Elucidating the Sorption Mechanism of ... - ACS Publications

Subscriber access provided by UNIV OSNABRUECK

Article

Elucidating the Sorption Mechanism of Dibromomethane in Disordered Mesoporous Silica Adsorbents Daniela Stoeckel, Dirk Wallacher, Gerald Zickler, Matthias Thommes, and Bernd M Smarsly Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b00705 • Publication Date (Web): 19 May 2015 Downloaded from http://pubs.acs.org on May 26, 2015

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 35

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

Langmuir

1

Elucidating the Sorption Mechanism of Dibromomethane

2

in Disordered Mesoporous Silica Adsorbents

3

Daniela Stoeckel,1 Dirk Wallacher,2 Gerald Zickler,3 Matthias Thommes,4 Bernd M.

4

Smarsly*,1

5

1

6

35392 Gießen (Germany)

7

2

8

14109 Berlin, Germany

9

3

Institute of Physical Chemistry, Justus-Liebig-Universität Gießen, Heinrich-Buff-Ring 58,

Helmholtz Zentrum Berlin für Materialien und Energie GmbH, Hahn-Meitner-Platz 1,

Institute of Mechanics, Montanuniversität Leoben, Franz-Josef-Strasse 18, 8700 Leoben,

10

Austria

11

4

Quantachrome Instruments, 1900 Corporate Dr., Boynton Beach, FL 33426, USA

12 13

______________________________________________

14

* Author to whom correspondence should be addressed.

15

Phone: +49-641-9934590. Fax: +49-641-9934509.

16

E-mail: [email protected].

17

18

KEYWORDS: in-situ SAXS, Contrast matching, Particulate adsorbents; Mesoporous silica;

19

Pore size distribution; Chord-length distribution; Nitrogen physisorption.

20

1

ACS Paragon Plus Environment

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

Page 2 of 35

21

ABSTRACT:

22

The mechanism of dibromomethane (DBM) sorption in mesoporous silica was investigated

23

by in-situ small-angle X-ray scattering (SAXS). Six different samples of commercial porous

24

silica particles used for liquid chromatography were studied, featuring a disordered

25

mesoporous structure, some of the samples being functionalized with alkyl-chains. SAXS

26

curves were recorded at room temperature at various relative pressures P/P0 during adsorption

27

of DBM. The in-situ SAXS experiment is based on contrast matching between silica and

28

condensed DBM with regard to X-ray scattering. One alkyl-modified silica sample was

29

evaluated in detail by extraction of the chord-length distribution (CLD) from SAXS data

30

obtained for several P/P0. On the basis of this analytical approach and by comparison with ex-

31

situ obtained data of nitrogen and DBM adsorption, the mechanism of DBM uptake was

32

studied. Results of average mesopore sizes obtained with the CLD method were compared

33

with pore size analysis using nitrogen physisorption (77 K) with advanced state-of-the-art

34

non-local density functional theory (NLDFT) evaluation. The dual SAXS/physisorption study

35

indicates that microporosity is negligible in all silica samples and that surface

36

functionalization with a hydrophobic ligand has a major influence upon the process of DBM

37

adsorption. Also, all of the mesopores are accessible as evidenced by in-situ SAXS. The data

38

suggest that no multilayer adsorption occurs on C18-(octadecyl-)modified silica surfaces

39

using DBM as adsorptive, and is possibly also negligible on bare silica surfaces.

40

2


Page 3 of 35

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

41

Langmuir

INTRODUCTION

42

The field of design and application of mesoporous materials with ordered or disordered

43

porosity is of high importance for material science. Especially in the development of silica-

44

based mesoporous adsorbents, used as support in high performance liquid chromatography

45

(HPLC) and heterogeneous catalysis, substantial improvements have been obtained in the last

46

years.1,2 Both implementations rely on the properties of the mesopore space, which provides

47

the area of contact between the analytes or reagents and the solid support. The performance of

48

the silica matrix in a particular application is therefore directly coupled with the accessible

49

mesopore volume, the mesopore size distribution (PSD), pore shape and the surface

50

chemistry. A comprehensive structural characterization of materials with nanometer-sized

51

pores has thus become highly important for the optimization of existing and potentially new

52

mesoporous adsorbents. Unfortunately only few techniques are available for an accurate and

53

quantitative characterization of disordered mesopore structures, since one prominent feature

54

of these materials is the lack of mesoscopic order. In the present study “disorder” is referred

55

to an inhomogeneous mesopore shape. Irregularity in the mutual spatial distribution can be

56

regarded as a form of “disorder” as well, but is not necessarily detrimental to the precise

57

analysis of mesoporosity, as shown for spherical mesopores with a certain deviation from

58

closed-packed lattices.3,4

59

Standard analysis methodologies applied for the characterization of mesoporous materials,

60

e.g., nitrogen physisorption, mercury intrusion porosimetry (MIP) and conventional

61

transmission electron microscopy (TEM) each bare specific disadvantages for a meaningful

62

analysis of disordered pore structures. Inasmuch as two dimensional TEM pictures are not

63

reliable in characterizing 3D structures without defined pore geometry;5 and bulk methods of

64

pore size characterization (such as physisorption and MIP) suffer from the fact that the

65

assumption of a defined pore shape is inevitable for data evaluation. Furthermore, only 3


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

Page 4 of 35

66

accessible pores are detectable by adsorption methods. In recent years, significant progress

67

has been achieved in the understanding of physisorption mechanism of fluids in highly

68

ordered pore systems.6–8 In spite of the advances in sorption theory, e.g., novel data analysis

69

tools, namely the nonlocal density function theory (NLDFT),9,10 independent methods are

70

necessary to validate physisorption results, especially for materials without a defined void

71

space geometry and PSD,6 which is the case for most, if not all chromatographic materials.

72

Likewise, materials featuring a modified surface chemistry, besides the standard types of

73

adsorbents, i.e., inorganic oxides and carbon, need further investigation. While DFT based

74

methods have been widely applied to obtain an accurate pore size analysis of pristine

75

oxidic/siliceous materials,11 the applicability of these methods for the characterization of

76

silicas with surface modification (e.g., silica adsorbents grafted with alkyl-chains, phenyl-

77

groups) still needs to be explored. The functionalization with hydrophobic ligands is

78

obligatory for adsorbents applied in reversed-phase (RP) chromatography, which is still the

79

most frequently used analysis mode in LC.12 Thus, the analysis of such materials requires

80

special attention.

81

Small-angle X-ray scattering (SAXS) analysis, another prominent method for the

82

characterization of materials at the nanometer scale,13–16 can be a useful complement to

83

physisorption analysis, since it is a non-invasive technique, being not prone to network

84

hysteresis or energetic effects that may affect the analysis of sorption data. In addition, it can

85

provide interesting information over a wide range of length scales. Among the analysis

86

methods for SAXS data there are different approaches for the assessment of disordered pore

87

systems. Foremost, the combined approach of SAXS and the concept of chord-lengths

88

distribution (CLD), already introduced by Méring and Tchoubar in the 1960s,17 offers a

89

general strategy to gain deeper insights into mesoporosity even for materials without defined

90

pore geometry and featuring an irregular mutual arrangement of the pores.18 A CLD is

91

basically a statistical distribution of the linear surface-to-surface distances,19 and it can readily 4


Page 5 of 35

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

Langmuir

92

be applied to interpret data obtained from a SAXS experiment of a two-phase (solid–void)

93

system with sharp or diffuse phase boundaries, as is the case for mesoporous oxides.20 Using

94

this dual SAXS/CLD approach, relevant parameters, such as an average pore size and the

95

prevalent length scale, can be derived, without the necessity to assume a specific model for

96

the mesopore geometry.16 This comprehensive strategy enables the comparison with results

97

obtained from physisorption analysis and has already successfully been used to characterize a

98

number of porous materials.3,21–26

99

An even more advanced approach offers the coupling of standard gas/vapor physisorption

100

with SAXS or small-angle neutron scattering (SANS) technique. Such in-situ method is based

101

on the acquisition of SAXS or SANS curves during a physisorption experiment. As has been

102

shown previously, this concept provides indispensable insights into the structure and pore

103

filling mechanism in meso- and microporous materials.3,22,27–40 The prerequisite for such

104

experiments is the occurrence of “contrast matching” between the matrix and the utilized

105

fluid. For instance, the mean electron densities of a silica matrix and the condensed adsorptive

106

(here: dibromomethane, DBM) have to be almost identical, leading to negligible scattering

107

contrast in the filled state. Under these circumstances, upon gradual filling of the pores during

108

an in-situ SAXS experiment, only unfilled pores contribute to the scattering signal.

