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Different models of polymer entanglement. (A) Conceptualization of reptation of a polymer chain (P) in the presence of fixed obstacles, as theorized by de Gennes. The chain can freely move between the fixed obstacles but is not allowed to cross any of them. The fixed obstacles are shown by black circles, and the linear polymer chain is shown by a black strand. The grey dashed lines and curves describe the polymer network. (B) Conceptualization of reptation of an infinitely
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Biomolecular condensation and phase separation are increasingly understood to play crucial roles in cellular compartmentalization and spatiotemporal regulation of cell machinery implicated in function and pathology. A key aspect of current research is to gain insight into the underlying physical mechanisms of these processes. Accordingly, concepts...
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... basic idea is that because polymer chains cannot cross through each other (without breaking bonds), under the above conditions, any polymer chain can be viewed as existing within a set of obstacles made up of all the other polymer chains surrounding it. A theory for this situation was developed by de Gennes for polymer motion in an environment of fixed obstacles such as crosslinked gels [39,61] and is illustrated in Figure 4A. Lateral motions of the polymer chain are, therefore, difficult because they are constrained by this crosslinked or entangled matrix of obstacles (in the original paper, the obstacles do not move). ...
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... model by de Gennes provided several predictions, including that the translational diffusion constant of the chain would scale as M −2 (very small for larger polymers; M is the polymer molecular weight; compare to a predicted M −0.33 scaling for a spherical particle following the Stokes-Einstein equation). Edwards and Doi developed the related tube model ( Figure 4B), in which the dynamics of the polymer chain are restricted within a tube formed by the (mean field of the) surrounding entangled chains, as discussed above, and similarly resulting in a reptation motion [62][63][64]. The early papers by Edwards et al. also made interesting predictions, including that the viscosity of entangled polymer solutions should follow a M 3 scaling law (M is the polymer molecular weight), which rapidly increases for longer polymers [63]. ...
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... Rubinstein, and Colby demonstrated a sticky reptation model for the dynamics of entangled networks possessing several temporary crosslinks [38]. Figure 4C depicts a fundamental process of chain diffusion in a reversible gel governed by sticker-sticker interactions, as proposed by Leibler, Rubinstein, and Colby. According to this model, a closed sticker that belongs to the crosslink I (yellow circle) between the chains P (black) and P 1 (dark gold) is allowed to move distances of the order of the confining tube diameter. ...
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... the crosslink I opens, the free sticker moves. If it is assumed that the equilibration time of the strand CD is shorter than the lifetime of the open sticker, and the sticker C and D remains closed within this timescale, the sticker would either recombine with chain P 1 at the crosslink I, resulting in zero net displacements, or it would associate with a different chain P 2 (purple), resulting in the formation of a new crosslink F (yellow circle) ( Figure 4C) [38]. During the process from breaking crosslink I to making the crosslink F, the center of mass of the section of chain P moves to a new average position with the assumption that the stickers remain closed during the equilibration of the strand. ...
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