Depletion effect interactions

Several theories have been put forward to account for the distributicm of polymer segments in the depletion zone. The theories of Feigin and Napper [48] and Scheutjens and Fleer [49] are qualitatively different from the theory of Asakura and Oosawa and de Cannes and coworkers [50,51] in that they predict not only depletion flocculation but also depletion stabilization. Depletion stabilization has not to date been verified experimentally although depletion fiocculation has been verified experimentally for several systems [52,53]. The effect of an adsorbed poljnner layer [54] and ordered solvent layers [55] on depletion flocculation is also under theoretical attack. The depletion stabilization interaction energy cannot simply be added to the other interaction energy terms to give the total interaction energy. 

It would appear that the effects of solvency on depletion flocculation and depletion phase separation are quite complex. The presence of steric layers means that depletion effects alone do not determine stability and proper allowance must be made for the effects of solvency on the steric interactions. 

Fig. 17.19. (a) The relative surface excess for two flat plates as a function of the distance of separation (b) characteristic free energy of interaction arising from depletion effects according to the thermodynamic approach. 

This chapter gives an introduction into colloidal interactions, including the depletion force in a historical context, and provides examples of the manifestations of depletion effects. First, we start with a brief overview on colloidal interactions in Sect. 1.2 including the basic concept of the depletion interaction. We sketch the effects of unbalanced forces, amongst which depletion forces in colloidal dispersions from a historical perspective in Sect. 1.3. Finally, we discuss some consequences of depletion forces in Sect. 1.4, followed by a brief Outline of the other Chapters of this book in Sect. 1.5. 

Theoretical work on depletion interactions and their effects on macroscopic properties such as phase stability commenced along various routes. First, Vrij [40] considered the depletion interaction between hard spheres due to dilute non-ad-sorbing polymers such as penetrable hard spheres (see Sect. 1.2.5 and Sect. 2.1). Vrij [40] referred to the work of Vester [82], Li-In-On et al. [55] and preliminary experiments at the Van t Hoff Laboratory on micro-emulsion droplets mixed with free polymer [40] for experimental evidence of depletion effects. 

Until the end of the 1990s most theoretical approaches were based on describing polymer chains as ideal or as penetrable hard spheres. Especially at the turn of the last century a wealth of different approaches were proposed to describe colloid-polymer mixtures in which interactions between polymer segments were accounted for. Essential was the progress made in Monte Carlo computer simulation studies on depletion effects [172-179] to test such theories. 

More recently, is has been realized that procedures based on the depletion interaction have the potential to enable fabrication of materials based on self-organized colloidal structures [239]. Also in biological systems, the importance of depletion effects are increasingly appreciated [240, 241]. To illustrate this, we discuss a few examples of depletion effects in systems of biological and technological interest in this section. 

In this chapter we provided an introduction to colloidal interactions, a historical perspective on early observations, and on later understanding of depletion effects and applications of depletion phenomena. In Chap. 2 we address the fundamentals of depletion interactions, including the effects of anisotropic depletants. The focus will be on small depletant concentrations which allow simple treatments using both the force method and the adsorption method to arrive at depletion potentials. The basics of phase behavior in colloidal dispersions with added depletants are set... 

This brings us to the conclusion that as far as the depletion interaction is concerned ideal polymer chains to a good approximation can be replaced by penetrable hard spheres with a diameter a = 2, where the depletion thickness bs now depends on the size ratio q = Rg/R. In dilute polymer solutions the ideal chain description suffices to describe depletion effects. In Chap. 4 we shall see that for polymers with excluded volume the depletion thickness not only depends on the size ration q but also on the polymer concentration, see also [36, 39-41]. Also the (osmotic) pressure is no longer given by the ideal (Van t Hoff) expression. Both features significantly affect depletion effects. 

When the colloidal particles are completely covered with adsorbing polymer, adding more polymer gives rise to excess polymer in the bulk solution, which is thus not adsorbed. This non-adsorbing polymer may lead to depletion interaction as well. In such a case depletion effects are weaker for two reasons. Firstly, more polymer is required before depletion-induced instability of the dispersion occurs because polymer is first consumed in order to cover the particles [1]. Secondly, the depletion interaction is weak due to the soft repulsion between the adsorbed polymer layers. It is known that depletion effects between such soft surfaces are rather small [1, 5]. 

In the introduction of this chapter we mentioned that rod-like colloids influence the phase behaviour of suspensions of spherical colloids significantly at very low concentration. For a review see [32]. This is not surprising as rod-like colloids give rise to a strong depletion interaction at low concentration, see (2.107). Here we will see that FVT (correctly) captures the above mentioned pronounced depletion effect caused by rod-like particles. 

Walz and Sharma [1439] calculated the depletion force between two charged spheres in a solution of charged spherical macromolecules. Compared to the case of hard-sphere interactions only, the presence of a long-range electrostatic repulsion increases greatly both the magnitude and the range of the depletion effect. Simulations and density functional calculations for polyelectrolytes between two planar surfaces extend these results [1440]. 

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