# Self-consistent field theory of tethered polymers: One dimensional, three dimensional, strong stretching theories and the effects of excluded-volume-only interactions

## Abstract

We examine end-tethered polymers in good solvents, using one- and three-dimensional self-consistent field theory, and strong stretching theories. We also discuss different tethering scenarios, namely, mobile tethers, fixed but random ones, and fixed but ordered ones, and the effects and important limitations of including only binary interactions (excluded volume terms). We find that there is a “mushroom” regime in which the layer thickness is independent of the tethering density, σ, for systems with ordered tethers, but we argue that there is no such plateau for mobile or disordered anchors, nor is there one in the 1D theory. In the other limit of brushes, all approaches predict that the layer thickness scales linearly with N. However, the σ{sup 1/3} scaling is a result of keeping only excluded volume interactions: when the full potential is included, the dependence is faster and more complicated than σ{sup 1/3}. In fact, there does not appear to be any regime in which the layer thickness scales in the combination Nσ{sup 1/3}. We also compare the results for two different solvents with each other, and with earlier Θ solvent results.

- Authors:

- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2 (Canada)

- Publication Date:

- OSTI Identifier:
- 22413252

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 20; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; DENSITY; INTERACTIONS; POLYMERS; SELF-CONSISTENT FIELD; SOLVENTS; THICKNESS; THREE-DIMENSIONAL CALCULATIONS; THREE-DIMENSIONAL LATTICES

### Citation Formats

```
Suo, Tongchuan, E-mail: suotc@physics.umanitoba.ca, and Whitmore, Mark D., E-mail: mark-whitmore@umanitoba.ca.
```*Self-consistent field theory of tethered polymers: One dimensional, three dimensional, strong stretching theories and the effects of excluded-volume-only interactions*. United States: N. p., 2014.
Web. doi:10.1063/1.4901925.

```
Suo, Tongchuan, E-mail: suotc@physics.umanitoba.ca, & Whitmore, Mark D., E-mail: mark-whitmore@umanitoba.ca.
```*Self-consistent field theory of tethered polymers: One dimensional, three dimensional, strong stretching theories and the effects of excluded-volume-only interactions*. United States. doi:10.1063/1.4901925.

```
Suo, Tongchuan, E-mail: suotc@physics.umanitoba.ca, and Whitmore, Mark D., E-mail: mark-whitmore@umanitoba.ca. Fri .
"Self-consistent field theory of tethered polymers: One dimensional, three dimensional, strong stretching theories and the effects of excluded-volume-only interactions". United States. doi:10.1063/1.4901925.
```

```
@article{osti_22413252,
```

title = {Self-consistent field theory of tethered polymers: One dimensional, three dimensional, strong stretching theories and the effects of excluded-volume-only interactions},

author = {Suo, Tongchuan, E-mail: suotc@physics.umanitoba.ca and Whitmore, Mark D., E-mail: mark-whitmore@umanitoba.ca},

abstractNote = {We examine end-tethered polymers in good solvents, using one- and three-dimensional self-consistent field theory, and strong stretching theories. We also discuss different tethering scenarios, namely, mobile tethers, fixed but random ones, and fixed but ordered ones, and the effects and important limitations of including only binary interactions (excluded volume terms). We find that there is a “mushroom” regime in which the layer thickness is independent of the tethering density, σ, for systems with ordered tethers, but we argue that there is no such plateau for mobile or disordered anchors, nor is there one in the 1D theory. In the other limit of brushes, all approaches predict that the layer thickness scales linearly with N. However, the σ{sup 1/3} scaling is a result of keeping only excluded volume interactions: when the full potential is included, the dependence is faster and more complicated than σ{sup 1/3}. In fact, there does not appear to be any regime in which the layer thickness scales in the combination Nσ{sup 1/3}. We also compare the results for two different solvents with each other, and with earlier Θ solvent results.},

doi = {10.1063/1.4901925},

journal = {Journal of Chemical Physics},

number = 20,

volume = 141,

place = {United States},

year = {Fri Nov 28 00:00:00 EST 2014},

month = {Fri Nov 28 00:00:00 EST 2014}

}