Adsorbed polymer configuration

Some polymer molecules can be regarded to maintain their approximate solution conformation upon adsorption (19). Adsorption of a nonionic polymer would lead to a coiled adsorbed polymer configuration with a small number of polymer segments in actual contact with the surface. The number of surface sites available for surfactant adsorption would remain quite large. 

PVA and TaM -for the 88%-hydrolyzed PVA. The same dependence was found for the adsorbed layer thickness measured by viscosity and photon correlation spectroscopy. Extension of the adsorption isotherms to higher concentrations gave a second rise in surface concentration, which was attributed to multilayer adsorption and incipient phase separation at the interface. The latex particle size had no effect on the adsorption density however, the thickness of the adsorbed layer increased with increasing particle size, which was attributed to changes in the configuration of the adsorbed polymer molecules. The electrolyte stability of the bare and PVA-covered particles showed that the bare particles coagulated in the primary minimum and the PVA-covered particles flocculated in the secondary minimum and the larger particles were less stable than the smaller particles. 

The determination of adsorption isotherms at liquid-solid interfaces involves a mass balance on the amount of polymer added to the dispersion, which requires the separation of the liquid phase from the particle phase. Centrifugation is often used for this separation, under the assumption that the adsorption-desorption equilibrium does not change during this process. Serum replacement (6) allows the separation of the liquid phase without assumptions as to the configuration of the adsorbed polymer molecules. This method has been used to determine the adsorption isotherms of anionic and nonionic emulsifiers on various types of latex particles (7,8). This paper describes the adsorption of fully and partially hydrolyzed PVA on different-size PS latex particles. PS latex was chosen over polyvinyl acetate (PVAc) latex because of its well-characterized surface PVAc latexes will be studied later. 

We present an improved model for the flocculation of a dispersion of hard spheres in the presence of non-adsorbing polymer. The pair potential is derived from a recent theory for interacting polymer near a flat surface, and is a function of the depletion thickness. This thickness is of the order of the radius of gyration in dilute polymer solutions but decreases when the coils in solution begin to overlap. Flocculation occurs when the osmotic attraction energy, which is a consequence of the depletion, outweighs the loss in configurational entropy of the dispersed particles. Our analysis differs from that of De Hek and Vrij with respect to the dependence of the depletion thickness on the polymer concentration (i.e., we do not consider the polymer coils to be hard spheres) and to the stability criterion used (binodal, not spinodal phase separation conditions). 

These include electrostatic interaction between the particles and interaction of particles with the fluid governed by their wettability, morphology and density (17-19) the extent of adsorption of the polymer and its influence on the interaction of particles, the orientation or configuration of the adsorbed polymers (and surfactant when it is present) and resultant interaction of adsorbed layers the hydrodynamic state of the system and its influence on the interaction of floes themselves. 

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. 

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... 

When particles collide, their adsorbed layers may be compressed without penetrating into one another. This denting mechanism will reduce the configurations available to the adsorbed polymer molecules therefore, there will be a decrease in entropy and an increase in free energy, and stability will be enhanced by an elastic... 

Because of restrictions on the number of possible configurations, non-adsorbing polymers tend to stay out of a region near the surfaces of the particles, known as the depletion layer. As two particles approach, the polymers in the solution are repelled from the gap between the surfaces of the particles. In effect the polymer concentration in the gap is decreased and is increased in the solution. As a result, an osmotic pressure difference is created which tends to push the particles together. The resulting attractive force is the reason for depletion flocculation. In contrast to this, depletion stabilisation has been mentioned above. 

Schick and Harvey (49) summarize an interesting investigation of the effect of the choice of solvent on the conformation of a polymer adsorbed at the solution interface with Spheron 6 carbon black. A noteworthy conclusion concerns the occurrence of extended and looped configurations of the adsorbed polymer molecules formed from good or poor solvents, respectively. 

Lattice models play a central role in the description of polymer solutions as well as adsorbed polymer layers. All of the adsorption models reviewed so far assume a one-to-one correspondence between lattice random-walks and polymer configurations. In particular, the general scheme was to postulate the train-loop or train-loop—tail architecture, formulate the partition function, and then calculate the equilibrium statistics, e.g., bound fraction, average loop... 

Under some conditions, though, an adsorbed layer may not be in full equilibrium with bulk solution. For restricted equilibrium, the adsorbed amount of polymer is held constant adsorbed chain configurations are assumed to be optimally distributed, but only solvent is free to move between the layer and bulk solution. Since ZA normalizes G(r, s)G(r, n — s)em integration of Eq. (79) with Eq. (69) over r gives c — (pi Jn where [Pg.182]

On closer inspection, one encounters here features that are typical for polymer chains. One is that the configurational entropy of the chain starts to exert its Influence. Adsorbed polymers are still to a large extent in contact with the solvent. The way in which the chains are folded is Important. For Instance. 

For the polymer to be effective, it must adsorb to the interface and maintain a certain configuration. Thus the following discussion describes various experimental techniques used for the study of adsorption density and configuration of polymer at the interface. After adsorption occurs, the main mechanisms of flocculation are due to the adsorption of a single polymer molecule on separate particles, interaction through the interpenetration of adsorbed polymer, and interactions due to the loss of freedom of movement of the polymer chains. 

One can also analyze the rotational relaxation of the adsorbed molecules.140 Figure 27a shows a time sequence of a single molecule with an overlay of the unit vector u(t) defined as the direction of the longer principal axis of the gyration tensor. An instantaneous polymer configuration may be described by an ellipse, and therefore, the simplest conformational change is the rotational motion of an ellipse. The time correlation function of u(t) decays exponentially where zr denotes the rotational relaxation time, °c exp(-f/rr). 

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. 

Two extreme cases can be envisaged, one in which the polymer chains mix, while the other involves no mixing but the layers become compressed on close approach of the surfaces. Both involve a reduction in the configurational freedom of the adsorbed polymer molecules, which results in a repulsive force. One or both types of interaction could be present in any particular system, depending on the nature of the polymer and solvent, and the structure of the adsorbed layer. There has been considerable theoretical analysis of both cases, and the relative merits of the two approaches are debated in the literature -. ... 

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