Probing particle heteroaggregation using analytical centrifugation

Marcel Rey ab, Maximilian J. Uttinger ab, Wolfgang Peukert ab, Johannes Walter *ab and Nicolas Vogel *ab
aInstitute of Particle Technology (LFG), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstrasse 4, 91058 Erlangen, Germany. E-mail:;
bInterdisciplinary Center for Functional Particle Systems (FPS), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Haberstrasse 9a, 91058 Erlangen, Germany

Received 5th January 2020 , Accepted 1st March 2020

First published on 2nd March 2020

The controlled aggregation of colloidal particles is not only a widespread natural phenomenon but also serves as a tool to design complex building blocks with tailored shape and functionalities. However, the quantitative characterization of such heteroaggregation processes remains challenging. Here, we demonstrate the use of analytical centrifugation to characterize the heteroaggregation of silica particles and soft microgels bearing similar surface charges. We investigate the attachment as well as the stability of the formed heteroaggregates as a function of particle to microgel surface ratio, microgel size and the influence of temperature. The attachment of microgels onto the colloidal particles induces a change in the sedimentation coefficient, which is used to quantitatively identify the number of attached microgels. We corroborate the shift in sedimentation coefficient by computer simulations of the frictional properties of heteroaggregates via a modified Brownian dynamic algorithm. The comparison between theoretical investigations and experiments suggest that the microgels deform and flatten upon attachment.


The controlled aggregation of colloidal particles has received significant interest due to its potential in producing defined colloidal clusters1–3 and supraparticles4,5 as well as its use in a range of technological applications such as mineral flocculation,6,7 waste water treatment8,9 and the manufacturing of composite materials.10,11 Heteroaggregation describes the aggregation of particles with different physico-chemical properties. In scientific applications, heteroaggregation of particles serves as tool to obtain defined building blocks with additional functionalities. For example, adding smaller particles to larger ones leads to a defined nanoscale roughness,12,13 which can be used to obtain superhydrophobic surfaces14 or universal emulsions stabilizers.15 Heteroaggregation can be further used to obtain defined colloidal patches16,17 or to modify the interaction potential of colloidal particles by the attachment of soft microgels.18

Typically, heteroaggregation is induced by mixing two species with opposite charges, which are attracted by long-range electrostatic interactions.19,20 In a mixture of equal particle numbers the heteroaggregates grow over time in size to structures with increasing fractal dimension.21,22 Macroscopic aggregation can be prevented by adding one particle species in excess, leading to defined, colloidally stable heteroaggregates.23,24 Interestingly, the heteroaggregation of soft microgels, consisting of a crosslinked polymeric network that is able to take up large amounts of solvent molecules, and rigid particles was observed for quasi-neutral colloids24–27 and even for colloids with similar surface charges.12,18,26 Aqueous microgel/particle systems have mostly been studied in terms of stability, which similarly depends on the surface ratio between the particles.24,25 If insufficient amounts of microgels are available, they tend to bridge two particles, causing aggregation.24,25 An increase in microgel concentrations leads to the attachment of a uniform monolayer of microgels on the particles, resulting in steric repulsion between the individual heteroaggregates.24,25

The characterization of heteroaggregation processes remains challenging. Qualitatively, the heteroaggregates can be characterized by scanning electron microscopy (SEM),24,26,28 requiring drying of the dispersion, which may affect the aggregation process.12 Optical microscopy can characterize clusters in dispersion29 granted the particles are above the detection limit. Static and dynamic light scattering (SLS/DLS),28,30–32 turbidity measurements33,34 and laser diffraction35,36 provide the average cluster size and allow the extraction of the aggregation rate constants. Individual clusters up to hexamers can be differentiated by single-cluster light scattering, although the process requires highly diluted samples and a high scattering intensity of the individual constituent particles.37,38 The high dilution can affect the attachment characteristics and the results may therefore differ for more concentrated systems. Furthermore, flow cytometry was used to characterize the bridging of microspheres with small particles, which allows quantification up to tetramers of microsphere aggregates but requires fluorescently labelled particles.39

