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Light scattering characterization of laporite sols
Light Scattering Characterization of Laponite Sols L. ROSTA* AND H. R. VON G U N T E N * ' t '1 * Radiochemisches Laboratorium, Universitdt Bern, CH-3000 Bern 9, Switzerland; and t Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland Received December 9, 1988; accepted May 2, 1989 The structure and dynamics of dilute Laponite RD sols were studied by static and dynamic light scattering. From the scattered light intensities the particle molecular weight was derived to be 3000 _+ 500 kg/mol. The static structure factor S depended very slightly on the scattering angle, but decreased rapidly with Laponite concentration in dilute sols, indicating long-range particle interactions. Collective diffusion coefficients Dc were determined by slope analysis of the autocorrelation functions. A combination of light scattering data with membrane filtration and electron microscopy suggests the existence oftactoids containing between two and four Laponite platelets with an average diameter of 30 _+ 10 nm. Variations of the electrolyte content (0 ~< [KC1] ~< 0.0025 M ) and of the Laponite concentration (0.025 ~< c ~< 5.0 g/liter ) of the sols allowed a systematic evaluation of the collective friction. Hard-body and electrostatic contributions to friction were determined and showed that electrostatic friction retards collective diffusion significantly. © 1990AcademicPress,Inc. INTRODUCTION
Because of its purity and easy dispersibility in water Laponite appears to be an ideal substance to investigate the properties of swelling clays in aqueous solutions. Laponite is a synthetic clay, belonging to the family of trioctahedral smectites with structure and composition similar to those of hectorites. Central positions in the octahedral sheets are occupied by divalent magnesium ions, some of which are replaced by monovalent lithium. As a result, suspended particles carry negative charges which are compensated by exchangeable cations. Early work (1) on the flocculation of Laponite in aqueous electrolytes has been extended by Perkins et al. (2). These authors interpreted turbidity and capillary data in terms of critical coagulation concentrations of various electrolytes and as a function of pH. In another study (3), the electrical properties of aqueous Laponite sols were investigated by conductivity and permittivity measurements. I TO whom all correspondence should be addressed.
It was concluded that the most probable structural unit in the suspension is a network of edge-to-face and edge-to-edge associated platelets ("card-house structure") with an equivalent spherical diameter of 0.7 ~m. By contrast, it has been argued recently (4), based on static and dynamic light scattering and small angle neutron scattering, that Laponite particles are present in water as single disklike units with an average disk diameter of about 30 nm. Yet another structural model was proposed by Fripiat and co-workers (5), who investigated the thermodynamic properties of adsorbed water layers on Laponite, among other clays, by means of calorimetric and nuclear magnetic resonance techniques. Heats of immersion as well as proton relaxation rates have demonstrated the presence of parallel, closely spaced platelets, so-called tactoids, separated by a few water layers. In light of the importance of clays in agricultural and industrial applications (2), we felt it worthwhile to further investigate some properties of Laponite sols. To elucidate on the validity of the proposed structural models
397 Journal of Colloidand InterfaceScience, Vol. 134,No. 2, February 1990
0021-9797/90 $3.00 Copyright© 1990by AcademicPress,Inc. All rightsof reproductionin any formreserved.
398
ROSTA
AND
we have used light scattering on dilute dispersions. Experiments were carried out at various ionic strengths and Laponite concentrations to estimate the importance of particle interactions and electrostatic friction. The average molar mass M of the particles and the static structure factor S were determined by static light scattering (SLS), whereas the collective diffusion coefficient Dc was derived from the combination of dynamic light scattering (DLS) with membrane filtration. From these parameters the electrostatic contribution to the hydrodynamic friction was evaluated as a function of ionic strength and particle concentration. THEORETICAL
BACKGROUND
Static Light Scattering For vertically polarized light the Rayleigh ratio Rv can generally be expressed in terms of the molecular weight M and concentration c (in g/ml) of spherical colloids,
Rv(q, c) = KcMP(q)S(q, c),
[1]
where the scattering wave vector q is defined as
q = (47r/~,)n sin(0/2),
[2]
with n being the refractive index of the dispersion medium, X the wavelength of light in vacuo, and 0 the scattering angle. K is an optical constant given by
VON
GUNTEN
factor can be expressed in terms of the isothermal osmotic compressibility (dTr/dCn)T
(6) S(O, c) = kT/(dTr/dcn)x,
[4]
where k is Boltzmann's constant, cn is particle number density and T is the absolute temperature. The molecular weight of the particles can be determined according to Eq. [1] by extrapolating the experimental data to zero angle and zero particle concentration.
Dynamic Light Scattering In a typical homodyne DLS experiment the measured intensity autocorrelation function, C(q, T), is related to the normalized autocorrelation function g(q, ~-) of the scattered electric field by (6, 7 )
C(q, r) = B(1 + bllg(q, r)l12),
[5]
where B is the experimental baseline, b is an instrumental constant, and r is the delay time. For noninteracting identical spheres, g(q, r) has the simple form
g(q, r) = e x p ( - F r ) ,
[6]
where the decay constant F is related to the translational diffusion coefficient D by
F = Dq 2.
[7]
In recent years interacting Brownian particles have attracted considerable attention (6, K = 47rn:(dn/dc)2/(~4N), [3] 8-10). For various, practically monodisperse polyelectrolytes it has been observed that g(q, where dn/dc is the refractive index increment T) strongly deviates from a single exponential. and N is Avogadro's number. The theoretical foundation of this phenomeFor point scatterers and in the limit of zero non has been reviewed thoroughly by Pusey scattering angle the particle scattering form and Tough (6). factor P(q) becomes unity. For q > 0, and if At low values of the scattering vector q, light the particle size exceeds that of about >,/20, scattering detects large scale motions of the then P(q) < 1; thus, the Rayleigh ratio is re- particles and D can be identified as the collecduced because of intraparticle interference. tive diffusion coefficient De. According to the On the other hand, the static structure factor generalized Stokes-Einstein equation S(q, c) accounts for interparticle interference. Dc = (dTr/dCn)T/f, [8] At vanishing concentrations particle interactions disappear and S(q, 0) = 1. In the low-q f being the collective friction factor. Experiregime (i.e., when q --~ 0) the static structure ments suggest that for polyelectrolytes in soJournal of Colloid and Interface Science, Vol. 134, No. 2, February 1990
LIGHT SCATTERING OF LAPONITE
lutions of low ionic strength f increases with the particle concentration and decreases with the ionic strength ( 11, 12). In the large-q regime, where S ( q , c) ~ 1, the initial decay of the correlation function is characterized by the free-particle self-diffusion coefficient Dse~f;s,whereas the slow component o f g ( q , r ) can be associated with a long-time self-diffusion coefficient Dself,L (6). EXPERIMENTAL
Materials Laponite RD was supplied as a white powder by Laporte Industries, Ltd. (GB). The RD grade has an enhanced purity and dispersibility. The approximate unit cell formula can be given as Sis [ Mgs. 5Lio.4H4024 ] 0.7- NaO:77+(4). For each series of experiments Laponite RD sols were freshly prepared by stirring 10.0 g powder in water for 1 day to give a total volume of 1000 ml. This stock sol was further diluted with distilled water (referred to as untreated sol) or analytical grade KC1 solutions. For some experiments the stock sol was dialyzed with distilled water until no change occurred in the conductivity of effluent water. Spectroscopic grade toluene served as a reference standard for static light scattering. Methods Instrumentation. The photon correlation spectrometer allowed us to measure simultaneously the total intensity of the scattered light Is(q) and the autocorrelation function C(q, r). DLS experiments were performed in the homodyne detection mode. The 488-nm line of a L E X E L Model 95 Argon laser was vertically polarized and focused to the center of an 8-mm-diameter cylindrical sample cell. The stabilized laser was operated at a constant power of 150 roW. It has been shown in preliminary experiments that the results were not affected between 50 and 300 mW. The sample cell was kept at a constant temperature of 20.0 + 0.1 °C and surrounded by an index-matching toluene bath. Sample cells were cleaned
