Adsorbed polymer chains

Fig. XI-4. Schematic diagram of the structure of an adsorbed polymer chain. Segments are distributed into trains directly attached to the surface and loops and tails extending into solution.

In many colloidal systems, both in practice and in model studies, soluble polymers are used to control the particle interactions and the suspension stability. Here we distinguish tliree scenarios interactions between particles bearing a grafted polymer layer, forces due to the presence of non-adsorbing polymers in solution, and finally the interactions due to adsorbing polymer chains. Although these cases are discussed separately here, in practice more than one mechanism may be in operation for a given sample. 

The second case involves non-adsorbing polymer chains in solution. It was realized by Asakura aird Oosawa (AO) [50] aird separately by Vrij [51] tlrat tlrese chains will give rise to air effective attraction between colloidal particles. This is kirowir as depletion attraction (see figure C2.6.4. We will summarize tire AO tlreory to explain tlris. 

In section C2.6.4.3 it was shown how tlie addition of non-adsorbing polymer chains induces a depletion attraction between colloidal particles. If sufficient polymer is added, tliese attractions can be strong enough to induce a phase separation of tire colloidal particles. An early application of tliis was tire creaming of mbber latex [93]. 

The polymers exist in saline solution as tightly coiled chains and are readily adsorbed owing to relatively low solubiUty in hard water. Subsequent injection of soft, low salinity water uncoils the adsorbed polymer chains increasing water viscosity and reducing rock permeabiUty. This technology could also be used to reduce the permeabiUty of thief 2ones adjacent to injection wells. However, mechanical isolation of these 2ones may be necessary for cost-effective treatments. 

Finally, we have studied the reaction of amino-terminated polyoxyethylenes with the poly(vinylbenzyl chloride) latex (18). The rate of this reaction was found to be independent of the length of the chain carrying the terminal amine. Attachment of these chains stabilized the latex against coagulation, in analogy with the "steric stabilization" produced by adsorbed polymer chains (19 ). ... 

Lee, J.J. Fuller, G.G. "Elllpsometry Studies of Adsorbed Polymer Chains Subjected to Flow", submitted to Macromolecules. 

The physical significance of the experimental profile is that it is the probability that a segment of an adsorbed polymer chain is at a distance z from the interface. In order to find the volume fraction (z) at a distance z from the interface we require the mass/unit area T and the partial molar volume of the polymer V (12), where (z) is given by... 

Decreased mobility of adsorbed chains has been observed and proved in many cases both in the melt and in the solid state [52-54] and changes in composite properties are very often explained by it [52,54]. Overall properties of the interphase, however, are not completely clear. Based on model calculations the formation of a soft interphase is claimed [51], while in most cases the increased stiffness of the composite is explained by the presence of a rigid interphase [55,56]. The contradiction obviously stems from two opposing effects. Imperfection of the crystallites and decreased crystallinity of the interphase should lead to lower modulus and strength and larger deformability. Adhesion and hindered mobility of adsorbed polymer chains, on the other hand, decrease deformability and increase the strength of the interlayer. 

Loops and tails of an isolated adsorbed polymer chain assume a number of different configurations and they substantially determine the configurational entropy of the adsorbed polymer, while the interaction energy between trains and the surface determines the enthalpy of adsorption. 

Before describing this theory, we outline the theory of Hoeve et al.41) formulated under the assumptions that the polymer chain is so long that end effects, i.e. tail formation, may be neglected and that the surface coverage is so low that the interaction of adsorbed polymer chains is negligible. 

Hoeve44,45) extended his theory further by considering not only interactions between the train segments but also interactions among the loops, and found that the latter lead to a decrease in the number of possible conformations of adsorbed polymer chains. He assumed that the segment density distribution in any loop is uniformly expanded in one dimension by a factor of at as a result of loop-loop interactions. The volume fraction of segments at a distance z > 6 is then given by... 

Silberberg47) used a quasi-crystalline lattice model for the adsorption of flexible macromolecules. If it is assumed that an adsorbed polymer chain with P segments consists of ma trains of length i and mBi loops of length i, the total number of configurations of the chains is given by... 

The thickness of the adsorbed region B which consists of a number of layers, each with Ms sites, is assumed to be <5 Pf where 6 and P are constants. Silberberg47) assumes that <5 = 1/2 and P = 1. Beyond this region is there a homogeneous bulk solution of polymer volume fraction < > from which adsorption has taken place. Except for solvent, all that is found in the region B are loop segments of the adsorbed polymer chains. Thus, the fraction of adsorbed polymer segments is expressed by... 

The same coordination number CB is assumed for both the region B and the bulk solution. The change CsB in the contact number which occurs when the adsorbed polymer chain goes from Ms surface sites to the region B is expressed by... 

The smaller expansion factor predicted by the theory of Hoeve originates from neglecting the tail portions of the adsorbed polymer chain, while the larger expansion factor predicted by Jones and Richmond is due to their failure of correctly evaluating the elastic free energy, as has been pointed out by Kawaguchi and Takahashi74. ... 

The stabilization of dispersed species induced by the interaction (steric stabilization) of adsorbed polymer chains. Example adsorbed proteins stabilize the emulsified oil (fat) droplets in milk by steric stabilization. Also termed depletion stabilization. See also Protection. 

Napper (14) has derived analytical expressions for the free energy of interpenetration and compression of the adsorbed polymer chains as a function of the distance of separation between two particles. The region of dose approach was divided into two domains ... 

When the concentration of the free polymer is set equal to zero, the situation corresponds to pure steric stabilization. The free energy of interaction due to the interpenetration of the adsorbed polymer chains has a range of 26, where 6 is the thickness of the adsorbed layer. This free energy is proportional to the quantity (0.5 - x), where x is the Flory interaction parameter for the polymer-solvent system. Thus, a repulsive potential is expected between two particles when x < 0.5 and this repulsion is absent when x = 0.5. For this reason, it was suggested [25] that instabilities in sterically stabilized dispersions occur for x > 0.5, hence for theta or worse-than-theta conditions. However, the correlation with the theta point only holds when the molecular weight of the added polymer is sufficiently high... 

The molecular model is confined to the case of weak adhesion (5 < 0) to ensure homogeneous contact [48, 65]. In this case, two sources contribute to the frictional stress of a gel elastic deformation of an adsorbing polymer chain Cei and the lubrication of the hydrated layer of the polymer network ffvis, which can be represented as follows (Fig. 12) ... 

FIGURE 5.25 Polymeric chains adsorbed at an interface (a) terminally anchored polymer chain of mean end-to-end distance L (b) a brush of anchored chains (c) adsorbed (but not anchored) polymer coils (d) configuration with a loop, trains, and tails (e) bridging of two surfaces by adsorbed polymer chains. 

FIGURE 7.27 Schematic representation of an adsorbed polymer chain at the solid-liquid interface. (From Sato, T. and Ruch, R., in Steric Stabilization of Colloidal Dispersion by Polymer Adsorption, Marcel Dekker, New York, 1980. With permission.)... 

Depletion Flocculation The flocculation of dispersed species induced by the interaction of adsorbed polymer chains. See Sensitization. 

The second case involves non-adsorbing polymer chains in solution. It was realized by Asakura and Oosawa (AO)... 

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