109

Consequently, this in-situ SAXS approach provides information about the adsorption

110

mechanism as well as the pore structure.

111

The present study addresses several questions. First, the study is focused on whether the

112

adsorbent particles contain inaccessible porosity, or if the pore accessibility is hindered and if

113

potential microporosity is inherent in the silica structure. These issues are of crucial relevance

114

for understanding and optimizing the transport in the particles. In particular, the accessibility

115

of the mesoporosity in these particles is important for the SAXS analysis described in our

116

previous publication (ref. 23), as certain assumptions are based on a full accessibility of the

117

mesoporosity. As a further main objective of this study, the different sorption behaviors of 5


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

Page 6 of 35

118

nitrogen and DBM were studied in greater detail. The two fluids exhibit considerable

119

differences in their physical properties, such as surface tension and saturation vapor pressure.

120

With the latter sorptive having a much larger kinetic diameter and sorption taking place at

121

room temperature, the study of physisorption of DBM is particularly interesting, since it

122

mimics more closely the application conditions of the adsorbents in an organic solvent.

123

However, so far only a few publications have been released that cover the sorption behavior

124

of organic vapors on porous silica materials,3,22,27,28,31–40 particularly silica materials featuring

125

a disordered pore space.27,37,38

126

In this work, the combined approach of SAXS with DBM physisorption measurements was

127

used to characterize silica adsorbents with disordered mesoporosity for application in high

128

performance liquid chromatography columns. The studied materials are commercial products,

129

featuring defined mesopore size distribution, mesopore volume and specific surface area.

130

Their PSD is designed for the separation of small- to medium-sized molecules and their

131

synthesis is optimized to allow for highly reproducible material properties. In-situ SAXS

132

experiments with DBM adsorption were performed with six commercial adsorbent materials,

133

whereof four samples were modified with C18-chains. The influence of the hydrophobic

134

surface modification and its consequences for the DBM adsorption process were investigated

135

by analyzing the quantitative change of the respective SAXS curves upon DBM adsorption. In

136

order to further elucidate the characteristics of the DBM uptake mechanism, one of the

137

surface modified samples was chosen for an extended analysis. By application of the

138

SAXS/CLD approach the material’s CLD was derived at different adsorption steps. In

139

addition, its mean mesopore size and the accessible remaining interface were evaluated for

140

designated pore filling fractions. Complementing, the total pore volume and PSD of the same

141

sample

was

evaluated

by

ex-situ

N2

and

DBM

sorption

measurements.

142 143 6


Page 7 of 35

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

Langmuir

144

EXPERIMENTAL SECTION

145

Chemicals and Materials. The studied particulate materials are commercially available

146

chromatographic adsorbents used as obtained from the manufacturer: 3.5 µm Atlantis

147

particles were purchased from Waters Corporation (Milford, MA); 3 µm Luna and 2.6 µm

148

Kinetex were provided by Phenomenex (Aschaffenburg, Germany); 3.5 µm Zorbax and

149

2.5 µm Poroshell particles were a gift from Agilent Technologies (Waldbronn, Germany);

150

2.7 µm Halo particles came from Advanced Materials Technologies (Wilmington, DE).

151

Dibromomethane (99%) was purchased from Sigma-Aldrich (Steinheim, Germany) and used

152

as received.

153

Ex-situ Physisorption Measurements. Measurements have been performed in an

154

automated gas adsorption station (Autosorb-1-MP, Quantachrome Corporation, Boynton

155

Beach, FL), which is dedicated to the standard characterization of nanostructured materials by

156

nitrogen sorption isotherms at 77 K. The instrument data reduction software supports standard

157

data reduction algorithms like Brunauer–Emmett–Teller (BET) and Barrett–Joyner–Halenda

158

(BJH) as well as the NLDFT kernels applicable to nitrogen adsorption at 77 K in siliceous

159

materials. Prior to these measurements, the samples were evacuated for 6 h at 393 K. The

160

nitrogen adsorption measurements were carried out with the liquid nitrogen filled standard

161

dewar flask in which the sample filled glass cuvette was cooled to a temperature of 77 K.

162

For the DBM sorption measurements the powder sample was filled in the copper sample

163

cell of a mini pulse tube refrigerator dedicated for gas adsorption and stabilized on the

164

measurement temperature of 295 K. The isotherm has been measured up to the equilibrium

165

vapor pressure P0 of the adsorptive (50.12 mbar at 295 K). The measurement of the DBM

166

isotherm took about 200 h, due to relaxation times as long as 20 h for one data point in the

167

different sorption regimes of the isotherm.

7


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

Page 8 of 35

168

The pore volume, which could be filled with dibromomethane, has been derived from the

169

adsorbed gas volume at P/P0 = 0.97. The liquid dibromomethane has a density of 2.477 g/cm³

170

and a surface tension of 39.74 mN/m at 20 °C, according to literature data.41,42

171

In-situ Small Angle X-Ray Scattering (SAXS). The in-situ SAXS experiments were run at

172

the BW4 beamline43 of the Hamburger Synchrotronstrahlungslabor (HASYLAB), Deutsches

173

Elektronen-Synchrotron (DESY) in Hamburg (Germany) using a continuous fluid sorption

174

approach. Details of the measuring setup are described in the Supporting Information. A total

175

range of s = 0.03–0.38 nm-1 was covered (s = (2/λ)(sinθ)), λ being the wavelength and 2θ the

176

scattering angle. An exposure time of 60 s yielded a scattering pattern with excellent

177

measuring statistics. The scattering patterns were corrected for background scattering,

178

electronic noise, transmission, and polarization using the data reduction program FIT2D.44 All

179

the specimens showed isotropic scattering patterns, which were azimuthally averaged for

180

equal radial distances from the central beam.

181 182

RESULTS AND DISCUSSION

183

Ex-situ Physisorption with Nitrogen (77K). Nitrogen physisorption measurements were

184

performed with Zorbax particles to address their mesoporosity and related parameters, e.g.,

185

the mesopore volume and the specific surface area. For data evaluation the NLDFT

186

nitrogen/silica kernels assuming a cylindrical pore model10 (using both dedicated adsorption

187

and desorption kernels) and the BJH model (desorption branch) were chosen and utilized to

188

calculate the PSD. In addition, sorption data were evaluated by the classical BET approach to

189

determine the specific surface area. The total mesopore volume was also estimated from the

190

amount of nitrogen adsorbed at P/P0 = 0.98, which corresponds to the plateau-like region of

191

the isotherm by applying the Gurvich rule.6 Results are summarized in Table 1, including the

192

intraparticle porosity of the material, as well as the modes of the PSDs determined by the 8


Page 9 of 35

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

Langmuir

193

NLDFT methods and the BJH approach. The obtained hysteresis loop is typical of

194

mesoporous materials and the isotherm is classified as type IV according to the IUPAC

195

classification (Figure 1a).45 The PSDs obtained by the NLDFT analysis confirm this

196

interpretation (Figure 1b), i.e., no microporosity has been detected. Furthermore, both PSDs

197

obtained by the cylinder pore model for the adsorption (by applying the NLDFT kernel

198

applied to the metastable adsorption branch, which correctly takes into account that

199

condensation occurs delayed due to metastable pore fluid) and desorption branch (by applying

200

the equilibrium NLDFT kernel) agree well and hence indicate that pore blocking/percolation

201

effects do not contribute in an appreciable way to hysteresis.4 The PSD acquired by the BJH

202

method (applied to the desorption/equilibrium branch of the hysteresis loop), is shifted to

203

smaller values compared to the PSD obtained by NLDFT-based analysis (by ≲ 20 nm), i.e.,

204

confirming that macroscopic thermodynamic methods underestimate the pore size.