399
thoroughly by chromic acid, washed with detergent, and rinsed exhaustively with doubly distilled and 0.22-~tm filtered water. Laponite sols were filtered to the cells through 0.45-urn Nucleopore filters. The photomultiplier (Thorn EMI, Model 9863 K A / 1 0 0 ) was mounted on the arm of a high precision goniometer (ALV-Laser, Model SP-86) which allowed angle-dependent measurements between 15 to 150 °. The scattered light passes through a selectable pinhole, usually set to 400 ~zm, and then falls onto the photocatode. The signal is amplified and transferred to the 136-channel 4-bit digital correlator (Brookhaven Instruments Corp., Model BI-2030). The positions of the laser beam and the photomultiplier are adjusted to give a maximum intensity of toluene at a scattering angle of 90 ° . Toluene intensity was checked frequently to correct for laser power fluctuations. Data collection. The modified correlatorcomputer can be operated in two modes. 2 In the statistics mode the number ofphotopulses are continuously counted and displayed on the monitor for any user-defined time intervals. Each DLS measurement is preceded by a 1to 2-min statistics run to set intensity limits for dust discrimination. After each measuring period,the autocorrelation function is sorted from the accumulator according to the predefined intensity levels. Autocorrelations are saved on diskette for subsequent data analysis. The Rayleigh ratios of the samples were obtained from the following expression Rv(q) = R v , T ( ( I s ( q ) ) L - (Is(q))w)/(I~(q))T,
[9]
where ( I s ( q ) ) L , ( I s ( q ) ) w and ( I s ( q ) ) T are the mean scattering intensities of Laponite sol, water, and toluene, respectively. We used Rv,a= 4 . 0 X 10 -7 m -1 f o r the Rayleigh ratio of toluene at 488 n m ( 1 3 ) . The correlator can operate with multiple sample time intervals and this feature allows 2 Programs for the BI-2030 were modified by J. Rieka and M. Meewes at the University of Bern. Journal of Colloid and Interface Science, Vol. 134,No. 2, February 1990
400
ROSTA AND VON GUNTEN
close monitoring of the initial decay at short times while also registering data near the background at longer times. For the majority of Laponite sols the following set of sample time intervals was adequate for each successive 32 correlator channels: 1, 4, 4, 4 us. The additional eight delayed channels were used for baseline measurements. The baseline was also computed directly from the data channels and only those correlation functions were accepted where the measured and computed baselines agreed to within 0.1%. As initial measurements showed no systematic variation of the autocorrelation function with the scattering angle, all DLS data presented in this paper were acquired at 0 = 90 °. Data analysis. Several techniques have been developed to extract useful information from nonexponentially decaying autocorrelation functions. In this work we tested the cumulants method (14), the double exponential method, and the slope analysis. The cumulants method utilizes the expansion o f g ( q , ~-) about the mean line width P. For Laponite sols, terms up to the fourth order were necessary to represent the initial decay accurately, implying strong interactions a n d / or polydispersity. So many adjustable parameters make data interpretation difficult, therefore this method was not pursued further in this study. In the double exponential method a bimodal size distribution of the particles is assumed and the normalized autocorrelation function is represented as the sum of two exponentials. Although this method provided very good fits to our experimental data, it was found to be inappropriate in light of membrane filtration results and transmission electron microscopy ( T E M ) pictures, as discussed later. In the slope analysis, linear fits were performed to the experimental data stored in the first 15-20 and the last 30-40 channels of the correlator. T h _ ~ i v e s of the initial and final slopes of In VC,(r) vs q2r are equal to the short-time (Ds) and long-time (DL) diffusion coefficients, respectively, as shown in Fig. 1. Journal of Colloid and Interface Science, Vol. 134, No. 2, February 1990
A crossover time rc was defined operationally as the delay time when the two slopes cross each other. If the DLS experiments probe the self-diffusion process then Ds = D~lf,S, DL = D~j~,Land a decrease in the interparticle interaction range should give larger rc values. On the other hand, under low-q conditions Ds = Dc and the meaning of~-~is not clear because the slow diffusion mode may be due to several effects (e.g., polydispersity, charge fluctuation, low-frequency friction; for details see Ref. ( 11 )). RESULTS AND DISCUSSION
Molecular Weight Determination The refractive index increment dn/dc for untreated Laponite RD sols was measured to be equal to 0.087 + 0.005 cm3/g which yields a value of 1.55 × 10-7+ 1.0 × 1 0 - S c m 2 m o l / g2 for the optical constant K. The angle-dependent scattering of Laponite sols was investigated from 0 = 30 ° to 0 = 150 ° in the concentration range of 0.025-5.0 g/liter. Measurements at small angles, especially for the more dilute samples, required very careful discrimination against dust scattering. Part of the results are illustrated in Fig. 2. Slight variations of the Rayleigh ratios with the scattering angle imply, as discussed under Theoretical Background, that P(q) ~ 1 and S(q, c)
-0.4
DS =1,51.10-7cm2 ts -0.8 - 1.2 - 1.8
3mD ~ o
DL= 6'O4" 10-8 cm2/s [ 3 ~
- 2.0 - 2.4 Tc = 9 . 5 4 . 1 0
-2.8
-5 s
, . . . . . . . . . 4 8 12 18 20 q2")" (106s/cm2)
D 24
28
FIG. l. Slopeanalysisof the normalizedautocorrelation function for untreated Laponite at a concentration ¢ of 2.0 g/liter and at a scatteringvectorq of 0.024 nm-t. Only everythird data point is shown.
LIGHT SCATTERING OF LAPONITE q ( 1 0 - 2 nm - 1 ) 0.89 I
10-3
1.71 i
2.42 I
2.97 I
A
A
A
A
A
A
A
A
O ×
0 x
0 x
0 ×
0 ×
0 x
0 x
0 x
+
+
+
+
+
Q
O
3.31 i
A
~7 10-4
0 x
g 0
0
0
+ 0
+
+ 0
+ 0
0
10-5 0
'
'3;'
' 6'0'
' 120 ' '
' 1 '5 0
o
FIG. 2. Angular distribution of Rayleigh ratios Rv (q, c) as a function of scattering angle 0 or scattering wave vector q. Laponite concentrations in g/liter: (D) 0.05, (+) 0.10, (×) 0.50, (~) 1.0, (A) 5.0.
S(0, c) in the experimental q range (8.8 × 10-3-3.3 × 10 -2 n m - 1 ) . All samples show the same angle-independent scattering, which means that an increase in the particle concentration does not give rise to coagulation. This was also confirmed by ultrasonication: no significant changes were observed in the scattered light intensities between sonicated and not sonicated samples for Laponite concentrations of 0.1, 1.0, and 5.0 g/liter. The interpretation scheme (Eqs. [ 1] - [ 4 ] ) is rigorously valid only for spherical particles, but in the low-q regime it can also be applied for small anisotropic particles ( 15 ); therefore, the Rayleigh ratios were extrapolated to q = 0 and plotted vs c as shown in Fig. 3. After scaling Rv by Kc we estimate M to be 3000 + 500 k g / m o l as the intercept at c = 0. Figure 3 illustrates that the relatively large error limits are due to the rapid change in MS at small Laponite concentrations. The Rayleigh ratios were also determined for a Laponite suspension at a concentration of 2.5 g/liter using a sample cell 18 m m in diameter. The measured intensities agreed with those obtained with the smaller sample cell, indicating that light absorption by Laponite is not responsible for the smaller than proportional increase in the scattered intensity with particle concentration. As particle aggregation would lead to up-
401
ward curving of Rv with increasing c, the observed behavior of Rv can be attributed to the decrease in the static structure factor S, while the molar mass of the particles remains constant, irrespective of c, in the range studied. Accordingly, we derive S by using M = 3000 k g / m o l as illustrated on the inside left-hand scale of Fig. 3. The large deviation of S from unity indicates strong particle interactions. Such a behavior of S has been confirmed by numerous experiments on polyelectrolyte systems (8-10, 15, 16).
Effect of Filtration Light scattering does not provide unequivocal results with respect to particle size and dynamics. To aid in the selection of the appropriate physical model, simultaneous DLS and SLS measurements were carried out on unfiltered and filtered 2.5 g/liter Laponite sols. The applied m e m b r a n e filters had the following nominal pore sizes in nm: 10, 50, 100, 220, and 450. Independent of the filter pore size, DLS data analysis by the double exponential method indicated two particle sizes with apparent hydrodynamic diameters of about 60 and 17 nm. Scattered intensities were insensitive to the pore size of the filters in the range 50-450 nm, but dropped down sharply to ~ 10% of the original value for the 10-nm
(/4
3000--1.0
2500~_
I 9"10-4
~
.0.75 ~
c° 2 0 0 0 "~-
==
¢n
• ,oOOo./ 5001/ O
0
"6"10-4
A 'T E o
.o.< . 1
. ~
.
