Magnetic Alignment of Block Copolymer Microdomains by Intrinsic Chain Anisotropy

We examine the role of intrinsic chain susceptibility anisotropy in magnetic field directed self-assembly of a block copolymer using in situ x-ray scattering. Alignment of a lamellar mesophase is observed on cooling across the disorder-order transition with the resulting orientational order inversely proportional to the cooling rate. We discuss the origin of the susceptibility anisotropy, $\mathrm{\Delta }\chi$, that drives alignment and calculate its magnitude using coarse-grained molecular dynamics to sample conformations of surface-tethered chains, finding $\mathrm{\Delta }\chi \approx 2\times 10^{-8}$. From field-dependent scattering data, we estimate that grains of $\approx 1.2\mu \mathrm{m}$ are present during alignment. These results demonstrate that intrinsic anisotropy is sufficient to support strong field-induced mesophase alignment and suggest a versatile strategy for field control of orientational order in block copolymers.

Figure 1

(a) Chemical structure of PS-b-P4VP. (b) Temperature-resolved SAXS data ($25\to 265\to 25°\mathrm{C}$) under a 6 T field applied vertically. The 2D diffractograms are shown as insets at three representative temperatures. $T_{\text{odt}}=257°\mathrm{C}$, $d$ $\mathrm{spacing}=9.5\mathrm{nm}$. (c) Schematic illustrating degenerate system alignment with lamellar normals perpendicular to the field.

Figure 2

TEM images and associated fast Fourier transforms (FFTs) of PS-b-P4VP aligned at 6 T, visualized (a) perpendicular to the field direction and (b) along the field direction.

Figure 3

(a) 2D SAXS data at selected temperatures showing the emergence of aligned lamellae during cooling from the isotropic, disordered state at $0.3°\mathrm{C}/\min$ at 6 T. (b) Diffractograms for samples under 6 T at $245°\mathrm{C}$ after cooling across $T_{\text{odt}}$ at the different rates indicated. (c) Dependence of azimuthal FWHM on field strength (at $0.3°\mathrm{C}/\min$) and cooling rate (at 4 and 6 T), on the bottom and top $x$ axis, respectively. (d) Diffractograms at $245°\mathrm{C}$ after cooling across $T_{\text{odt}}$ at $0.3°\mathrm{C}/\min$ at the indicated field strengths.

Figure 4

(a) Illustration of a polystyrene chain tethered at an impenetrable surface. The phenyl rings can rotate around the side bond to the backbone. (b) Simulated backbone $⟨P_2^b⟩$ and side chain $⟨P_2^s⟩$ orientation distribution coefficients as functions of areal density $\sigma$ for varying $N_p$. (c) Simulated brush height $H(\sigma )$ for varying $N_p$.

Figure 5

Field-dependent orientation distribution coefficients [Eq. (4)] for various grain sizes $\xi$ for $\mathrm{\Delta }\chi =-1.6\times 10^{-8}$ at $245°\mathrm{C}$. Black circles show experimentally derived values for samples cooled $0.3°\mathrm{C}/\min$. Fitting Eq. (4) (red circle trace) to experimental data yields $\xi \approx 1.2\mu \mathrm{m}$.