Inhomogeneity of block copolymers at the interface of an immiscible polymer blend

We present the effects of structure and stiffness of block copolymers on the interfacial properties of an immiscible homopolymer blend. Diblock and two-arm grafted copolymers with variation in stiffness are modeled using coarse-grained molecular dynamics to compare the compatibilization efficiency, i.e., reduction of interfacial tension. Overall, grafted copolymers are located more compactly at the interface and show better compatibilization efficiency than diblock copolymers. In addition, an increase in the stiffness for one of the blocks of the diblock copolymers causes unusual inhomogeneous interfacial coverage due to bundle formation. However, an increase in the stiffness for one of blocks of the grafted copolymers prevents the bundle formation due to the branched chain. As a result, homogeneous interfacial coverage of homopolymer blends is realized with significant reduction of interfacial tension which makes grafted copolymer a better candidate for the compatibilizer of immiscible homopolymer blend.

Figure 1

The images of (a) A homopolymer, (b) B homopolymer, (c) diblock copolymer, and (d) two-arm grafted copolymer. A/B homopolymers are modeled by connecting 30 A beads and 30 B beads, respectively. The diblock copolymer is described by linearly connected 10 A beads and 10 B beads and the grafted copolymer is modeled with two B blocks, which are composed of 5 B beads, grafted on the third and eighth beads along the backbone chain consisting of 10 beads of type A.

Figure 2

Density distribution normal to the A/B interface (a–c) when diblock copolymers (A-b-B) and (d–f) two-arm grafted copolymers (A-g-B) are used as compatibilizer. The PA, PB, ${\mathrm{A}}_{\mathrm{co}}$, and ${\mathrm{B}}_{\mathrm{co}}$ in the legend represent A homopolymer, B homopolymer, A block of copolymers, and B block of copolymers, respectively. Snapshots of diblock and grafted copolymers with different stiffness are given in insets of (a) and (d), respectively. The number of copolymers $M_{\mathrm{co}}$ is 63 in both cases.

Figure 3

(a) Shape factor $q$ of copolymers defined as the relative difference of squared radius of gyration between normal $R_{g,N}^2$ and parallel $R_{g,L}^2$ to the interface. The snapshots of parallel (b) and normal (c) to the interface of diblock copolymers which form bundles at the interface. The snapshots of parallel (d) and normal (e) to the interface of grafted copolymers which cover the interface homogeneously. Simulation condition ($M_{\mathrm{co}}=63,k_{\theta }=100\varepsilon /\mathrm{ra}{\mathrm{d}}^2$) is applied for both diblock and grafted copolymers for the snapshots.

Figure 4

The snapshots for the case of $N_{\mathrm{homo}}=$ (a) 1, (b) 2, and (c) 15 are also shown. (d) The shape factor $q$ of diblock copolymer with ($M_{\mathrm{co}}=63,k_{\theta }=100\varepsilon /\mathrm{ra}{\mathrm{d}}^2$) as a function of chain length $N_{\mathrm{homo}}$ of the A and B homopolymers.

Figure 5

The pair distribution function for A and B types of bead, $g_{\mathrm{AB}}\left(r\right)$, which represents the probability of finding B type of bead at a distance of $r$ away from A type of bead.

Figure 6

(a) The coordination number $z_{\mathrm{AB}}$ between A and B beads defined as the integral of $g_{\mathrm{AB}}\left(r\right)$ from 0 to the first minimum $m_1$, $z_{\mathrm{AB}}={\int }_0^{m_1}4\pi r^2\rho g_{\mathrm{AB}}\left(r\right)dr$. (b) The number density of beads of copolymer ${\rho }_{\mathrm{co}}$ situated in the range from $z_0-0.5\sigma$ to $z_0+0.5\sigma$, where $z_0$ is the center of the interface.

Figure 7

Ratio of interfacial tension with copolymers to the interfacial tension without any copolymers $\gamma /{\gamma }_0$, where ${\gamma }_0=0.69\pm 0.04\varepsilon {\sigma }^{-2}$, is shown. The interfacial tension $\gamma$ is calculated using $\gamma =1/2\langle L_z\left(P_N-P_T\right)\rangle$, where $P_N$ and $P_T$ are the pressure normal and tangential to the interface, respectively.