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LIGHT SCATTERING FOR STRUCTURAL INVESTIGATIONS OF SILICA AEROGELS AND
ALCOGELS
A. Beck, O. Gelsen, P. Wang, J. Fricke
To cite this version:
A. Beck, O. Gelsen, P. Wang, J. Fricke. LIGHT SCATTERING FOR STRUCTURAL INVESTIGA-
TIONS OF SILICA AEROGELS AND ALCOGELS. Journal de Physique Colloques, 1989, 50 (C4),
pp.C4-203-C4-208. �10.1051/jphyscol:1989433�. �jpa-00229509�
REVUE DE PHYSIQUE
APPLIQUEE
Colloque C4, Suppl6ment au n 0 4 , Tome 24, avril 1989
LIGHT SCATTERING FOR STRUCTURAL INVESTIGATIONS OF SILICA AEROGELS AND ALCOGELS
A. BECK, 0. GELSEN, P. WANG and J. FRICKE
Physikalisches Institut der Universitat, Am Hubland, 0-8700 Wiirzburg, F.R.G.
Resume : On decrit un appareil de diffusion qui perrnet 1'6tude des gels et des aerogels dans la lumibre visible. Les formules permettant de corriger les resultats pour divers types de gbrn4ries sont explicitees. Nous reportons les resultats de diffusion obtenus pour des aerogels de silice ayant des densites de 71, 105 et 143 Kg/m3 ; les longueurs de correlation ac varient entre 10 et 25nm ; ces valeurs diminuent lorsque la densite augmente. Nous reportons aussi les resultats de diffusion de lumiere realises tors de la transformation sol-gel.
Abstract
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A scattering apparatus is described which allows the investigation of gels and aerogels with visible light. The correction formulas for various typical geometries are derived. Scattering data for silica aerogels with densities 71, 105 and 143 kg/mA3 are provided; the derived correlation lenghts a, are in the range 10 to 25 nm; they show a systematic decrease with increasing density. We also provide results for light scattering in a sol-gel process.I
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INTRODUCTIONSilica aerogels 11.21 have a wide pore size distribution, with micro, meso and macro porosity. Structural entities below or within the 10 nm range are conveniently investigated by small angle X-ray scattering (SAXS) /3/ and neutron scattering (SANS) 141. Analysis of macroporosity requires values for the momentum transfer in the range Q L it-' and thus very high angular resolution with SAXS and SANS. Small momentum transfer also occurs in light scattering experiments /5/ with access to the range 3-10+ 1-' L Q I 2.10-' 1-' for photons with wavelengths X of 633 nm and scattering into angles 20' < 8 < 160'. A discussion of structural investigations of aerogels has been presented recently 161.
2
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THEORYAn exponential correlation function ~ ( r ) = exp(-r/a,) is assumed to describe the structural fluctuations in density; r is the length of the "measuring stick" and a, the correlation length. This equation can be derived for a two phase medium 1 7 1 . The scattered intensity from such a medium is given by
where Q = 2(2n/h)-sin(812) is the momentum transfer divided by h; 8 is the scattering-angle, A the wavelength within the specimen. If only small deviations from isotropic or Rayleigh scattering is observed, the measured intensities are usually plotted as 1-lI2 versus sin2(8/2) or
--
for small.correlation lengths (a,-Q 9 . 1 )--
as intensity I versus sin2(8/2).This is known as Rayleigh-Gans approximation for which 4n-(n-1)-a, << A holds. n means the relative index of refraction. Froa a, a relation between the averaged spacial extension, a,l and a,,, of the structural entities for the two phases can be derived:
For the two quantities a,% = a,/0* and a,, = a,/$, holds. 0, and 0, are the volume fractions for both phases (0, + 0, = 1).
3
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EXPERIMENTAL ARRANGEMENTThe vertically polarized He-Ne laser beam (A = 633 nn) is chopped before entering the specimen (see fig. 1). The scattered light is monitored via a photodiode systen, which accepts radiation
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989433
REVUE DE PHYSIQUE APPLIQUEE
PoIarizer
Laser
A
Lens
Fig. 1
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Experimental arrangement with specimen, laser beam and detector system.within an angle of about 2" and rotates about the fixed point P. The angular position of the detector controlled by computer can be varied from 6 = 170" through 0 = 0' towards negative angles in steps of 0 . 5 ' . The electronic signal from the scattered and transmitted intensity, respectively, is fed into a lock-in amplifier.