205

206 207

Figure 1. a) Nitrogen physisorption isotherm for the Zorbax particles. Lines connecting the

208

data points serve as a guide to the eye. b) Pore size distributions for the Zorbax particles

209

derived from the desorption branch by the BJH model, and from the desorption and the

210

adsorption branch of the nitrogen physisorption isotherm by application of a NLDFT method

211

based on a cylindrical pore model for the system nitrogen (77 K)/silica. The NLDFT method

212

applied on the adsorption branch takes correctly into account the existence of metastable pore 9


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

Page 10 of 35

213

fluid, whereas the NLDFT method applied on the desorption branch reflects the equilibrium

214

transition.

215

Ex-situ Physisorption with Dibromomethane (295 K). The DBM isotherm looks similar

216

to the nitrogen isotherm (Figure 2). The upper closure point is observed at P/P0 ∼ 0.9, and the

217

onset of capillary condensation is located at P/P0 ∼ 0.6. For nitrogen (77 K) the lower closure

218

point is P/P0 ~ 0.4. Using DBM the adsorption/desorption isotherm revealed a so-called low

219

pressure hysteresis isotherm, which can indicate extremely slow desorption kinetics (from

220

poorly accessible areas of the sample, possibly caused by the C18-chains on the silica

221

surface). In contrast to the nitrogen adsorption isotherm the obtained DBM isotherm

222

resembles a type V isotherm, indicating that, contrary to nitrogen at 77 K, DBM only partially

223

wets the adsorbent surface at 295 K, i.e., the adsorbent–adsorbate interaction is weak. Such

224

isotherms are typical of water vapor adsorption on nanoporous carbon (where the pore filling

225

process is dominated by a clustering mechanism),45 but have also been found for other

226

systems.38-40 As indicated above, contrary to the case of the nitrogen adsorption isotherm,

227

multilayer film formation cannot occur for DBM, due to the hydrophobicity that was

228

introduced by C18-modification of the silica surface. Incomplete wetting of the surface, i.e., a

229

finite contact angle, thus leads to patches (cluster) of adsorbate. However, the total pore

230

volume obtained from the plateau region of the DBM isotherm is Vtotal = 0.249 cm³/g, yielding

231

a porosity of ε = 0.354, which is in good agreement with the pore volume/porosity obtained

232

from nitrogen adsorption, suggesting that DBM is able to fill the pore space at higher relative

233

pressures.

234

10


Page 11 of 35

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

Langmuir

235 236

Figure 2. a) Nitrogen and DBM physisorption isotherms for the Zorbax particles. Lines

237

connecting the data points serve as a guide to the eye. b) Change of total transmission T

238

during the in-situ SAXS experiment for increasing filling fractions P/P0 plotted together with

239

the ex-situ DBM physisorption isotherm for the Zorbax particles.

240

The corresponding correlation between the change of the absolute transmission of X-rays

241

during the in-situ SAXS experiment and the DBM isotherm measured ex-situ is shown in

242

Figure 2b. The 57 in-situ measurements SAXS were performed using a continuous

243

measurement approach, while the ex-situ adsorption measurements were performed after the

244

equilibrium conditions were reached for each point in the isotherm. From this graph one can

245

see how well the two adsorption isotherms match, despite the different measuring parameters.

246

The data points only deviate for the highest filling fractions in the range 0.7 < P/P0 < 0.9,

247

which is possibly due to not fully equilibrated measurement conditions regarding the data

248

obtained in-situ. Due to the limitation of beamline availability, the long measurement times

249

(up to 20 hours), which are necessary to reach fully equilibrated conditions for each data

250

point, could not be granted for the in-situ measurements. This is why the continuous

251

measurement approach (see Supporting Information for a detailed description) was utilized.

252

However, this approach seems reasonable as the changes in the measured SAXS curves are

253

usually negligible after very short equilibration times (on the time-scale of minutes), while the

254

measured pressure needs hours to relaxate towards its equilibrium value, which is clearly

255

confirmed by the good match of the ex-situ/in-situ adsorption isotherm branches. (Besides, the 11


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

Page 12 of 35

256

in-situ SAXS curves obtained in the range 0.7 < P/P0 < 0.9 were not used for further data

257

evaluation, e.g., the CLD calculation.)

258

Table 1. Summary of the Zorbax particle characteristics derived from the ex-situ

259

physisorption measurements. Ex-situ Physisorption Pore diameter w (mode) (NLDFTads) [nm] 7.3

Pore diameter w (mode) (NLDFTdes) [nm] 7.7

Surface area (BET) [m2g-1]

Total pore volume* Vtotal [cm3g-1]

Porosity (from Vtotal)

N2 @ 77 K

Pore diameter w (mode) (BJHdes) [nm] 5.8

112

0.252

0.357

CH2Br2 @ 295 K

-

-

-

-

0.249

0.354

260

*The total pore volume Vtotal was calculated following the Gurvich method.

261

In order to withdraw more detailed information from the obtained DBM-isotherm we applied

262

the Kelvin equation:

263

ln = −

L

(1)

264

where P/P0 is the relative pressure, γ the surface tension, VL the molar volume of the bulk

265

liquid adsorbate and θ its contact angle on the adsorbent. R is the gas constant, T the

266

temperature, and rm is the mean radius of curvature. As Thomson has shown,49 this equation

267

links the change of vapor pressure at which capillary condensation occurs within pores on the

268

microscopic scale, with rm being the radius of a curved liquid–vapor interface. If a special

269

model for the geometry of pores is applied, rm can be correlated with the mean pore radius w.

270

Most commonly a cylinder with infinite length is chosen as geometric model. Cohan has

271

proposed that in cylindrical pores desorption occurs from a hemispherical meniscus.50

272

Assuming a contact angle θ = 0° this results in a mean radius of curvature rm = w – t, where t

273

is the thickness of the adsorbed fluid-film. This model serves as the basis for the popular

274

method for mesopore analysis of porous solids by Barret et al. (BJH).51 12


Page 13 of 35

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

Langmuir

275

From the Kelvin equation (eq 1) and the desorption branch of the DBM isotherm, accordingly

276

the cumulative value nCH2Br2 vs. was derived as a function of the mesopore diameter w (see

277

Figure 3a). Subsequent differential analysis of this plot resulted in the PSD shown in Figure

278

3b and 3c.

279

Because of the delayed layer formation the adsorption branch of the DBM isotherm should in

280

principal not be utilized for calculation of the PSD, therefore solely the results derived from

281

the desorption branch are shown. The thickness t of the adsorbed film is assumed to be

282

negligible, since from the shape of the isotherm no layer formation is indicated. Jähnert et

283

al.33 have shown that t ranges between 0–0.5 nm for DBM adsorption on SBA-15 silica and

284

even decreases after the onset of capillary condensation. In their study they applied a density

285

gradient model to fit measured scattering curves obtained during an in-situ SAXS experiment

286

to derive information about the adsorbate layer in the ordered pores. Further decreasing the t-

287

values used for correction of w causes the PSD curve to shift towards smaller pore size values,

288

because w = rm + t. As shown in Figure 3b, the PSD obtained from the Kelvin equation

289

without any correction for the film thickness t almost matches the PSD obtained from NLDFT

290

analysis of the nitrogen desorption branch.

291

In Figure 3c a film thickness of t = 0 was combined with various values for the contact angle

292

of DBM on silica for the calculation of the PSD. Since a value of θ = 0° can be excluded, θ

293

was increased stepwise and compared with the results derived with the BJH model for the

294

nitrogen (77 K)/silica system (desorption branch). Relating the PSDs calculated with the two

295

macroscopic approaches – the BJH method and the Kelvin equation – for the adsorptives

296

nitrogen and DBM, respectively, seems in this case more appropriate, even though the BJH

297

model is known to underestimate pore sizes for pores smaller than 20 nm.6 A good agreement

298

of the PSD curves is achieved for a value θ = 45°. Relating the DBM-PSD obtained using the

299

Kelvin equation to the NLDFT derived PSD (nitrogen (77 K)/silica), a suitable match is found

300

for a contact angle of θ ∼ 25°, which is by a factor of 1.8 smaller than the value found for the 13


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

Page 14 of 35

301

BJH/nitrogen result (see Figure S1 in the Supporting Information). Jähnert et al. measured an

302

initial contact angle of θ ∼ 20° for drops of DBM on silicon wafers possessing a native oxide

303

layer that quickly increased to a steady value of 32°. Comparing θ to the value found by

304

Jähnert et al.33, a slight divergence seems reasonable since the silica sample studied here was

305

subject to an additional hydrophobic surface modification step.