An alternative hydrodynamic method to determine disperse properties of (nano-) particles in liquid phase is analytical centrifugation (AC) and analytical ultracentrifugation (AUC). AUC has been mostly used to characterize biological systems,40,41 synthetic polymers42,43 and has recently found increasing interest for the characterization of nanoparticles.44–48 Moreover, it allows characterizing interactions in complex colloidal systems, as was demonstrated for the aggregation of gold nanoparticles and proteins,49 and to quantitatively characterize the aggregation of polystyrene dispersions upon the addition of salt.50 From AUC measurements, the sedimentation coefficient distribution alongside the diffusion coefficient of various analytes can be determined by tracking the temporal and spatial evolution of the concentration profile within the measurement cell at accelerations up to 250[thin space (1/6-em)]000 g. The size, shape and density of the analytes can be calculated directly in their native liquid environment from the measured sedimentation and diffusional properties. Since the sedimentation properties measured by AUC and AC are sensitive to small changes in particle mass and density, both techniques serve as an ideal method to quantitatively characterize heteroaggregation of two different colloidal building blocks.

In this study, we quantitatively characterize the heteroaggregation of soft and rigid model particles by the change in sedimentation coefficient using AC. Stöber silica particles and poly(N-isopropylacrylamide) (PNIPAM) microgels, both stabilized by negative surface charges, were used as a model system. The technique measures the heteroaggregates directly in dispersion and is sensitive enough to distinguish the attachment of individual microgels onto the silica particles. We investigate the formation of heteroaggregates as a function of the ratio between the different particles and the time available for the aggregation process. We characterize the process both in the regime where microgels are in excess and stable heteroaggregates can be formed, as well as in the regime where the silica colloids are in excess and colloidally unstable systems result from microgels bridging multiple silica particles. The experimental studies are supported by theoretical predictions of sedimentation coefficients using a modified Brownian dynamics algorithm. In summary, we demonstrate the full strength of the sedimentation measurements to quantitatively characterize heteroaggregation processes in aqueous dispersions.



All chemicals were purchased from commercial sources. N,N′-Methylenebis(acrylamide) (BIS; 99%, Sigma Aldrich), ammonium persulfate (APS, Sigma Aldrich, 98%), ethanol (EtOH, Sigma Aldrich, 99.9%), potassium chloride (≥99.0%, Sigma Aldrich), hexane (≥99%, Sigma Aldrich), sodium dodecyl sulfate (SDS, Sigma Aldrich, 98%) were used as received. N-Isopropylacrylamide (NIPAM; 97%, Sigma Aldrich) was purified by recrystallization from hexane (95%, Sigma Aldrich). Water was double deionized using a Milli-Q system (18.2 MΩ cm, Elga™ PURELAB™ Flex).


The set of PNIPAM microgels with similar size in the collapsed state but different crosslinking densities was synthesized by surfactant-free precipitation polymerization as described in a previous publication.51 In short, in a 500 mL three-neck round bottom flask equipped with reflux condenser and stirrer, 2.83 g of NIPAM and 38.5–385 mg BIS were dissolved in 249 mL of water. The solution was heated to 80 °C and purged with nitrogen gas. After an equilibration for 30 minutes, the reaction was initiated by adding a solution of 14.3 mg of APS dissolved in 1 mL of water. After 5 hours of reaction, the suspension was cooled down to room temperature and purified by centrifugation and redispersion in water three times, followed by dialysis against water for one week and replacement of the water phase once per day.

Smaller PNIPAM microgels were synthesized using SDS as surfactant to control the size during the precipitation polymerization adapted by Wu et al.52 In a 500 mL round-bottom flask equipped with condenser 3.4 g NIPAM, 0.23 BIS and 0.02 g SDS were dissolved in 195 mL water. The mixture was heated to 70 °C and degassed by bubbling nitrogen for 30 minutes. 0.1 g APS, dissolved in 5 mL water, was added to initiate the polymerization. The reaction was stopped after 4 hours. After cooling to room temperature, the dispersion was purified by centrifugation and redispersion as well as by dialysis against water for 2 months, changing the water each day to ensure removal of SDS.

The silica particles were synthesized via Stöber process (details in ESI).53 The hydrodynamic diameter xH, zeta potential and polydispersity index (PDI) were characterized by dynamic light scattering (DLS) (Malvern Zetasizer Nano-ZS). The zeta potential was calculated form the electrophoretic mobility using the Smoluchowski model. Scanning electron microscopy (SEM) images were obtained using a Zeiss Gemini SEM 500.

