Multilevel morphology of complex nanoporous materials - Langmuir

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Multilevel morphology of complex nanoporous materials Ahmad Motahari, Naiping Hu, Amir Vahid, Abdollah Omrani, Abbas Ali Rostami, and Dale W. Schaefer Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b00970 • Publication Date (Web): 14 May 2018 Downloaded from http://pubs.acs.org on May 15, 2018

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Multilevel morphology of complex nanoporous materials

Ahmad Motahari1,2, Naiping Hu1, Amir Vahid3, Abdollah Omrani2, Abbas Ali Rostami2, Dale W. Schaefer1,*

1

Department of Chemical and Environmental Engineering, University of Cincinnati, Cincinnati, OH, 45220-0012, USA 2

Department of Physical Chemistry, Faculty of Chemistry, University of Mazandaran, P. O. BOX 453, Babolsar, Iran 3

Research Institute of Petroleum Industry, Tehran, 1485733111, Iran

* Corresponding author. Tel: +1 513 377 2166; Fax: +1 206 600 3191 E-mail: [email protected] (D. W. Schaefer).

1 ACS Paragon Plus Environment

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Abstract This work exploits gas adsorption and small-angle X-ray scattering (SAXS) to illuminate morphology of complex nanoporous materials.

We resolve multiple classes of porosity

including previously undetected large-scale texture that significantly compromises the canonical interpretation of gas adsorption. Specifically, a UVM-7 class mesoporous silica was synthesized that has morphological features on three length scales: macropores due to packing of 150-nm globules, 1.9-nm-radius spherical mesopores inside the globules and >7-nm pockets on and between the globules. The total and external surface areas, as well as the mesopore volume, were determined using gas adsorption (αs-plot) and SAXS. A new approach was applied to the SAXS data using multi-level fitting to determine the surface areas on multiple length scales. The SAXS analysis code is applicable to any two-phase system and is freely available to the public. The total surface area determined by SAXS was 12% greater than that obtained by gas adsorption. The macropore interfacial area, however, is only 30% of the external surface adsorption by determined by αs-plot. The overestimation of the external surface area by the αs-plot method is attributed to capillary condensation in nanoscale surface irregularities. The discrepancy is resolved assuming the macropore-globule interfaces harbor fractally distributed nooks and crannies, which lead to gas adsorption at pressures above the mesopore filling pressure.


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1. Introduction Ordered nanoporous silicas have been extensively investigated in fields, such as optical devices,1 nanostructure synthesis,2 environmental purification,3 catalysis,4 separation technology5 and drug delivery.6 The utility of these materials depends on their morphology, which is often complex, extending over multiple length scales. This work focuses on gas adsorption and small-angle X-ray scattering (SAXS) analysis for a complex nanoporous silica. Using SAXS, we sort out the length-scale-dependent contributions to the gas adsorption isotherm.

Gas adsorption methods are popular because of their wide

availability. SAXS, on the other hand, reveals pore structure as a function of length scale ranging from nanometers to micrometers. The primary structural characteristics are the surface area, pore volume, and pore size distribution. In principle, pore size can be measured by a variety of techniques including gas adsorption, SAXS, mercury porosimetry, NMR,7 and transmission electron microscopy (TEM). Experience shows that these methods seldom lead to consensus on the morphology.8 Of these methods, only SAXS and TEM reveal structure over a broad range of length scales. TEM images, however, are typically 2-dimensional and subject to operator selectivity.9 Finally, all analysis methods suffer limitations due to assumptions required to reduce the raw data. As porous structures become more complex, methods of porosity characterization based on capillary condensation become equivocal.10,11 Interpretive models have restrictive assumptions regarding pore geometry (e. g. cylindrical, spherical or slit-like pores). In addition, accuracy of pore-size distributions declines rapidly for pores greater than 10 nm.12 Moreover, these methods differ in the assumed physics of multilayer adsorption, which leads to considerable discrepancy


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in the calculated pore-size distributions. A fundamental limitation of all sorption methods is inability to determine pore ordering. For simple morphologies surface area and mean pore size can be inferred from BET surface area, assuming all pores are accessible. The BET approach, however, gives the average pore size, which is misleading for complex systems with multiple structural levels. The αs and t-plot methods were developed to deal with multilevel morphology by distinguishing total surface area from so-called external surface area. As we will show, the difference between external and internal is equivocal for complex pore morphologies. There is a large body of literature questioning the accuracy of the BET surface area. Large deviations13,14 from the true surface area can occur especially if micropores are present.15 Our samples do not have microporosity and we find agreement within 12 % among BET, αs-plot and scattering methods for determination of the total surface area. A UVM-7 class mesoporous silica16 was synthesized and characterized by N2 gas adsorption, transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS). We find evidence for porosity on three length scales. One length scale is associated with 1.9-nm radius (spherical equivalent) nanoscale pores (Fig. 1). The second length scale is associated with larger pores that exist between the 150-nm globules that harbor the mesopores (Fig. 1). We refer to these two classes of pores as mesopores (subscript 1) and macropores (subscript 2). A third length scale is due to >7-nm surface texture. Capillary condensation in surface nooks and crannies occurs over a broad pressure range after the mesopores are filled. A new approach to SAXS analysis was adopted to determine the surface area, porosity and pore sizes based on length scale. Starting with only the measured sample density and the X-ray data, we calculate surface area, pore size, strut size, pore volume, pore volume fraction and strut mass


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density on two length scales. The pore characteristics determined from the SAXS data are compared with the gas adsorption using the αs approach, which purportedly separates adsorption on internal and external surfaces. Harmonization of SAXS and gas adsorption data, however, requires introduction of a third length scale associated with texture. This observation clarifies the limitations of the αs method for complex morphologies.

