Rheological properties of polymer chains at a copper oxide surface: Impact of the chain length, surface coverage, and grafted polymer shape

We employ a recently derived semirealistic set of coarse-grained interactions to simulate polymer brushes of cis-1,4-polybutadiene grafted on a cuprous-oxide surface within the framework of dissipative particle dynamics. We consider two types of brushes, I and Y, that differ in the way they are connected to the surface. Our model explores the impact of free polymer chain length, grafting density of the brush, and imposed shear rate on the structural and dynamic properties of complex metal oxide polymer interfaces.

Figure 1

Schematic CG representation of grafted system of (a) I and (b) Y polymers. The ${\mathrm{Cu}}_2\mathrm{O}$ beads (red) form the substrate to which the grafted polymers (gray) are connected via a short spacer (blue). The remaining light spheres represent monomers of the free polymer chains.

Figure 2

Snapshots of equilibrated CG systems of polymers of 41 monomers without shear at different grafting densities. (a), (b), (c) I-polymers, (d), (e), (f) Y-polymers, (a), (d) ${\varphi }_g=0.25/{\text{nm}}^2$, [(b),(e)] ${\varphi }_g=0.50/{\text{nm}}^2$, and (c), (f) ${\varphi }_g=1.00/{\text{nm}}^2$. The large dark gray spheres represent the crystalline substrate, grafted polymers (green) are connected to the surface by a short spacer, and free polymers are shown in light gray.

Figure 3

The monomer density profiles as a function of the wall distance for different grafting densities ${\varphi }_g$. (a), (c), (e) The I polymers and (b), (d), (f) Y polymers are 81 monomers long, and the profiles are for (a), (b) all monomers and (c), (d) end monomers of the brush and (e), (f) free polymers.

Figure 4

Snapshots of CG systems of polymers of 81 monomers and a brush of type I. (a), (b), (c) ${\varphi }_g=0.25/{\text{nm}}^2$, (d), (e), (f) ${\varphi }_g=1.00/{\text{nm}}^2$, (a), (d) $v=0\text{m/s}$, (b), (e) $v=5\text{m/s}$, and (c), (f) $v=10\text{m/s}$. The large dark gray spheres represent the crystalline substrate, grafted polymers (orange) are connected to the surface by a short spacer, and free polymers are shown in light gray.

Figure 5

The monomer density profiles for 81 monomers long polymers at different shear rates, with the brush of type I for grafting density (a), (c), (e) ${\varphi }_g=0.25/{\text{nm}}^2$ and (b), (d), (f) ${\varphi }_g=1.00/{\text{nm}}^2$. (a), (b) the total monomer density profiles, (c), (d) the brush profiles (including spacer), (e), (f) the free polymers.

Figure 6

Velocity profiles of brushes of I polymers with polymers of 81 monomers. (a) ${\varphi }_g=1.00/{\text{nm}}^2$ and $v=20\text{m/s}$, (b) for different grafting densities and shear rates, with the relative speed of the substrates being $v=20\mathrm{m}/\mathrm{s}$ (black), 10 m/s (red), and 5 m/s (green).

Figure 7

The height of the brush as estimated by Eq. (5) as a function of the grafting density (a) without shear, (b) the maximum shear, and as a function of the relative velocity of the substrates for (c) the grafting densities ${\varphi }_g=0.25/{\text{nm}}^2$ and (d) ${\varphi }_g=1.00/{\text{nm}}^2$. (open symbols and dotted lines correspond to Y brushes)

Figure 8

The interpenetration length $w$ of the brush as a function of the grafting density (a) without shear, (b) the maximum shear, and as a function of the relative velocity of the substrates for (c) the grafting densities ${\varphi }_g=0.25/{\text{nm}}^2$ and (d) ${\varphi }_g=1.00/{\text{nm}}^2$. (open symbols and dotted lines correspond to Y brushes)

Figure 9

The friction coefficient as estimated by Eq. (7) as a function of (a), (b) the grafting density ${\varphi }_g$, (c), (d) the imposed shear, (a), (c) polymers of 41 monomers, and (b), (d) 81 monomers. (open symbols correspond to Y brushes)

Figure 10

The shear viscosity as estimated by Eq. (8) as a function of (a), (b) the grafting density ${\varphi }_g$, (c), (d) the imposed shear, (a), (c) polymers of 41 monomers, and (b), (d) 81 monomers. (open symbols correspond to Y brushes)

Figure 11

The radius of gyration of free polymers in the three main directions as function of the imposed shear and at grafting density ${\varphi }_g=0.50$.

Figure 12

The $P_2\left(u_{\alpha }\right)$ of the unit direction corresponding to the largest eigenvalue of the radius of gyration tensor for free polymers at ${\varphi }_g=0.50$.