We present results of temperature resolved scattering studies of a liquid crystalline block copolymer undergoing an order-disorder transition (ODT) in the presence of magnetic fields and time-resolved measurements during isothermal field annealing at sub-ODT temperatures. In each case, field interactions produced strongly textured mesophases with the cylindrical microdomains aligned parallel to the field. We find there is no measurable field-induced shift in the ODT temperature ($T_{ODT}$) which suggests that selective melting does not play a role in mesophase alignment during isothermal experiments. Our data indicate instead that sub-ODT alignment occurs by slow, large scale grain rotation whereas alignment during cooling from the disordered melt is rapid and driven by the nucleation of weakly ordered but preferentially aligned material. We identify an optimum sub-cooling that maximizes alignment during isothermal field annealing. This is corroborated by a simple model incorporating the competing effects of an exponentially decreasing mobility and divergent, increasing magnetic anisotropy on cooling below $T_{ODT}$. The absence of measurable field-effects on $T_{ODT}$ is consistent with rough estimates derived from the relative magnitudes of the free energy due to field interaction and the enthalpy of the isotropic-LC transition.
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