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Highly ordered microstructure of flocculated aggregates
~ r
~ee
Publishers B.V.,:~
m
-
Printed in The Netherlands
355
ghly.0rdered Microstructure of Flocculated Aggregat K. WONG1,13. CABANr and P. SOMASUNDARAN' 1Henry Krumb .~choo!of Mines, Columbia University, New York, N Y 10027 (U.S.A.) ~C1MT~-I,aboru~toire de Physique des Soffdes, Universite de Paris-Sud, 91405 O r g y (France)
(Received90 Ap~11987. accepted 5 October 1987) ABSTRACT By contrast to recent descriptions of fractal aggregates,we report the struLq~reof non-fractal we m m a highly~ i f o ~ ~ c e on the order of 1-2 particle d~metembetweenparticles in a f l ~ ~ i s a ~ e t short ~ Orderinthe fl?e ~ which is not apparent from macule ~ents of the ~ Co~reely, the ~ of ~ t e s resulting from coagulationby the addition of an inorganic electrolyte (CaCI±) shows no preferred distance between particles. The application of SANS to the study of aggregationby floccelationand coagulation is discussecL
INTRODUCTION Considerable interest exists in t h e structure o f aggegates, both in industrial a n d engineering practice, s u c h as beneficiation o f mineral fines ( S o m a s u n d~ran, 1980), water purification (Axelos e t al., 1985), paper m~king (Pelton, 1986), as well as in a m u l t i t u d e of other fields r a n g i n g from biology (blood clotting a n d aggregation o f fibrin m o n o m e r , ef. Wfltzius et al., 1982; flocculation o f bacteria, cf. T a m s o v a e t al., 1984) to a s t r o n o m y (clusters o f galaxies, cf. Burns, 1986), T h e s t u d y o f solid particle aggregates i s problematic: colloids o f pra.ctical i n t e ~ s t gene~-ally~~fall outside t h e applica_b'di_'.tyloflX-rays t u d i e s ; ox~en m e aggregates are a e n s e masses w m e n a r e opaque ~o ugn~, a n n are u n suitable to be studied macroscopically by s e d i m e n t a t i o n or viscometry. Recently, fractal t h e o r y h a s b e e n very s u ~ f u l l y used to study aggregation. Thi~ type o f analysis is used to give a statistical description t o c e r t a i n t y p e s of aggregates . . (diffusion . . . limited . . aggregation, cluster-cluster aggregat i o n ) a n d thus to distinguish different structures a n d to elucidate t h e m e c h a n i s m of formation ( W i t t e n a n d Cates, 1986). Indeed, the field has b e e n practically dominated b y t h e application o f fractals, a n d one might conclude t h a t aggegation processes which are controlled b y kinetic f a ~ . ~ r.~her ~han 0166-6622/88/~r~)3,50
© 1988 l~L~evier Science Publishers B.V.
.
.
.
.
.
.
