Escape Transitions and Force Laws for Compressed Polymer Mushrooms

Abstract

PACS. 36.20Ey -Macromolecules and polymer molecules: conformation (statistics and dynamics). PACS. 87.15 -v -Molecular biophysics. PACS. 46.30Lx -State buckling and instability.

Force measurements with the atomic force microscope: Technique, interpretation and applications

“…Theory and simulations showed that the polymer chains partially avoid compression by escaping from underneath the AFM tip [838][839][840][841]. This escaping of chains is not only effective in the mushroom regime [842] but also in the brush regime [843].…”

Partition function, metastability, and kinetics of the escape transition for an ideal chain

“…The goal of this paper is to present a rigorous analytical theory for a phase transition in a single macromolecule that has received much attention recently, namely the escape transition observed for an end-tethered chain compressed between two pistons [8][9][10][11][12][13][14][15][16][17][18]. At weak compressions, the chain is deformed uniformly to make a relatively thick pancake; the resistance force due to the compressed chain increases monotonously as the distance between two pistons, H, decreases.…”

“…The equilibrium properties of the escape transition were investigated thoroughly by scaling theory [8,9], numerical calculations [10,15], and computer modeling [13,14,18]. The main result relates the critical compression distance H * to the piston radius, L, and the chain length, Na.…”

“…For ideal chains, it is given by H * ϳ Na / L. Excluded-volume interactions change the relationship between H * and the N / L ratio, H * ϳ͑Na / L͒ /͑1− ͒ , where Ϸ 3 / 5, but the nature of the transition remains the same [8,9]. In their pioneering paper based on the blob picture of the compressed and escaped phases, Subramanian et al [8,9] predicted the possibility of metastable states and indicated the broad range of parameters within which these states exist. They also indicated that the free energy barrier to be overcome by a compressed chain in order to escape is due to the elastic free energy invested in the stretching.…”

Compression and Escape of a Star Polymer

“…For example, we can alternatively employ an approximate scaling approach or "blobology" instead of the Flory approach, as has been done in the simpler end-tethered squashing problem. 3,4 However the adoption of blobology would not change the qualitative results as can be demonstrated by redoing the end-tethered problem in Subramanian et al 3,4 using the Flory approach. We acknowledge that by using the size R of the nucleus as a minimization variable (rather than performing a functional minimization to find the density distribution which in turn provides R) we imprecisely predict the size of the nucleus, R. However, as long as the radius of the compressing cylinders is sufficiently large, i.e., we choose L > R, then the inarguable qualitative results will remain the same: compression will result in multiple escapes and with each partial escape of an arm, the nucleus will decrease with size.…”