Aggregation and Gelation in Colloidal Suspensions - American

Chapter 9

Aggregation and Gelation in Colloidal Suspensions: Time-Resolved Light and Neutron Scattering Experiments 1

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Downloaded by CORNELL UNIV on August 31, 2016 | http://pubs.acs.org Publication Date: August 17, 2003 | doi: 10.1021/bk-2003-0861.ch009

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Peter Schurtenberger , Hugo Bissig , Luis Rojas , Ronny Vavrin , Anna Stradner , Sara Romer , Frank Scheffold , and Veronique Trappe 1,2

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Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland Current address: Swiss Federal Lab for Materials Testing and Research, CH-8600 Duebendorf, Switzerland

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We present a time-resolved study of the aggregation and sol -gel transition in concentrated colloidal suspensions. We use diffusing wave spectroscopy (DWS) to obtain quantitative information about the microscopic dynamics all the way from an aggregating suspension to the final gel, thereby covering the whole sol-gel transition. In order to obtain additional information on the corresponding structural changes we have designed a combined S A N S - D W S experiment. This allows us to simultaneously measure both the time evolution of the local dynamics as well as the microstructure as the aggregation and gelation proceeds.

© 2003 American Chemical Society

Case and Alexandridis; Mesoscale Phenomena in Fluid Systems ACS Symposium Series; American Chemical Society: Washington, DC, 2003.

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Understanding the structure and dynamics of colloidal particle suspensions and gels is of significant interest both for research and industry (/). Moreover colloidal systems serve as convenient models to address fundamental issues such as liquid-like ordering, crystal and glass formation, fractal growth and structural properties of random networks. This is primarily due to the fact that colloidal particles can be produced with well defined properties such as shape, size or surface charge density, and that the strength as well as the range o f the interaction potential can be tuned easily. We can for example use highly charged polystyrene particles at very low ionic strength, which leads to an effective pair potential that is well described by a so-called Yukawa potential, i.e. a long range exponential decay with the Debye length as the characteristic decay length of the potential. On the other hand we can add salt or use colloidal particles stabilized by a polymer layer, which then leads to a typical hard sphere interaction potential. If we add even higher quantities of salt to charge stabilized colloids or remove the stabilizing polymer layer, the attractive van der Waals interactions completely dominate and the particles start to aggregate irreversibly. These idealized cases are shown in figure 1.

Figure 1: (a) Interaction potential for sterically and charge stabilized particles as a function of the distance r normalized with the particle diameter 2a. (b) From stable suspensions to cluster formation and gelation.



145 Aggregation and gelation in complex fluids has been for a long time a field of intense research where both fundamental as well as applied questions are equally important. Applications of gels and sol-gel processing include such different areas as ceramics processing, cosmetics and consumer products, food technology, to name only a few. Despite the randomness and the complexity of the sol-gel transition it has always attracted fundamental researchers due to the unique features of gels and the strong similarities between very different gels. The sol-gel transition displays a very rich behavior of different physical properties that can be characterized by distinct scaling laws (2). Irreversible aggregation of colloidal particles is known to result in the formation of space filling gels, where the motion of the constituent particles becomes constrained and non-ergodic behavior is observed in dynamic light scattering. These gels show solid-like properties and exhibit for example a low frequency plateau modulus in oscillatory shear experiments. Considerable efforts have been made to obtain a more detailed understanding of the relation between microscopic and macroscopic properties, and for gels formed at low particle concentrations this was successfully done using fractal concepts.[3,4] However, until now only few attempts have been made to study and understand aggregation and gelation at high particle concentrations, despite the fact that the high concentration regime is of crucial interest in many technical applications as for instance in the processing of inorganic particles for the production of ceramics. In this chapter we shall present results from a study of aggregation and gelation in concentrated colloidal suspensions using a combination of smallangle neutron scattering (SANS) and DWS. We in particular investigate whether the concepts that have been so successful in understanding the behavior of dilute systems can also be applied to concentrated suspensions and gels. At low volume fractions and in the absence of gravitational forces colloidal particles with attractive interactions aggregate into large clusters and finally form a macroscopic gel. In the gel network the individual clusters show a fractal structure that leads to a power law dependence of the structure factor S(q) ~ dr

q~ for a < Mq < Rc, where the fractal dimension is a measure for the compactness of the individual cluster. For diffusion limited cluster-cluster aggregation (DLCCA) dF = 1.8, while for reaction limited cluster-cluster aggregation (RLCCA) d = 2.1 is expected (5-7). However higher values are possible if the cluster become more compact due to internal restructuring or cluster-cluster interactions (e.g. at elevated densities) (for a more detailed description see e.g. (6,7) and references therein). In the most simple picture the individual clusters grow at the same rate until they fill up the whole accessible volume, with a critical cluster radius given by F

m dF)

