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.

1.
Anastassopoulos
,
D. L.
,
Vradis
,
A. A.
,
Toprakcioglu
,
C.
,
Smith
,
G. S.
, and
Dai
,
L.
, 1998, “
Neutron Reflectivity Study of End-Attached Telechelic Polymers in a Good Solvent
,”
Macromolecules
0024-9297,
31
, pp.
9369
9371
.
2.
Levicky
,
R.
,
Koneripalli
,
N.
,
Tirrell
,
M.
, and
Satija
,
S. K.
, 1998, “
Concentration Profiles in Densely Tethered Polymer Brushes
,”
Macromolecules
0024-9297,
31
, pp.
3731
3734
.
3.
Currie
,
E. P. K.
,
,
Wagemaker
,
M.
,
Cohen Stuart
,
M. A.
, and
van Well
,
A. A.
, 2000, “
Structure of Grafted Polymers, Investigated With Neutron Reflectometry
,”
Physica B
0921-4526,
283
, pp.
17
21
.
4.
Marzolin
,
C.
,
Auroy
,
P.
,
Deruelle
,
M.
,
Folkers
,
J. P.
,
Léger
,
L.
, and
Menelle
,
A.
, 2001, “
Neutron Reflectometry Study of the Segment-Density Profiles in End-Grafted and Irreversibly Adsorbed Layers of Polymer in Good Solvents
,”
Macromolecules
0024-9297,
34
, pp.
8694
8700
.
5.
Taunton
,
H. J.
,
Toprakcioglu
,
C.
,
Fetters
,
L. J.
, and
Klein
,
J.
, 1988, “
Forces Between Surfaces Bearing Terminally Anchored Polymer Chains in Good Solvents
,”
Nature (London)
0028-0836,
332
, pp.
712
714
.
6.
Dunlop
,
I. E.
,
Briscoe
,
W. H.
,
Titmuss
,
S.
,
Sakellariou
,
G.
,
Hadjichristidis
,
N.
, and
Klein
,
J.
, 2004, “
Interactions Between Polymer Brushes: Varying the Number of End-Attaching Groups
,”
Macromol. Chem. Phys.
1022-1352,
205
, pp.
2443
2450
.
7.
Drobek
,
T.
,
Spencer
,
N. D.
, and
Heuberger
,
M.
, 2005, “
Compressing PEG Brushes
,”
Macromolecules
0024-9297,
38
, pp.
5254
5259
.
8.
Yamamoto
,
S.
,
Ejaz
,
M.
,
Tsujii
,
Y.
,
Matsumoto
,
M.
, and
Fukuda
,
T.
, 2000, “
Surface Interaction Forces of Well-Defined, High-Density Polymer Brushes Studied by Atomic Force Microscopy. 1. Effect of Chain Length
,”
Macromolecules
0024-9297,
33
, pp.
5602
5607
.
9.
Yamamoto
,
S.
,
Ejaz
,
M.
,
Tsujii
,
Y.
, and
Fukuda
,
T.
, 2000, “
Surface Interaction Forces of Well-Defined, High-Density Polymer Brushes Studied by Atomic Force Microscopy. 2. Effect of Graft Density
,”
Macromolecules
0024-9297,
33
, pp.
5608
5612
.
10.
McLean
,
S. C.
,
Lioe
,
H.
,
Meagher
,
L.
,
Craig
,
V. S. J.
, and
Gee
,
M. L.
, 2005, “
Atomic Force Microscopy Study of the Interaction between Adsorbed Poly(ethylene oxide) Layers: Effects of Surface Modification and Approach Velocity
,”
Langmuir
0743-7463,
21
, pp.
2199
2208
.
11.
Alexander
,
S.
, 1977, “
Adsorption of Chain Molecules With a Polar Head. A scaling Approach
,”
J. Phys. (Paris)
0302-0738,
38
, pp.
983
989
.
12.
de Gennes
,
P. G.
, 1985, “
Films of Polymer-Solutions
,”
C. R. Acad. Sci.
,
300
, pp.
839
843
.
13.
Milner
,
S.
,
Witten
,
T.
, and
Cates
,
M.
, 1988, “
Theory of the Grafted Polymer Brush
,”
Macromolecules
0024-9297,
21
, pp.
2610
2619
.
14.
Murat
,
M.
, and
Grest
,
G. S.
, 1989, “
Structure of a Grafted Polymer Brush: A Molecular Dynamics Simulation
,”
Macromolecules
0024-9297,
22
, pp.
4054
4059
.
15.
Murat
,
M.
and
Grest
,
G. S.
, 1989, “
Interaction Between Grafted Polymeric Brushes—A Molecular-Dynamics Study
,”
Phys. Rev. Lett.
0031-9007,
63
, pp.
1074
1077
.
16.
Israelachvili
,
J. N.
, 1992,
Intermolecular and Surface Forces
, 2nd ed.,
Academic
,
London
.
17.
de Gennes
,
P. G.
, 1979,
Scaling Concepts in Polymer Physics
,
Cornell University Press
,
Ithaca, NY
.
18.
Milner
,
S. T.
,
Witten
,
T. A.
, and
Cates
,
M. E.
, 1988, “
A Parabolic Density Profile for Grafted Polymers
,”
Europhys. Lett.
0295-5075,
5
, pp.
413
418
.
19.
Klein
,
J.
, 1996, “
Shear, Friction, and Lubrication Forces Between Polymer-Bearing Surfaces
,”
Annu. Rev. Mater. Sci.
0084-6600,
26
, pp.
581
612
.
20.
Witten
,
T. A.
,
Leibler
,
L.
, and
Pincus
,
P.
, 1990, “
Stress Relaxation in the Lamellar Copolymer Mesophase
,”
Macromolecules
0024-9297,
23
, pp.
824
830
.
21.
Gibra
,
I. N.
, 1973,
Probability and Statistical Inference for Scientists and Engineers
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
22.
de Gennes
,
P. G.
, 1987, “
Polymers at Interfaces: A Simplified View
,”
Adv. Colloid Interface Sci.
0001-8686,
27
, pp.
189
209
.
23.
Kuhl
,
T. L.
,
Leckband
,
D. E.
,
Lasic
,
D. D.
, and
Israelachvili
,
J. N.
, 1995,
Stealth Liposomes
,
CRC
,
Boca Raton, FL
.
24.
Kenworthy
,
A. K.
,
Hristova
,
K.
,
Needham
,
D.
, and
McIntosh
,
T. J.
, 1995, “
Range and Magnitude of the Steric Pressure Between Bilayers Containing Phospholipids with Covalently Attached Poly(Ethylene Glycol)
,”
Biophys. J.
0006-3495,
68
, pp.
1921
1936
.
25.
Efremova
,
N. V.
,
Bondurant
,
B.
,
O’Brien
,
D. F.
, and
Leckband
,
D. E.
, 2000, “
Measurements of Interbilayer Forces and Protein Adsorption on Uncharged Lipid Bilayers Displaying Poly(Ethylene Glycol) Chains
,”
Biochemistry
0006-2960,
39
, pp.
3441
3451
.
26.
Taunton
,
H. J.
,
Toprakcioglu
,
C.
,
Fetters
,
L. J.
, and
Klein
,
J.
, 1990, “
Interactions Between Surfaces Bearing End-Adsorbed Chains in a Good Solvent
,”
Macromolecules
0024-9297,
23
, pp.
571
580
.
You do not currently have access to this content.