Elucidating the Sorption Mechanism of Dibromomethane in

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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

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Langmuir

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Elucidating the Sorption Mechanism of Dibromomethane

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in Disordered Mesoporous Silica Adsorbents

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

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Smarsly*,1

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1

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35392 Gießen (Germany)

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2

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14109 Berlin, Germany

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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,

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Austria

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4

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

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______________________________________________

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* Author to whom correspondence should be addressed.

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

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E-mail: [email protected].

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

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

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1

ACS Paragon Plus Environment

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ABSTRACT:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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2


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Langmuir

INTRODUCTION

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

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

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

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

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

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

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

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

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

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

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

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quantitative characterization of disordered mesopore structures, since one prominent feature

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

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

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

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

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closed-packed lattices.3,4

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Standard analysis methodologies applied for the characterization of mesoporous materials,

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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special attention.

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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

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number of porous materials.3,21–26

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

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

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

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

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

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

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

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

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

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

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

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mechanism as well as the pore structure.

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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a disordered pore space.27,37,38

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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sample

was

evaluated

by

ex-situ

N2

and

DBM

sorption

measurements.

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EXPERIMENTAL SECTION

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Chemicals and Materials. The studied particulate materials are commercially available

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

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

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

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

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

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

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as received.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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different sorption regimes of the isotherm.

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

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

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

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

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

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

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

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

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

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

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

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

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equal radial distances from the central beam.

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RESULTS AND DISCUSSION

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

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

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confirming that macroscopic thermodynamic methods underestimate the pore size.

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

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

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

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

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

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


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

214

transition.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

233

pressures.

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10


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

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

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

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

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

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

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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

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

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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.

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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


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

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

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

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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

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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.

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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


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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

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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

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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

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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

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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,

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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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

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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


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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


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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


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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

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

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

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