Critical pore sizes

The studies presented here along with helical bundle approaches provide a vehicle for exploring in detail the structure-function relationships of ion channels through the synthesis of artificial molecules with simple and controllable structural features. The control of electric fields at the ion-selective filter may elucidate the molecular mechanism of K /Na and NaflCa selectivities. Variation of the critical pore size by synthetic elaboration may give direct clues on the magnitude of conductance and discrimination of metal ions. Further studies on voltage depend-... 

The NLDFT predicts the critical point for capillary condensation phase transition (capillary critical pore size) at ca. 2 nm, which is approximately the minimum pore size in which capillary condensation is experimentally observed [21,27], However, the theory fails to predict the disappearance of the hysteresis loop for pores smaller than ca. 4 nm (hysteresis critical point) [20,15], It should be noted that the theory of Broekhoff and de Boer fails to predict both critical points unless some additional semi-empirical corrections are made [16]... 

Therefore, for a given intrinsic pore size distribution (foUowing the approach of Inoue et al. [8]), At (= ts - ta), and the hysteresis critical pore size (Dch=2R) can be evaluated by simultaneously solving Eqs. (2) and (3). 

A critical pore size Is defined as the largest pore that can carry 100% non-freezing water. Pores of size larger than critical pore size will have freezing and non-freezing water. The critical pore size for pulp fibers Is estimated as 40 A. Since more than 98% of the surface area may be In pores smaller than 40 most of the non-freezing or the bound water will be In pores smaller than critical pore size. 

The structure breaker salts decrease the bound water whereas the structure maker salts Increase the bound water. To explain the observed bound water trend. It Is hypothesized that structure breakers decrease the critical pore size and structure makers Increase this value. The viscosities of aqueous salt solutions are used as criteria to separate structure breaker from structure maker salts. 

Filtering is a method for the separation of materials. Materials with a particle diameter larger than the pores of the filter are collected as a filter cake, particles, which are smaller than the pores, can pass through the filter. With a fine filter one expects a transmission curve in the shape of a step function. For particles, which are smaller than the pore size, the transmission is 1 for particles, which are larger than the pore size, the transmission is zero, cf. Fig. 20.2. We will refer the diameter of particles that are in the range of the pore size of the filter the critical particle diameter, or consequently also as the critical pore size in the reverse view. 

The DCMD flux will increase with an increase in the membrane pore size and porosity and with a decrease in the membrane thickness and pore tortuosity. In other words, to obtain a high DCMD permeability, the surface layer that governs the man-brane transport must be as thin as possible and its surface porosity as well as its pore size must be as large as possible. However, it must be mentioned here that there exists a critical pore size equal to the mean free path of the water vapor molecules for the given experimental DCMD conditions. In the DCMD process, air is always trapped within the membrane pores with pressure values close to the atmospheric pressure. Therefore, if the pore size is comparable to the mean free path of the water vapor molecules, the molecules of the water vapor collide with one another and diffuse among the air molecules. In this case, the vapor transport takes place via the combined Knudsen/molecular diffusion flow. On the other hand, if the pore size is smaller than the mean free path of the water vapor molecules, the molecule-pore wall collisions become dominant and the Knudsen type of flow will be responsible for the mass transport in DCMD. It should be noted that for the given experimental conditions, the calculated DCMD flux based on the Knudsen mechanism is higher than that based on the combined Knudsen/molecular diffusion mechanism. 

Figure 5.10 Potential energy difference (W) for a single oxygen molecule at the entrance of a carbon cylindrical pore of diameter d. The pore regions where the diffusion mechanisms (activated diffusion, surface, and Knudsen flow) dominate are separated by the critical pore sizes dm, (where W = 0) and d,f (where W = 0.04eV), indicated by...

In order to detect species which are produced at an electrode surface by mass spectrometry, they have to be transferred from the electrolyte phase to vacuum. Fortunately, for aqueous systems [2] and also for some organic electrolytes with a high surface tension, e.g., propylene carbonate [7], the separation of the electrolyte from the vacuum can be achieved by using porous Teflon membranes. Due to their hydrophobicity, the liquid does not penetrate into the pores, whereas dissolved gaseous and other volatile species readily evaporate in them. The critical pore size depends on the... 

From a thermodynamic perqiective, it is immaterial whether r or P is used to probe the range of critical pore sizes. The only relevant variables in the Kelvin equation, in addition to file radius of curvature, are yaad and it should be possible to correct for the T variations of these parameters. In principal, the pore size distribution should not depend upon the combination of T and P used to probe a particular critical pore size. For exanqile, sufqiose that... 

Critical pore sizes for the penetration of corrosive liquids in refractory materials are discussed for every specific material. 

For nitrogen adsorbing on porous carbon this critical pore size corresponds roughly to the conventional boundary between micropores and mesopores at 2nm [9]. The pore filling mechanism is not accounted for in the thermodynamic methods, which are therefore incapable of determining pore size distributions in the micropore range. 

The predictions of mean-field theory for phase equilibrium in pores are equivalent, in the large pore limit, to the thermodynamic model. However, it provides a more redistic representation of the fluid behavior as the pores become smaller. In particular, it predicts the thickening of the adsorbed layers on the pore walls, and the change from capillary condensation to pore Ailing at the critical pore size. 

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