Semiflexible polymer solutions. I. Phase behavior and single-chain statistics

We study the thermodynamics and single-chain statistics of wormlike polymer solutions with Maier–Saupe-type interactions using self-consistent-field (SCF) theory. The SCF equations are derived using a systematic field-theoretical approach which yields the SCF equations as the lowest order approximation, but permits fluctuation corrections to be incorporated. We solve the SCF equations using the spheroidal functions, which provides a nonperturbative description of the thermodynamics and single-chain statistics in the nematic state for arbitrary degrees of nematic order. Several types of phase diagrams are predicted, with an emphasis on the limit of metastability (spinodal) associated with each phase. The shape and location of these spinodals suggest interesting scenarios for the phase transition kinetics. A large but finite persistence length is shown to significantly decrease the isotropic–nematic transition temperature relative to that for rigid rods. In the nematic state, the mean-square end-to-end distance in the parallel and perpendicular directions are governed by two separate correlation lengths. An exact relationship between these correlation lengths and the eigenvalues of the spheroidal functions is provided, which reproduces the analytical expressions predicted from earlier studies in the limit of large nematic strength. The dominant contribution to the single-chain thermodynamics is shown to arise from small amplitude undulations in the directions perpendicular to the nematic direction; the presence of hairpins, though crucial for determining the dimensions of the polymer, has insignificant consequences on the single-chain thermodynamics

End-to-end distance vector distribution with fixed end orientations for the wormlike chain model

We find exact expressions for the end-to-end distance vector distribution function with fixed end orientations for the wormlike chain model. This function in Fourier-Laplace space adopts the form of infinite continued fractions, which emerges upon exploiting the hierarchical structure of the moment-based expansion. Our results are used to calculate the root-mean-square end displacement in a given direction for a chain with both end orientations fixed. We find that the crossover from rigid to flexible chains is marked by the root-mean-square end displacement slowly losing its angular dependence as the coupling between chain conformation and end orientation wanes. However, the coupling remains strong even for relatively flexible chains, suggesting that the end orientation strongly influences chain conformation for chains that are several persistence lengths long. We then show the behavior of the distribution function by a density plot of the probability as a function of the end-to-end distance vector for a wormlike chain in two dimensions with one end pointed in a fixed direction and the other end free (in its orientation). As we progress from high to low rigidity, the distribution function shifts from being peaked at a location near the full contour length of the chain in the forward direction, corresponding to a straight configuration, to being peaked near zero end separation, as in the Gaussian limit. The function exhibits double peaks in the crossover between these limiting behaviors

Semiflexible Polymer Confined to a Spherical Surface

We develop a formalism for describing the kinematics of a wormlike chain confined to the surface of a sphere that simultaneously satisfies the spherical confinement and the inextensibility of the chain contour. We use this formalism to study the statistical behavior of the wormlike chain on a spherical surface. In particular, we provide an exact, closed-form expression for the mean square end-to-end distance that is valid for any value of chain length L, persistence length lp, and sphere radius R. We predict two qualitatively different behaviors for a long polymer depending on the ratio R/lp. For R/lp>4, the mean square end-to-end distance increases monotonically with the chain length, whereas for R/lp<4, a damped oscillatory behavior is predicted

Magneto-transport in impurity-doped few-layer graphene spin valve

Using Keldysh nonequilibrium Green's function method we study the spin-dependent transport through impurity-doped few layer graphene sandwiched between two magnetic leads with an arbitrary mutual orientations of the magnetizations. We find for parallel electrodes magnetizations that the differential conductance possesses two resonant peaks as the applied bias increases. These peaks are traced back to a buildup of a magnetic moment on the impurity due to the electrodes spin polarization. For a large mutual angle of the electrodes magnetization directions, the two resonant peaks approach each others and merge into a single peak for antiparallel orientation of the electrodes magnetizations. We point out that the tunneling magnetoresistance (TMR) may change sign for relatively small changes in the values of the polarization parameters. Furthermore, we inspect the behaviour of the differential conductance and TMR upon varying the temperature.Comment: 8 pages, 7 figures, accepted by Phys. Rev.

Novel thick-foam ferroelectret with engineered voids for energy harvesting applications

This work reports a novel thick-foam ferroelectret which is designed and engineered for energy harvesting applications. We fabricated this ferroelectret foam by mixing a chemical blowing agent with a polymer solution, then used heat treatment to activate the agent and create voids in the polymer foam. The dimensions of the foam, the density and size of voids can be well controlled in the fabrication process. Therefore, this ferroelectret can be engineered into optimized structure for energy harvesting applications

Effective SU(2)_L x U(1) theory and the Higgs boson mass

We assume the stability of vacuum under radiative corrections in the context of the standard electroweak theory. We find that this theory behaves as a good effective model already at cut off energy scales as low as 0.7 TeV. This stability criterion allows to predict m_H= 318 +- 13 GeV for the Higgs boson mass.Comment: Latex, 5 pages, 1 Postscript figure include