Figure 1. TEM images of the synthesized nanoporous silica at two magnifications. The left image reveals the mesopores. This image shows a narrow distribution of quasi-spherical 3.8-nm-diameter pores, some of which are interconnected. The right image is a superposition of multiple globules. Macroporosity exists between the globules. A higher magnification image is found in Figure S1 of the supplementary information.

2. Experimental 2.1. Materials Cetyltrimethylammoniumbromide (CTAB, C19H42BrN), tetraethylorthosilicate (TEOS) and triethanolamine (TEAH3) were purchased from Merck. All chemicals were used without further treatment. 2.2. Synthesis of nanoporous silica We used the atrane method to synthesize nanoporous silica in which the TEAH3 polyalcohol is a key factor used to balance the hydrolysis and condensation rates.17,18 In a typical synthesis, 5 ACS Paragon Plus Environment

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TEOS is added to predetermined amounts of TEAH3 and heated to 140 °C for 30 min or until no phase separation is observed after stirring. After cooling to 90 °C, CTAB is added to this solution. Water is then added slowly with stirring until a white suspension results. The final composition of reactants was 1.0 mole TEOS, 3.5 mole TEAH3, 0.25 mole CTAB, and 90 mole H2O. This suspension is aged for 4 h at room temperature. The precipitate was filtered, washed with water and then acetone followed by oven drying at 80 °C overnight. Thermo-calcination of the as-synthesized sample is carried out under flowing air at 550 °C for 6 h. The nitrogen adsorption–desorption profile of the resulting material is shown in Fig. 2.

600

500

'Desorption' 'Adsorption'

3

Volume (cm STP/g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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400

300

200

0.0

0.2

0.4

0.6

0.8

1.0

P/Po Figure. 2. N2 physisorption isotherm of nanoporous silica. The step at P/Po = 0.3 is characteristic of capillary condensation in mesopores. The second step, at P/Po > 0.85, corresponds to the filling of the large macropores that form the void space between globules. Between 0.40 and 0.85 adsorption occurs on the features attributed to capillary condensation in irregularities on and between the globules.

2.3. Preparation of samples for X-ray scattering For SAXS measurements the silica powder was packed in a cylindrical GRACE Bio-LabS SecureSealTM 8-mm diameter hybridization chambers with 1-mm path length. An empty cell was used as a blank. The mass of the sample was measured by subtracting the weight of the cell 6 ACS Paragon Plus Environment

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packed with sample from that of empty cell. The bulk density of the packed cells was measured to be 0.190 ± 0.006 g/cm3. A total of 4 samples were measured. 2.4. Characterization Ultra-small-angle X-ray scattering (USAXS) and pin-hole small-angle X-ray scattering (SAXS) data were collected using two instruments on the 15 ID-D beamline at the Advanced Photon Source (APS), Argonne National Laboratories (Argonne, Illinois, USA).

For USAXS, the

measured scattered intensity, I(q), is the differential scattering cross section per unit scattering volume on an absolute scale, measured as a function of the modulus of the momentum transfer, q, which depends on the X-ray wavelength and scattering angle. The instruments cover the range 10-4 ≤ q ≤ 2 Å-1, corresponding to length scales from 1.5 Å to 3 µm. Details on the instrument configuration can be found elsewhere.19,20 All data were subjected to an air-background subtraction. The USAXS data were desmeared using APS routines.21 The SAXS data were vertically shifted to match the desmeared USAXS data. The combined data were then fit to a 4level unified function using the Irena code.21 TEM was performed with a Philips CM 20 electron microscope. The sample was sonically dispersed in ethanol and transferred on to a Lacey carbon (on Cu mesh) grid. The carbon film was examined after the complete evaporation of ethanol. The applied accelerating voltage was 120 kV. N2 adsorption–desorption isotherms were obtained at liquid nitrogen temperature (77 K) using Micromeritics Gemini Surface Area Analyzer. Prior to N2 adsorption, 0.080 g of the sample was degassed under helium atmosphere at 250 °C for 2 h in the degassing port of the instrument. The nitrogen adsorption isotherms were collected at pressures, P, relative to the saturation pressure,


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Po. The relative pressure Pr = P/Po ranged from 0.05 to 0.98. The molecular area of nitrogen was assumed to be 0.162 nm2. 3. Results and discussion 3.1. N2 physisorption isotherm The adsorption data show two sorption processes (Fig. 2). The first step (Pr between 0.3 and 0.4) is a type IV isotherm (IUPAC nomenclature) characteristic of capillary condensation in mesopores. Between 0.4 and 0.85 we attribute sorption to globular surfaces, which show up as “external surface” in the αs plot (Fig. 3). Interpretation of data in this region is challenging, but possible with the aid of SAS data. The upturn at 0.85 is due to capillary condensation in the macropores. Because there is no hysteresis in the adsorption-desorption data, we do not believe that adsorption-induce deformation22 plays a significant role in the interpretation of the data. We used the αs-plot method (Fig. 3)

23,12

to determine the fraction of porosity in the mesopore

region. Sorption data for the LiChrospher Si-1000 silica reported by Jaroniec et al. was used as a non-porous reference adsorbent in the αs analysis.24 In the αs-method, the adsorption isotherm, V(Pr), is expressed as a function of the adsorbed amount for the non-porous reference adsorbent normalized by adsorbed amount at a relative pressure of 0.4:

=

(1)

.