.
2
3
4
0
(g/,)
FIG. 3. RayleighratiosRv (0, c) and apparent molecular weights MS (0, c) (=Rv (0, c)/Kc), see Eqs. [1]-[4] of Laponite sols as a function of particle concentration c. Static structure factor S (0, c) (inside of left-hand scale) based on M = 3000 kg/mol. Journal of Colloid and Interface Science, V ol. 134, No. 2, F e b ru a ry 1990
402
ROSTA AND VON GUNTEN
filter. These SLS results suggest that the major dimension of the particles is between 10 and 50 nm, contradicting interpretations with the double exponential method. TEM pictures of Laponite obtained in our institute 3 are similar to those published in Ref. (17), revealing a monomodal particle size distribution around 30 + 10 nm. This, together with our SLS data on filtered samples, provides evidence that the double exponential method is inadequate for Laponite sols. Therefore, further DLS experiments were evaluated exclusively by slope analysis.
Effect of Ionic Strength
crease in S with the ionic strength. An opposite correlation can be observed in Fig. 4b, as the short-time diffusion coefficient Ds increases with the ratio c/[KC1]. For c > 1.0 g/liter, dialyzed samples exhibit much larger diffusivity and more interactions (as inferred from the small S values) than untreated samples, indicating the importance of even a minute amount of ionic impurity. The long time diffusion coefficient DE varied randomly between a lower (4 × 10 -8 c m 2 / s ) and upper limit (8 × 10 -8 cmZ/s), showing no correlation with ionic strength and particle concentration. Crossover times were insensitive to changes in c and [KC1 ]. These results suggest, in agreement with scattering angleindependent S values, that light scattering ex-
First the effect of KC1 addition was studied at a fixed c = 2.5 g/liter Laponite concentration. The pH of the samples was relatively constant around the value 9.8. A steep increase was observed in the scattered light intensity 0.8 above the ionic strength region 0.0025-0.0030 0.6 M. From the experimental data we derived 0.4 0.0026 M as the critical coagulation concentration, ccc, of KC1. This is in satisfactory 0.2 agreement with the results of Perkins et al. (2) I I I I I who investigated the aggregation of CP grade 2.4 Laponite in aqueous electrolytes. From their Fig. 4a, the cec value for KC1 appears to be "~" 2 . 0 about 0.0035 M in the pH range 9.7-10.0. E o The following series of simultaneous SLS 1.6 2 v and DLS experiments were carried out on 1.2 samples of different Laponite concentrations at various ionic strengths below the ccc where I I I I I 0.8 the particles exist as constant-size textural units irrespective of [KC1]. Static structure factors were calculated from the measured Rayleigh ratios by Eq. [1] using M = 3000 kg/ mol. Short-time and long-time diffusion coefficients as well as crossover times were deter~ 6 V mined from DLS data by slope analysis. A ~ Figure 4a shows that in different solutions 4 O 1 2 3 4 5 (dialyzed, untreated, KC1 added) the static c (g/I) structure factor S decreases with Laponite concentration. The screening effect of the FIG. 4. Light scattering data for Laponite sols. (a) Static small ions is manifested in an appreciable in- structure factor S. (b) Short-timediffusioncoefficientDs (=De, see text). (c) Collectivefrictionfactorf. (11)Dialyzed 3Electronmicroscopicpicturesweretaken by R. Giov- system, (I-q) untreated system, (v) [KC1] = 0.0005 M, anoli at the Universityof Bern. (V) [KCI] = 0.001 M, (A) [KC1] = 0.0025 M. Journal of Colloid and Interface Science, Vol.
134, No. 2, F e b r u a r y 1990
LIGHT
SCATTERING
periments are carried out in the low-q regime; therefore, we interpret Ds as the collective diffusion coefficient Dc of Laponite. A combination of Eqs. [4] and [8] shows that the collective friction factor f can be defined in terms of the static structure factor S and the collective diffusion coefficient Dc: f = kT/DcS(O, c).
[10]
Figure 4c shows f values calculated from the experimental Dc and S data (Figs. 4a and 4b ). The error limits are estimated to be _+5% for Dc and S; therefore, the maximum error is within 10% forf. Structure
The molecular weight of an aggregate formed by the association of i identical, disklike platelets can be expressed as M = ipNhrrd2/4,
[11]
where o, h, and d are, respectively, the specific weight, thickness, and diameter of the individual platelets. For Laponite using M = 3000 kg/mol (this study), o -- 2530 k g / m 3, and h = 1 nm (Ref. ( 1 )), Eq. [11] leads to id 2 = 2510 nm 2. Combining this result with membrane filtration, electron microscopy and DLS suggest that, within the accuracy of our measurements, doublets, triplets, and quadruplets are possible tactoid configurations with diameters of 35.4, 28.9, and 25.0 nm, respectively. These findings contradict the conclusions of Lockhart (3) who proposed a huge cardhouse model for Laponite in water. Fripiat and co-workers (5) measured water adsorption isotherms to determine the specific total surface area of Laponite to be 345 mZ/g. This result implies, in agreement with our measurements, the presence of tactoids composed of several individual platelets. Avery and Ramsay determined a molecular weight of 710 k g / m o l for Laponite RD by static light scattering (4). These authors also established that there is neither association nor considerable interaction among the single platelets. Our data are qualitatively consistent
OF LAPONITE
403
with those reported in Ref. (4), but our interpretations are different. The rationale for this lies in the different concentration ranges studied: 0.025-5.0 g/liter (this work) and 2.5-30 g/liter (Ref. (4)). It can be seen in Fig. 3 that changes in MS are relatively small at concentrations higher than 1.0 g/liter. Extrapolation to infinite dilution from this region yields a much lower molecular weight and, consequently, larger static structure factors than extrapolation from the dilute region. As far as the size of the platelets is concerned, our result agrees with that of Avery and Ramsay, who also quote an average particle diameter of 30 nm (4). It remains to be decided what causes the nonexponential behavior of the autocorrelation function, C(q, r). As discussed earlier, at low q the faster mode can be assigned to collective diffusion which arises from overall concentration fluctuations due to the Brownian motion of the particles. The interpretation of the slow mode is nontrivial. In his theoretical analysis, Weissmann attributed it to polydispersity, i.e., to the local fluctuation of particles with different size a n d / o r scattering power (18). This slow relaxation process is understood to reflect the motion of a single "tracer" particle in the "cage" of its neighbors (6, 18, 19). Other processes which can contribute to the nonexponentiality of C(q, r) include macroion charge fluctuation, extralow frequency friction (both discussed in Ref. ( 11 )), anisotropy (20), or fluctuations in the small ion distribution around the macroion (9). Our DLS measurements on Laponite sols demonstrated that the short-time decay becomes faster as the ionic strength is lowered, whereas the long-time decay remains relatively unperturbed by changes in the ionic strength. These results indicate (i) the strong influence of long-range electrostatic repulsion on collective diffusion; (ii) that particle interactions are significant even in dilute sols; and that (iii) small ion redistributions and charge fluctuations have little effect on the slow component of C(q, r). Journal of Colloid and Interface Science, Vol. 134, No. 2, February 1990
404
ROSTA AND VON GUNTEN
Clay sols are always polydisperse and elecfE = fE,0(1 + flee), [14] tron micrographs of Laponite indicate that this where JE,0 is the infinite dilution electrostatic synthetic smectite is no exception to that. But friction factor due to macroion-small ion even if the anisotropic, disk-like Laponite parcoupling and fie is the electrostatic virial coefticles were uniform in size, the suspension ficient representing direct macroion-macroion would still appear to be slightly polydisperse interactions. by light scattering because the form factor P(q) For asymmetric particles, such as Laponite, depends on the orientation of the platelets with f0 can be expressed by a modified Stokes forrespect to q (20). We find it plausible that a mula (21 ), combination of this effect with intrinsic size and charge polydispersity is manifested in the f0 = 67r~TrH = 67r,ht/G, [15] long-time tail of the autocorrelation function. where r/is the viscosity of the dispersing meHowever, a more detailed analysis of this very dium, rH is the spherical equivalent hydrocomplex phenomenon would require addidynamic radius, ht is the thickness of the hytional scattering experiments at higher q drated aggregate, and G is the shape factor. (SAXS, SANS). On the basis of Refs. ( 5 ) and (22) we assume that electrostricted water layers have the same Friction 1-nm thickness between the platelets and Figure 4c shows that collective friction in- the outside, leading the ht = 7 nm. The shape creases linearly with particle concentration factor, G = 0.6, was evaluated by Perrin's and decreases with the ionic strength. To es- expression for oblate ellipsoids (taken from timate the importance of electrostatic inter- Ref. (21)). Substitution into Eq. [15] gives rn actions in the friction of Laponite, we analyzed = 11.7 nm andfo = 2.2 X 10 -l° kg/s. our data by a simple virial expansion method. The hydrodynamic virial coefficient of hardNumerical results are presented only for the body interactions was calculated by the triplet tactoid, because the friction parameters expression of Beenakker and Mazur (23): fl differed less than 10% for the other two pos- = 1.7~/e, where • is the volume fraction of sible structures (doublet, quadruplet). the particles. This contribution to the collecThe translating motion of a macroion in tive friction factor turned out to be negligible aqueous solutions is hindered by hydrody- compared with its electrostatic counterpart. namic and electrostatic forces. Presuming that The electrostatic parametersfE.0 and fiE were these forces are not coupled, derived from our experiments by performing linear fits to the f data (see Fig. 4c) at each f = fH + fE, [12] ionic strength where f n and fE are, respectively, the hydrodynamic and electrostatic friction factors. Expandingfn in terms of the particle concentration to the first order gives flJ = f 0 ( l + fie),
[13]
where the virial coefficient 13takes into account hydrodynamic interparticle interactions. The single-particle friction factor f0 represents zero concentration friction of an uncharged particle due to the presence of solvent molecules. The net electrostatic effect can be expressed by a first order virial approximation as Iournal of Colloid and Interface Science, Vol. 134, No. 2, February 1990
fE,0 = (intercept) c=0 - fo fie =
slope/JE,0.