I~:!':!~L!~III:~.I!I ~ ~<:i? i~-:~,.i~ii i~i
~,ii .i . j , : . i ~ i:
~
~
i
equilibri,m conditions. ~ g e n e r a l l y lead ~. s ~ e invariant s t r u t , s (Wit~n ~ ~,i.~1); B~ ~ n t ~ s t , we:repo~ in t ~ paper non,fractal aggregates made ~ addition of p o ~ e r tO :a s ~ e n s i o n of particles. i ~
~
METHODS We applied s m ~ a n g l e neutron scattering to study the s t r u ~ of aggregates of s i l i ~ p~icleS' Which:have ~ n flocculated by cationic polyacrylamide~iScatte~d intensities for 0'004 < Q < 0,18 (A - t ) w e ~ m e s s e d On the cRmem PACE 0f the L a b o r a t o ~ Leon B ~ o u i n , SACLAY, France. Here Q is the s c a t t e ~ g vector for a scattering angle of 20 ° with neutron wavelength Jl. Q=2nsine/~
S ~ I ~ c o ~ for sample transmissions, background scattering and detector efficienCies: ~ e particles ~ were of silica made by precipitation (a variation of the method Of Stober et al;, 1968 ) ; t h e y ~ ~ h e r e s of 400 A in djRmeter which, from l i g h t i ~ a t t e ~ g ~ d e l ~ h mic~graphy, showed little polydispemity. The n ~ w s ~ i distribution was ~So e ~ d e n t from a ~ ~ of a dilute suspension of this s i l i ~ i ~ s ~ n ~ Fig' 1, the scattering curve s h o ~ the e ~ p r i m ~ oscillation for spheres: the peak at log Q - - 1 . 5 2 (Q-O.03 A -~ or R~205A*) is the resul~ of the particle form factor, P ( Q ) , i.e. interferences arising from scattering centers from within the sphere. It compares favorably o ACTUAL DATA V HARD SPHERE MODEL
3
tin go
z v~
.-'N .~'1 %
II
%X°
oOO o ° ° e . o,, z. 0 -O.5 J -2.s
-,10 ............. O00ftfl ,
o" ;'.1
0.001 0.0015 Q ~ L ; ~ g ' r I SQUARES) -~.1 ' ~lLq - z~
"1 '
- t . 'T
'
-'L~
LOG Q
l;~g. 1. IsoLated silica spheres m oscillation at large Q (log Q--- - 1.55) indicates spheres diameter is ca 400 A an(] that the sample is very monodisperse(L Hazd-sphere mode! ( 400 _+40 A) shows
goodagreementwith the experimentalresults. Insert: Guinierplot of isolatedspheres; from the slope,the outer radius computed is Ro=205 ~,. *Forordered structures, the distance,D, in real space is inverselyproportional to Q as givenby the Bragg relation, D = 2~ /Q.
357
with a simulation* o f scattering for non-interacting (isolated) spheres of 200+20 A radius. Also from the Guinier plot (insert), the calculated outer radius is 205 A, The floceulant we used, kindiy provided by the Laboratoire de Physico Chimie (Ecole Superieurede Physico-Chimie Industrielle, Paris)m.~ co,polymer of a c r y l ~ d e and trimethy}Aminoethyl acrylate (~ tool.%), w i t h a molecular weight of ca 1.73< 10 e daltons, henceforth "PAM5% +"; Thus the co-polymer is slightly cationic and can adsorb to the negatively charged silica surface. Preparation of the floc ~ p l e s made with polymer consists of shaking vigorously ( 1 0 s).ca 1 m g :PAM5%÷ per m 2 silica; the floe which sediments immediately is then transferred to the irradiation cell. Preliminary results suggest that neither polymer concentration (ca 150-1500 ppm) nor handling of the floc alter the structure at the scale of d i s ~ c e s accessible With this c-mera. These samples are prepared immediately before the measurement. T h e coagulated ~qmple is made by adding CaCI2 (44 raM) to a suspension of spheres; this is left overnight, then measured. RESULTS
Figure 2 shows a typical log-log scattering spectrum of a floc. Two peaks in intensity are observed. Beginning at large Q, a "subsidiary" peak (log 3"
O 0
o o 0°[~000
2-
eo D
~t~q3
OD
au
~ 0 O
°°ooo -1
~
-2
-2.5 '-2'.3
|
t
-2.1
m
-i~9
i
-1.~/ ~"-1~5 LOG Q
'-13
-13
'
D
-0.9 '
' -0.'?
Ff~. 2- ~ 1 ~ o f silica made with cationic polyacryl-mide (5%) ca 1 mg m - 2 , natural p H (7.4). Oscillation at low Q (log Q = - 1.9) indicates highly ordered structure in floc with preferred nearest neighbor distance on the order of 1-1.5 diameters.
