An in situ small angle neutron scattering study of expanded graphite under a uniaxial stress

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An in situ small angle neutron scattering study of expandedgraphite under a uniaxial stress

Felix Balima a, Vittoria Pischedda a, Sylvie Le Floch a, Annie Brulet b, Peter Lindner c,Laurent Duclaux d, Alfonso San-Miguel a,*

a Institut Lumiere Matiere, UMR5306 Universite Lyon 1-CNRS, Universite de Lyon, 69622 Villeurbanne Cedex, Franceb Laboratoire Leon Brillouin, UMR12 CEA-CNRS, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, Francec Institut Max von Laue–Paul Langevin, 38042 Grenoble Cedex, Franced LCME, Universite de Savoie, 73376 Le Bourget du Lac Cedex, France

A R T I C L E I N F O

Article history:

Received 18 September 2012

Accepted 5 February 2013

Available online 12 February 2013

A B S T R A C T

The present article studies the in situ evolution of the pore structure of compressed

expanded graphite under a uniaxial stress up to 1000 bar using small-angle neutron scat-

tering (SANS). The uniaxial stress was applied in the direction of the average c-axis of

the graphite crystallites composing the sample. Ex situ characterization by electrical resis-

tivity and mercury intrusion porosimetry was performed on the compressed samples. The

anisotropic SANS pattern indicates the presence of spheroidal pores in the 4–100 nm

detectable range. The stress dependence of the different extractable parameters (fractal

dimension, apparent specific surface area and apparent porosity) was related to the meso

and macro pore structure evolution. In particular, the fractal dimension increases irrevers-

ibly with the applied stress. We propose a model of evolution under uniaxial load in which

the irreversible collapse and splitting of larger pores into smaller size ones provides a

coherent description of the experimental observations.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Expanded graphite is obtained by submitting intercalated

graphite to a thermal shock [1]. This shock leads to the sud-

den volatilization of the intercalated compounds, forcing

apart the lattice graphite planes. A kind of black snow made

of pure graphite worms is recovered. Expanded graphite is

therefore characterized by long-range disorder, preserving

nevertheless an important degree of crystallinity, and a high

degree of porosity at the meso and macro scale (from a few

to hundreds nanometres). Expanded graphite retains the

lamellar structure of graphite and can exhibit high porosity

(up to 99%) [1].

Expanded graphite is often used in its compressed form,

obtained from a binderless compression of expanded graphite

worm-like particles and known as flexible graphite. Flexible

graphite has a higher degree of preferentially oriented crystal-

lites and lower porosity (less than 70%) than raw expanded

graphite. Flexible graphite of density 1 g cm�3 shows a large

asymmetric distribution of pore size, with its peak at

250 nm [2]. The high and controllable porosity of flexible

graphite confers many interesting mechanical properties:

resilience, high compressibility and elastic recovery as well

as chemical resistance and good thermal and electrical con-

duction in the in-plane direction. This has led to numerous

industrial uses such as sealing gaskets, heating elements,

adsorbents, lubricants or electrochemical support in a wide

range of applicative domains as diverse as the nuclear indus-

try and food processing [1,3–6].

Several theoretical and experimental studies have exam-

ined the correlation of such parameters as pore distribution

or the fractal dimension of the pore–matrix interface, to mac-

0008-6223/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.carbon.2013.02.019

* Corresponding author: Fax: +33 472432648.E-mail addresses: [email protected], [email protected] (A. San-Miguel).

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roscopic features such as permeability [7,8], mechanical or

electrochemical properties [9,10].

As many industrial applications entail static or dynamic stress

(sealing, vibration damping or absorption in pressurized media),

the effect of mechanical stress on porosity is a topical subject.

The change in porosity after compaction and release, and the

influence of this change on sample properties, were studied by

Celzard [5]. However, the evolution of macro–meso pore structure

during the application of stress conditions was not examined.

In this work we study compressed expanded graphite un-

der uniaxial mechanical load by small angle neutron scatter-

ing to probe the in situ evolution of its pore structure under

compression.