306

307 308

Figure 3. a) Cumulative amount of adsorbed DBM derived from the desorption branch of the

309

isotherm by the Kelvin equation without correction for the film thickness t and for a contact

310

angle θ = 0°, together with the cumulative pore volume derived from the desorption branch of

311

the nitrogen physisorption isotherms by the NLDFT method with a cylindrical pore model and

312

the BJH method for the system nitrogen (77 K)/silica. b) PSDs for the Zorbax particles

313

derived from the cumulative pore volume plots shown in Figure 3a. c) PSDs derived from the

314

desorption branch of the DBM physisorption isotherm without correction for the film

315

thickness t, but with varied values for the contact angle θ in comparison with the PSD derived

316

from the desorption branch using the BJH model for the system nitrogen (77 K)/silica. 14


Page 15 of 35

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

317 318

Langmuir

In-situ SAXS Experiments. The SAXS patterns of the mesoporous silica at different adsorption states are depicted in Figure 4.

319

320 321

Figure 4. a) SAXS patterns for the different filling fractions P/P0. b) Double-logarithmic plot

322

of the SAXS patterns for designated filling fractions P/P0.

323

The SAXS curves themselves are typical of a random mesopore structure. None of the I(s)

324

curves shows any distinct features or pronounced interference maxima. Only a slight

325

shoulder, possibly due to a preferred average distance between the mesopores (s ~ 0.07 nm-1),

326

is visible for the ex-situ SAXS curve (P/P0 = 0). Up to P/P0 ~ 0.2 the shape and scattering

327

intensity of the obtained SAXS curves does not change, in accordance with the anticipated

328

absence of film formation. Between P/P0 ~ 0.2–0.4 the intensity slightly increases, but the

329

overall shape shows no major changes, just a slight shift of the shoulder’s maximum towards

330

smaller scattering values is noticeable. This shift can be attributed to the increase of the

331

average pore-to-pore distance between empty mesopores, due to the filling of the smallest

332

pores during the initial adsorption steps, or alternatively, if a bimodal pore size distribution is

333

present in the material, due to the filling of the smaller pore size distribution. However, the

334

existence of such a bimodal pore size distribution is not indicated by the physisorption data

335

and in addition we were able to model the entire SAXS curve by a model assuming a

336

monomodal mesopore size distribution featuring a local mutual ordering (see Supporting Info 15


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

Page 16 of 35

337

Fig. S2). Moreover, a deformation, i.e., slight widening, of the porous structure caused by the

338

interaction with the adsorbing fluid could also induce a shift of the shoulder.52,53 With the

339

onset of pore condensation (P/P0 ~ 0.5) the shoulder slowly disappears and for adsorption

340

steps beyond P/P0 ~ 0.7 the shoulder is no longer distinguishable. As the shoulder disappears,

341

the scattering intensity I(s) for smaller scattering vectors (s < 0.05 nm-1) increases between

342

P/P0 ~ 0.5–0.75 from approximately 110 to 150 a.u. A similar effect has been observed for

343

microporous structures due to the enhancement of scattering contrast caused by the filling of

344

the micropores in the matrix.22,28–30 However, for such materials this increase in scattering

345

intensity can be observed already in the low pressure region. After a maximum for I(s = 0.03

346

nm-1) at P/P0 ≈ 0.75 is reached, I(s = 0.03 nm-1) decreases rapidly upon increasing pressure

347

until it reaches a value about a factor 5 smaller than the initial intensity and a factor 10

348

smaller than the maximally reached intensity. The overall SAXS intensity almost vanishes

349

when the mesopores are filled. This substantial decrease of the SAXS intensity at P/P0 = 0.99

350

indicates almost perfect contrast matching, and furthermore one can conclude that the vast

351

majority of mesopores is completely accessible. It is also apparent that the SAXS curve for

352

larger s gets flat, indicating that the diffuse scattering caused by the liquid inside the

353

subsequently filled pores increases. The higher the filling fraction P/P0, the greater the range

354

for which this flattening is significant.

355

Another important aspect deduced from the in-situ SAXS curves is the absence of a larger

356

amount of micropores, as already indicated by the physisorption experiments. In consequence

357

of the marginal change of the SAXS curves between the evacuated state and P/P0 ~ 0.2 (see

358

Figure 4a and 4b), the relative pressure range in which the micropores are filled, and the weak

359

scattering intensity for s > 0.35 nm-1, the presence of a significant amount of micropores can

360

be excluded, as micropores would generate SAXS intensity for scattering vectors

361

s > 0.4 nm-1.3 If micropores existed, one should observe a major change in the scattering

362

intensity for the first adsorption steps, due to the enhanced contrast between the unfilled 16


Page 17 of 35

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

Langmuir

363

mesopores and the microporous silica matrix, as has been pointed out in previous

364

studies.22,28-30 The absence of microporosity is important with respect to the application of

365

these particles in HPLC, since microporosity exhibits a negative impact on the separation

366

quality.

367

To obtain further information about the sorption process in the disordered mesoporous

368

particles, we applied the CLD concept for the SAXS curves as a function of P/P0. Therefore

369

the experimental SAXS data were parameterized (“fitted”) by means of analytical basis

370

functions.25 In this process various structural parameters, e.g., the average pore size and

371

correlation lengths as well as the specific surface area, can be derived from the initial SAXS

372

curve.16 The double-logarithmic plot of selected SAXS curves (Figure 4b) illustrates that the

373

curves follow Porod’s law reasonably well, i.e., the intensity I(s) is proportional to s-4 for

374

larger values of s, up to a filling fraction P/P0 ~ 0.5. Slight deviations from ideal Porod

375

behavior were addressed taking into account a constant background scattering a finite width

376

of the transition layer dz between the silica phase and the pore space (dz was set to a value of

377

∼ 0.5 nm for the fitting process). For higher filling fractions, as capillary condensation sets in,

378

the deviation from ideal Porod behavior was too severe for reasonable background correction

379

and the data was cut after s = 0.2–0.25 nm-1. Following correction, the Porod plots (I(s)s4 vs.

380

s) reached a plateau with the data points fluctuating slightly and statistically around the Porod

381

constant, providing a sufficiently high quality of the data for further analysis. The complete

382

fitting is described elsewhere.23 (A comparison of the experimental SAXS curves and the

383

curves acquired using the fitting routine is provided in the Supporting Information: see Figure

384

S3 and S4).

385

Since the system under study presents a void–wall structure and almost perfect contrast

386

matching was observed, the two-phase assumption seems appropriate, because the CLD has

387

direct physical meaning only for ideal two-phase systems. The combined SAXS/CLD

388

approach fortunately enables us to withdraw a quantitative description of the porous structure 17


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

Page 18 of 35

389

without the necessity to initially proclaim a specific pore shape, although care has to be taken

390

when interpreting CLDs. The CLD is a superposition of the CLD of void space and pore

391

walls. Therefore, maxima and minima visible in a CLD do not necessarily directly reveal the

392

corresponding pore or wall size.

393

The relationship between the CLD g(r) and the autocorrelation function γ(r) is given by

() = "(), > 0 ,

394

(2)

395

lP (“Porod length”)46 is the average chord-length of the system, e.g., the first moment of g(r),

396

and is directly related to the specific surface area per volume (Sφ/V) by

= 4#(1 − #) % ,

397

(3)

&

398

where # is the volume fraction of one of the two phases (here: mesoporosity). Once the Porod

399

length lP has been obtained, the average pore (void) size lV and wall thickness lW can be

400

directly calculated by

401

' ()

'

'

*

,

'

'

= ( + ( = -( = ('.-)( , *

(4)

,

402

and given that the volume fraction of the pores # is known. Thus lP allows calculating an

403

average pore size and average wall thickness without assuming any pore geometry.