Note that = 1 when = 0.4. The line in the low-pressure region in Fig. 3 can be written as: = +

0 < < 0.75

(2)

Here, subscript mi stands for micropore. For our data Vmi is zero within error. From the slope, , of line in the low-pressure region (small ) we determine the total surface area, Stot, as:

=

! "#$%,

(3)

.


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SBET,ref is the BET surface area of the reference sample. Eq. (3) assumes the absence of micropores. 1.0

0.8

3

Volume Adsorbed (cm /g)

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2

Sext = 112 m /g 3 V1 = 0.76 cm /g

0.6

0.4

0.2

2

Stot = 1004 m /g

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

αs Figure 3. The αs-plot for the adsorption branch of nanoporous silica using LiChrospher Si-1000 silica as the non-porous reference adsorbent. The near zero intercept indicates the absence of microporosity (below 2-nm diameter).

The equation for the line in the high-pressure region can be written as: = &' + (

1.25 < < 2.0

(4)

Here, the subscript 2 stands for the macropores that account for the external surface area. The intercept, Vicpt, is sum of the mesopore and micropore volumes. &' = + ≅

(5)

In our case, is negligible. is the mesopore specific volume. When microporosity is absent, we determine the external surface area (Sext) from the slope ( :

,- =

. "#$%,

/ .

(6)

the surface area of the mesopores, S1, is: = − ,-

(7)


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The pore volumes and surface areas are listed in Table 1. Vtot is defined as the observed adsorption volume at Pr = 0.99, which underestimates the actual total pore volume since sorption in the macropores occurs very close to saturation. These measured parameters are compared with those determined by small-angle scattering (SAS) as will be discussed in Section 3.2. If the sorption and SAS data were naively consistent, Stot would equal S3 and Sext would equal S2. The subscripts 1, 2 and 3 refer to surface areas associated with different length scales (1 = meso, 2 = macro, 3 = total of meso + macro). Table 1 shows that SAS finds more total surface area (S3 > Stot) and less macropore (or external) surface area (S2 < Sext) compared to the αs-plot. These discrepancies are explained in Section 3.5. Table 1. Surface areas and pore volumes determined using N2 sorption and SAS.

SAS

10-2×Stot

10-2×S3

10-2×Sext

10-2×S2

10-2×S1

(m2/g)

(m2/g)

(m2/g)

(m2/g)

(m2/g)

10.0±0.2

Vmi

(cm3/g) (cm3/g)

V1 (cm3/g)

1.0±0.1

0

0.76±0.05

0.34±0.02 11.3±0.7 4.7±0.3

0

0.71±0.1

1.12±0.12

11.6±0.6

Vtot

8.92±0.3

3.2. Small-Angle Scattering (SAS) Using SAS, it is possible to sort out morphological features as a function of length scale. Figure 4 shows the combined, desmeared ultra-small-angle X-ray scattering (USAXS) and small-angle X-ray scattering (SAXS) data. The USAXS and SAXS instruments cover different ranges of momentum transfer, q: ~ 10-4 ≤ q ≤ 10-1 Å-1 for USAXS and ~ 10-1 ≤ q ≤ 1 Å-1 for SAXS. Using both SAXS and USAXS we cover length scales (roughly π/q) from 3 Å (0.3 nm) to 3 µm (Fig. 4). The combined data are dubbed SAS data.


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We successfully fit the combined USAXS/SAXS data with a four-level unified function (Fig. 4) using the Irena code21 available from Argonne National Laboratory. Level 1, at large q, shows a diffraction peak at q = 0.154 ± 0.006 Å-1. This peak is due to scattering from partially ordered mesopores. Partial ordering observed by SAXS is consistent with both the TEM images (Fig. 1) the broadened transition in the adsorption profile in the mesopore region (Fig. 2). A correlatedsphere structure factor21 was used for level 1. A small power-law region is observed around q = 0.3 Å-1, corresponding to length scales about 10 Å. In the analysis, we force the limiting powerlaw exponent to -4, the value appropriate to a smooth surface.25 A background is also needed to fit near q = 1 Å-1.

10 10 10 10 10

9

10 10 10 10 10 10

level 4 G = 1.99e+09 RG = 1.69e+04 B = 0.201 P = 2.46

8

7

USAXS SAXS Unified Fit Unified Lvl 3 + 4

6

5

-1

Intensity (cm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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4

3

level 3 G = 7.37e+05 RG = 907 B = 1.89e-05 P=4

Level 2 G = 47.9 RG = 57.7 B = 0.00725 P = 2.23

2

1

level 1 G = 4.20 RG = 9.18 B = 0.00374 P=4 η = 38.4 Pack = 9.14

0

-1

-2

10 0.0001

0.001

0.01

0.1

1

-1

q (Å )

Figure 4. Combined SAXS (green) and de-smeared USAXS data (red) for one of four samples studied. The peak at q = 0.15 Å-1 is due to regularly spaced mesopores. The dotted line is the fit to level 3 + 4, which are attributed to macropores. G[cm-1] is the Guinier prefactor, P is the magnitude of the power-law exponent, RG[Å] is the Guinier radius and B[cm-1Å-4] is the Porod constant. Parameters η[Å] and Pack reflect the position and shape of the peak.