Among the methods used to investigate porous materials,

small angle neutron scattering (SANS) is a well-established

non-destructive technique [11–13]. It is well adapted for prob-

ing both open and closed porosity [14], and for characterizing

pore morphology as well as the fractal nature of the pore-ma-

trix interface [12,14–16]. SANS has been used to investigate

the porous structure of raw expanded graphite [6] and flexible

graphite [17] with the fractal dimension being a key parame-

ter for data interpretation [18].

The aim of our study is to further the understanding of the

relationship between the evolution of porosity under

mechanical load on one hand, and the macroscopic proper-

ties of the material such as elastic parameters on the other

hand. From an applied point of view, the knowledge gained

of the relationship between pore structure and physical

parameters should help to optimize the design of new mate-

rials, surpassing for instance the current thermodynamic or

elastic conditions of use of expanded graphite.

2. Sample description and compression

Our Compressed Expanded Graphite (CEG) samples were made

by stacking several flexible graphite sheets 1 mm thick of

0.9 g cm�3 density and 60% porosity. Flexible graphite (pur-

chased from MERSEN France) is obtained from a mixture of nat-

ural flakes of graphite mixed with concentrated nitric and

sulphuric acids, leading to the formation of a graphite interca-

lation compound. After washing and drying, the intercalated

system is exfoliated by thermal shock at 900–1000 �C. The exfo-

liated graphite is then compressed to reach the desired porosity

(about 60%) by taking a skeletal density of 2.23 g cm�3. Mea-

surements of open porosity by mercury intrusion on our sam-

ples give a mean pore size of 270 ± 30 nm.

The flexible graphite sheets were out-of-plane compressed

at 50 bar (Fig. 1a and b). By out-of-plane compression we mean

that the average graphene plane of the graphite crystallites is

perpendicular to the compression. After pressure release we

obtained a compact sample with a length l = 23 mm, a height

h = 15 mm, a thickness t = 5 mm and a porosity of 51% as cal-

culated from the apparent density of CEG sample. This com-

pact sample was used for our in situ SANS high pressure

study. A specific high pressure cell was designed in which a

uniaxial stress was applied in the same out-of-plane direction

via a piston connected to a hydraulic pump [19] (Fig. 1c). The

pump generated a pressure adjustable up to 150 bar, corre-

sponding to a maximum pressure of 1000 bar on the sample.

The CEG sample filled the t = 5 mm thickness and

h = 15 mm height compression chamber. The sample was

maintained by two transparent monocrystalline sapphire

windows (4 mm thick) to avoid any extrusion and to keep

the thickness of the sample constant (t = 5 mm) along the

beam direction during the in situ SANS experiments. This de-

sign reproduces the working conditions of industrial sealing

materials. The transparent windows allow full spectroscopic

access to the sample. Sapphire high pressure cells have been

used for SANS studies of liquids or fluids [20,21].

As will be explained in Section 4, we also prepared a CEG

sample of t = 2 mm along the neutron beam direction for

SANS collection at ambient pressure. This thinner CEG was

prepared by stacking 2 mm flexible graphite sheets. It was

studied at ambient conditions to probe the presence of neu-

tron multiple scattering effects.

3. Small angle neutron scattering

3.1. Experimental

The SANS experiments were performed on two different

beamlines: (a) the PAXE beamline at LLB (Saclay, France) using

a 6 A wavelength incident beam having 7 mm diameter and a

BF3 detector and b) the D11 beamline at the ILL neutron

source (Grenoble, France) using a 4.51 A wavelength, 5 mm

diameter beam size and a 3He detector. The observable parti-

cle/pore size ranges were 2–280 nm on the D11 beamline (ILL)

and 4–100 nm on the PAXE beamline (LLB).

In both cases, the sample was placed on the neutron beam

as explained in the previous section. The raw scattering

intensities were corrected to account for empty pressure cell

scattering, sample transmission as well as sample thickness

following classical SANS data treatment procedures [22]. Dif-

ferential scattering cross-sections per unit sample volume in

absolute units (cm�1) were obtained using precalibrated sec-

ondary standards (water at D11, plexiglass at PAXE) and direct

determination of incident neutron beam flux.

