Document [original]

Hierarchically porous and mechanically stable

monoliths from ordered mesoporous silica and

their water ﬁltration potential†

Laura M. Henning, *

Julian T. M¨

uller,

Glen J. Smales, *

Brian R. Pauw,

Johannes Schmidt,

Maged F. Bekheet,

Aleksander Gurlo ‡

and Ulla Simon ‡

Mechanically stable structures with interconnected hierarchical porosity combine the beneﬁts of both small

and large pores, such as high surface area, pore volume, and good mass transport capabilities. Hence,

lightweight micro-/meso-/macroporous monoliths are prepared from ordered mesoporous silica COK-12

by means of spark plasma sintering (SPS, S-sintering) and compared to conventionally (C-) sintered

monoliths. A multi-scale model is developed to ﬁt the small angle X-ray scattering data and obtain

information on the hexagonal lattice parameters, pore sizes from the macro to the micro range, as well as

the dimensions of the silica population. For both sintering techniques, the overall mesoporosity, hexagonal

pore ordering, and amorphous character are preserved. The monoliths' porosity (77–49%), mesopore size

(6.2–5.2 nm), pore volume (0.50–0.22 g cm

3

), and speciﬁc surface area (451–180 m

1

) decrease with

increasing processing temperature and pressure. While the diﬀerence in porosity is enhanced, the

structural parameters between the C-and S-sintered monoliths are largely converging at 900 C, except

for the mesopore size and lattice parameter, whose dimensions are more extensively preserved in the

S-sintered monoliths, however, coming along with larger deviations from the theoretical lattice. Their

higher mechanical properties (biaxial strength up to 49 MPa, 724 MPa HV 9.807 N) at comparable

porosities and ability to withstand ultrasonic treatment and dead-end ﬁltration up to 7 bar allow S-sintered

monoliths to reach a high permeance (2634 L m

2

1

bar

1

), permeability (1.25 10

14

), and ability to

reduce the chemical oxygen demand by 90% during ﬁltration of a surfactant-stabilized oil in water

emulsion, while indicating reasonable resistance towards fouling.

1 Introduction

Ordered mesoporous silica (OMS) materials are commonly used

as nano-sized powders, which are usually obtained directly from

synthesis.

1,2

While OMS nanoparticles (NPs) are suitable for

many applications such as (surface functionalized) adsorbents

and supports for (photo)catalytic and drug delivery systems,

3–6

several drawbacks constrain their application. Firstly, NP

handling requires extensive safety precautions to avoid dust

inhalation and associated hazards, hampering large-scale

industrial usage. Secondly, NP powder beds usually exhibit

high pressure drops during operation, while NP suspension

systems normally require high energy or long times for NP

segregation. Lastly, the ecofriendly and eﬃcient recovery of NPs

for reutilization remains a challenge.

The coating of mesoporous lms on various substrates is

developed as one pathway to overcome those challenges.

Therefore, OMS precursors are usually deposited by dip coating

or spin coating onto a membrane substrate.

Alternatively, OMS

monoliths are directly obtained by sol–gel processes, spinodal

decomposition, solvothermal routes, hard/so/ice templating,

frothing, as well as combinations of those techniques.

8–14

However, little or no information is available about their

mechanical properties. Their low processing temperatures

suggest overall weak mechanical resistances, which might

hinder deployment in pressure-loaded applications such as

ltration. Additionally, a great number of listed applications

would benet from hierarchical pore structures, allowing to

combine high specic surfaces and pore volumes with high

Technische Universit¨

at Berlin, Faculty III Process Sciences, Institute of Material

Science and Technology, Chair of Advanced Ceramic Materials, Straße des 17. Juni

135, 10623 Berlin, Germany. E-mail: [email protected]-berlin.de; Tel:

+49 30 314 70483

Bundesanstalt f¨

ur Materialforschung und -pr¨

ufung (BAM), Division 6.5 –Polymers in

Life Sciences and Nanotechnology, Unter den Eichen 87, 12205 Berlin, Germany.

E-mail: glen-jacob.sma[email protected]; Tel: +49 30 8104 3314

Technische Universit¨

at Berlin, Faculty II Mathematics and Natural Sciences, Institute

of Chemistry, Chair of Functional Materials, Straße des 17. Juni 135, 10623 Berlin,

Germany

†Electronic supplementary information (ESI) available. See

https://doi.org/10.1039/d2na00368f

‡Equal contribution.

Cite this: Nanoscale Adv., 2022, 4,

3892

Received 12th June 2022

Accepted 15th August 2022

DOI: 10.1039/d2na00368f

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mechanical properties while benetting from high accessibility

and controlled mass transfer.

Spark plasma sintering (SPS), also known as eld-assisted

sintering technique (FAST), pulsed electric current sintering

(PECS), electric discharge sintering (EDS), or pulsed current

processing (PCP), is a promising one-step technique for rapid

powder consolidation to obtain mechanically robust single-

phase OMS monoliths. During SPS, uniaxial pressure is

applied on the powder while an electric current is deployed on

the electrically conductive pressing die, usually made from

graphite, to facilitate sintering by Joule heating in a controlled

atmosphere, although neither sparks nor plasma have been

observed yet.

15,16

In comparison to conventional sintering

techniques, high heating and cooling rates, along with short

dwell times in the range of seconds or minutes, allow for rapid,

one-step processing with the possibility for grain growth

adjustment, while no pre-compaction of the powder is

required.

Initial restrictions of the SPS process, such as scal-

ability or structural limitations, have been overcome by the

development of multi-sample dies, machinable parts, and semi-

continuous systems.

18,19

While one focus of SPS remains on the

densication of conventional and hard-to-sinter materials,

recently, the production of porous products came into focus.

20,21

SPS was previously applied to fabricate porous OMS monoliths

from sol–gel derived SBA-15 powder,

22,23

mesoporous spherical

particles,

and hydrothermally produced OMS.

The studies

used the nonionic block copolymer Pluronic P123 as a tem-

plating agent, the latter one also Pluronic L121 and F127,

resulting in ordered structures of hexagonal, lamellar, and

cubic character, respectively. However, current literature both

lacks and demands a comparative analysis of porous materials

prepared by diﬀerent sintering techniques, but with similar

pore fraction and size.

Furthermore, the inuence of the SPS

conditions on the mechanical properties of porous sintered

materials remains marginally researched.

The aim of this work is to produce and thoroughly charac-

terize binder-free, hierarchically porous monoliths from one

large batch of more environmentally friendly synthesized OMS

COK-12 powder

8,26,27

by solid state sintering methods, namely

SPS as well as conventional sintering, to enhance the under-

standing of OMS sintering and the eﬀect of sintering pressure

and temperature on the micro-, meso-, and macroporosity,

among other properties. Therefore, an elaborate, custom small

angle X-ray scattering (SAXS) model for powder and partially

sintered hexagonal OMS is presented. This obtains a thorough

structural examination further complemented by additional

characterization techniques. Additionally, because of the

structural diﬀerences, the monolith's mechanical properties,

their water permeability and suitability for separation applica-

tions, and COK-12's higher sintering resistance compared to

SBA-15 are discussed.

2 Experimental

2.1 Chemicals

Pluronic P123 (M

5800 g mol

1

) and Tween 80 were ob-

tained from Sigma-Aldrich (Merck, Germany). Citric acid

($99.5%, anhydrous), trisodium citrate dihydrate ($99%), and

sodium silicate (7.8–8.5 wt% Na

O, 25.8–28.5 wt% SiO

) were

purchased from Carl Roth (Germany). Hydraulic oil Tellus Oil

46 with a kinematic viscosity of 46 mm

1

(40 C) was acquired

from Shell (Shell Deutschland Oil GmbH, Germany). Deionized

water (DIW) was used for the synthesis and testing.