4
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CORRECTIONS FOR THE DETECTED SCATTERED INTENSITY 4.1-
TILE GEOMETRYThe scattered intensity from specimens with tile geometry has to be corrected for a series of effects (see fig. 2):
r the laser beam is attenuated due to the extinction coefficient E on its way through the aerogel tile;
the laser beam has a width 2w; thus photons being emitted from the front parts of the scattering volume have a shorter path length within the specimen.
r the scattered radiation has to pass through parts of the tile before reaching its surface (and then the detector); this causes an attenrration which is strongly dependent on the scattering angle 0 ;
the length (generally the shape) of the viewed scattering volume changes dramatically with 6.
8 due to the refraction at the aerogel-air-interface the position P' of the actual scattering volume is changed (for 0' < 0 ' < 90' beam-downward and for 90" < 6' < 180' beam-upward); apparently the scattered intensity is emitted from the fixed point P.
. . . . . .
...pi..P"... 0
!. . .
laser bea m
. .
Fig. 2
-
Scattering geometry witbin an aerogel tile. The scattering area is determined by the overlap between the laser beam and the viewing range of the detector. The shape of the scattering area dependents strongly on the scattering angle 6 (or 0 ' ) .The angular dependence of the detected signal f(6) for an isotropically scattering specimen
i s d e r i v e d from summation of t h e s c a t t e r e d i n t e n s i t i e s o v e r t h e i l l u m i n a t e d viewing range:
with x = x ' + d - H ( 0 ) ,
H(8) = l / t a n 0
-
~ o s 0 / ( n ~ - c o s ~ ~ ) ' / ~ ,x,,, = - b / ( 2 - s i n B ) + y I t a n 0 and x,, = b / ( 2 - s i n 0 ) + yItan0.
A f t e r i n t e g r a t i o n and f o r E b / ( 2 - s i n e )
*
1 and Ewg(0) << 1 we g e t4-K(0)
where D(0) = and
n - [ K ( 0 ) / n + 1
l 2
The i n v e r s e of t h i s r a t i o i s shown i n f i g . 3 f o r t y p i c a l e x t i n c t i o n v a l u e s of h i g h l y t r a n s p a r e n t a e r o g e l t i l e s (E = 10 m-'f. Due t o t h e f a c t o r l / s i n 0 , one observes a dramatic
scattering angle
€3Fig. 3 - C o r r e c t i o n f u n c t i o n s f o r c y l i n d e r geometry ( 1 ) and t i l e geometry ( 2 ) ( l e f t o r d i n a t e ) a s w e l l a s f o r p l a t e l e t s ( 3 ) ( r i g h t o r d i n a t e ) , f o r b u l k e x t i n c t i o n c o e f f i c i e n t E = 10 m-', d = 0.002 m , b = 0.008 m, w = 0.0005 m and n = 1.022.
i n c r e a s e of f ( 8 ) / f ( 9 O 0 ) f o r a n g l e s 60" P 0 z 120". I n a d d i t i o n , f(6) i s n o n s y m e t r i c a l with r e s p e c t t o 8 = 90". The t r a n s f o r m a t i o n 8 -> 0 ' ( s e e f i g . 2) i s determined from t h e index of r e f r a c t i o n n of t h e a e r o g e l t i l e :
I t s h o u l d be p o i n t e d o u t t h a t t h e p o l a r i z a t i o n of t h e s c a t t e r e d l i g h t always h a s t o be p e r p e n d i c u l a r t o t h e s c a t t e r i n g plane. Neglect of t h i s requirement can cause erroneous s c a t t e r i n g p a t t e r n s .
4.2
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CYLINDER GEOMETRYI n t h i s c a s e t h e c o r r e c t i o n procedure.of t h e d e t e c t e d l i g h t s i g n a l i s simpler ( s e e f i g . 4 a ) .
(24-206 REVUE DE PHYSIQUE APPLIQUEE
F o r w << r t h e r e m a i n i n g c o r r e c t i o n s a r e g i v e n a s f o l l o w s -Eb/sinO
f ( 9 0 ° ) - E b / 2 - ( 1 - l / s i n e ) -1-e
- - 8-Ew s i n e + c o s 8 - 1
- e
-
(1---
f ( 0 ) 3n s i n e i .
