Scanning Studies on Capillary Condensation and Evaporation of Nitrogen Part 1.-Apparatus and Calculation Method BY JOHAN c. P. BROEKHOF" AND WIM P. VAN BEEK Unilever Research, Vlaardingen, The Netherlands Received 17th February, 1978 For collection of extensive sets of data on scanning behaviour within nitrogen sorption hysteresis- loops at 77.6 K, an apparatus has been described by which a preprogrammed sequence of adsorption- desorption cycles within the hysteresis region can be recorded fully automatically. This has enabled the determination of up to 3000 datum points distributed over some 60 primary scanning curves, in a single run, without interruption of the measurement. Subsequently, a method has been described for obtaining quantitative information on capillary evaporation and condensation phenomena from scanning data.It has been shown that the slope and intercept of the tangent lines to a set of primary scanning curves at the point of pressure reversal can be directly related to the actual porous structure. This leads to a new independent method for determining pore size distributions. The common method for assessing the pore size distribution in the mesopore range is based on the interpretation of the adsorption-desorption hysteresis loop for physically adsorbed vapours in terms of capillary condensation. In practice, nitrogen at its normal boiling point is commonly used as adsorbate, The method is based upon a number of (largely unproven) assumptions, such as the validity in the mesopore range of the Kelvin relation between meniscus curvature and vapour pressure of the capillary-condensed phase, the predominance of one simple geometrical pore shape (e.g.either regular tubular pores or equidistant slits) and the neglect of effects related to the occurrence of networks of interconnected pores. The validity of these and similar assumptions is of great interest for actual porous systems and commonly used adsorbates. The potential use of scanning experiments within the hysteresis region to gain a better insight into the fundamentals of physical adsorption in the hysteresis region has been pointed out by a number of author~.l-~ Up to now the most extensive set of experimental data has been presented by Everett and c o ~ o r k e r s , ~ who have also provided a detailed formal framework for inter- pretation and correlation of scanning behaviour in the independent domain t h e ~ r y .~ - ~ In spite of the practical importance the number of scanning studies with nitrogen as adsorbate has been very small. In general, scanning studies are tedious and time- consuming and require very accurate measurements. Some years ago, a fully automated volumetric nitrogen adsorption apparatus was developed in our laboratory by Osinga, Wildschut and van Duyn to meet the need for a large number of nitrogen isotherms. The complete adsorption-desorption sequence was directly controlled through on-line coupling to an IBM-1800 process computer. After optimization of accuracy and reliability, this apparatus has been adapted for the automatic recording of a preprogrammed series of scanning curves throughout the hysteresis-region.A significant extension of the application of scanning curves can be made by combining the independent domain theory with the t-plot method of a n a l y s i ~ , ~ ~ lo 36J . C . P . BROEKHOFF AND W. P . VAN BEEK 37 in order to obtain estimates of the cumulative surface area and volume of the pore domains emptied or filled in each particular state of the system.ll In Part 1 of this series of two papers, we will discuss the essentials of the apparatus and the computational procedure for a t-plot analysis of the scanning curves. In Part 2 we will discuss information obtained from this analysis on the breakdown of the capillary-condensed state below a critical relative pressure along the desorption branch and on the mechanism of filling narrow mesopores along the adsorption branch.EXPERIMENTAL DESCRIPTION OF APPARATUS A constant-volume gas reservoir (V) at a fixed temperature was connected through a two-way dosing pump to a small sample vessel ( S ) immersed in a liquid nitrogen bath (fig. 1). The pressure in the gas reservoir and that in the sample vessel (pg) were recorded with Texas Instruments digitalised Bourdon gauges (resolution < 10 Pa). A third Bourdon gauge recorded the vapour pressure of pure liquid nitrogen ( p o ) at the temperature of the cryostat bath. The signals of the three gauges were converted into binary numbers through a pulse- counting technique in the read-out unit.I2 The dosing pump and read-out unit were operated by the command unit which is on-line to an IBM 1800 computer.The piston dosing pump of adjustable stroke-length was fitted with two magnetically ,operated vacuum-tight valves. Its dead space in the neutral position is small whereas the dead space is thermostatted by water flowing through a channel in the metal pump housing. Gas burette Equilibrium Reference pressure pressure - - pressure reading reading reading \ / Dosing pimp SC. C T " I- L 323 K 78 K Thermostat Liquid ndrogen 298 K bath I / IBM le00 / FIG. 1 .