J. CHEM. SOC. FARADAY TRANS., 1994, 90(14), 2085-2093 Determination of Aggregate Structures by Combined Light-scattering and Rheological Studies Stephen D. T. Axford" and Thelma M. Herrington Department of Chemistry, University of Reading, Whiteknights, Reading, Berkshire , UK RG62AD The structures of aggregates of a clay, sodium bentonite, formed during the rapid (diffusion-limited) aggregation of a destabilised colloidal suspension have been studied using a combination of three experimental techniques. The first two of these were static and dynamic (quasi-elastic) light-scattering measurements, while the third involved rheological studies. The system was studied as a function of the pH of the aggregating suspension, between pH 2.3 and 10.2. Analysis of the light-scattering results leads directly to a determination of the fractal dimension, d,, of the aggregates formed.The value of d, for the aggregates showed a rapid transition from 3.0 below pH 4.3, to 1.8 above pH 4.3. This implied a close-packed structure for aggregates formed under highly acidic conditions, but a more open one in less acidic and in slightly alkaline suspensions. Rheological measure- ments showed minima in the Bingham yield stresses for both aggregated and unaggregated bentonite suspen- sions, at the cross-over point, pH 4.3, between the two structures. In addition, the ratio of the storage modulus to the loss modulus took only two values: a higher one below pH 4.3, and a lower one above pH 4.3. It was concluded that hetero-flocculation is induced in the aggregation of sodium bentonite below a certain acidity, resulting in aggregates which have a card-house, as opposed to band-like, structure.Furthermore, these open aggregates showed more viscous, and less elastic, behaviour than those with a higher fractal dimension. A recent study by Herrington and Midmorel of the rapid aggregation of dilute kaolinite suspensions concluded that the flocs showed a transition from loosely packed, volu- minous, card-house structures in slightly acidic conditions, to compact, flake-like, structures in moderately acidic condi- tions. Their work relied on the determination of fractal dimensions by dynamic scaling (e.g. Weitz et aL2) measure-ments, made during a study of the growth of the aggregates by photon correlation spectroscopy (PCS).In the current work, the aggregates of another clay, sodium bentonite (predominantly a montmorillonite clay), are studied. The technique of dynamic scaling is again used, but in addition, static light-scattering experiments are performed, which are also able to give information directly about the fractal struc- ture of the aggregates. The results from both sets of experi- ments are compared with the information implied in a series of rheological studies. The basis behind dynamic scaling measurements is the theory of aggregation kinetics originally propo~ed~,~ by Smoluchowski, who also dealt with the coagulation and coalescence of larger aggregates, and precipitation. Sub-sequent ~tudies~-~ of colloidal aggregation tested this theory and found that it was generally a good description of the initial stages of aggregation.Only recently, with the advent of computer-based simulations of aggregation, has aggregate behaviour which deviates from the simple Smoluchowskian scheme been more accurately modelled. Typically, such advances have taken place in the simulation of both perikinetic' and orthokineticg aggregation. The application of the concept of fractal behaviour for col- loidal aggregates leads to the relationship between the radius, r, of an aggregated cluster of mass, m,and the radius, a, and mass, rno ,of a single particle, uiz. :".(ym0 (1) This expression serves as a formal definition for the fractal dimension, d,, of any object which shows fractal-like behav- iour.It is now generally recognised that random aggregates are fractal objects,"." a result based on the observation of a power-law dependence of scattered light intensity, Z(q), on the scattering vector, q, where q is related to the scattering angle, 8, by q = (4nn/A)sin(8/2); here n is the refractive index of the medium, and Iz. the wavelength of the incident light. There- fore, when the cluster size is suficiently large to show true fractal behaviour (i.e. containing a sufficient number of single particles to enable the cluster to show the same, repeating, internal structure over a length much greater than the char- acteristic size of the component particles themselves), this dependence may be written where df is the fractal dimension of the aggregate, defined by eqn.(1) above. This relationship is the basis for the sub- sequent determinations of fractal dimension of large clay aggregates, by measurements of static light intensity. One such recent studyI2 by Lin et ai. has shown the differences in colloidal gold and silica aggregate structure, when the aggre- gation mechanism is either diffusion- or reaction-limited. The time dependence of the growing characteristic cluster mass, rn, can be determinedI3 from the Smoluchowski equa- tions. For diffusion-limited cluster aggregation, it can be shown that a linear relationship between mass and time ensues. Because the rate of increase in mass, rn, of an aggre- gate growing under diffusion-limi ted conditions, remains con- stant as a function of time, the mass term in eqn. (1) may be replaced by time.Thus, we may immediately write an expres- sion for the radius, I, at some time, t, after the start of the aggregation cc (t)'ldf (3)a If it proves possible to measure r experimentally, as a func- tion of time, then a value of d, may be derived using eqn. (3). Dynamic, or quasi-elastic, light-scattering measurements, which are the basis of PCS (see below), enable the average hydrodynamic radius of the clusters to be determined. There- fore, providing that the rate of aggregation remains constant throughout the timescale of the experiment, the fractal dimension of the aggregates may be deduced.Extensive rheological studies14-' of a similar clay, kaolin- ite, have been made previously, though most have used samples with a large volume