1-e -Eb
T h i s e q u a t i o n i s d e p i c t e d i n f i g . 3 . A s c a n b e s e e n t h e d i f f e r e n c e s between t h e t i l e and t h e c y l i n d e r geometry become n o t i c e a b l e o n l y f o r 0 < 60' and 0 > 120".
4.3
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PLATELETSI n t h i s c a s e ( s e e f i g . 4 b ) t h e w i d t h b f o r t h e d e t e c t e d r a d i a t i o n was always chosen l a r g e
scattering specimen
'<f ' detector
scattering specimen
h/
vY
d e t e c t o rF i g . 4a - C y l i n d e r s c a t t e r i n g geometry; F i g . 4b
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P l a t e l e t s c a t t e r i n g geometry;enough i n o r d e r t o view t h e t o t a l s c a t t e r i n g volume. I f t h e s u r f a c e i s smooth and d o e s n o t c o n t r i b u t e t o s c a t t e r i n g p r o c e s s e s , t h e c o r r e c t i o n f u n c t i o n becomes
T h i s c o r r e c t i o n i s shown i n f i g . 3 . C r i t i c a l a r e t h e s c a t t e r i n g a n g l e s between
80' < < 120" upon approach of 8 '
'
01,,,,-, w i t he',,,,.
b e i n g t h e a n g l e of t o t a lr e f l e c t i o n w i t h i n t h e specimen.
I n p r i n c i p l e a l l 3 t e c h n i q u e s a r e e q u i v a l e n t and ought +.o g i v e t h e same s c a t t e r i n g d i s t r i b u t i o n . However, t h e p l a t e l e t geometry i s t h e most c r i t i c a l o n e , i f b u l k e f f e c t s a r e t o be s t u d i e d . I n t h i s c a s e t h e l a s e r beam p e n e t r a t e s t h e s u r f a c e s e c t i o n , which i s w i t h i n t h e d e t e c t o r viewing r a n g e , and t h u s s u r f a c e s c a t t e r i n g w i l l mask t h e weak volume s c a t t e r i n g c o n t r i b u t i o n . T h i s h o l d s e s p e c i a l l y upon approach of t h e a n g l e of t o t a l r e f l e c t i o n .
5
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MEASUREMENTS AND DISCUSSIOFS u p e r c r i t i c a l d r y i n g 181 of a l c o g e l s a l l o w s t h e p r o d u c t i o n of e x t r e m e l y p o r o u s s o l i d b o d i e s of SiO, ( p o r o s i t y up t o 98%) / 9 / . The h i g h - q u a l i t y t r a n s p a r e n t a e r o g e l s p e c i m e n s produced a t DESY (Hamburg) and Lund (Sweden) from TMOS ( T e t r a m e t h o x y s i l a n ) u n d e r b a s i c c o n d i t i o n s a r e mainly R a y l e i g h s c a t t e r e r s and t h e r e f o r e show a more o r l e s s i s o t r o p i c s c a t t e r i n g p a t t e r n . The o b s e r v e d s l o p e s ( s e e f i g . 5 ) i n a v e r s u s s i n 2 e / 2 p l o t d e r i v e d from a t i l e geometry t h u s a r e g e n e r a l l y v e r y s m a l l . Under c l o s e o b s e r v a t i o n , however, we o b s e r v e a s y s t e n a t i c d e c r e a s e
Fig. 5
-
Scattering behavior of monolithic aerogels produced unaer basic conditions; the data sets belong to the densities p n 71 kg/m3 ( + ) p 2 105 kg/m3 ( 0 ) and p'
143 kg/m3(Dl; the corresponding correlation lengths are a, = 23 nm, 17.5 nm and 13.5 nm.
of slope (or correlation length a,) with increasing density. This is plausible, as the sol- gel process for the higher density tiles, i.e. a more concentrated initial TMOS solution can be assumed to start off from more nucleation centers. In this case the number of skeleton- forming "secondary" SiO, particles (diameter a few nm) 161 is higher than for the low- density aerogels. This leads to density fluctuatio~s for the skeleton which occur more frequently and are spacially less extended. We want to point out, that in addition to density also the pH-value and, in general, the detailed recipe for gel formation and supercritical drying influence the transparence.