2.2 COK-12 synthesis

The synthesis of COK-12 was performed as previously re-

ported.

8,26,28

A batch upscaled by the factor of 50 was produced

as follows. Firstly, 200 g P123 was dissolved in 5375 mL DIW.

Aer P123 dissolution, 168.1 g anhydrous citric acid and 144.1 g

trisodium citrate dihydrate were added to buﬀer the solution.

Aer stirring for 24 h, a solution of 520 g sodium silicate and

1500 mL DIW was incorporated into the buﬀered solution. An

immediate solid formation was observed, and stirring was

maintained for 5 min, aer which the slurry was aged for 24 h

without stirring. Subsequently, the solid was separated from the

synthesis solution by vacuum ltration and washed with 25 L

DIW. Finally, the material was dried at 60 C overnight and

calcined in air at 500 C with a 1 K min

1

heating ramp and 8 h

dwell time to remove the templating agent.

2.3 Spark plasma sintering of COK-12

Spark plasma sintering, subsequently referred to as S-sintering,

of COK-12 was performed in custom, cylindrical three-sample

graphite dies of 3B10 mm in a parallel conguration, see

Fig. S1,†using a Desktop Sinter System SPS-211Lx (Dr Sinter Lab

Jr., Japan) under vacuum. The weighed portion, heating rate,

and dwell time were constant with 0.11 g COK-12 per sample,

100 K min

1

, and 1 min, respectively. Pressures of 2.5 MPa,

12.5 MPa, 25 MPa, and 50 MPa and temperatures of 600 C,

700 C, 800 C, and 900 C were applied. For reference, dense

samples were produced at 50 MPa and 1045 C using 0.22 g

COK-12 per sample, a heating rate of 25 K min

1

, and a dwell

time of 45 min.

2.4 Conventional sintering of COK-12

For comparison, conventional sintering, subsequently referred

to as C-sintering, was performed by uniaxial pressing of COK-12

in a universal testing machine Z020 (ZwickRoell, Germany) at

25 MPa and 50 MPa. Equally, the weighed portion was 0.11 g

COK-12 per sample. Aer pressing, the samples were subse-

quently sintered at 600 C, 700 C, 800 C, and 900 C with

a dwell time of 12 h in a muﬄe furnace (Nabertherm, Germany).

2.5 Characterization

The apparent porosity and bulk density of the monoliths were

determined using Archimedes' method based on ISO

18754:2020.

Impregnation was carried out by the boiling

method.

The biaxial strength was ascertained using the ball-on-three

balls (B3B) test.

In comparison to the common ring-on-ring

test, the B3B test minimizes fraction and inhomogeneous

load distribution and is suitable for investigating small, as-

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processed disc-shaped samples.

Three as-processed silica

monoliths per parameter set were tested in a universal testing

machine Z020 (ZwickRoell, Germany) equipped with a 20 kN

load cell using high precision bearing balls of 6.5 mm in

diameter. Testing was performed with a loading rate of 1 N s

1

The biaxial strength was calculated using a Poisson's ratio of 0.3

for mesoporous silica.

A Weibull analysis was performed on

a set of 30 S-sintered monoliths processed at 800 C and

12.5 MPa using the default Weibull probability plot function in

Origin 2021b (OriginLab Corporation, USA).

The Vickers hardness was ascertained on a Z3212 hardness

tester (ZwickRoell, Germany) based on EN ISO 14705:2021 with

a test force of 9.807 N applied for 15 s.

Therefore, the samples

were embedded in Epox epoxy resin (Struers, Germany),

ground, and polished to 3 mm. Indents from the central part of

the polished cross sections were measured using a DM 4000 M

light microscope (Leica, Germany).

The biaxial strength and Vickers hardness were tted using

the Ryshkewitch model, yielded by Duckworth

p¼p0expðc3Þ;(1)

the Hashin model

p¼p0ð13Þ

ð1þc3Þ;(2)

and Bal'shin model

p¼p0ð13Þc

;(3)

where pis the property of the material with the porosity 3,p

the property at zero porosity, and cis the respective tting

parameter. Furthermore, the mechanical properties were tted

using the percolation law

p¼p013

3Mn

;(4)

where 3

is the maximum porosity of the powder mass, and nis

the tting parameter.

was ascertained to be 0.95 by using

the COK-12 powder apparent density of 0.1 g cm

3

and COK-12

true density of 2.2 g cm

3

The pore structure, pore size, pore volume, and specic

surface area of the COK-12 powder and monoliths were studied

using nitrogen sorption analysis in a QuadraSorb apparatus

(Quantachrome, USA). Isotherms were recorded at 77 K aer

degassing under vacuum for 10 h at 200 C. The surface area

was determined using the Brunauer, Emmett and Teller (BET)

method. Model applicability was ensured using the Rouquerol

plot.

38,39

The mesopore sizes were estimated based on non-local

density functional theory (NLDFT) calculations using the

adsorption branch of the isotherm and a cylindrical geometry.

All nitrogen sorption data was analyzed using the QuadraWin

soware (Quantachrome, USA). Mercury intrusion porosimetry

was conducted on a Porosimeter 2000 (Carlo Erba Instruments,

Italy) to extend the measuring range to macropores for S-

sintered monoliths processed at 800 C and 12.5 MPa. The

classication of the pore sizes within this work was undertaken

according to the IUPAC denition.

Small-/wide-angle X-ray scattering (SAXS/WAXS) measure-

ments were performed on the heavily customized MOUSE

instrument at the Bundesanstalt f¨

ur Materialforschung und

-pr¨

ufung (BAM).

Here, monochromatized Cu Ka(l¼1.5406 ˚

X-rays were generated from a sealed-tube micro-source, and

data was collected on an in-vacuum Eiger 1 M detector (Dectris,

Switzerland), which was placed at multiple distances between

57 and 2507 mm from the sample. The monoliths, cut into

1 mm slices using a Model 3400 diamond wire saw (Well Dia-

mantdrahts¨

agen GmbH, Germany), and the loosely compacted

COK-12 powder were measured between two pieces of Scotch

Magic™tape. The obtained data was then processed to an

absolute intensity scale using the DAWN soware package

according to extensive (standardized) data correction proce-

dures, which include a thorough assessment of the measure-

ment uncertainties.

41,42

Fitting of the SAXS data was performed

using SASt,

allowing to obtain information on the lattice

parameter, macropore size, mesopore size, two populations of

micropores, as well as the silica peak position and width. More

detailed information on the SAXS modelling can be found in the

ESI (Fig. S2–S8†).

The wall thickness w

and wall area w

were calculated

according to

¼a

D,(5)

and

wa¼a02ﬃﬃﬃ

4pD2

8;(6)

respectively, where a

and Dare the lattice parameter and pore

diameter, respectively, as obtained by SAXS.

44,45

X-ray total scattering data of S-sintered COK-12 monoliths

processed at 25 MPa, ground to powder, was collected at

beamline P02.1, PETRA III at the DESY at a wavelength of

0.20735 ˚

A at a sample to detector distance of 280 mm using

a Varex XRD 4343CT detector. A LaB

(NIST 660c) standard and

an empty capillary were measured to account for instrumental

contributions and capillary glass contribution, respectively. 2D

data was processed using Dioptas 0.5.2.

