Aggregation and deposition of fullerene nanoparticles in aquatic system

Colloidal stability of C₆₀ nanoparticles in aquatic system

Fullerene C₆₀ is likely to take the form of crystalline C₆₀ nanoparticles once released into aquatic system. In the presence of water, these extremely hydrophobic C₆₀ molecules tend to self-assemble and form very stable nanoparticles.

It has been confirmed by several groups that the supposedly purely carbon-based fullerene C₆₀ nanoparticles are negatively charged. However, the source of the negative surface charge is not clear at this time. In addition, the dependence of the electrokinetic properties of the fullerene nanoparticles on solution chemistry, including electrolyte concentration and solution pH, has been reported by various groups. In particular, the electrokinetic mobilities of these nanoparticles were found to be less negative with increasing electrolyte concentration, implying that charge screening could be taking place. This is an important implication to colloidal stability of fullerene C₆₀ nanoparticles.

Aggregation

Introduction

Aggregation is defined as the formation of particles into clusters. It involves two steps: (1) the transport of one nanoparticle to anther through Brownian motion, fluid motion or sedimentation and result a collision and (2) the permanent contacts between nanoparticles must be formed by overcoming the repulsive interactions, which depends on the nature of nanoparticles and the solution chemistry.

Aggregation is a key process which strongly influences the transport and ultimate fate of nanoparticles in both natural and engineered aquatic systems. First, the settling rate of nanoparticles in natural waters depends on the nature of aggregates formed. Second, in engineered aquatic system, aggregation favors the particle separation processes such as sedimentation, flotation and filtration. Aggregation also influences the bioavailability of nanoparticles in natural aquatic system.

Prediction by the classic DLVO theory

The classic Derjaguin, Landau, Verwey and Overbeek theory (DLVO) theory plays an important role to understand the behavior of colloidal particles in aquatic system. Ideally, we consider particles as spheres to simpify the calculation. Van der Waals and electrostatic double layer interactions between two spherical colloidal particles are evaluated from the corresponding interaction energies between two infinite flat plates using Derjaguin approximation.

Since the interaction of double layer is still not fully understand, the calculations are usually made on the basis of constant charge, constant potential or linear superposition approximation. Below is a formula raised by Gregory (1975) by combining linear superposition and Derjaguin approximation.

$V_{EDL}=\frac{128\Pi a_1 a_2 n_b kT}{(a_1+a_2)\kappa^2}\gamma_1\gamma_2 exp(-\kappa h)$

Where

• $\gamma = tanh\left(\frac{ze\phi}{4kT}\right)$ is the reduced surface potential;
• a is the particle radius;
• h is the surface to surface separation distance;
• κ is the Debye-Hückel reciprocal length;
• k is the Boltzmann constant;
• n_b is the bulk number density of ions.

To calculate the van der Waals interaction, we combine Hamaker-type expressions with corrections to account for retardation. Below is a widely formula raised by Gregory (1981).

$V_{vdw}=-\frac{A a_1 a_2}{6h(a_1+a_2)}\left[1-\frac{bh}{\lambda}ln(1+\frac{\lambda}{bh})\right]$

Where

• λ is the characteristic wavelength of the interaction and it is a value around 100nm for most of materials;
• b=5.32;
• A is the Hamaker constant depends only on the materials of particles and the medium;
• a is the particle radius;
• h is the surface to surface separation distance.

Thus, the total interaction energy can be expressed by combine the interaction of double layer together with van der Waals interaction, which is listed as followed.

$V_{T}=\frac{128\Pi a_1 a_2 n_b kT}{(a_1+a_2)\kappa^2}\gamma_1\gamma_2 exp(-\kappa h)-\frac{A a_1 a_2}{6h(a_1+a_2)}\left[1-\frac{bh}{\gamma}ln(1+\frac{\gamma}{bh})\right]$

An important predicted value called Critical Coagulation Concentration(CCC) can be obtained by letting V_T = 0  and dV_T/dh = 0  theoretically. This point is of great importance since it shows the place where the fast aggregation starting to take place.

