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MECHANICAL PROPERTIES OF SiO2 - AEROGELS
J. Cross, R. Goswin, R. Gerlach, J. Fricke
To cite this version:
J. Cross, R. Goswin, R. Gerlach, J. Fricke. MECHANICAL PROPERTIES OF SiO2 - AEROGELS.
Journal de Physique Colloques, 1989, 50 (C4), pp.C4-185-C4-190. �10.1051/jphyscol:1989430�. �jpa-
00229506�
R E W E DE PHYSIQUE
APPLIQUEE
Colloque C4, Supplement au n04, Tome 24, avril 1989
MECHANICAL,PROPERTIES OF SiO,
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AEROGELSJ. CROSS, R. GOSWIN, R. GERLACH and J. FRICKE
Physikalisches Institut der Universitdt, Am Hubland, 0 - 8 7 0 0 Wiirzburg.
F.R.G.
Resum4 : Le comportement m4canique des aerogels de silice a
QB
6tudi6 par des mQhodes ultrasonores et par compression statique. Dans cat article nous presentons ies valeurs de la vitesse du son en fonction de la densite, de la charge externe et de la pression de gaz interne. Nous demontrons que la vkesse du son varie localement sur des distances de quelques millimbtres. De plus nous avons Uudie le frittage des aerogels en fonction de la temperature et de la dur6e du trakement et nous en dMuisons ainsi des lois d'echelle pour les constantes Blastiques.Abstract
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The mechanical behavior of S i 0 2-
a e r o g e l s was i n v e s t i g a t e d i n u l t r a s o n i c and s t a t i c compression experiments. I n our paper we p r e s e n t d a t a on t h e sound v e l o c i t y as a f u n c t i o n of d e n s i t y , of e x t e r n a l load and i n t e r n a l g a s p r e s s u r e . We a l s o demonstrate l o c a l v a r i a t i o n of sound v e l o c i t y over d i s t a n c e s of a few mm.Furthermore we i n v e s t i g a t e d t h e s i n t e r i n g behavior of a e r o g e l s w i t h r e s p e c t t o temperature and d u r a t i o n of treatment and derived s c a l i n g laws f o r t h e e l a s t i c c o n s t a n t s .
I
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I n t r o d u c t i o r iAerogels w i t h t h e i r high degree of p o r o s i t y d i s p l a y mechanical p r o p e r t i e s which a r e d r a s t i c a l l y d i f f e r e n t from t h o s e of SiO, g l a s s . A s was shown / I / sound v e l o c i t i e s a r e i n t h e
100 m s-l range ( f i g . 11, t h e Young's modulus is of t h e o r d e r of
lo6
N m-2. Sound propaga- t i o n proceeds v i a t h e s o l i d s k e l e t o n , which was demonstrated by evacuation / 1 , 2 / .Suggested a p p l i c a t i o n s f o r t h e low d e n s i t y aerogel a r e t h e i r use i n impedance matching devices, a c o u s t i c delay l i n e s o r dampers. I n a more fundamental view, t h e i n t r i g u i n g a c o u s t i c a l p r o p e r t i e s a r e c o r r e l a t e d with t h e huge v i b r a t i o n a l d e n s i t y of s t a t e s /3/ i n t h e 1 t o 1000 GHz range and t h u s w i t h t h e l a r g e s p e c i f i c h e a t of a e r o g e l s a t low temperatures.
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Experimental ~ n v e s t i ~ a t i o n s and Discussion2.1 Untreated Aerogels
E a r l i e r i n v e s t i g a t i o n s have shown t h a t t h e e l a s t i c moduli m of a e r o g e l s approximately s c a l e with d e n s i t y : m a pa, w i t h m being e i t h e r t h e Young's modulus Y o r t h e e l a s t i c c o n s t a n t s c,, and c++; a is a s c a l i n g exponent ranging from 2.9 t o 3.6. The exact value of a depends on t h e
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989430
Fig 1. Sound velocities c, and c, versus density p for different aerogels.
density variation taken into account. However, for individual specimens a considerable deviation of the elastic constants from the above general scaling behavior has to be recognized. Fig. 2 shows a log
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log-
plot of elastic constants c,, and c,, for various SiO, materials versus density p.
Fig 2. Elastic constants of aerogels, silica gels (xerogels) and silica glass versus density p. The derived scaling exponents are a l l = 3.17 t 0 . 1 1 and a,, = 3.25 2 0.15.
We want t o point out t h a t the measured sound v e l o c i t i e s a r e averaged over volumes o f s e v e r a l 10 cm3. I t is obvious t h a t on a microscopic s c a l e (l...lOOnm) aerogels a r e not a t a l l homogeneous and therefore considerable l o c a l v a r i a t i o n of e l a s t i c behaviour is expected. I t was a s u r p r i s e f o r us t o detect local sound velocity v a r i a t i o n s of about 10% even on a mm s c a l e . This was discovered by using l a s e r d i f f r a c t i o n by u l t r a s o n i c waves.
