Abstract
The rate of binding of a grafted polymer to the surface is controlled by entropic barriers. Using a mean-field approximation of ideal polymer dynamics, we first calculate the characteristic binding time for a tethered ligand reaching for a binding site located on the tethering surface. This time is determined by two separate entropic effects: a barrier for the chain to be stretched sufficiently to reach the distant target and a restriction on chain conformations near the surface, versus the increase in available phase space for longer chains. The competition between these two constraints determines the optimal (shortest) binding time. The theory is then extended to model bridging between two surfaces, in particular relevant for cell adhesion. Here the tethered ligand reaches for a receptor on a parallel surface, and the binding time depends on the gap between the two constraining surfaces. Again, an optimal binding time is determined for the given tether geometry. The results look similar to those for fre...
Highlights
Ordered self-assembly requires the ability to organize and bind many molecules into a coherent structure
The kinetics of self-assembly is a broad and rich topic, which offers a fundamental understanding of processes being used in the construction of structured and functional aggregates
We examine a trade-off in the entropic barrier faced by reaching the distant target, which is on the same surface a fixed distance a away, against the reduction in chain confinement
Summary
Ordered self-assembly requires the ability to organize and bind many molecules into a coherent structure. The resulting effective potential that the binding ligand on the Nth chain segment experiences is a function of distance from the target receptor and depends on two relevant length scales in the problem: the chain radius of gyration Rg = N1/2b and the distance to target a We find a very accurate interpolation formula for the mean time of bridging between two surfaces, which spans across the whole range between the two limiting cases:
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