-Block-diagram of automatic volumetric sorption apparatus suitable for recording scanning curves. S = sample holder ; T = liquid-nitrogen thermometer ; V = constant-volume nitrogen burette, The level in the liquid nitrogen bath was controlled by a capacitative buoyancy level sensor which operates a magnetic valve between the bath and a large storage dewar vessel.However, a periodic fluctuation in the liquid nitrogen level could not be avoided. Therefore, the connection between the sample vessel and the rest of the system was water-jacketed and this jacket was surrounded by a vacuum chamber reaching into the liquid nitrogen bath. Variations in the effective dead space in the sample holder with the liquid nitrogen level were hereby largely suppressed. The dead space of the rest of the system was minimized; moreover the temperature of the working volumes of the Bourdon gauges was kept constant. The liquid nitrogen bath was open to the atmosphere, in such a way that the possibility of condensing atmospheric oxygen was minimized, even during long runs.The value of p o was still influenced by variations in the barometric pressure (as well as by the purity of the liquid nitrogen), but almost always fell within the range 102-106 kPa (= 765-795 mmHg),38 CAPILLARY CONDENSATION BY SCANNING which corresponds to 77.4-77.8 K. This temperature range was found acceptable for the present purpose, since no systematic influence of the temperature on the relation between amount adsorbed and pg/po in this range was found. STANDARD PROCEDURE First, the gas reservoir was carefully calibrated with nitrogen from a burette. For the determination of the gas volume in the sample holder space a complete blank isotherm was run under the measuring conditions, but without sample. In the actual measurement, the amount adsorbed was calculated from the pressure decrease in the gas reservoir as compared with that obtained in the blank run.An additional correction was made for the material volume of the solid, in the way described by Lippens.13 The optimum amount of sample to be used is dependent on its specific surface area, S (x 70 mg for 100 < (S/m2 g-') < 300). As many materials of interest are sensitive to heat, the standard sample pretreatment chosen was drying in air at 120 "C for 24 h, followed by degassing in sit& at 100 "C until a vacuum of w Pa had been reached. This left oxidic surfaces covered with one mono- layer of strongly bound water.14 Under these conditions non-porous oxides conform to the t-curve of nitrogen adsorption of De Boer et aZ.15 At the start of an experiment the pressure in the gas reservoir was read by the computer and stored.Then the dosing pump was activated uia the command unit and some nitrogen dosed to the evacuated sample. The pressure in the sample vessel was read by the computer at regular time intervals and compared with its preceding value. Equilibrium was regarded to be established if at least 50 pairs of readings are identical. This was found to be satisfactory if a time interval of 2 s in between readings was allowed. At equilibrium the pressure readings were stored for future processing and the '' distance " from this experi- mental point on the isotherm to its predecessor was calculated in terms of the amount adsorbed against the relative nitrogen pressure (pg/po).The dosing pump was then activated to transfer a calculated number of nitrogen doses in order to ensure a smooth spacing of points along the isotherm. During routine determination of the isotherm the dosing was automatically reversed at saturation adsorption, and the desorption branch of the isotherm was traced down top,/po = 0.25. SCANNING PROCEDURE The IBM 1800 process computer was preprogrammed to reverse the direction of the sorption sequence at certain specified relative pressures. In this way ascending as well as descending scanning curves could be recorded, or any desired sorption pathway within the hysteresis region. At present, up to 200 reversal points can be assigned to a single run. Upon approaching a reversal point, the dosing rate was automatically diminished in order to minimize " overshoot " and to assure an accurate recording of the start of the scanning curve.The number of experimental points to be recorded in a single run was not restricted: when the assigned memory storage capacity of the computer had been surpassed, its contents were automatically dumped on punched cards for further processing. In practice long runs were usually terminated only for maintainance of the mechanically moving parts of the system or in the case of leakage in stopcocks or greased joints. The actual number of experimental points in a single uninterrupted run has now exceeded some 3000, which corresponds to a few weeks' continuous operation. RESULTS t-PLOT ANALYSIS OF PRIMARY SCANNING CURVES : THE v-s CURVE The principle of t-plot analysis of scanning curves is based upon a theorem of the independent domain theoryY4 which states that directly after any direction reversal along a scanning pathway, sorption procedures correspond to reversible changes inJ .C. P. BROEKHOFF AND W . P. VAN BEEK 39 the state of the system. Such reversible changes in the state of the system will be largely due to variations with relative pressure of the thickness t of the adsorbed layers at the walls of the part of the porous system which was not filled with capillary condensate at the point of direction reversal, although reversible capillary pore filling cannot be excluded. True reversible capillary pore filling in an actual mesopore system is a rare phenomenon : no case of capillary condensation without hysteresis is known to us.For capillary condensation to be reversible, pores should possess closed ends and the pore geometry should be such that filling can take place without an increase in curvature of the adsorbate/vapour interface at any stage of the filling process. Reversible capillary pore filling should be discernible as an upward deviation from linearity in the t-plot of the initial part of the scanning curve following a direction reversal. In the absence of reversible capillary pore filling, the initial slope of a t-plot of any scanning curve in the vicinity of a direction reversal point