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In the unified analysis levels j = 2, 3 and 4 are fit to four parameters each: a Guinier radius, RG,j, a Guinier prefactor, Gj, a power-law prefactor called the Porod constant, Bj, and a power-law exponent, -Pj. The index j signifies the unified-fit level, which is different from the index x, which distinguishes porosity (x = 1 for meso, 2 for macro, 3 for total). The distinction is necessary because a specific type of pore may scatter into more than one unified level. Macroporosity (x = 2), for example, scatters into unified levels 3 and 4, whereas total porosity (x = 3) scatters into unified levels 1 through 4. Because of mesopore ordering two additional parameters are needed for unified-level 1, which covers the diffraction peak.

The “Pack”

parameter reflects the peak width and η is approximately the inter-mesopore spacing. The regions covered by the 4-level unified fit are shown in Fig. 4 along with the fitted parameters. The level-2 region is actually a transition between level 1 and level 3. Level 2 is not interpretable as distinct structure since it is due to disorder in the mesopores and surface irregularities on the macropores. Two unified levels are needed for macroporosity scattering because of the large polydispersity in globule size. The power-law exponent of level 3 is P = 4, indicating that the interface between the macropores and the globules is smooth on the scale of π/q ≅ 300 Å. The RG of level 4 (1.69 × 104 Å) is proportional to harmonic mean of the macropore and globule radii.26 When the pore volume fraction is large, which is the case here, the harmonic mean is closer to the globule radius than the macropore radius. The unified parameters, averaged over the four samples examined, are found in Table S1 of the Supporting Information. 3.3. Density and Surface area SAS is capable of measuring surface areas associated with different length scales (≅ π/q). Since micropores, mesopores and macropores scatter in different q regions, the associated surface areas 12 ACS Paragon Plus Environment

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can be distinguished. In the present case, surface area due to macroporosity (S2) is proportional to the level-3 Porod constant (B3) whereas the total surface area (S3) is proportional to the level-1 Porod constant (B1). The surface area of the mesopores, S1, is the difference between the total surface area and the macropore surface area: S1 = S 3 - S 2

(8)

Note that Eq. (8) differs from Eq. (7) since gas adsorption and SAS do not necessarily measure the same surface areas. At this point in the analysis, all surface areas are in units of (length)-1. Specific surface areas (length2/mass) are calculated downstream once the appropriate densities have been determined. The procedure for extracting skeletal density and surface area from SAS data for a single unified level is found in previous publications.27,28 Here we extend the analysis to a hierarchical system. Three pore classes (meso, macro, total) are needed for the current system. Additional pore classes, if present, can be treated by the same formalism. The surface areas can be calculated from SAS data for a specific unified level, j, when the scattered intensity, I(q), follows Porod’s Law for smooth interfaces:25

I j (q) ~ B j q −4 ,

(9)

In the present case, Eq. (9) is obeyed by levels 1 and 3 (Fig. 4 and Table 2). The Porod constant, Bj, for unified level j is related to the surface area per unit volume, Sx, as,21

Sx ( j, k) =

π B jϕ x (1− ϕ x ) Qx ( j, k )

(x = 2, 3)

(10)

where
- 1 − >-


(11)

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is the Porod invariant integrated between levels j and k. The limits j and k depend on which levels are appropriate to the porosity class, x (1 = meso, 2 = macro, 3 = total). >- is the volume fraction of the pores that scatter in the q-range of levels j through k. The variable : is the specific scattering length of the solid component. For silica, : = 8.47 × 10 ABC/EF

(12)

The strut mass density, ; , also depends on the pore class, x, as discussed below. These equations are specialized to particular structural features by assignment of i, j and x. Assignment is done inductively by seeking consistency between SAS, gas adsorption and TEM. In the present case, the total surface area, S3, is gotten from B1 and Q1-4, whereas the macropore surface area, S2, is gotten from B3 and Q3-4. Q1-4 is the invariant under the entire SAS curve whereas Q3-4 is the invariant under unified levels 3 plus 4 only. Note that there are three densities in the problem: ρ1 = skeletal density between the mesopores, ρ2 = the strut density between the macropores (= globule mass density) and ρ3 = the sample density (= weight/volume). Because each level adds additional porosity, ρ3 < ρ2 < ρ1. The density ; in Eq. (11) is the strut density between the pores that scatter in the q-region of the invariant 2 3, 4. For total porosity: j =1, k =4 and ; = ; . For macroporosity: j = 3, k = 4 and ; = ;(. The pore volume fractions in Eqs. (10) and (11) are related to these densities as: G

> = 1 − . G !

meso porosity

(13 A)

>( = 1 −

GH

macro porosity

(13 B)

>I = 1 −

GH

total porosity

(13 C)

G. G!


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The silica-strut density, ; , and the globule density, ;( , are calculated from the SAS data by substituting Eq. (13 B and C) in Eq. (11) and solving for ; and ;( : J ,

; = ;I + H. . (K G

(14 A)

H

J I,

;( = ;I + .. . (K G

(14 B)

H

The invariants. Qx(j,k) come from integrals over the SAS data, Eq. (11). The macropore and total surface areas (S2 and S3) are calculated by Eq. (10) using the volume fractions, >( and >I , the measured Porod constants (B3 and B1) and the measured invariants, Q(3,4) and Q(1,4), respectively. The mesopore surface area, S1, follows from Eq. (8). There are four volume fractions in the problem. > is the fraction of the globules occupied by mesopores; >( is the fraction of the sample occupied by macropores; >I is the fraction of the sample occupied by mesopores + macropores. These values are calculated from Eq. (13). An additional volume fraction, >, , is the volume fraction of the sample occupied by the mesopores:

>, = >I − >( = ;I O − P G G .

!