*The scattering I~ (Q) for a sphere of radius R and volume V, and differences of scattering length density p is given by Rayleigh (1911) as
F~.mQR- QR co~QR]~
I,(Q)=p2v2L"
~
J
358 Q = - 1 . 5 2 ) emerges f r o m typical Q - 4 behavior in the Porod region; it corresponds to t h e same i n t r ~ - p ~ l e ~ a k as seen i n t h e spectvlm for free spheres. Indeed this is anticipated since aggregation o f this type should n o t change t h e particles shape n o r size. T h e peak at low Q (log Q = - 1 . 9 2 ) results from interferences between objects which are ca 520 A apart: the distance corresponds to the center to center distance between spheres*. Continuing from large to small Q, the subsequent decrease in i n t e n s i t y and intensity r n i n i r n . m (Ca log Q = - 2.2 ) indicates t h a t there are certain positions in space with respect to a reference sphere w h i c h are "forbidden" to o t h e r spheres, i.e. there are uniformly void region between the spheres. Finally, ~he increase at small Q suggests t h a t t h e overall d;mension for t h e scattering objects are very large, b e y o n d the longest distance seen in this experiment. Negatively charged siliCa particles can be coagulated using inorganic electrolytes. T h e spectrum for an a g g ~ g a t e formed by coagulation with CaCI~ is given in Fig. 3. It can be seen t h a t t h e intra-particle peak is still clearly observable at the high Q end, however t h e absence of a n Gs~illation in the low Q region indicates t h a t t h e r e is no preferred distance between particles. Clearly J 3.0 Q
0 (3 0
t- 2.0
0 D
Z
0
01~
z
D O o
,.I
1.0
0
0.0 -0.5
,
-2.5
- 2.5
,
- ,
.
- 2.1
-1.9 LOG
,
.
-1,1'
,
,
-1.5
Q
Fig. 3. Silica coagulated with CaCl~ (44 raM). Absence of an oscillation at intermediate Q shows reduction in short range structural oxder for aggregates made with -;norganic electrolyte. Apparent fractal behavior at large scale (low Q). *The completv structural description is given by the pair-pair correlation function, g ( r ) , which is the fourier transform of the structure factor S(Q), g(r):
S R(Q) exp (-iQr) d3Q --oD
359
the microstructure of these aggregates is different from those resulting by flocculation with polymer. The log I versus log Q plot is nearly linear at small angles: thus it is tempting to speculate t h a t at a larger scale of distances the system van be described by a fractal exponent. However, such considerations may only be addressed when measurements have been extende~ to lower Q. DISCUSSION
Strikingly different spectra result from aggregates made by flocculation with this polymer and by coagulation with salt. Dissimilar structures may, therefore, be attributed to t he aggregates, and subsequently different mechanisms may be h ~ o t h e s i z e ~ According to current models, coagulation and flocculation are the two main categories of aggregation. Thus it is of interest to r~concile the data with these models. Coagulation is mediated by salt (or concentration changes in the potential determining ions); it results from compression of the double layer, subsequent dominance of van der Waals attxactive forces a n d ultimately destabili~ation of the suspension. Recent spectroscopic work has exclusively studied coagulation. Scale im,ariant synvme~ry with fractul exponents (for an euclidean dimension of 2) varying from 1.5 (ghost model of Ball, 1984), 1.75 (Weitz, 1984). 2.08 (Cannell and Aubert, 1986), to 2.12 (Schaeffer et al., 1984) have been found, and in general the work has s u ~ p o r t ~ diffusion limited an d cluster-cluster aggregation models. On the other hand, flocculation of particles in suspension by adsorption of organic polymers is widely accepted to be either "physical" (bridging) or electrical (charge neutr~li~stion as above in the case of salts ). The forme~ model and variations on it (patchwork bridgin~ Gregory, 1973; Sato and Ruch, 1980; Mabire et al., 1984), envisions long polymer arms attaching to the surface of particles and gathering them into a voltlme which is a fraction of the original. Aggregation by flocculation -~ generally very rapid and largely irreversible by simple dilution. The spectra in Figs 2 and 3 indicate dissimilar structures in the samples. With two such different mechanisms operational in flocculation and coagulation, this is perhaps expecte~ However, it is quite surprising t h a t flocs show such regular short order structure as evidenced in the inter-particle peak for the scattering curve. Whether structural order of this type proves to be a fea~ r e unique to flocs, the consequences it has on possible subsequent fractal behavior and finally its effect on macroscopic properties of the material, are areas which remain to be understoocL The ability to observe flocculation at the microscopic level enables us to ask several questions about the process, which has, thus far, only been possible indirectly, if at all. Among these are, what is the role of polymer (chain length, type of interaction with particle), of particle (charge, sir ~~ ~,~ solution prop-
360
er~ies o n t h e s t r u c t u r e o f a fioc_, F t t r t h e r m o r e , t h e e a s e w i t h w h i c h t h e c u r r e n t models of ~ o ~ ~ n ~ t ~ m c ~ . ~ t e t h e s e n e w ~ f o r m a t i o n s will b e a t e s t o f their validity andllmlts. ACKlqOI~TIr.I~J~EME~Yr P,S, and ILW. wish to thenk the National Science Foundation for its financ e d assi ce (cPZ-S3-18163).
