Acoustic attenuation in silica porous systems

Journal of Non-Crystalline Solids 322 (2003) 29–34

www.elsevier.com/locate/jnoncrysol

Acoustic attenuation in silica porous systems

S. Caponi a,b,*, A. Fontana b,c, M. Montagna b,c, O. Pilla b,c,F. Rossi b,c, F. Terki e, T. Woignier e

a Dipartimento di Fisica, Universit�aa di L’Aquila, I-67100, L’Aquila, Italyb Istituto Nazionale di Fisica della Materia Unit�aa di Trento, I-38050 Povo (Trento), Italy

c Dipartimento di Fisica Universit�aa di Trento, I-38050 Povo (Trento), Italye Universit�ee Montpellier II, F34095, Montpellier cedex, France

Abstract

The mechanisms responsible for phonon attenuation in glasses and in porous systems have been investigated. The

acoustic attenuation has been measured by Brillouin light scattering using a Fabry–P�eerot apparatus. Melt-quenched

vitreous SiO2 (q ¼ 2200 kg/m3), silica xerogels with different densities (q ¼ 510 � 50, 770� 80, 1380� 140 and

2190� 200 kg/m3), and silica aerogel (q ¼ 760 � 80 kg/m3) have been investigated. The porosity of the samples was

measured by N2 adsorption/desorption techniques. For pores sizes smaller than �8 nm the acoustical attenuation, at

the Brillouin frequency, at room temperature, is the same as in v-SiO2 and consequently is attributed to dynamical

processes. For larger pore sizes, the Brillouin line width increases and its variation is related to the effect of phonons

scattering from the growing structural disorder. On the basis of the present experiment, in porous systems, static and

dynamical attenuation mechanisms have been found.

� 2003 Elsevier B.V. All rights reserved.

PACS: 61.43.Fs; 78.35.+c; 78.40.Pg; 78.55.Mb; 81.05.Rm

1. Introduction

A amorphous solids have universal physical

properties that are not observed in their crystalline

counterpart [1]. These properties have stimulated

both theoretical and experimental investigations tounderstand the properties of amorphous media [1].

The vibrational dynamics in topologically disor-

dered systems are an intriguing problem of con-

* Corresponding author. Tel.: +39-0461 881 543; fax: +39-

0461 881 696.

E-mail address: [email protected] (S. Caponi).

0022-3093/03/$ - see front matter � 2003 Elsevier B.V. All rights res

doi:10.1016/S0022-3093(03)00167-4

densed matter physics. For example the specific

heat is much larger than expected from a Debye

model [1] and the thermal conductivity between 5

and 20 K has approximately a slope of zero [1].

The density of states has an excess band in the plot

of gðxÞ=x2 referred to as Boson peak [2,3]. Theexcess modes have been the object of different

speculations [1] particularly in the case of vitreous

silica (v-SiO2) which is considered as a prototype

of strong glasses [4]. In fact, according to the

Angell�s terminology [4], we can distinguish two

kind of glasses plotting the viscosity data of su-

percooled liquids as a function of the reduced

temperature T=Tg, where Tg is the glass transition

erved.

mail to: [email protected]

30 S. Caponi et al. / Journal of Non-Crystalline Solids 322 (2003) 29–34

temperature. We can compare the viscosity,gðT=TgÞ, of structurally different glasses such as

inorganic network glasses and organic liquids; the

different temperature dependences of the data, in

this presentation, was taken to distinguish fragile

and strong glasses. The first group (i.e. o-therphenil)

has a non-Arrhenius dependence of gðT=TgÞ, on the

contrary a nearly Arrhenius temperature depen-

dence for the relaxation times and the viscosity ischaracteristic of the strong glasses (i.e. v-SiO2) [4].

The topological disorder of amorphous mate-

rials, like v-SiO2, causes deviations from the plane

wave vibrational modes: in fact speaking about

phonons, as a plane wave, is strictly correct only in

crystalline solids. Studying porous structure, we

will introduce a further degree of structural dis-

order with respect to that of the amorphous v-SiO2. In fact varying sample preparation, the

microscopic structure can be modified. We can have

highly porous media, such as aerogels, character-

ized by a self-similar microscopic structure and

fracton like vibrations [5,6], or systems like xero-

gels with a larger distribution of the densities. The

pore size distribution in xerogels is smaller than in

aerogels (generally the maximum size of pore is<15 nm) and the fractal structure disappears.

A measure of the sound attenuation can be ob-

tained by monitoring the line width (C) of the

Brillouin peak. The measured attenuation is caused

by different mechanisms. One is due to the topo-

logical disorder present in the glassy structure [7].