The in situ high pressure SANS experiments were per-

formed in the 0–1000 bar range. The stress was increased

stepwise up to the maximum pressure and decreased step-

wise back to ambient pressure. The SANS spectra were col-

lected in situ at each 200 bar step.

Fig. 1 – (a) 1 mm Sheets of flexible graphite, cut to 5 · 23 mm

to fit the pressure cell. (b) To obtain the CEG sample used for

our experiment we compressed out-of-plane at 50 bar

stacks of about 20 of the 1 mm sheets. (c) Pressure cell used

for the SANS experiment showing the incoming beam and

the direction of applied stress. The dashed line drawing

indicates the initial sample volume.

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Integrated spectra were obtained from the raw data using

ILL’s standard SANS software package [23] and the LLB in-

house software PAsiNET [24]. The obtained SANS patterns

were elliptic due to the strong preferential orientation of

graphite crystallites and the fact that the neutron beam was

perpendicular to the compression axis ~z. The intensity was

integrated along the two axis directions of these elliptic pat-

terns (Fig. 2) in a 30� angular width section around each axis

(shaded in white on the diagram), following a commonly used

method for data analysis [12,23,25]. This method of direc-

tional analysis has been shown to be appropriate for SANS

studies of anisotropic systems [26].

Specific fitting scripts were written, in order to extract

quantitative parameters (apparent specific surface areas,

apparent porosities and fractal dimension) from each of the

two 30� integrated sections.

3.2. Data analysis

The small angle scattering differential cross section from an

inhomogeneous system is given as a function of the modulus

of the scattering vector~q defined as jj~qjj ¼ q ¼ 4p sin h=k where

2h is the scattering angle and k the neutron wavelength.

dRðqÞ=dX is the probability, normalized to the unit sample vol-

ume, of the incident beam particle being scattered into the

solid angle dX [27]:

dRðqÞ=dX ¼ ð1=VÞZ

V

qð~rÞei q! r! dr�!��������2

ð1Þ

where V is the sample volume and qð~rÞ is the scattering length

at~r. For our study, an average contrast Dq between the pores

and the graphite matrix was calculated from tabulated values

of scattering lengths.

The scattered intensity I(q) provides information on the

density of scattering particles in the sample, which are the

pores in our case. Its analysis allows us to extract quantitative

information on the pore structure of the material.

Let us here consider the different structural parameters

which can be extracted from the SANS data. First, in the high

q region, I(q) is described by the power-law function [17]:

IðqÞq!1 ¼ 2pDq2Sq�ð6�dÞ ð2Þ

where d is the fractal dimension of the interface between the

matrix material and the pore and S the corresponding specific

fractal surface in the case of isotropic systems. In our case, S

corresponds to the apparent quantities extracted in each of

the two directions. If the parameter d is not an integer, the

interface is described through a fractal geometry and

2 6 d 6 3 characterizes the degree of surface roughness or

irregularities of the pore interface. For a perfectly smooth sur-

face d = 2; while d = 3 for a very rough surface sufficiently con-

voluted to fill a 3D volume [28]. Eq. (2) shows that

S / IðqÞqð6�dÞðS in mdÞ ð3Þ

Knowing the sample density g, S is given by the relation

S ¼limq!1

IðqÞqð6�dÞ

pDq2gFðdÞ ð4Þ

with FðdÞ ¼ Cð5�dÞ sin½ð3�dÞp=2�ð3�dÞ as calculated by Bale and Schmidt

[18] and re-evaluated by Wong and Bray [29].