fraction of solids. Similar studies have also been made'**'' on the flow properties of concen- trated bentonite suspensions. In the current work, despite the inherent difficulty in working with very dilute suspensions, measurements relating to aggregate and network structure have been made. There are some fundamental differences between the kaolinite used in previous' studies, and the ben- tonite clays described here. The main differences are struc- tural, with one particularly important physical result. The structure of kaolinite consists of repeated sheets of tetra- hedrally coordinated Si atoms, and octahedrally coordinated A1 atoms, stacked in a 1: 1 ratio.A typical basal spacing is ca. 7 A. On contact with water, there is no penetration of water between the aluminosilicate layers, and the clay does not expand. Bentonite comprises layers with two tetrahedral sheets sandwiching an octahedral sheet, and is thus referred to as a 2 :1 layer clay. Typical basal spacings are of the order of 9 A. In the presence of water, this is taken up by the clay between the layers, leading to interlayer swelling, and increas- ing the basal spacing to between 12 and 15 A. Thus the effec- tive volume fraction taken up by bentonite dispersed in water is greater than that calculated simply from the mass of ben- tonite added to the water; this behaviour is the main differ- ence compared with the non-expanding kaolinite.These effects are described in more detail2' by van Olphen. The use of two complementary light-scattering techniques should lend more support to the resulting postulated struc- tures, than would be the case using only one method. Cer- tainly, recent studies by Lin et ~1.~' .and Rarity et ~ 1have ~ shown the two methods to be capable of giving an under- standing of the fractal geometry, and a measurement of the fractal dimension, of the aggregates. Likewise, the inclusion of rheological measurements may well demonstrate that the suggested aggregate structures, as obtained from both kinds of light-scattering experiments, are those most likely to exist. Theory Static Light Scattering Of the two light-scattering techniques used, the first case to be considered is that of static light scattering.Here, the angular dependence of the intensity of light, scattered by aggregates in suspension, is recorded. It is necessary to know the dependence of scattered light intensity on both scattering vector, q,defined above, and cluster mass, m. This relation- ship may be written (4) where I,&) is the intensity of light scattered by a single fractal cluster with mass, rn, and concomitant radius of gyra- tion, R, ,at an angle corresponding to the scattering vector, q. The structure factor for a cluster of mass, m, is SJqR,). This latter variable is responsible for the widely varying behaviour of eqn.(4) seen with very differently sized aggregates. Eqn. (4) may be rewritten for a suspension consisting of a large number of aggregates of different masses, uiz. m= 1 where n, is the fraction of clusters with mass, m. This expres- sion is dependent on both the aggregate size distribution, through the n,m2 term, and the shape of the clusters, through the S,(qR,) term. The radius of gyration, R,, of the aggregates, is the characteristic length for each cluster, and can be related to the radius, a, of a single particle, and the mass of the aggregate, through the fractal scaling of the clus- J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 ters R, = aml/df (6) In addition, the limiting values for the structure factor may be written as a function of qR, as follows (7) It is possible to see that eqn.(5) leads to two limiting expres- sions for I(q), depending on the relevant S(qR,) term in eqn. (7). Clearly, for small aggregates, with qR, 41, the internal structure is not resolved, and the cluster behaves essentially as a point particle as far as the light probe is concerned. Such an aggregate scatters light coherently, and the resulting intensity scales solely as a function of m2, from eqn. (5). However, for large aggregates, satisfying qR, 9 1, the fractal nature of the cluster is revealed, since the light scattered from different parts of the aggregate adds incoherently. Substitut- ing eqn. (6) and (7) into (3,and eliminating R,, gives a dependence of scattered intensity for large aggregates which is linear both in m, and in q-df.It is also abundantly clear that there will be a cross-over regime, with qR, x 1, where neither asymptotic region of eqn. (7) is reached. This point has been studied in some detail by Rarity et ~1.~~and Lin et ~1.'~previously. A more complex expression for S(4R.J has been derived2' by Lin et al., which shows the desired behav- iour at both extremes of qR,, and which also describes the transition in the cross-over region. If it is desired to make ~ measurements of the fractal dimension of a suspension of aggregates by a static light-scattering technique, then the main prerequisite is that the average radius of the clusters is much greater than the length probed by the light source.This length is essentially l/q, the inverse of the magnitude of the scattering wave vector. Dynamic Light Scattering Dynamic, or quasi-elastic, light scattering is a most useful experimental tool for studying colloidal aggregates. By mea- suring the temporal fluctuations in scattered light intensity over very short timescales, the technique can give informa- tion about the motion of the scattering particles. In a normal colloidal suspension, this is Brownian motion, arising from collisions with the molecules of the suspending medium. The velocity of a particle is then determined solely by its ability to diffuse through the fluid. It thus becomes possible to derive an average diffusion coefficient, (D,,,), for the aggregates in suspension, and this in turn may be related to an average hydrodynamic radius, r, using Stokes' law.However, it should be remembered that dynamic scattering only yields informa- tion about diffusion coefficients, and that all other param- eters must be derived from these. In the application of dynamic light scattering to the