Pair distribution

functions (PDFs) were processed from the total scattering data

using PDFgetX3 with Q

max

¼16 ˚

1

and Q

maxinst

¼24 ˚

1

X-ray diﬀraction (XRD) patterns were collected on COK-12

powder and monoliths produced at the highest processing

pressure of 50 MPa using a Bruker D8 ADVANCE with Cu Ka

radiation (l¼1.5406 ˚

A), operated at 40 kV in Bragg–Brentano

geometry with a LINXEYE 1D detector (Bruker, Germany).

Visualization of the surface morphology, including sintering

necks, was performed on the fractured surfaces aer B3B

testing by means of scanning electron microscopy (SEM) using

a LEO Gemini 1530 (Zeiss, Germany) at 5 kV with an InLens

electron detector and an aperture size of 30 mmaer sputtering

with a thin carbon layer.

The mesostructure of an S-sintered COK-12 monolith pro-

cessed at the highest pressure and temperature, i.e., 50 MPa and

900 C, respectively, was visualized with a transmission electron

microscope (TEM) in a FEI Tecnai G

20 S-TWIN (FEI, USA)

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equipped with a LaB

-source at 200 keV acceleration voltage

upon grinding. Images were recorded with a GATAN MS794 P

CCD-camera.

Pure water permeability was determined using a custom-built

dead-end ltration setup as previously reported.

48,49

Therefore,

the samples were cleaned in DIW for 10 s using a Sonorex RK 52

H (Bandelin, Germany) ultrasonic bath. Following, the samples

were inserted into the stainless steel container and xed with O-

rings, resulting in an available sample area of 28.3 mm

.Subse-

quently, the container was lled with DIW and pressurized with

synthetic air up to pressures of 1, 2.5, 4, 5.5, and 7 bar, respec-

tively. The mass of the permeated DIW was automatically recor-

ded every 5 s using an Adventurer Analytical precision scale

(OHAUS, USA) until either 75 g DIW were collected or 30 min

passed, whichever occurred rst. Aerwards, the volumetric ux

at each pressure was calculated according to

J¼V

A$t;(7)

where Jis the ux in L m

2

1

,Vis the volume of permeated

water in L, Ais the sample area in m

, and tis the permeation

time in h. The water permeance L

in L m

2

1

bar

1

was

obtained from the slope of the linear regression of the ux–

pressure curve according to the linear relationship

J¼L

Dp,(8)

where Dpis the pressure drop in bar. The permeability kin m

was calculated according to Darcy's law for single phase ow

according to

k¼L

hl,(9)

using the water permeance in m

2

1

, the dynamic

viscosity of water hin Pa s, and the thickness lof the membrane

in m. Permeability data was tted using the Kozeny–Carman

equation

k¼1

c0s2s2

ð13Þ2¼A33

ð13Þ2;(10)

where c

is the Kozeny coeﬃcient, sis the tortuosity, sis the

specic surface area with respect to the unit volume of the solid

matrix in m

3

,3is the unitless porosity and Ais the Cozeny–

Karman parameter.

50–52

For the ltration experiment, a surfactant-stabilized oil in

water emulsion with an oil concentration of 100 mg L

1

was

prepared by mixing 0.2 g hydraulic oil with 25 mL of 2 g L

1

Tween 80 in DIW and made up to 2 L with DIW and blending

with a hand blender (Kult S; WMF, Germany) for 1 min at

medium speed. Aerwards, the emulsion was degassed in

a vacuum cabinet. The initial oil droplet size distribution was

ascertained using a laser particle size analyzer LS 13 320

(Beckman Coulter, USA). Oil in water ltration was performed

in the same custom dead-end ltration setup described above at

1 bar on an S-sintered COK-12 monolith processed at a pressure

of 12.5 MPa and a temperature of 800 C. Filtration was per-

formed for 40 min. The oil restraint was assessed by measuring

the chemical oxygen demand (COD) before and aer ltration

by dichromate oxidation in a DR 5000 spectrophotometer (Hach

Lange GmbH, Germany).

3 Results and discussion

The results of the nitrogen sorption analysis, shown in Fig. S9,†

reveal type IVa isotherms with type H1 hysteresis loops for COK-

12 powder and S- and C-sintered COK-12 monoliths, charac-

teristic for mesoporous materials with a narrow pore size

distribution such as COK-12.

With increasing pressure and

temperature, the hysteresis loops decrease in size and are

shied towards lower relative pressures (earlier for S- than C-),

indicating a decrease in pore size and pore volume. Further-

more, the slope of the hysteresis gradually decreases with

increasing pressure and temperature, more particularly, which

is more pronounced in the S- than in the C-sintered monoliths,

indicating irregularities in the pore diameter. Thereby, the

adsorption and desorption branches of the H1 hysteresis loop

remain approximately parallel, but slightly convex, indicating

a minor change in pore geometry, yet no signicant pore

blocking or the presence of complex structures. Interestingly, at

pressures above ca. 0.85 p/p

a second hysteresis loop can be

found, which is most pronounced for S-sintered monoliths

produced at the highest temperature and pressure. Due to the

limited amount of measurement points in this area, an

assessment of the hysteresis loops' slope is delicate. However,

the presence of a second hysteresis loop at higher relative

pressures implies the presence of macropores larger than ca.

50 nm. Those can be associated to interparticle pores, resulting

from the cavity compaction between the COK-12 particles, and

are in line with what has been reported previously.

In accordance, the NLDFT pore size distributions reveal

a decrease in modal mesopore diameter and pore volume with

increasing pressure and temperature, as shown in Fig. S10.†

Micro- and large macropore analysis are omitted, as they were

not measured or cannot be adequately estimated by NLDFT.

However, the micropore development can be appraised by the

truncated peak around 2 nm, revealing a signicant loss in

microporosity for all sintered monoliths. Within the mesopore

range, the modal pore diameter of the S-sintered monoliths

initially rises to 6.6 nm and then remains at 6.1 nm, corre-

sponding to the mesopore size of the COK-12 powder, compare

Fig. S11.†Subsequently, the modal pore diameter of the S-

sintered monoliths produced at 700 C and 800 Catthe

lowest (2.5 MPa) and highest (50 MPa) pressures declines to

5.9 nm, and nally to 5.7 nm at 900 C, regardless of the pres-

sure. For the C-sintered COK-12 monoliths, a linear decrease in

the pore diameter down to 5.3 nm at 900 C is apparent. It is

noticeable that the computation of the modal pore size by

NLDFT yields only distinct pore sizes, allowing for only limited

meaningfulness with data points so close. This inaccuracy in

the pore size analysis can be ascribed to the small steps in the

calculated theoretical isotherms, which do not account for

chemically and geometrically heterogeneous surfaces.

39,53

The decrease in the mesopore size is associated with a loss in

pore volume and a decrease in specic surface area and

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apparent porosity, as depicted in Fig. 1. Thereby, the linear

decrease indicates a reduction of the pore sizes in the mono-

liths. The sintering temperature has a more pronounced inu-

ence on the BET specic surface area (SSA) and pore volume in

comparison to the eﬀect of the applied pressure, as can be seen

from Fig. 1a. The higher preservation of these structural prop-

erties in C-sintered monoliths over S-sintered monoliths is

greatly reduced with increasing temperature, resulting in

a vanishing low diﬀerence between S- and C-sintered monoliths

at 900 C. In detail, starting from 645 m

1

BET SSA for the

original COK-12 powder, 69% and 49% of the BET SSA were

preserved at 600 C and higher pressures for C- and S-sintered

monoliths, respectively, before declining to ca. 29% at 900 C,

compare Table S1.†Similarly, the initial pore volume of

0.61 cm

1

reduces to 80% and 66% at 600 C for the C- and

S-sintered monoliths, respectively, and nally decreases to ca.

