Analysis of uncertainties in manometric gas-adsorption measurements

Journal of Colloid and Interface Science 326 (2008) 1–7

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Journal of Colloid and Interface Science www.elsevier.com/locate/jcis

Analysis of uncertainties in manometric gas-adsorption measurements II. Uncertainty in α S -analyses and pore volumes A. Badalyan, P. Pendleton ∗ Center for Molecular and Materials Sciences, Sansom Institute, University of South Australia, Adelaide, South Australia 5000, Australia

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 18 April 2008 Accepted 1 July 2008 Available online 4 July 2008

We describe procedures to propagate the uncertainty in adsorption data and α S -values to generate uncertainty in apparent primary, secondary, and total micropore volumes for porous activated carbons exhibiting Type I and IV character. The α S -data are interpolated from selected non-porous reference material (NPRM) adsorption isotherm data with some adsorbents exhibiting surface chemistry quite different from and some similar to that of the porous adsorbents (PA). We show that a statistically constant apparent total micropore volume can be determined independent of the NPRM surface chemistry. In contrast, NPRM surface chemistry appears to influence our ability to identify unequivocally the filling and condensation ranges of micropore filling, leading to statistically different apparent primary and secondary micropore volumes. © 2008 Elsevier Inc. All rights reserved.

Keywords: Experimental uncertainty Nitrogen adsorption α S -Method Micropore volume

1. Introduction A major theme of our gas adsorption research is to define the sources of adsorption measurement uncertainty in gas adsorption and to determine how their propagation influences the results used for porous materials characterization. The focus of this communication is to define the uncertainty in apparent pore volumes derived from the widely used α S -plot method via nitrogen gas adsorption isotherm comparison [1]. We show how the uncertainty in amount adsorbed leads to uncertainty in apparent pore volumes and how the uncertainty in the α S -values are due to uncertainty in the amounts adsorbed by the NPRMs. Although some researchers claim that the application of α S method gives overestimated pore volume values for highly microporous solids [2], they still agree that this method is one of the most widely used for pore volume determination. This method, together with its predecessor t-plot, does provide a very important and useful generalized procedure for micropore volume determination in many recently published papers to mention a few [3–7]. Using the α S -method one derives values of primary, secondary and total micropore volumes. Primary micropore filling according to Sing et al. [8] associates with molecular sized pores at very low relative pressures, whereas at higher relative pressures adsorbate molecules fill secondary micropores. For nitrogen adsorbate Rouquerol et al. [9] give the following “permitted” ranges for primary and secondary effective pore widths: 0.4–0.7 and 0.7–1.8 nm, respectively. Vari-

*

Corresponding author. Fax: +61 8 8302 1087. E-mail address: [email protected] (P. Pendleton).

0021-9797/$ – see front matter doi:10.1016/j.jcis.2008.07.001

©

2008 Elsevier Inc. All rights reserved.

ous modifications of Sing’s original method now exist [10,11], but the basic premise of the method remains constant: the material selected as the NPRM should exhibit surface chemistry, and hence affinity towards the adsorptive, similar to that of the test or suspected PA. Jaroniec and co-workers [10] examined this hypothesis for nitrogen gas adsorption isotherms on porous carbons using a Sterling FT-G (2700) graphitized carbon black and a series of Black Pearl (oil furnace) carbon blacks as the NPRM. Their general observation was that the presence or absence of filling and condensation swings depended on the choice of NPRM surface. Previously, Mikhail and co-workers [12] promulgated the concept of matching BET c-coefficients, equivalent to similarity in adsorption enthalpy. Their hypothesis lost favor due to the difficulty in decoupling the coefficient for adsorption by the external surface from that for the pore network. To perform a critical inspection of the dependence of micropore swings in α S -plots we suggest that one should be able to distinguish between the influence of measurement uncertainty on the amount adsorbed by the NPRM and the test PA. Now that the sources of uncertainty in amount adsorbed have been readily defined and evaluated [13,14], it is appropriate to examine the concept of uncertainty in the α S -plot method, the uncertainty of the amount adsorbed data for the NPRM, and the apparent pore volume and its uncertainty for PA. In this work, we refer to our NPRM in contrast with non-porous standard reference materials (NPSRM) whose classification is due to extensive independent testing and comparison of the adsorption data on the same samples prepared reproducibly and tested in various laboratories. A determination of the combined standard uncertainty (CSU) in apparent pore volume will provide an