tech- nique of PCS, the intensity correlation function is obtained by making successive measurements of scattered light inten- sity as a function of time elapsed from some reference point. The empirical normalised intensity function, g(2)(z), is deter- mined directly by where the intensity, I, is measured at the arbitrary reference time, t, and then later at a time, t + z. Eqn. (8) is then related to the theoretical normalised field autocorrelation function, g(')(z), by the Siegert relation g'2'(z) = 1 + cIg"'(z) 12 (9) J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 where C is a constant. The autocorrelation function, g(')(T), for a dispersion of monosized particles, may be related to the diffusion coefficients as follows g(')(z) = exp(-q2Dt) (10) However, for polydisperse systems, such as are formed by the aggregation of a monodisperse sample, the autocorrelation function becomes where n, is the number density (normalised to Zz= n, = 1) of aggregates with mass, rn, and diffusion coefficient, D,. In order to make comparison with real experimental data, the correlation function obtained experimentally needs to be described more simply than by eqn.(1 l), which includes diffu- sion coefficients for every size of aggregate. In the simplest analysis, known as a cumulants analysis, therefore, the right- hand side of eqn. (11) may be expanded about the mean (q2D,), which yields Here the term (q2D,) is called the first cumulant, pl, of the correlation function. The departure from a pure exponential, which would be the form of eqn. (ll), i.e. it would reduce to eqn. (10) if all the aggregates were of the same size, is now modelled as a polynomial in the logarithm of the correlation function. The initial slope of a plot of the left-hand side of eqn. (12) against z [obtained by differentiating eqn. (12) with respect to z,and setting z = 01, gives the mean diffusion coef- ficient, (D,), and p2/p1gives a measure of the polydispersity of the sample.Whilst the above cumulants analysis yields an expression for (Dm), a model-independent form for the mean diffusion coefficient may be given as follows, in terms of the diffusion coefficients for every cluster mass Here, the individual diffusion coefficients are weighted by the scattering intensity and the number of clusters of each aggre- gate mass. Note that the above analysis makes no allowance for the effects of a rotational contribution to the autocorrela- tion function, as is described21 by Lin et al., for fractal flocs with qR, > 1. Another study, by Axford et al., concluded23 that for certain systems, such as those described below, rota- tional diffusion effects do not contribute significantly to the value of the first cumulant, (q2D,).In a typical experiment, the average diffusion coefficient is calculated from eqn. (8), (9) and (12); only when a more com- plete understanding of the aggregate size distribution is required, is a rather more complex deconvolution of the light intensity data applied in terms of eqn. (8), (9), (11) and (13). Such an analysis then requires estimates of the cluster struc- ture factors, S(qR,),used in eqn. (13); these may be generated by Rayleigh-Gans-Debye theory. Their use in interpreting PCS results in terms of cluster aggregation and polymer theory has been successfully demon~trated~~ by Herrington and Midmore. Simple Rheology Theory In this section, some of the simpler aspects of a small part of an enormous subject are dealt with.Given the nature of the study being undertaken, our interest is inevitably in the flow behaviour of suspensions, which will tend to be non-Newtonian fluids, and in whatever information may generally 2087 be derived about the possible structures of particles dispersed in a liquid. The most typical non-Newtonian fluid is a shear-thinning liquid. Such fluids show a widely varying shear viscosity as a function of shear rate, in complete contrast to a Newtonian liquid which has a constant shear viscosity. In the Newtonian case the shear stress, 0, generated in simple shear flow, is directly proportional to the applied shear rate, p, i.e., Is = qj (14) where q is the viscosity, and is constant.However, for a shear-thinning fluid, the apparent viscosity decreases with increasing shear rate. One of the simplest models for non-Newtonian flow is that of 'Bingham' plastic behaviour. In this case a fluid does not start to flow until a critical, or yield, stress is reached. In other words, the apparent viscosity is extremely large until this critical stress is attained; thereafter, the viscosity falls sig- nificantly, and the fluid shear stress increases as a function of shear rate. In practice, this subsequent rise in stress is not usually linear with shear rate, though this assumption is made in the Bingham model. Thus, for this idealised model, we may write 0 = OY + qpj (15) where oYis the yield stress, and qp the plastic viscosity, both of which are constants.In reality, the concept of a yield stress is sometimes flawed, and fluids do flow at very low shear rates, often showing Newtonian behaviour. However, the derivation of a yield stress for a fluid may well have many important practical purposes, in the sense that for normal applications and typical shear rates, there is some point at which the fluid starts to flow with a considerable reduction in apparent viscosity. In the current work, the calculation of a yield stress for a suspension in which there are a number of inter-particulate forces may reveal information about the nature of the binding between particles, and hence indicate the presence of long-range structure within the suspension.Another rheological aspect we shall consider is that of the viscoelastic behaviour of a material. The term 'visco-elastic' means that the material shows properties which are a mixture of rigidity (i.e. elastic properties) and fluidity (i.e. viscous properties). It is often useful, in attempting to understand the viscoelastic behaviour of a material, to discuss the response of that material to an applied small-amplitude oscillatory shear. It should be recalled that the shear rate is the rate