37% at 900 C. It should be noticed that the pore volume

obtained by NLDFT does not reect the total monolith's pore

volume, but only the pore volume up to macropores of ca.

80 nm. Hence, the apparent porosity, including the total

macroporosity as determined by the Archimedes method, is

displayed in Fig. 1b. A decreasing porosity with increasing

temperature and pressure can be observed for both the C- and

S-sintered monoliths, whereas the reduction in porosity is more

distinct for the S-sintered monoliths in comparison to the C-

sintered monoliths due to the combined application of pres-

sure and temperature resulting in enhanced densication. The

overall porosities are high, reaching up to 82% for the lowest

pressure and temperature set (2.5 MPa, 600 C) and preserving

50% for the highest pressure and temperature parameter set

(50 MPa, 900 C), even for the S-sintered monoliths. Thereby, for

all monoliths, closed porosity is negligibly low as the apparent

solid density remains approximately constant for all monoliths,

as shown in Table S1.†

The TEM images of a ground, S-sintered monolith, pro-

cessed at the highest pressure and temperature, i.e., 50 MPa and

900 C, respectively, displayed in Fig. 2, show the distinct

preservation of the hexagonally ordered mesopores within the

COK-12 and thus, conrm the nitrogen sorption results. In

some areas, such as in the upper center of Fig. 2b, pore defor-

mations towards slit-like pores can be observed, which were

proven credible upon sample reorientation. TEM images of

unprocessed COK-12 powder for comparison are available in

the literature.

28,45

The SAXS data and the corresponding ts are shown in Fig. 3.

All patterns exhibit at least four well-resolved diﬀraction

reections at distances of q

¼1: ﬃﬃﬃ

p:ﬃﬃﬃ

satisfying the conditions for the 2D hexagonal symmetry P6m

and thus, can be indexed as (10), (11), (20), and (21). With

increasing sintering temperature, the reections considerably

shitowards higher scattering vectors, indicating a decrease in

d-spacing, and, accordingly, a decrease in lattice parameter, as

depicted in Fig. 4. Starting with a lattice parameter of 10.4 nm

for the COK-12 powder, the hexagonal unit of the monoliths is

contracted by up to ca. 13% when processed by C-sintering at

the highest pressure and temperature, as listed in Table S1.†A

roughly linear decrease of the lattice parameter can be observed

with temperature for C-sintered monoliths, merely inuenced

by the processing pressure. In comparison, the decrease in the

lattice parameter is less pronounced at higher pressures, in

particular at higher temperatures, for S-sintered monoliths.

Due to their geometrical linkage, the overall behavior of the

lattice parameter with processing pressure and temperature is

similar to the development of the mesopore sizes discussed

Fig. 1 Sintering temperature and pressure dependence of (a) the BET speciﬁc surface area (SSA) and pore volume (NLDFT, adsorption branch)

and (b) the apparent porosity as obtained from Archimedes' method for COK-12 powder as well as S- and C-sintered COK-12 monoliths.

Fig. 2 TEM images of a ground S-sintered COK-12 monolith pro-

cessed at 50 MPa and 900 C show the signiﬁcant preservation of the

hexagonally ordered mesopores (a and b) and areas of pore defor-

mation (b).

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previously. It can be supposed that at higher pressures, despite

the thermal energy supplied, atom movement is more restricted

and hence, equilibrium is not reached within the short duration

of the S-sintering process, resulting in a higher preservation of

the unit cell size. However, with higher temperatures, the

overall deviation of the lattice parameter from the theoretical

hexagonal lattice, represented in the form of error bars in Fig. 4,

increases markedly for the S-sintered monoliths, while the

inuence of pressure is only minor. In contrast, the deviation

from the theoretical hexagonal lattice remains approximately

constant for the C-sintered monoliths for both varying

temperatures and pressures. It can be derived that due to the

simultaneous application of pressure and temperature during

the S-sintering, temperature-induced stresses are intensied,

which during C-sintering can be compensated by unrestricted

readjustment of the sample diameter and height.

As described, the tting of the SAXS data additionally allows

for pore size determination from the micro- to the macroscale

scale, i.e., from ca. 1–350 nm, resulting from the q-range limits

of the SAXS measurements. However, larger pores are expected

to also be present, with their size estimated by means of SEM

and mercury intrusion porosimetry, as discussed below. The

mean pore sizes derived from the SAXS ttings are displayed in

Fig. 5. While the mesopores are homogeneous in size due to the

assumed polydispersity of 10%, compare the exemplary data for

the COK-12 powder in Fig. S12,†a substantial polydispersity can

be found for the macro- and micropores, whose corresponding

log-normal volume-weighted pore size distributions are shown

in Fig. S13–S15.†

Fig. 3 SAXS patterns and corresponding ﬁts for the COK-12 powder and monoliths produced by S- and C-sintering with y-oﬀsets at (a) 600 C,

(b) 700 C, (c) 800 C, and (d) 900 C at varying pressures. Vertical lines are added to aid the eye in observing the peak shift.

Fig. 4 Lattice parameters of the hexagonal structure of the COK-12

powder and S- and C-sintered monoliths. Within the temperature

columns, the data points are horizontally spaced for legibility. The

error bars show the mean deviation between the expected theoretical

lattice peak positions for the (11), (20), and (21) reﬂections included in

the analysis, hinting towards the presence of strain or disorder.

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The mean macropore diameter, initially being 256 nm for

the loosely compacted COK-12 powder, is only slightly reduced

at 2.5 MPa, before decreasing below 220 nm with increasing

temperature and pressure for both S- and C-sintered monoliths,

as shown in Fig. 5a. However, the mean macropore diameter of

the C-sintered monoliths is up to 50 nm larger than for the S-

sintered monoliths, which can be attributed to the absence of

pressure during the sintering step in the conventional sintering

process, eliciting less densication. In contrast to the evolution

of the lattice parameter, the diminution in the main macropore

size is enhanced at high temperatures, in particular at high

pressures, which can be attributed to the progressive elimina-

tion of interparticle voids. Hence, the volume-weighted mac-

ropore size distributions in Fig. S13†show a distinct increase in

the volume of these macropores for C-sintered monoliths and S-

sintered monoliths at lower pressures, presumably resulting

from the compaction of larger macropores into the SAXS

measurement range.

The general trend of decreasing pore size with increasing

temperature and pressure is also apparent for the mean meso-

pore diameters shown in Fig. 5b. While the mesopore diameter

remains approximately constant at ca. 6.1 nm for monoliths

processed at 600 C for both sintering techniques, a linear

decrease of the mesopore diameter, down to 5.2 nm, with

increasing temperature can be observed for C-sintered mono-

liths, with only a slight inuence from the processing pressure.

No such clear trend can be observed for the S-sintered mono-

liths. A comparison of the mesopore sizes obtained from SAXS

and nitrogen sorption/NLDFT, see Table S1,†reveals a high

accordance between the methods' results, exhibiting an average

and maximum deviation of 0.2 and 0.5 nm, respectively.

Considering the limited set of default diameters that can be

obtained from NLDFT analyses, the presented SAXS tting can

be considered a more robust method for obtaining mesopore

diameters. The mechanism of mesopore reduction with heat

treatment for SBA-15, structurally comparable to COK-12, is

reported to be due to contraction of the cylindrical pores

without considerable changes in the length of the pore channels

and elimination of intrawall porosity and has previously been

observed for SBA-15 and COK-12.

