Loop-train adsorption

Of particular interest has been the study of the polymer configurations at the solid-liquid interface. Beginning with lattice theories, early models of polymer adsorption captured most of the features of adsorption such as the loop, train, and tail structures and the influence of the surface interaction parameter (see Refs. 57, 58, 62 for reviews of older theories). These lattice models have been expanded on in recent years using modem computational methods [63,64] and have allowed the calculation of equilibrium partitioning between a poly-... 

Hesselink attempted to calculate theoretical adsorption isotherms for flexible polyelectrolyte chains using one train and one tail conformation (1) and loop-train conformation (2) as functions of the surface charge, polyion charge density, ionic strength, as well as molecular weight. His theoretical treatment led to extensive conclusions, which can be compared with the relevant experimental data. 

In his second paper, Hesselink57 developed a new theory for the adsorption of polyelectrolyte by assuming loop-train conformations but neglecting tail formation. The partition function for Na polyelectrolytes adsorbed on the surface with an area S from the solution of volume V is still given by Eq. (B-21), but AF is now the sum of the following five contributions. 

Figure 16.1. Various conformations of polymeric surfactants adsorbed on a plane surface (a) random conformations of loops-trains-tails (homopolymer) (b) preferential adsorption of short blocks (c) chain lying flat on the surface (d) AB block copolymer with loop-train conformation of B and long tail of A (e) ABA block copolymer, as in (d) (f) BA graft with backbone B forming small loops and several tails of A ( teeth )...

Adsorption of a polymer necessarily implies a change in the conformation the most common description is the loop-train-tail model (Jenkel and Rum-bach 1951) shown schematically in figure 5.10. The trains are made up of segments in direct contact with the surface, whereas loops have no direct contact with the surface but are in close proximity. Tails are non-adsorbed chain ends. Although tail segments may constitute a small proportion of all segments, they determine the hydrodynamic layer thickness of the adsorbed polymer. Many other properties of adsorbed polymers are determined by the total segment concentration profile as a function of the distance from the surface. 

Figure 5.4. Schematic view of polymer adsorption at a solid-liquid interface showing loops, trains and tails and the corresponding segment distribution function, p(z).

As the concentration of the macromolecules in equilibrium with the interface increases, so that the coil population becomes crowded, a sudden reaching of a very gently upward sloping plateau is observed, but hardly ever any multilayer formation, since no proper outer boundary of the adsorbed layer of coils develops (see below). Instead, as more coils compete for the same interfacial area, adsorption of further molecules occurs as interpenetration is still resisted, at the expense of the site areas held per molecule, i.e., the adsorbed trains become shorter, the loops longer, and the area under the coils smaller the coils become sideways and upwards compressed, (15) (16), Fig. 3. Experimentally,... 

Scheutjens, J. M. H. M., and G. J. Fleer (1980), "Statistical Theory of the Adsorption of Interacting Chain Molecules. 2. Train, Loop, and Tail Size Distribution", J. Phys. Chem. 84/2, 178-90. 

In general, the adsorption of a surfactant on particles with previously adsorbed polymer can be influenced by (i) a reduction of surface area available for adsorption as a result of the presence of adsorbed polymer, (ii) possible interactions between polymer and surfactant in the bulk solution or in the interfacial region (that is, surfactant with loops, tails or trains of adsorbed polymer molecules), (iii) the steric effect of adsorbed polymer, preventing approach of surfactant molecules for adsorption at the surface, or (iv) possible electrostatic effects if polymer and/or surfactant are charged species. 

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... 

Zheligovskaya et al. [55] have simulated the adsorption of quasirandom adsorption-tuned copolymers (ATC). The critical adsorption energy as well as some characteristics of the adsorbed single chains (statistics of trains, loops, and tails) were studied. All these properties were compared with those... 

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... 

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