of change of strain with respect to time. In oscillatory shear we define a complex shear modulus, G*,(much like the modulus for an elastic, or Hookean, solid) relating stress, 0, to strain, y, uiz. = G*(W)Y(t) (16) where stress and strain are inevitably functions of time as a result of the oscillatory shear applied. The complex modulus is also a function of applied frequency, o,and can be resolved into two components, as follows G* = G' + iG" (17) where G'and G" are referred to as the storage modulus and loss modulus, respectively.Thus it is found that there are two components to the resulting stress in the sample. One part is always in phase with the applied strain, while the other is out of phase, by 42. In the simplest of interpretations, the rela- tive magnitudes of G' and G" will give an indication of the degree of rigidity, as opposed to fluid-like behaviour, of a material. Therefore, should very different values of G’/G’’ be found for suspensions containing clusters or networks formed under a variety of experimental conditions, it may be possible to interpret the results as indicating the presence of different structures within the fluid.Experimental The experiments to determine aggregate structure were carried out using sodium bentonite, predominantly a smec- tite, or montmorillonite, clay; this was supplied as a finely divided powder by Allied Colloids. All exchangeable cation sites within the clay are taken up by sodium ions; the clay was also free from the presence of other ions and salts. Ca. 5 g of bentonite were added to 250 ml water, and dispersed using an ultrasonic bath. The resulting suspension was left for 24 h to allow the sedimentation of any larger particles. The suspension was decanted and allowed to stand for another 24 h.Again, the suspension was decanted in order to discard those particles which had sedimented. Two further suspen- sions were prepared, each one a ten-fold dilution of the first. The volume fractions of solids, 4, for the three preparations were found to be ca. and respectively. The effective volume fractions of each dispersion may well be up to 50% greater than calculated, owing to the swelling nature of the bentonite clay; however, the order of magnitude of 6 is as given. The two most dilute suspensions were sized using PCS, and the average particle diameter was found to be 212 nm, with a polydispersity index (the ratio of the variance to the mean) of between 0.1 and 0.2. This diameter is, of course, only an effective hydrodynamic diameter, and the actual shape of the clay particles is almost certainly not spherical.In fact, given that the clay is a layered aluminosilicate structure, the smallest particles are likely to be flake-like fragments. This suggested structure for the single particles is supported25*26 by scanning electron microscopy of bentonite. In each experiment, 5 ml of a suitable strength of bentonite suspension was placed in a cylindrical Burchard cell, made from high optical quality quartz. To this was then added 4 ml of aqueous HCl, of between and mol I-’. Finally, to initiate aggregation, 1.0 ml of 0.1 mol 1-’ aqueous KC1 was added, making a total sample volume of 10 ml. There- fore, in all experiments, the concentration of KCl was con- stant, at 0.01 mol 1-’, whilst the pH was varied at will.All’ the solutions were kept at 25°C at all times. The Burchard cell was then placed in the PCS apparatus, and the increase in hydrodynamic radius monitored as a function of time. The choice of KCl solution strength was the minimum which removed the electrostatic repulsions between the clay par- ticles and enabled aggregation to take place. The final pH of the aggregating mixture was measured using a standard glass electrode after the run was completed. It was confirmed that the final pH was in fact reached immediately on the addition of the HCl and KCI to the bentonite, and took values between pH 2.3 and 10.2. The reaction was followed until the increase in radius had slowed somewhat, probably due to sedimentation of the largest aggregates.The conditions of each run were chosen so that the growth in radius took place over a suitable timescale of, say, between 30 min and 2 h. At the end of this time, intensity measure- ments as a function of scattering angle were made. Results were collected over a short period during which the size of the aggregates changed negligibly. These static light-scattering experiments were carried out on aggregates with an average diameter of ca. 2000 nm, which ensured that the condition qR, % 1 was met. At this point, the measurement of time in dynamic scaling measurements is briefly considered. Because the technique J. CHEM. SOC. FARADAY TRANS., 1994, VOL.90 deals with perikinetic aggregation, it is possible to define a dimensionless time parameter, E, in terms of the theoretical Smoluchowski rate coefficient, k,, the initial particle number concentration, No,and the time elapsed from the start of the aggregation, t. This ‘reduced’ time takes the form E = k, Not, and is the time parameter quoted in the results presented in the following section. Whilst not strictly necessary for dynamic scaling measurements, in which solely the logarithm of time is important, it enables aggregation experiments, taking place at different particle concentrations, to appear to occur over similar dimensionless timescales. Finally, suspensions of the bentonite with 4 = were treated with aqueous HC1, to give a pH range between 1.1 and 9.3.Two samples at each pH were made, and one was then treated with aqueous KCl in order to induce aggre- gation. It should be realised, however, that the aggregated clay is still likely to show some long-range order in the form of networking or gelling behaviour, with bonding existing throughout the dispersion, because of the somewhat higher (4> 0.01 in water) volume fraction, compared with the dis- persions studied by light scattering alone. Obviously, the majority of clay particles will reside within compact aggre- gates, but some will remain loosely bonded in the suspending fluid. Therefore, all rheological measurements on these