10,908 research outputs found
Segment Motion in the Reptation Model of Polymer Dynamics. I. Analytical Investigation
We analyze the motion of individual beads of a polymer chain using a discrete
version of De Gennes' reptation model that describes the motion of a polymer
through an ordered lattice of obstacles. The motion within the tube can be
evaluated rigorously, tube renewal is taken into account in an approximation
motivated by random walk theory. We find microstructure effects to be present
for remarkably large times and long chains, affecting essentially all present
day computer experiments. The various asymptotic power laws, commonly
considered as typical for reptation, hold only for extremely long chains.
Furthermore, for an arbitrary segment even in a very long chain, we find a rich
variety of fairly broad crossovers, which for practicably accessible chain
lengths overlap and smear out the asymptotic power laws. Our analysis suggests
observables specifically adapted to distinguish reptation from motions
dominated by disorder of the environment.Comment: 38 pages in latex plus 8 ps figures, submitted to J. Stat. Phys. on
September 18, 1997, please note part II on cond-mat/971006
Segment Motion in the Reptation Model of Polymer Dynamics. II. Simulations
We present simulation data for the motion of a polymer chain through a
regular lattice of impenetrable obstacles (Evans-Edwards model). Chain lengths
range from N=20 to N=640, and time up to Monte Carlo steps. For we for the central segment find clear -behavior as an
intermediate asymptote. The also expected -range is not yet developed.
For the end segment also the -behavior is not reached. All these data
compare well to our recent analytical evaluation of the reptation model, which
shows that for shorter times (t \alt 10^{4}) the discreteness of the
elementary motion cannot be neglected, whereas for longer times and short
chains (N \alt 100) tube renewal plays an essential role also for the central
segment. Due to the very broad crossover behavior both the diffusion
coefficient and the reptation time within the range of our simulation do not
reach the asymptotic power laws predicted by reptation theory. We present
results for the center-of-mass motion, showing the expected intermediate
-behavior, but again only for very long chains. In addition we show
results for the motion of the central segment relative to the center of mass,
where in some intermediate range we see the expected increase of the effective
power beyond the -law, before saturation sets in. Analysis and
simulations agree on defining a new set of criteria as characteristic for
reptation of finite chains.Comment: 19 pages in latex plus 13 ps figures, submitted to J. Stat. Phys. on
September 18, 199
Calculation of the persistence length of a flexible polymer chain with short range self-repulsion
For a self-repelling polymer chain consisting of n segments we calculate the
persistence length L(j,n), defined as the projection of the end-to-end vector
on the direction of the j`th segment. This quantity shows some pronounced
variation along the chain. Using the renormalization group and
epsilon-expansion we establish the scaling form and calculate the scaling
function to order epsilon^2. Asymptotically the simple result L(j,n) ~
const(j(n-j)/n)^(2nu-1) emerges for dimension d=3. Also outside the excluded
volume limit L(j,n) is found to behave very similar to the swelling factor of a
chain of length j(n-j)/n. We carry through simulations which are found to be in
good accord with our analytical results. For d=2 both our and previous
simulations as well as theoretical arguments suggest the existence of
logarithmic anomalies.Comment: 28 pages, 8 figures, changed conten
The connection between single transverse spin asymmetries and the second moment of
We point out that the size of the photon single spin asymmetry in
high--energy proton proton collisions with one transversely polarized proton
can be related to , the twist three contribution to the second moment
of . Both quantities should be measured in the near future. The first was
analysed by Qiu and Sterman, the second was estimated by Balitsky, Braun, and
Kolesnichenko. Both experiments measure effectively the strength of the
collective gluon field in the nucleon oriented relative to the nucleon spin.
The sum rule results suggest that the single spin asymmetry is rather small for
the proton, but could be substantial for the neutron.Comment: 6 pages, UFTP preprint 348/199
Corrections to scaling in multicomponent polymer solutions
We calculate the correction-to-scaling exponent that characterizes
the approach to the scaling limit in multicomponent polymer solutions. A direct
Monte Carlo determination of in a system of interacting
self-avoiding walks gives . A field-theory analysis based
on five- and six-loop perturbative series leads to . We
also verify the renormalization-group predictions for the scaling behavior
close to the ideal-mixing point.Comment: 21 page
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