A single crystal grain or amorphous sphere obtained from synthesis is called a primary particle; when several primary particles touch and bind together into a larger unit, an agglomerate is formed.
Agglomerates are usually divided into two classes according to the strength of the bonding: soft agglomerates are held together mainly by weak physical interactions such as van der Waals forces, whereas hard agglomerates are held by chemical bonds or by connections formed during sintering. The former can still be re-dispersed with external energy such as ultrasound; in the latter the points of contact have already grown into one body, and conventional dispersion operations can hardly break them apart.
The smaller the particles, the higher the proportion of surface atoms, and the specific surface area and the surface free energy of the system increase accordingly. Once particles touch one another, part of their surface becomes a contact interface and the free energy decreases, which is why nanoparticles tend to agglomerate.
This kind of agglomeration is present in commercial γ-Al₂O₃ nanopowders: transmission electron microscopy (TEM) showed that for two samples with nominal sizes of 5 nm and 10 nm the primary particles averaged about 10 nm, and after the powders were dispersed in 1 mM NaCl by probe sonication for 30 min, the hydrodynamic diameter under acidic conditions was still 202–266 nm.
TEM measures the projected size of individual primary particles, whereas dynamic light scattering records the fluctuation of the scattered light intensity with time and converts it, by means of the Stokes–Einstein equation, into the hydrodynamic diameter, which corresponds to the dispersion unit actually moving in the liquid.
For γ-Al₂O₃ the hydrodynamic diameter is more than 20 times the primary particle size, indicating that each dispersion unit contains a large number of primary particles. The piles of particles seen in the electron micrographs include both the agglomeration originally present in the powder and the contacts newly formed on the TEM grid while the droplet dried.
The new contacts on the grid come from solvent evaporation: the shrinking liquid bridges between particles generate a capillary force strong enough to overcome the electrostatic repulsion between the particles. While the particles are still in the liquid, what acts between them is mainly a competition between van der Waals attraction and electric double layer repulsion or the steric hindrance of an adsorbed layer. Once the temperature rises to calcination or catalytic reaction temperatures, sintering necks also grow at the points of contact; atoms diffuse along the contact interface and neighbouring particles gradually fuse into one larger particle.
When two nanoparticles meet in a liquid, the van der Waals attraction increases rapidly as the separation shrinks. The classical DLVO theory writes the interparticle interaction as the sum of electric double layer electrostatic repulsion and van der Waals attraction; when the repulsion is strong enough, a repulsive energy barrier appears on the total interaction energy curve, and most collisions cannot surmount it.
The charge on the particle surface provides electrostatic repulsion, while polymer adsorbed on the surface provides steric hindrance; the two respond differently to the salt concentration of the solution.
In water the surface of oxide particles is usually covered with hydroxyl groups. At low pH the surface hydroxyls bind protons and the particles become positively charged; at high pH the hydroxyls lose protons and the particles become negatively charged. The pH at which the zeta potential is zero is called the isoelectric point.
The isoelectric point of titanium dioxide P25 is about pH 6.2; Na⁺ and Cl⁻ do not specifically adsorb on its surface, and the value does not change when the NaCl concentration is varied. At a pH close to 6.2 the particle surface carries almost no net charge, and large flocs appear in the dispersion.
Figure 2.Zeta potential and average hydrodynamic diameter of titanium dioxide nanoparticle dispersions as a function of pH in NaCl solutions of different ionic strengths. DOI: 10.1007/s11671-010-9772-1
A higher NaCl concentration compresses the electric double layer around the particles. When the pH is far from the isoelectric point, an increase in ionic strength lowers the absolute value of the zeta potential and the particles aggregate more readily: at an ionic strength of 0.001 M the hydrodynamic diameter of the P25 dispersion at pH 3–4 and above pH 8.5 is about 200 nm; when the ionic strength rises to 0.01 M and 0.1 M, the diameter at pH 3–4 increases to about 1 μm.
The magnitude of the salt effect varies with the system: for γ-Al₂O₃ at a pH below the point of zero charge (about pH 7.5–8), the dispersion remains stable up to a NaCl concentration of 100 mM and aggregates markedly once the concentration is raised to 1000 mM.
For dispersions stabilized by electrostatic repulsion, both adjusting the pH to a value far from the isoelectric point and washing away the salts left over from synthesis with deionized water raise the repulsive energy barrier. When the dispersion medium itself contains a great deal of salt, this approach is hard to apply: at pH 7.4 and 150 mM NaCl (physiological salinity), citrate-stabilized gold nanoparticles aggregate because their surface charge is partially neutralized.
When polymer chains are firmly adsorbed on the particle surface and extend into the solvent, two particles that approach each other compress their respective adsorbed layers, producing steric repulsion that does not depend on surface charge.