The apparent specific surface area A in m2 g�1 can be cal-

culated using an appropriate probe scale r0 which is often ta-

ken in the order of magnitude of the radius of molecules (such

as nitrogen, krypton or argon) [30] used in porosity character-

ization by the Brunauer–Emett–Teller (BET) theory. Then A

and S are related by:

A ¼ Sr2�d0 ð5Þ

On the other hand, size parameters are extractable in the

low-q region. A common approach is to use Guinier’s law

[17] to determine the radius of gyration of the pore Rg. The

10-2 10-1

100

102

Pore short axis Pore long axis

I (q)

q (Å-1)

a) b) c)

Fig. 2 – SANS experiments and pore geometry. (a) SANS pattern of CEG sample: shaded sectors indicate the angular sections

used to obtain the integrated intensity on each of the two elliptic axes (long and short axes). (b) The corresponding integrated

intensities at ambient pressure. The artefacts at high q on the intensity curves are not related to the sample structure but to

the detector pixel defections (c) Schematic oblate spheroid representing the pore morphology and its xyz orientation where z

represents the direction perpendicular to the stacked flexible graphite sheets.

462 C A R B O N 5 7 ( 2 0 1 3 ) 4 6 0 – 4 6 9

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condition qRg�1 should be valid in the experimental low-q

domain. For a random two-phase system, the Debye model

[31] is adapted to determine the correlation length n in the

intermediate q domain. Obviously, our system is not random

due to its anisotropy. However, we may use this model by

introducing different correlation lengths for each of the two

axes [32].

Finally, the void volume fraction u (porosity) for a random

two-phase system can be determined by integrating the

quantity I(q)q2 over the whole range of q, leading to the Por-

od’s invariant:

Q ¼Z 1

0

q2IðqÞdq ¼ 2p2Dq2uð1� uÞ ð6Þ

The apparent Porod’s invariants were calculated using the

integrated intensities on the two axis directions.

In the case of huge scattering, the multiple scattering phe-

nomenon (MS) likely occurs. While single scattering can be

treated as a random phenomenon, MS is usually more deter-

ministic. The models proposed above cannot be applied if MS

dominates the total scattering data. As will be discussed later,

MS was present in our data, but it was still possible to extract

reliable information from the SANS data.

4. Results and discussion

The experimental anisotropic SANS patterns of CEG sample

suggests the presence of non spherical pores within the

graphite matrix at ambient pressure. Thus, we modelled the

pores with a spheroid, whose axes are inverted compared to

the 2D pattern in the reciprocal space. Fig. 2c describes the

pore shape in a ~x ~y ~z basis where z is the direction of the ap-

plied load, x or y the direction of the incident beam. The short

axis, b, of the oblate spheroid coincides with the ~z direction

and the long axis, a, belongs to the xy plane. Following the

averaging method explained in Section 3, the spheroid sur-

face corresponding to a 30� solid angle around each axis

was assumed to be spherical. As in previous studies on aniso-

tropic materials [33,34] we observe a partial internal pore sur-

face (the extracted apparent surface).

Before starting the analysis of the high pressure SANS data

it is important to consider the possible effect of MS on our

measurements. The low neutron transmission value (around

0.25) indicates the possible presence of MS. The effect of MS is

characterized by the weakening or broadening of the scatter-

ing profile. By varying the sample thickness or the wavelength

of the incident neutron beam, scattering distortions charac-

teristic of MS might be detected [35–39]. Thus, to investigate

the MS occurrence, we collected spectra at ambient condi-

tions and various wavelengths on a t = 5 mm sample (Fig. 3a

and b), then at a constant wavelength varying the sample

thickness (Fig. 3c and d). The integrated intensity versus q

plots (Fig. 3) show that the distortion caused by MS affects

only the q region below 4 · 10�2 A�1.

To extract information on the initial pore shape, we used

the reliable low q-domain of the 2 mm sample. The experi-

mental low q-range is more suited for the Debye approxima-

tion. The scattered intensity (green1 symbols in Fig. 3c and d)

10-2 10-110-1

101

103

5 mm 2 mm

I(q)

q (Å-1)

(d) Long axis10-2 10-1

100

102

104

5 mm 2 mm

I(q)

q (Å-1)

(c) Short axis

10-2 10-1

100

102

104 4,51 Å (ILL) 6 Å (LLB)

I(q)

q (Å-1)

(a) Short axis

10-2 10-1

100

102

104

4,5 Å (ILL)6 Å (LLB)

I(q)

q (Å-1)

(b) Long axis

Fig. 3 – SANS intensity versus q plot at ambient pressure: (a) and (b) for a t = 5 mm CEG sample collected at two different beam

wavelengths; (c) and (d) for two different CEG sample thicknesses collected at 6 A wavelength (LLB). Spectra were rescaled to

superimpose the linear domains.