R ~a- c

(1)

Most of the fundamental research has been carried out on the macroscopic properties of gels, e.g. their viscoelastic behavior, and attempts have been made to interpret them based onfractalmodels for the gel structure. However, it is much more difficult to access information about the microstructural properties


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and furthermore link them to the macroscopic properties of the gel. New developments both in light scattering techniques and in theory now allow us for the first time to bridge this gap even for very concentrated and turbid systems


Structure and dynamics of stable suspensions Before turning to aggregation and gelation, we characterize the structure and dynamics of the initial stable suspensions. The relevant length (several hundred nanometers to micrometers) and time (microseconds to hours) scales in colloidal suspensions are typically much larger than in atomic or molecular systems and are thus easy to access in experimental studies. This is one of the main reasons why colloidal suspensions are ideal model systems to investigate phase transitions or the structure and dynamics of metastable states such as glasses or gels. The interaction between colloidal particles is of fundamental importance for the phase behavior of colloidal suspensions, as well as for their mechanical properties and, most importantly for applications in the paint and food industry, their stability against aggregation induced by van-der-Waals forces or depletion attraction. Interaction effects and the correspondingly strongly influenced positional correlations between the particles will also strongly influence the optical properties of dense systems. These specific features of concentrated and strongly correlated colloidal systems have recently attracted considerable attention (12,13). We can investigate the structure and dynamics of stable suspensions using scattering experiments. For charge stabilized particles at low ionic strength, the Debye length is large and we observe the formation of highly ordered suspensions ("supercooled liquids") already at relatively low volume fractions. The corresponding static structure factor S(q) measured in a scattering experiment exhibits a pronounced peak at relatively low values of the scattering vector q, which can only be seen with light but not with neutron or X-ray scattering due to the accessible range of q values in these measurements. However, the large scattering contrast of these particles in aqueous suspension leads to strong multiple scattering even at very low volumefractions,and static (SLS) and dynamic (DLS) light scattering experiments thus become very difficult or impossible. One can overcome this problem and suppress contributions from multiple scattering in SLS and DLS using different cross correlation schemes. In particular the so-called 3D cross correlation (3DDLS) experiments has been very successful (8, 9, 14). This is demonstrated in figure 2, where the resulting structure factors are shown for two deionized suspensions of polystyrene latex particles (radius a=58.7 nm) at two different volume fractions (Φ = 0.0042 and Φ = 0.0105, for details see ref. 14). Two photographs of the suspensions are shown as an inset and demonstrate the considerable turbidity of these samples and the power of the 3DDLS technique that allows measuremenzs of the static and dynamic structure factor even under these extreme conditions.



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Figure 2: Static structure factors S(qa) of deionized suspensions ofpolystyrene latex particles (radius a=58.7 nm) at two different volume fractions (Φ = 0.0042 and Φ = 0.0105) measured with 3 DDLS. Solid lines: best-fit polydisperse HNC calculations using a Yukawa interaction potential with adjustable volume fraction and effective charge 2 g(see ref (15)). Also shown are pictures of the two samples that illustrate the considerable turbidity. e

It is important to point out that previous studies o f suspensions o f highly charged systems at these volume fractions have often been hampered by difficulties to find systems that do not readily crystallize. In fully deionized aqueous suspensions o f monodisperse spheres normally crystallization occurs already at very low volume fractions (Φ < 10' ) (16,17). If electrolyte is added it is often found difficult to control, maintain and determine the ionic strength with the required precision, though carefully performed experiments of this kind have been reported (16, 18, 19). We have chosen a different way to avoid these complications by using a mixture o f alcohol and water as a solvent which efficiently avoids crystallization by modifying the solvent dielectric constant. Thus we are able to work at full deionized conditions thereby providing a well controlled model system o f charged spheres with volume fractions well above Φ = ΙΟ . If we now add salt to these suspensions, the electrostatic repulsion will be screened and we can tune the interaction potential such that we first obtain an effective hard sphere potential. Under these conditions the structure factor is much less pronounced, and we have to go to much higher concentrations in order to observe a measureable peak. Moreover, for this particle size the peak is shifted to higher values o f q (it occurs at a value that corresponds to the characteristic distance for the next nearest neighbor shell that for hard spheres is q « 2fl/2a) and is almost independent o f concentration. Therefore we now have to go to small-angle neutron scattering in order to investigate S(q). A typical example for the resulting q-dependence of the scattering intensity and the 3

