal motion), due to stochastically formed pores filled with water for an instant and thus accessible for the electrolytes in the solution with which the membrane is in contact. Various active (natural or synthetic) substances... 

M H2C204 180 g/liter H2C204-2H20 Pore filling TEM N(Ua) ... 

Pyrolytic carbon was inserted into the pores of these silica matrices by chemical vapor infiltration (CVI). The silica template was contacted with a flow of propylene Pr, (2.5 vol%) diluted in argon at 750°C during 15 hours. A quite uniform pore filling can be obtained by CVI. At the end, the carbon represents about 50 wt% of the C/Si02 material. Since the deposition... 

Fig. 4.4 Pore-filling models for protein adsorption in a mesopore channel (a) separated single-molecularadsorption (b) separated double-molecular adsorption (c) separated triple-molecular adsorption (d) interdigitated triple-molecular adsorption where adjacent layers are interdigitated by 1/4 of the protein diameter through changing the relative orientation. Adapted from [37],...

More recently, ionic liquids have also been used as additives. Lee and coworkers explain that ionic liquids may ad as a template during the sol-gel process redudng the shrinkage of the matrix by pore filling and behave as a stabilizer to proted Candida rugosa lipases [184]. 

At 9 hours of immersion, instead, isotherms do not show the pore filling associated with mesopores, which in turn appears again between 25 and 26 hours. After 28 hours of soaking, no mesopore filling is observed (figure 3). The DFT pore size distributions also confirm the presence of mesopores (around 2.2 nm) only at 2 hours of immersion and between 25 and 26 hours. The peak at around 5 nm is probably due to the textural interparticles porosity (figure 3 inset). 

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