1 For interpretation of colour in Fig. 3, the reader is referred to the web version of this article.

C A R B O N 5 7 ( 2 0 1 3 ) 4 6 0 – 4 6 9 463

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can be fitted by the equation IðqÞ ¼ I0ð1þ q2n2Þ2. From the lin-

ear slope of I(q)�1/2 versus q2 plot, the correlation length was

estimated to be 105 ± 5 A along the short axis and 138 ± 5 A

along the long axis. This indicates a spheroid pore shape.

The low aspect ratio is probably due to the fact that the flex-

ible graphite sheets in the 2 mm sample were not pre-com-

pressed to 50 bar.

Let us consider now the effects of MS on the determination

both of the fractal dimension and of the pore volume fraction.

Fig. 4 shows the evolution of the integrated intensity versus q

for our CEG sample along the two pore axes at ambient pres-

sure, at 1000 bar and again at ambient pressure after

decompression.

The fractal dimension is extracted from the linear domain.

Fractal systems characterized by small angle scattering are

found to show a power law behaviour over at least one decade

in length scale [40–44,45]. However, Fig. 4 shows that the lin-

ear domain of our spectra for the t = 5 mm sample does not

exceed a decade. Nonetheless, the fractal nature of our sam-

ple is demonstrated by the fact that the linear domain for the

t = 2 mm sample (or for lower neutron wavelengths) extends

beyond one decade. The reduction of linear q-domain exten-

sion for the t = 5 mm samples must then be due to the effects

of MS. MS effects do not however alter the slope of the linear

domain from where the value of the fractal dimension is ob-

tained [36–38]. Due to the different preparation of the two

samples (the t = 5 mm sample was pre-compressed at 50 bar

whereas the t = 2 mm sample was not pre-compressed) a di-

rect confrontation of the fractal dimension values is not

possible.

To conclude the above discussion, the analysis of the lin-

ear q-domain of the t = 5 mm samples, even if restricted to

less than one decade, does allow us to extract reliable values

of the sample fractal dimension.

Let us now turn to the apparent porosity that can be ex-

tracted from Porod’s invariant Eq. (6). Given our data are af-

fected by MS from q = 0 to the highest measured value

(0.5 A�1), reliable absolute values in the 4–100 nm size range

cannot be extracted. We analyse only the partial and relative

evolution of the apparent porosity with stress. The volume

fraction is calculated from the two angular sections of Fig. 2

as mentioned above.

The evolution of apparent porosity plotted against applied

stress up to 1000 bar is shown in Fig. 5a. A significant reduc-

10-2 10-1100

101

102

103

ambient pressure 1000 bar ambient pressure (after decompression)

I(q)

q (Å-1)

(a) Short axis

10-2 10-110-1

100

101

102

103

ambient pressure 1000 bar ambient pressure (after decompression)

I(q)

q (Å-1)

(b) Long axis

Fig. 4 – Evolution of SANS intensity versus q along the pore short axis (a) and long axis (b) directions of the CEG sample at

ambient pressure, 1000 bar, and after decompression. To improve readability, intermediate pressure steps are not shown.

0 200 400 600 800 1000

0.1

0.2

0.3

0.4

0.5

0.2

0.4

0.6

0.8

1.0

Poro

sity

evo

lutio

n

Stress (bar)

Por

osity

rela

tive

evol

utio

n

(b)

0 200 400 600 800 10000.5

0.6

0.7

0.8

0.9

1.0 Short axis Long axis

(P0-Δ

P)/P

0

Stress (bar)

(a)

Fig. 5 – (a) Evolution of the apparent porosity (from SANS data) in the 4–100 nm size range of CEG sample as a function of

applied stress for the two axes of the pores, relative to the initial apparent porosity P0. Filled symbols correspond to the

compression and empty symbols to the decompression. (b) Absolute and relative porosity evolution extracted from the

sample volume variation with applied stress (initial porosity 51%). In both panels, lines are visual guides and the arrows

show the experimental paths.