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effective (statistical) means for comparison of apparent pore volumes derived from NPRM with different surface chemistry. We acknowledge that various earlier researchers found differences in monolayer regions of adsorption isotherms when using NPRM with surface chemistry different from that for the investigated microporous materials [15–18] cited among other publications by Sing and Williams [4]. However, the quantification of such differences (or if these differences are significant or not) was not substantiated due to the unavailability of a “comparison measure,” which is CSU in micro- and mesopore volumes. To date, there are no publications outlining a rigorous analysis of uncertainties in pore (microand meso-) volumes. Thus, we deliberately compare NPRM offering chemistry similar to and quite different from that of the porous test adsorbents to establish the extent of the surface chemistry effect on thus evaluated micropore volumes. Such analyses become feasible once the uncertainty in the amount adsorbed by each of the adsorbents becomes known [13]. Absolute values of the apparent micropore volumes of porous activated carbon adsorbents via nitrogen adsorption typically vary from 0.2 to 0.6 cm3 /g, with researchers reporting their values to 2 and sometimes 3 significant figures without justification or indication of CSU. The vast majority, if not all, of the published papers have the same form of result presentation. It is, therefore, not correct to compare micropore volumes for various materials or check the quality of any theoretical model when experimental data and calculated from the results are given only with their values without the range of their validity, which is defined by CSU. Distinctions between various adsorbents can be addressed only on the basis of CSU of respective measurements for these materials obtained using either the same or different experimental equipment. It is, therefore, not possible before measurements to say what level or value of uncertainty in the measurements is needed to make distinctions between various adsorbents via α S -method; the CSU will be known only after measurement and calculation. We suggest that a detailed uncertainty (analysis) in the experimental data will provide numerical criteria for comparison between various adsorbents and closeness of fit between theoretically and experimentally derived data. In the present communication we provide a summary of the methodology to evaluate and propagate the uncertainty in adsorption data leading to an uncertainty in apparent micropore volumes defined via Sing’s method of α S -plot analysis. We present an analysis and discussion of two types of porous activated carbons, and then discuss how uncertainty data can be used to guide and/or control the identification of linear sections of the α S -plot leading to apparent primary and total micropore volumes. It is very important to understand that our approach results in the value of CSU in micropore volume, which should not be confused or interchangeably used with concepts of accuracy, precision, repeatability and reproducibility. Both, accuracy and precision are qualitative concepts, therefore “such terms not to be used as synonyms or labels for quantitative estimates” [19,20]. Since in our calculations we used results of a single isotherm for each of NPRMs and porous adsorbents where measurements were carried out only once for each experimental adsorption point and resulted in values of primary, secondary and total micropore volumes, it would be wrong to talk about precision of results, since precision deals with “the closeness of agreement between independent test results obtained under stipulated test conditions” [20]. Likewise, repeatability and reproducibility are not applicable to our calculations, since both of these terms are related to repetitive measurements of the same quantity under the same and changed conditions of measurements, respectively [19]. Therefore, CSU is associated with the result of a single measurement and/or calculation [20], which in our case is micropore (primary and secondary) or mesopore volumes. Every measurement outcome must be accompanied with its experimental

uncertainty, thus “implying increased confidence in the validity of a measurement result” [20]. Nonetheless, each of these objectives are addressed in the calibration of our adsorption apparatus [13]. We suggest that the material presented here, although brief in detail is sufficient enough for any researcher involved in the routine gas adsorption measurements to apply this methodology to their experimental gas adsorption data to further validate them. 2. Materials and methods 2.1. Materials Three non-porous materials with different surface chemistry were used to develop reference α S -plots: non-graphitized carbon black (ex. Micromeritics, GA, USA); graphite cloth (ex. National Carbon Company, MA, USA); and Aerosil 200 silica (ex. Degussa, Düsseldorf, Germany). These α S -plots were used for the evaluation of apparent pore volumes and their respective CSU for FM1/250, a steam-activated carbon cloth (ex. Calgon Carbon Corp., PA, USA) and a phosphoric acid-activated, wood-based carbon, Picazine (ex. PICA, Australia). The choice of these two porous adsorbents is driven by the fact that FM1/250 is wholly microporous material, whereas Picazine’s structure is both microporous and mesoporous [21]. Therefore, by applying the α S -method to these materials and having established CSU in respective pore volumes, we will be able to quantify the deviations in pore volumes for these classes of adsorbents. We do not intend to consider other mesoporous materials with hysteresis loops, since our approach in establishing the procedure for CSU calculations can be equally applied to other mixed micro- and mesoporous adsorbents. Both porous carbons were washed continuously with 18-MOhm resistance de-ionized water to remove any residual water-soluble activating agents, until the effluent resistance matched that of the influent resistance. The samples were dried in an oven at 398.15-K, then stored in a desiccator until further use. 2.2. Nitrogen adsorption measurements Manometric nitrogen adsorption by the non-porous and porous adsorbents was carried out at 77-K using our automated manometric gas adsorption apparatus [22]. All samples were heated to 473-K at a rate of 2-K/min, soaked for 4-h and allowed to cool convectively to room temperature, generating a residual 0.7-mPa (5 × 10−6 -mmHg) pressure over the sample. Dead-space measurements were made at 77-K by the exposure of samples to gaseous helium. Gaseous nitrogen was used for adsorption experiments. Both gases were supplied by BOC Gases Australia, and were of Ultra High Purity Grade (99.999%). Thermal transpiration effects were accounted for at pressures below 266-Pa. Throughout the adsorption–desorption process the liquid nitrogen level was controlled constant ±0.15-mm. 3. Results and discussion 3.1.