~ C E S Axelos, M~ Tchoubar, D., Bottero, J.Y. and Fieesinger, F., 1985. J. Phys. ( Paris ). 46: 1587-1593.
B~
e.c 19e4,
J...1986,S c L ~
s, 27: s7. 255:~ 9 .
~ e l L D . a and Aubert~ C'; ~1986' In H ~ Stanley and N. Ostrowski (Eds), Proc. NATO Adv. S~ ~ ~ G ~ ~ d F o ~ VoL 100, pp. 187-197. Gregozy,Jq 1973, J, Coiloid Interfa~ ScL, 4~" 448. Mabire, F , Audebert, P~~ d Quivo~n, C., 1984. J. Colloid Interface Sci., 97: 120-136. Peiton, I~H.~~i986' J, Colloid ~ ScL, 111: 475-485. Ra~ieigh; L , 1911. ~ : R . ~ London Set. A, 84: 25. Schaeffer, D.W,, ~ J.E., W i l ~ P. and Cannell, D.S., 1984. Phys. Rev. Lett., 52: 2371. Sato, T. and Ruth, R., 1980. Surface Science Series. Vol. 9, Marcel Dekker, New York. Somammderan, P. (F_~L),1980. F~ne Particles Prorating, _Am.lust. Min. Metall. Pet. Eng., New York. Stober, W., Fink~ A. and Bohn, E., 1968. J. Colloid Interface Sci., 16: 341. G.V., Teslenko, A.Y~, Lazarenko, E.N. and Alekseeva, V.V., 1984. Kolloidn. Zh., 47: 737-744. Weitz, D ~ and Oliveria, M., 1984. Phys. Rev. Lett., 52: 1433. Wiltzlus, P., Die'.ler, G., Kanzig, W., Haberli, A. and Straub, P.W., 1982. Biopolymers, 21: 2205. Witten, T.A_ and Sander, L.M., 1981. Phys. Hey. Lett., 47: 1400. Witten, T~A.and Cares, M.E., 1985. Science, 232: 1607.