464 C A R B O N 5 7 ( 2 0 1 3 ) 4 6 0 – 4 6 9

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tion in porosity, close to 50%, is observed along the short pore

axis at 1000 bar. This loss is not fully recovered after the stress

is released (25% loss). Along the long pore axis, the reduction

in porosity is approximately 25% at 1000 bar but it is fully

recovered after the pressure cycle.

The evolution of total porosity under stress (Fig. 5b) was

obtained from the sample volume variation (calculated from

the piston displacement) under compression and during

decompression. The loss of total porosity is about 80% at

1000 bar and 70% after decompression. The comparison of

Fig. 5a and b shows that the global porosity reduction under

stress is higher than that in the 4–100 nm detectable range.

This could be due to a higher proportion of pores falling into

the detectable range with applied stress.

Fig. 6 shows the evolution of the fractal dimension during

compression and decompression along the two axes as ob-

tained from the linear domain of Fig. 3 spectra using Eq. (2).

The initial fractal dimension for both axes is around 2.1, indi-

cating the homogeneous and strong 2D character of the pore-

matrix interface in the considered q-range. The fractal dimen-

sion then increases continuously during compression, the

maximum value being higher for the short axis. During the

decompression steps the fractal dimension decreases but

does not return to the initial values.

The densification of our samples during compression

probably causes texture changes. Consistent with theory

[46], the higher the surface fractal dimension the rougher

the interface between the pore and graphite matrix. Two dif-

ferent mechanisms can operate to change pore morphology:

(i) pore closure [47] or pore coalescence, as was previously

proposed in porous media [48–50], accompanied by fracture

or rearrangement of the plate-like graphite grains; (ii) a

stress-induced pore flattening and collapse, similar to what

has been observed in carbon nanotubes under pressure

[51,52]. The discussion below, including electrical resistivity

and mercury intrusion measures taken ex situ, will help us

to discriminate between these two possibilities.

Another parameter which can be extracted from the high q

region of the SANS data is the apparent specific surface area

[28]. Eq. (5) was used with r0 = 2.58 A corresponding to the ra-

dius of krypton atom [31]. As seen with the fractal dimension

above, the directional analysis of our SANS data allows us to

obtain two partial surfaces corresponding to a solid angle of

30� along the pore long and short axes [53]. The apparent spe-

cific surface observed on the short axis (hereafter AS_S) is

much higher than the apparent specific surface along the long

axis (hereafter AS_L) (Fig. 7). This observation can be ex-

plained by the strong anisotropy of the worm-like crystallite

orientation in the sample [1]. MS effects are known to lead

to overestimation of the Porod’s constant in the high q region

[54,55]. In fact, the specific surface area of porous systems has

been found to be dependent on the numbers of scatterers

[56,57] which are overestimated in the case of MS. Conse-

quently, only the relative apparent specific surface areas in

the two directions are plotted in Fig. 7. Upon load/unload cy-

cle the apparent specific surface area follows two different

behaviours for the two directions. A partially reversible de-

crease is observed along the short axis direction, while an in-

crease of the apparent specific area is observed along the long

axis.

The general evolution of AS_S (Fig. 7a) consists of a strong

reduction during compression and a partial recovery on stress

release. This behaviour is consistent with a reduction of pore

size and densification of the porous media [1,58,59].

0 200 400 600 800 10002.1

2.2

2.3

2.4

Long axisShort axis

Frac

tal d

imen

sion

Stress (bar)

Fig. 6 – Evolution of the fractal dimension for pore sizes

between 4 and 100 nm, as a function of the applied uniaxial

stress for CEG sample. The fractal dimension was calculated

for each compression and decompression step along the

two directions defined by the mean spheroid pore

morphology. Lines are visual guides.

