Crumpled globule formation during collapse of a long flexible and semiflexible polymer in poor solvent

Abstract

By introducing explicit solvent particles and hydrodynamic interactions we demonstrate that crumpled globules are formed after the collapse of long polymer chains (N = 10(4)) in a poor solvent. During the collapse crumples of all sizes form sequentially, but small crumples are not stable and convert to blobs with Gaussian statistics. The observed effective mean squared distance R(2)(n) ∼ n(0.38) at n > Ne and contact probability index p(n) ∼ n(-0.5) at n ≫ Ne, which is not following either the model of a fractal globule, or the predictions for an equilibrium globule. Polymer chain stiffness pushes the system to form globular crystallite, and this freezes crumpled structure with R(2)(n) ∼ n(0.33) at n > Ne as a stable state. We note that there is some similarity to crumple globule formation and crystallization of polymer melt.

Effects of topological constraints on globular polymers

“…Recent computational studies examined the role of topological constraints in the non-equilibrium (or quasiequilibrium) polymer states that emerge upon polymer collapse [15][16][17][18][19]. This non-equilibrium state, often referred to as the fractal globule [6,15], can indeed possess some properties of the conjectured equilibrium crumpled globule.…”

Coalescence Model for Crumpled Globules Formed in Polymer Collapse

“…The end-to-end distance r m of segments of length m in the resulting globule is predicted to scale as r m ∼ m 1=d in d space dimensions (throughout the Letter d ¼ 3). This is in contrast to the equilibrium state reached at much later times [10], where r m ∼ m 1=2 for small m, saturating at the globule size r max ¼ N 1=d , where N is the length of the polymer [21].These predictions have been tested in several simulations of polymer compaction [2,[4][5][6]11], which generally confirm that the rapidly collapsed state is not entangled, and is indeed different from the equilibrium globule. However, they do not agree upon its fractal nature.…”

“…These predictions have been tested in several simulations of polymer compaction [2,[4][5][6]11], which generally confirm that the rapidly collapsed state is not entangled, and is indeed different from the equilibrium globule. However, they do not agree upon its fractal nature.…”

“…The large finite-size effects are at least partly explained by partial mixing of short polymer segments, for which the topological constraints do not apply [1,[15][16][17][18][19][20]22]. More generally, various protocols for constructing crumpled globules have been suggested [2,[4][5][6]12,22], and it is not clear if the different procedures yield the same state. Settling these issues seems to require even larger simulations, or new theoretical insights.…”

“…The rapid collapse of a polymer into a dense globule is a long-standing problem [1][2][3][4][5][6][7][8][9][10][11][12]. Such a collapse may be triggered by changes in solvent quality, causing the polymer to reduce its solvent-exposed surface area by forming a dense globule.…”