aggre- gated systems are likely to derive from contributions from both the aggregates and the suspending liquid.Experiments using two types of Bohlin rheometer were then performed on these samples. Of the two different sets of measurements obtained, one used shear viscometry to deter- mine yield stresses, whilst for the other the suspension was subjected to oscillatory flow in order to derive the relative magnitudes of the storage and loss moduli of the aggregates. In these latter experiments the methods of Tadros and co- worker~~~-~’were followed. This involves initially fixing the oscillatory frequency and measuring the rheological para- meters as a function of strain amplitude. This allows us to find the linear viscoelastic region, where G*, G and G” are independent of strain. Once the linear region has been deduced, measurements may be made as a function of fre- quency, at fixed amplitude.Thus it is often desirable to con- centrate on either one frequency or a small range of frequencies, and make comparisons between the measured rheological parameters of different systems under the same experimental conditions. In this way, variations in visco- elastic properties may be seen for a range of colloidal clay systems. Results Light-scattering Results The results of dynamic scaling measurements using PCS made on the bentonite are shown in Fig. 1 and 2. It was found that plots of log(r/a) against dimensionless time, E, elapsed from the start of the aggregation, showed only two gradients, namely ca. 0.33 and ca. 0.56, corresponding to fractal dimensions of 3.0 and 1.8, respectively.No other slope was seen at any pH, or in any experiment. Fig. 1 shows the results obtained at low pH for three runs, all of which exhibit a high fractal dimension. Fig. 2, in contrast, shows four plots, all obtained at higher pH values where the fractal dimension is much lower. The results of static light-scattering experiments, on the same samples, are illustrated in Fig. 3 and 4. Here are plotted log[Z(q)] against -log q, such that the slope equals the fractal dimension, d,. Fig. 3 is for aggregates formed at relatively low pH, whilst Fig. 4 is for suspensions which are less acidic. Reliable plots were obtained in slightly fewer cases than with J. CHEM. SOC. FARADAY TRANS., 1994, VOL.90 0.7 0.6 1.8 2.0 2.2 2.4 2.6 2.8 log E Fig. 1 Logarithmic plots of aggregate size against time from the start of aggregation, for three suspensions of sodium bentonite, as determined by dynamic light scattering. All results were obtained below pH 4.3, as follows: A, pH 2.3; 0,pH 4.01 ;0,pH 4.21. All the plots have slopes of ca. 0.33, corresponding to d, x 3.0. quasi-elastic light scattering, probably because of dust con- tamination which causes large problems at the smaller scat- tering angles. Again, it may be seen in Fig. 3 and 4, that essentially only two slopes are found, corresponding to fractal dimensions of around 2.9 for aggregates in a more acidic medium, or of about 1.9, at higher pH. 0.9 0.8 0.7 0.6 k ,,& .O 0.4 / ,o / / / 0.3 o?' I IIIIII II1IIII 1.4 1.8 2.2 2.6 3.O 3.4 log E Fig.2 As for Fig. 1, but for aggregates formed above pH 4.3, as follows: A,pH 4.55; 0, pH 5.7; 0,pH 7.5; 0,pH 10.21. The four plots all have slopes of between 0.5 and 0.6, corresponding to d, z 1.8. n r I cn ,-I2.0 nllo lIIIII1I'I 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 -log (q/nm-') Fig. 3 Logarithmic plots of intensity against scattering vector, obtained from two static light-scattering experiments. The plots are for the following pH values: 0,pH 4.01; 0,pH 4.21. The slopes in each case equal ca. 2.9-3.0. 4.0 -3.6 r I v) m ,o-' 3.2 A, ' 11'""'~""'""'1''''''' 1.5 1.6 1.7 1.8 1.9 2.0 -log (q/nm -I) Fig. 4 As for Fig.3, but at higher pH values: A,pH 4.55; 0, pH 5.7. The two plots have slopes, equal to the fractal dimension, of between 1.9 and 2.2. If all the results of determinations of fractal dimension as a function of pH are combined, then we obtain the plot shown in Fig. 5. It is clear from this that there is a sudden transition at ca. pH 4.3, between an aggregate structure which possesses the maximum possible fractal dimension at less than pH 4.3, and a structure with a much lower fractal dimension above this point. Rheological Results Two different types of rheological study were performed on the bentonite. In the first, shear viscometry was used on sus-pensions of aggregated and unaggregated bentonite, over a wide pH range. Fig.6 shows typical plots of shear stress against applied shear rate, for one of each kind of sample. It can be seen in Fig. 6 that the suspensions behave as Bingham plastics with a clearly defined Bingham yield stress, obtained by extrapolating the linear portion of the plots back to a shear rate of zero. Fig. 7 shows all the yield stress results, for both aggregated and unaggregated bentonite, as a function of pH. It is seen that there is a minimum in the yield stress at ca. pH 4.3 in both cases, though the curve is more pronounced for the aggregated suspension. Also, in this case, the yield stresses all tend to lie at lower values than the corresponding values, where these exist, for unaggregated bentonite. It should be noted that Fig. 6 shows that the suspensions do actually flow at low shear rates, and therefore the yield stress is perhaps only a useful tool, rather than a physical reality.However, it 3.0 1--+----JI, 1a't 4'1 I I 1 2.0.-g n L+ 1.0 12 3 4 5 6 7 8 91011 PH Fig. 5 All the dynamic (0)and static (+)light-scattering results of the previous four figures, plotted to show fractal dimension as a func-tion of the pH of the aggregating bentonite suspension 2090 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 10.5 1.2 10.0 1.o 8 0.8 2 0.6 m Q-. c L v) * c3P 9.5 9.O 0.4 8.5 I I I I I I I I I I 0.2 0 50 100 150 200 2 3 4 PH 5 6 7 shear ratels-’ Fig. 6 Two plots of shear stress against shear rate.One is for a typical aggregated suspension of sodium bentonite, at pH 4.3 (+); the other is an unaggregated suspension, at pH 6.8 (A). does describe a point where there is a change in the flow properties of the liquid, and as such will help with an under- standing of the forces existing, either between or within the aggregates or particles in the fluid. The results of the second class of experiments, involving oscillatory shear, are shown in Fig. 8 and 9. Fig. 8 shows the results of calculations of G/G” as a function of applied strain frequency, a,for three typical aggregated suspensions, at various values of pH. The oscillatory frequency is seen in Fig. Fig. 9 The magnitude of G/G“ (the ratio of storage to loss modulus) for aggregated sodium bentonite, shown as a function of pH. Measurements were made over an oscillatory frequency range, GO,of 0.1-1.0 Hz, as in Fig.8. 