0 200 400 600 800 100090

100

110

120(b) Long axis direction

Rela

tive

evol

utio

n of

AS_

L

Stress (bar)0 200 400 600 800 1000

40

60

80

100

Rela

tive

evol

utio

n of

AS_

S

Stress (bar)

(a) Short axis direction

Fig. 7 – Evolution of the apparent specific area under uniaxial stress (up to 1000 bar) of CEG sample (a) for the pore short axis,

and (b) for the pore long axis, relative to an initial value arbitrarily set to 100 (see text for discussion).

C A R B O N 5 7 ( 2 0 1 3 ) 4 6 0 – 4 6 9 465

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The evolution of AS_L (Fig. 7b) is more surprising: the area

remains practically constant under compression and in-

creases during decompression. The stability of AS_L during

compression suggests an additional contribution. In agree-

ment with our discussion of apparent porosity evolution

(Fig. 5a), this contribution can be due to a transfer of larger

pores inside the observable SANS size range. Its increase after

decompression indicates clearly the creation of new void-ma-

trix interfaces on the long axis.

A simple pore closure [47] or pore coalescence mechanism

under uniaxial compression as suggested by Bustin et al. [50]

are incompatible with the AS_L evolution (Fig. 7a).

We rationalize the apparent specific area behaviour under

uniaxial stress as related to the collapse and splitting of pores

concomitant with the formation of pore interfaces as shown

in Fig. 8.

We have performed two further characterizations of the

CEG samples after the pressure cycle, mercury intrusion

porosimetry and electrical resistivity, which support the pro-

posed scenario of pore evolution.

Mercury intrusion measures were taken on the CEG sam-

ple compressed at 1000 bar and quenched to ambient condi-

tions, and, for comparison, on the initial flexible graphite

sheets. The mercury intrusion curves for the two samples

are shown in Fig. 9. We obtain a 270 ± 30 nm mean pore size

for the initial flexible graphite sheet. The pore structure of

the CEG sample quenched from 1000 bar shows a large asym-

metric distribution with a mean pore size of 20 nm. There is

therefore an order of magnitude difference in mean pore size,

supporting the scenario proposed in Fig. 8.

We further measured the in-plane electrical resistivity,

using the four probe method on the CEG sample before and

after compression at 1000 bar. The electrical charge displace-

ment occurred parallel to the graphite sheet and along the

pore long axis. Results are shown in Table 1 and compared

with the known value for highly oriented pyrolytic graphite

(HOPG).

The measurements show higher resistivity in the com-

pressed sample. This resistivity increase is explained by an

increase in pore density, consistent with an interface creation

along the long pore axis as observed in SANS data (Fig. 7b) and

attributed to the irreversible collapse mechanism. An electri-

cal resistance measurement perpendicular to the flexible

graphite sheet has been done by Luo and Chung [61] under re-

peated compression. It was found to decrease with the ap-

plied stress.

To summarize, experimental results from SANS, together

with the complementary techniques of mercury intrusion

porosimetry and electrical resistivity, support the model of

pore collapse and splitting in the CEG sample under compres-

sion. We relate the decrease in porosity (Fig. 5) after compres-

sion to the formation of smaller pores (in the detectable size

range). The pores are more affected by the reduction of their

dimension along the direction of applied stress which corre-

sponds to the short pore axis. In fact, as the applied uniaxial

stress was parallel to the short axis of the pore, the collapse

should preferentially take place also in this direction (Fig. 8).

The pore size shift towards smaller values must be accompa-

nied by the formation of new rough interfaces along the long

axis, consistent with the increase of fractal dimension in this

direction. The increase of apparent specific area after decom-

pression further confirms both the irreversible character of

the mechanism and the appearance of new void-matrix inter-

faces on the long axis.

The irreversibility of the stress-induced collapse implies

that the elastic energy introduced through the creation of lar-

ger curvature interfaces should be compensated through the

interactions between the newly created contact surfaces. A

parallel can be drawn with the pressure induced collapse ob-

served in carbon nanotubes [51,52,62] leading to peanut-

shaped tubes on which the van der Waals inter-wall interac-

tions compensate for the elastic energy created in the higher

Fig. 8 – Proposed pore collapse and splitting mechanism in compressed expanded graphite samples under uniaxial stress.

