Effect of Heterogeneous Energies on Adsorption Properties: Adsorption of Copolymers, Comb Polymers, and Stars onto a Surface

Abstract

With a view to understanding how a dilute sprinkling of strong hydrogen bonds affect the bulk properties and the colligative properties of polymers, we examine three polymer adsorption problems. They are (1) a copolymer between two adsorbing plates, (2) a comb polymer between two adsorbing surfaces, and (3) a star polymer between two absorbing surfaces. Matrix methods are used to solve each of these problems. Numerical results for a block copolymer with a periodic repeat of a single strong bond and r weak bonds show that the adsorption is not well represented by a model which replaces the segments by those of an average energy. This means that the specifics of molecular architecture cannot be ignored as has been done in so much of the previously published work on adsorption. Because the matrices do not commute, block polymers and random copolymers of the same composition are expected to show different adsorption profiles. IntroductionWe are interested generally in how a relatively few but very strong bonds affect the properties of polymer systems.l One example is a two-component polymer blend that has a few hydrogen bonds per molecule between the unlike polymers. The hydrogen bonds have the effect of compatibilizing the polymers.2 Another example is a bulk copolymer which contains a few strong bonds per molecule that act as cross-links between the chains, thus creating a rubbery material rather than just a viscous material.3 Each of these systems is important industrially.In order to gain further insight into the sparse but strong bonds problem (SBSB) in bulk systems, we thought it best to proceed methodically by treating the two-molecule problem, then the three-molecule problem, and so on until the n-molecule problem is solved. However, even the two-molecule problem is difficult as one sees readily since the two-molecule problem is closely related to the double-strained DNA problem (imperfect matching model). The imperfect matching DNA model has been solved when the bonds are all the same ~t r e n g t h ,~ and the perfect matching model has been solved for copolymer^,^ but for the case of a sparse sprinkling of strong bonds (the copolymer problem) the imperfect matching model is not solved. So we thought it best to gain insight by looking for any exactly solvable problem that contains SBSB. It is to be stressed that we are looking for exact solutions; mean-field treatments will miss the characteristic features of the SBSB problem.The adsorption of a polymer lying between two parallel plates is an exactly solvable lattice model problem6 (self-excluded volume is not treated). A trivial generalization of this model allows us to treat the general linear copolymer problem exactly, and by choosing a copolymer with only a few A monomers that are strongly adsorbed and many B monomers that are weakly adsorbed, we immediately have an entry into an exactly solvable SBSB problem.We have also extended the lattice model of a chain between two parallel plates to architectures other than pure linear since for these materials al...

Analytical theory of finite-size effects in mechanical desorption of a polymer chain

“…5 are exact numerical calculations according to the matrix method. 38 The agreement with the analytical results is excellent not only for the bound fraction but also for the heat capacity and the stretching. This demonstrates the validity of the analytical approach.…”

“…The symbols are numerical data obtained by the matrix method. 38 The agreement is excellent. Only for N = 30 do some minor deviations occur at relatively high T.…”

Interactions of complex polymers with nanoporous substrate

“…In the case of alternating copolymer, one may treat (AB) as a new monomer, and naturally this would behave just like a homopolymer. Nevertheless this question was studied using different theoretical approaches [66][67][68][69][70][71] and the conclusion is that statistical AB copolymers have a CAP just like a homopolymer. A few Monte Carlo simulations have also determined the CAP for a statistical copolymer with different compositions of A and B, but the general equation that gives the dependence of CAP of statistical random copolymers on the chemical compositions were only discussed in Brun's paper 72,73 and in our paper.…”

Exact solution of the thermodynamics and size parameters of a polymer confined to a lattice of finite size: Large chain limit

“…In our previous approaches to chromatography using the onedimensional matrix method, we varied the interaction of the chain with the surface by varying the energy of interaction or temperature of a single chain with the surface, 4, 6 and then changed from a homopolymer to a copolymer and showed the effect of interaction of the different parts of the copolymer with the wall. 10,14 Through the latter approach, it was shown (1) that it is insufficient to model a copolymer as a homopolymer by using some average of the copolymer adsorption energies and (2) that the matrix formalism is useful in predicting the elution behavior of copolymers, e.g., random or block, near the critical condition. In a block copolymer, by using a mixed solvent one can tune out one of the blocks so that it is neutral towards the surface (this happens at its critical point).…”