8 to vary between 0.1 and 1.0 Hz, over which range the values of G’/G”may be taken, to a reasonable approximation, as being constant. Clearly, over a complete range of fre- quencies, the ratio G/G” will actually take all values from zero to infinity, since at very high frequencies the dispersion’ shows only elastic behaviour and G’/G”-+ a;at low fre- quencies only viscous behaviour will be observable and G/ G” -+0. However, by concentrating on the region, in this case one decade, where G/G remains independent of frequency, we may make comparisons between the viscoelastic behav- ~~~~ iour of different suspensions.The use of such measurements l~l~l~1.4 llll 1.2 1.o 0.8 0.6 0.4 123456789 9” Fig. 7 Plots of all the yield stresses, for both aggregated (+) and unaggregated (A) systems, as a function of pH in the bentonite sus- has been proved re~ently~’-~’ to be of considerable value in studying the stability and flocculation of colloidal disper- sions. These observations are necessarily only applicable over the frequencies covered in Fig. 8, but obviously any observed viscoelastic rheological parameter is ultimately frequency dependent. Measurements of G‘/G as a function of pH for all the aggregated bentonite samples are shown in Fig. 9. Here it becomes clear that G’/G”takes only two values, one of about 10.2 for bentonite aggregated at less than pH 4.3, and the other of ca.9.1, for aggregates formed above pH 4.8. There-fore, there appears to be a critical pH value, much as for the fractal dimension calculations shown in Fig. 5, either side of which, G‘/G is well defined and constant. Discussion pension. We may now consider the results of all three types of experi- ment in more detail. The results shown in Fig. 5 indicate a clear change in fractal dimension of the bentonite aggregates which are formed in diffusion-limited aggregation. If we con- sider the nature of the smallest clay fragments in the colloidal dispersion, then certain clays, e.g. kaolinite, are kn~wn~**~’ 10.0 to have negatively charged faces and positively charged edges. 5One consequence of this dual charge character is the possi- bility of heteroflocculation between the edges and faces of the clay particles, resulting in a three-dimensional, voluminous, ‘card-ho~se’~~.~~structure.If, however, the growth of the clusters proceeds via face-face aggregation, a far more dense, close-packed structure will result. Kaolinite was shown’ by Herrington and Midmore, using dynamic light scattering, to 9.5 c3 09.0 E 0 0 0 0 00 I I I I IIII form aggregates with two possible fractal dimensions over a 0.I 02 0.4 0.6 0.8 1.0 range of pH values, very much like the plot in Fig. 5. There-o/Hz fore, it would seem reasonable to assume that the bentonite Fig. 8 Plots of the ratio of the magnitude of the storage modulus to particles are behaving quite similarly to the kaolinite, and loss modulus, for aggregated sodium bentonite, as a function of the forming two rather different structures upon aggregation.frequency of the applied oscillatory shear. Two typical cases are Note that no value for the fractal dimension of the aggre- shown: 0,pH 6.8; 0,pH 4.3. gates was found to be greater than 3.0, which is, of course, the J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 maximum possible, when the solids in the aggregate are com- pletely space-filling. Similarly, the minimum measured fractal dimension is ca. 1.8, a value which corresponds to that fo~nd~.~~for the rapid, i.e. diffusion-limited, aggregation of gold and other sols. It may be reasonable to suppose that bentonite particles aggregating via a face-edge mechanism, and giving a random, open structure, will lead to the forma- tion of clusters not unlike those generated by the rapid aggre- gation of monodisperse spheres, clusters which will also have a low fractal dimension3' in such a system.The transition from high to low fractal dimension takes place at pH 4.3, as can be seen in Fig. 5. At df = 3.0, the only realistic candidate for the structure of the aggregates is a band-like one, with clay particles packing face-to-face, build- ing a layer by layer, and leaving no space in the structure. For d, = 1.8, however, there are still two possibilities, namely, a less tightly formed band-like structure, or a card-house built up by edgeface aggregation. The evidence would seem to point to edge-face, heteroflocculated, structures at high pH, since it is quite difficult to envisage a band-like structure which will not immediately rearrange to a close-packed one with d, = 3.0.Also, given that the background ionic strength is fairly high (with 0.01 mol 1-' KCl present), so that there is a very thin electrical double layer around the aggregate, then the positively charged edges will not be swamped by the effects of the larger, negatively charged faces. At lower ionic strengths the negative charge on the faces then overlaps the edges, and envelops the whole of the clay fragment. If the aggregation was carried out in water alone, as was done with kaolinite clay by Herrington and Midmore,' it proved impos- sible to form aggregates with the lowest fractal dimension for this very reason, that the positive edges seemed unable to participate in interparticle electrostatic 'bond' formation.If the structure were band-like at low fractal dimension, it is difficult to conceive why the background ionic strength would be such an important influence. It is necessary to consider the various factors which lead to the