From left to right: pore evolution under a uniaxial stress until irreversible splitting into smaller pores.

0.01 0.1 1 10 100

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7100 10 1 0,1 0,01

Flexible graphite Sample quenched at 1000 bar

Cum

ulat

ive

volu

me

(ml/g

)

Pore size (µm)

Pressure (MPa)

Fig. 9 – Mercury intrusion curves for the initial flexible

graphite sheet (black) and for the CEG sample quenched

from 1000 bar (red). The cumulative volume is plotted as a

function of pore size (low axis) and of mercury pressure

(upper axis). Black and red symbols indicate the

corresponding mean pore size. The small step observed at

low compression in the black curve is related to the material

compression before mercury intrusion. (For interpretation of

the references to colour in this figure legend, the reader is

referred to the web version of this article.)

466 C A R B O N 5 7 ( 2 0 1 3 ) 4 6 0 – 4 6 9

Author's personal copy

curvature sections of the collapsed tube. This mechanism is

strongly dependent on the geometrical characteristics such

as diameter or number of tube walls and can be stable at

ambient pressure [63]. The more complex structure of ex-

panded graphite allows for other mechanisms which could

account for an irreversible collapse. The expanded graphite

worm structure can be described as the stacking of graphene

nanosheets with inter-sheet distances much larger than the

graphite interlayer distance [63]. A mechanical inter-sheet

locking of the expanded graphite worms after or during pore

collapse can bring about the splitting of the pores and an irre-

versible change in orientation of the nanosheets. Mechanical

interlocking has been invoked to explain the binderless for-

mation of flexible graphite through the compaction of ex-

panded graphite worms [5]. The two interactions proposed

to explain the irreversible nature of the collapse and splitting

process, i.e., van der Waals interactions and mechanical inter-

locking, can act together. They may not be exclusive.

5. Conclusion

The in situ evolution of the pore structure of compressed ex-

panded graphite was studied under a uniaxial stress up to

1000 bar using small angle neutron scattering, which permit-

ted the observation of pores in the range 4–100 nm. The uni-

axial stress was applied in the direction of the average c-axis

of the graphite crystallites composing the sample. The aniso-

tropic aspect of SANS patterns suggests an oblate spheroidal

pore shape. The analysis of fractal dimension, apparent spe-

cific surface area and apparent porosity was performed con-

sidering the two anisotropic symmetry axes. Upon a load/

unload cycle, we observed: (i) a reduction of the apparent

porosity, and (ii) an increase of the fractal dimension. This

is consistent with the densification of the material. However,

the apparent specific surface area follows two different

behaviours for the two directions. As expected it decreases

along the direction parallel to the applied stress, while, sur-

prisingly, increases along the direction perpendicular to the

applied stress. We interpret this as due to microstructural

changes in the sample involving the creation of new pore-ma-

trix interfaces.

In order to elucidate the mechanism of porosity loss and

the creation of new interfaces during the uniaxial compres-

sion, we propose a model of irreversible collapse and splitting

of pores into smaller size ones. Ex situ characterization by

electrical resistivity and mercury intrusion porosimetry cor-

roborated this mechanism.

These results could be extended to other lamellar porous

systems, and could then be taken into account in material

modelling or design. Moreover, the high pressure SANS tech-

nique developed for the present study is well adapted for the

study of a wide range of porous materials under stress.

Acknowledgements

This research was supported by the Agence Nationale de la

Recherche (ANR) through MATETPRO project ANR- 08-MAPR-

0011. We would like to thank Technetics Group France for pro-

viding samples and Herve Feret for technical assistance in the

pressure cell development. We are grateful to Dr. S. Pailhes

(CNRS, France) for his help on the electrical transport mea-

surements and to Dr. L. Gremillard (MATEIS, INSA-Lyon,

France) for his assistant with mercury porosimetry.

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Table 1 – Resistivity values of the uncompressed CEG and of the CEG compressed at 1000 bar (measurement taken afterdecompression). The known resistivity value for highly oriented pyrolytic graphite (HOPG) [60], taken parallel to the graphitesheet, is given for comparison.

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