When a dispersion of 15 nm gold nanoparticles was adjusted to pH 7.4 and 150 mM NaCl, the samples with no polyethylene glycol (PEG) and with linear PEG bearing hydroxyl or methoxy end groups immediately turned from red to grey-blue and precipitated, whereas the samples with thiol-terminated linear PEG and with cyclic PEG were still red after 1000 min. The authors hold that once the surface charge has been screened by the high salt concentration, the adsorbed PEG layer still prevents the particles from touching one another.
Figure 3.Photographs and UV–vis absorption spectra of gold nanoparticle dispersions containing different polyethylene glycols before adding concentrated phosphate buffer, immediately after adding it, and after 1000 min. DOI: 10.1038/s41467-020-19947-8
The thickness of this PEG layer can be estimated by dynamic light scattering: the gold particles without PEG had a diameter of 19 nm, which increased only to 20 nm after linear PEG with hydroxyl or methoxy end groups was added; thiol PEG forms a chemical bond with the gold surface and increased the diameter to 28 nm, while cyclic PEG, relying on physical adsorption, also increased it to 26 nm, showing that the latter two form thicker adsorbed layers around the particles.
Molecules that are too small are likewise ineffective: after 18-crown-6 with a diameter of about 0.7 nm was added, all the gold particles precipitated.
The degree of coverage of the adsorbed layer depends on the amount of polymer used: for 5 nm gold particles with cyclic PEG of molecular weight about 5000 at a concentration of 0.025 wt%, only 22% of the relative absorbance remained after standing for 1000 min at physiological salinity; at concentrations of 0.25 wt% and 2.5 wt%, 78% and almost no change were retained, respectively. When the coverage is insufficient, bridging can also occur.
In drying experiments with drop-cast gold particles, when bovine serum albumin was used at about 1/20 of the optimum amount, the protein molecules could adsorb on several particles at the same time, linking the particles into large clusters.
When particles are dried into a powder, the solvent retreats into the gaps between the particles and forms liquid bridges; the capillary force generated by the curved liquid surface pulls the particles towards one another.
An estimate for two 20 nm silica particles shows that the liquid bridge energy during evaporation is about 10³ kBT, far higher than the electrostatic repulsion energy barrier, and sufficient to bring the particles to a distance at which van der Waals attraction acts. As the particle surfaces continue to lose water, the attraction between them is further strengthened.
The capillary pressure can be estimated with the Young–Laplace equation: ΔP = 2γcosθ/r, where γ is the surface tension of the solvent, θ the contact angle and r the pore radius. The smaller the pore, the greater the capillary pressure; since the gaps between nanoparticles are only on the nanometre scale, the capillary pressure during drying is very large.
Replacing the water between the particles with a low-surface-tension solvent such as ethanol before drying reduces γ and therefore the capillary pressure. For silica wet gels whose surface carries silanol groups, a silylating reagent such as trimethylchlorosilane is also added before drying at ambient pressure. Such reagents replace the hydrogen of Si–OH with alkyl groups such as methyl, so that the surface becomes hydrophobic, the contact angle θ increases and the capillary pressure is lowered further.
Besides capillary pressure, as the liquid bridge shrinks even smaller particles migrate towards the contact point. In a polydisperse system composed of silica particles from 20 nm to 90 μm, the small particles gather in the shrinking liquid bridges and form solid bridges between the large particles after drying; in bidisperse and polydisperse deposits the detachment energy of 20 μm particles is about 15 and 20 times higher, respectively, than in a monodisperse system, and the clusters remain stable when re-wetted and scoured by a water flow.
Both the capillary force and the solid bridges originate from the receding liquid surface. Supercritical drying raises the temperature and pressure inside the vessel above the critical point of the solvent, so that the liquid turns into a supercritical fluid; the liquid–gas interface and the surface tension then disappear, and the capillary force no longer arises. Low-temperature supercritical drying first replaces water with an organic solvent such as ethanol and then with CO₂, whose critical temperature is close to room temperature; this route relies on pressure-resistant equipment and is relatively costly.
Freeze-drying, by contrast, lets the water freeze first and then sublimes it at a low pressure of about one ten-thousandth of atmospheric pressure, thus avoiding the evaporation of liquid water. The freezing stage, however, brings new problems: as water keeps freezing, the solutes concentrate in the remaining unfrozen liquid, the interactions between the particles become stronger, and the growth of ice crystals also generates mechanical stress.
After 15 nm gold nanoparticles were frozen with liquid nitrogen and freeze-dried, the samples with no PEG and with hydroxyl- or methoxy-terminated linear PEG became grey-blue solids that could not be re-dispersed on adding water, their relative absorbance being no more than 9%; the thiol PEG and cyclic PEG samples stayed red and recovered to 84% and 91%, respectively, after re-dispersion.
Figure 4.State of the samples in the three stages of freeze-drying — freezing, primary drying and secondary drying — and schematic of the shelf temperature and chamber pressure as a function of time. DOI: 10.3390/ijms241814041
Besides adsorbing PEG on the particle surface, adding trehalose or sucrose is more commonly used when freeze-drying nanoparticles. These lyoprotectants are believed to form a glassy matrix surrounding the particles at low temperature, keeping the particles apart and also buffering the stress caused by the growth of ice crystals. The temperature of primary drying likewise affects re-dispersion: once the product temperature exceeds the collapse temperature, the porous freeze-dried cake collapses, the residual moisture increases and the particles become harder to re-disperse.