404

Figure 5a shows the plot of the CLDs derived at distinct filling fractions P/P0 during

405

adsorption of DBM. All CLDs feature small values for g(0). In general, a positive value of

406

g(0) hints towards the presence of angularity in the samples, as reported by Ciccariello et

407

al.55–58 Hence, a g(0) value close to zero provides further evidence for the absence of

408

microporosity or narrow slit pores in the sample.

409

18


Page 19 of 35

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

Langmuir

410 411

Figure 5. a) Chord-length distributions g(r) and b) the representation g(r)r for the Zorbax

412

particles calculated from SAXS data shown in 4b).

413

The CLD of the evacuated Zorbax sample shows a minimum in the region

414

r ∼ 15–25 nm, probably indicating a preferred pore–pore distance. Pronounced oscillations

415

imply a higher order of the system, eventually resulting in a Bragg peak in the SAXS pattern.

416

A comprehensive representation of the CLD is the plot g(r)r vs. r (Figure 5b), because it

417

points out the most prominent pore size (respectively wall size) of a system. In addition, the

418

representation as g(r)r helps to visualize which pore size actually contributes to the inner

419

surface of the porous sample. All CLDs show their most relevant contributions at lengths

420

between 2–15 nm. The apparent first maximum at r ∼ 7.5–10 nm (Figure 5a) therefore might

421

be interpreted as corresponding to the average diameter of the pores, respectively pore walls.

422

The subsequent minima and maxima between 15–25 nm possibly reflect chords penetrating

423

two (or more) interfaces, thus corresponding to “pore(s) plus pore wall”, respectively.

424

However, such an assignment is speculative for disordered pore systems and should be

425

validated using independent methods, e.g., high-resolution TEM measurements. Obvious is

426

the shift of the first maximum from r = 7.5 nm to r = 10 nm and the decrease in the first

427

maximum, as adsorption progresses. This can be explained by the fact that the smallest pores

428

are filled at first while the average radius of the remaining unfilled pores, successively

429

increases, according to the Kelvin equation. At early adsorption stages this displacement is 19


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

Page 20 of 35

430

small, but after capillary condensation sets in, it becomes substantial. In addition a slight shift

431

might be due to some deformation of the silica structure, caused by the onset of capillary

432

condensation and fluid-wall interactions. But these strains are much smaller than the pore

433

diameter differences due to polydispersity and therefore only minorly influence the pore

434

filling as compared with the PSD.33,52,53 Close to saturation the distribution curve slightly

435

flattens and increases in width. The oscillations disappear as randomly pores of increasing

436

radius are filled.

437

More detailed information about the pore network filling during adsorption can be withdrawn

438

from the change of the Porod length lP. Using eq 4, the average pore size lv and the average

439

wall thickness lw of the porous samples can be calculated. The porosity # in this equation

440

corresponds to the total mesopore volume measured by DBM physisorption at P/P0 = 0.97.

441

The resulting pore size lv calculated for P/P0 = 0 is in good agreement with the average pore

442

size value found by nitrogen physisorption NLDFT analysis. Though, for a more systematic

443

quantitative interpretation of the CLD, knowledge about the pore (wall) morphology is

444

required. A summary of the resulting chord-lengths at designated relative pressures P/P0 is

445

given in Figure 6a and Table S1. The Porod length and respective values for the pore size and

446

wall thickness were calculated up to a filling fraction of P/P0 = 0.61. For higher filling

447

fractions the error of lP became too large to obtain reliable lv/lw values, due to the increase in

448

diffuse scattering caused by the liquid DBM inside the subsequently filled pores.

449

Additionally, with eq 3 the surface area per weight unit Sφ of a material can be estimated. The

450

remaining interface can alternatively be estimated from the changes in the Porod invariant Q

451

and lP as described in detail in the Supporting Information. The values of the so derived

452

relative surface area Sint./Sint.,0 are plotted together with the values for Sφ/Sφ,0 in Figure 6b and

453

listed in Table S1. Figure 6b visualizes the dependency of the free interface areas on P/P0 in

454

relation to the evacuated sample.

455 20


Page 21 of 35

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

Langmuir

456 457

Figure 6. a) Plot of the Porod length lP as function of the relative pressure P/P0 and the

458

average wall lw and pore size lv derived from SAXS/CLD analysis. b) Relative Porod constant

459

Q/Q0 as obtained via integration according to eq S2 as a function of P/P0. The change of the

460

relative Porod constant is plotted together with the relative interface area of the Zorbax

461

substrate, which was calculated from the Porod constant lP via the SAXS curve integration

462

method (Sint./Sint.,0, eq S1) and using the porosity values (Sφ/Sφ,0, eq S4).

463

Both curves show a similar behavior, as there is only a marginal decrease in the relative

464

surface area until the onset of capillary condensation at P/P0 > 0.5. After that S has to

465

decrease substantially in order to reach a value close to zero as for the completely pore-filled

466

state. The small drop of the relative surface area derived with both approaches Sφ and Sint. in

467

the range of small relative pressures is additional evidence for the absence of microporosity in

468

the system. If micropores were present, a more drastic decrease in interface area S should be

469

noted between 0 < P/P0 < 0.2.

470

We have already mentioned that for high values of the modulus of the scattering vector s the

471

SAXS intensity derives mostly from the internal interface. Another interesting aspect is

472

therefore the change of the slope α, I(s) ∝ 1⁄0 1 , during the adsorption process and also the

473

small deviation of Porod’s law for surface-modified adsorbent samples, showing values of

474

α > 4, depending on the position from which onwards a scaling behavior is set. Figure S5 in

475

the Supporting Information illustrates in detail the dependency of α on P/P0 for the Zorbax 21


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

Page 22 of 35

476

particles. The values of α are average values over the s intervals as given in the graph, and

477

demonstrate a clear trend.

478

In case of an abrupt density change from a constant density in the body of the silica to a value

479

of zero in the pore, the classical exponent α = 4 (see Porod’s law) should be observed.

480

Negative deviations (α < 4) of Porod’s law are observed for fractal systems I(s) ∝ 1⁄0 134.5 ,

481

where D is the surface fractal dimension (D = 2 for sharp boundaries, 2 < D < 3 for fractal

482

surfaces).59 However, the phenomenon of surface fractality requires many orders of self-

483

similarity, and thus power law asymptotes should be observed in SAXS over several orders of

484

magnitude of s. In case the experimental results span only one decade, the label ‘fractal’ is not

485

suitable.60 Otherwise, short range density fluctuations may also lead to α < 4.61 Positive

486

deviation of Porod’s law was found for a finite width of the transition layer between the

487

phases in a two-phase system. A Gaussian density profile thus leads to an apparent slope

488

α > 4, because

489

6(0) ~ 0 .8 9 . :;
=

(5)

490

with dz being a measure of the transition layer width.62 This effect has already been observed

491

for silicas used in reversed-phase HPLC.63 The surface of RP silicas is modified with alkyl-

492

chains in order to increase the hydrophobicity of the materials and change the selectivity in

493

specific separation applications. Thus, their scattering density does not fall abruptly to zero,

494

but decreases continuously towards the pore center.

495

For the dry Zorbax sample the scattered intensity at high values for s decays with an apparent

496

non-integer power law of α = 4.2, indicating a diffuse surface (α > 4, dz > 0). As adsorption

497

progresses α decreases in the designated s intervals, and for 0.4 < P/P0 < 1.0 the exponent

498

becomes distinctly smaller than α = 4, due to the increase of contributions of scattering from

499

short range three-dimensional density fluctuations. These contributions are expected to

500

increase steadily as the pores fill with liquid DBM, and eventually dominate the scattering

22


Page 23 of 35

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

Langmuir

501

curve for s > 0.2. Thus, the decrease in α is supposed to be an effect of the progressing pore

502

condensation, which we were able to confirm with simulations of the scattering curves.

