Capillary evaporation

Fig. 3.11 Capillary condensation in cylindrical pores, (a) Cylinder closed at one end, B. The meniscus is hemispherical during both capillary condensation and capillary evaporation, (h) and (c) Cylinder open at both ends. The meniscus is cylindrical during capillary condensation and hemispherical during capillary evaporation. Dotted lines denote the...

The droplets pick up charge as they exit the capillary evaporation of the solvent leaves highly charged molecules. 

Figure 14.3 Principle of atmospheric pressure chemical ionization. The dissolved analyte is sprayed through a capillary. Evaporation of the solvent is supported by a heated gas stream. Within the source, a plasma is formed by a Corona discharge needle, which creates the charged reagent gas (here HgO+j. The ionization of the analyte (M) is performed by the transfer of the charge (proton) via ion-molecule reactions.

Swelling method. Measurement of swelling is a second method used to estimate water absorption of a sample. A swelling apparatus was devised and described by Hermansson (, 13). In this method, a small amount of sample is dusted on a wet filter paper fastened on a glass filter. The filter is fitted on top of a thermostated funnel filled with water and connected to a horizontally located capillary. The uptake of fluid is followed in the capillary evaporative losses are prevented by a glass lid... 

Figure 1. (a) Experimental relations between the capillary condensation pressure and the pore diameter (hollow circles) and between the capillary evaporation pressure and the pore diameter (filled circles) for nitrogen adsorption at 77 K. The dashed line corresponds to the Kelvin equation with the statistical film thickness correction. The solid line corresponds to Eq. 2 derived using the KJS approach, (b) Relation between pore diameters calculated on the basis of Eq. 1 and the KJS-calibrated BJH algorithm using nitrogen adsorption data at 77 K. 

As already discussed, DFT can be used to predict the capillary condensation and capillary evaporation pressures for pores with homogeneous surface and well-defined geometry. To generate model adsorption isotherms for heterogeneous pores, it is convenient to employ hybrid models based on both DFT data for homogeneous pores and experimental data for flat heterogeneous surfaces [6-9]. Such model adsorption isotherms can be used to calculate PSDs in mesopore [6-9] and micropore [9] ranges. This approach is particularly useful for pores of diameter below 2-3 nm (micropores and narrow mesopores), where an assumption about the common t-curve for pores of different sizes is less accurate, which in turn makes the methods based on such an assumption (even properly calibrated ones) less reliable [18],... 

Kelvin equations describing capillary evaporation from slit-shaped pores or the filling and emptying of ink bottle pores can be calculated quite easily by using the appropriate expressions for cLA/dJV (see ref. 16). 

Let us suppose that the amount of nitrogen removed in each desorption step j is 5/ (y) for the purpose of the pore size calculations, this amount is expressed as the volume 8u (J), of liquid nitrogen. In the first desorption step 0 = 1) the initial removal is the result of capillary evaporation alone and therefore the volume of core space released is equal to the volume of nitrogen removed, i.e. 8uK(l) = 8v (1). 

Broekhoff, J.C.P. and de Boer, J.H. (1968). Studies on pore systems in catalysis. Xll. Pore distributions from the desorption branch of a nitrogen sorption isotherm in the case of cylindrical pores. A. An analysis of the capillary evaporation process. J. Catai, 10, 368-76. 

The increase of the bulk pressure at a small increment after achievement of the equihbrium density distribution allows obtaining the adsorption branch of the isotherm. If the pore is wide enough, the capillary condensation will occur, with the pressure of the condensation being corresponded to the vapor-like spinodal point. Similarly, desorption branch of the isotherm will be obtained at the decrease of pressure. In this case, the capillary evaporation will occur at a hquid-like spinodal point. The equilibrium transition pressure is obtained by comparing the grand thermodynamic potentials corresponding to the adsorption and the desorption branches of the isotherm. It corresponds to the equality of these values of the grand thermodynamic potential. 

The BJH, Cl and DH methods assume the same general picture of the adsorption-desorption process. Adsorption in mesopores of a given size is pictured as the multilayer adsorption followed by capillary condensation (filling of the pore core, i.e., the space that is unoccupied 1 the multilayer film on the pore walls) at a relative pressure determined by the pore diameter. The desorption is pictured as capillary evaporation (emptying of the pore core with retention of the multilayer film) at a relative pressure related to the pore diameter followed by thinning of the multilayer. 

Type IV. Isotherms commonly showing adsorption-desorption hysteresis, and always a steep drop in the absorbed amount on reduction of p, due to capillary evaporation effects. 

A type H2 hysteresis loop has a triangular shape and a very steep desorption branch. Such behavior was observed for many porous inorganic oxides and was attributed to pore coimectivity effects [80], which were often defined as the presence of pores with narrow mouths (inkbottle pores), but the latter identification may be grossly oversimplified [50]. Indeed, triangular hysteresis loops were observed even for highly ordered MCM-41 materials with pore sizes of about 4-5 nm [39,55,57]. For such samples, desorption (capillary evaporation) of nitrogen from primary mesopores takes place at relative pressures of 0.4-0.5, i.e., in the region where... 