α S —Uncertainty analysis in NPRM data

Fig. 1 summarizes the nitrogen adsorption isotherms for the non-porous reference and the porous adsorbents. The uncertainty in amount adsorbed, u C (na ), was calculated as described previously [13]. The non-porous adsorbents exhibit the classical Type II shape according to IUPAC recommendations [23]. For comparison purposes the BET-nitrogen specific surface area, A BET , for each adsorbent is given in Table 1 with their associated u C ( A BET ). The A BET for the non-porous carbon black is 109.42 ± 0.72 m2 /g, which compares excellently with that published previously (110.31 ± 0.58 m2 /g) [13].

A. Badalyan, P. Pendleton / Journal of Colloid and Interface Science 326 (2008) 1–7

3

The definition and propagation of the CSU in interp

α S -values re-

quires na0.4 )NPRM and the uncertainty in the polynomials employed as spline functions. Following the previous logic, we calculate CSUs in α S )NPRM -values, identified as u C (α S )NPRM ). Applying Eq. (1) to the usual definition of

interp a α S )NPRM = (na )exper NPRM )/n0.4 )NPRM gives [25]:

u C (α S )NPRM )



=



∂ α S )NPRM exper ∂ na )NPRM

 interp na ) NPRM

exper

dna )NPRM



2 +

∂ α S )NPRM



interp ∂ na )NPRM

exper na ) NPRM

interp

dna )NPRM

2

.

(2) exper As expected from the form of Eq. (2), since u C (na )NPRM ) is cumulative with relative pressure, then u C ( S )NPRM ) also becomes

α

cumulative [25]. The α S -data for hydroxylated silica reported by Bhambhani et al. [26] and for carbon black by Kaneko et al. [27,28] widely used as NPRM are not included in our α S -uncertainty analysis because exper neither data set includes information on the u C (na )NPRM ) nor any indication of apparatus volumes from which one can develop such uncertainty analysis [13]. Fig. 1. Nitrogen adsorption–desorption isotherms for: (1) FM1/250; (2) carbon black; (3) Aerosil 200 silica; (4) Picazine adsorption; (5) Picazine desorption. Table 1 A BET values for NPRM and PA Material

A BET (m2 /g)

u C ( A BET ) (m2 /g)

RCSU in na (STP) (%)

p / p ◦ range

Carbon black Graphite cloth Aerosil 200 silica FM1/250 Picazine

109.42 5.043 207.81 1033.9 1682.3

0.72 0.005 1.89 10.9 13.4

0.25–1.01 0.02–0.06 0.48–1.79 0.37–1.81 0.39–3.97

8.0 × 10−6 –0.9743 5.8 × 10−6 –0.9995 4.3 × 10−6 –0.9851 8.2 × 10−7 –0.9608 1.3 × 10−6 –0.9845

One of the features of Sing’s α S -method is to determine the amount adsorbed for NPRM at 0.4p ◦ , na0.4 )NPRM . It is not convenient to experimentally determine the amount adsorbed exactly at this value of relative pressure. For this reason, an analytical inexper terpolation of experimental adsorption data, na )NPRM = f ( p / p ◦ ), ◦ in close vicinity of 0.4p should be carried out. Any interpolation introduces additional error. Therefore, an analytical polynomial expression which reproduces NPRM experimental adsorption data with an error less than CSU in these data should be chosen. We used the MATLAB® Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) subroutine [24] to spline-fit the NPRM adsorpinterp

tion isotherm data to determine na0.4 )NPRM , and to calculate values of α S )NPRM . The subroutine returned differences between thus interpolated and experimental amounts adsorbed two orders lower than CSUs in the latter. CSUs in the interpolated data were evaluated via implicit differentiation of the cubic Hermite polynomial expressions; since interp

