Verlag des Forschungszentrums Jülich
JUEL-2876
Netz, Roland
Membranenstapel und Fadenbündel
133 S., 1994
Membranes and strings are non-crossing manifolds, which can, under suitable
conditions and if interacting via sufficiently attractive potentials, undergo adhesion
transitions. At low temperatures or strong attraction, the manifolds are tightly
bound together; at high temperatures or weak attraction, they are completely separated.
At the adhesion transition, the separation between the manifolds diverges,
which leads to critical phenomena characterized by critical exponents.
In this work, the adhesion behavior of stacks of more than two manifolds is
studied. Corresponding experiments are performed on multimembrane systems.
Functional renormalization predicts the adhesion behavior of membrane stacks and
string bundles to be completely analogous, as indeed confirmed by the detailed
results presented here. The considered interactions include short-ranged potentials,
represented by square-wells, as well as long-ranged potentials. Experimentally,
these potential forms correspond to the van der Waals attraction and to an external
pressure.
For vanishing external pressure, the adhesion is caused by the short-ranged attraction
alone and shows the following behavior: In the case of a stack consisting of
identical manifolds, the manifolds unbind simultaneously at a temperature T: which
does not depend on the number of manifolds. The effective exponents do depend
on this number over the numerically accessible length scales. In the case where the
stack is bound to a flat substrate (where the potential between the substrate and
the lowest manifold is identical to the potentials acting between the manifolds) the
manifolds unbind separately at different temperatures. The topmost manifold of a
semi-infinite stack on a flat substrate unbinds at the same temperature T: as free
stacks. The critical exponents characterizing these single-manifold adhesion transitions
are universal and the same as the critical exponents for the adhesion of two
manifolds.
An infinitesimally small pressure P suffices to bind the manifolds; the adhesion
takes place at P = o. The distance between manifolds is determined by the balance
of the external pressure and the effective repulsion due to thermal undulations of
the manifolds. The strength of this repulsion, which has been determined experimentally,
depends only very weakly on the number of manifolds, as demonstrated
for free and adsorbed stacks. An additional short-ranged attraction between the
manifolds is irrelevant, if it is not sufficiently strong to bind the manifolds by itself.
In the case where the attraction is of critical strength, the amplitude of the
fluctuation-induced repulsion decreases by a factor of about 12.
For the potentials considered, the different length scales such as the distance
between the manifolds, the parallel and the perpendicular correlation length, are
related by universal amplitude ratios.
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