Aggregates of rod-coil diblock copolymers adsorbed at a surface

The behaviour of rod-coil diblock copolymers close to a surface is discussed by using extended scaling methods. The copolymers are immersed in selective solvent such that the rods are likely to aggregate to gain energy. The rods are assumed to align only parallel to each other, such that they gain a maximum energy by forming liquid crystalline structures. If an aggregate of these copolymers adsorbs with the rods parallel to the surface the rods shift with respect to each other to allow for the chains to gain entropy. It is shown that this shift decays with increasing distance from the surface. The profile of this decay away from the surface is calculated by minimisation of the total free energy of the system. The stability of such an adsorbed aggregate and other possible configurations are discussed as well.Comment: 10 pages, 11 figure

Entropy-induced Microphase Separation in Hard Diblock Copolymers

Whereas entropy can induce phase behavior that is as rich as seen in energetic systems, microphase separation remains a very rare phenomenon in entropic systems. In this paper, we present a density functional approach to study the possibility of entropy-driven microphase separation in diblock copolymers. Our model system consists of copolymers composed of freely-jointed slender hard rods. The two types of monomeric segments have comparable lengths, but a significantly different diameter, the latter difference providing the driving force for the phase separation. At the same time these systems can also exhibit liquid crystalline phases. We treat this system in the appropriate generalization of the Onsager approximation to chain-like particles. Using a linear stability (bifurcation) analysis, we analytically determine the onset of the microseparated and the nematic phases for long chains. We find that for very long chains the microseparated phase always preempts the nematic. In the limit of infinitely long chains, the correlations within the chain become Gaussian and the approach becomes exact. This allows us to define a Gaussian limit in which the theory strongly simplifies and the competition between microphase separation and liquid crystal formation can be studied essentially analytically. Our main results are phase diagrams as a function of the effective diameter difference, the segment composition and the length ratio of the segments. We also determine the amplitude of the positional order as a function of position along the chain at the onset of the microphase separation instability. Finally, we give suggestions as to how this type of entropy-induced microphase separation could be observed experimentally.Comment: 16 pages, 7 figure

Automatised full one-loop renormalisation of the MSSM I: The Higgs sector, the issue of tan(beta) and gauge invariance

We give an extensive description of the renormalisation of the Higgs sector of the minimal supersymmetric model in SloopS. SloopS is an automatised code for the computation of one-loop processes in the MSSM. In this paper, the first in a series, we study in detail the non gauge invariance of some definitions of tan(beta). We rely on a general non-linear gauge fixing constraint to make the gauge parameter dependence of different schemes for tan(beta) at one-loop explicit. In so doing, we update, within these general gauges, an important Ward-Slavnov-Taylor identity on the mixing between the pseudo-scalar Higgs, A^0, and the Z^0. We then compare the tan(beta) scheme dependence of a few observables. We find that the best tan(beta) scheme is the one based on the decay A^0 -> tau^+ tau^- because of its gauge invariance, being unambiguously defined from a physical observable, and because it is numerically stable. The oft used DRbar scheme performs almost as well on the last count, but is usually defined from non-gauge invariant quantities in the Higgs sector. The use of the heavier scalar Higgs mass in lieu of tan(beta) though related to a physical parameter induces too large radiative corrections in many instances and is therefore not recommended.Comment: 34 pages, 1 figure, typos corrected, accepted for publication in Phys. Rev.

Preservation of equilibrium in orthograde and inverted body positions

The mechanism for regulation of the vertical pose with retention of equilibrium in the inverted body position was investigated

Symmetric Diblock Copolymers in Thin Films (I): Phase stability in Self-Consistent Field Calculations and Monte Carlo Simulations

We investigate the phase behavior of symmetric AB diblock copolymers confined into a thin film. The film boundaries are parallel, impenetrable and attract the A component of the diblock copolymer. Using a self-consistent field technique [M.W. Matsen, J.Chem.Phys. {\bf 106}, 7781 (1997)], we study the ordered phases as a function of incompatibility $\chi$ and film thickness in the framework of the Gaussian chain model. For large film thickness and small incompatibility, we find first order transitions between phases with different number of lamellae which are parallel oriented to the film boundaries. At high incompatibility or small film thickness, transitions between parallel oriented and perpendicular oriented lamellae occur. We compare the self-consistent field calculations to Monte Carlo simulations of the bond fluctuation model for chain length N=32. In the simulations we quench several systems from $\chi N=0$ to $\chi N=30$ and monitor the morphology into which the diblock copolymers assemble. Three film thicknesses are investigated, corresponding to parallel oriented lamellae with 2 and 4 interfaces and a perpendicular oriented morphology. Good agreement between self-consistent field calculations and Monte Carlo simulations is found.Comment: to appear in J.Chem.Phy

A DC Programming Approach for Solving Multicast Network Design Problems via the Nesterov Smoothing Technique

This paper continues our effort initiated in [9] to study Multicast Communication Networks, modeled as bilevel hierarchical clustering problems, by using mathematical optimization techniques. Given a finite number of nodes, we consider two different models of multicast networks by identifying a certain number of nodes as cluster centers, and at the same time, locating a particular node that serves as a total center so as to minimize the total transportation cost through the network. The fact that the cluster centers and the total center have to be among the given nodes makes this problem a discrete optimization problem. Our approach is to reformulate the discrete problem as a continuous one and to apply Nesterov smoothing approximation technique on the Minkowski gauges that are used as distance measures. This approach enables us to propose two implementable DCA-based algorithms for solving the problems. Numerical results and practical applications are provided to illustrate our approach