Another s t r i k i n g f e a t u r e of sound propagation i n aerogels is the decrease of e l a s t i c con- s t a n t s by nearly 20% upon external uniaxial s t r e s s i n g with loads of 6
.
l o 4 N m-= ( f i g . 3 ) . This e f f e c t can be explained with "knee-
bending" deformation of the microstructure. I n such a configuration the restoring forces become weaker with decreasing angle between the legs.An e f f e c t which, on a macroscopic s c a l e , is known a s water induced g l a s s cracking 1 4 1 , may a l s o occur on a microscopic s c a l e i n s t r e s s e d aerogels. This can be concluded from s t a t i c compression measurements with hydrophilic aerogels: a constant small s t r e s s ( 3 lo3 N m-2) leads t o creeping with exponentially decreasing velocity; v i r t u a l l y non
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limited creeping is observed f o r l a r g e r s t r e s s e s (6.
l o 4 N m-2). The t y p i c a l r a t e of r e l a t i v e decrease of length is lower thanlo-'
h-'.An i n t e r e s t i n g question is the influence of "trapped" a i r on the sound velocity. A s can be seen from f i g . 4 t h e experimental data excelently f i t the t h e o r e t i c a l curves calculated assuming isothermal compression of a i r within t h e pore space 121.
Fig. 3. E l a s t i c modulus c l x versus external Fig. 4. Relative change of sound v e l o c i t i e s c, s t r e s s p,,, ( p = 100 kg rn-'). The upper d a t a and c, versus gas pressure p, f o r a p = 105 p o i n t s a r e derived from t h e loading, t h e kg m-' aerogel. The s o l i d l i n e s represent the lower from the unloading phase. t h e o r e t i c a l curves f o r isothermal compression.
2.2 Sintered Aerogels
For production of s i n t e r e d SiO, aerogels with predictable density a s e r i e s of heating cycles were applied t o pieces of one s e l e c t e d aerogel t i l e . I n f i g . 5 the density v a r i a t i o n with s i n t e r i n g time and temperature a s parameter i s depicted. The observed density increase i s
/
l i n e a r i n time, suggesting a cdnstant s i n t e r i n g r a t e a t each temperature. If an Arrhenius law is assumed, where the r a t e i s proportional t o exp ( - AE / kT), the a c t i v a t i o n energy AE can be derived; here we get AE = (2.2 5 0.3) eV ( f i g . 6 ) . This is comparable t o a value of 2.8 eV found f o r s i n t e r i n g aerogels i n a steam environment 151.
Fig. 5 . Density p of sintered aerogels versus time t , with temperature 3 a s a parameter.
Fig. 6 . Sintering rate r versus
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1 / kT (Arrhenius p l o t ) . The rates r are derived from the slopes i n Fig. 5 .Using the specimens from the above sintering procedure we performed ultrasonic velocity measurements for longitudinal and transverse sound propagation. From these data we calculated the elastic moduli cll and c,, between p = 150 and 750 kg m-'. These moduli are shown to scale with density (scaling exponents
a
= 3.18 t 0 . 0 4 and 3.09+
0 . 0 4 ; respectively, see fig. 7 ) .Fig. 7 . Elastic moduli c,, and c,, versus density p of sintered aerogels. The scaling expo- nents are equal withiqtheir error limits (a = 3 . 1 8
+
0 . 0 4 and 3.09+
0 . 0 4 , respectively);The data points for densities above 600 kg m-' are not included in the fit, as in these cases surface roughness prevented accurate sound velocity measurements.
Remarkably, the deviation from the straight lines which represent the least squares fits is very small, compared with those in fig. 2. Still open is the scaling behavior of sintered aerogels with other initial densities.
Generally sintered aerogels show elastic constants which are up to two times higher than for untreated aerogels of the same density.
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OutlookA variety of phenomena and parameters still need be investigated:
creeping of heat treated and evacuated specimens
local variations of sound velocity in a large variety of differently produced aerogels ultrasonic attenuation from audio to ultra high frequencies
sintering behavior under systematic variation of initial density.
REVUE DE PHYSIQUE APPLIQUEE
Acknowledgement
This work was supported by t h e German Bundesministerium f i i r Forschung und Technologic (BMFT).
We a r e indebted t o D r . G. Poelz 1 DESY, Hamburg, D r . S. Henning / A i r g l a s s , S t a f f a n s t o r p , Sweden and D r . L. W. Hrubesh / Lawrence Livermore National Lab., Univ. of Cal. a t Livermore, USA f o r generously providing aerogel specimens.
References
/ I / Gronauer, M., Kadur, A. and Fricke, J., Mechanical and Acoustic P r o p e r t i e s of S i l i c a Aerogel, i n : F r i c k e , J . , Aerogels, Springer, B e r l i n 1986.
/ 2 / Gross, J., Reichenauer, G. and Fricke, J., accepted f o r P u b l i c a t i o n i n J. Phys. D.
/ 3 / Reichenauer, G., Fricke, J. and Buchenau, U., Neutron S c a t t e r i n g Study of Low Frequency V i b r a t i o n s i n S i l i c a Aerogels, submitted t o Europhysics L e t t e r s .
/ 4 / Michalske, T. A . , Bunker, B. C . , The Fracturing of Glass, S c i e n t i f i c American 12 (1987) / 5 / I l e r , R. K., The Chemistry of S i l i c a , Wiley 6 Sons Inc., Boston, USA, (1979) 541