[ 16 ] [17]
The data obtained are listed in Table I. A comparison o f f 0 (=2.2 X 10 -1° kg/s) with fE,0 values shows that electrolytic friction is significant in Laponite sols. Schurr has recently proposed a theory for electrolytic friction on isolated spherical macroions (24). We found that Schurr's theory overestimates fE,0 by 25-40%. The discrepancy, which decreases upon an increase in the ionic strength, may be due to the fact that the conditions in La-
LIGHT SCATTERING OF LAPONITE TABLE I Infinite Dilution Electrostatic Friction Factor fE,0 and Electrostatic Friction Virial Coefficientt3Eof Laponite RD as a Function of Added KC1 [KCI] (M)
JE,o(10-1° kg/s)
flu (cm3/g)
0a 0b 0.0005 0.0010 0.0025
3.1 3.1 2.9 2.7 2.4
292 104 98 95 71
Dialyzed sample. b Untreated sample.
ponite suspensions do not agree with Schurr's assumption of spherical particles with low surface potential. It should also be mentioned that an earlier treatment by Booth (25) would underestimate our fE,0 data by about a factor o f 7. Table I illustrates that fz,0 increases as the ionic strength is lowered. This trend, which is consistent with the predictions of Schurr, as well as with other experimental data (9, 11 ), can be explained by the following argument. A decrease in the ionic strength leads to a thicker double-layer around the macroion. During its Brownian motion, the macroion drags along this thick ionic cloud and, as a result, experiences larger friction. Inspection of the electrostatic virial coefficient/]E data in Table I reveals a striking difference between the dialyzed and untreated systems. As ionic impurities are removed from the sols by dialysis, Laponite particles experience additional hindrance in motion due to the longer range of double-layer repulsion. Even the smallest/3E values (in 0.0025 M K C 1 ) are large enough to demonstrate that macroi o n - m a c r o i o n coupling can lead to increased friction, for colloid concentrations used generally in light scattering experiments. For a comparison with theory (15) one should be able to calculate the electrostatic pair potential of the particles. This is, unfortunately, not feasible as neither the ionic strength dependency of the surface potential of Laponite nor
405
the necessary correction factors for particle anisotropy and charge heterogenity are available. CONCLUSION Static and dynamic light scatterings have been applied to obtain useful information about the structure and dynamics of Laponite R D in aqueous solutions. These techniques, combined with m e m b r a n e filtration and electron microscopy, suggest that the majority of the sol particles are present in the form of a tactoid composed of two to four single platelets with a lateral dimension of about 30 n m and an average molecular weight of 3000 + 500 kg/mol. The concentration and ionic strength dependence of the static structure factor, collective diffusion coefficient, and friction factor indicate strong interactions a m o n g the colloids. Neutral and electrostatic contributions to the collective friction factor were evaluated by first order virial expressions. Infinite dilution electrolytic friction fE,0 varied inversely with the concentration of added electrolyte and was always larger than the usual Stokes friction factor f0 at the ionic strengths studied (<0.0025 M ) . It has been demonstrated that electrostatic coupling a m o n g macroions contributes significantly to collective friction. ACKNOWLEDGMENTS The authors are indebted to R. Giovanoli for the preparation of electron micrographs. Stimulating discussions with J. Ricka and M. Meewes are acknowledged. We are thankful to the two unknown refereesfor their suggestions. We thank Laporte Industries for providing a sample of Laponite RD. This work was partly supportedby the Swiss National Science Foundation. REFERENCES 1. Neumann, B. S., and Sansom, K. G., [srael,L Chem. 8, 315 (1970). 2. Perkins, R., Brace, R., and Matijevic, E., J. Colloid Interface Sci. 48, 417 (1974). 3. Lockhart, N. C., J. Colloid Interface Sci. 74, 509 (1980). 4. Avery,R. G., and Ramsay,J. D. F., J. Colloidlnterface Sci. 109, 448 (1986). Journal of Colloid and Interface Science, VoL 134, No. 2, February 1990
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5. Fripiat, J., Cases, J., Francois, M., and Letellier, M., J. Colloid Interface Sci. 89, 378 (1982). 6. Pusey, P. N., and Tough, J. A., in "Dynamic Light Scattering and Velocimetry: Applications of Photon Correlation Spectroscopy" (R. Pecora Ed.). Plenum, New York, 1985. 7. Cummins, H. Z., and Pike, E. R. (Eds.), "Photon Correlation and Light Beating Spectroscopy," Nato Advanced Study Institutes Series B, Physics, Vol. 3. Plenum, New York, 1974. 8. Degiorgio, V., Corti, M., and Giglio, M. (Eds.), "Light Scattering in Liquids and Macromolecular Solutions." Plenum, New York, 1980. 9. Schmitz, K. S., Lu, M., and Gauntt, J., J. Chem. Phys. 78, 5059 (1983). 10. Cantu, L., Corti, M., and Degiorgio, V., Faraday Discuss. Chem. Soc. 83, 287 (1987). 1 l. Weissman, M. B., and Marque, J., J. Chem. Phys. 73, 3999 (1980). 12. Tivant, P., Turq, P., Drifford, H., Magdelenat, H., and Menez, R., Biopolymers 22, 643 (1983). 13. Bender, T. M., Lewis, R. J., and Pecora, R., Macromolecules 19, 244 (1986). 14. Koppel, D. E., J. Chem. Phys. 57, 4814 (1972). 15. Drifford, M., Belloni, L., Dalbiez, J. P., and Chatto-
Journal of Colloid and Interface Science, Vol. 134, No. 2, February 1990
16. 17.
18. 19.
20.
21.
22. 23. 24. 25.
padhyay, A. K., J. Colloid Interface Sci. 105, 587 (1985). Neal, D. G., Purich, D., and Cannell, D. S., J. Chem. Phys. 80, 3469 (1984). van Olphen, H., and Fripiat, J. J., Eds., in "Data Handbook for Clay Minerals and Other Non-Metallic Minerals," OECD and Clay Minerals Society, p. 229. Pergamon, Oxford, 1979. Weissman, M. B., aT.Chem. Phys. 72, 231 (1980). van Veluwen, A., Lekkerkerker, H. N. W., de Cruif, C. G., and Vrij, A., Faraday Discuss. Chem. Soc. 83, 59 (1987). Hayter, J. B., in "Physics of Amphiphiles: Micelles, Vesicles and Microemulsions" (V. Degiorgio and M. Corti Eds.), p. 70. North-Holland, Amsterdam, 1985. Zero, K., and Pecora, R., in "Dynamic Light Scattering and Velocimetry: Applications of Photon Correlation Spectroscopy" (R. Pecora Ed.), p. 66. Plenum, New York, 1985. Grauer, Z., Malter, A. B., Yariv, S., and Avnir, D., Colloids Surf. 25, 41 (1987). Beenakker, C. W. J., and Mazur, P., Phys. Lett. A 91, 290 (1982). Schurr, J. M., Chem. Phys. 45, 119 (1980). Booth, F., J. Chem. Phys. 22, 1956 (1954).