~ee
Publishers B.V.,:~
m
-
Printed in The Netherlands
355
ghly.0rdered Microstructure of Flocculated Aggregat K. WONG1,13. CABANr and P. SOMASUNDARAN' 1Henry Krumb .~choo!of Mines, Columbia University, New York, N Y 10027 (U.S.A.) ~C1MT~-I,aboru~toire de Physique des Soffdes, Universite de Paris-Sud, 91405 O r g y (France)
(Received90 Ap~11987. accepted 5 October 1987) ABSTRACT By contrast to recent descriptions of fractal aggregates,we report the struLq~reof non-fractal we m m a highly~ i f o ~ ~ c e on the order of 1-2 particle d~metembetweenparticles in a f l ~ ~ i s a ~ e t short ~ Orderinthe fl?e ~ which is not apparent from macule ~ents of the ~ Co~reely, the ~ of ~ t e s resulting from coagulationby the addition of an inorganic electrolyte (CaCI±) shows no preferred distance between particles. The application of SANS to the study of aggregationby floccelationand coagulation is discussecL
INTRODUCTION Considerable interest exists in t h e structure o f aggegates, both in industrial a n d engineering practice, s u c h as beneficiation o f mineral fines ( S o m a s u n d~ran, 1980), water purification (Axelos e t al., 1985), paper m~king (Pelton, 1986), as well as in a m u l t i t u d e of other fields r a n g i n g from biology (blood clotting a n d aggregation o f fibrin m o n o m e r , ef. Wfltzius et al., 1982; flocculation o f bacteria, cf. T a m s o v a e t al., 1984) to a s t r o n o m y (clusters o f galaxies, cf. Burns, 1986), T h e s t u d y o f solid particle aggregates i s problematic: colloids o f pra.ctical i n t e ~ s t gene~-ally~~fall outside t h e applica_b'di_'.tyloflX-rays t u d i e s ; ox~en m e aggregates are a e n s e masses w m e n a r e opaque ~o ugn~, a n n are u n suitable to be studied macroscopically by s e d i m e n t a t i o n or viscometry. Recently, fractal t h e o r y h a s b e e n very s u ~ f u l l y used to study aggregation. Thi~ type o f analysis is used to give a statistical description t o c e r t a i n t y p e s of aggregates . . (diffusion . . . limited . . aggregation, cluster-cluster aggregat i o n ) a n d thus to distinguish different structures a n d to elucidate t h e m e c h a n i s m of formation ( W i t t e n a n d Cates, 1986). Indeed, the field has b e e n practically dominated b y t h e application o f fractals, a n d one might conclude t h a t aggegation processes which are controlled b y kinetic f a ~ . ~ r.~her ~han 0166-6622/88/~r~)3,50
© 1988 l~L~evier Science Publishers B.V.
.
.
.
.
.
.
I~:!':!~L!~III:~.I!I ~ ~<:i? i~-:~,.i~ii i~i
~,ii .i . j , : . i ~ i:
~
~
i
equilibri,m conditions. ~ g e n e r a l l y lead ~. s ~ e invariant s t r u t , s (Wit~n ~ ~,i.~1); B~ ~ n t ~ s t , we:repo~ in t ~ paper non,fractal aggregates made ~ addition of p o ~ e r tO :a s ~ e n s i o n of particles. i ~
~
METHODS We applied s m ~ a n g l e neutron scattering to study the s t r u ~ of aggregates of s i l i ~ p~icleS' Which:have ~ n flocculated by cationic polyacrylamide~iScatte~d intensities for 0'004 < Q < 0,18 (A - t ) w e ~ m e s s e d On the cRmem PACE 0f the L a b o r a t o ~ Leon B ~ o u i n , SACLAY, France. Here Q is the s c a t t e ~ g vector for a scattering angle of 20 ° with neutron wavelength Jl. Q=2nsine/~
S ~ I ~ c o ~ for sample transmissions, background scattering and detector efficienCies: ~ e particles ~ were of silica made by precipitation (a variation of the method Of Stober et al;, 1968 ) ; t h e y ~ ~ h e r e s of 400 A in djRmeter which, from l i g h t i ~ a t t e ~ g ~ d e l ~ h mic~graphy, showed little polydispemity. The n ~ w s ~ i distribution was ~So e ~ d e n t from a ~ ~ of a dilute suspension of this s i l i ~ i ~ s ~ n ~ Fig' 1, the scattering curve s h o ~ the e ~ p r i m ~ oscillation for spheres: the peak at log Q - - 1 . 5 2 (Q-O.03 A -~ or R~205A*) is the resul~ of the particle form factor, P ( Q ) , i.e. interferences arising from scattering centers from within the sphere. It compares favorably o ACTUAL DATA V HARD SPHERE MODEL
3
tin go
z v~
.-'N .~'1 %
II
%X°
oOO o ° ° e . o,, z. 0 -O.5 J -2.s
-,10 ............. O00ftfl ,
o" ;'.1
0.001 0.0015 Q ~ L ; ~ g ' r I SQUARES) -~.1 ' ~lLq - z~
"1 '
- t . 'T
'
-'L~
LOG Q
l;~g. 1. IsoLated silica spheres m oscillation at large Q (log Q--- - 1.55) indicates spheres diameter is ca 400 A an(] that the sample is very monodisperse(L Hazd-sphere mode! ( 400 _+40 A) shows
goodagreementwith the experimentalresults. Insert: Guinierplot of isolatedspheres; from the slope,the outer radius computed is Ro=205 ~,. *Forordered structures, the distance,D, in real space is inverselyproportional to Q as givenby the Bragg relation, D = 2~ /Q.