Sedimentation theory

Lamm's equation describes the evolution of the concentration c of individual non-interacting particles subject to sedimentation and diffusion in a sector shaped cell:
image file: d0sm00026d-t1.tif(1)

The angular rotor velocity is denoted as ω, r is the radial position within the cell and D is the diffusion coefficient of the particles. The sedimentation coefficient s is defined by the ratio of the sedimentation velocity u and the acceleration ω2r:

image file: d0sm00026d-t2.tif(2)

The molar mass M of the analyte can be calculated via the Svedberg equation:

image file: d0sm00026d-t3.tif(3)

R is the gas constant, T the temperature, ρs the solvent density and [small nu, Greek, macron] is the partial specific volume. Stokes' law can be used to calculate the sedimentation equivalent size xs from the sedimentation coefficient:

image file: d0sm00026d-t4.tif(4)
ρp is the particle density, and η the viscosity of the solvent.

Quantitative heteroaggregation characterization

For the sedimentation experiments, a fixed silica concentration of 2 g L−1 was chosen (Fig. S1, ESI). We define the surface area ratio RA = Amicrogel/Asilica as the outer surface area of the microgels in the swollen state divided by the surface area of the silica particles. The surface areas were calculated assuming spherical, non-porous and monodisperse particles. The binary dispersions were obtained by mixing a 2 mL silica dispersion (4 g L−1) with 2 mL microgel dispersion with different concentrations to adjust the ratio of the total surface area of both particles RA = Amicrogel/Asilica between 0 and 15. The dispersions were ultrasonicated for 10 min and then kept under constant stirring to avoid settling during storage. For each sedimentation experiment, polycarbonate cells with a path length of 2 mm were filled with 400 mL of each dispersion. AC experiments were carried out using the LUMiSizer LS611 (L.U.M. GmbH, Berlin, Germany). Sedimentation data was acquired at a wavelength of 470 nm, with a rotor speed of 700 rpm and fixed temperature of 20 °C for all measurements. The data was analyzed using the implemented tool of the SEPView software, which is based on the method by Detloff et al.54 The “constant position” method was applied, which tracks the optical signal in the AC at a fixed radial position.55 From this, the sedimentation velocity was determined, which is directly related to the particle size. In the software, it was averaged over three radial positions for better statistics. Subsequent size to sedimentation coefficients conversion was carried out using eqn (4). For the mixing experiment at 60 °C, both dispersions were mixed at 60 °C, ultrasonicated and stirred in a water bath at 60 °C. For each sedimentation experiment, 400 mL of the dispersions were transferred into the polycarbonate cells and then cooled to room temperature over 10 min, to ensure identical sedimentation conditions.

Theoretical analysis

The theoretical shift in sedimentation coefficient upon attachment of microgels onto the colloids was calculated using three different models. In the “liquid-like” model, the heteroaggregates were simplified by assuming that the microgel uniformly coats a spherical silica particle. Thus, in this model the attachment of the microgels only leads to a change in size and density but not in shape. The change in sedimentation coefficient was then calculated by Stokes’ law (eqn (4)).

In the second model, the attached microgels were modeled as rigid spheres. The calculation of the theoretical hydrodynamic diameters xH for the heteroaggregate was carried out via a modified Brownian dynamics algorithm based on the method by Zhou et al.56 The details of the algorithm are provided in the ESI. Next, the frictional coefficients of a volume equivalent sphere f0 were calculated via:

f0 = 3πηxV(5)
where xV is the diameter of a sphere having the same volume as the heteroaggregate. Based on the shape factor f/f0= xH/xV, the frictional coefficients f of the anisotropic particles were determined. The sedimentation coefficients was calculated according to:
image file: d0sm00026d-t5.tif(6)
with known particle mass m and density.

In the third soft-sphere model, we assumed the microgels to be deformed upon attachment to the silica particles. To implement this model, the particles and microgels were overlapped while keeping the overall mass constant to mimic the deformation of the microgels upon attachment. The shift in sedimentation coefficient was calculated similar to the second method.