interp u C (na )NPRM )

exper  u C (na )NPRM ), we also determined interp subroutine for u C (na0.4 )NPRM ) = f ( p / p ◦ ),

u C (na0.4 )NPRM ) via a PCHIP since this CSU has a cumulative nature. All these preliminary interp

calculations were necessary to ensure that u C (na0.4 )NPRM ) is not exper greater than u C (na )NPRM ) values for data points on either side of 0.4p ◦ . Relative combined standard uncertainties (RCSU) in the experimental amounts adsorbed range around 0.93, 0.05, and 1.67% for carbon black, graphite cloth, and Aerosil 200 silica, respectively. The CSU in a general expression composed of independent variables is given by Eq. (1) [25]

   2  2   ∂y ∂y uC ( y) =  dx1 + · · · + dxn . ∂ x1 i =2,...,n ∂ xn i =1,...,n−1 (1)

3.2.

α S —Uncertainty analysis in PA adsorption data

The activated carbon cloth sample FM1/250 exhibits a Type I nitrogen adsorption isotherm shape implying the presence of micropores according to IUPAC recommendations [23]. Desorption showed no statistically significant hysteresis. To explore the influence of mesopores on uncertainty analyses, we included the powdered activated carbon Picazine because for nitrogen adsorption it gives a Type II H3 according to IUPAC recommendations [23] or Type IIb isotherm according to Rouquerol et al. [9]. The loop effectively closes at ≈0.42p ◦ ; we say “effectively” since the exper exper u C (naads )PA ) and u C (nades )PA ) overlap at pressures <0.42p ◦ implying the amounts adsorbed are similar valued. If uncertainty in the amount adsorbed had not been calculated then the criticism that the isotherm is not an equilibrium representation could be leveled against the data. The enhanced amounts adsorbed by Picazine at pressures <0.1p ◦ imply the presence of micropores. For reference purposes only, we defined the monolayer equivalent A BET specific surface area for FM1/250 to be 1033.9 ± 10.9 and 1682.3 ± 13.4 m2 /g for Picazine. The next step is interpolation of α S -values from α S )NPRM data for NPRM in the whole range of relative pressures, p / p ◦ )NPRM . One can use piecewise interpolation, since a single polynomial expression cannot well represent these data. We again used a PCHIP subroutine to obtain the relationship α S )NPRM = f ( p / p ◦ )NPRM ). Again, the interpolated data agree with those experimentally obtained within their CSUs. Using coefficients of this polynomial we calcuinterp

lated the relationship in the form α S )NPRM = f ( p / p ◦ )PA ). Thus, we obtained α S -values for the α S -plot. The CSUs in these values were evaluated from a polynomial u C (α S )NPRM ) = f ( p / p ◦ )NPRM ) by substituting p / p ◦ )NPRM by p / p ◦ )PA . Evaluation of apparent pore volumes from α S -plots requires conversion from the amount adsorbed at STP to volume adsorbed as V P , cm3 /g. The cumulative nature of the uncertainty in the amount adsorbed and the independence of the coefficients for conversion, allows us to calculate u C ( V pore ) via Eq. (1) also with an accumulated value. In this case, of course, y represents the volume of liquid adsorbed and xi ,...,n the amount adsorbed and the various conversion factors, of which the liquid-phase density has the largest uncertainty. Overall, the uncertainty contributions from exper the conversion factors are very small compared with u C (na )PA ), and the RCSU in V pore are similar in value to the adsorption data ranging between 0.371 and 1.809%. Thus we are able to generate several α S -plots shown in Figs. 2 and 3. interp

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Gregg and Sing originally postulated that the data points should lie on a straight line when determining the apparent primary and total pore volumes [29]. Unlike in the BET analysis which restricts the linear regression analysis to a specified relative pressure range, curvature in the α S -plots and no specified α S -values’ range for

analysis complicates accurate and inter-laboratory selection of the best linear range for pore volume evaluation. Inclusion of the uncertainty in both abscissa and ordinate data points in a graphical analysis guides the selection of the linear range and the calculation of the uncertainty in both slope and intercept, as shown in

Fig. 2. α S -Plot analysis of FM1/250 using the NPRM: (1) carbon black; (2) Aerosil 200 silica; (3) graphite cloth.

Fig. 3. α S -Plot analysis of Picazine using the NPRM: (1) carbon black; (2) Aerosil 200 silica; (3) graphite cloth.

