Peeling a polymer from a surface or from a line

Abstract

We calculate the force on a long linear polymer molecule whose one end is zippered down onto a surface or onto a line and whose other end is at a perpendicular distance R from the surface or line. Random coil statistics are used for the unattached portion of the chain. The method is extended to the case when the bonds within the zippered portion are breaking and reforming. We also consider the case where the attached portion is in the form of loops and trains. Although the energy equations of state for these various systems are different from each other, the force equation of state is always given by f=((6)1/2/l)(k TΔg)1/2, where l is the bond length between monomers and Δg is the free energy change in pulling one monomer off of the surface. The force is independent of R except for small R. Applications are discussed briefly. They include (1) self‐healing systems of gels and rubbers where the cross links may be hydrogen bonds; (2) adhesion; (3) the degree of crystallinity in crystal‐amorphous lamellar systems; (4) the packing of DNA into the head of a bacteriophage virus and pulling apart of double stranded DNA; (5) an insight into the theory of rubber elasticity; (6) understanding the critical force for flow in thixotropic systems.