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Kim, Jaeup U.
Nanostructured Polymer Materials Theory Lab
Research Interests
  • block copolymers, soft matter, nanostructures & patterning, machine learning

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Nanoinclusions in dry polymer brushes

Cited 67 times inthomson ciCited 62 times inthomson ci
Title
Nanoinclusions in dry polymer brushes
Author
Kim, Jaeup U.O'Shaughnessy, B
Keywords
Chain fluctuation scale; Dry polymer brushes; Nanoinclusions; Self-consistent mean field (SCF) theory
Issue Date
2006-01
Publisher
AMER CHEMICAL SOC
Citation
MACROMOLECULES, v.39, no.1, pp.413 - 425
Abstract
A theory of dry polymer brushes containing nanoinclusions is presented. Polymer brush-nanoparticle mixtures arise in various applications and in experimental systems where block copolymer materials, providing brushlike environments, organize nanoparticles to generate materials with novel properties. The ease with which a nanoinclusion enters a brush is measured by the free energy cost to introduce the inclusion, ΔF inc. This depends strongly on particle shape and size b, as does the degree to which brush chain configurations are perturbed. For inclusions smaller than the typical chain fluctuation scale or blob size ξ̄ blob, by extending the self-consistent mean field (SCF) theory for pure brushes, we show ΔF inc = P(z)V p for an inclusion of volume V p a distance z from the grafting surface. Here P(z) is the quadratic SCF "pressure" field. Equilibrium particle distributions within a brush of chains of length N grafted at density σ depend strongly on particle size: (i) particles smaller than a scale b* ∼ σ -2/3 distribute uniformly, dominated by entropy, while (ii) larger inclusions penetrate the soft surface region of the brush in a layer of thickness δ ≈ h(b*/b) 3 where h is brush height and (iii) complete expulsion occurs for sizes above b max ∼ (N/σ) 1/4. Inclusions bigger than ξ̄ blob affect chain configurations much more strongly and require a different theoretical approach. We show ΔF inc = βP(z)V p, where β is a shape-dependent constant for which we obtain rigorous bounds. Vertically oriented cylinders achieve the minimum energy cost (β = 1). Motivated by exact results for the approximate Alexander-de Gennes brush (chain ends fixed at brush surface), we argue that disk-shaped inclusions incur maximum energy cost (β ∼ t where t is the disk aspect ratio).
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DOI
10.1021/ma050817i
ISSN
0024-9297
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PHY_Journal Papers
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