(17)

Since >, depends on the powder packing density (;I ) this parameter may not be of interest. These equations are coded in the Analyze Results option, which is part of the Unified Fit tool in the Irena analysis package.19 The only inputs are the sample density, ρ3, and the specific scattering length in Eq. (12). The user has the option of picking the appropriate levels, j and k, of the unified fit. The code implements “Approach C” of Hu et al.27 by choosing Two-Phase System 3 in the Analyze Results panel. The code is maintained on the Argonne Advanced Photon Source USAXS web site. The specific volumes also follow from the densities:


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- = G

QR!

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− G ; T = 1, 2

(18 A)

Q

I = − G G

(18 B)

!

H

Table 2 lists all of the parameters calculated from the SAS data and the sample density. First ; and ;( are gotten from the sample density and the SAS data using Eq. (14). The pore volume fractions, φx, and specific pore volumes, Vx, follow from these densities using Eq. (13) and Eq. (18). Next, S1 and S3 are calculated from Eq. (10). S2 is the difference S3 - S1. Table 2 lists the equations used for the calculations as well as the meaning of each parameter. These calculations are all performed within the Irena analysis package, but judgment is required in the assignment of i, j and x. The chord lengths in Table 2 are discussed in Section 3.4. Table 2. Properties calculated from the Unified-Fit parameters (Table S1) and the sample density, ρ3. Pore

meso

macro

total

Param.

Value

ρ1 φ1 φmeso V1 S1

1.9 ± 0.2

Units g/cm3

0.57 ± 0.06 0.14 ± 0.03 3

Equation ρ3 + Q1-4/(2π2r2 ρ3)

Description skeletal density between mesopores

1 - ρ 2/ ρ 1

fraction of globules occupied by mesopores

ρ3(1/ρ2 - 1/ρ1)

fraction of sample occupied by mesopores

0.71 ± 0.10

cm /g

1/ρ2 - 1/ρ1

specific volume occupied by mesopores

1127 ± 68

2

m /g

S3 - S2

specific mesopore surface area

l1,p l1,s

2.5 ± 0.5

nm

4V1/S1

mean chord of mesopores

1.9 ± 0.3

nm

4/(S1 × ρ1)

mean chord of mesopore struts

ρ2 φ2 V2 S2

0.80 ± 0.05

g/cm3

ρ3 + Q3-4/(2π2r2 ρ3)

skeletal density between macropores

1- ρ3/ρ2

fraction of sample occupied by macropores

0.76 ± 0.03 3

4.0 ± 0.4

cm /g

1/ρ3 – 1/ρ2

specific volume occupied by macropores

34 ± 2

2

m /g

πB3φ2(1-φ2)/Q3-4

specific surface area of macropores

l2,p l2,s

473 ± 73

nm

4V2/S2

mean chord of macropores

147 ± 19

nm

4/(S2× ρ2)

mean chord of globules

ρ3

0.19 ± 0.01

g/cm3

weight/volume

sample density

φ3 V3 S3 l3,p l3,s

0.90 ± 0.01

1 – ρ3/ρ1

fraction of sample occupied by all pores

3

4.7 ± 0.3

cm /g

1/ρ3 - 1/ρ1

specific volume occupied by all pores

1161 ± 65

2

m /g

πB1φ3(1-φ3)/Q1-4

total specific surface area

16 ± 2

nm

4V3/S3

mean overall pore chord

18 ± 2

nm

4/(S3 × ρ3)

mean overall solid chord


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3.4. Pore size The parameters calculated in section 3.3 are now used to determine the morphology and structural parameters of the sample. The mean pore chord length, U-,' , and mean strut chord length, U-, , follow from the specific surface areas and specific volumes:28

U-,' = U-, =

Q

(20)

"Q

(21)

"Q GQ

As above, x =1 for mesopores, x = 2 for macropores and x = 3 for overall porosity. These values are included in Table 2. Equations (20) and (21) have been derived many times in different fields29 including by Roe in the context of scattering.30 The pore dimension can be calculated if a pore geometry is assumed such as sphere, cylinder or slit. TEM shows primarily spherical mesopores for which: V'W =

IX!,Y

= 1.9 ± 0.4 \C

(22)

3.5. Mesopore packing As a consistency check, the mesopore volume fraction can be calculated assuming the mesopores form a simple cubic Bravais lattice. > =

H K]^Y_

I`H

= 0.4 ± 0.3

(25)

where, d is the interpore distance, which is calculated from the high-q peak in the SAS data 8 = 29/6',a< = 4.08 nm. This volume fraction is consistent with > = 0.57 ± 0.06 reported in Table 2. If this consistency check is applied to the gas adsorption data in Table 1, S1 = 897 ± 20 m2/g, Rsph = 2.5 ± 0.3 nm and > = 1.0 ± 0.3, which exceeds the maximum packing of a simple cubic lattice (> = 0.52). This discrepancy indicates that the mesopore surface area 17 ACS Paragon Plus Environment

Langmuir

captured by Eq. (7) is underestimated. This issue is discussed further in the section 3.6. Note also that the overall porosity, V3 = 4.7 cm3/g, determined by SAS (Table 2), is much greater than Vtot = 1.0 cm3/g measured by gas adsorption at Pr = 0.99 (Table 1), indicating that the macropore volume is not filled at Pr = 0.99. 3.6. Impact of globule surface texture Although both gas sorption (Fig. 3) and SAS (Fig. 4) are qualitatively consistent with the presence of porosity on two length scales, the αs-plot method gives a much larger macropore surface area (Sext = 112 m2/g) compared to SAS (S2 = 34 m2/g) and a slightly smaller total surface area (Stot =1004 m2/g, S1 = 1164 m2/g), which could be due to closed porosity. These differences lead to substantially different conclusions regarding the size of the mesopores.

