No abstract

A theory describing layers of polymer chains grafted to a flat surface (polymer 'brush') is developed. We consider a brush of chains with arbitrary extensibility and, within the framework of molecular field theory, we suggest a general scheme for calculating the selfconsistent pseudo-potential, which determines the structure of the brush. This potential appears to be defined only by the mechanism of extensibility and is independent of the interactions between chains in the brush. A model potential for freely jointed chains (FJC) was calculated and used for describing an FJC polymer brush in good solvent conditions. We found good agreement between our results and the numerical calculations of Skvortsov e t a / .

Liquid crystalline ordering in polymer brushes formed by macromolecules with mesogenic groups in the main chain and immersed in a solvent is investigated theoretically by numerical calculations within a self-consistent field approximation. Existence of a microphase-segregated brush regime with a collapsed orientationally ordered intrinsic sublayer and a swollen external sublayer is shown. At high grafting density (σ), the transition from a conventional brush state to the microphase-segregated state is continuous. At small σ, it is a jumpwise first-order phase transition for a finite chain length (N), the magnitudes of the jumps in the average characteristics of the brush tend to zero in the limit N → ∞.

Significant progress has been made in interpreting the effects of non-axisymmetric "error" fields on a plasma through ideal MHD stability and a dominant "least stable" ideal mode through which the fields couple to the tearing resonant surface. However, in contrast to expectations from such theories, experiments have found limited success in correcting error fields, with single correction coil arrays giving benefits of between 0% and $50% correction (in terms of improvement to a low density locked mode limit), dependent on the structure of the error and correcting fields. With additional coils up to $70% is possible. It was unclear whether this represented an intrinsic stability or control limit, or higher order toroidal or poloidal harmonic effects. Thus, studies on the DIII-D tokamak explored correction of a proxy error field, using two differently structured coil arrays. This enabled the principles of error correction to be tested at high amplitudes and operational densities, with known pure n ¼ 1 fields. Results showed substantial residual effects from the corrected n ¼ 1 field, with improvements of only $50% in the low density locked mode limit. This suggests that n ¼ 1 error fields must couple to more than one surface in the plasma, and this is conjectured to be through more than one ideal mode, thereby requiring precise correction. For ITER, updated predictions of field error have been obtained and compared with revised scalings for tearing mode thresholds, indicating 50% or better error field correction will be needed. This will likely require more than one well coupled correction coil array and sets a challenge for theory to model the behavior, in order to clarify the plasma response and braking mechanisms, and so the effectiveness of ITER's correction coils and the possible need for support from its edge localized mode control coils. V C 2012 American Institute of Physics.

Liquid crystalline ordering in planar polymer brushes is investigated theoretically by numerical calculations within a self‐consistent field approximation. The brushes are formed by macromolecules with mesogenic groups in main chain and immersed in a solvent. Existence of a microphase segregated brush (MSB) regime with a collapsed orientationally ordered intrinsic sublayer and a swollen external sublayer is shown. At small grafting density, the transition from a conventional brush state to the microphase segregated state is a jump‐wise first order phase transition for a finite chain length (N). The magnitudes of the jumps in the average characteristics of the brush tend to zero in the limit N → ∞ since this transition occurs only in a vanishingly small part (∝ N−1/2) of the brush. High compressibility of MSB brush is demonstrated. The origin of phase transition in planar brushes is discussed.