This process should be almost temperature inde-

pendent [8]. Another one is related to the presenceof thermally activated processes, such as relax-

ations and two level systems, which are tempera-

ture dependent. These mechanisms have been

proposed to explain the experimental data in v-

SiO2 especially in the temperature range from liq-

uid helium to room temperature [9]. Analyzing the

porous systems we will introduce another kind of

attenuation. The structural disorder due to thepores presence, is responsible for a sort of �Ray-

leigh scattering processes� of the phonons owing to

the presence of defect in the structure. When the

wavelength of the excitation is comparable with the

defects sizes of the system, the scattering by struc-

tural disorder starts to be important and the pho-

non description as plane-waves loses meaning [7].

In this work, we report the attenuation data atroom temperature of silica aerogel and xerogels

with different porosities. The choice of this class of

systems is justified by the fact that silica xerogels

and aerogels are materials with porosities of the

order of nm and can be produced with different

macroscopic densities [11]. In fact, by varying the

temperature and the length of thermal treatment

or the preparation procedure, it is possible toproduce disordered solids with a range of macro-

scopic densities and porosities [11]. The random

network is composed by covalently bonded cor-

ner-linked SiO4 tetrahedra as in v-SiO2 and so, the

short-range structure and the microscopic density

of the solid phase between the pores are approxi-

mately those of melt quenched silica. The degree of

structural disorder induces differences of the vib-rational properties [10]. Brillouin light scattering

probes vibrational modes with wavelengths of

hundreds of nm, larger than the typical pore size of

the xerogels and aerogels. The sound velocity is

therefore reduced with respect to that of the more

compact structure of v-SiO2 and, increasing the

structural disorder, the Brillouin line width in-

creases.

2. Experimental procedure

Alcogel samples are prepared by hydrolysis and

polycondensation reactions of tetramethoxysilane

dissolved in methanol [11]. To control the density

after drying, some of the alcogels are aged at 200�C temperature in autoclave at a pressure of 4

MPa. The obtained xerogels have surface areas

(Table 1) covered by dangling bonds [12]. The

porous structure absorbs H2O molecules, which

can be bonded to the surface (hydrogen-bonded

silanols) [12,13] or physically adsorbed [12,13]. To

eliminate the most part of physical water [14], the

samples are heated at 600 �C for 24 h. The aerogelis prepared by a two steps process: the supercriti-

cal drying necessary to synthesize aerogels [15]

is followed by a sintering in the temperature

range 1000–1100 �C. After the supercritical drying

at 300 �C and 18 MPa for 3 h, aerogels have a

macroscopic density �300 kg/m3. By a sintering

heat treatment the macroscopic density is almost

7.0 7.5 8.0 8.5 9.0

Am

plitu

de (

a.u.

)

Table 1

In Table 1, the density, q, the specific surface area, S, the maximum of the pore distribution, Lp, and the hydraulic diameter, Dh, are

reported. Moreover also the frequency shift, Dx, and the C (HWHM) of the Brillouin peak at T ¼ 300 K are given

q (kg/m3)� 10% S (m2/g)� 10% Lp (nm)� 5% Dh (nm)� 5% C (MHz)� 0.1%

(300 K)

Dx (GHz)

(300 K)

Aerogel 760 210 14.0 16.5 240 8.0� 0.8

Xerogel 510 470 12.3 13.1 160 5.35� 0.005

770 565 6.6 5.9 77 11.5� 0.01

1380 460 3.5 3.1 76 21.4� 0.02

Aerogel glass 2190 – – – 85 34� 0.03

SiO2 2200 – – – 75 34� 0.03

S. Caponi et al. / Journal of Non-Crystalline Solids 322 (2003) 29–34 31

760 kg/m3. Because of the larger pore size theaerogel samples have a smaller specific surface area

and a smaller OH content [16]. The maximum of

the pore size distribution is measured by nitrogen

adsorption–desorption experiments [17] and the

specific surface area is obtained by BET analysis

[18].

Most of the Brillouin scattering experiments are

performed in backscattering configuration with atandem six-pass Fabry–P�eerot (FP) interferometer

using different mirror distances to have free spec-

tral ranges (FSR) between 37.5 and 7.5 GHz.

(FSR: the range in the frequency space between

two successive order of the response function of

the FP interferometer). The resolution, obtained

by the width of the elastic peak, varies from �500

to �100 MHz. A second high-resolution spec-trometer consists of a double-pass plane FP in-

terferometer, used as a pre-filter, and a confocal

FP, used as resolving unit, (for a complete de-

scription see Ref. [19]). The free spectral range of

the plane interferometer is equal to 75 GHz and

finesse to 40; the frequency corresponding to the

maximum transmission of the pre-filter is matched

with the frequency of the Brillouin line. The con-focal FP has a free spectral range of 1.48 GHz and

a finesse of 50, owing a total contrast of �107. The

accuracy of the experimental data for the sound

velocity and the attenuation is, respectively, �0.1%

and �5%.