Because of its purity and easy dispersibility in water Laponite appears to be an ideal substance to investigate the properties of swelling clays in aqueous solutions. Laponite is a synthetic clay, belonging to the family of trioctahedral smectites with structure and composition similar to those of hectorites. Central positions in the octahedral sheets are occupied by divalent magnesium ions, some of which are replaced by monovalent lithium. As a result, suspended particles carry negative charges which are compensated by exchangeable cations. Early work (1) on the flocculation of Laponite in aqueous electrolytes has been extended by Perkins et al. (2). These authors interpreted turbidity and capillary data in terms of critical coagulation concentrations of various electrolytes and as a function of pH. In another study (3), the electrical properties of aqueous Laponite sols were investigated by conductivity and permittivity measurements. I TO whom all correspondence should be addressed.
It was concluded that the most probable structural unit in the suspension is a network of edge-to-face and edge-to-edge associated platelets ("card-house structure") with an equivalent spherical diameter of 0.7 ~m. By contrast, it has been argued recently (4), based on static and dynamic light scattering and small angle neutron scattering, that Laponite particles are present in water as single disklike units with an average disk diameter of about 30 nm. Yet another structural model was proposed by Fripiat and co-workers (5), who investigated the thermodynamic properties of adsorbed water layers on Laponite, among other clays, by means of calorimetric and nuclear magnetic resonance techniques. Heats of immersion as well as proton relaxation rates have demonstrated the presence of parallel, closely spaced platelets, so-called tactoids, separated by a few water layers. In light of the importance of clays in agricultural and industrial applications (2), we felt it worthwhile to further investigate some properties of Laponite sols. To elucidate on the validity of the proposed structural models
397 Journal of Colloidand InterfaceScience, Vol. 134,No. 2, February 1990
0021-9797/90 $3.00 Copyright© 1990by AcademicPress,Inc. All rightsof reproductionin any formreserved.
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ROSTA
AND
we have used light scattering on dilute dispersions. Experiments were carried out at various ionic strengths and Laponite concentrations to estimate the importance of particle interactions and electrostatic friction. The average molar mass M of the particles and the static structure factor S were determined by static light scattering (SLS), whereas the collective diffusion coefficient Dc was derived from the combination of dynamic light scattering (DLS) with membrane filtration. From these parameters the electrostatic contribution to the hydrodynamic friction was evaluated as a function of ionic strength and particle concentration. THEORETICAL
BACKGROUND
Static Light Scattering For vertically polarized light the Rayleigh ratio Rv can generally be expressed in terms of the molecular weight M and concentration c (in g/ml) of spherical colloids,
Rv(q, c) = KcMP(q)S(q, c),
[1]
where the scattering wave vector q is defined as
q = (47r/~,)n sin(0/2),
[2]
with n being the refractive index of the dispersion medium, X the wavelength of light in vacuo, and 0 the scattering angle. K is an optical constant given by
VON
GUNTEN
factor can be expressed in terms of the isothermal osmotic compressibility (dTr/dCn)T
(6) S(O, c) = kT/(dTr/dcn)x,
[4]
where k is Boltzmann's constant, cn is particle number density and T is the absolute temperature. The molecular weight of the particles can be determined according to Eq. [1] by extrapolating the experimental data to zero angle and zero particle concentration.
Dynamic Light Scattering In a typical homodyne DLS experiment the measured intensity autocorrelation function, C(q, T), is related to the normalized autocorrelation function g(q, ~-) of the scattered electric field by (6, 7 )
C(q, r) = B(1 + bllg(q, r)l12),
[5]
where B is the experimental baseline, b is an instrumental constant, and r is the delay time. For noninteracting identical spheres, g(q, r) has the simple form
g(q, r) = e x p ( - F r ) ,
[6]
where the decay constant F is related to the translational diffusion coefficient D by
F = Dq 2.
[7]
In recent years interacting Brownian particles have attracted considerable attention (6, K = 47rn:(dn/dc)2/(~4N), [3] 8-10). For various, practically monodisperse polyelectrolytes it has been observed that g(q, where dn/dc is the refractive index increment T) strongly deviates from a single exponential. and N is Avogadro's number. The theoretical foundation of this phenomeFor point scatterers and in the limit of zero non has been reviewed thoroughly by Pusey scattering angle the particle scattering form and Tough (6). factor P(q) becomes unity. For q > 0, and if At low values of the scattering vector q, light the particle size exceeds that of about >,/20, scattering detects large scale motions of the then P(q) < 1; thus, the Rayleigh ratio is re- particles and D can be identified as the collecduced because of intraparticle interference. tive diffusion coefficient De. According to the On the other hand, the static structure factor generalized Stokes-Einstein equation S(q, c) accounts for interparticle interference. Dc = (dTr/dCn)T/f, [8] At vanishing concentrations particle interactions disappear and S(q, 0) = 1. In the low-q f being the collective friction factor. Experiregime (i.e., when q --~ 0) the static structure ments suggest that for polyelectrolytes in soJournal of Colloid and Interface Science, Vol. 134, No. 2, February 1990
LIGHT SCATTERING OF LAPONITE
lutions of low ionic strength f increases with the particle concentration and decreases with the ionic strength ( 11, 12). In the large-q regime, where S ( q , c) ~ 1, the initial decay of the correlation function is characterized by the free-particle self-diffusion coefficient Dse~f;s,whereas the slow component o f g ( q , r ) can be associated with a long-time self-diffusion coefficient Dself,L (6). EXPERIMENTAL
Materials Laponite RD was supplied as a white powder by Laporte Industries, Ltd. (GB). The RD grade has an enhanced purity and dispersibility. The approximate unit cell formula can be given as Sis [ Mgs. 5Lio.4H4024 ] 0.7- NaO:77+(4). For each series of experiments Laponite RD sols were freshly prepared by stirring 10.0 g powder in water for 1 day to give a total volume of 1000 ml. This stock sol was further diluted with distilled water (referred to as untreated sol) or analytical grade KC1 solutions. For some experiments the stock sol was dialyzed with distilled water until no change occurred in the conductivity of effluent water. Spectroscopic grade toluene served as a reference standard for static light scattering. Methods Instrumentation. The photon correlation spectrometer allowed us to measure simultaneously the total intensity of the scattered light Is(q) and the autocorrelation function C(q, r). DLS experiments were performed in the homodyne detection mode. The 488-nm line of a L E X E L Model 95 Argon laser was vertically polarized and focused to the center of an 8-mm-diameter cylindrical sample cell. The stabilized laser was operated at a constant power of 150 roW. It has been shown in preliminary experiments that the results were not affected between 50 and 300 mW. The sample cell was kept at a constant temperature of 20.0 + 0.1 °C and surrounded by an index-matching toluene bath. Sample cells were cleaned
399