503

In order to understand the SAXS data at larger s, we simulated the SAXS data of polydisperse

504

cylinders of infinite length. The simulated data were blurred by both, a constant background

505

scattering and a finite width of the interface.64 By adjusting the parameters pore diameter,

506

size distribution (polydispersity), finite width of the transition layer, and magnitude of

507

background scattering in the scattering simulation the original SAXS data were approximated.

508

As can be seen from the simulated curves in Figure 7a, the qualitative behavior of

509

experimental and simulated data sets is in good agreement. The increasing contribution of

510

density fluctuations induced through the progressing pore filling with DBM can be accounted

511

for by simply increasing the scattering background value. For a finite transition layer width

512

dz = 0.8 nm the slope α positively deviates from the ideal value of α = 4, but with increasing

513

background contribution the apparent value of the exponent rapidly decreases to α < 4.

514 515

Figure 7. a) Resulting curves of the simulations with increasing background contribution

516

(bg). The radius of the model cylinders was set to Rc = 3.9 nm and the cylinder polydispersity

517

to σ(Rc) = 1. The finite width of the transition layer was approximated by a value of

518

dz = 0.8 nm and the increasing contribution of density fluctuations, induced through the

519

progressing pore filling with DBM, were accounted for by gradually increasing the scattering 23


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

Page 24 of 35

520

background value bg from 0 to 20 a.u. The black curve represents a system with a sharp phase

521

boundary in the case of insignificant background contribution. b) Slopes of the scattering

522

curves α (in a log-log plot) measured for the range 0.2 < s < 0.4 at designated relative

523

pressures P/P0 for six types of adsorbent materials. Atlantis, Luna, Zorbax and Poroshell

524

particles underwent surface modification with C18-chlorosilane, whereas Halo and Kinetex

525

particles still feature an unmodified bare silica surface.

526

In Figure 7b the measured values of the slope α are shown for 3 distinct filling fractions for a

527

variety of adsorbents. The main parameter causing the slope α of the unfilled samples

528

(P/P0 = 0) to be larger or smaller than 4 is the hydrophobic surface modification that was

529

applied to some of these samples. Namely Atlantis, Luna, Zorbax and Poroshell particles were

530

treated with octadecylchlorosilane/chlorodimethyloctadecylsilane after preparation and thus

531

feature a layer of C18-chains on top of the silica skeleton. Schmidt et al. have shown that the

532

larger the carbon content C%, i.e. the thickness and density of the alkyl layer, the larger the

533

deviation from ideal Porod behavior α > 4.63 They explained their findings by a so-called

534

“diffuse pore boundary” model, assuming that the alkyl-chains are uniformly distributed over

535

the surface, in compliance with Ruland’s finite width of density transition dz. It was

536

concluded that the observation α > 4 in the power-law decay of I(s) is related to a power-law

537

variation of the scattering density ρ(x), with x being the distance to the silica surface. Hence,

538

measuring the slope α gives particular information about the surface modification of this type

539

of materials. Our in-situ experiments further show the alternated adsorption characteristics

540

induced by the hydrophobic alkyl-layer. For P/P0 = 0.2 the change in α is equally small in all

541

of the studied samples. Since no micropores should be present and no film formation is

542

expected, the uptake in DBM is marginal. But with increasing relative pressure from

543

P/P0 = 0.2 to P/P0 = 0.6, the drop in α is much more pronounced for the bare silica samples,

24


Page 25 of 35

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

Langmuir

544

since the adsorbate–adsorbent interaction should be significantly stronger between the free

545

silanol groups and DBM than between DBM and the C18-chains.

546 547

CONCLUSIONS

548

In this work in-situ SAXS sorption of organic vapor (dibromomethane) together with state-

549

of-the-art nitrogen physisorption with NLDFT analysis was applied to the pore space

550

characterization of mesoporous chromatographic silica adsorbents. The studied materials

551

feature a disordered pore space but their synthesis is highly reproducible, thus generating

552

mesoporous silica with defined pore size distribution, pore volume and specific surface area.

553

Using different evaluation methods we were able to detect and quantify these specific

554

mesoporous properties and found good agreement between quantitative parameters (surface

555

area/volume and average mesopores size), regardless of the methods’ different underlying

556

concepts. A meaningful average mesopores size can be obtained from the average chord-

557

lengths obtained from SAXS evaluation; hence, routine chord-length distribution (CLD

558

evaluation software in combination with SAXS lab setups can be a welcome complement to

559

physisorption. By the in-situ SAXS measurements we could even distinguish between varying

560

surface modifications of the materials. The surface chemistry and its consequences for the

561

adsorption process were investigated and significant differences regarding the uptake of DBM

562

were observed. We were moreover able to conclude that pore filling of one designated sample

563

using DBM occurs randomly with respect to the spatial location of the pores, but that the

564

smallest pores are filled first. Insights of that kind cannot be acquired with any of the

565

techniques alone; therefore the combination of physisorption and SAXS is especially valuable

566

for evaluating the pore structure and the pore filling mechanism in mesoporous materials.

567

Hence, the presented analysis thus aims at a better understanding of the adsorption

25


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

Page 26 of 35

568

mechanism of organic vapors (here DBM) in such materials, which still poses a major

569

challenge in the field of physisorption analysis.

570

The in-situ SAXS method allowed us further excluding the presence of micropores (in

571

agreement with the NLDFT pore size analysis of the nitrogen adsorption data) and

572

inaccessible porosity in the studied samples and to evaluate the distinct adsorption mechanism

573

of DBM in comparison with nitrogen adsorption. The absence of inaccessible voids is an

574

important finding with respect to the applicability of the quantification of such disordered

575

mesoporosity as described in our previous publication on these materials.25 All of the

576

mesopores being accessible for nitrogen or DBM, the average mesopore size and specific

577

surface area can be quantified using the concept of the chord-length distribution. Otherwise,

578

the SAXS data and the respective CLD data would contain contributions from inaccessible

579

voids, thus impeding the combined analysis of SAXS and physisorption data as described in

580

ref. 23.

581

Although, materials with disordered porosity are widely used in technological applications,

582

this in-situ SAXS approach has rarely been used for their comprehensive evaluation. Hence,

583

more work is planned in order to further explore the mechanism contributing to the observed

584

hysteresis by performing in-situ SAXS experiments coupled with hysteresis scanning

585

adsorption/desorption experiments. This will allow one to develop reliable pore network

586

models which can be applied for an in-depth pore structural analysis by advanced physical

587

adsorption methods.

588 589

26


Page 27 of 35

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

Langmuir

590

ASSOCIATED CONTENT

591

Supporting Information. Details about the in-situ SAXS measuring setup, the DBM/silica

592

contact angle evaluation, and the calculation procedure of the relative surface area S/S0.

593

Figures of a modelled SAXS curve for the evacuated Zorbax sample, the fitted and

594

experimental SAXS curves used for the CLD evaluation, as well as a plot showing the

595

dependency of the slope α of the scattering curves at large s-values on P/P0. This material is

596

available free of charge via the Internet at http://pubs.acs.org.

597

AUTHOR INFORMATION

598

Corresponding Author

599

* Phone: +49-641-9934590. Fax: +49-641-9934509.

600

E-mail: [email protected].

601

ACKNOWLEDGMENT

602

This project was supported by the Laboratory of Materials Research (LaMa) at Justus-Liebig-

603

Universität Giessen and by the Deutsche Forschungsgemeinschaft DFG (Bonn, Germany)

604

under grant TA 268/5. The authors thank Christoph Weidmann and Jan Perlich for the help in

605

performing the experiments at the HASYLAB/DESY, Hamburg, Germany. The research

606

leading to these results has received funding from the European Community's Seventh

607

Framework Programme (FP7/2007-2013) under grant agreement n° 226716.

27


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

608

609 610

Page 28 of 35

REFERENCES (1) Guiochon, G.; Gritti, F. Shell particles, trials, tribulations and triumphs. J. Chromatogr. A 2011, 1218, 1915–1938.

611

(2) Unger, K. K.; Liapis, A. I. Adsorbents and Columns in Analytical High-Performance

612

Liquid Chromatography: A Perspective with Regard to Development and Understanding. J.

613

Sep. Sci. 2012, 35, 1201–1212.