Results and discussion

In order to characterize the heteroaggregation behavior of soft PNIPAM microgels and rigid silica particles, we require their density. PNIPAM microgels are particularly interesting as they undergo a volume phase transition from a swollen state at room temperature to a collapsed state above 32 °C.57 From the sedimentation coefficients obtained by AC and the size obtained from DLS using eqn (4), a density of the silica particles (xH = 514 nm, PDI = 4.7%, Fig. S2, ESI) of 1.850 g cm−3 was determined, in accordance with literature values.58 We further characterized the partial specific volume, effective density and non-bound water content of the PNIPAM microgels with varying crosslinker concentration by combining AUC, DLS and densimetry (ESI, Fig. S3). The AUC was used to determine the sedimentation coefficients of the microgels due to their low density, which requires a high acceleration. The effective density of microgels with 5 mol% crosslinking density was determined to be 1.013 g cm−3 at 20 °C in the swollen state and 1.071 g cm−3 at 40 °C in the collapsed state (ESI, Fig. S3).

We apply AC to investigate the heteroaggregation of rigid silica particles and soft PNIPAM microgels (5 mol% crosslinker, xH (20 °C) = 540 nm, measured at 20 °C in the swollen state, PDI = 2.0%). We measured the full sedimentation coefficient distributions of the binary colloidal mixtures. The attachment of microgels onto the surface of the silica particles leads to a difference in mass and density of the heteroaggregate, which, in turn, translates to changes in the hydrodynamic and volume equivalent diameter. On the one hand, the increase in mass of the heteroaggregate leads to faster sedimentation, on the other hand, the decrease in effective density and increase in friction cause a retardation of the sedimentation (see eqn (4)).

In the next step, we systematically varied the composition of the mixed system by changing the relative concentrations to adjust the ratio of surface areas RA = Amicrogel/Asilica between 0 and 15, transiting from excess silica to excess microgel (Fig. 1a). Since the heteroaggregation is a surface-dominated process, we chose the surface area ratio RA over a volume or number ratio. The sedimentation coefficient of these mixtures was then measured via AC at different time intervals after mixing to gain information on the attachment kinetics. Fig. 1 depicts the retrieved extinction-weighted cumulative sedimentation coefficient distributions at 20 °C. Two hours after mixing, a distinct shift was observed upon attachment of the microgels (Fig. 1b). For pure silica colloids, the experiments led to a monomodal sedimentation coefficient distribution, which can be assigned to a single species of colloidally stable silica particles without aggregates (Fig. 1b and c, red curve). In the presence of microgels, the cumulative sedimentation coefficient distributions show several steps, indicating the presence of defined heteroaggregates. While the majority of the silica particles did not have any attached microgels (Fig. 1b and c, (i)), additional populations with lower sedimentation coefficient indicate the presence of silica particles with one (Fig. 1b and c, (ii)) and two attached microgels (Fig. 1b and c, (iii)).

image file: d0sm00026d-f1.tif
Fig. 1 Heteroaggregation of silica particles and PNIPAM microgels at 20 °C characterized by analytical centrifugation (AC). (a) Schematic representation of the heteroaggregation of silica colloids and PNIPAM microgels after mixing at 20 °C. (b and c) Extinction-weighted cumulative sedimentation coefficient distributions measured two hours (b) and five hours (c) after mixing for different surface ratios RA. Compared to pure silica (red curve), we notice a shift to lower sedimentation coefficients of the silica particles by the addition of microgels. We identify the distinct populations as: (i) no attached microgels, (ii) one attached microgel, (ii) two attached microgels, (iv) three attached microgels. These populations were also identified in SEM images (inset) with RA = 2. We further observed some larger aggregates in the SEM images (v), which we were unable to measure via AC, as they sediment much faster compared to individual heteroaggregates consisting of a single particle with attached microgels. Scale bar: 1 μm.