-0.2

Ds = 2.96 3 V' = 0.8 cm /g

-0.4 -0.6

3

ln(V, cm /g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-0.8 -1.0 -1.2 -1.4 -3

-2

-1

0

o

1

ln(ln(P /P)

Figure. 5. Fractal adsorption plot (Eq. 26) used to extract the surface fractal dimension, Ds, and characteristic volume, d , of surface roughness at the macropore interface. A possible explanation for the difference in macropore surface is that texture on the surface of the globules creates points of capillary condensation in the surface nooks and crannies. Although this effect could be due densification of capillary-condensed adsorbate with increasing pressure


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as predicted by density functional theory,31 the work of Quao et al., implies that inter-globule capillary condensation is the culprit.32 These authors observed texture–dependent changes in the adsorption profile of a series of mesoporous silicas with similar mesopore structure, but varying large-scale texture (Figures 11 and 12 of Qiao, et al.32). Another way to think of the problem is that silica standard used in the αs-plot is not valid, since the standard is smooth and the sample is not. We approach the discrepancy by comparing the length scales where surface texture impacts both the adsorption isotherm and the SAS profile. For the gas sorption data we use the adsorption isotherm proposed by Avnir and Jaroniec for fractally distributed surface features.33,34 Fractally distributed means that the nooks and crannies follow a power-law capillary (meniscus) size distribution.35,36 In this case the isotherm has the following form,

g^ hI

= d eU\ O Pf

(26)

where the characteristic volume, ′, is the adsorbed volume when Po/P = e, the base of the natural logarithm. Eq. (26) is a modified Frankel-Halsey-Hill isotherm, applicable in the pore condensation regime.26 This equation is applied to the high relative-pressure region where all the mesopores are filled and capillary condensation occurs in the pockets on the globule surfaces. Such pockets can be imagined in the TEM in Fig. 1. Of course it is not possible to determine if the sizes are fractally distributed from the 2-dimensional image. The surface fractal dimension, Ds, and characteristic volume, ′, are determined from the slope and intercept of a plot of

U\ jk. lneU\ O Pf as in Fig. 5. Ds must lie between 2, for a smooth texture, and 3, for a

maximally rough texture. From Fig. 5, Ds = 2.9, which implies a very broad range of surface feature sizes, and ′ = 0.76 cm3/g.


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The characteristic length scale, l′, where Eq. (26) becomes applicable can be estimated from d and Sext: d

l =

m

= 7 nm (27) "Qn For l ≳ l′ capillary condensation occurs in fractally distributed surface irregularities. The crossover occurs at

p

> r h = 0.37, which is at the end of the mesopore filling region (Fig. 2).

The characteristic length scale for SAS is determined from Fig. 4. We observe a Porod exponent of -4, characteristic of a smooth globule surface, for q < 0.02 Å-1, corresponding to a length scale of

(K

. ( Åt!

= 30 \C. For q < 0.02 Å-1 SAS doesn’t resolve surface features smaller than

30-nm in diameter, so in the relevant q-range, the globules appear to be smooth. Therefore, the apparent interfacial area, Sext, due to surface texture on the 7-nm scale is not included in the macropore surface area, S3, determined from Porod analysis of levels 3 plus 4. Scattering in this length scale regime occurs in Level-2 transition region of the unified fit in Figure 4. Because of the impact of surface texture on gas adsorption, Eq (20) cannot be used to calculate the chord lengths of the meso and macro-pores from Stot and Sext reported in Table 1. Sext is overestimated so the macropore size is underestimated. The mesopore surface area, S1 = Stot Sext, is underestimated so the mesopore size is overestimated, which explains the packing problem encountered in Section 3.5. We conclude that, in general, the chord lengths cannot be determined from an αs-plot for a structurally complex specimen. Chord lengths can be calculated from SAS data, however, provided the length scales are such that a Porod slope of -4 is observed at large length scales, as is the case in the example analyzed here.


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As with most problems involving fractal distributions, at least a decade of length scale is required to confirm a fractal size distribution. Because the length-scale range is much less than a decade all we can say is the adsorption data are consistent with fractally distributed capillary sizes. If there were a factor of 10 difference in size between the largest and smallest surface irregularities, we would expect to observe the signature of a rough surface in the SAXS data. 4. Conclusion Inconsistencies between various pore characterization methods have occupied the literature for decades, particularly related to gas sorption methods. The problem is that gas sorption is not directly related to pore morphology. Intervening physical models are required to both analyze and interpret the data. This work demonstrates how one can extract meaningful structural information from SAS data for a complex hierarchical porous material. It is possible to determine the surface areas, pore volumes, strut densities, mean pore sizes and mean strut sizes on two length scales corresponding to meso and macroporosity. Systems with multiple pore class can be handled by simple extension of the equations given. The pore sizes, however, need to be sufficiently distinct to determine the surface area associated with each pore class. We also show that for systems with multiple levels of porosity, gas adsorption methods become quantitatively unreliable. For a simple material with porosity on one length scale, the BET method gives a reliable measure of the pore and strut chords, assuming the absence of microporosity. For more complex materials, however, it is necessary to assign surface area to specific pore classes. The αs and t-plot methods, for example, were developed to separate meso from external macroporosity. We demonstrate, however, that these methods are compromised if points of interfacial condensation exist on the macropore surfaces, where capillary condensation 21 ACS Paragon Plus Environment