When a dried powder is added back into a liquid, the mechanical energy supplied by ultrasound can break up soft agglomerates; the energy input is usually expressed as energy per unit volume (J/mL). In one particle size measurement of a titanium dioxide pigment, the sample was first dispersed by ultrasound at 562 J/mL in water containing 2% polyphosphate, and some agglomerates reappeared after standing overnight; treating it in an 80 W ultrasonic bath for 1 min before measurement gave a higher proportion of primary particles in the size distribution than a sample that was merely shaken by hand.
Figure 5.Particle size distributions measured by single-particle inductively coupled plasma mass spectrometry for a titanium dioxide pigment pre-dispersion after 1 min of ultrasonic bath treatment and after re-dispersion by hand shaking only. DOI: 10.3762/bjnano.15.29
The researchers chose 562 J/mL on the grounds that above about 250 J/mL hard agglomerates and primary particles do begin to break up, but at a very low rate; as the energy is raised further, the primary particles themselves may also break, and the measured particle size then becomes smaller. Even after thorough dispersion, some hard agglomerates remain in the sample.
During calcination, atomic diffusion accelerates, particles in contact become joined through sintering necks and gradually fuse into larger particles. Metal particles supported on a carrier can also grow in two further ways: a whole particle migrates and merges with a neighbouring particle, or atoms transfer from a small particle to a large one, the latter being Ostwald ripening. Both ways require contact or exchange of matter between the particles.
Upconversion YVO₄:Yb,Er nanoparticles synthesized by the sodium citrate complexation method are smaller than 10 nm but have low crystallinity and need annealing; after direct calcination at 750 °C for 2 h, the particle size distribution broadens and agglomeration occurs.
A silica coating layer was first grown around the particles with tetraethyl orthosilicate, and the powder was then calcined at 750 °C for 2 h. Subsequent soaking in 0.5 M NaOH solution for 4 h dissolved most of the silica, giving well-dispersed particles of high crystallinity with a size of 10–15 nm as measured by TEM.
Figure 6.Process of coating YVO₄:Er,Yb upconversion nanoparticles with silica, calcining them and then removing the coating layer with alkali, together with TEM images of the particles obtained by calcination at 750 °C for 2 h with and without the coating. DOI: 10.3390/nano11061535
During calcination the coating layer occupies the space between the particles, so that neighbouring YVO₄ particles do not touch directly: the crystallinity inside the particles increases, yet the particles lack the contact points at which sintering necks could form. When the coating layer is removed, the study controlled the thickness of the residual silica layer through the concentration of the NaOH solution and the soaking time.
For metal particles supported on a carrier, two lengths can be compared: the distance d that neighbouring particles must travel in order to meet, and the migration length r of a single particle at a given temperature. When d < 2r, neighbouring particles readily meet and grow. Particles dispersed on a flat surface can move in two dimensions; when they are confined in a one-dimensional pore they can move only along the pore, but particles within the same pore still meet.
Figure 7.Relationship between the meeting distance d of neighbouring particles and the migration length r of a single particle on three carriers — a flat surface, a one-dimensional pore and a wide-mouth compartment — and schematic of the state of the particles after calcination. DOI: 10.1038/srep41773
On the wide-mouth compartment-type silica carrier the number of compartments is more than 7 times the number of platinum particles, most compartments hold at most one particle, and the compartment walls make the actual travel distance of neighbouring particles far greater than the straight-line separation of about 30 nm.
Platinum particles of about 1.7 nm encapsulated in dendrimers were loaded at about 0.07 wt% on the three silica carriers; after calcination in air at 550 °C for 4 h, the platinum particles on the compartment carrier were still 1.7 ± 0.4 nm, while they grew to 7.1 ± 1.8 nm in the mesoporous channels of SBA-15 and to 10.1 ± 3.6 nm on the surface of solid silica nanospheres.
In in-situ heating observations under vacuum, one particle inside the same SBA-15 channel became smaller while a neighbouring particle became larger, which is consistent with Ostwald ripening.
Figure 8.Electron micrographs and particle size distributions of platinum particles supported on compartment-type silica, SBA-15 mesoporous silica and silica nanospheres before and after calcination in air at 550 °C for 4 h. DOI: 10.1038/srep41773
When the platinum loading was raised to 0.84 wt%, the chance of several particles appearing in the same compartment increased, and after calcination the particles grew to 2.7 ± 2.1 nm. The open compartments also allow reactants to reach the particle surface easily: the platinum dispersion measured by CO chemisorption was 67%, 22% and 18% on the compartment carrier, SBA-15 and silica nanospheres, respectively. The platinum particles in SBA-15 also block the channels, so that the CO oxidation rate normalized to the active sites is lower.
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