^{1,a)}, Flemming Y. Hansen

^{2,b)}, Günther H. Peters

^{3,c)}and Ole Hassager

^{1,d)}

### Abstract

The confinement analysis from bulk structure (CABS) approach [Y. Wang *et al.*, J. Chem. Phys.128, 124904 (2008)] is extended to determine the depletion profiles of dilute polymer solutions confined to a slit or near an inert wall. We show that the entire spatial density distributions of any reference point in the polymer chain (such as the center of mass, middle segment, and end segments) can be computed as a function of the confinement size solely based on a single sampling of the configuration space of a polymer chain in bulk. Through a simple analysis based on the CABS approach in the case of a single wall, we prove rigorously that (i) the depletion layer thickness is the same no matter which reference point is used to describe the depletion profile and (ii) the value of equals half the average span (the mean projection onto a line) of the macromolecule in free solution. Both results hold not only for ideal polymers, as has been noticed before, but also for polymers regardless of details in molecular architecture and configuration statistics.

Y.W. acknowledges support by the Danish Research Council for Technology and Production Sciences under Grant No. 26-04-0074. G.H.P. acknowledges financial support from the Danish National Research Foundation via a grant to MEMPHYS-Center for Biomembrane Physics. Simulations were performed at the Danish Center for Scientific Computing at the Technical University of Denmark.

I. INTRODUCTION

II. THE CABS APPROACH

III. AND THE DEPLETION LAYER THICKNESS

IV. NUMERICAL RESULTS AND DISCUSSIONS

V. CONCLUSIONS

### Key Topics

- Polymers
- 80.0
- Molecular conformation
- 9.0
- Conformational dynamics
- 7.0
- Solution polymerization
- 7.0
- Molecular configuration
- 5.0

## Figures

Schematic illustration of a polymer chain in a slit confinement. The confinement size is denoted by , and the orientation of the slit is denoted by , which is a unit vector normal to the slit plane. is the span in the direction of the polymer chain with configuration , which is divided into two parts, and , by the projection point of bead located at distance from the slit plane at .

Schematic illustration of a polymer chain in a slit confinement. The confinement size is denoted by , and the orientation of the slit is denoted by , which is a unit vector normal to the slit plane. is the span in the direction of the polymer chain with configuration , which is divided into two parts, and , by the projection point of bead located at distance from the slit plane at .

Normalized density distribution of the Com near a single wall for linear Gaussian bead-spring chains of beads. The distance to the wall is normalized by (a) the radius of gyration and (b) the steric exclusion radius of the unconfined molecule. The analytical solution by Eisenriegler and Maassen (Ref. 61) is included, which corresponds to .

Normalized density distribution of the Com near a single wall for linear Gaussian bead-spring chains of beads. The distance to the wall is normalized by (a) the radius of gyration and (b) the steric exclusion radius of the unconfined molecule. The analytical solution by Eisenriegler and Maassen (Ref. 61) is included, which corresponds to .

Simulation results of the radius of gyration and steric exclusion radius with respect to the theoretical values of the radius of gyration , which is predicted by Eq. (30), are plotted as a function of the total number of beads in a linear Gaussian bead-spring polymer chain. A numerical fit of the data is also included.

Simulation results of the radius of gyration and steric exclusion radius with respect to the theoretical values of the radius of gyration , which is predicted by Eq. (30), are plotted as a function of the total number of beads in a linear Gaussian bead-spring polymer chain. A numerical fit of the data is also included.

Normalized Com density distributions for a linear Gaussian bead-spring polymer of beads in a slit confinements of different width. The number inserted for each curve corresponds to the slit width with respect to . The axis is chosen such that in (a) the center of the slit is at zero and at (b) the bottom plane of the slit is at zero. The full profile is shown in (a), while only half the profile (from the bottom plane up to the axis of symmetry) is shown in (b). The analytical solution (Ref. 61) corresponds to and .

Normalized Com density distributions for a linear Gaussian bead-spring polymer of beads in a slit confinements of different width. The number inserted for each curve corresponds to the slit width with respect to . The axis is chosen such that in (a) the center of the slit is at zero and at (b) the bottom plane of the slit is at zero. The full profile is shown in (a), while only half the profile (from the bottom plane up to the axis of symmetry) is shown in (b). The analytical solution (Ref. 61) corresponds to and .

Results of are shown as a function of for linear Gaussian bead-spring polymers of beads in a slit confining geometry of width , where is the effective depletion thickness introduced in Eq. (28), and is the steric exclusion radius of the unconfined polymer chain.

Results of are shown as a function of for linear Gaussian bead-spring polymers of beads in a slit confining geometry of width , where is the effective depletion thickness introduced in Eq. (28), and is the steric exclusion radius of the unconfined polymer chain.

## Tables

Characteristic ratios between the steric exclusion radius and the root-mean-square radius of gyration for ideal chain polymers of linear, ring (Ref. 72), and -arm symmetric star (Ref. 34) architectures.

Characteristic ratios between the steric exclusion radius and the root-mean-square radius of gyration for ideal chain polymers of linear, ring (Ref. 72), and -arm symmetric star (Ref. 34) architectures.

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