614

(3) Mascotto, S.; Wallacher, D.; Kuschel, A.; Polarz, S.; Zickler, G. A.; Timmann, A.;

615

Smarsly, B. M. Adsorption in Periodically Ordered Mesoporous Organosilicas Materials

616

Studied by Small-Angle X-ray Scattering and Small-Angle Neutron Scattering. Langmuir

617

2010, 26, 6583–6592.

618

(4) Thommes, M.; Smarsly, B. M.; Groenewolt, M.; Ravikovitch, P. I.; Neimark, A. V.

619

Adsorption Hysteresis of Nitrogen and Argon in Pore Networks and Characterization of

620

Novel Micro- and Mesoporous Silicas. Langmuir 2006, 22, 756–764.

621

( 5 ) Stoeckel, D.; Kübel, C.; Hormann, K.; Höltzel, A.; Smarsly, B. M.; Tallarek, U.

622

Morphological Analysis of Disordered Macroporous–Mesoporous Solids Based on Physical

623

Reconstruction by Nanoscale Tomography. Langmuir 2014, 30, 9022–9027.

624 625 626 627

(6) Thommes, M.; Cychosz, K. A. Physical Adsorption Characterization of Nanoporous Materials: Progress and Challenges. Adsorption 2014, 20, 233–250. (7) Sarkisov, L.; Monson, P.A. Modeling of Adsorption and Desorption in Pores of Simple Geometry Using Molecular Dynamics. Langmuir 2001, 17, 7600–7604.

628

(8) Barton, T. J.; Bull, L. M.; Klemperer, W. G.; Loy, D. A.; McEnaney, B.; Misono, M.;

629

Monson, P. A.; Pez, G.; Scherer, G. W.; Vartuli, J. C.; Yaghi, O. M. Tailored Porous

630

Materials. Chem. Mater. 1999, 11, 2633–2656.

631 632

(9) Neimark, A. V.; Ravikovitch, P. I. Capillary Condensation in MMS and Pore Structure Characterization. Microporous Mesoporous Mater. 2001, 44, 697–707. 28


Page 29 of 35

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

633 634 635 636 637 638 639 640 641 642 643 644

Langmuir

(10) Ravikovitch, P. I.; Neimark, A. V. Characterization of Nanoporous Materials from Adsorption and Desorption Isotherms. Colloids Surf. A 2001, 187, 11–21. (11) Landers, J.; Gor, G. Yu.; Neimark, A. V. Density Functional Theory Methods for Characterization of Porous Materials. Colloids Surf. A 2013, 437, 3–32. (12) Snyder, L. R.; Kirkland, J. J. Introduction to Modern Liquid Chromatography, 3rd ed., John Wiley & Sons, Inc., Hoboken, NJ. 2010. (13) Guinier, A.; Fournet, G. Small-Angle Scattering of X-Rays; John Wiley & Sons: New York, 1955; ch. 2. (14) Feigin, L. A.; Svergun, D. I. Structure Analysis by Small-Angle X-Ray and Neutron Scattering; Plenum Press: New York, 1987; ch. 2. (15) Glatter, O.; Kratky, O. Small Angle X-ray Scattering; Academic Press: London, 1982; ch. 1.

645

(16) Smarsly, B.; Groenewolt, M.; Antonietti, M. SAXS Analysis of Mesoporous Model

646

Materials: A Validation of Data Evaluation Techniques to Characterize Pore Size, Shape,

647

Surface Area, and Curvature of the Interface. Progr. Colloid Polym. Sci. 2005, 130, 105–113.

648 649

(17) Méring, J.; Tchoubar, D. J. Interprétation de la Diffusion Centrale des Rayons X par les Systèmes Poreux. I. Appl. Crystallogr. 1968, 1, 153–165.

650

(18) Smarsly, B. M.; Kaper, H.; Mascotto, S.; Weidmann, C. Charakterisierung Meso-

651

poröser Materialien Mittels Kleinwinkelstreuung (SAXS/SANS). Chem.-Ing.-Tech. 2010, 82,

652

823–828.

653 654 655 656 657 658

( 19 ) Torquato, S.; Lu, B. Chord-length Distribution Function for Two-Phase Random Media. Phys. Rev. E 1993, 47, 2950–2953. (20) Burger, C.; Ruland, W. Analysis of Chord-Length Distributions. Acta Crystallogr. Sect. A 2001, 57, 482–491. (21) Enke, D.; Janowski, F.; Gille, W.; Schwieger, W. Structure and Texture Analysis of Colloidal Silica in Porous Glasses. Colloids Surf. A 2001, 187, 131–139. 29


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

Page 30 of 35

659

(22) Mascotto, S.; Wallacher, D.; Brandt, A.; Hauss, T.; Thommes, M.; Zickler, G. A.;

660

Funari, S. S.; Timmann, A.; Smarsly, B. M. Analysis of Microporosity in Ordered

661

Mesoporous Hierarchically Structured Silica by Combining Physisorption With in-situ Small-

662

Angle Scattering (SAXS and SANS). Langmuir 2009, 25, 12670–12681.

663

(23) Stoeckel, D.; Wallacher, D.; Zickler, G. A.; Perlich, J.; Tallarek, U.; Smarsly, B. M.

664

Coherent Analysis of Disordered Mesoporous Adsorbents Using Small Angle X-ray

665

Scattering and Physisorption Experiments. Phys. Chem. Chem. Phys. 2014, 16, 6583–6592.

666 667 668 669

(24) Perret, R.; Ruland, W. The Microstructure of PAN-Base Carbon Fibres. J. Appl. Crystallogr. 1970, 3, 525–532. (25) Smarsly, B.; Antonietti, M.; Wolff, T. Evaluation of the Small-Angle X-ray Scattering of Carbons Using Parametrization Methods. J. Chem. Phys. 2002, 116, 2618–2627.

670

(26) Gille, W.; Braun, A. SAXS Chord-length Distribution Analysis and Porosity Esti-

671

mation of Activated and Non-Activated Glassy Carbon. J. Non-Cryst. Solids 2003, 321, 89–

672

95.

673 674

(27) Ramsay, J. D. F.; Hoinkis, E. SANS Investigations of Benzene Adsorption on Porous Silica Gel. Physica B 1998, 248, 322–326.

675

(28) Sel, O.; Brandt, A.; Wallacher, D.; Thommes, M.; Smarsly, B. Pore Hierarchy in

676

Mesoporous Silicas Evidenced by in-situ SANS During Nitrogen Physisorption. Langmuir

677

2007, 23, 4724–4727.

678

(29) Favvas, E. P.; Stefanopoulos, K. L.; Papageorgiou, S. K.; Mitropolous, A. C. In-situ

679

Small Angle X-ray Scattering and Benzene Adsorption on Polymer-Based Carbon Hollow

680

Fiber Membranes. Adsorption 2013, 19, 225-233.

681

(30) Mileeva, Z.; Ross, D. K.; Wilkinson, D.; King, S. M.; Ryan, T. A.; Sharrock, H. The

682

Use of Small Angle Neutron Scattering with Contrast Matching and Variable Adsorbate

683

Partial Pressures in the Study of Porosity in Activated Carbons. Carbon 2012, 50, 5062-5075.

30


Page 31 of 35

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

Langmuir

684

(31) Zickler, G. A.; Jähnert, S.; Funari, S. S.; Findenegg, G. H.; Paris, O. Pore Lattice

685

Deformation in Ordered Mesoporous Silica Studied by in-situ Small-Angle X-ray Diffraction.

686

J. Appl. Crystallogr. 2007, 40, s522–s526.

687

(32) Zickler, G. A.; Jähnert, S.; Wagermaier, W.; Funari, S. S.; Findenegg, G. H.; Paris, O.

688

Physisorbed Films in Periodic Mesoporous Silica Studied by in-situ Synchrotron Small-Angle

689

Diffraction. Phys. Rev. B 2006, 73, 184109.

690

(33) Jähnert, S.; Müter, D.; Prass, J.; Zickler, G. A.; Paris, O.; Findenegg, G. H. Pore

691

Structure and Fluid Sorption in Ordered Mesoporous Silica. I. Experimental Study by in-situ

692

Small-Angle X-Ray Scattering. J. Phys. Chem. C 2009, 113, 15201–15210.