28,54,55

As the rigid, plate-like

particles do not allow for any signicant reduction of the pore

channel lengths, barely any additional contraction is expected

to occur even under higher pressures.

In addition to the macro- and mesopores, two populations of

micropores could be identied, i.e., smaller ones in the range of

0.75–1.02 nm and larger ones in the range of 1.2–2.31 nm,

referred to as micropores of the population 1 (P1) and 2 (P2),

respectively, as shown in Fig. 5c and d. P2 micropores are likely

to be associated to the pores, which have previously been

generated in the silica walls upon removal of the hydrophilic

polyethylene oxide tails of the triblock copolymer.

28,56–58

With

increasing temperature and pressure, initially an increase in the

P2 micropore size can be observed from 1.21 nm for the COK-12

powder up to 2.31 nm for S-sintered monoliths at 800 C and

50 MPa, as depicted in Fig. 5c. While increasing micropore P2

diameters can be observed for S-sintered monoliths at high

pressures, possibly due to crack growth, micropore consolida-

tion, or distinct mesopore blocking, above 700 C a decrease can

be seen for low-pressure-sintered and C-sintered monoliths,

possibly due to enhanced mesopore blocking or surface-

smoothing silanol condensation in the micropores at high

temperatures, resulting in the elimination of intrawall micro-

porosity.

54,55

This view is encouraged by the decrease in micro-

pore volume with temperature, as shown in the volume-

weighted pore size distributions of the P2 micropores in

Fig. S14.†Furthermore, the development of the P2 micropore

sizes might be associated to the random orientation of the

Fig. 5 (a) Macro-, (b) meso-, and (c, d) micropore (P2, P1) diameters

obtained from ﬁtting the SAXS data of COK-12 powder and S- and C-

sintered monoliths. No P1 micropores were determined for the COK-

12 powder and the monoliths sintered at 800 and 900 C.

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particles, which result in a micropore crushing or micropore

expansion for micropores aligned perpendicular or along the

axis of applied pressure, respectively. Thereby, the loss of pore

volume due to collapsed micropores cannot be compensated by

the additional volume gained by micropore expansion, which

can be seen from the decreased micropore contribution to the

SAXS scattering patterns and nitrogen sorption data in

comparison to the COK-12 powder, compare Fig. 3 and S10.†

Overall, the decrease in P2 micropore size is less pronounced

for the S-sintered monoliths, which can be associated to the

shorter processing times. Additionally, P1 micropores could be

found for the monoliths processed at 600 and 700 C, shown in

Fig. 5d, yet not for those processed at 800 and 900 C, inde-

pendent of the sintering technique, as well as for the COK-12

powder. Hence, the P1 micropores might directly be related to

the processing and could be associated to intraparticle cracks,

which emerged upon processing, yet vanished again due to

enhanced micropore collapse at higher temperatures. Accord-

ingly, a decrease in the micropore volume with increasing

temperature can be observed in the volume-weighted pore size

distributions of the P1 micropores in Fig. S15.†In contrast,

inconsistent results on micropore information were obtained

from the I

intensity ratio of the SAXS patterns in the

literature,

which can be ascribed to the neglected interplay

between the hexagonal structure factor and cylindrical form

factor, which was accounted for in the present model, as can be

seen from Fig. S3 and S6†and the corresponding sections in the

ESI.†These results highlight the importance of collecting a wide

q-range for such hierarchical systems, so that information on

the interplay of diﬀerent pore structures can be elucidated and

exploited. SAXS also has the benet of being able to access

closed pores contained within a system, due to diﬀerences

observed in the contrast.

With wide-ranging SAXS data it is

possible to ascertain information on both micro- and macro-

structures within a sample, even when such structures are

only apparent in small volumes, compare the micropore size

distributions obtained by nitrogen sorption depicted in

Fig. S16.†

The inuence of the processing conditions on the parame-

ters wall thickness and wall area, calculated according to eqn (5)

and (6), respectively, derived from the SAXS lattice parameters

and mesopore sizes, is shown in Fig. 6. The powder wall

thickness of 4.2 nm is maintained for S-sintered monoliths

produced at 600 C at high pressures, before rstly decreasing

with increasing temperature and nally, reaching plateau

regions of about 3.85 and 4.0 nm for S-sintered monoliths at

medium and high pressures and C-sintered monoliths,

respectively. Thus, an increase in pore wall thickness, as re-

ported in high-temperature stability studies of SBA-15 powder,

could not be observed for sintered COK-12 monoliths.

Compared to the wall thickness, the wall area, shown in

Fig. 6b, allows observing the eﬀects of changing lattice param-

eter and mesopore size in a larger, 2D environment. Starting oﬀ

with a wall area of 31.8 nm

for the COK-12 powder, the wall

area constantly decreases with increasing temperature for the C-

sintered monoliths, enabled by unrestricted shrinkage of the

diameter and suﬃcient time to reach equilibrium during

pressureless sintering for 12 h. In comparison, the wall area was

preserved to a greater extent when high pressures were applied

during S-sintering, restricting both lattice parameter and mes-

opore shrinkage.

While commonly high specic surface areas are accompa-

nied by enhanced sinterability, for mesoporous materials

especially the pore arrangement and a high pore diameter to

wall thickness ratio were found to be crucial to strong sintering

performance.

For example, nite element modelling yielded

higher von Mises stresses and thus, easier mesopore collapse

and cracking in cubic systems in comparison to hexagonal

systems. The pore diameter to wall thickness ratio of COK-12 is

1.47 or 1.44, as determined using the mesopore size obtained

from SAXS or NLDFT, respectively, which is in the range of the

ratio for SBA-15 reported with 1.5 0.06.

However, the pore

size for the calculation of the ratio for SBA-15 was calculated

using the pore size obtained from the Barrett–Joyner–Halenda

(BJH) model, which is known to severely underestimate small-

and medium-sized mesopores and thus, results in an over-

estimated pore diameter to thickness ratio.

53,61

Hence, a lower

pore diameter to wall thickness ratio can be postulated for COK-

12 in comparison with SBA-15. COK-12's higher resilience

towards sintering is furthermore supported by a higher

condensation degree of the silica framework within COK-12,

which is reported to increase its resistance towards compac-

tion,

26,62

and the higher temperatures and processing times

required to obtain dense structures by S-sintering. To fully

eliminate the porosity in SBA-15 structures, temperatures of

900 C, in between 930 and 980 C, 1020 C, and 1040 C were

reported,

22,60,63,64

being only slightly higher than the 900 C

Fig. 6 (a) Wall thickness and (b) wall area calculated according to eqn

(5) and (6), respectively, from the SAXS data for COK-12 powder and S-

and C-sintered monoliths.

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applied to COK-12 during S- and C-sintering, resulting in

porous monoliths. Hence, further parameters aﬀecting the

densication, namely pressure, dwell time, and heating rate,

were reported to be the same or smaller, ensuring reasonable

comparability. For comparison, approaches within this work to

densify COK-12 required S-sintering with a slow heating rate of

25 K min

1

, a long dwell time of 45 min, and temperature and

pressure of 1045 C and 50 MPa, respectively.

The silica peak positions and peak widths of the COK-12

powder and monoliths obtained by SAXS tting at around 15

1

are shown in Fig. S17.†Aer a slight increase at 600 C for

medium and high pressures, the silica peak positions slightly

shitowards lower q-values with increasing temperature,

indicating a small increase in the overall silica structure size.

Similarly, a decrease in the silica peak width can be observed

with increasing temperature, indicating a narrower population

of the silica species. To gain a deeper understanding on the

atom surroundings in the processed COK-12 with increasing

temperature, a series of S-sintered monoliths processed at

a pressure of 25 MPa at varying temperatures was measured in

Fig. 7 SEM images of the fractured surfaces of S- and C-sintered COK-12 monoliths after mechanical testing.