A reasoning similar to that described above for desorption from the largest pores during the first pressure-lowering step can be applied to subsequent decreases in the adsorbed amount. But in these cases, the decrease in adsorption is caused not only by the capillary evaporation but also by thinning of the adsorbed layer in pores in which the capillary evaporation has already taken place. The calculations are repeated until a sufficiently low pressure value is reached or the cumulative pore volume obtained using the procedure described above equals or exceeds the total pore volume. The BJH procedure follows the sequence of events during desorption measurements it actually does not make any difference whether adsorption or desorption data are used. However, different relations between the pressure and the pore size may need to be used for capillary condensation and evaporation [74]. It needs to be noted that the Kelvin equation [Eq. (1)] was shown to underestimate... 

Equations (3) and (4) can conveniently be used in different methods of mesopore size evaluation, of which the BJH approach appears to be particularly suitable [55]. These relations were carefully tested on numerous MCM-41 samples and shown to be in excellent agreement with pore sizes calculated using Eq. (2), with differences usually below 0.1-0.2nm. Pore size calculations based on Eqs. (3) and (4) can conveniently be performed for both modified and unmodified ordered mesoporous silicas and can be expected to provide highly accurate results, especially for siliceous samples with cylindrical pores. Therefore, the BJH method of calculations based on these equations was used in our recent studies of modified MCM-41 materials [46,59]. It needs to be noted that Eq. (3) was derived for nitrogen capillary condensation (adsorption) data and should not be used in calculations based on desorption data. Moreover, it was shown that the desorption data are not appropriate for the pore size evaluation for mesoporous materials with pore sizes in the range of about 4-5.5 nm, due to the transition between reversible and irreversible adsorption behavior at relative pressures of about 0.4, as already described above. Because of this behavior, the relation between the capillary evaporation (desorption) pressure and the pore size would have a more complicated and less useful form than Eq. (3) derived for the capillary condensation process [55]... 

J. C. P. Broekhoff and J. H. de Boer, Pore Systems in Catalysts. XII. Pore Distributions from the Desorption Branch of a Nitrogen Sorption Isotherm in the Case of Cylindrical Pores. 1. An Analysis of the Capillary Evaporation Process, J. Catal., 10, pp. 368-76, 1968. 

The chapter is organized as follows. We start with macroscopic thermodynamic predictions and discuss the phase behavior of confined liquids in general in the absence of applied electric field. The primary focus is on capillary evaporation, a phenomenon that can be reversed in the presence of the electric field. The reader is directed to extensive excellent reviews [26] of capillary condensation. Next we focus on the combined effect of confinement and electric field on liquids structure and thermodynamics, water in particular, its stability against evaporation, and resilience of the hydrogen bond network in polarized water. We devote increased attention to issues of external conditions, as they determine how the system responds to applied electric field. We concentrate on systems maintaining... 

These predictions [45] have been confirmed in studying the capillary evaporation events within hydrophobic pockets of melittin dimers [50],... 

Leung K, Luzar A (2000) Dynamics of capillary evaporation. IL Free energy barriers. J Chem Phys 113(14) 5845-5852... 

The major difficulty with standard apparatus is that working close to the saturation pressure may lead to instabilities because of a lack of temperature control. This problem is illustrated in table 1, where the relative pressure at which capillary evaporation should occurs is calculated by the Kelvin equation as a function of Kelvin radius. This calculation is made for water at 25°C. From the relative pressure, the equilibrium pressure can be calculated. From the equilibrium pressure the temperature at which this equilibrium pressure becomes saturating is also shown. If the data for a pore size around 10pm are considered, one can observe that the equilibrium pressure should be 23.754 torrs, which corresponds to a saturation temperature of 24.988°C. It means that a temperature fluctuation of 0.012°C is sufficient to create a cold point in the system leading to condensation outside the pore system. It means also that a temperature control better than lO K is needed for a safe measurement of the relative pressure in that range with a sensitivity better than 10". ... 

R, Roth and M. Kroll, Capillary evaporation in pores,/ Phys. Condens. Matter, 18, 6517-6530 (2006],... 

A visual inspection of argon and nitrogen desorption branches, which represent capillary evaporation steps, show that they are steep too, and indicate high uniformity of the pore entrance sizes. Adsorption and desorption branches... 

Diffusion coefficients of solids into fluids can conveniently be measured by capillary evaporation [109-111] or evaporation from flat plates or surfaces of one sort or another. The Taylor Aris dispersion technique [112-115] can be used not only for solids but also for any component which will dissolve in the solvent of interest. The above two techniques are probably the ones most frequently used in connection with near-critical solvents. 

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