Fig. 4. Analysis of linear regression including data uncertainty effects on intercept uncertainty: (a) All data points; (b) lowest 3-data points; (c) middle 3-data points; (d) highest 3-data points.

A. Badalyan, P. Pendleton / Journal of Colloid and Interface Science 326 (2008) 1–7

Table 2 Impact of data range and uncertainty selection on intercept uncertainty

All data Lowest 3-data Middle 3-data Highest 3-data

Intercept

Graphical method u C (intercept)

0.5 0 .5 0 .5 0. 5

±1.0 ±1.2 ±3.2 ±6.0

WMLS-method u C (intercept)

±0.38 ±0.66 ±4.94 ±17.63

Fig. 4a [30]. As an example, consider a monotonically increasing abscissa with a fixed value uncertainty (±0.1) leading to an increasing uncertainty in the ordinate values via, e.g. y = 2x + 0.5. Although we have a constant slope and intercept, depending on whether all five (Fig. 4a), the lowest (Fig. 4b), the middle (Fig. 4c), or the highest (Fig. 4d) three data-pair values and their uncertainty are considered, we generate very different u C (intercept)-values, as summarized in Table 2. A standard analytical method linear data curve-fitting is the weighted mean least squares (WMLS) method [13]. Establishing a linear range over a small number of data points which may exhibit slight curvature increases the difficulty in accurately determining the intercept and slope values. The inclusion of a weighted mean value in the u C (intercept) calculation demonstrates the influence of the uncertainty in the ordinate values. For either method of analysis, the selection of an incorrect range will impact on uncertainty in the pore volume determined by this method. Figs. 2 and 3 show comparisons of the α S -plots for the porous test adsorbents using the three non-porous reference adsorbents and include the CSU in the data in both coordinates. For FM1/250 in Fig. 2, the plots converge asymptotically for α S > 0.8, which is not too surprising since the test isotherm is strongly Type I. We conclude that at relative pressures equivalent to α S > 0.8 all of the pores are completely filled and the external surface is covered by at least a statistical monolayer amount adsorbed. Actually, if these data were to be considered as an adsorption isotherm, the form of the equation describing the isotherm would be similar to the Frenkel, Halsey, Hill equation. We suggest that for relative pressures equivalent to α S > 0.8 the standard surface chemistry has no influence on the adsorption comparison. For α S < 0.8, the range from where we expect to identify the porous adsorbent’s apparent primary micropore volume, we see that the three non-porous reference adsorbents produce different linear and curved sections of the plot, implying that surface chemistry has a great influence on the comparison curves. This observation does not intrinsically confirm Sing’s original hypothesis of matching reference adsorbent surface chemistry with that of the external surface of the porous test adsorbent because we have not (yet) attempted to match surface chemistry. In most α S -plots, curvature exists at the limits of the linear ranges used to identify the apparent primary and total micropore prim.

total volumes, V micropore and V micropore , respectively. With some pore structures, no obvious linear range can be identified due to an apparently smooth curve. Identification of at least the minimum number of data points in a linear range then becomes especially important in defining the uncertainty in the apparent pore volumes. Our approach is to determine the maximum number of data points and include an additional criterion for linearity, the Pearson linear correlation coefficient, R 2 . Our subroutine for data analysis searches for a data range (of >3 points) yielding R 2  0.9990 in conjunction with a WMLS analysis of the data. These ranges are summarized in Table 3. One needs to appreciate that in the presence of curvature, increasing the number of data analyzed prim.

total can affect the V micropore - and V micropore -values as well as their prim.

total CSUs, u c ( V micropore ) and u c ( V micropore ), respectively, as commented

5

Table 3 α S -Ranges used to determine apparent micropore volume for FM1/250 Standard material

prim. α S -Range for V micropore

total α S -Range for V micropore

Carbon black Aerosil 200 silica Graphite cloth

0.27–0.40 0.24–0.29 0.13–0.19

1.15–3.72 0.93–3.06 0.89–2.19

Table 4 α S -Ranges used to determine apparent micropore volume for Picazine Standard material

prim. α S -Range for V micropore

total α S -Range for V micropore

Carbon black Aerosil 200 Graphite cloth

0.09–0.40 0.11–0.42 0.07–0.15

0.94–1.43 0.93–1.54 0.90–1.92

above. In practice, one should select the data range that minimizes these latter parameters and maximizes R 2 . Although the data in Fig. 2 show convergence for α S > 0.8, subtly different α S -value ranges are employed for the WMLS analysis for apparent total micropore volume determination because each set of data was analyzed separately. These ranges are summarized in Table 3. When attempting a WMLS analysis of a set of data that either are close to or are horizontal, the correlation coefficient tends to zero, not unity, implying that there is a weak relationship between V a and α S . By selecting volume adsorbed data points, V a , that are close to horizontal as the linear range for apparent total micropore volume determination, we need to compare the standard deviation of these adsorbed voltotal ume data, σ ( V a ), with u c ( V micropore ) [25]. Statistically, if σ ( V a ) < total u c ( V micropore ) then the volume adsorbed data points correspond-