formation of one structure in preference to the other. A number of different mechanisms may be envisaged which account for the observed transition of pH 4.3. First, it may be the case that, as the pH is lowered, the increasing ionic strength finally reduces the face-face repul- sions to such an extent that the particles favour aggregation as a band-like structure.Obviously at higher pH values, with long-range face-face repulsion still existing, positivenegative charge coupling (i.e. face-edge) is energetically favourable. The situation appears to change at low pH, since the ability to aggregate through van der Waals attractions over a larger surface area (i.e. face-face) is then apparently preferable. This latter scenario does, however, require that the face-face elec-trostatic repulsions are removed, and so does not appear to take place until the acidity is increased to pH 4.3. However, it should be borne in mind that the relative increase in ionic strength is quite small, e.g. an acidity of pH 4 implies that H+ and C1- ions from added HCl represent only ca.1% of the total number of ionic species, when the background solution is 0.01 mol 1-' KCl. Further evidence that the differences in ionic strength with changing pH are not responsible for the transition between face-face and face-edge bonding is given by the reasonable independence of transition pH with molar- ity of KC1. In other words, experiments at any molarity of KCl, sufficient to induce aggregation, always resulted in a structure transition at around pH 4.3. Secondly, once any electrical double layers have been SUE-ciently reduced in thickness for aggregation to occur, as is the case at every pH studied here with 0.01 mol 1-' KCl present, then the likely magnitude and extent of electrical charge on both the edges and the faces of the clay particles may be con- 2091 sidered.Accepting that for clay particles in water alone the faces are negatively charged, and the edges positively charged, then it would appear that the strongest interparticle bonds should result from face-edge interactions. However, even if all the surfaces were negatively charged, then aggre- gation would still occur, as with e.g. polystyrene spheres, pro- vided that the background electrolyte concentration is sufficient to reduce the range of electrostatic forces, and hence allow attractive van der Waals potentials to overcome the repulsive terms. This situation certainly exists here, but we must also consider the initial, i.e. electrostatic, particle- particle interaction, which is either repulsive (face-face) or attractive (face-edge), depending on the proposed structure.It would appear that the attractive electrostatic interaction leads to the favoured structure above pH 4.3, provided that the clay particles retain their dual charge character, and despite the fact that face-face bonding would take place over a much larger surface area. Thus we may conclude that the overall bond energy between two particles is strongest for an attractive electrostatic interaction, even if this bonding takes place over the relatively small area of a face-edge bond. If the pH of the dispersion is lowered, i.e. made more acidic, then electron donation from negatively charged oxygen atoms on the faces, to the increased number of H30+ ions in the water, will lead to a reduction in the total negative surface charge.Such interactions will result in a form of hydrogen bonding, since H30+ is heavily hydrated, giving rise to a network of bound H+ and H,O over the faces of the clay. This surface reaction will have two effects: weakening the face-edge electrostatic attractive forces ; and decreasing the face-face electrostatic repulsions. If, during the formation of aggregates, it becomes energetically favourable to over- come the much reduced repulsive terms, in order ultimately to form bonding interactions over the large surface area of the faces, then a compact structure will be produced. In this situation, the pH at which bonding between surface oxygen atoms and aqueous H30+ becomes significant may be quite well defined, and is unlikely to be dependent on clay or KCl concentrations to any great extent.Lastly, one further contribution to the dramatic reduction of face-face repulsions at lower pH, may be the partial decomposition of the clay, with a concomitant release of A13+ ions into the aqueous phase. The efficiency of these ions in removing any residual electrostatic repulsions, and thus encouragmg the formation of the most stable (i.e. with the largest possible fractal dimension, bonded by the largest areas available on the clay) aggregates or networks, will be in accordance with the Schultze-Hardy rule. The sharpness of the transition at pH 4.3 may well be indicative of the passage of such trivalent ions from the clay into the solution, at this particular level of acidity.This effect might reasonably be expected to be independent of the molarity of KCl, because the increase in ionic strength due to the formation of aqueous A13+ could exceed that caused by the KC1 alone. Further- more, the start of such clay decomposition may well be so sensitive to pH that the sharp transition at pH 4.3 is inevit- able for a wide range of clay volume fractions and back- ground electrolyte concentrations. If we conclude that the possible structures for bentonite aggregates are close-packed and band-like with a high fractal dimension below pH 4.3, or open and card-house-like above pH 4.3, then an examination of the rheological results should be made, in order to see whether these assumptions are justi- fied, and supported by the results.The results of the yield stress measurements were shown in Fig. 7. Here values of yield stress are presented for suspen- sions of bentonite with and without 0.01 mol 1-' KCl present. In the former, aggregates will have formed with the J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 two possible fractal dimensions, depending on the pH of the suspension, while in the latter, aggregation only occurs at the lowest pH, i.e. pH 1.1, where the hydrogen ion concentration is sufficiently high to induce