The scattered intensity increases by about 20 to 40% in our experiments if the scattering angle is changed from 8 = 160" (backward scattering) to 8 = 20° (forward scattering). This is typical for Rayleigh-Gans scattering / 7 / with inhomogeneities a, r X / 2 0 . Our finding thus is in contrast to the strongly enhanced backscattering found in the displayed scattering intensity of reference 151. A possible explanation for the unusual angular intensity profile in /5/ could be intensity changes due to birefringence effects which were not taken into account, which however, are often observed in aerogel tiles. Another explanation could be the neglect of the correction term in equ.(5).
For comparison of the three geometries discussed in the above scattering measurements using the same aerogel sample were performed. As we can see from fig. 6 tile and cylinder geometry provide basicly the same angular scattering pattern. Expected deviations occur for the platelet geometry upon approaching the angle, when the angle of total reflection is approached, and for forward scattering. Obviously large surface inhomogeneities increase the scattering intensity in this angular region.
internal scattering angle 8
Fig. 6
-
Scattering intensity I versus internal scattering angle 0 for tile(a),
cylinder( 0 ) and platelet ( + ) geometry.
We also investigated the sol-gel transition in a TEOS-ethanol-water solution / l o / . Most evident is the strong forward scattering. resulting from inpuriti1es. In the sol-gel process
the scattering intensity increases over the total observed Q range. Use of equ.(l) allows to extract a correlation length a, a 20 nm, which remains constant for all times after gelation. We conclude that the spatial extend of the formed network has to remain fixed.
Only the density contrast increases after gelation (aging).
Fig. 7
-
Change of scattered intensity I of a gelling TEOS-solution with time versus momentum transfer; time after mixing:a
= 0.5 h, 0 = 3.8 h , O = 6.6 h,+=
8.3 h, X = 3 dand A = 6 d.
6
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OUTLOOKThe constructed scattering apparatus is currently used to investigate granular aerogels as well as alcogels and gelling solutions. For these studies also a 320 nm He-Cd laser is employed. As the extinction mechanism is Rayleigh scattering a dramatic variation of E with wavelength A is expected : E
-.
l/X4. We want to point out that for these investigations with visible light a prerequisite is a size of the structural entities which is at least of the order of XI60 s 10 nm. This.means for example that the growth of nm particles in a gelling solution cannot be dete'cted with visible light (however with SAXS or SANS). However, the growth of large particles as in base-catalysed (ammonia concentration about 0.085 mol/l) sol-gel transitions is conveniently investigated with light scattering. The same holds for aging processes.REFERENCES
Fricke, J., Scientific American, May issue, (1988) 92
Fricke, J., Aerogels
-
a Fascinating Class of High-
Performance Porous Solids, in : Aerogels, Springer Proc. in Physics6 ,
Ed. J. Fricke, Springer Verlag, Berlin, Heidelberg, New York, Tokyo, (1986) 2Schaefer, D.W., Martin, J.E., Hurd, A.J., and Keefer, K.D., Structure of Randon Materials, in : Physics of Finely Divided Matter, Spring Proc'. in Physics
5 .
N. Boccara and M. Daoud (Eds), Springer Verlag Heidelberg (1985)
Sinha, S.H., Freltoft, T., and Kjems, J., Observation of Power Law Correlations in Silica-Particle Aggregates by Small-Angle Neutron Scattering, in : Kinetics of
Aggregation and Gelation, F: Family, D.P. Landau (Eds) Elsevier Sc. Publ. London (1984) Hunt, A.J., and Berdahl, P., Mat. Res. Soc. (1984) 275
Fricke, J., and Reichenauer, G., J. Non Cryst. Solids 9_5 &
96
(1987) 1135 Kerker, M., The Scattering of Light, Academic Press, New York and London (1986) Kistler, S.S., Nature 1 2 7 (1931) 741Poelz, G., Aerogels in High Energy Physics, in: Aerogels, Springer Proc. in Physics
6 .
J, Fricke (Ed), Springer Verl. Berlin Heidelberg, New York Tokyo (1986) 176
Mulder, C.A.M., and van Lierop, J.G., Preparation, Densification and Characterization of Autocalve Dried SiO, Gels, in: Aerogels, Springer Proc. in Phys.
6 ,
J. Fricke (Ed), Springer Verl. Berlin Heidelberg, New York Tokyo (1986) 68Acknowledgements
We would like to thank Dr. G. Poelz/DESY, Hamburg, and Dr. S. HenningIAirglass, Lund for generously providing aerogel samples.