Five hours after mixing, we observed an increase in the populations of silica particles with attached microgels. This is evidenced by the increased fraction of lower sedimentation coefficients in the cumulative distribution (Fig. 1c). Furthermore, a population of particles with three attached microgels at even lower sedimentation coefficients (Fig. 1c, (iv)) appeared, which was not present after two hours. A small kink in the cumulative sedimentation coefficient distribution for the highest microgel/silica ratio may be indicative of the presence of silica particles with four attached microgels (Fig. 1c, purple color). A correlation between RA and the number and fraction of attached microgels is evident from these studies. A separated representation of the individual fractions of the formed species after 2 h and 5 h are exemplary presented in Fig. S6 (ESI). With increasing microgel concentration, a higher concentration of silica colloids with one or multiple attached microgels was measured. In addition, an overall shift towards lower sedimentation coefficients with increasing microgel concentration is observable, which we attribute to an increase in viscosity of the dispersion.

Furthermore, SEM was applied to characterize the heteroaggregates ex situ after dilution to avoid the attachment of free microgel during drying12 and drop-casting the sample onto a silicon wafer. All postulated heteroaggregate structures expected from the analytical centrifugation experiment were identified in the SEM images, taken from a sample with a RA = 2 (Fig. 1, insets). In the images, free microgels (not shown), defined aggregates with one, two, and three microgels attached to a central silica particle (Fig. 1, (ii)–(iv)), as well as larger aggregates (Fig. 1, (v)) were observed. In such larger aggregates, which were the focus of previous studies,24,25 the microgels bridge two or more colloidal silica particles, leading to the formation of ill-defined, larger structures. These aggregates cannot be observed in the AC measurements of the chosen colloidal system, as they sediment much faster than individual heteroaggregates formed with a single silica particle. The formation of aggregates by bridging will be characterized in more details for a different system below.

We measured a zeta potential of the silica colloids of −55.6 ± 4.0 mV and −3.9 ± 4.6 mV for PNIPAM microgels at 20 °C. The quasi-neutral zeta potential for PNIPAM microgels is related to their highly swollen nature, but the presence of negative charges can be clearly seen by the increased negative value of the zeta potential in the collapsed state discussed below. We attribute the relatively slow attachment of the microgels onto the silica particles to the like-charged nature of the particle surfaces. The similar surface charge may act as an electrostatic barrier slowing the attachment process, which itself is driven by hydrophobic interactions59,60 or, potentially, hydrogen bonding. The existence of an energy barrier may also explain the observation of free silica particles even in the presence of excess microgels. We also measured the sedimentation coefficient after one day but did not observe any changes compared to the results after five hours. A possible explanation could be heterogeneities at the surface of particles in such an ensemble, which means that not all silica particles may be equal in their surface properties. Such heterogeneities are not well understood to this point. However, wide distributions of contact angles of particles at the interface hint at such differences.61,62

The same measurements were repeated after mixing and stirring the suspensions at 60 °C. At this temperature the PNIPAM microgels are in a collapsed state (xH (60 °C) = 280 nm). Due to their lower volume, the microgels would theoretically pack more densely on the surface of the silica particle, which would allow for a higher number of microgels onto the silica particle. Prior to the AC measurement, the dispersions were cooled to 20 °C over 10 min for two reasons. First, the cooling provides the same experimental conditions as for the previous experiment. Second, experiments at higher temperatures are highly sensitive to temperature induced convection due to the low density of the heteroaggregates and therefore complicate accurate measurements.63

Interestingly, our results showed no significant differences to the results with microgels mixed at room temperature. Two hours after mixing, the cumulative sedimentation coefficient distribution indicated the presence of populations of free silica particles (Fig. 2b and c, (i)), as well as species with one (Fig. 2b and c, (ii)) and two (Fig. 2b and c, (iii)) attached microgels. Five hours after mixing, the fraction of the populations with attached microgels significantly increased, and a fourth population of species with even lower sedimentation coefficient appeared, which we attribute to silica particles with three attached microgels (Fig. 2c, (iv)).

image file: d0sm00026d-f2.tif
Fig. 2 Heteroaggregation of silica particles and collapsed PNIPAM microgels at 60 °C characterized by AC. (a) Schematic representation of the heteroaggregation of silica particles and PNIPAM microgels after mixing at 60 °C. The samples were cooled to room temperature prior to the AC measurement. (b and c) Extinction-weighted cumulative sedimentation coefficient distributions measured two hours (b) and five hours (c) after mixing for different surface ratios RA. Interestingly, we observe a similar attachment behavior at 60 °C (microgels are in the collapsed state) compared to at 20 °C (microgels are in the swollen state) with the following populations: (i) no microgels, (ii) one microgel, (ii) two microgels, (iv) three microgels attached.