will be proportional to the surface area of the walls of the pore domains not filled with capillary condensate at the direction reversal point. This proportionality takes a particularly simple form in cases where the radius of the wall curvature of the domains is large in comparison with the thickness of the adsorbed layer.For a scanning curve i, we may then write : where V, = the total volume of the adsorbate at a certain point along a scanning route directly after a pressure reversal, Vpi = the volume of all domains completely filled (and thus not accessible to changes in adsorbed volume), Sci = the surface area of the walls of all " empty " domains, and t = the statistical thickness of the adsorbed layer at the corresponding p g / ~ o (assumed to be independent of the domain geometry), in which case it can be derived from a suitable standard t-curve for the class of materials under investigati0n.l * Application of eqn (1) requires the assumptions that the density of the adsorbed layer equals that of the bulk liquid at the same temperature, and that changes in free liquid-vapour meniscus area (e.g.at pore mouths) between neighbouring states are negligible. The importance of eqn (1) lies in the possibility of characterizing quantitatively changes in the state of the domain system between two neighbouring reversal points in terms of pore volume and surface area. In particular the VPi-Sci relation for subsequent reversal points along either the adsorption or the desorption boundary curve (denoted here by the V-S curve), yields direct information about the " pore size " ri of domains filling or emptying along the boundary curves : For ideal tubular pores ri would equal Rp/2, for equidistant slits Op/2 and for spheroidal cavities Rp/3.In principle this will enable us to assess directly the characteristic dimensions of domains in pore space without recourse to any relation of the Kelvin-type 17* l8 and thus to make a qualitative and quantitative check upon the validity of the capillary condensation-evaporation model for hysteresis of physical adsorption in mesopores. More extensive sets of data taken in different parts of the hysteresis region will lead to an insight into the validity of the assumption of indepen- dent behaviour of domains in pore space, as in that case all Vp,-Sci points should lie on a single V-S curve which contains the essential information about the size distri- bution in the porous system. As stated, applicability of eqn (1) requires a negligible contribution of reversible capillary pore filling as well as negligible influence of pore wall curvature upon the40 CAPILLARY CONDENSATION BY SCANNING thickness of the adsorbed layer.If the t-plot of the adsorption boundary curve of the hysteresis loop is predominantly linear or shows a downward inflexion for increasing t-values, then it is reasonable to assume for a mesopore system that both conditions are well satisfied : such behaviour is generally associated with open slit-shaped pores. Even so, it must be stressed that eqn (1) can only be expected to hold for states in the direct vicinity of a direction reversal point. At larger separations from a direction reversal point, irreversible pore filling (ascending scanning curves) or emptying (descending scanning curves) is bound to occur.It would in principle be possible to determine experimentally the extent of the reversible part of a scanning curve after a direction reversal point by measuring, from each point of the scanning curve, a secondary scanning curve in the direction of the reversal point. In a few particular cases such measurements were made, and it was then found that in those cases the initial part of primary scanning curves was indeed reversible. In view of the large number of primary scanning curves required for the present analysis, such a procedure did not prove feasible as standard practice. Therefore, we were faced with the necessity of selecting the maximum number of consecutive experimental points on a scanning curve after direction reversal which is compatible with eqn (l), with due regard for the unavoidable experimental error in each of the datum points.The following procedure was adopted. A set of three or (preferably) more consecutive datum points, including the reversal point on the boundary curve of the hysteresis loop, was fitted to eqn (1) by means of linear regression. The regression coefficient and the 90 % confidence intervals for slope and intercepts were calculated according to ref. (19). The size of the ultimate set chosen was such that the correlation coefficient was maximal and the confidence intervals were minimal. There was usually a well-defined number of consecutive datum points that could be included in the set in order to satisfy these criteria.Inclusion of more datum points then led to larger confidence intervals and less satisfactory correlations, due to systematic deviations from linearity at larger distances from the reversal point at the boundary curve. This choice of the optimum number of datum points to be included in the regression procedure was checked by visual inspection for linearity of the initial part of the t-plot selected for the regression procedure from the complete t-plot of the scanning curve. The optimum set usually consisted of some five to ten experimental points. Application of this t-plot method to the analysis of scanning data, will be discussed elsewhere.20 We thank Mr. J. van Duijn and Mr. J. Siebesma for solving the problems in the electronics of the process control, Mr.B. H. van Wijngaarden and Mr. J. Bohm for programming the process control and Mr. E. 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