ing to σ ( V a ) should be chosen. In our present measurements, 0.0002 < σ ( V a ) < 0.0004 cm3 /g, which is considerably less than total total the corresponding u c ( V micropore )-values; the u c ( V micropore )-values vary within their corresponding CSU irrespective of the number of experimental points chosen for analysis. Although it may seem ideal to choose 2-points which would give R 2 = 1.000, this total case corresponds to a relatively high u c ( V micropore ). We evaluated

σ ( V a ) and R 2 data sets of 2 to 7 experimental points, and selected a 5-points data set because these two variables are at their minimum. If one measures more adsorption points, one may assume that a lower level of uncertainty in apparent volume will be achieved, however, one also needs to appreciate that the uncertainty in the amount adsorbed will also increase, possibly invoking the observations drawn from Fig. 2. In contrast with apparent total micropore volume analyses, non-porous reference adsorbent selection affects (or even governs) the range of the α S -values used for identification of the linear section of the plot and thus the value of the apparent primary micropore volume. The choice of α S -value range used for determination of apparent micropore volumes for FM1/250 and Picazine prim.

are given in Tables 3 and 4. Since V micropore is determined from a sloping linear section of the graph, using the additional criterion that R 2 > 0.9990 simplifies the identification of an appropriate α S -range for analysis. Considering the effect of uncertainty in the prim.

values for an intercept as described in Fig. 4, the V micropore -value for FM1/250 was determined using carbon black as the reference range from 0.192 to 0.193 for a series of 3–7 data points in the linear range. Since the CSU ranged from 0.006 to 0.011 any combination of these data point ranges gives a statistically constant apparent primary micropore volume of 0.193 ± 0.008 cm3 /g. This value corresponds to 5-data points in the analysis. prim.

total The V micropore - and V micropore -values for FM1/250 determined using the above analytical procedures are summarized in Table 5. We report 3-significant figures for each volume [31], however, if

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A. Badalyan, P. Pendleton / Journal of Colloid and Interface Science 326 (2008) 1–7

Table 5 Apparent micropore volumes for FM1/250 prim.

Standard material

V micropore (cm3 /g)

second. V micropore (cm3 /g)

total V micropore (cm3 /g)

Carbon black Aerosil 200 silica Graphite cloth

0.193 ± 0.008 0.220 ± 0.016 0.125 ± 0.005

0.267 ± 0.011 0.238 ± 0.020 0.330 ± 0.022

0.460 ± 0.008 0.458 ± 0.011 0.455 ± 0.022

uncertainty in the volume adsorbed is unavailable, pore volumes should only be reported with 2-significant figures [25]. Clearly, from Table 5, the apparent total micropore volumes for FM1/250 are statistically constant and independent of the non-porous reference adsorbent. The methodology used to evaluate these volumes is discussed below. The presence of mesopores in a porous material may lead to difficulty in clearly defining the linear range to establish the apparent total micropore volume. If the material contains both micropores and mesopores then we can exploit the expected downwards and upwards trends to guide the location of the linear section of the plot to define the total micropore volume. For the Picazine sample in Fig. 3, the α S -plots for the three non-porous reference adsorbents converge to an approximately single line for α S > 0.9, which may be coincidental with FM1/250, and shows an expected upwards turn (due to mesopores) for α S > 1.5. This convergence also helps to establish the relative pressure at which micropore filling is most probably completed and the upwards departure that for the onset of mesopore condensation. The presence of mesopores creates a well defined slope in the α S -plot and thus, we can employ the criteria of maximum data range including data uncertainty and R 2 > 0.9990. Quantifying the effect of α S total -values for Picazine, we selected range selection on the V micropore total 6-data points to establish the V micropore -value giving the minimum total total u c ( V micropore )-value and maintaining R 2 > 0.9990. The V micropore value for Picazine in Table 6 with the carbon black used as the NPRM agrees excellently and within the CSU with our previously published data for Picazine [32]. The agreement is within 0.63% total total for V micropore , 1.44% for V mesopore , and 0.61% for V pore . The analprim.

ysis method for the V micropore is the same as that for FM1/250, leading to 5-data points’ selection.

