Colloids and Surfaces A: Physicochemical and Engineering Aspects
Irreversible adsorption of colloidal particles on solid substrates
Introduction
Deposition of colloidal particles, as well as adsorption of proteins to solid surfaces, are of fundamental importance in a large field of applications. Depending on the final aim, adhesion of colloidal particles, or, in an opposite way, lack of adhesion and desorption, are often specifically required. Thus, irreversible adhesion of microorganisms in industrial bioreactors or of cells onto biomaterials are often requested, whereas adhesion for biomedical applications, in particular with respect to microorganism adhesion, has to be prevented.
Generally one considers that colloidal particles adhere on a solid surface by means of non specific interactions, whereas cells or microorganisms interact through specific and non specific links. In a similar manner, proteins are bound to a solid surface by means of specific and non specific interactions. However, all these interactions are based on the same fundamental interactions: van der Waals, hydrophobic and electrostatic forces, and hydrogen bondings. All these interactions share a common property since they lead either to ‘reversible’ or ‘irreversible’ attachment to the collector. This latter issue implies that, once fixed on a surface, the particle neither desorb from it, nor diffuse on it. In the former case, since the particle can explore the whole surface through surface diffusion and desorption, the process can be investigated by means of the methods of the equilibrium statistical mechanics.
If the adhesion is irreversible, once fixed on the surface, the particle remains infinitely glued; the particle configuration possesses thus an infinite memory. Such observations are also often made for proteins or macromolecules establishing with time a large number of links with the surface that render the adsorption irreversible. For these processes, after a short contact time, the interaction energy becomes significantly larger than the thermal energy kT. One of the most important aspect of such irreversible deposition processes, which cannot be investigated on the basis of the classical statistical methods devoted to the analysis of equilibrium states, concerns the structural properties of the deposited layers. In this respect, the specific role of gravitational, electrostatic and hydrodynamic forces on the configuration structure are particularly important.
Our presentation will not be exhaustive, recent reviews perfectly fulfil this objective [1], [2], [3]. In particular, the problem of the adhesion of biological cells is not addressed here, but we focus on model synthetic particles. In the same way, specific properties like protein deformability, interfacial denaturation and protein flattening will not be evoked in this paper.
As for equilibrium statistical mechanics, many one-dimensional irreversible deposition processes can be solved exactly. The resolution of these 1D problems has allowed us to get a better understanding of these processes and to test the validity of different approximations introduced for the treatment of deposition processes on surfaces for example. We shall, however, not discuss these 1D cases and focus our attention on the irreversible deposition on planar surfaces, which has a closer connection to experimental results. Also, the formation of multilayers will not be discussed.
In the following, we first introduce the main tools serving to characterize the configurations of adsorbed particles (Section 2). In Section 3, we describe the most popular models, namely the random sequential adsorption (RSA) and ballistic deposition (BD) models, developed for the description of irreversible adsorption phenomena. We also evoke some extensions of these approaches. In the next section (Section 4), the diffusion is introduced, which leads to the diffusional models allowing to take into account, in a realistic way, the Brownian diffusion, notably in the presence of deterministic forces (electrostatic, van der Waals, gravitational, hydrodynamic). In the last section (Section 5), experimental results are shown, in particular with the goal to test the validity of various models described above. We focus here the discussion especially on colloidal particles. In particular, we give some first results concerning the kinetics of deposition of ‘heavy particles’ and test the validity of the BD model which is generally restricted to predict static properties of particle assemblies.
Section snippets
General concepts related to irreversible deposition
As pointed out in the introduction, equilibrium statistical mechanics does not apply to systems of particles deposited on surfaces through irreversible deposition processes. However, some concepts and tools that have been developed in equilibrium statistical mechanics still remain useful for the description of irreversible deposition processes and will be briefly described in this section.
Deposition models based on statistics and geometry
All the models developed to describe the irreversible deposition processes share a common property: the particles are deposited sequentially onto the surface and the initial location of the deposition trial is chosen randomly and uniformly above the adsorbing surface. One can then distinguish roughly between two types of models: (i) The models for which the initial position of the particle above the plane determines totally its final position if one takes the microscopic configuration of the
Extended RSA model taking diffusion into account
If one observes the deposition of particles on a surface with a microscope one realizes an important aspect which is not taken into account in the RSA model, namely the Brownian motion of these particles in the vicinity of the adsorbing plane. This diffusion process implies that, even if a depositing particle interacts with an already deposited one, it is not rejected from the system but can diffuse around its initial position and eventually still adhere to the surface. To account for these
Validity of the Langmuir model
Adsorption kinetics of macromolecules or colloidal particles on solid surfaces are often described by the Langmuir model, in which the kinetic law is given by:where ka and kd represent respectively the adsorption and the desorption constant, θmax corresponds to the maximum attainable surface coverage and cb represents the concentration of adsorbing species in the bulk but in the vicinity of the adsorption plane. Eq. (5.1) implies that the available surface function is a
Acknowledgements
One of us (P.S.) is indebted to the ‘Institut Universitaire de France’ for financial support.
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