Research Papers

Effect of Fluctuations in the Brush Conformation on the Interaction Between Polymer Brushes in a Good Solvent

[+] Author and Article Information
Yan Xing Shen

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan

Jen Fin Lin1

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwanjflin@mail.ncku.edu.tw


Corresponding author.

J. Appl. Mech 75(5), 051009 (Jul 17, 2008) (7 pages) doi:10.1115/1.2937155 History: Received September 27, 2007; Revised March 09, 2008; Published July 17, 2008

This study presents a novel approach for analyzing the interaction between two parallel surfaces grafted with polymer brushes in a good solvent. In the proposed approach, molecular dynamics simulations are performed to establish the mean brush height and the standard deviation of the brush height distribution for a given value of the surface separation. The corresponding probability density function (PDF) of the brush height is then determined and a statistical technique is applied to compute the corresponding interaction free energy per unit area of the grafted substrates. Finally, the Derjaguin approximation is employed to determine the corresponding value of the interaction force between the two surfaces. At relatively high surface grafting density as well as under low to moderate compressions of these two parallel plates, the interdigitation effect of the brushes is quite weak and is not considered in the present study. The results obtained for the interaction free energy and interaction force are compared with those derived using the Alexander and de Gennes (AdG) model [1977, “Adsorption of Chain Molecules With a Polar Head. A Scaling Approach  ,” J. Phys. (Paris), 38, pp. 983–989, 1985, “Films of Polymer-Solutions  ,” C. R. Acad. Sci., 300, pp. 839–843] and the Milner, Witten, and Cates (MWC) model [1988, “Theory of the Grafted Polymer Brush  ,” Macromolecules, 21, pp. 2610–2619], respectively. The value of the normalized interaction free energy computed using the present method is higher than that obtained from the AdG and MWC models at larger surface separations. However, the three sets of results are in good agreement particularly at smaller values of the surface separation. In addition, the results obtained by the current method for the interaction force are found to be in better agreement with the experimental data than those obtained using the AdG or MWC models. The enhanced performance of the proposed method is attributed primarily to the use of an adaptive non-Gaussian PDF of the brush height to model the effects of fluctuations in the brush conformation at different distances from the grafting plane.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 3

The standard deviation σ of brush heights distributions obtained from the MD simulations at different compressions and the fitting expressions

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Figure 4

PDF of brush heights under different compressions (h∕Lp). The distance z is normalized by the equilibrium thickness of the brushes Lp.

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Figure 5

Normalized interaction free energy per unit area between the two parallel plates grafted with polymer brushes versus dimensionless surface separation. The results predicted by the AdG model and the MWC model are rescaled to compare to that of the present method.

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Figure 2

The mean values of brush heights hm obtained from the MD simulations at different compressions and the fitting curve

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Figure 1

Schematic of one solid surface grafted with polymer brushes compressed by another parallel solid surface

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Figure 6

The measured force parameters obtained at different apparent surface separations between mica surfaces in a (5.6±1)×10−5 weight fraction solution of PS-X(M¯w=65kDa) in toluene (6). The experimental force profiles are presented to compare them to that of the present method, the AdG model, and the MWC model.



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