3,084 research outputs found
Dynamics of Polymers: a Mean-Field Theory
We derive a general mean-field theory of inhomogeneous polymer dynamics; a
theory whose form has been speculated and widely applied, but not heretofore
derived. Our approach involves a functional integral representation of a
Martin-Siggia-Rose type description of the exact many-chain dynamics. A saddle
point approximation to the generating functional, involving conditions where
the MSR action is stationary with respect to a collective density field
and a conjugate MSR response field , produces the desired dynamical
mean-field theory. Besides clarifying the proper structure of mean-field theory
out of equilibrium, our results have implications for numerical studies of
polymer dynamics involving hybrid particle-field simulation techniques such as
the single-chain in mean-field method (SCMF)
Hydrodynamic Self-Consistent Field Theory for Inhomogeneous Polymer Melts
We introduce a mesoscale technique for simulating the structure and rheology
of block copolymer melts and blends in hydrodynamic flows. The technique
couples dynamic self consistent field theory (DSCFT) with continuum
hydrodynamics and flow penalization to simulate polymeric fluid flows in
channels of arbitrary geometry. We demonstrate the method by studying phase
separation of an ABC triblock copolymer melt in a sub-micron channel with
neutral wall wetting conditions. We find that surface wetting effects and shear
effects compete, producing wall-perpendicular lamellae in the absence of flow,
and wall-parallel lamellae in cases where the shear rate exceeds some critical
Weissenberg number.Comment: Revised as per peer revie
Reliability considerations in the design, assembly, and testing of the mariner iv power system
Reliability considerations in design, assembly, and testing of Mariner IV power syste
Microphase separation in polyelectrolytic diblock copolymer melt : weak segregation limit
We present a generalized theory of microphase separation for charged-neutral
diblock copolymer melt. Stability limit of the disordered phase for salt-free
melt has been calculated using Random Phase Approximation (RPA) and
self-consistent field theory (SCFT). Explicit analytical free energy
expressions for different classical ordered microstructures (lamellar, cylinder
and sphere) are presented. We demonstrate that chemical mismatch required for
the onset of microphase separation () in charged-neutral
diblock melt is higher and the period of ordered microstructures is lower than
those for the corresponding neutral-neutral diblock system. Theoretical
predictions on the period of ordered structures in terms of Coulomb
electrostatic interaction strength, chain length, block length, and the
chemical mismatch between blocks are presented. SCFT has been used to go beyond
the stability limit, where electrostatic potential and charge distribution are
calculated self-consistently. Stability limits calculated using RPA are in
perfect agreement with the corresponding SCFT calculations. Limiting laws for
stability limit and the period of ordered structures are presented and
comparisons are made with an earlier theory. Also, transition boundaries
between different morphologies have been investigated
An external potential dynamic study on the formation of interface in polydisperse polymer blends
The formation of interface from an initial sharp interface in polydisperse
A/B blends is studied using the external potential dynamic method. The present
model is a nonlocal coupling model as we take into account the correlation
between segments in a single chain. The correlation is approximately expressed
by Debye function and the diffusion dynamics are based on the Rouse chain
model. The chain length distribution is described by the continuous Schulz
distribution. Our numerical calculation indicates that the broadening of
interface with respect to time obeys a power law at early times, and the power
law indexes are the same for both monodisperse and polydisperse blend. The
power law index is larger than that in the local coupling model. However there
is not a unified scaling form of the broadening of the interface width if only
the interfacial width at equilibrium is taken into account as the
characteristic length of the system, because the correlation makes an extra
characteristic length in the system, and the polydispersity is related to this
length.Comment: 15 pages, 5 figure
Orientational phase transitions in the hexagonal phase of a diblock copolymer melt under shear flow
We generalize the earlier theory by Fredrickson [J. Rheol. v.38, 1045 (1994)]
to study the orientational behaviour of the hexagonal phase of diblock
copolymer melt subjected to steady shear flow. We use symmetry arguments to
show that the orientational ordering in the hexagonal phase is a much weaker
effect than in the lamellae. We predict the parallel orientation to be stable
at low and the perpendicular orientation at high shear rates. Our analysis
reproduces the experimental results by Tepe et al. [Macromolecules v.28, 3008
(1995)] and explains the difficulties in experimental observation of the
different orientations in the hexagonal phase.Comment: 21 pages, 6 eps figures, submitted to Physical Review
Orientations of the lamellar phase of block copolymer melts under oscillatory shear flow
We develop a theory to describe the reorientation phenomena in the lamellar
phase of block copolymer melt under reciprocating shear flow. We show that
similar to the steady-shear, the oscillating flow anisotropically suppresses
fluctuations and gives rise to the parallel-perpendicular orientation
transition. The experimentally observed high-frequency reverse transition is
explained in terms of interaction between the melt and the shear-cell walls.Comment: RevTex, 3 pages, 1 figure, submitted to PR
Self-diffusion of Rod-like Viruses Through Smectic Layer
We report the direct visualization at the scale of single particles of mass
transport between smectic layers, also called permeation, in a suspension of
rod-like viruses. Self-diffusion takes place preferentially in the direction
normal to the smectic layers, and occurs by quasi-quantized steps of one rod
length. The diffusion rate corresponds with the rate calculated from the
diffusion in the nematic state with a lamellar periodic ordering potential that
is obtained experimentally.Comment: latex, 4 pages, 4 figures, accepted in Phys. Rev. Let
Stability of Quasicrystals Composed of Soft Isotropic Particles
Quasicrystals whose building blocks are of mesoscopic rather than atomic
scale have recently been discovered in several soft-matter systems. Contrary to
metallurgic quasicrystals whose source of stability remains a question of great
debate to this day, we argue that the stability of certain soft-matter
quasicrystals can be directly explained by examining a coarse-grained free
energy for a system of soft isotropic particles. We show, both theoretically
and numerically, that the stability can be attributed to the existence of two
natural length scales in the pair potential, combined with effective three-body
interactions arising from entropy. Our newly gained understanding of the
stability of soft quasicrystals allows us to point at their region of stability
in the phase diagram, and thereby may help control the self-assembly of
quasicrystals and a variety of other desired structures in future experimental
realizations.Comment: Revised abstract, more detailed explanations, and better images of
the numerical minimization of the free energ
Reactions at polymer interfaces: A Monte Carlo Simulation
Reactions at a strongly segregated interface of a symmetric binary polymer
blend are investigated via Monte Carlo simulations. End functionalized
homopolymers of different species interact at the interface instantaneously and
irreversibly to form diblock copolymers. The simulations, in the framework of
the bond fluctuation model, determine the time dependence of the copolymer
production in the initial and intermediate time regime for small reactant
concentration . The results are compared to
recent theories and simulation data of a simple reaction diffusion model. For
the reactant concentration accessible in the simulation, no linear growth of
the copolymer density is found in the initial regime, and a -law is
observed in the intermediate stage.Comment: to appear in Macromolecule
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