thoroughly by chromic acid, washed with detergent, and rinsed exhaustively with doubly distilled and 0.22-~tm filtered water. Laponite sols were filtered to the cells through 0.45-urn Nucleopore filters. The photomultiplier (Thorn EMI, Model 9863 K A / 1 0 0 ) was mounted on the arm of a high precision goniometer (ALV-Laser, Model SP-86) which allowed angle-dependent measurements between 15 to 150 °. The scattered light passes through a selectable pinhole, usually set to 400 ~zm, and then falls onto the photocatode. The signal is amplified and transferred to the 136-channel 4-bit digital correlator (Brookhaven Instruments Corp., Model BI-2030). The positions of the laser beam and the photomultiplier are adjusted to give a maximum intensity of toluene at a scattering angle of 90 ° . Toluene intensity was checked frequently to correct for laser power fluctuations. Data collection. The modified correlatorcomputer can be operated in two modes. 2 In the statistics mode the number ofphotopulses are continuously counted and displayed on the monitor for any user-defined time intervals. Each DLS measurement is preceded by a 1to 2-min statistics run to set intensity limits for dust discrimination. After each measuring period,the autocorrelation function is sorted from the accumulator according to the predefined intensity levels. Autocorrelations are saved on diskette for subsequent data analysis. The Rayleigh ratios of the samples were obtained from the following expression Rv(q) = R v , T ( ( I s ( q ) ) L - (Is(q))w)/(I~(q))T,
[9]
where ( I s ( q ) ) L , ( I s ( q ) ) w and ( I s ( q ) ) T are the mean scattering intensities of Laponite sol, water, and toluene, respectively. We used Rv,a= 4 . 0 X 10 -7 m -1 f o r the Rayleigh ratio of toluene at 488 n m ( 1 3 ) . The correlator can operate with multiple sample time intervals and this feature allows 2 Programs for the BI-2030 were modified by J. Rieka and M. Meewes at the University of Bern. Journal of Colloid and Interface Science, Vol. 134,No. 2, February 1990
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ROSTA AND VON GUNTEN
close monitoring of the initial decay at short times while also registering data near the background at longer times. For the majority of Laponite sols the following set of sample time intervals was adequate for each successive 32 correlator channels: 1, 4, 4, 4 us. The additional eight delayed channels were used for baseline measurements. The baseline was also computed directly from the data channels and only those correlation functions were accepted where the measured and computed baselines agreed to within 0.1%. As initial measurements showed no systematic variation of the autocorrelation function with the scattering angle, all DLS data presented in this paper were acquired at 0 = 90 °. Data analysis. Several techniques have been developed to extract useful information from nonexponentially decaying autocorrelation functions. In this work we tested the cumulants method (14), the double exponential method, and the slope analysis. The cumulants method utilizes the expansion o f g ( q , ~-) about the mean line width P. For Laponite sols, terms up to the fourth order were necessary to represent the initial decay accurately, implying strong interactions a n d / or polydispersity. So many adjustable parameters make data interpretation difficult, therefore this method was not pursued further in this study. In the double exponential method a bimodal size distribution of the particles is assumed and the normalized autocorrelation function is represented as the sum of two exponentials. Although this method provided very good fits to our experimental data, it was found to be inappropriate in light of membrane filtration results and transmission electron microscopy ( T E M ) pictures, as discussed later. In the slope analysis, linear fits were performed to the experimental data stored in the first 15-20 and the last 30-40 channels of the correlator. T h _ ~ i v e s of the initial and final slopes of In VC,(r) vs q2r are equal to the short-time (Ds) and long-time (DL) diffusion coefficients, respectively, as shown in Fig. 1. Journal of Colloid and Interface Science, Vol. 134, No. 2, February 1990
A crossover time rc was defined operationally as the delay time when the two slopes cross each other. If the DLS experiments probe the self-diffusion process then Ds = D~lf,S, DL = D~j~,Land a decrease in the interparticle interaction range should give larger rc values. On the other hand, under low-q conditions Ds = Dc and the meaning of~-~is not clear because the slow diffusion mode may be due to several effects (e.g., polydispersity, charge fluctuation, low-frequency friction; for details see Ref. ( 11 )). RESULTS AND DISCUSSION
Molecular Weight Determination The refractive index increment dn/dc for untreated Laponite RD sols was measured to be equal to 0.087 + 0.005 cm3/g which yields a value of 1.55 × 10-7+ 1.0 × 1 0 - S c m 2 m o l / g2 for the optical constant K. The angle-dependent scattering of Laponite sols was investigated from 0 = 30 ° to 0 = 150 ° in the concentration range of 0.025-5.0 g/liter. Measurements at small angles, especially for the more dilute samples, required very careful discrimination against dust scattering. Part of the results are illustrated in Fig. 2. Slight variations of the Rayleigh ratios with the scattering angle imply, as discussed under Theoretical Background, that P(q) ~ 1 and S(q, c)
-0.4
DS =1,51.10-7cm2 ts -0.8 - 1.2 - 1.8
3mD ~ o
DL= 6'O4" 10-8 cm2/s [ 3 ~
- 2.0 - 2.4 Tc = 9 . 5 4 . 1 0
-2.8
-5 s
, . . . . . . . . . 4 8 12 18 20 q2")" (106s/cm2)
D 24
28
FIG. l. Slopeanalysisof the normalizedautocorrelation function for untreated Laponite at a concentration ¢ of 2.0 g/liter and at a scatteringvectorq of 0.024 nm-t. Only everythird data point is shown.
LIGHT SCATTERING OF LAPONITE q ( 1 0 - 2 nm - 1 ) 0.89 I
10-3
1.71 i
2.42 I
2.97 I
A
A
A
A
A
A
A
A
O ×
0 x
0 x
0 ×
0 ×
0 x
0 x
0 x
+
+
+
+
+
Q
O
3.31 i
A
~7 10-4
0 x
g 0
0
0
+ 0
+
+ 0
+ 0
0
10-5 0
'
'3;'
' 6'0'
' 120 ' '
' 1 '5 0
o
FIG. 2. Angular distribution of Rayleigh ratios Rv (q, c) as a function of scattering angle 0 or scattering wave vector q. Laponite concentrations in g/liter: (D) 0.05, (+) 0.10, (×) 0.50, (~) 1.0, (A) 5.0.
S(0, c) in the experimental q range (8.8 × 10-3-3.3 × 10 -2 n m - 1 ) . All samples show the same angle-independent scattering, which means that an increase in the particle concentration does not give rise to coagulation. This was also confirmed by ultrasonication: no significant changes were observed in the scattered light intensities between sonicated and not sonicated samples for Laponite concentrations of 0.1, 1.0, and 5.0 g/liter. The interpretation scheme (Eqs. [ 1] - [ 4 ] ) is rigorously valid only for spherical particles, but in the low-q regime it can also be applied for small anisotropic particles ( 15 ); therefore, the Rayleigh ratios were extrapolated to q = 0 and plotted vs c as shown in Fig. 3. After scaling Rv by Kc we estimate M to be 3000 + 500 k g / m o l as the intercept at c = 0. Figure 3 illustrates that the relatively large error limits are due to the rapid change in MS at small Laponite concentrations. The Rayleigh ratios were also determined for a Laponite suspension at a concentration of 2.5 g/liter using a sample cell 18 m m in diameter. The measured intensities agreed with those obtained with the smaller sample cell, indicating that light absorption by Laponite is not responsible for the smaller than proportional increase in the scattered intensity with particle concentration. As particle aggregation would lead to up-
401
ward curving of Rv with increasing c, the observed behavior of Rv can be attributed to the decrease in the static structure factor S, while the molar mass of the particles remains constant, irrespective of c, in the range studied. Accordingly, we derive S by using M = 3000 k g / m o l as illustrated on the inside left-hand scale of Fig. 3. The large deviation of S from unity indicates strong particle interactions. Such a behavior of S has been confirmed by numerous experiments on polyelectrolyte systems (8-10, 15, 16).
Effect of Filtration Light scattering does not provide unequivocal results with respect to particle size and dynamics. To aid in the selection of the appropriate physical model, simultaneous DLS and SLS measurements were carried out on unfiltered and filtered 2.5 g/liter Laponite sols. The applied m e m b r a n e filters had the following nominal pore sizes in nm: 10, 50, 100, 220, and 450. Independent of the filter pore size, DLS data analysis by the double exponential method indicated two particle sizes with apparent hydrodynamic diameters of about 60 and 17 nm. Scattered intensities were insensitive to the pore size of the filters in the range 50-450 nm, but dropped down sharply to ~ 10% of the original value for the 10-nm
(/4
3000--1.0
2500~_
I 9"10-4
~
.0.75 ~
c° 2 0 0 0 "~-
==
¢n
• ,oOOo./ 5001/ O
0
"6"10-4
A 'T E o
.o.< . 1
. ~
.
.