aggregation, and play the role of the added salt. Both sets of results in Fig. 7 show a minimum at between pH 4 and 5. If we consider the aggregated benton- ite below pH 4.3,then a rise in yield stress is seen as the pH is reduced.Since the aggregates form close-packed structures in this region, it is clear that an increase in ionic strength will lead to an increase in the face-face attraction between par- ticles, and so give rise to an increase in yield stress, since this is a measure of the binding energy between the particles in the fluid. This effect will be particularly noticeable if the repulsion terms have been dramatically reduced by the pres- ence of A13+, as discussed previously. Above pH 5, there is an increase again in yield stress, this time for aggregates which possess a card-house structure. The reduction in hydrogen ion concentration would appear to favour the strengthening of the faceeedge bonds between the particles.This effect manifests itself in an increase in yield stress from 0.46 Pa at pH 4.3,to 1.2 Pa at pH 9.3.It is not easy to see how the reduction in acidity strengthens the face-edge bonds, but one possibility is that reducing [H’] leads to the positively charged edges being more strongly attracted to the negative faces, since the conditions of greater [OH-] and smaller [H’] will tend to increase the thickness and range of influ- ence of the electrical double layer on the negatively charged faces. This, of course, makes face-face aggregation even less likely, as explained above, but will actually enhance face- edge bonding. A similar trend is seen for the case of bentonite which has not been aggregated. This observation implies that, even without forming discrete aggregates or clusters, the same type of order, or bonding, exists throughout the suspension. It is certainly the case that at pH 1.1, the suspension appears to be a slightly thickened gel, and this may also be true at pH 1.9.Therefore, the same arguments, either for face-face or for face-edge bonding between clay particles, may be proposed. It is interesting that all the measurements of yield stress in an unaggregated suspension of sodium bentonite are greater than those made in the flocculated case. One reason may be that, whilst the variation in yield stress as a function of pH does derive from the type of bonding within the aggregates, the total amount of resistance to flow will be less than for an unaggregated suspension where there may be more long-range order.In other words, the suspending liquid between the aggregates, once these have been formed, contains fewer particles per unit volume than the unaggregated dispersion. This fluid will make only a limited contribution to the yield stress, though it may still be capable of transmitting stress through the suspension. In contrast to this, the unaggregated bentonite suspension will be more uniformly dispersed, and may offer a greater resistance to flow, even if the individual bonds between the networked particles are considerably weaker than those bonds which exist only within an aggre- gate. Finally, we may consider the results presented in Fig.9. Here the values of G’/G’’for the aggregated sodium bentonite are shown as a function of pH. The ratio G‘/G‘‘is the ratio of the storage modulus to the loss modulus of the entire suspen- sion. In this case, there will be some contribution to G’ from the suspending liquid, so that G’/G’’is in fact a measure of the amount of rigidity, compared to viscous or fluid-like behav- iour, of a mixture both of the aggregates and of the liquid containing weakly bound, unaggregated, clay particles. Immediately it may be noticed that the graph takes the same form as Fig. 5, with a rapid transition from a high value for G’/G” of ca. 10.2below pH 4.5,to a lower value of ca. 8.9-9.1 above pH 4.5.As with the measurements of fractal dimen- sion, essentially only these two values of G’/G”are found over all the pH range studied.Making the assumption that the contribution to G/G” from the suspending fluid remains roughly constant, then differences in G’/G’’ should relate to differences in the viscoelastic behaviour of the clusters, as a function of pH. Whilst it is clear that the absolute variation in G/G” is not large, Fig. 9 shows the change is outside the bounds of experimental error, and is clearly pronounced at ca. pH 4.5.It may also be reasoned that the contributions of the suspending fluid, to the elastic and viscous moduli, serve to limit the measurable difference in G’/G’’for the two struc- tures; the change in G’/G” seen in Fig. 9 is likely to increase with increasing volume fraction of the bentonite.However, the differences in rigidity of clusters formed either side of pH 4.5,still appears to be measurable. If the previous deductions about the two likely structures over these different pH ranges are applied, then it would appear that the band-like structure has greater rigidity, whilst the card-house structure is more prone to viscous behaviour, and is less rigid. This is, perhaps, what one would inherently expect from two such dissimilar structures, and these measurements serve to support this view. What is more important is that this last result confirms the idea of a card-house, rather than a weak, band-like struc- ture, for the aggregates with a lower fractal dimension. Conclusions The work presented here has shown that for very dilute sus- pensions of sodium bentonite, the formation of two types of floc is possible. One is a tightly bound, band-like structure, with a fractal dimension of ca. 3.0,whilst the other is similar to a house-of-cards, with a lower fractal dimension of ca.1.8. The ability to form one or other of these structures depends simply on the pH of the suspending medium. At the cross- over point of ca. pH 4.3,there is also a minimum in the yield stress of the suspension, with respect to shear flow. In addi- tion to these points, there is a clear difference in the dynamic rigidity of the two structures, with the close-packed structure being more rigid than the open structure. 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