### Abstract

Analytical expressions are derived for the polymer excess amount and the grand potential (surface free energy) of flat and spherical surfaces immersed in a solution of nonadsorbing polymer chains in the mean-field approximation. We start from a recent mean-field expression for the depletion thickness δ which takes into account not only the effect of the chain length N but also that of the polymer concentration φb and the solvency χ. Simple expressions are obtained for the interfacial properties at a colloidal surface, using both the adsorption method and the osmotic route. For a sphere of radius a, the excess amount can be separated into a planar contribution Γ = -φbδ and a curvature correction Γ_{c} = -(π^{2}/12)φbδ_{c}
^{2}/a, where δ_{c} is a "curvature thickness" which is close to (but smaller than) δ. The grand potential has a planar contribution ω = (2/9)_{φb}/δ and a curvature part ω_{c} = (π/18)φb/a. We test the results against numerical lattice computations, taking care that the boundary conditions in the continuum and lattice models are the same. We find good agreement up to a polymer segment volume fraction of 10%, and even for more concentrated solutions our simple model is reasonable. For spherical geometry we propose a new equation for the segment concentration profile which excellently agrees with numerical lattice computations. The results can be used as a starting point for the pair interaction between colloidal particles in a solution containing nonadsorbing chains, which is discussed in the following paper.

Original language | English |
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Pages (from-to) | 8754-8763 |

Number of pages | 10 |

Journal | Macromolecules |

Volume | 37 |

Issue number | 23 |

DOIs | |

Publication status | Published - 16 Nov 2004 |

Externally published | Yes |