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structure factor as obtained using a theoretical calculation based on integral equation theories with the Perçus-Yevick closure relation is shown infigure3 for latex particles (a = 80 nm, polydispersity approximately 3%) at a volume fraction of about Φ = 0.3 (20). It is important to point out that in this case I(q) contains contributions bothfromthe effective structure factor S(q) as well as from the particle form factor P(q), and that instrumental resolution effects result in a considerable smearing of I(q) that needs to be taken into account in any attempt to quantitatively analyze SANS data.

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Figure 3: Neutron scattering intensity I(q) (left) and resulting structure factor S(q) (right) for a polystyrene suspension with particle radius a = 80 nm, polydispersity 3% and effective volume fraction Φ = 0.289 (see ref (20) for details)

In addition to the structural properties we can also investigate the dynamic behavior as a function of particle concentration and salt content. Information about the dynamic properties on lengths scales comparable to the size of the particles is usually obtained from dynamic light scattering in the single scattering regime (21, 22). However, we have already seen that in dense suspensions DLS cannot be applied in most cases due to strong multiple scattering of light. In addition the q-range and hence the length scales probed by standard light scattering techniques (λ/η - 400nm) are limited to q < 0.03 nm which is not sufficient for many concentrated systems. An elegant way to overcome this limitation is to either use 3DDLS for systems where we look at highly charged particles at low ionic strength, or then take advantage of the multiple scattering process rather than avoiding it by using Diffusing Wave Spectroscopy (DWS). DWS works in the limit of very strong multiple scattering, where a diffusion model can be used in order to describe the propagation of the light across the sample (23-25). Using such a diffusion approximation, one can then determine the distribution of scattering paths and calculate the temporal autocorrelation of the intensity fluctuations analogous to DLS. It is thus still possible to study the dynamics of a colloidal suspension by measuring the intensity fluctuations of the scattered light observed either in 1


149 transmission or reflection. The fluctuations of the scattered light measured in transmission result from the variation of the total path length by a wavelength of light. However, since the light is scattered from a large number of particles, each individual particle must move only a small fraction of a wavelength for the cumulative change in path length to be a full wavelength. Therefore, despite the fact that D W S does not yield explicit information on the q-dependence of the socalled dynamic structure factor S(q,t), it is capable in providing unique information about the local dynamical properties, i.e. the mean square displacement of the individual particles. It probes particle motion on very short length scales and can for example measure motions of particles of order Ιμπι in diameter on length scales o f less than lnm (10). We have in fact used both 3 D D L S and D W S / S A N S in order to investigate the dynamics of strongly interacting colloidal suspensions, and in particular investigated the role of hydrodynamic interactions in such systems (14,15,20). However, our general approach o f combining S A N S and D W S is not limited to stable particle suspensions, but can be equally well applied to other colloidal systems, such as aggregating and gelling suspensions. It is this particular feature that we shall concentrate on in the remainder of this chapter.