Frequency shift (GHz)

Fig. 1. Experimental Brillouin light scattering spectra at room

temperature of silica aerogel (q ¼ 760 kg/m3), with resolution of

30 MHz. The two lateral peaks are the repetitions of the reso-

lution�s peak, which are related to the free spectral range of the

measurement.

3. Results

The mean pore size of the samples used in this

work is determined by N2 adsorption/desorption

techniques which gives the maximum of the poresize distribution. Moreover from the specific sur-

face area, S, obtained by BET analysis, and the

pore volume, Vp, deduced from the macroscopic

density, we calculate the hydraulic diameter,

Dh ¼ 4 Vp=S. Within the experimental errors, Ta-

ble 1 shows the agreement between the maximum

of the pore size distribution, Lp, and the hydraulic

diameter, Dh.Fig. 1 shows the Brillouin spectrum (BS) of the

aerogel at room temperature. This spectrum is

collected using the spherical Fabry–P�eerot inter-

ferometer with resolution of about 30 MHz. The

frequency of the Brillouin peak is �8 GHz and the

width at half maximum amplitude is �250 MHz;

0 4 8 12 160

100

200

300

aco

c = 75 MHz

T= 300 K

Γ/2

(M

Hz)

Lp(nm)

Fig. 2. Half width (HWHM) of Brillouin peak at room tem-

perature versus the mean pore size. The full square is relative to

silica aerogel, the full circles to silica xerogels, the open circle to

fully densified silica aerogel, the full triangle to vitreous silica

(this datum is taken from Ref. [7]) and the full diamond is

relative to the a-quartz of Ref. [20]. The dashed and the full

lines are drawn as a guide for the eye.

0 5 10 15

2000

4000

6000

0.5 1.0 1.5 2.00

2000

4000

6000

Soun

d ve

loci

ty (

m/s

)

Lp (nm)

v L (m

/s)

Density (g/cm3)

Fig. 3. Longitudinal sound velocity, vL, versus the mean pore

size, Lp: the full square is relative to silica aerogel, the full circles

to silica xerogels, the open circle to fully densified silica aerogel,

the full triangle to vitreous silica with the same notation, in the

inset longitudinal sound velocity vL versus the density, q, is also

reported. The dashed line is drawn as a guide for the eye.


the two lateral peaks are the repetitions of the

resolution�s peak. For comparison, we recall thatthe frequency of the Brillouin peak in v-SiO2 is at

�34 GHz and its width is �75 MHz [7]. For all the

samples, the frequency shift and the width of the

Brillouin peaks are summarized in Table 1. The Cof the v-SiO2 is taken from Ref. [7].

In Fig. 2, we report the C (half width at halfmaximum of the Brillouin peak) as a function of

mean pore size Lp. The Cs of v-SiO2 and of fully

densified aerogel are also reported at Lp ¼ 0, be-

cause there is no porosity in these samples. For

comparison the Brillouin width of a-quartz at

T ¼ 300 K is also reported [20]. In Fig. 3, we re-

port the longitudinal sound velocity, vL, as a

function of the pore size, and in the inset thelongitudinal sound velocity, vL, as a function of

the density q of the system.

4. Discussion

To correlate the acoustic attenuation to the

system�s disorder, it is important to note the dif-ference between the width of the Brillouin peak

relative to crystalline quartz and that of v-SiO2

reported in Fig. 2. The larger acoustic attenuation

in v-SiO2, is determined by the presence of struc-

tural disorder compared to that of a crystal and by

dynamical processes [8]. In fact vitreous systems

are different from their crystalline counterparts for

two characteristic properties. The amorphoussystems have a more complicated microscopic

dynamic that comprise relaxations, two levels

systems, hopping and anharmonic properties.

These processes are temperature dependent and

they contribute to the dynamical absorption [8].

Moreover the vitreous systems do not present a

long-range order and the structural disorder can

produce phonon scattering. This mechanism con-tributes to the static absorption and it should be

almost temperature independent. It is well known

[7] that in Brillouin light scattering measurements

of v-SiO2 at T ¼ 300 K, the dynamical absorption

is the largest contribution. In fact, reducing the

temperature, the width of the Brillouin peak has a

decrease and the attenuation is a maximum at

about 100 K [7]. On the contrary, in the BrillouinX-ray scattering measurements, probing the THz

region, the structural disorder seems to be larger

and the attenuation is temperature indepen-

dent [21]. These different results between BLS

and X-ray scattering could be related to the wave-

length of the phonons investigated by the two

techniques.

