77 research outputs found
Molecular elasticity and the geometric phase
We present a method for solving the Worm Like Chain (WLC) model for twisting
semiflexible polymers to any desired accuracy. We show that the WLC free energy
is a periodic function of the applied twist with period 4 pi. We develop an
analogy between WLC elasticity and the geometric phase of a spin half system.
These analogies are used to predict elastic properties of twist-storing
polymers. We graphically display the elastic response of a single molecule to
an applied torque. This study is relevant to mechanical properties of
biopolymers like DNA.Comment: five pages, one figure, revtex, revised in the light of referee's
comments, to appear in PR
Thermal Degradation of Adsorbed Bottle-Brush Macromolecules: Molecular Dynamics Simulation
The scission kinetics of bottle-brush molecules in solution and on an
adhesive substrate is modeled by means of Molecular Dynamics simulation with
Langevin thermostat. Our macromolecules comprise a long flexible polymer
backbone with segments, consisting of breakable bonds, along with two side
chains of length , tethered to each segment of the backbone. In agreement
with recent experiments and theoretical predictions, we find that bond cleavage
is significantly enhanced on a strongly attractive substrate even though the
chemical nature of the bonds remains thereby unchanged.
We find that the mean bond life time decreases upon adsorption by
more than an order of magnitude even for brush molecules with comparatively
short side chains $N=1 \div 4$. The distribution of scission probability along
the bonds of the backbone is found to be rather sensitive regarding the
interplay between length and grafting density of side chains. The life time
declines with growing contour length as ,
and with side chain length as . The probability
distribution of fragment lengths at different times agrees well with
experimental observations. The variation of the mean length of the
fragments with elapsed time confirms the notion of the thermal degradation
process as a first order reaction.Comment: 15 pages, 7 figure
Thermal Fluctuations of Elastic Filaments with Spontaneous Curvature and Torsion
We study the effects of thermal flucutations on thin elastic filaments with
spontaneous curvature and torsion. We derive analytical expressions for the
orientational correlation functions and for the persistence length of helices,
and find that this length varies non-monotonically with the strength of thermal
fluctuations. In the weak fluctuation regime, the persistence length of a
spontaneously twisted helix has three resonance peaks as a function of the
twist rate. In the limit of strong fluctuations, all memory of the helical
shape is lost.Comment: 1 figur
Localization and Capacitance Fluctuations in Disordered Au Nano-junctions
Nano-junctions, containing atomic-scale gold contacts between strongly
disordered leads, exhibit different transport properties at room temperature
and at low temperature. At room temperature, the nano-junctions exhibit
conductance quantization effects. At low temperatures, the contacts exhibit
Coulomb-Blockade. We show that the differences between the room-temperature and
low temperature properties arise from the localization of electronic states in
the leads. The charging energy and capacitance of the nano-junctions exhibit
strong fluctuations with applied magnetic field at low temperature, as
predicted theoretically.Comment: 20 pages 8 figure
Theory of strong inelastic co-tunneling
We develop a theory of the conductance of a quantum dot connected to two
leads by single-mode quantum point contacts. If the contacts are in the regime
of perfect transmission, the conductance shows no Coulomb blockade oscillations
as a function of the gate voltage. In the presence of small reflection in both
contacts, the conductance develops small Coulomb blockade oscillations. As the
temperature of the system is lowered, the amplitude of the oscillations grows,
and eventually sharp periodic peaks in conductance are formed. Away from the
centers of the peaks the conductance vanishes at low temperatures as , in
agreement with the theory of inelastic co-tunneling developed for the
weak-tunneling case. Conductance near the center of a peak can be studied using
an analogy with the multichannel Kondo problem. In the case of symmetric
barriers, the peak conductance at is of the order of . In
the asymmetric case, the peak conductance vanishes linearly in temperature.Comment: 22 pages, 4 figures, uses REVTEX 3.0, epsf.sty and multicol.st
Higher-Order Results for the Relation between Channel Conductance and the Coulomb Blockade for Two Tunnel-Coupled Quantum Dots
We extend earlier results on the relation between the dimensionless tunneling
channel conductance and the fractional Coulomb blockade peak splitting
for two electrostatically equivalent dots connected by an arbitrary number
of tunneling channels with bandwidths much larger than the
two-dot differential charging energy . By calculating through second
order in in the limit of weak coupling (), we illuminate
the difference in behavior of the large- and
small- regimes and make more plausible extrapolation to the
strong-coupling () limit. For the special case of
and strong coupling, we eliminate an apparent ultraviolet
divergence and obtain the next leading term of an expansion in . We show
that the results we calculate are independent of such band structure details as
the fraction of occupied fermionic single-particle states in the weak-coupling
theory and the nature of the cut-off in the bosonized strong-coupling theory.