2
3
4
0
(g/,)
FIG. 3. RayleighratiosRv (0, c) and apparent molecular weights MS (0, c) (=Rv (0, c)/Kc), see Eqs. [1]-[4] of Laponite sols as a function of particle concentration c. Static structure factor S (0, c) (inside of left-hand scale) based on M = 3000 kg/mol. Journal of Colloid and Interface Science, V ol. 134, No. 2, F e b ru a ry 1990
402
ROSTA AND VON GUNTEN
filter. These SLS results suggest that the major dimension of the particles is between 10 and 50 nm, contradicting interpretations with the double exponential method. TEM pictures of Laponite obtained in our institute 3 are similar to those published in Ref. (17), revealing a monomodal particle size distribution around 30 + 10 nm. This, together with our SLS data on filtered samples, provides evidence that the double exponential method is inadequate for Laponite sols. Therefore, further DLS experiments were evaluated exclusively by slope analysis.
Effect of Ionic Strength
crease in S with the ionic strength. An opposite correlation can be observed in Fig. 4b, as the short-time diffusion coefficient Ds increases with the ratio c/[KC1]. For c > 1.0 g/liter, dialyzed samples exhibit much larger diffusivity and more interactions (as inferred from the small S values) than untreated samples, indicating the importance of even a minute amount of ionic impurity. The long time diffusion coefficient DE varied randomly between a lower (4 × 10 -8 c m 2 / s ) and upper limit (8 × 10 -8 cmZ/s), showing no correlation with ionic strength and particle concentration. Crossover times were insensitive to changes in c and [KC1 ]. These results suggest, in agreement with scattering angleindependent S values, that light scattering ex-
First the effect of KC1 addition was studied at a fixed c = 2.5 g/liter Laponite concentration. The pH of the samples was relatively constant around the value 9.8. A steep increase was observed in the scattered light intensity 0.8 above the ionic strength region 0.0025-0.0030 0.6 M. From the experimental data we derived 0.4 0.0026 M as the critical coagulation concentration, ccc, of KC1. This is in satisfactory 0.2 agreement with the results of Perkins et al. (2) I I I I I who investigated the aggregation of CP grade 2.4 Laponite in aqueous electrolytes. From their Fig. 4a, the cec value for KC1 appears to be "~" 2 . 0 about 0.0035 M in the pH range 9.7-10.0. E o The following series of simultaneous SLS 1.6 2 v and DLS experiments were carried out on 1.2 samples of different Laponite concentrations at various ionic strengths below the ccc where I I I I I 0.8 the particles exist as constant-size textural units irrespective of [KC1]. Static structure factors were calculated from the measured Rayleigh ratios by Eq. [1] using M = 3000 kg/ mol. Short-time and long-time diffusion coefficients as well as crossover times were deter~ 6 V mined from DLS data by slope analysis. A ~ Figure 4a shows that in different solutions 4 O 1 2 3 4 5 (dialyzed, untreated, KC1 added) the static c (g/I) structure factor S decreases with Laponite concentration. The screening effect of the FIG. 4. Light scattering data for Laponite sols. (a) Static small ions is manifested in an appreciable in- structure factor S. (b) Short-timediffusioncoefficientDs (=De, see text). (c) Collectivefrictionfactorf. (11)Dialyzed 3Electronmicroscopicpicturesweretaken by R. Giov- system, (I-q) untreated system, (v) [KC1] = 0.0005 M, anoli at the Universityof Bern. (V) [KCI] = 0.001 M, (A) [KC1] = 0.0025 M. Journal of Colloid and Interface Science, Vol.
134, No. 2, F e b r u a r y 1990
LIGHT
SCATTERING
periments are carried out in the low-q regime; therefore, we interpret Ds as the collective diffusion coefficient Dc of Laponite. A combination of Eqs. [4] and [8] shows that the collective friction factor f can be defined in terms of the static structure factor S and the collective diffusion coefficient Dc: f = kT/DcS(O, c).
[10]
Figure 4c shows f values calculated from the experimental Dc and S data (Figs. 4a and 4b ). The error limits are estimated to be _+5% for Dc and S; therefore, the maximum error is within 10% forf. Structure
The molecular weight of an aggregate formed by the association of i identical, disklike platelets can be expressed as M = ipNhrrd2/4,
[11]
where o, h, and d are, respectively, the specific weight, thickness, and diameter of the individual platelets. For Laponite using M = 3000 kg/mol (this study), o -- 2530 k g / m 3, and h = 1 nm (Ref. ( 1 )), Eq. [11] leads to id 2 = 2510 nm 2. Combining this result with membrane filtration, electron microscopy and DLS suggest that, within the accuracy of our measurements, doublets, triplets, and quadruplets are possible tactoid configurations with diameters of 35.4, 28.9, and 25.0 nm, respectively. These findings contradict the conclusions of Lockhart (3) who proposed a huge cardhouse model for Laponite in water. Fripiat and co-workers (5) measured water adsorption isotherms to determine the specific total surface area of Laponite to be 345 mZ/g. This result implies, in agreement with our measurements, the presence of tactoids composed of several individual platelets. Avery and Ramsay determined a molecular weight of 710 k g / m o l for Laponite RD by static light scattering (4). These authors also established that there is neither association nor considerable interaction among the single platelets. Our data are qualitatively consistent
OF LAPONITE
403
with those reported in Ref. (4), but our interpretations are different. The rationale for this lies in the different concentration ranges studied: 0.025-5.0 g/liter (this work) and 2.5-30 g/liter (Ref. (4)). It can be seen in Fig. 3 that changes in MS are relatively small at concentrations higher than 1.0 g/liter. Extrapolation to infinite dilution from this region yields a much lower molecular weight and, consequently, larger static structure factors than extrapolation from the dilute region. As far as the size of the platelets is concerned, our result agrees with that of Avery and Ramsay, who also quote an average particle diameter of 30 nm (4). It remains to be decided what causes the nonexponential behavior of the autocorrelation function, C(q, r). As discussed earlier, at low q the faster mode can be assigned to collective diffusion which arises from overall concentration fluctuations due to the Brownian motion of the particles. The interpretation of the slow mode is nontrivial. In his theoretical analysis, Weissmann attributed it to polydispersity, i.e., to the local fluctuation of particles with different size a n d / o r scattering power (18). This slow relaxation process is understood to reflect the motion of a single "tracer" particle in the "cage" of its neighbors (6, 18, 19). Other processes which can contribute to the nonexponentiality of C(q, r) include macroion charge fluctuation, extralow frequency friction (both discussed in Ref. ( 11 )), anisotropy (20), or fluctuations in the small ion distribution around the macroion (9). Our DLS measurements on Laponite sols demonstrated that the short-time decay becomes faster as the ionic strength is lowered, whereas the long-time decay remains relatively unperturbed by changes in the ionic strength. These results indicate (i) the strong influence of long-range electrostatic repulsion on collective diffusion; (ii) that particle interactions are significant even in dilute sols; and that (iii) small ion redistributions and charge fluctuations have little effect on the slow component of C(q, r). Journal of Colloid and Interface Science, Vol. 134, No. 2, February 1990
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ROSTA AND VON GUNTEN
Clay sols are always polydisperse and elecfE = fE,0(1 + flee), [14] tron micrographs of Laponite indicate that this where JE,0 is the infinite dilution electrostatic synthetic smectite is no exception to that. But friction factor due to macroion-small ion even if the anisotropic, disk-like Laponite parcoupling and fie is the electrostatic virial coefticles were uniform in size, the suspension ficient representing direct macroion-macroion would still appear to be slightly polydisperse interactions. by light scattering because the form factor P(q) For asymmetric particles, such as Laponite, depends on the orientation of the platelets with f0 can be expressed by a modified Stokes forrespect to q (20). We find it plausible that a mula (21 ), combination of this effect with intrinsic size and charge polydispersity is manifested in the f0 = 67r~TrH = 67r,ht/G, [15] long-time tail of the autocorrelation function. where r/is the viscosity of the dispersing meHowever, a more detailed analysis of this very dium, rH is the spherical equivalent hydrocomplex phenomenon would require addidynamic radius, ht is the thickness of the hytional scattering experiments at higher q drated aggregate, and G is the shape factor. (SAXS, SANS). On the basis of Refs. ( 5 ) and (22) we assume that electrostricted water layers have the same Friction 1-nm thickness between the platelets and Figure 4c shows that collective friction in- the outside, leading the ht = 7 nm. The shape creases linearly with particle concentration factor, G = 0.6, was evaluated by Perrin's and decreases with the ionic strength. To es- expression for oblate ellipsoids (taken from timate the importance of electrostatic inter- Ref. (21)). Substitution into Eq. [15] gives rn actions in the friction of Laponite, we analyzed = 11.7 nm andfo = 2.2 X 10 -l° kg/s. our data by a simple virial expansion method. The hydrodynamic virial coefficient of hardNumerical results are presented only for the body interactions was calculated by the triplet tactoid, because the friction parameters expression of Beenakker and Mazur (23): fl differed less than 10% for the other two pos- = 1.7~/e, where • is the volume fraction of sible structures (doublet, quadruplet). the particles. This contribution to the collecThe translating motion of a macroion in tive friction factor turned out to be negligible aqueous solutions is hindered by hydrody- compared with its electrostatic counterpart. namic and electrostatic forces. Presuming that The electrostatic parametersfE.0 and fiE were these forces are not coupled, derived from our experiments by performing linear fits to the f data (see Fig. 4c) at each f = fH + fE, [12] ionic strength where f n and fE are, respectively, the hydrodynamic and electrostatic friction factors. Expandingfn in terms of the particle concentration to the first order gives flJ = f 0 ( l + fie),
[13]
where the virial coefficient 13takes into account hydrodynamic interparticle interactions. The single-particle friction factor f0 represents zero concentration friction of an uncharged particle due to the presence of solvent molecules. The net electrostatic effect can be expressed by a first order virial approximation as Iournal of Colloid and Interface Science, Vol. 134, No. 2, February 1990
fE,0 = (intercept) c=0 - fo fie =
slope/JE,0.