Fig. 5. α S -Values = f (log p / p ◦ ) for the NPRM: (1) carbon black; (2) Aerosil 200 silica; (3) graphite cloth showing low pressure “curvature.”

In Figs. 2 and 3 of course, data convergence is not caused by standard data normalization but is due to a similarity in adsorption processes. A physical adsorption interpretation of data convergence is to assume that it is probably due to the (porous) adsorbent’s surface being covered with at least a complete adsorbed layer (as opposed to a statistical monolayer) and probably more, such that the underlying surface has no influence on adsorption at subsequent higher relative pressures. What is the implication of this observation on the comparison with porous adsorbents? The adsorption data in Figs. 2 and 3 show convergence above α S > 0.9 suggesting that due to micropore filling and/or external surface coverage of the porous test adsorbent and of the surface of the reference adsorbent occurring at pressures equivalent to α S > 0.9, any non-porous material may be used as a non-porous reference total -value of a porous material adsorbent to determine the V micropore

3.3. Effect of reference adsorbent surface chemistry on apparent pore volume determination

total as follows from Tables 5 and 6. Consequently, the V micropore -values are statistically constant for both porous adsorbents. An interesting observation can also be made for α S -ranges cor-

Each of the three reference adsorbents used in this work offer a different surface chemistry on comparison with the porous test adsorbents. Of the three, we suggest that carbon black offers the closest match. Adsorption isotherm comparisons are made for these standards as α S )ref = f (log( p / p ◦ )) in Fig. 5 allowing us to examine and compare the lowest pressures adsorption data. As expected, considerable differences exist in the normalized amount adsorbed for a given, fixed, low relative pressure, however, as the α S -values approach unity, the process of normalizing the data appears to make them somewhat independent of the adsorbent. Data convergence occurs at a value of approximately 0.4p ◦ . Mathematically, this observation is not too surprising since normalization of the data to the amounts adsorbed at 0.3p ◦ and 0.5p ◦ return convergence at the (expected) equivalent relative pressures.

responding to the V micropore where appropriate rotation of either Figs. 2 or 3 and 5 allows us to overlay the general shape of these plots. For data clarity in Fig. 5, we have removed the uncertainty in the α S -values and relative pressure values. Clearly, for a fixed low relative pressure below 0.1p ◦ the α S -values or relative amounts of nitrogen adsorbed increase with increasing oxygen content of the non-porous adsorbents. From this observation we concur with Sing’s original hypothesis that the non-porous reference adsorbent surface chemistry plays an important role in defining the apparent primary micropore volume. In both Figs. 2 and 3 we see that the carbonaceous reference adsorbents produce the filling and condensation swings while the Aerosil 200 silica reference adsorbent results in a rounded curve for which linear analyses are position dependent. These observations are consistent with Jaroniec and co-

prim.

Table 6 Apparent pore volumes for Picazine prim.

Standard material

V micropore (cm3 /g)

second. V micropore (cm3 /g)

total V micropore (cm3 /g)

V mesopore (cm3 /g)

Carbon black Aerosil 200 silica Graphite cloth

0.069 ± 0.001 0.081 ± 0.002 0.095 ± 0.002

0.408 ± 0.030 0.421 ± 0.023 0.415 ± 0.009

0.477 ± 0.030 0.502 ± 0.023 0.510 ± 0.009

0.832 ±0.038 0.807 ±0.033 0.799 ±0.025

A. Badalyan, P. Pendleton / Journal of Colloid and Interface Science 326 (2008) 1–7

workers’ [10] analyses using Sterling and Black Pearls carbon blacks prim.

second. as reference adsorbents. The V micropore - and subsequent V micropore values deduced from each plot, and summarized in Tables 5 and 6, are statistically different. More work is required to properly address the observation of surface chemistry influence on apparent primary micropore volume evaluation, possibly along the lines of Gregg and Langford’s pre-adsorption method [33].