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Aggregation and gelation in destabilized suspensions Strongly aggregated colloidal particle gels have been extensively investigated in the past, and have been found to possess fractal character over a range of length scales whose width primarily depends on the particle volume fraction, Φ. Because of the fascinating properties of fractals most investigations were restricted to low volume fractions, where the fractal character extends over a wide range of length scales, and where the structural and dynamic properties of the system are determined by the fractal structure. We extended the range o f volume fractions studied to larger Φ. In our investigations, the aggregation and gelation o f charge stabilized and buoancy-matched concentrated latex dispersions with volume fractions typically in the range of 0.01 < Φ < 0.3 is induced through an increase of the ionic strength. However, for highly concentrated samples it is very difficult to achieve a homogeneous; reproducible destabilization by simply adding salt. Recently a novel method based on an insitu variation of the ionic strength has been introduced (26). The destabilization of the colloidal suspensions is induced with an internal chemical reaction which allows to slowly produce ions (the urease catalyzed hydrolysis o f urea). We have subsequently extended this approach to concentrated suspensions of polystyrene particles (27). Figure 4 shows a typical example of the temporal evolution o f the rheological properties (storage (G ) and loss (G") moduli) o f such a destabilized suspension o f polystyrene particles (a = 85 nm, polydispersity 4%) at a volume fraction of Φ = 0.045. Initially the suspension has typical Newtonian fluid properties and G " dominates. Due to the formation of larger clusters both G* and G " then increase. A t approximately 300 seconds 1


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G', G" [Pa]

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1Q4 time [s]

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Figure 4: Time evolution of the storage modulus G'(t) (solid squares) and the loss modulus G"(t) (open circles) for a suspension of destabilized latex particles with radius a = 85 nm and a volume fraction of Φ = 0.045. Measurements were made with a MCR 300 rheometerfromPaar Physica using a double gap couette system at a constantfrequency (ω = 10 rad/s).

we then observe a steep increase of G \ which is now larger than G " . This is the classical signature of the gel point. After about 1 hour the elastic modulus changes only gradually with time. While such experiments are capable of yielding an estimate of the gel point and of the viscoelastic properties of the suspension and the final gel, they do not provide us with any information on the structural evolution of the system. Moreover, despite the fact that one generally tries to work at low strain values, rheological measurements are not really non-invasive, which is particularly important for weak gels formed close to the gel point and at lower volume fractions, and they require a considerable amount of material. We have thus started to use DWS and SANS as non-invasive tools for a true in-situ and real time investigation of aggregation and gel formation in concentrated suspensions. Figure Sa shows typical snapshots out of a sequence of correlation functions g(x)-l during aggregation and gelation of a latex particle suspension (particle radius a = 85 nm, volume fraction Φ = 0.11). For ergodic systems, the mean square displacement of the correlated Brownian particles can be successfully modeled by means of an averaged short-time diffusion coefficient. This leads to a correlation function well approximated by a single exponential decay (10). During the initial period the formation of large aggregates and clusters leads to a dramatic slowing down of the single particle diffusion and a corresponding shift of the characteristic relaxation time % of the intensity autocorrelation function to longer decay times. However, at later stages in the aggregation process the clusters fill the entire sample volume and gelation occurs. Because of the high volume fraction the network is very stiff, and as a consequence the trapped particles can only execute limited motions about their fixed averaged positions. After about 10 days the gel changes only very little and we take that time as the terminal state. The correlation function now exhibits a distinctly different decay which is described by a stretched exponential with an arrested decay leading to a plateau. After the sol-gel transition, we are confronted with an additional difficulty due to the non-ergodicity of these systems. In solid-like media, such as gels, the c



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Figure 5: Sol-gel transition of a colloidal suspensions ( radius a = 85 nm, volume fraction Φ = 0.11) measured over 10 days with a two-cell setup. A) The destabilized system shows a transition from a liquid state (solid points), characterized by an almost exponential decay of the correlation function, to a solid state (open symbols) after about 80 min. In the gel-state a continuously increasing plateau builds up in the correlation function, g2(t)-l, characteristic for the finite storage modulus of a solidlike system. B) Particle mean square displacement of a colloidal system in the sol and the gel. C) Mean square displacement as function of time for gels composed ofpolystyrene spheres (a = 85nm) at different volume fractions.^ = 0.25 [triangle down], Φ = 0.20 [hexagon],Φ = 0.11 [circle],Φ = 0.045 [triangle up],Φ = 0.010 [square]. The inset shows the master curve obtained by normalizing t by r and by δ*. The solid line represents the calculation according to Eq. 2 with ρ = 0.65. 2