[ 16 ] [17]
The data obtained are listed in Table I. A comparison o f f 0 (=2.2 X 10 -1° kg/s) with fE,0 values shows that electrolytic friction is significant in Laponite sols. Schurr has recently proposed a theory for electrolytic friction on isolated spherical macroions (24). We found that Schurr's theory overestimates fE,0 by 25-40%. The discrepancy, which decreases upon an increase in the ionic strength, may be due to the fact that the conditions in La-
LIGHT SCATTERING OF LAPONITE TABLE I Infinite Dilution Electrostatic Friction Factor fE,0 and Electrostatic Friction Virial Coefficientt3Eof Laponite RD as a Function of Added KC1 [KCI] (M)
JE,o(10-1° kg/s)
flu (cm3/g)
0a 0b 0.0005 0.0010 0.0025
3.1 3.1 2.9 2.7 2.4
292 104 98 95 71
Dialyzed sample. b Untreated sample.
ponite suspensions do not agree with Schurr's assumption of spherical particles with low surface potential. It should also be mentioned that an earlier treatment by Booth (25) would underestimate our fE,0 data by about a factor o f 7. Table I illustrates that fz,0 increases as the ionic strength is lowered. This trend, which is consistent with the predictions of Schurr, as well as with other experimental data (9, 11 ), can be explained by the following argument. A decrease in the ionic strength leads to a thicker double-layer around the macroion. During its Brownian motion, the macroion drags along this thick ionic cloud and, as a result, experiences larger friction. Inspection of the electrostatic virial coefficient/]E data in Table I reveals a striking difference between the dialyzed and untreated systems. As ionic impurities are removed from the sols by dialysis, Laponite particles experience additional hindrance in motion due to the longer range of double-layer repulsion. Even the smallest/3E values (in 0.0025 M K C 1 ) are large enough to demonstrate that macroi o n - m a c r o i o n coupling can lead to increased friction, for colloid concentrations used generally in light scattering experiments. For a comparison with theory (15) one should be able to calculate the electrostatic pair potential of the particles. This is, unfortunately, not feasible as neither the ionic strength dependency of the surface potential of Laponite nor
405
the necessary correction factors for particle anisotropy and charge heterogenity are available. CONCLUSION Static and dynamic light scatterings have been applied to obtain useful information about the structure and dynamics of Laponite R D in aqueous solutions. These techniques, combined with m e m b r a n e filtration and electron microscopy, suggest that the majority of the sol particles are present in the form of a tactoid composed of two to four single platelets with a lateral dimension of about 30 n m and an average molecular weight of 3000 + 500 kg/mol. The concentration and ionic strength dependence of the static structure factor, collective diffusion coefficient, and friction factor indicate strong interactions a m o n g the colloids. Neutral and electrostatic contributions to the collective friction factor were evaluated by first order virial expressions. Infinite dilution electrolytic friction fE,0 varied inversely with the concentration of added electrolyte and was always larger than the usual Stokes friction factor f0 at the ionic strengths studied (<0.0025 M ) . It has been demonstrated that electrostatic coupling a m o n g macroions contributes significantly to collective friction. ACKNOWLEDGMENTS The authors are indebted to R. Giovanoli for the preparation of electron micrographs. Stimulating discussions with J. Ricka and M. Meewes are acknowledged. We are thankful to the two unknown refereesfor their suggestions. We thank Laporte Industries for providing a sample of Laponite RD. This work was partly supportedby the Swiss National Science Foundation. REFERENCES 1. Neumann, B. S., and Sansom, K. G., [srael,L Chem. 8, 315 (1970). 2. Perkins, R., Brace, R., and Matijevic, E., J. Colloid Interface Sci. 48, 417 (1974). 3. Lockhart, N. C., J. Colloid Interface Sci. 74, 509 (1980). 4. Avery,R. G., and Ramsay,J. D. F., J. Colloidlnterface Sci. 109, 448 (1986). Journal of Colloid and Interface Science, VoL 134, No. 2, February 1990
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5. Fripiat, J., Cases, J., Francois, M., and Letellier, M., J. Colloid Interface Sci. 89, 378 (1982). 6. Pusey, P. N., and Tough, J. A., in "Dynamic Light Scattering and Velocimetry: Applications of Photon Correlation Spectroscopy" (R. Pecora Ed.). Plenum, New York, 1985. 7. Cummins, H. Z., and Pike, E. R. (Eds.), "Photon Correlation and Light Beating Spectroscopy," Nato Advanced Study Institutes Series B, Physics, Vol. 3. Plenum, New York, 1974. 8. Degiorgio, V., Corti, M., and Giglio, M. (Eds.), "Light Scattering in Liquids and Macromolecular Solutions." Plenum, New York, 1980. 9. Schmitz, K. S., Lu, M., and Gauntt, J., J. Chem. Phys. 78, 5059 (1983). 10. Cantu, L., Corti, M., and Degiorgio, V., Faraday Discuss. Chem. Soc. 83, 287 (1987). 1 l. Weissman, M. B., and Marque, J., J. Chem. Phys. 73, 3999 (1980). 12. Tivant, P., Turq, P., Drifford, H., Magdelenat, H., and Menez, R., Biopolymers 22, 643 (1983). 13. Bender, T. M., Lewis, R. J., and Pecora, R., Macromolecules 19, 244 (1986). 14. Koppel, D. E., J. Chem. Phys. 57, 4814 (1972). 15. Drifford, M., Belloni, L., Dalbiez, J. P., and Chatto-
Journal of Colloid and Interface Science, Vol. 134, No. 2, February 1990
16. 17.
18. 19.
20.
21.
22. 23. 24. 25.
padhyay, A. K., J. Colloid Interface Sci. 105, 587 (1985). Neal, D. G., Purich, D., and Cannell, D. S., J. Chem. Phys. 80, 3469 (1984). van Olphen, H., and Fripiat, J. J., Eds., in "Data Handbook for Clay Minerals and Other Non-Metallic Minerals," OECD and Clay Minerals Society, p. 229. Pergamon, Oxford, 1979. Weissman, M. B., aT.Chem. Phys. 72, 231 (1980). van Veluwen, A., Lekkerkerker, H. N. W., de Cruif, C. G., and Vrij, A., Faraday Discuss. Chem. Soc. 83, 59 (1987). Hayter, J. B., in "Physics of Amphiphiles: Micelles, Vesicles and Microemulsions" (V. Degiorgio and M. Corti Eds.), p. 70. North-Holland, Amsterdam, 1985. Zero, K., and Pecora, R., in "Dynamic Light Scattering and Velocimetry: Applications of Photon Correlation Spectroscopy" (R. Pecora Ed.), p. 66. Plenum, New York, 1985. Grauer, Z., Malter, A. B., Yariv, S., and Avnir, D., Colloids Surf. 25, 41 (1987). Beenakker, C. W. J., and Mazur, P., Phys. Lett. A 91, 290 (1982). Schurr, J. M., Chem. Phys. 45, 119 (1980). Booth, F., J. Chem. Phys. 22, 1956 (1954).