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total scattering and analyzed by the PDF method. As shown in

Fig. S18,†the peak positions at around 1.7, 2.2 and 2.7 ˚

A, which

can be associated to the rst order pairs of Si–O, O–O, and Si–Si,

respectively, remain stationary for all temperatures. However, in

comparison to uncompressed amorphous silica, whose Si–O

peak position is commonly found at around 1.6 ˚

A, the COK-12

monoliths' peaks appear at higher interatomic distances,

whereas the position of the O–O and Si–Si reections,

commonly found in the range of 2.3–3.4 and 2.7–3.1 ˚

respectively, are shied towards lower interatomic

distances.

65–68

Accordingly, the peak shis might be associated

to a pressure-induced increase in the Si–O distances and

a decrease in the O–O and Si–Si distances.

Furthermore, as the

following peaks are distinguished, a high ordering of SiO

tetrahedra can be assumed.

However, the distinct peak at

around 3.4 ˚

A, associated to the second order of the O–O

distances, can also be an indication of the evolution of an SiO

network with oxygen edge-sharing atoms in contrast to the SiO

network with oxygen corner-sharing atoms.

While there is no

shiin the monoliths' peak positions, the intensity of the Si–O

peak increases with increasing processing temperature, signi-

fying a higher probability of occurrence for this atomic pair and

a higher coordination number and/or higher ordering.

69,70

This

is in accordance with the small increase of the overall silica

structure size and its narrowed population observed by SAXS.

Overall, the observed changes in the monoliths' structure size

and population as well as bond lengths are minor, which is in

agreement with the XRD results shown in Fig. S19,†revealing

only marginal diﬀerences in the respective short-range order

around 20, whereas the COK-12 monoliths processed by S-and

C-sintering remain amorphous up to 50 MPa and 900 C.

Signicant structure changes, in the form of enhanced silica

structure growth and partial crystallization, can only be

observed in the dense sample processed at 50 MPa and a higher

temperature of 1045 C.

The macrostructure of the S- and C-sintered monoliths can

be appraised from the SEM images in Fig. 7. In addition to the

small macropores ascertained by SAXS, macropores not larger

than a few micrometers can be observed in the SEM images. The

particle shape and size were maintained to a large extent for S-

sintered monoliths up to a processing temperature and pres-

sure of 800 C and 25 MPa, respectively, compare the

morphology of the COK-12 powder in Fig. S20.†For higher

temperatures and pressures, the presence and dimension of

sintering necks, a result of progressing densication, becomes

more evident. However, grain growth remains moderate even at

high temperatures. This can be attributed to the high heating

rate and short dwell time during the SPS process. Surprisingly,

sintering necks, densication, and grain coarsening can also

hardly be observed for C-sintered monoliths, despite the long

sintering time and shrinkage of up to 10.5% in sample diam-

eter. While commonly, the sintering of NPs such as COK-12 is

kinetically enhanced due to the high surface area, it can be

concluded that the energy provided at 600–900 C was not

enough of a driving force to progress the sintering process

adequately. Furthermore, phenomena such as interparticle

friction, NP agglomeration, and the pinning action of open

pores in the NP structure present additional challenges for the

sintering process,

all being applicable to OMS materials such

as COK-12. As those phenomena are expected to be counter-

acted to a certain extent by the application of external pressure

during the sintering process, resulting in stronger, porous COK-

12 monoliths when produced by S-sintering in comparison to C-

sintering as discussed in detail below.

The pore size distribution histogram obtained from the

mercury intrusion porosimetry data on S-sintered monoliths

processed at 12.5 MPa and 800 C is shown in Fig. 8 and reveals

information in the small to medium macropore range, in

particular, complementing nitrogen sorption, SAXS, and SEM

information. The porosimetry data reveals a uniform pore size

distribution with a median pore diameter of 322 nm (by

volume), suitable for microltration applications. Those mac-

ropores can be attributed to interparticle cavities as a result of

the deliberately incomplete sintering process. Furthermore,

a noticeable amount of mesopores were detected at the lower

measurement limit of the mercury porosimeter, which is in

overall agreement with the nitrogen sorption and SAXS data.

Deviations towards the results obtained by other measurement

techniques may be ascribed to the somewhat arbitrary nature of

the mercury porosimetry results due to the assumption of

cylindrical pores and the inability to ascertain the true inner

pore size in the presence of wider pore openings.

The porosity dependence of the biaxial strength obtained

from B3B testing and the apparent hardness obtained from

Vickers testing for the S- and C-sintered COK-12 monoliths

sintered at diﬀerent temperatures and pressures are shown in

Fig. 9. Overall, an expected increase in the mechanical proper-

ties with decreasing porosity, concomitant with increasing

processing pressure and temperature, can be observed, which

can be associated to the elimination of pores and thus, an

increase in the eﬀective cross section of the sample. It can be

observed that the S-sintered monoliths exhibit 4–8 times higher

biaxial strength values and 4–10 times higher Vickers hardness

values, reaching up to 49 MPa and 736 MPa HV 9.807 N,

respectively, while presenting 4–17% lower porosity in

Fig. 8 Pore size distribution histogram obtained from mercury

intrusion porosimetry data of S-sintered COK-12 monoliths processed

at 12.5 MPa and 800 C.

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comparison to the C-sintered monoliths at the same processing

pressure and temperature.

While no biaxial strength values are yet reported in the

literature for S-sintered samples, the Vickers hardness of SBA-15

was reported with 92–250 MPa for S-sintering temperatures of

600–900 C at a processing pressure of 10.6 MPa and resulting

porosities of 75–65% at an indentation load of 100 g.

These

values are slightly higher than those presented for COK-12 at

comparable processing conditions, compare Fig. 9b. On the

contrary, SBA-15 based silicon-boron-carbon-nitrogen mono-

liths yielded Vickers hardness values of 16.7–21.8 MPa at an

indentation load of 30 N for SPS temperatures of 800–900 C,

a pressure of 16 MPa, and resulting porosities of only 69–65%,

being signicantly lower in comparison to the COK-12. Those

diﬀerences can be attributed to the indentation size eﬀect,

which describes decreasing hardness with increasing test load,

wherefore the application of standards is encouraged.

For a xed processing pressure, the porosity was found to

decrease in a linear manner with increasing temperature, as

depicted in Fig. 1b. The porosities of the C-sintered monoliths

processed at 25 and 50 MPa can be located between the poros-

ities of the S-sintered monoliths processed at 2.5 and 12.5 MPa.

While also the dependence of the porosity on the mechanical

properties is oen considered to be linear, usually due to the lack

of data over a suﬃcient porosity range, it is known to be non-

linear.

Hence, Fig. 9 includes the tting of the mechanical

strength data over porosity with the non-linear relationships

according to the Bal'shin, Ryshkewitch, and Hashin model listed

in eqn (1)–(3), using s

¼124.3 MPa and HV

¼5360 MPa.

Furthermore, the percolation law from eqn (4) was applied,

which interestingly has not been proposed yet to tthe

mechanical properties over porosity, whereas however, the power

law expression by Rzhevsky and Novik, a particular case of the

percolation law, is commonly applied.