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in the surface irregularities leads to an overestimate of the macropore surface area and underestimate of the mesopore surface area. As a result, the mesopore size is overestimated, which leads to a packing inconsistency. Supporting Information. 1. Unified parameters averaged over four samples. 2. High magnification TEM image. Acknowledgment We thank Jan Ilavsky for his efforts in writing and maintaining the Igor code used in this analysis. We thank Melodie Fickenscher for the TEM images. We thank Gunugunuri K. Reddy for the gas adsorption data. Funding ChemMatCARS Sector 15 beamline was principally supported by the National Science Foundation/Department of Energy under grant number NSF/CHE-0822838. Use of the Advanced Photon Source, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract No. DE-AC02-06CH11357. References (1) (2) (3)

(4) (5)

Kochergin, V.; Foell, H. Commercial Applications of Porous Si: Optical Filters and Components. Phys. Status Solidi 2007, 4, 1933–1940. Wan, Y.; Zhao, D. On the Controllable Soft-Templating Approach to Mesoporous Silicates. Chem. Rev. 2007, 107, 2821–2860. Inada, M.; Enomoto, N.; Hojo, J. Fabrication and Structural Analysis of Mesoporous Silica-Titania for Environmental Purification. Microporous Mesoporous Mater. 2013, 182, 173–177. Nakajima, K.; Tomita, I.; Hara, M.; Hayashi, S.; Domen, K.; Kondo, J. N. A Stable and Highly Active Hybrid Mesoporous Solid Acid Catalyst. Adv. Mater. 2005, 17, 1839–1842. Nakanishi, K.; Tanaka, N. Sol–Gel with Phase Separation. Hierarchically Porous Materials Optimized for High-Performance Liquid Chromatography Separations. Acc. Chem. Res. 2007, 40, 863–873. 22 ACS Paragon Plus Environment

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Slowing, I. I.; Vivero-Escoto, J. L.; Wu, C.-W.; Lin, V. S.-Y. Mesoporous Silica Nanoparticles as Controlled Release Drug Delivery and Gene Transfection Carriers. Adv. Drug Deliv. Rev. 2008, 60, 1278–1288. Schmidt, R.; Hansen, E. W.; Stocker, M.; Akporiaye, D.; Ellestad, O. H. Pore Size Determination of MCM-41 Mesoporous Materials by Means of ’H NMR Spectroscopy, N2 Adsorption, and HREM. A Preliminary Study. J. Am. Chem. Soc. 1995, 117, 4049– 4056. Sonwane, C. G.; Bhatia, S. K. Structural Characterization of MCM-41 over a Wide Range of Length Scales. Langmuir 1999, 15 (8), 2809–2816. Ishii, Y.; Nishiwaki, Y.; Al-Zubaidi, A.; Kawasaki, S. Pore Size Determination in Ordered Mesoporous Materials Using Powder X-Ray Diffraction. J. Phys. Chem. C 2013, 117 (35), 18120–18130. Sonwane, C. G.; Bhatia, S. K. Characterization of Pore Size Distributions of Mesoporous Materials from Adsorption Isotherms. J. Phys. Chem. B 2000, 104, 9099–9110. Kruk, M.; Jaroniec, M. Gas Adsorption Characterization of Ordered Organic-Inorganic Nanocomposite Materials. Chem. Mater. 2001, 13 (10), 3169–3183. Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity; Academic Press: London, 1982. Rouquerol, J.; Llewellyn, P.; Rouquerol, F. Is the BET Equation Applicable to Microporous Adsorbents?; Elsevier B.V., 2007; Vol. 160. Sing, K. The Use of Nitrogen Adsorption for the Characterisation of Porous Materials. Colloids Surfaces A-Physicochemical Eng. Asp. 2001, 187, 3–9. Tian, Y.; Wu, J. A Comprehensive Analysis of the BET Area for Nanoporous Materials. AICHE J. 2017, 64 (1), 286–293. Huerta, L.; Guillem, C.; Latorre, J.; Beltrán, A.; Martínez-Máñez, R.; Marcos, M. D.; Beltrán, D.; Amorós, P. Bases for the Synthesis of Nanoparticulated Silicas with Bimodal Hierarchical Porosity. Solid State Sci. 2006, 8 (8), 940–951. Ortiz de Zárate, D.; Fernández, L.; Beltrán, A.; Guillem, C.; Latorre, J.; Beltrán, D.; Amorós, P. Expanding the Atrane Route: Generalized Surfactant-Free Synthesis of Mesoporous Nanoparticulated Xerogels. Solid State Sci. 2008, 10, 587–601. Haskouri, J. El; Ortiz de Zárate, D.; Guillem, C.; Latorre, J.; Caldés, M.; Beltrán, A.; Beltrán, D.; Descalzo, A. B.; Rodríguez-López, G.; Martínez-Máñez, R.; et al. SilicaBased Powders and Monoliths with Bimodal Pore Systems. Chem. Commun. 2002, 330– 331. Ilavsky, J.; Jemian, P. R.; Allen, A. J.; Zhang, F.; Levine, L. E.; Long, G. G. Ultra-SmallAngle X-Ray Scattering at the Advanced Photon Source. J. Appl. Crystallogr. 2009, 42 (3), 469–479. Ilavsky, J.; Zhang, F.; Allen, A. J.; Levine, L. E.; Jemian, P. R.; Long, G. G. Ultra-SmallAngle X-Ray Scattering Instrument at the Advanced Photon Source: History, Recent Development, and Current Status. Metall. Mater. Trans. A 2013, 44, 68–76. Ilavsky, J.; Jemian, P. R. Irena : Tool Suite for Modeling and Analysis of Small-Angle Scattering. J. Appl. Crystallogr. 2009, 42, 347–353. Gor, G. Y.; Neimark, A. V. Adsorption-Induced Deformation of Mesoporous Solids: 23 ACS Paragon Plus Environment