S. Caponi et al. / Journal of Non-Crystalline Solids 322 (2003) 29–34 33

Fig. 2 shows that systems with mean pore sizes<8 nm have the C of v-SiO2 (C ¼ 75 MHz) at

T ¼ 300 K. Based on this occurrence, we suggest

the dynamic origin of the acoustic absorption in

this range and we deduce that in the samples with

smallest pore size, the microscopic dynamic (in-

cluded relaxation processes and TLS) is similar to

that of v-SiO2. The dynamical absorption is the

dominant phenomenon until the structural disor-der becomes much bigger. When the pore size is

greater than 8 nm, C increases with increasing Lp.

Therefore, the contribution of phonon scattering

by the structural disorder becomes more important

and, only for pore sizes >8 nm, starts to be the

dominant one.

We can form the hypothesis that aCO ¼ 8 nm is

the cross-over pore size: for Lp greater than aCO,the increasing of the line widths is mainly due to

structural disorder effects and so it has a static

origin. This absorption�s part must increase with

the pore size and it has to be zero when the pores

vanish. Anyway the two mechanisms, the dynam-

ical and the static one, can coexist, at least, in the

range of porosities in our samples. The tempera-

ture dependence of C will give a more detailedinformation, such measurements are in progress.

We note that the significant parameter, in our

case, is the mean pore size and not the density of

the sample. As an example, the density of the

studied aerogel and of one of the xerogel samples

are almost the same, whereas the sizes and the

shapes of pores differ in the two samples (the pore

size distribution of the aerogel is much larger thanthat of the xerogels). In these two samples, indeed,

the sound attenuation differs, as shown in Table 1.

We explain the phonon attenuation shown in

Fig. 2 by the following consideration. The phonon

scattering by a disordered structure should be

similar to that of elastic light scattering from the

same system. The main difference is that the light

can propagate in the vacuum whereas the phononscannot: this fact will have the consequence that the

disordered structure has a larger effect on phonons

than on photons. This comparison is only quali-

tatively correct because it is known [22] that in

Rayleigh scattering, the interference effects cannot

be neglected when there are a lot of near scatterers

(separated by distance that are of the order of

wavelength of the light) and moreover their actualstructure should be considered. Rayleigh scatter-

ing of light depends on the fourth power of the

frequency and of the sixth power of particle size, a[22]. Therefore samples with the same density but

different pore size should scatter the light differ-

ently: few big particles produce greater scattering

than many small particles. This difference is due to

the a6 dependence, which is reduced to an a3 de-pendence if, in the approximation of equal pore

volume, the volume�s dependence is considered. If

the phonons are scattered with a mechanism sim-

ilar to that of photons, the pore size dependence of

the Brillouin line width can be explained.

Concerning of the sound velocity, reported in

Fig. 3, this has not a simple interpretation. As a

matter of fact the sound velocity is directly relatedto the densities [23], the connectivity [24], and the

shape and size of pores. In general, in compacted

sample it could be reasonable to expect a linear

dependence of sound velocity versus the density,

shown by the dashed line in the inset of Fig. 3.

Vitreous silica and fully densified aerogel have the

same sound velocity. In the xerogel samples, we

increase the total volume of the pores, the system�srigidity decrease and the sound velocity linearly

decrease with the density. In low density xerogel

and aerogel the connectivity of the system, the

shape and sizes of pores start to become important.

This effect is demonstrated by the deviation of

linearity of vL versus q (inset of Fig. 3) and versus

Lp, that happens at about Lp � aCO and q � 0:8 g/

cm3. This could be the explanation of the invari-ance of the sound attenuation up to pore size �8

nm, while, in this range, the sound velocity de-

creases linearly departing from the v-SiO2 velocity.

5. Conclusions

In conclusion by using Brillouin light scattering,we have shown that, in porous systems with dif-

ferent densities two distinct attenuation mecha-

nisms are present.

A crossover in pore size seems to exist at

aCO � 8 nm. For the pore size smaller than aCO the

largest contribution in the absorption comes from

the attenuation due to dynamic mechanism as for


instance relaxation processes and two level sys-tems. For Lp larger than aCO, a greater sound at-

tenuation is observed and it is attributed to the

scattering of phonons by a sample�s topological

heterogeneities. A similar change is shown in the

sound velocity, that exhibit a deviation from the

linear dependence by the density and the pore size

at the same cross-over. In conclusion both the

velocity and the attenuation of the sound waveseem to have a consistent dependence on pore size.

Acknowledgement

This work was supported by MURST Progetto

di Ricerca di Interesse Nazionale.

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Acoustic attenuation in silica porous systems

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