We rationalize the similar attachment behavior at 20 °C and 60 °C by a competition between different physicochemical properties. While the smaller size and less hydrophilic nature may favor attachment,25 an increase in surface charge may counteract this tendency. In the collapsed state, the zeta potential of the particles significantly increased (to −23.2 ± 5.3 mV) as the charged moieties at the surface are closer together compared to the swollen state. These negative surface charges thus increase the energy barrier for the attachment of microgels onto the silica particles. Interestingly, the number of attached microgels is almost identical at 20 °C and at 60 °C. We cooled the sample to 20 °C over 10 min prior to measurement, which is sufficient for the microgels to swell. We cannot exclude a systematic error that microgels are ejected from the particle surface upon swelling. We hypothesize, however, that the similar attachment behavior may be attributed to the spreading of microgels even in the collapsed state. Recent results indicate that dangling chains of the microgel are able to expand at liquid interfaces and form a corona even above their volume phase transition temperature.64,65 The microgels thus cover a similar area per particle whether they are adsorbed below or above their volume phase transition temperature.64,65 We believe that the spreading in the collapsed state may similarly occur during the attachment to the solid surface of the silica colloids. This would lead to a much higher area coverage of the microgels compared to what is expected from their hydrodynamic diameter in the collapsed state, and would explain the similarities in the sedimentation coefficient distributions.

Finally, we used AC to quantitatively characterize the bridging of multiple silica particles by microgels into larger aggregates, which has been qualitatively discussed in previous studies.24,25 To avoid macroscopic aggregates, which sediment fast and are beyond the detection limit of AC, we mixed the silica particles with smaller PNIPAM microgels (5 mol%, xH (20 °C) = 360 nm) and characterized their sedimentation properties (Fig. 3). The smaller microgel size reduced the likelihood of a microgel to bridge two silica particles together, thus reducing the average size of the aggregates. The bridging mechanism is schematically shown in Fig. 3a.

image file: d0sm00026d-f3.tif
Fig. 3 Heteroaggregation of silica colloidal particles and smaller PNIPAM microgels at 20 °C characterized by AC. (a) Schematic representation of the heteroaggregation of silica particles and PNIPAM microgels. (b) Extinction-weighted cumulative sedimentation coefficient distribution measured after three hours indicating silica particles with zero (i) or one (ii) attached microgel. (c) Cumulative sedimentation coefficient distribution normalized to the extinction of pure silica at 470 nm after five days. A surface ratio RA – dependent aggregation peaking for RA = 0.3 is observable. Dimers (two colloids bridged by one microgel) (iii) as well as larger aggregates (iv) can be identified in the sedimentation coefficient distribution. An excess of microgels is needed in order to stabilize the silica colloidal particles against aggregation (v). (d) Colloidally stable individual silica particles as a function of surface ratio RA.

Similar to before, we prepared mixed dispersions of silica particles and PNIPAM microgels with different surface area ratios RA. We especially focused on RA < 1 (i.e. in the regime of comparably small numbers of microgels), as these ratios favor the formation of larger aggregates by bridging.24 Three hours after mixing, the cumulative sedimentation coefficient distribution indicates that the majority of silica particles had no attached microgels, while a small population with lower sedimentation coefficients indicates the presence of silica particles with a single attached microgel (Fig. 3b, (i)). While the time required for the attachment of microgels onto individual silica particles is comparable to larger microgels (Fig. 1a), the formation of aggregates consisting of multiple silica particles takes longer. After an extended equilibration time of five days, a significant portion of species with very high sedimentation coefficients was observed, indicating that agglomerates must have formed (Fig. S4a, ESI).

