Adsorption of charged diblock copolymers : effect on colloidal stability

In this thesis we present Scheutjens-Fleer (SF) calculations on the adsorption of diblock copolymers. More specifically, we restrict ourselves to adsorption at uncharged surfaces, while the specific type of block copolymers we consider have one uncharged adsorbing "anchor" block and one non-adsorbing charged "buoy" block. We compare these systems with a more simple one, that of the charged brushes. A polymer brush is the structure that is formed when polymer molecules are attached by one end to a surface, with a density high enough so that the chains are obliged to stretch away from the interface. Complementary to the numerical computations, the scaling behaviour of these systems is discussed. We study the structure of the adsorbed layer, and try to answer ultimately the question what the effect of the adsorption is on colloidal stability.In the introductory Chapter 1 we explain the most important terms and discuss the relevance of this study. Furthermore, we introduce the SF model and compare it to two other approaches: Monte Carlo and Scaling. Finally, we briefly present the available information on the two systems under consideration, and compare them to a number of related systems.The body of this work is divided in two parts. In Chapters 2 and 3 we discuss charged brushes, systems that are simpler than diblock copolymer adsorption, but still exhibit similar characteristics. In the subsequent two chapters we then proceed to the adsorption of diblock copolymers (Chapter 4) and its effect on colloidal stability (Chapter 5).In Chapter 2 we present numerical results from the SF model for the structure and sealing behaviour of charged brushes and compare these with predictions of an analytical model on the same system. The relevant parameters are the chain length <em>N</em> , the average anchoring density σ, the average segmental charge αon the chains, and the salt concentration φ _{<font size="-2">S</font>} .At high anchoring densities, three regimes of brush behaviour may be distinguished. In the salt-free case, the behaviour of the brush is dominated by electrostatic interactions if the charges are high (the so-called <em>Osmotic Brush)</em> or by non-electrostatic excluded volume interactions if the charges are low (the <em>quasi-Neutral Brush</em> regime). Upon adding salt a third regime can be found: the <em>Salted Brush.</em> The behaviour in this regime, although resulting from electrostatic interactions, is very similar to that in a neutral brush and can effectively be described using an electrostatic excluded volume parameter <em>v</em>_{<font size="-1">el</font>} ≈ φ _{<font size="-2">S</font>}<sup>-<font size="-2">1α2</font></SUP>. We find excellent agreement regarding structure as well as scaling relations between the two theories in these three (high anchoring density ) regimes. At extremely low anchoring densities, the agreement with the analytical theory is less good. This is due to the breakdown at low densities of the mean-field approximationpresently used in the numerical model.In between, at intermediate anchoring densities, the analytical theory predicts a very peculiar regime, where the thickness <em>H</em> scales as <em>H ≈N</em><sup><font size="-2">3σ</font>-<font size="-2">1α2</font></SUP>. This so-called " <em>Pincus Brush</em> ", named after the author who originally described it, is not recovered with the numerical theory. For the wide range of parameters used, we find the <em>Pincus regime</em> is too small to be detected. This is probably true for any reasonable set of parameters.In Chapter 3 we consider the acid-base equilibrium of the charged brush segments, so that grafted weak polyacids may be studied. For these systems the charge of a brush segment depends on its local environment and on the pH in the solution. The scaling dependence of the thickness <em>H</em> on the salt concentration φ _{<font size="-2">S</font>} for such a brush is very different from that for a conventional charged brush with constant charge density.In Chapter 4 we proceed to the adsorption of ionic diblock copolymers. One block, the "anchor", consists of <em>N _{<font size="-1">A</font>}</em> uncharged adsorbing A segments, whereas the "buoy" block has <em>N _{<font size="-1">B</font>}</em> segments which carry a fixed charge and are non-adsorbing. Upon adsorption these sorbed amount and layer thickness as a function of the block lengths <em>N _{<font size="-1">A</font>}</em> and <em>N _{<font size="-1">B</font>} ,</em> the charge αe on the <em>B</em> segments, and the salt concentration φ _{<font size="-2">S</font>} in each of the four regimes. The scaling relations axe checked using SF calculations.The existence of two regimes for uncharged diblock copolymer adsorption has been reported previously. We argue that those HU and LU regimes are closely related to the two regimes HC and LC we find for charged molecules. Scaling relations can be translated from the uncharged to the corresponding charged regimes by replacing the excluded volume parameter v of the buoy segments by an effective electrostatic excluded volume parameter <em>v</em>_{<font size="-2">e</font>} = α <sup><font size="-2">2</font></SUP>/φ _{<font size="-2">S</font>} .In the LC regime the chain density σscales as σ α( <em>N _{<font size="-1">A</font>} /N _{<font size="-1">B</font>}</em> ) <sup><font size="-2">3/2</font></SUP><em>v</em>_{<font size="-2">e</font>}<sup>-<font size="-2">1</font></SUP>and the layer thickness <em>H</em> as <em>H α</em> ( <em>N _{<font size="-1">A</font>} /N _{<font size="-1">B</font>}</em> ) <sup><font size="-2">1/2</font></SUP><em>.</em> The latter scaling is independent of <em>v</em>_{<font size="-2">e</font>} . Using the SF model, these relations axe found to be valid for an adsorbed amount of A segments below 10% of monolayer coverage.In the HC regime the adsorption is dominated by the anchoring block and the scaling relation σ α1/ <em>N _{<font size="-1">A</font>}</em> for the chain density is identical to that for uncharged molecules. The SF calculations show that this regime will not be reached in practical situations.Finally, we address in Chapter 5 the effect of the adsorption of charged diblock copolymers on colloidal stability. Using again a scaling as well as the SF approach, we focus on the LC regime and find that the adsorbed layer may cause a significant repulsive interaction between two surfaces, despite the very low adsorbed amounts. The magnitude of this repulsion is well within the range that could be mea, sured using a surface force apparatus. Moreover, we estimate that the repulsive interaction may be strong enough to induce kinetic stability, provided the particle radius is large enough. Upon lowering the salt concentration, however, a critical concentration φ _{<font size="-2">S</font>} * is reached eventually, below which the repulsion is no longer strong enough to effect colloidal stability. The scaling analysis predicts that this critical concentration scales as:φ _{<font size="-2">S</font>} * ≈ <em>N _{<font size="-1">Bα</font>}</em><sup><font size="-2">2</font></SUP>/ <em>RN _{<font size="-1">A</font>}<sup><font size="-2">3</font></SUP></em>where <em>R</em> is the radius of the particles and the other parameters have been defined above. Thus the repulsive interaction decreases when the relative importance of charge effects increases, i.e., with decreasing salt concentration, and increasing buoy block length or buoy block charge. This counterintuitive behaviour can be explained from the effect that electrostatic interactions have on the adsorbed amount: stronger interactions lead to a lower adsorbed amount, which, in turn, leads to a weaker repulsion. The SF calculations confirm these scaling predictions.