^{1}, W. Rżysko

^{1}, S. Sokołowski

^{1,a)}, Z. Sokołowska

^{2}and Z. Usatenko

^{3,b)}

### Abstract

We propose application of density functional theory to calculate the force acting on a selected segment of a tethered polymer chain that leads to stretching the chain. The density functional allows one to determine the effects due to the presence of other chains and solvent molecules. For high and moderate solvent densities the plot of the force versus the distance of the segment from the surface exhibits oscillatory behavior that has not been predicted by other approaches.

This work was supported by ERA under Grant No. PIRSES 268498.

I. INTRODUCTION

II. THEORY

III. RESULTS AND DISCUSSION

IV. SUMMARY

### Key Topics

- Density functional theory
- 22.0
- Polymers
- 12.0
- Solvents
- 8.0
- Monte Carlo methods
- 7.0
- Molecule surface interactions
- 5.0

## Figures

Schematic graph of a polymer chain, partially pulled off from the plane by an external force which keeps its Jth segment at height H, cf. Fig. 2(b) of Ref. 18 .

Schematic graph of a polymer chain, partially pulled off from the plane by an external force which keeps its Jth segment at height H, cf. Fig. 2(b) of Ref. 18 .

(Part (a)) The force acting on the last segment of a single chain, , in the limit of . A comparison of the computer simulations (symbols) with the DFT results (solid lines) for the chains built of M = 10, 20, and 30 segments. Dotted line denotes the results of Eq. (2) . The bulk fluid density is . (Parts (b) and (c)) Comparisons of MC (symbols) and DFT forces for the chains of M = 10 (part (b)) and 20 (part (c)) segments. The grafting density is 0.01 and the bulk fluid density is . (Part (d)) The force for the ideal chain model and for M = 10, 20, and 30. The computer simulation data are displayed as symbols and the DFT results as lines. The inset shows the behavior of the force at small values of (only computer simulation results are displayed).

(Part (a)) The force acting on the last segment of a single chain, , in the limit of . A comparison of the computer simulations (symbols) with the DFT results (solid lines) for the chains built of M = 10, 20, and 30 segments. Dotted line denotes the results of Eq. (2) . The bulk fluid density is . (Parts (b) and (c)) Comparisons of MC (symbols) and DFT forces for the chains of M = 10 (part (b)) and 20 (part (c)) segments. The grafting density is 0.01 and the bulk fluid density is . (Part (d)) The force for the ideal chain model and for M = 10, 20, and 30. The computer simulation data are displayed as symbols and the DFT results as lines. The inset shows the behavior of the force at small values of (only computer simulation results are displayed).

(Parts (a) and (b)) The force acting on the segments J for the system of 16-mers. The grafting density is (black lines) and 0.05 (red lines). The bulk fluid density is (part (a)) and 0.6 (part (b)). The nomenclature of the lines is explained in part (a). Black symbols illustrate forces for M = 8 (filled circles) and M = 4 (stars) obtained for . Part (c) illustrates systematic changes of with for the system of 32-mers at the grafting density . All lines are explained in the figure.

(Parts (a) and (b)) The force acting on the segments J for the system of 16-mers. The grafting density is (black lines) and 0.05 (red lines). The bulk fluid density is (part (a)) and 0.6 (part (b)). The nomenclature of the lines is explained in part (a). Black symbols illustrate forces for M = 8 (filled circles) and M = 4 (stars) obtained for . Part (c) illustrates systematic changes of with for the system of 32-mers at the grafting density . All lines are explained in the figure.

The fluid density profile (part (a)) and the total segment density profile (part (b)) (dashed line) for the system of 16-mers. The bulk fluid density is ρ b [σ(F)]3 = 0.6 and the grafting density is ρ P [σ(P)]2 = 0.01. The legend is given in Fig. 4(a).

The fluid density profile (part (a)) and the total segment density profile (part (b)) (dashed line) for the system of 16-mers. The bulk fluid density is ρ b [σ(F)]3 = 0.6 and the grafting density is ρ P [σ(P)]2 = 0.01. The legend is given in Fig. 4(a).

Dependence of the force on the size of fluid molecules. The values of all the parameters are given in the figure.

Dependence of the force on the size of fluid molecules. The values of all the parameters are given in the figure.

A comparison of the forces f av and f dJ for J = 10, 8, 6, and 3 for 10-mers.

A comparison of the forces f av and f dJ for J = 10, 8, 6, and 3 for 10-mers.

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