Self-assembled lamellar structures composed of block copolymers are simulated by molecular dynamics. The response of a bulk system to external shear is investigated, in particular, the average energy, the entropy production, and the stability of the lamellae's orientation. We distinguish two orientations, a parallel orientation in which the normal to the lamellae sheets lies in the direction of the shear gradient, and a perpendicular orientation in which the normal lies perpendicular to the shear gradient and shear direction. The perpendicular phase is stable throughout all shear rates. The parallel phase has higher internal energy and larger entropy production than the perpendicular phase and moreover becomes unstable at relatively small shear rates. The perpendicular orientation should therefore be more stable at any finite shear rate. Surface effects are probably responsible for the stability of the parallel phase observed experimentally at small shear rates.

Self-assembled ordered structures composed of block copolymers are simulated by molecular dynamics under stress-free conditions and under shear. We address several methodological points. The system must be allowed to adjust its size to accommodate natural periods of self-assembled structures. In addition, these structures need to be capable of rotating freely under shear. An examination of the diffusion of polymer molecules in the lamellar phase reveals subdiffusion along translationally invariant directions between the ballistic and diffusive regime. The diffused distance d increases with time t as d ! t 1/3 . We also examine the possibility of mapping structures such as cylindrical phases onto particle-field types of models. Using measurements of the wavevector-dependent dynamic matrix, we show that this cannot be done with only two-body potentials. We then examine the molecular origin of shear alignment of lamellar phases. Lamellae oriented parallel to the shear direction become unstable at high shear rates when the major axis of the tensor of gyration of individual polymers forms an average angle of 458 with the lamellae. This instability can be understood in analogy to similar transitions in liquid crystals. C 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 970-982, 2005

We present a method in which a chaotic signal is used to mask a message securely. It depends on separating the two tasks of synchronizing the chaotic oscillators and encrypting the message. A sporadic drive together with a function f of the ciphertext and response system variables is used to make extraction difficult. We give a choice of f that makes the method similar to a one-time pad, with pseudorandom numbers provided by the chaos.