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152 scatterers are only able to make limited Brownian excursions. As a consequence, the time-averaged intensity correlation function of the scattered light is different from the ensemble-averaged correlation function. For dilute, nonergodic samples different approaches have been proposed in order of properly average the signal (28). The extension to turbid systems is however not always practicable. We were able to develop a completely new and simple experimental scheme in order to investigate nonergodic samples with DWS (27, 29). We overcome the nonergodicity limitation of light scattering in concentrated systems by using a combination of two cuvettes. The first cuvette contains the gelling sample that can be either ergodic or nonergodic, whereas the second one is a turbid ergodic system that leads to an additional decay of the correlated signal at long delay times. We thus obtain the true gel contribution over a wide lag-time interval from 10 ns < t < 1 ms. The dramatic change in the local particle dynamics becomes even more clearly visible when looking at the time dependence of the corresponding mean square displacement . The particle dynamics in the initial stable suspensions as well as in the aggregating suspensions prior to the gel point (solid symbols) exhibit the typical characteristics offreeparticle diffusion due to Brownian motion. This is reflected by an almost exponential decay of the correlation functions and leads to a linear dependence of on time (indicated with a line with slope one infigure5b). During the initial period the formation of large aggregates and clusters leads to a dramatic slowdown of the single particle diffusion. Later the long time behavior of becomes more and more constrained. In this regime, before gelation, the particle shows simple diffusive motion only on a length scale of « l-2nm, representing only a smallfractionof the particle diameter (27). At the gel point a quite dramatic change in the particle dynamics occurs, and the short time behavior changes from Brownian to a subdiffusive motion (open symbols) well described by a power law ~ t . We find that in the gel state the average mean square displacement is well described for all t by a stretched exponential 2

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(2)

leading to a plateau at long times (with ρ = 0.7 ± 0.05). We find, within our time resolution, that the exponent for diffusion ρ = 1 drops at the gel point and takes a value of ρ « 0.7 for all times t > t i. This indicates that already at the gel pointfedalmost all particles are connected to the gel network. A comparison between time-resolved rheological measurements and the DWS experiments demonstrates that the qualitative change in microscopic particle dynamics indeed coincides with a dramatic change in the macroscopic viscoelastic properties of the samples at the gel point. This is shown in figure 6, where the storage (G ) and loss (G") moduli measured at a single oscillationfrequencyand the exponents ρ obtained from DWS are plotted ge

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F/gwre tf; Comparison ofresults from classical rheology and DWS during the aggregation and sol-gel transition for a suspension of latex particles (radius a = 85 nm, volume fraction Φ = 0.045) (a); Time evolution of the exponent ρ obtainedfrom the short-time mean square displacement ;(b): Time evolution of the storage modulus G'(t) (solidsquares) and the loss modulus G"(t) (open circles) obtainedfrom an oscillating rheological measurement.

as a function o f time. We observe the steep increase o f G ' , indicating the transition from a sol to a gel, at the same time where the exponent ρ drops from 1 to about 0.7. Clearly, the volume fraction also has a profound effect on the dynamic properties of the gels. A t the lowest volume fraction, Φ = 0.01, the mean square displacement first rises sub-linearly at short times, and then curves towards a constant plateau value, indicating that the particle excursion is restricted to a maximum mean square displacement, δ . A s the volume fraction increases δ systematically decreases to lower values, reflecting the increased restriction to particle motion. Moreover, the cross-over time, x , at which the time dependence of changes from sub-diffusive to a time independent plateau behavior, clearly shifts towards lower values between Φ = 0.01 and Φ = 0.11, while remaining roughly constant for Φ = 0.11-0.25. Remarkably, all data can be scaled onto a single master-curve by normalizing t with the characteristic crossover time and with the maximum mean square displacement, as 2

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shown in the inset of Figure 5c. This mastercurve is well described by eqn. 2, as denoted by the solid line in the inset of Fig. 5c. The short time dynamics (eqn. 2) observed for the concentrated colloidal gels is qualitatively similar to what has previously been found in dilute fractal gels. However, for concentrated gels we obtain reduced values for x and δ , reflecting the compactness of the dense gel (3). This suggests that the exponent ρ = 0.7 is a common feature o f colloidal gels even when the development o f a loose fractal structure is suppressed due to the high space filling. Based on their data obtained at low volume fraction gels, Krall and Weitz (3) suggested to describe the short time fluctuations of the gel as a series of overlayed damped oscillators with a upper cut-off linked to the characteristic size, Rc, of the gel. Thus, the maximum mean-square displacement and the characteristic relaxation time are both related to a characteristic spring constant K«

Aggregation and Gelation in Colloidal Suspensions - American

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