Equilibrium polymers at interfaces : analytical self-consistent-field theory

J. van der Gucht, N.A.M. Besseling, G.J. Fleer

    Research output: Contribution to journalArticleAcademicpeer-review

    26 Citations (Scopus)

    Abstract

    An analytical mean-field theory is constructed for equilibrium (or "living") polymers with excluded volume at a surface. Within a mean-field approximation, exact analytical expressions are obtained for the monomer concentration profile at the surface and for the excess amount, both for adsorbing and nonadsorbing surfaces, and for the whole concentration range from the dilute to the marginal regime. A ground-state approximation is not needed. For nonadsorbing polymers there is a depletion layer next to the surface with a thickness that passes through a maximum as a function of the monomer concentration. If the equilibrium polymers adsorb on the surface, their behavior is qualitatively different from that of monodisperse chains. For weak adsorption, the excess amount increases gradually as the adsorption energy increases. At a certain finite value of the adsorption energy (which depends on the average length of the chains in the bulk), the excess amount starts to increases very rapidly by orders of magnitude. For chains without excluded volume the excess amount diverges at this point, whereas for real chains it remains finite. Adsorption isotherms of equilibrium polymers show a similar behavior: a gradual increase at low concentrations, then a very steep increase at some finite concentration, and a plateau at higher concentrations.
    Original languageEnglish
    Pages (from-to)3026-3036
    JournalMacromolecules
    Volume37
    Issue number8
    DOIs
    Publication statusPublished - 2004

    Fingerprint

    Polymers
    Adsorption
    Monomers
    Mean field theory
    Adsorption isotherms
    Ground state

    Keywords

    • interacting chain molecules
    • living polymers
    • supramolecular polymers
    • polydisperse polymers
    • surface segregation
    • reversible polymers
    • statistical-theory
    • adsorption
    • lattice
    • dilute

    Cite this

    van der Gucht, J. ; Besseling, N.A.M. ; Fleer, G.J. / Equilibrium polymers at interfaces : analytical self-consistent-field theory. In: Macromolecules. 2004 ; Vol. 37, No. 8. pp. 3026-3036.
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    abstract = "An analytical mean-field theory is constructed for equilibrium (or {"}living{"}) polymers with excluded volume at a surface. Within a mean-field approximation, exact analytical expressions are obtained for the monomer concentration profile at the surface and for the excess amount, both for adsorbing and nonadsorbing surfaces, and for the whole concentration range from the dilute to the marginal regime. A ground-state approximation is not needed. For nonadsorbing polymers there is a depletion layer next to the surface with a thickness that passes through a maximum as a function of the monomer concentration. If the equilibrium polymers adsorb on the surface, their behavior is qualitatively different from that of monodisperse chains. For weak adsorption, the excess amount increases gradually as the adsorption energy increases. At a certain finite value of the adsorption energy (which depends on the average length of the chains in the bulk), the excess amount starts to increases very rapidly by orders of magnitude. For chains without excluded volume the excess amount diverges at this point, whereas for real chains it remains finite. Adsorption isotherms of equilibrium polymers show a similar behavior: a gradual increase at low concentrations, then a very steep increase at some finite concentration, and a plateau at higher concentrations.",
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    author = "{van der Gucht}, J. and N.A.M. Besseling and G.J. Fleer",
    year = "2004",
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    Equilibrium polymers at interfaces : analytical self-consistent-field theory. / van der Gucht, J.; Besseling, N.A.M.; Fleer, G.J.

    In: Macromolecules, Vol. 37, No. 8, 2004, p. 3026-3036.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Equilibrium polymers at interfaces : analytical self-consistent-field theory

    AU - van der Gucht, J.

    AU - Besseling, N.A.M.

    AU - Fleer, G.J.

    PY - 2004

    Y1 - 2004

    N2 - An analytical mean-field theory is constructed for equilibrium (or "living") polymers with excluded volume at a surface. Within a mean-field approximation, exact analytical expressions are obtained for the monomer concentration profile at the surface and for the excess amount, both for adsorbing and nonadsorbing surfaces, and for the whole concentration range from the dilute to the marginal regime. A ground-state approximation is not needed. For nonadsorbing polymers there is a depletion layer next to the surface with a thickness that passes through a maximum as a function of the monomer concentration. If the equilibrium polymers adsorb on the surface, their behavior is qualitatively different from that of monodisperse chains. For weak adsorption, the excess amount increases gradually as the adsorption energy increases. At a certain finite value of the adsorption energy (which depends on the average length of the chains in the bulk), the excess amount starts to increases very rapidly by orders of magnitude. For chains without excluded volume the excess amount diverges at this point, whereas for real chains it remains finite. Adsorption isotherms of equilibrium polymers show a similar behavior: a gradual increase at low concentrations, then a very steep increase at some finite concentration, and a plateau at higher concentrations.

    AB - An analytical mean-field theory is constructed for equilibrium (or "living") polymers with excluded volume at a surface. Within a mean-field approximation, exact analytical expressions are obtained for the monomer concentration profile at the surface and for the excess amount, both for adsorbing and nonadsorbing surfaces, and for the whole concentration range from the dilute to the marginal regime. A ground-state approximation is not needed. For nonadsorbing polymers there is a depletion layer next to the surface with a thickness that passes through a maximum as a function of the monomer concentration. If the equilibrium polymers adsorb on the surface, their behavior is qualitatively different from that of monodisperse chains. For weak adsorption, the excess amount increases gradually as the adsorption energy increases. At a certain finite value of the adsorption energy (which depends on the average length of the chains in the bulk), the excess amount starts to increases very rapidly by orders of magnitude. For chains without excluded volume the excess amount diverges at this point, whereas for real chains it remains finite. Adsorption isotherms of equilibrium polymers show a similar behavior: a gradual increase at low concentrations, then a very steep increase at some finite concentration, and a plateau at higher concentrations.

    KW - interacting chain molecules

    KW - living polymers

    KW - supramolecular polymers

    KW - polydisperse polymers

    KW - surface segregation

    KW - reversible polymers

    KW - statistical-theory

    KW - adsorption

    KW - lattice

    KW - dilute

    U2 - 10.1021/ma0351773

    DO - 10.1021/ma0351773

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