^{1,a)}

### Abstract

We study the structure and interfacial properties of model athermal mixtures of colloids and excluded volume polymers. The colloid particles are modeled as hard spheres whereas the polymer coils are modeled as chains formed from tangentially bonded hard spheres. Within the framework of the nonlocal density functional theory we study the influence of the chain length on the surface tension and the interfacial width. We find that the interfacial tension of the colloid-interacting polymer mixtures increases with the chain length and is significantly smaller than that of the ideal polymers. For certain parameters we find oscillations on the colloid-rich parts of the density profiles of both colloids and polymers with the oscillation period of the order of the colloid diameter. The interfacial width is few colloid diameters wide and also increases with the chain length. We find the interfacial width for the end segments to be larger than that for the middle segments and this effect is more pronounced for longer chains.

This work was supported by KBN of Poland under the Grant No. 1P03B03326 (years 2004–2006).

I. INTRODUCTION

II. THEORY

III. RESULTS

IV. CONCLUSIONS

### Key Topics

- Polymers
- 53.0
- Colloidal systems
- 43.0
- Critical point phenomena
- 11.0
- Free energy
- 8.0
- Density functional theory
- 7.0

## Figures

The binodals (solid lines), the spinodals (dashed lines), and the critical points (black dots) for the demixing transition in colloid-excluded volume polymer mixtures resulting from the TPT1 theory. The phase diagrams are evaluated for the constant ratio of colloid diameter to polymer segment diameter and for , 100, 120, 200, and 500 from top to bottom, respectively. The dotted line marks the line of critical points of the demixing transition for different chain lengths.

The binodals (solid lines), the spinodals (dashed lines), and the critical points (black dots) for the demixing transition in colloid-excluded volume polymer mixtures resulting from the TPT1 theory. The phase diagrams are evaluated for the constant ratio of colloid diameter to polymer segment diameter and for , 100, 120, 200, and 500 from top to bottom, respectively. The dotted line marks the line of critical points of the demixing transition for different chain lengths.

Colloid density profiles across the liquid-liquid interface calculated for the system with and . The profiles are evaluated for the reduced pressures (a), 6 (b), 4 (c), and 3.58 (d). The inset shows an enlargement of the profile.

Colloid density profiles across the liquid-liquid interface calculated for the system with and . The profiles are evaluated for the reduced pressures (a), 6 (b), 4 (c), and 3.58 (d). The inset shows an enlargement of the profile.

Average polymer segment density profiles across the liquid-liquid interface calculated for the system with and . The profiles are evaluated for the reduced pressures (a), 6 (b), 4 (c), and 3.58 (d).

Average polymer segment density profiles across the liquid-liquid interface calculated for the system with and . The profiles are evaluated for the reduced pressures (a), 6 (b), 4 (c), and 3.58 (d).

The reduced surface tension plotted against the difference in the colloid packing fractions in the coexisting liquid (colloid-rich, ) and vapor (colloid-poor, ) phases, . The chain lengths are given in the figure.

The reduced surface tension plotted against the difference in the colloid packing fractions in the coexisting liquid (colloid-rich, ) and vapor (colloid-poor, ) phases, . The chain lengths are given in the figure.

Critical behavior of the reduced surface tension of colloids with and excluded-volume polymers with . The open circles denote the DFT results whereas the solid lines have slopes corresponding to the classical (mean-field) critical exponents. (a) The logarithm of the reduced surface tension plotted against the logarithm of the difference in the colloid packing fractions in the coexisting liquid (colloid-rich, ) and vapor (colloid-poor, ) phases. (b) The logarithm of the reduced surface tension plotted as a function of the logarithm of the relative distance to the critical point in terms of the pressure difference .

Critical behavior of the reduced surface tension of colloids with and excluded-volume polymers with . The open circles denote the DFT results whereas the solid lines have slopes corresponding to the classical (mean-field) critical exponents. (a) The logarithm of the reduced surface tension plotted against the logarithm of the difference in the colloid packing fractions in the coexisting liquid (colloid-rich, ) and vapor (colloid-poor, ) phases. (b) The logarithm of the reduced surface tension plotted as a function of the logarithm of the relative distance to the critical point in terms of the pressure difference .

The interfacial width as a function of the relative distance to the critical point expressed in terms of the pressure difference . The main plot shows the interfacial width calculated for (solid line), 200 (dashed line), and 500 (dot-dashed line). The inset shows a double-logarithmic plot of the same quantities evaluated for . The open circles denote the DFT results whereas the solid lines have slopes corresponding to the classical (mean-field) critical exponents.

The interfacial width as a function of the relative distance to the critical point expressed in terms of the pressure difference . The main plot shows the interfacial width calculated for (solid line), 200 (dashed line), and 500 (dot-dashed line). The inset shows a double-logarithmic plot of the same quantities evaluated for . The open circles denote the DFT results whereas the solid lines have slopes corresponding to the classical (mean-field) critical exponents.

Middle (the solid lines) and end (the dashed lines) segment density profiles across the liquid-liquid interface calculated for the system with and . The profiles are evaluated for the reduced pressures (system ), 4.5 (system ), and 3.58 (system ).

Middle (the solid lines) and end (the dashed lines) segment density profiles across the liquid-liquid interface calculated for the system with and . The profiles are evaluated for the reduced pressures (system ), 4.5 (system ), and 3.58 (system ).

The interfacial width of the segment density profile as a function of the relative distance to the critical point expressed in terms of the pressure difference . The solid and dotted lines denote the interfacial width of the mid-segment and end-segment density profile for whereas the dashed and dot-dashed lines denote the interfacial width of the mid-segment and end-segment density profile for .

The interfacial width of the segment density profile as a function of the relative distance to the critical point expressed in terms of the pressure difference . The solid and dotted lines denote the interfacial width of the mid-segment and end-segment density profile for whereas the dashed and dot-dashed lines denote the interfacial width of the mid-segment and end-segment density profile for .

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