693

(34) Müter, D.; Jähnert, S.; Dunlop, J. W. C.; Findenegg, G. H.; Paris, O. Pore Structure and

694

Fluid Sorption in Ordered Mesoporous Silica. II. Modeling. J. Phys. Chem. C 2009, 113,

695

15211–15217.

696

(35) Findenegg, G. H.; Jähnert, S.; Müter, D.; Prass, J.; Paris, O. Fluid Adsorption in

697

Ordered Mesoporous Solids Determined by In-situ Small-Angle X-ray Scattering. Phys.

698

Chem. Chem. Phys. 2010, 12, 7211–7220.

699

(36) Erko, M.; Wallacher, D.; Brandt, A.; Paris, O. In-Situ Small-Angle Neutron Scattering

700

Study of Pore Filling and Pore Emptying in Ordered Mesoporous Silica. J. Appl. Cryst. 2010,

701

43, 1–7.

702

(37) Mitropoulos, A. C.; Haynes, J. M.; Richardson, R. M. Characterization of Porous Glass

703

by Adsorption of Dibromomethane in Conjunction with Small-Angle R-ray Scattering. Phys.

704

Rev. B 1995, 52, 10035–10042.

705 706

(38) Mitropoulos, A. C. Small-Angle X-ray Scattering Studies of Adsorption in Vycor Glass. J. Coll. Interf. Sci. 2009, 336, 679–690.

707

( 39 ) Favvas, E. P.; Stefanopoulos, K. L.; Vairis, ·A.; Nolan, J. W.; Joensen, K. D.;

708

Mitropoulos, A. C. In-situ SAXS Investigation of Dibromomethane Adsorption in Ordered

709

Mesoporous Silica. Adsorption 2013, 19, 331–338. 31


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

Page 32 of 35

710

(40) Favvas, E. P.; Stefanopoulos, K. L.; Mitropoulos, A. C.; Kanellopoulos, N. K. In-situ

711

SAXS Study of Dibromomethane Adsorption on MCM-41. Microp. Mesop. Mater. 2015,

712

209, 122–125.

713

(41) Stanton, D. T.; Jurs, P.C. Development and Use of Charged Partial Surface Area

714

Structural Descriptors in Computer-Assisted Quantitative Structure-Property Relationship

715

Studies. Anal. Chem. 1990, 62, 2323–2329.

716 717

(42) Korosi, G.; Kovats, E. S. Density and Surface Tension of 83 Organic Liquids. J. Chem. Eng. Data 1981, 26, 323–332.

718

(43) Roth, S. V.; Döhrmann, R.; Dommach, M.; Kuhlmann, M.; Kröger, I.; Gehrke, R.;

719

Walter, H.; Schroer, C.; Lengeler, B.; Müller-Buschbaum, P. Small-Angle Options of the

720

Upgraded Ultrasmall-Angle X-Ray Scattering Beamline BW4 at HASYLAB Rev. Sci.

721

Instrum. 2006, 77, 085106.

722

(44) Hammersley, A. P.; Svensson, S. O.; Hanfland, M.; Fitch, A. N.; Häusermann, D.

723

Two-Dimensional Detector Software: From Real Detector to Idealised Image or Two-Theta

724

Scan. High Press. Res. 1996, 14, 235–.248

725 726

(45) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity; Academic Press: London, 1982; 2nd ed., ch. 3.

727

(46) Naono, H.; Hakuman, M.; Joh, H.; Sakurai, M.; Nakai, K. Characterization of Porous

728

Silica Gel by Means of Adsorption-Desorption Isotherms of Water Vapor and Nitrogen Gas.

729

Ceramic Transactions 1993, 31, 203–212.

730 731

(47) Branton, P. J.; Hall, P. G.; Sing, K. S. W. Physisorption of Alcohols and Water Vapour by MCM-41, a Model Mesoporous Adsorbent. Adsorption 1995, 1, 77–82.

732

(48) Bambrough, C. M.; Slade, R. C. T.; Williams, R. T. Steric Effects in the Sorption of N-

733

Butanol and Tert-Butanol by Tailored Phenyl-Modified Porous Silicas. Phys. Chem. Chem.

734

Phys. 2000, 2, 3499–3502.

32


Page 33 of 35

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

735 736 737 738

Langmuir

(49) Thomson, W. LX. On the Equilibrium of Vapour at a Curved Surface of Liquid. Philos. Mag. Ser. 4 1871, 42, 448–452. (50) Cohan, L. H. Sorption Hysteresis and the Vapor Pressure of Concave Surfaces. J. Am. Chem. Soc.1938, 60, 433–435.

739

(51) Barrett, E. P.; Joyner, L. G.; Halenda, P. P. The Determination of Pore Volume and

740

Area Distribution in Porous Substances. I. Computations from Nitrogen Isotherms. J.

741

Am.Chem. Soc. 1951, 73, 373–380.

742 743 744 745 746 747 748 749

(52) Guenther, G.; Prass, J.; Paris O.; Schoen, M. Novel Insights into Nanopore Deformation Caused by Capillary Condensation. Phys. Rev. Lett. 2008, 101, 086104. (53) Prass, J.; Müter, D.; Fratzl, P.; Paris, O. Capillarity-Driven Deformation of Ordered Nanoporous Silica. Appl. Phys. Lett. 2009, 95, 083121. (54) Porod, G. Small Angle X-ray Scattering; Glatter, O., Kratky, O.,Eds.; Academic Press: London, 1982; pp 17–51. (55) Ciccariello, S.; Cocco, G.; Benedetti, A.; Enzo, S. Correlation Functions of Amorphous Multiphase Systems. Phys. Rev. B, 1981, 23, 6474–6485.

750

(56) Ciccariello, S.; Benedetti, A. Singularities of Phase Boundaries and Values of the

751

Second-Order Derivative of the Correlation Function at the Origin. Phys. Rev. B 1982, 26,

752

6384–6389.

753 754 755 756 757 758 759 760

( 57 ) Ciccariello, S. Edge Contributions to the Kirste-Porod Formula: The Truncated Circular Right Cone Case. Acta Crystallogr. Sect. A 1993, 49, 398–405. (58) Ciccariello, S.; Sobry, R. The Vertex Contribution to the Kirste-Porod Term. Acta Crystallogr. Sect. A 1995, 51, 60–69. (59) Bale, H. B.; Schmidt, P. W. Small-Angle X-Ray Scattering Investigation of Submicroscopic Porosity with Fractal Properties. Phys. Rev. Lett. 1984, 53, 596–599. (60) Avnir, D.; Biham, O.; Lidar, D.; Malcai, O. Is the Geometry of Nature Fractal? Science 1998, 279, 39–40. 33


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

761 762 763 764

Page 34 of 35

( 61 ) Page, J. H.; Liu, J.; Abeles, B.; Deckmann, H. W.; Weitz, D. A. Pore–Space Correlations in Capillary Condensation in Vycor. Phys. Rev. Lett. 1993, 71, 1216–1219. ( 62 ) Ruland, W. Small-Angle Scattering of Two-Phase Systems: Determination and Significance of Systematic Deviations from Porod’s Law. J. Appl. Cryst. 1971, 4, 70–73.

765

(63) Schmidt P. W.; Avnir, D.; Levy, D.; Höhr, A.; Steiner, M.; Röll, A. Small-Angle X-

766

Ray Scattering from the Surface of Reverse-Phase Silicas: Power-Law Scattering Exponents

767

of Magnitudes Greater than Four. J. Chem. Phys. 1991, 94, 1474–1479.

768

(64) Ruland, W; Smarsly, B. M. Two-Dimensional Small-Angle X-Ray Scattering of Self-

769

Assembled Nanocomposite Films with Oriented Arrays of Spheres: Determination of Lattice

770

Type, Preferred Orientation, Deformation and Imperfection. J. Appl. Cryst. 2007, 40, 409–

771

417.

772

34


Page 35 of 35

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

773 774

Langmuir

Table of Contents Graphic

775

35


Elucidating the Sorption Mechanism of ... - ACS Publications

Recommend Documents