The tting of the

Rzhevsky and Novik as well as the Eudier model were not

meaningful as they yielded a local hardness minimum at

a porosity of around 78% or include an intrinsic porosity limit of

75%, respectively. While tting of the Hashin and Ryshkewitch

models did not yield satisfactory regression coeﬃcients for the

processed COK-12, although the Ryshkewitch model, in partic-

ular, is commonly applied to assess and extrapolate the

mechanical properties for S-sintered samples with reasonable

results for metallic titanium foams

and only mediocre esti-

mates for ceramic silica and silica composites,

22,75

the percola-

tion law and the Bal'shin model yielded better ttings for the

COK-12 monoliths with regression coeﬃcients of 0.865–0.964

and 0.829–0.947, respectively. The similar regression coeﬃcients

can be attributed to the fact that the Bal'shin model is a partic-

ular case of the percolation law. The higher tting values for the

C-sintering and the slightly better t of the percolation law can

be attributed to the lower porosity range of the data and the

additional parameter 3

, respectively. However, even without

this information, reasonable tting is possible using the Bal'shin

model. The resulting percolation tting parameters are 1.9 and

2.5 for the biaxial strength and 3.2 and 3.4 for the Vickers

hardness for S- and C-sintered monoliths, respectively. A

summary of all regression coeﬃcients and corresponding tting

parameters can be found in Tables S2 and S3.†The tting

parameter for the percolation law, also referred to as the char-

acteristic exponent, describes the change of the property towards

Thus, the higher tting parameters of the C-sintered

monoliths can be associated to a faster loss in the mechanical

properties with increasing porosity in comparison to the S-

sintered monoliths. Thus, it can be assumed that the sintering

necks between the COK-12 particles are more resilient when

processed with S- in comparison to C-sintering, even considering

Fig. 9 Biaxial strength (a) and (c) and Vickers hardness HV 9.807 N (b) and (d) over porosity for varying sintering temperatures and pressures for S-

and C-sintered COK-12 monoliths as well as corresponding Percolation, Bal'shin, Ryshkewitch, and Hashin ﬁts.

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that diﬀerent processing pressures and temperatures are needed

to achieve comparable porosities. The diﬀerence in the tting

parameter between the S- and C-sintering is more distinct for the

biaxial strength than for the hardness. This can be associated to

the additional tensile portion of the B3B test in comparison to

the hardness testing, which is performed in compression mode.

To predict the probability of failure of S-sintered COK-12

monoliths, a Weibull analysis was performed on biaxial

strength data for S-sintered monoliths processed at 12.5 MPa

and at 800 C with an apparent porosity of 66%, whose results

are shown in Fig. 10. The results reveal maximum likelihood

estimates of the Weibull characteristic strength b

sqand Weibull

modulus m^of 13.7 MPa and 3.7, respectively. With an average

standard deviation of 1.2 MPa within the three monoliths ob-

tained per S-sintering run, it can be concluded that the parallel

conguration of the graphite die works reliably. The obtained

Weibull modulus is lower than the common range of 5–10,

which is usually expected for engineered ceramics.

A low

Weibull modulus is reported to be associated with high poros-

ities and pore volumes in general, but in particular with high

interparticle porosities and wide pore size distributions, which

both is applicable to the sintered COK-12, whose hierarchical

pore structure comes along with an increased probability for

crack growth.

78–80

It should be highlighted that the latter applies

only for tests performed in bending mode, as crack propagation

is diﬀerent in compressive mode. The data points displayed in

Fig. 10 show a P-type behavior, i.e., a positive deviation from the

well-known linear behavior, which occurs when the lower tail of

the failure stresses deviates from the tted line towards the

mean failure stress. P-type behavior, also referred to as three

parameter distribution, is reported to be associated with pore

pairs favoring enhanced stress localization in brittle porous

materials and to be related to internal compressive stresses in

general, such as surface stresses.

81,82

The porosity dependence of the pure water permeance for the

S-sintered monoliths is shown in Fig. 11a. The pure water uxes

at diﬀerent pressures and the corresponding linear ts, from

which the permeance was derived, can be found in Fig. S21.†As

expected, higher porosities resulted in higher water permeance.

Themonolithsproducedatthelowestpressureof2.5MPa

and highest pressure of 50 MPa show permeances above

1000 L m

1

bar

1

and below 100 L m

1

bar

1

, respectively.

For the lowest and highest pressure, a distinct permeance deteri-

oration can be observed with increasing temperature. In compar-

ison, for moderate pressures of 12.5 MPa and 25 MPa the

permeance scattering with temperature is markedly less

pronounced while spreading over a wider porosity range. As the

macropore volume can be expected to have a major inuence on

the mass transport, relative to the total porosity including also the

micro- and mesopore volume, the dependence of the permeance

on the estimated macropore volume is shown in Fig. S22.†In

comparison to the dependence of the porosity, a sharper increase

in the permeance can be observed with increasing macropore

volume, in particular for low macropore volumes up to

0.36 cm

1

, predominantly corresponding to monoliths pro-

cessed at the highest pressure of 50 MPa, before reaching

a maximum at 1.82 cm

1

for the lowest processing pressure and

temperature of 2.5 MPa and 600 C.Atthesametime,the

percentage of the macropore volume from the total pore volume

increases from 51% to 62% and nally to 83%, respectively,

enabling reasonable water permeance. While all S-sintered

monoliths withstood applied pressures of up to 7 bar in the

experiments without being damaged, it was not possible to

determine the water ow behavior of the C-sintered COK-12

monoliths due to collapse prior to or at pressurization of 1 bar.

As the monolith thickness varied signicantly with the pro-

cessing pressure and temperature, the permeability k,

Fig. 10 Weibull probability plot for biaxial strength values obtained by

B3B test on S-sintered monoliths processed at 800 C and 12.5 MPa.

Fig. 11 Relation between porosity and pure water ﬂow behavior for S-sintered monoliths. (a) water permeance L

(b) permeability kand cor-

responding Kozeny–Carman ﬁt.

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calculated from eqn (9), was obtained as an intrinsic, thickness-

independent parameter and plotted against the porosity term of

the Kozeny–Carman equation in Fig. 11b. During the tting of

the Kozeny–Carman equation, an outlier exhibiting a studen-

tized residual larger than three, namely the S-sintered monolith

processed at 2.5 MPa and 700 C, was removed from the data for

tting purposes. Fitting with the complete data and the list of

corresponding studentized residuals can be found in Fig. S23

and Table S4,†respectively. The permeability values were found

to be in the range of 5.5 10

17

to 1.3 10

14

. Fitting the

Kozeny–Carman equation resulted in a reasonable regression

coeﬃcient of 0.876 and yielded a Kozeny–Carman parameter A

of 7.37 10

16

. Deviations from the model can be explained by

simplications and assumptions that are violated, such as

isotropic porous media and structure consisting of well-packed

spheres of a specic size opposing uniaxial pressing and

consolidation of plate-like particles. However, as other models

are based on considerably more assumptions, the Kozeny–

Carman equation seems to be the best expression available for

modelling ow through porous media.

Using the obtained

Kozeny–Carman parameter, compare eqn (10), the common

range of c

being 1/6–1/2, and a specicsurfaceareaS

with respect

to the unit volume of the solid matrix of 6.45 10

3

utilizing a COK-12 powder density of 0.1 g cm

3

, the tortuosity

factor scan be estimated.

62,84

Considering the denition of s¼

(L/L

)

<1withLand L

being the length of the porous medium

and eﬀective ow path length, respectively, swas determined to

0.81–1. Transposing the tortuosity factor into the more common

parameter tortuosity L

/Lyields values in the range of 1–1.11,

which can be considered underestimated, because on the one

hand the monoliths do not exhibit straight-through pores,

compare Fig. 7, and on the other hand tortuosity values for porous

membranes and unconsolidated mesoporous silica materials are

typically found in the range of 1.5–5and1.4–4.2, respectively.