The scattering cross-section and thus extinction coefficient of these aggregates differ from the individual silica particles,66 which restricts quantitative analysis of the heteroaggregates. However, as the total amount of silica is the same for each sample and the free silica particles can be clearly distinguished in the sedimentation coefficient distribution, we are able to draw conclusions on the amount of free silica. This information is directly accessible from the cumulative distributions when the cumulative distributions are normalized to the extinction of free silica (Fig. 3c). This is possible because the concentration of free silica can directly be converted to the extinction of free silica with known extinction coefficient based on Lambert–Beer's law. We can therefore gain quantitative information on the percentage of free silica particles as well as the total amount of heteroaggregates. It has to be noted that the quantitative contributions from different heteroaggregate structures cannot be determined due to their unknown extinction coefficients. Moreover, since these aggregates are ill-defined in shape and size, we were not able to distinguish distinct aggregate structures by their sedimentation coefficient (Fig. 3c, (iv)). Noteworthily, however, one distinct population, identified by a kink in the cumulative distribution at around 160[thin space (1/6-em)]000 S (Fig. 3c, (iii)), was present in all samples. A comparison with theoretical sedimentation coefficients reveals that this feature can be assigned to defined dimeric aggregates consisting of two silica particles and a single microgel (see below).

Fig. 3d shows the percentage of colloidally stable, non-aggregated individual silica particles, extracted from Fig. 3c, as a function of surface ratio RA. This includes colloidally stable silica particles with and without attached microgels. The surface ratio RA strongly affects the formation of aggregates. At RA = 0.1 (Fig. 3c, orange), i.e. with an excess of silica particles, approximately 42 wt% of the initial silica particles in the mixed dispersion aggregated. The amount of aggregated silica particles increases for RA = 0.3 (Fig. 3c, light green) to 97 wt%. The fraction of aggregated species in the mixed dispersion decreased from 86 to 83 wt% when increasing RA from 0.5 and 1 (Fig. 3c, dark green, blue), which we rationalize by the onset of attachment of multiple microgels onto individual free silica particles. The microgels form a shell around the silica particles and therefore provide steric stability against aggregation. Further increase of microgel (RA = 3, Fig. 3c, purple) strongly reduced the amount of aggregated silica particles. However, even with such excess microgels, approximately 11 wt% of the silica particles were still aggregated. The distribution did not allow identification of defined populations related to the attachment of individual microgels, most likely due to their small size. However, the shift of the sedimentation coefficient distribution to smaller values, along with a broadening of the distribution qualitatively confirms that microgels attached to the silica particles (Fig. 3c, (v)). Noteworthily, as the aggregates sediment rapidly, the concentration of particles in the remaining dispersion, and thus its viscosity is reduced, which translates into a slightly faster sedimentation of remaining uncoated silica particles according to eqn (4) (Fig. 3c).

Theoretical investigations

In addition to the experimental studies, we analyzed the expected shift in sedimentation coefficient upon microgel attachment onto silica particles using three different hydrodynamic models (Fig. 4) and compared the theoretical changes in sedimentation to the experimental data for the large microgels (Fig. 1 and 2).67 To calculate the sedimentation coefficients, we considered the change in size, density and volume equivalent diameter upon microgel attachment. First, the shape of the heteroaggregate structure was assumed to be spherical and the change in sedimentation coefficient was calculated using eqn (4). This simplistic scenario translates into an extreme case where the microgels are considered “liquid-like” and uniformly coat the surface of the silica particles. The calculations (Fig. 4b, blue) qualitatively reproduce the experimentally observed trends (Fig. 4b, black), showing a decrease in sedimentation coefficient which gradually levels off with increasing number of microgels where the change in density becomes less significant. However, these calculations systematically underestimate the measured shift in sedimentation coefficient, which we attribute to the approximation of sphericity that neglects any anisotropy caused by the microgel attachment. Such anisotropies are known to decrease the sedimentation coefficient due to an increase in the frictional coefficient.68
image file: d0sm00026d-f4.tif
Fig. 4 Theoretical investigation of the change in sedimentation coefficient of silica particles upon the attachment of microgels. (a) Schematic illustration of the different models used for the calculation of the shift in sedimentation coefficient as a function of attached microgels. (b) Measured and calculated shift in sedimentation coefficient as a function of attached microgels. The inset corresponds to the different relative positioning for two attached microgels in the case of the rigid-sphere model.

To account for the change in shape upon the attachment of microgels, we derived the shape factor of the heteroaggregate via a modified Brownian dynamics algorithm (details in ESI).56 First, we simulated the extreme case where the spherical microgels do not deform upon attachment and calculated the sedimentation coefficient accordingly using eqn (6).

