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Surface grafted polymers are important to various fields including biocompatible surfaces, colloidal suspension stabilization, and stimuli-responsive structures. As grafted chain density increases, chain-chain interactions cause extension of the polymer chains, forming what is known as a “polymer brush”. Because these chain-chain interactions also affect the brush’s physical properties, a fundamental understanding of chain extension in surface grafted polymers is critical to engineering polymer brush behavior. The most basic relationship for polymer brushes is the power scaling law relation between swollen brush thickness (h) and grafting density (σ), h ~ σn. It is well known that this exponent abruptly changes from n = 0 to n = 1/3 when grafted polymer chain spacing becomes less than the radius of gyration (mushroom-to-brush transition, see Fig. 1). Another transition is believed to occur at higher grafting densities, but less is known about the scaling law behaviors of these “high-density brushes”. This work used liquid-cell ellipsometry measurements of prototypical PMMA chains grafted to silicon to elucidate the power scaling law behavior of swollen polymer brushes in the high-density regime. In good solvent, we show that the moderate-density to high-density transition occurs around 0.4 chains/nm2 (Fig. 2a). As solvent quality is made poorer, the brush reverts to a single scaling law behavior (Fig. 2b), with the transition occurring near θ-solvent conditions. In a poor solvent, the scaling law exponent approaches 1, consistent with mean field theory calculations.
Lionel Moh conducted the experimental work for this project as part of his undergraduate thesis project, which was completed under Mark’s guidance.
Fig. 1: (a) Depiction of the power scaling law behavior between swollen polymer thickness (h) and grafting density (σ) for surface grafted polymer chains in a good solvent. When polymer spacing is greater than the radius of gyration (Rg), chains do not interact (mushroom regime). Once spacing is less than Rg, chain-chain interactions cause extension and show the well-known h ~ σ1/3 behavior (brush regime). A second transition from moderate-density brush to high-density brush is known, but has not previously been well investigated.
Scaling Behavior of High-Density Polymer Brushes
Related Publications
1. L. C. H. Moh, M. D. Losego, and P. V. Braun, “Ellipsometric investigation on the effects of solvent quality on scaling behavior of poly(methyl methacrylate) brushes in the moderate and high density regimes.” Langmuir 27 3698. (2011). DOI
Fig. 2: (a) Measurements collected for PMMA chains swollen in acetone (good solvent) showing a transition in the scaling law behavior for brushes having a grafting density >0.4 chains/nm2. (b) Measurements for PMMA chains swollen in solvents of systematically varied solvent quality illustrating a transition in behavior from two different scaling regimes (good solvents) to a single power law scaling regime (poor solvent).
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