85–87

Furthermore, it is worth noticing that the tortuosity values were

obtained from tting of monoliths among a wide porosity range,

so that changes in the tortuosity with the processing parameters

pressure and temperature were not considered, which, however,

can reasonably be assumed.

The oil droplet size distribution of the surfactant-stabilized

oil in water emulsion used for the ltration experiment is

shown in Fig. S24†and reveals a mean oil droplet size of 25 mm

and d

values of 47.9 and 2.3 mm, respectively. Filtra-

tion of this emulsion using an S-sintered monolith processed at

12.5 MPa and 800 C, exhibiting a benecial pure water per-

meance to porosity ratio, at a transmembrane pressure of 1 bar

resulted in a ux of about 298 L m

2

1

, as depicted in Fig. 12.

While the ux declined by 20% in comparison to the pure water

ux of 373 L m

2

1

, it remained stable along the ltration

time of 40 min, which allows concluding a reasonable resis-

tance towards fouling, which can be attributed to the hydro-

philic character of the COK-12 due to the presence of surface

hydroxyl groups, which inhibit the adherence of foulants to the

surface by steric repulsion as commonly introduced by surface

modication of polymeric membranes.

88–91

During ltration,

the COD was reduced by 90%, meaning from 366 to 35 mg L

1

Thus, the smallest diameter retained can be estimated to

correspond to the d

value of 2.3 mm. The overall performance,

including the required pressure, ux, and retained diameter,

classies the COK-12 monoliths within the microltration

membrane category. The higher condensation degree and

thicker silica walls in comparison to other mesoporous silica

materials such as SBA-15 facilitate a higher stability for COK-12

in an aqueous environment.

While high pH cleaning is rather

unsuitable for the regeneration of oil-loaded silica surfaces due

to limited chemical resistance, the monolith's resistance

towards ultrasonic and thermal cleaning can potentially be

utilized to enhance the ltration process as well as an envi-

ronmentally friendly cleaning method.

The oil in water ltra-

tion of the S-sintered COK-12 monolith is more eﬀective in

comparison to S-sintered monoliths produced from volcanic

shirasu balloon, which exhibit lower porosities and larger pores

at comparable processing parameters.

Further S-sintered

materials such as diatomite were suggested to be suitable for

water purication applications.

Furthermore, the produced

COK-12 monoliths may present additional benets, such as

molecule capture, due to their hierarchical pore structure from

the macro-to the meso-/micropore scale. Their properties also

make them interesting for applications in HPLC separation and

membrane reactors, as catalysis support, host system for

controlled drug delivery, or for tissue engineering.

4 Conclusions

Lightweight, hierarchically porous monoliths were processed

from OMS COK-12 by SPS (S-sintering) using a custom graphite

multi-sample die in a parallel conguration, thoroughly exam-

ined with respect to their structural, mechanical, and water

permeability properties, and compared to conventionally (C-)

sintered monoliths.

Data tting with a customized SAXS model allowed to

examine the inuence of the processing parameters on the

lattice parameter, micro-/, meso-, and macropore sizes, as well

as silica population parameters over a wide q-range, making it

Fig. 12 Time-dependent ﬂux during the ﬁltration of surfactant-

stabilized oil in water emulsion with 100 mg L

1

oil at a transmembrane

pressure of 1 bar through an S-sintered monolith processed at

12.5 MPa and 800 C. The initial COD of 366 mg L

1

could be reduced

by 90% to 35 mg L

1

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interesting as a multi-scale method bridging nitrogen sorption

and mercury intrusion measurements. Overall, it was found

that for both sintering methods the temperature has a more

pronounced eﬀect on the structural parameters than the pres-

sure. Due to the simultaneous application of pressure and

temperature, the reduction in porosity, specic surface area,

and pore volume was more pronounced in S-sintered monoliths

prepared at comparable processing conditions, however,

becoming negligible for high processing temperatures. In

contrast, the distinct decrease in the mesopore size, micropore

volume, and lattice parameter in C-sintered monoliths was

attenuated for the S-sintered monoliths due to the restricted

particle movement and shorter processing times, resulting in

a higher preservation of wall thickness and wall area for the

latter. At the same time, higher stress-induced deviations from

the theoretical lattice were revealed for the S-sintered mono-

liths. Overall, COK-12's superior resistance towards sintering in

comparison to SBA-15 could be ascribed to COK-12's lower pore

diameter to wall thickness ratio and higher silica condensation

degree.

The mechanical properties were found to follow the perco-

lation law. Thereby, the S-sintered monoliths showed higher

mechanical properties than the C-sintered monoliths at

comparable porosities. While the diﬀerence was small for the

Vickers hardness, it was higher for the B3B biaxial strength

data, which can be attributed to the more demanding, biaxial

character of the test, emphasizing the higher bending stability

for S-sintered monoliths, making them more interesting for

load-bearing applications.

In contrast to C-sintered monoliths, S-sintered monoliths

could withstand ultrasonic cleaning and pressures of 7 bar in

a dead-end water ltration setup, yielding high permeances and

permeabilities while following the Kozeny–Carman relation-

ship. A selected S-sintered monolith, utilized for the ltration of

a surfactant-stabilized oil in water emulsion, presented a high

separation eﬃciency and a stable ux, indicating a reasonable

resistance towards fouling, likely due to COK-12's surface

hydroxyl groups.

Future work might include the generation of a mesopore

gradient throughout the monoliths thickness by layer-wise

deployment of COK-12 powder with diﬀerent pore sizes or

shapes. Thereby, also larger macropores could be introduced

through a secondary sacricial templating agent, such as

sodium chloride crystals. Furthermore, P123's potential on the

mesopore and lattice stabilization, when only removed aer the

S-sintering process, might be studied. In addition, the large

accessible surface area and pore volume might be used for the

functionalization with various functional groups. Overall, their

structural and mechanical properties along with their devel-

opment potentialities make the hierarchically porous and

mechanically stable COK-12 monoliths promising for applica-

tions in separation and catalysis.

Author contributions

L. M. H. conceptualization, methodology, formal analysis,

investigation, data curation, writing –original dra,

visualization, project administration; J. T. M. investigation,

writing –review & editing; G. J. S. conceptualization, method-

ology, soware, validation, formal analysis, data curation,

writing –original dra, visualization; B. R. P. methodology,

soware, writing –review & editing; M. F. B. conceptualization,

methodology, writing –review & editing; supervision; J. S.

formal analysis, writing –review & editing; A. G. conceptuali-

zation, resources, writing –review & editing, supervision,

funding acquisition; U. S. conceptualization, writing –review &

editing, supervision.

Conﬂicts of interest

There are no conicts to declare.

Acknowledgements

We acknowledge Christina Eichenauer for nitrogen sorption

measurements, Germany's Excellence Strategy—EXC 2008–

390540038—UniSysCat, Fabian Zemke for SEM imaging, Jan R.

J. Simke for TEM imaging (ZELMI), Peter Schneppm¨

uller for the

graphite die manufacturing, and Jonas Pluschke for spectro-

photometric measurements, all from Technische Universit¨

Berlin. Furthermore, we acknowledge Martin Etter and DESY

(Hamburg, Germany), a member of the Helmholtz Association

HGF, for the provision of experimental facilities. Parts of this

research were carried out at PETRA III, beamline P02.1 within

the rapid access program 2021A under proposal ID RAt-

20010275. We acknowledge support by the German Research

Foundation and the Open Access Publication Fund of TU Berlin.

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