4. Conclusions The uncertainty in α S -data requires a detailed analysis of the uncertainty in the amounts adsorbed by both reference and porous test adsorbents. Cubic spline interpolation of the amounts adsorbed and α S -data and of their respective uncertainty values is an excellent method for defining such data as a f ( p / p ◦ ). Uncertainty in the volume adsorbed, combined with the weighted mean least squares analysis with the additional criterion of the linear correlation coefficient provides a reliable and reproducible strategy to identify linear ranges in the α S -plot associated with pore volumes, and pore volume uncertainty. The apparent total micropore volume definition may be made against any non-porous adsorbent since adsorbent surface chemistry is masked by the adsorbed layer. Matching porous test and non-porous reference adsorbent surface chemistry appears to be important and to affect the identification of micropore filling and condensation processes, and their associated apparent pore volumes. Acknowledgments We thank Prof. Ken Sing for fruitful discussions during the preparation of this manuscript. The authors thank the Australian Research Council Linkage Program and the University of South Australia for funding support. References [1] K.S.W. Sing, Chem. Ind. (London) 44 (1968) 1520. [2] M.J. Briggs, A. Buts, D. Williamson, Langmuir 20 (2004) 7123. [3] M. Seredych, B. Charmas, T. Jablonska-Pikus, A. Gierak, Mater. Chem. Phys. 82 (2003) 165. [4] K.S.W. Sing, R. Williams, Adsorp. Sci. Technol. 23 (2005) 839.

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[5] P. Prokesova-Fojtikova, S. Mintova, J. Cejka, N. Zilkova, A. Zukal, Microporous Mesoporous Mater. 92 (2006) 154. [6] S. Kubo, K. Kosuge, Langmuir 23 (2007) 11761. [7] T. Sunao, T. Takashi, F. Masayoshi, C. Masatoshi, J. Colloid Interface Sci. 268 (2003) 435. [8] K.S.W. Sing, in: S.J. Gregg, K.S.W. Sing, H.F. Stoeckli (Eds.), Characterisation of Porous Solids: Proceedings of a Symposium Held at the Université de Neuchâtel, Switzerland, from 9 to 12 July 1978, Society of Chemical Industry, London, 1979, p. 392. [9] F. Rouquerol, J. Rouquerol, K. Sing, Adsorption by Powders and Porous Solids, Academic Press, Sydney, 1999. [10] M. Kruk, M. Jaroniec, J. Choma, Carbon 36 (1998) 1447. [11] N. Setoyama, T. Suzuki, K. Kaneko, Carbon 36 (1998) 1459. [12] S. Brunauer, S. Mikhail, E.E. Bodor, J. Colloid Interface Sci. 24 (1967) 451. [13] A. Badalyan, P. Pendleton, Langmuir 19 (2003) 7919. [14] P. Pendleton, A. Badalyan, Adsorption 11 (2005) 61. [15] A.P. Karnaukhov, J. Colloid Interface Sci. 103 (1985) 311. [16] J. Fernandez-Colinas, R. Denoyel, Y. Grillet, F. Rouquerol, J. Rouquerol, Langmuir 5 (1989) 1205. [17] M.R. Carrott, P. Carrott, M.B. de Carvalho, K.S.W. Sing, J. Chem. Soc. Faraday Trans. 87 (1991) 185. [18] K. Fukasawa, T. Ohba, H. Kanoh, T. Toyoda, K. Kaneko, Adsorpt. Sci. Technol. 22 (2004) 595. [19] B.N. Taylor, C.E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, National Institute of Standards and Technology, 1997. [20] EURACEM/CITAC Guide CG4, Quantifying Uncertainties in Analytical Measurements, 2000. [21] P. Pendleton, S.H. Wu, A. Badalyan, J. Colloid Interface Sci. 246 (2002) 235. [22] A. Badalyan, P. Pendleton, H. Wu, Rev. Sci. Instrum. 72 (2001) 3038. [23] IUPAC, Pure Appl. Chem. 57 (1985) 603. [24] F.N. Fritsch, R.E. Carlson, SIAM J. Numer. Anal. 17 (1980) 238. [25] J.R. Taylor, An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, University Science Books, New York, 1982. [26] M.R. Bhambhani, P.A. Cutting, K.S.W. Sing, D.H. Turk, J. Colloid Interface Sci. 38 (1972) 109. [27] K. Kaneko, J. Membr. Sci. 96 (1994) 59. [28] K. Kaneko, C. Ishii, H. Kanoh, Y. Hanzawa, N. Setoyama, T. Suzuki, Adv. Colloid Interface Sci. 76–77 (1998) 295. [29] S.J. Gregg, K.S.W. Sing, Adsorption, Surface Area and Porosity, Academic Press, London, 1982. [30] D.P. Schoemaker, C.W. Garland, J.W. Nibler, Experiments in Physical Chemistry, McGraw–Hill, Sydney, 1989. [31] R.L. Burden, J.D. Faires, Numerical Analysis, Brooks Cole, New York, 2004. [32] S.H. Wu, P. Pendleton, J. Colloid Interface Sci. 243 (2001) 306. [33] S.J. Gregg, G.A. Langford, J. Chem. Soc. Faraday Trans. 1 73 (1977) 747.