The behaviour of an ideal polymer chain interacting with two parallel surfaces

Abstract

The behaviour of a long isolated ideal chain polymer interacting with two parallel surfaces is investigated within the context of a simple cubic lattice model in three dimensions. In order to be able to obtain information about the contacts of the polymer with the plates the full chain is subdivided into trains, loops and bridges. A maximum term method is used to calculate the configuration sum of the polymer. In order to find the distribution of the subchains that maximises the partition function in the limit of infinite molecular weight a Lagrange multiplier method has been applied. This gives a closed set of equations from which one can uniquely calculate all relevant thermodynamic quantities as a function of the interaction energy, the temperature and the distance between the plates. In addition to the free energy and the entropy of the chain also the fraction of monomers on the surface and the number of trains is calculated. Next we give results about the ratio between the number of bridges and loops and the fraction of monomers in these loops and bridges. Finally the effective force between the plates due to the polymer material is calculated.The results for large plate separation are compared with those of the single plate.

Modeling of amorphous polymer surfaces in computer simulation

“…These typical periodic changes of the density distribution close to the surface [10] are due to the external pressure produced by the plates, which leads to a local partial crystallization. The same behaviour has been found in simulations analyzing surface phenomena [11] and studied in the context of one long chain between two parallel plates [12]. The chains experience strong packing constraints as well as a loss in entropy that must show up also in the surface properties that can be observed during indentation.…”

Critical adsorption of a flexible polymer confined between two parallel interacting surfaces

“…However, the transition of D = 10 is far below T c , possibly because the polymer forms a bridge structure more easily when D is small, i.e., it contacts both surfaces at the same time. Strong confinement is a disadvantage for the polymer chain forming a 2D conformation [32].…”

“…They found a second-order transition at CAP for both an infinitely large system and an infinitely long polymer [26]. The attractive interaction can also significantly change the conformational structure and the dynamics of a polymer [32][33][34]. The polymer adopts structures containing trains, loops, bridges, and tails at high temperature, while it is fully adsorbed on one of the two surfaces at low temperature.…”

Effect of confinement and stiffness on the conformational change of a semiflexible homopolymer chain

“…Advances in the single molecule based experiments have made it possible to study conformational change of a confined macromolecule. Therefore, the study of the conformational properties and the possibility of polymerization of the polymer chain segments with either one end of the chain lying on the constraints (polymer train) or both the ends lying on the flat geometrical constraints (polymer bridge and polymer loop) have attracted attention in the recent years, see [3,4,5,6,7,8,9,10,11,12,13], and the references quoted therein. The polymer bridge [13] corresponds to the confined chain segments with chain ends lying on two different geometrical constraints, however, arc corresponds to the chain segments with both end monomers of the chain lying on a constraint.…”