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Macroscopic Approach and Density Functional Theory. Langmuir 2011, 27 (11), 6926– 6931. Kruk, M.; Jaroniec, M.; Ryoo, R.; Man Kim, J. Monitoring of the Structure of Siliceous Mesoporous Molecular Sieves Tailored Using Different Synthesis Conditions. Microporous Mater. 1997, 12, 93–106. Jaroniec, M.; Kruk, M.; Olivier, J. P. Standard Nitrogen Adsorption Data for Characterization of Nanoporous Silicas. Langmuir 1999, 15 (16), 5410–5413. Porod, G. General Theory. In Small-Angle X-ray Scattering; Glatter, O., Kratky, O., Eds.; Academic Press: New York, 1982; pp 17–52. Schaefer, D. W.; Beaucage, G.; Loy, D. A.; Shea, K. J.; Lin, J. S. Structure of AryleneBridged Polysilsesquioxane Xerogels and Aerogels. Chem. Mater. 2004, 16 (8), 1402– 1410. Hu, N.; Borkar, N.; Kohls, D. J.; Schaefer, D. W. Characterization of Porous Materials Using Combined Small-Angle X-Ray and Neutron Scattering Techniques. J. Memb. Sci. 2011, 379 (1–2), 138–145. Schaefer, D. W.; Pekala, R.; Beaucage, G. Origin of Porosity in Resorcinol Formaldehyde Aerogels. J. Non. Cryst. Solids 1995, 186, 159–167. Underwood, E. E. Quantitative Stereology; Addison-Wesley Pub. Co.: Reading, Mass., 1970. Roe, R.-J. Methods of X-Ray and Neutron Scattering in Polymer Science. New York. 2000. Ravikovitch, P. I.; Vishnyakov, A.; Neimark, A. V. Density Functional Theories and Molecular Simulations of Adsorption and Phase Transitions in Nanopores. Phys. Rev. E Stat. Physics, Plasmas, Fluids, Relat. Interdiscip. Top. 2001, 64 (1), 20. Qiao, S. Z.; Yu, C. Z.; Hu, Q. H.; Jin, Y. G.; Zhou, X. F.; Zhao, X. S.; Lu, G. Q. Control of Ordered Structure and Morphology of Large-Pore Periodic Mesoporous Organosilicas by Inorganic Salt. Microporous Mesoporous Mater. 2006, 91 (1–3), 59–69. Avnir, D.; Jaroniec, M. An Isotherm Equation for Adsorption on Fractal Surfaces of Heterogeneous Porous Materials. Langmuir 1989, 5 (6), 1431–1433. Lowell, S.; Shields, J. E.; Thomas, M. A.; Thommes, M. Characterization of Porous Solids and Powders: Surface Area, Pore Size and Density; Kluwer Academic Publishers: Dortrect, Netherlands, 2004. Schmidt, P. W. Interpretation of Small-Angle Scattering Curves Proportional to a Negative Power of the Scattering Vector. J. Appl. Crystallogr. 1982, 15 (5), 567–569. Schmidt, P. W. Fractal Pores or a Distribution of Pore Sizes: Alternative Interpretations of Power-Law Small-Angle Scattering. In Materials Research Society Symposia Proceedings; 1986; Vol. 73, pp 351–356.


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Table of Contents


Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1. TEM images of the synthesized nanoporous silica at two magnifications. The left image reveals the mesopores. This image shows a narrow distribution of quasi-spherical 3.8-nm-diameter pores, some of which are interconnected. The right image is a superposition of multiple globules. Macroporosity exists between the globules. A higher magnification image is found in Fig. S1 of the supplementary information. 309x137mm (72 x 72 DPI)

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Figure 2. N2 physisorption isotherm of nanoporous silica. The step at P/Po = 0.3 is characteristic of capillary condensation in mesopores. The second step, at P/Po > 0.85, corresponds to the filling of the large macropores that form the void space between globules. Between 0.40 and 0.85 adsorption occurs on the features attributed to capillary condensation in irregularities on and between the globules. 134x132mm (288 x 288 DPI)


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Figure 3. The αs-plot for the adsorption branch of nanoporous silica using LiChrospher Si-1000 silica as the non-porous reference adsorbent. The near zero intercept indicates the absence of microporosity (below 2nm diameter). 134x129mm (288 x 288 DPI)


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Figure 4. Combined SAXS (green) and de-smeared USAXS data (red) for one of four samples studied. The peak at q = 0.15 Å-1 is due to regularly spaced mesopores. The dotted line is the fit to level 3 + 4, which are attributed to macropores. G[cm-1] is the Guinier prefactor, P is the magnitude of the power-law exponent, RG[Å] is the Guinier radius and B[cm-1Å-4] is the Porod constant. Parameters η[Å] and Pack reflect the position and shape of the peak. 140x182mm (288 x 288 DPI)


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Figure. 5. Fractal adsorption plot (Eq. 26) used to extract the surface fractal dimension, Ds, and characteristic volume, V', of surface roughness at the macropore interface. 135x129mm (288 x 288 DPI)


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Table of Contents Graphic 83x47mm (72 x 72 DPI)


Multilevel morphology of complex nanoporous materials - Langmuir

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