357
with a simulation* o f scattering for non-interacting (isolated) spheres of 200+20 A radius. Also from the Guinier plot (insert), the calculated outer radius is 205 A, The floceulant we used, kindiy provided by the Laboratoire de Physico Chimie (Ecole Superieurede Physico-Chimie Industrielle, Paris)m.~ co,polymer of a c r y l ~ d e and trimethy}Aminoethyl acrylate (~ tool.%), w i t h a molecular weight of ca 1.73< 10 e daltons, henceforth "PAM5% +"; Thus the co-polymer is slightly cationic and can adsorb to the negatively charged silica surface. Preparation of the floc ~ p l e s made with polymer consists of shaking vigorously ( 1 0 s).ca 1 m g :PAM5%÷ per m 2 silica; the floe which sediments immediately is then transferred to the irradiation cell. Preliminary results suggest that neither polymer concentration (ca 150-1500 ppm) nor handling of the floc alter the structure at the scale of d i s ~ c e s accessible With this c-mera. These samples are prepared immediately before the measurement. T h e coagulated ~qmple is made by adding CaCI2 (44 raM) to a suspension of spheres; this is left overnight, then measured. RESULTS
Figure 2 shows a typical log-log scattering spectrum of a floc. Two peaks in intensity are observed. Beginning at large Q, a "subsidiary" peak (log 3"
O 0
o o 0°[~000
2-
eo D
~t~q3
OD
au
~ 0 O
°°ooo -1
~
-2
-2.5 '-2'.3
|
t
-2.1
m
-i~9
i
-1.~/ ~"-1~5 LOG Q
'-13
-13
'
D
-0.9 '
' -0.'?
Ff~. 2- ~ 1 ~ o f silica made with cationic polyacryl-mide (5%) ca 1 mg m - 2 , natural p H (7.4). Oscillation at low Q (log Q = - 1.9) indicates highly ordered structure in floc with preferred nearest neighbor distance on the order of 1-1.5 diameters.
*The scattering I~ (Q) for a sphere of radius R and volume V, and differences of scattering length density p is given by Rayleigh (1911) as
F~.mQR- QR co~QR]~
I,(Q)=p2v2L"
~
J
358 Q = - 1 . 5 2 ) emerges f r o m typical Q - 4 behavior in the Porod region; it corresponds to t h e same i n t r ~ - p ~ l e ~ a k as seen i n t h e spectvlm for free spheres. Indeed this is anticipated since aggregation o f this type should n o t change t h e particles shape n o r size. T h e peak at low Q (log Q = - 1 . 9 2 ) results from interferences between objects which are ca 520 A apart: the distance corresponds to the center to center distance between spheres*. Continuing from large to small Q, the subsequent decrease in i n t e n s i t y and intensity r n i n i r n . m (Ca log Q = - 2.2 ) indicates t h a t there are certain positions in space with respect to a reference sphere w h i c h are "forbidden" to o t h e r spheres, i.e. there are uniformly void region between the spheres. Finally, ~he increase at small Q suggests t h a t t h e overall d;mension for t h e scattering objects are very large, b e y o n d the longest distance seen in this experiment. Negatively charged siliCa particles can be coagulated using inorganic electrolytes. T h e spectrum for an a g g ~ g a t e formed by coagulation with CaCI~ is given in Fig. 3. It can be seen t h a t t h e intra-particle peak is still clearly observable at the high Q end, however t h e absence of a n Gs~illation in the low Q region indicates t h a t t h e r e is no preferred distance between particles. Clearly J 3.0 Q
0 (3 0
t- 2.0
0 D
Z
0
01~
z
D O o
,.I
1.0
0
0.0 -0.5
,
-2.5
- 2.5
,
- ,
.