Experimental results for aggregation behavior of C₆₀ nanoparticles

Previous research has been focused on homoaggregation between fullerene C₆₀ nanoparticles. It is of great interest to know whether the classic Derjaguin, Landau, Verwey and Overbeek theory (DLVO) theory can well predict the critical coagulation concentration of fullerene C₆₀ nanoparticles in aquatic system by simplify the forces into van der Waals attraction and double layer repulsion.

Surprisingly, it has been reported that the experimental data was in quantitative agreement with the theoretical prediction in the absence of humic acid , which is an important natural organic matter in the environment. In the presence of humic acid, the steric stabilization effect can be caused by the adsorption of macromolecules to the fullerene C₆₀ nanoparticles and therefore reduces aggregation rates.

Deposition

Introduction

Deposition can be treated as an extreme case of heteroaggregation if we consider one of the particle's radius goes to infinity. Like aggregation, the process of deposition also includes two steps, transport and attachment to the surface. First, suspended particles need an opportunity to reach the surface. Under low Reynolds number's condition, this transport process is mainly controlled by Brownian diffusion. According to Stoke-Einstein Equation, we know that the smaller the particle is , the stronger the Brownian diffusion is. Thus, we can expect the smaller particles always have more chances to deposit onto a surface than bigger ones. Under other fluid condition, the fluid motion can also help to bring the particles onto the surface. Second, the kinetic energy of the particles must be strong enough to overcome the energy barrier between particle and surface in order to facilitate a permanent attachment to occur.

Deposition process is important for both industrial and natural environment. In drinking water treatment plants, deposition controls many processes such as coagulation, sedimentation and filtration by influencing the efficiency of contaminants removal processes. Deposition is also important to the fate and transport of natural occurring colloid particles in aquatic system. Take fullerene C₆₀ nanoparticles as an example, its deposition on mineral surface contributes to the removal of these particles from aqueous phase, which therefore reduces the public concerns about its toxicity.

Description by DLVO theory

The theory part of DLVO for deposition, that is sphere-plate interaction, is similar to the part of aggregation, in which the surface is assumed to be a very big particle with an infinite radius. Generally, there are two parts of interaction energy. One is attractive energy, called Van der Waals attraction, which is a kind of additive effect of intermolecular forces between particle and surface and is inverse proportional to distance between particle and surface. The other is repulsive energy, called electrostatic repulsion, which comes from the interference of the diffuse double layers of both particle and surface and decreases with the exponential of distance. The total interaction energy is the sum of these two energies.

There is a repulsive energy barrier in the profile of total energy, which is determinant factor on whether particle can attach to the surface. In order to overcome this energy barrier, particles must have sufficient kinetic energy. The less the energy barrier is, the more easily the deposition can happen. The height of energy barrier is dependent on solution chemistry, such as pH, ionic strength and other solutes with various chemical characteristics. There exists a critical coagulation concentration (CCC). The deposition efficiency will be 1.0 if the solution concentration is equal to or higher than CCC, that means the energy barrier is low enough so that every collision between particles and surface will lead to permanent attachment.

Experimental deposition behavior of C60 nanoparticles

To investigate deposition behavior of nanoparticles in experiments, one should preclude the aggregation effect on deposition rate, because the aggregation will lead to bigger particle size and as a result diminish the chance of particle collision onto the surface. Otherwise, the deposition rate will decrease as the aggregation happens and there is no CCC in the deposition efficiency profile.

For example, because of the aggregation of fullerene in sample bottle during experiments but no aggregation consideration in favorable deposition condition, the deposition efficiency profile at different salt concentration doesn’t follow DLVO theory. After considering the aggregation effect during deposition process by comparing deposition rate at different salt concentration to a series of favorable deposition rate at corresponding salt concentration, the deposition efficiency profile follows DLVO theory and there is CCC.