Throughout the calculation of the shape, one important feature was the relative positioning of the microgels if the number of microgels on a particle was greater than one. If two or more microgels attach on the silica particles’ surface, the hydrodynamic properties of the overall structure and hence the shape factor depends on the exact positions of the microgels. Therefore, we exemplary calculated the change in shape factor and the respective shift in sedimentation coefficient for two attached microgels as a function of their relative angular position (Fig. 4b, orange curve, i–iv). The results from these calculations show that the positioning of the microgels significantly affects the shift in sedimentation coefficient.

For the experimental results, a random sequential attachment mechanism of the microgels onto the silica particles69 is expected to produce a range of different geometries and thus shape factors, which leads to an overall broadening of the sedimentation coefficient distributions in the case of two or more attached microgels. The experimental observations support this theoretical prediction as the distribution broadening for more than one microgel attached to a silica particle can be clearly observed in Fig. 1 and 2. Due to the high degree of freedom, we simplified our model for the following considerations and assumed a trigonal planar structure in the case of three microgels and a tetragonal configuration in the case of four microgels.

The theoretical predictions from the rigid-sphere models systematically overestimate the change in sedimentation coefficient as they do not take into account the deformability of the microgels.51,70 In the soft-sphere model, we therefore simulated the deformation of the microgels by overlapping the microgel sphere with the silica sphere, while keeping the overall mass constant. For a single microgel that attaches to the silica core particle, a volume overlap of almost 20% was approximated (details are in ESI). It is reasonable to assume that the microgels’ volume decreases during attachment due to the spreading at the interface,51,70 causing release of water from the structure. Thus the deformation is expected to lead to an increase in density. Yet, since the density of the microgels is similar to that of water (Fig. S3, ESI), the change in density can be safely neglected. For a single attached microgel, we found very good agreement with the experimental results using an overlap of 200 nm (Fig. S5, ESI). We further tested the model with a constant microgel volume (increase in microgel diameter while overlapping microgel and particle) to compensate the overlap (Fig. S5, ESI), but found a similar shift in sedimentation coefficient. We used the same overlap to simulate the shift in sedimentation coefficient for more than one attached microgel (Fig. 4b, green curve) and found close agreement to the experimentally measured shifts. Thus, it is possible to accurately predict the morphology of the heteroaggregates while investigating them in their native solution environment.


We quantitatively characterized the attachment of soft microgels onto silica particles using analytical centrifugation. The attachment of microgels onto silica particles induces a change in the sedimentation coefficient, which is sensitive towards changes in mass and density upon attachment and thus serves as a perfect measure for quantitative identification for the attachment of individual microgels.

The colloidal stability of the heteroaggregates depends on the surface ratio between the two species. Having an excess of silica particles leads to the formation of large aggregates, where one microgel bridges multiple particles together, with a maximum at a RA = 0.3. If the microgels are in excess, the heteroaggregates are colloidally stable as the attached microgels provide steric stabilization.

We corroborated the experimental shifts in sedimentation coefficient by theoretical investigation testing different assumptions for the shape of the microgels. We found close agreement with the experiment for an aggregation model that describes the microgels as soft, deformable spheres. Additionally, while the attachment of one microgel to a colloid leads to a defined shift in the sedimentation coefficient, the attachment of multiple microgels further leads to a broadening of the sedimentation coefficient distributions due to multiple possibilities of relatively arranging the microgels on the silica surface. Our study introduces a promising methodology for high throughput and quantitative analysis of heteroaggregation processes in general, allowing a precise determination not only of the exact number of attached species, but also of the amount of free and functionalized/aggregated silica particles.

Conflicts of interest

There are no conflicts to declare.


The research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 416229255 – SFB 1411. NV and MR acknowledge funding by the DFG under grant number VO 1824/6-1. MJU and WP acknowledge funding by the DFG through project PE 427/33-1. We thank Herbert Canziani for the synthesis of the silica colloidal particles. We further acknowledge Roman Guenther and Jo Sing Julia Tang for the synthesis of the PNIPAM microgels.


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Electronic supplementary information (ESI) available. See DOI: 10.1039/d0sm00026d

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