The results agree with calculations for metallic junctions in the
limit and improve the previous good
agreement with recent two-channel experiments.Comment: 27 pages, 1 RevTeX file with 4 embedded Postscript figures. Uses eps
Conformational transitions of heteropolymers in dilute solutions
In this paper we extend the Gaussian self-consistent method to permit study
of the equilibrium and kinetics of conformational transitions for
heteropolymers with any given primary sequence. The kinetic equations earlier
derived by us are transformed to a form containing only the mean squared
distances between pairs of monomers. These equations are further expressed in
terms of instantaneous gradients of the variational free energy. The method
allowed us to study exhaustively the stability and conformational structure of
some periodic and random aperiodic sequences. A typical phase diagram of a
fairly long amphiphilic heteropolymer chain is found to contain phases of the
extended coil, the homogeneous globule, the micro-phase separated globule, and
a large number of frustrated states, which result in conformational phases of
the random coil and the frozen globule. We have also found that for a certain
class of sequences the frustrated phases are suppressed. The kinetics of
folding from the extended coil to the globule proceeds through non-equilibrium
states possessing locally compacted, but partially misfolded and frustrated,
structure. This results in a rather complicated multistep kinetic process
typical of glassy systems.Comment: 15 pages, RevTeX, 20 ps figures, accepted for publication in Phys.
Rev.
Thermodynamics and structure of self-assembled networks
We study a generic model of self-assembling chains which can branch and form
networks with branching points (junctions) of arbitrary functionality. The
physical realizations include physical gels, wormlike micells, dipolar fluids
and microemulsions. The model maps the partition function of a solution of
branched, self-assembling, mutually avoiding clusters onto that of a Heisenberg
magnet in the mathematical limit of zero spin components. The model is solved
in the mean field approximation. It is found that despite the absence of any
specific interaction between the chains, the entropy of the junctions induces
an effective attraction between the monomers, which in the case of three-fold
junctions leads to a first order reentrant phase separation between a dilute
phase consisting mainly of single chains, and a dense network, or two network
phases. Independent of the phase separation, we predict the percolation
(connectivity) transition at which an infinite network is formed that partially
overlaps with the first-order transition. The percolation transition is a
continuous, non thermodynamic transition that describes a change in the
topology of the system. Our treatment which predicts both the thermodynamic
phase equilibria as well as the spatial correlations in the system allows us to
treat both the phase separation and the percolation threshold within the same
framework. The density-density correlation correlation has a usual
Ornstein-Zernicke form at low monomer densities. At higher densities, a peak
emerges in the structure factor, signifying an onset of medium-range order in
the system. Implications of the results for different physical systems are
discussed.Comment: Submitted to Phys. Rev.
Quantum state engineering with Josephson-junction devices
We review recent theoretical and experimental progress in quantum state
engineering with Josephson junction devices. The concepts of quantum computing
have stimulated an increased activity in the field. Either charges or phases
(fluxes) of the Josephson systems can be used as quantum degrees of freedom,
and their quantum state can be manipulated coherently by voltage and current
pulses. They thus can serve as qubits, and quantum logic gates can be
performed. Their phase coherence time, which is limited, e.g., by the
electromagnetic fluctuations in the control circuit, is long enough to allow a
series of these manipulations. The quantum measurement process performed by a
single-electron transistor, a SQUID, or further nanoelectronic devices is
analyzed in detail.Comment: An article prepared for Reviews of Modern Physics, 46 pages, 23
figure
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