- 2.1
-1.9 LOG
,
.
-1,1'
,
,
-1.5
Q
Fig. 3. Silica coagulated with CaCl~ (44 raM). Absence of an oscillation at intermediate Q shows reduction in short range structural oxder for aggregates made with -;norganic electrolyte. Apparent fractal behavior at large scale (low Q). *The completv structural description is given by the pair-pair correlation function, g ( r ) , which is the fourier transform of the structure factor S(Q), g(r):
S R(Q) exp (-iQr) d3Q --oD
359
the microstructure of these aggregates is different from those resulting by flocculation with polymer. The log I versus log Q plot is nearly linear at small angles: thus it is tempting to speculate t h a t at a larger scale of distances the system van be described by a fractal exponent. However, such considerations may only be addressed when measurements have been extende~ to lower Q. DISCUSSION
Strikingly different spectra result from aggregates made by flocculation with this polymer and by coagulation with salt. Dissimilar structures may, therefore, be attributed to t he aggregates, and subsequently different mechanisms may be h ~ o t h e s i z e ~ According to current models, coagulation and flocculation are the two main categories of aggregation. Thus it is of interest to r~concile the data with these models. Coagulation is mediated by salt (or concentration changes in the potential determining ions); it results from compression of the double layer, subsequent dominance of van der Waals attxactive forces a n d ultimately destabili~ation of the suspension. Recent spectroscopic work has exclusively studied coagulation. Scale im,ariant synvme~ry with fractul exponents (for an euclidean dimension of 2) varying from 1.5 (ghost model of Ball, 1984), 1.75 (Weitz, 1984). 2.08 (Cannell and Aubert, 1986), to 2.12 (Schaeffer et al., 1984) have been found, and in general the work has s u ~ p o r t ~ diffusion limited an d cluster-cluster aggregation models. On the other hand, flocculation of particles in suspension by adsorption of organic polymers is widely accepted to be either "physical" (bridging) or electrical (charge neutr~li~stion as above in the case of salts ). The forme~ model and variations on it (patchwork bridgin~ Gregory, 1973; Sato and Ruch, 1980; Mabire et al., 1984), envisions long polymer arms attaching to the surface of particles and gathering them into a voltlme which is a fraction of the original. Aggregation by flocculation -~ generally very rapid and largely irreversible by simple dilution. The spectra in Figs 2 and 3 indicate dissimilar structures in the samples. With two such different mechanisms operational in flocculation and coagulation, this is perhaps expecte~ However, it is quite surprising t h a t flocs show such regular short order structure as evidenced in the inter-particle peak for the scattering curve. Whether structural order of this type proves to be a fea~ r e unique to flocs, the consequences it has on possible subsequent fractal behavior and finally its effect on macroscopic properties of the material, are areas which remain to be understoocL The ability to observe flocculation at the microscopic level enables us to ask several questions about the process, which has, thus far, only been possible indirectly, if at all. Among these are, what is the role of polymer (chain length, type of interaction with particle), of particle (charge, sir ~~ ~,~ solution prop-
360
er~ies o n t h e s t r u c t u r e o f a fioc_, F t t r t h e r m o r e , t h e e a s e w i t h w h i c h t h e c u r r e n t models of ~ o ~ ~ n ~ t ~ m c ~ . ~ t e t h e s e n e w ~ f o r m a t i o n s will b e a t e s t o f their validity andllmlts. ACKlqOI~TIr.I~J~EME~Yr P,S, and ILW. wish to thenk the National Science Foundation for its financ e d assi ce (cPZ-S3-18163).
~ C E S Axelos, M~ Tchoubar, D., Bottero, J.Y. and Fieesinger, F., 1985. J. Phys. ( Paris ). 46: 1587-1593.
B~
e.c 19e4,
J...1986,S c L ~
s, 27: s7. 255:~ 9 .
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