1,468 research outputs found
Reactions at Polymer Interfaces: Transitions from Chemical to Diffusion-Control and Mixed Order Kinetics
We study reactions between end-functionalized chains at a polymer-polymer
interface. For small chemical reactivities (the typical case) the number of
diblocks formed, , obeys 2nd order chemically controlled kinetics, , until interfacial saturation. For high reactivities (e.g. radicals) a
transition occurs at short times to 2nd order diffusion-controlled kinetics,
with for unentangled chains while and
regimes occur for entangled chains. Long time kinetics are 1st order and
controlled by diffusion of the more dilute species to the interface: for unentangled cases, while and regimes
arise for entangled systems. The final 1st order regime is governed by center
of gravity diffusion, .Comment: 11 pages, 3 figures, uses poliface.sty, minor changes, to appear in
Europhysics Letter
Coating thermal noise for arbitrary shaped beams
Advanced LIGO's sensitivity will be limited by coating noise. Though this
noise depends on beam shape, and though nongaussian beams are being seriously
considered for advanced LIGO, no published analysis exists to compare the
quantitative thermal noise improvement alternate beams offer. In this paper, we
derive and discuss a simple integral which completely characterizes the
dependence of coating thermal noise on shape. The derivation used applies
equally well, with minor modifications, to all other forms of thermal noise in
the low-frequency limit.Comment: 3 pages. Originally performed in August 2004. Submitted to CQG. (v2)
: Corrections from referee and other
Kinetic Regimes and Cross-Over Times in Many-Particle Reacting Systems
We study kinetics of single species reactions ("A+A -> 0") for general local
reactivity Q and dynamical exponent z (rms displacement x_t ~ t^{1/z}.) For
small molecules z=2, whilst z=4,8 for certain polymer systems. For dimensions d
above the critical value d_c=z, kinetics are always mean field (MF). Below d_c,
the density n_t initially follows MF decay, n_0 - n_t ~ n_0^2 Q t. A 2-body
diffusion-controlled regime follows for strongly reactive systems (Q>Qstar ~
n_0^{(z-d)/d}) with n_0 - n_t ~ n_0^2 x_t^d. For Q<Qstar, MF kinetics persist,
with n_t ~ 1/Qt. In all cases n_t ~ 1/x_t^d at the longest times. Our analysis
avoids decoupling approximations by instead postulating weak physically
motivated bounds on correlation functions.Comment: 10 pages, 1 figure, uses bulk2.sty, minor changes, submitted to
Europhysics Letter
ON THE MODE OF DETECTING NITRIC ACID, And the total inefficacy of the New Test of decolorizing the
n/
The Slowly Formed Guiselin Brush
We study polymer layers formed by irreversible adsorption from a polymer
melt. Our theory describes an experiment which is a ``slow'' version of that
proposed by Guiselin [Europhys. Lett., v. 17 (1992) p. 225] who considered
instantaneously irreversibly adsorbing chains and predicted a universal density
profile of the layer after swelling with solvent to produce the ``Guiselin
brush.'' Here we ask what happens when adsorption is not instantaneous. The
classic example is chemisorption. In this case the brush is formed slowly and
the final structure depends on the experiment's duration, . We find
the swollen layer consists of an inner region of thickness with approximately constant density and an outer region
extending up to height which has the same density decay as for the Guiselin case.Comment: 7 pages, submitted to Europhysics Letter
Irreversible Adsorption from Dilute Polymer Solutions
We study irreversible polymer adsorption from dilute solutions theoretically.
Universal features of the resultant non-equilibrium layers are predicted. Two
cases are considered, distinguished by the value of the local monomer-surface
sticking rate Q: chemisorption (very small Q) and physisorption (large Q).
Early stages of layer formation entail single chain adsorption. While single
chain physisorption times tau_ads are typically microsecs, for chemisorbing
chains of N units we find experimentally accessible times tau_ads = Q^{-1}
N^{3/5}, ranging from secs to hrs. We establish 3 chemisorption universality
classes, determined by a critical contact exponent: zipping, accelerated
zipping and homogeneous collapse. For dilute solutions, the mechanism is
accelerated zipping: zipping propagates outwards from the first attachment,
accelerated by occasional formation of large loops which nucleate further
zipping. This leads to a transient distribution omega(s) \sim s^{-7/5} of loop
lengths s up to a size s_max \approx (Q t)^{5/3} after time t. By tau_ads the
entire chain is adsorbed. The outcome of the single chain adsorption episode is
a monolayer of fully collapsed chains. Having only a few vacant sites to adsorb
onto, late arriving chains form a diffuse outer layer. In a simple picture we
find for both chemisorption and physisorption a final loop distribution
Omega(s) \sim s^{-11/5} and density profile c(z) \sim z^{-4/3} whose forms are
the same as for equilibrium layers. In contrast to equilibrium layers, however,
the statistical properties of a given chain depend on its adsorption time; the
outer layer contains many classes of chain, each characterized by different
fraction of adsorbed monomers f. Consistent with strong physisorption
experiments, we find the f values follow a distribution P(f) \sim f^{-4/5}.Comment: 18 pages, submitted to Eur. Phys. J. E, expanded discussion sectio
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