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Rouse Mode Analysis of Chain Relaxation in Homopolymer Melts.

Kalathi JT, Kumar SK, Rubinstein M, Grest GS - Macromolecules (2014)

Bottom Line: We analyze the resulting trajectories using the Rouse modes of the chains and find that entanglements strongly affect these modes.The monomeric relaxation rates of longer modes vary approximately inversely with chain length due to kinetic confinement effects.None of these trends are found in models that allow for chain crossing.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemical Engineering, Columbia University , New York, New York 10027, United States.

ABSTRACT
We use molecular dynamics simulations of the Kremer-Grest (KG) bead-spring model of polymer chains of length between 10 and 500, and a closely related analogue that allows for chain crossing, to clearly delineate the effects of entanglements on the length-scale-dependent chain relaxation in polymer melts. We analyze the resulting trajectories using the Rouse modes of the chains and find that entanglements strongly affect these modes. The relaxation rates of the chains show two limiting effective monomeric frictions, with the local modes experiencing much lower effective friction than the longer modes. The monomeric relaxation rates of longer modes vary approximately inversely with chain length due to kinetic confinement effects. The time-dependent relaxation of Rouse modes has a stretched exponential character with a minimum of stretching exponent in the vicinity of the entanglement chain length. None of these trends are found in models that allow for chain crossing. These facts, in combination, argue for the confined motion of chains for time scales between the entanglement time and their ultimate free diffusion.

No MeSH data available.


Chain crossing(CC) model: (a) Effective monomeric relaxation ratesof melts of different chain lengths with kθ = 0.75ε. (b) Comparison of effective monomeric relaxationrates of chains with different lengths between CC model (upper setof curves) and KG model (lower set of curves). (c) Effective relaxationtimes of chains in melts for different chain length for kθ = 0.75ε. (d) Stretching parameter βp for melts with CC chains of different lengths.
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fig4: Chain crossing(CC) model: (a) Effective monomeric relaxation ratesof melts of different chain lengths with kθ = 0.75ε. (b) Comparison of effective monomeric relaxationrates of chains with different lengths between CC model (upper setof curves) and KG model (lower set of curves). (c) Effective relaxationtimes of chains in melts for different chain length for kθ = 0.75ε. (d) Stretching parameter βp for melts with CC chains of different lengths.

Mentions: Results for the chain-crossing (CC)model are shown in Figure 4. In the CC model,chain relaxations are Rouse-like for any given N astopological constraints are eliminated by chain crossing. The effectivemonomeric relaxation rates are constant for N/p > 5 (Figure 4a). For smaller N/p, the results are similar to those forthe KG model (Figure 4b). The effective relaxationtimes for different length scales fall on a master curve which scalesas τp ∼ (N/p)2 (especially for small p) as shown in Figure 4c. The stretching exponentβp monotonically increases with N/p (see Figure 4d) as for unentangled noncrossing chains (Figure 3e). Comparison of the CC chains to the chains that cannotcross (Figure 4b) clearly shows that entanglementsaffect the relaxation starting at the intermediate length scales around Ne. The extent of the effect depends on N as Weff decreases graduallywith N/p in the KG model, whereasit is constant in the CC model. For large N/p, the plateau in Weff for theCC model shows that it better satisfies the assumptions inherent inthe Rouse model than the KG model. The much lower plateau values of Weff for the entangled chains clearly show thatthe presence of topological constraints serve to significantly slowdown chain motion.


Rouse Mode Analysis of Chain Relaxation in Homopolymer Melts.

Kalathi JT, Kumar SK, Rubinstein M, Grest GS - Macromolecules (2014)

Chain crossing(CC) model: (a) Effective monomeric relaxation ratesof melts of different chain lengths with kθ = 0.75ε. (b) Comparison of effective monomeric relaxationrates of chains with different lengths between CC model (upper setof curves) and KG model (lower set of curves). (c) Effective relaxationtimes of chains in melts for different chain length for kθ = 0.75ε. (d) Stretching parameter βp for melts with CC chains of different lengths.
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Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4196748&req=5

fig4: Chain crossing(CC) model: (a) Effective monomeric relaxation ratesof melts of different chain lengths with kθ = 0.75ε. (b) Comparison of effective monomeric relaxationrates of chains with different lengths between CC model (upper setof curves) and KG model (lower set of curves). (c) Effective relaxationtimes of chains in melts for different chain length for kθ = 0.75ε. (d) Stretching parameter βp for melts with CC chains of different lengths.
Mentions: Results for the chain-crossing (CC)model are shown in Figure 4. In the CC model,chain relaxations are Rouse-like for any given N astopological constraints are eliminated by chain crossing. The effectivemonomeric relaxation rates are constant for N/p > 5 (Figure 4a). For smaller N/p, the results are similar to those forthe KG model (Figure 4b). The effective relaxationtimes for different length scales fall on a master curve which scalesas τp ∼ (N/p)2 (especially for small p) as shown in Figure 4c. The stretching exponentβp monotonically increases with N/p (see Figure 4d) as for unentangled noncrossing chains (Figure 3e). Comparison of the CC chains to the chains that cannotcross (Figure 4b) clearly shows that entanglementsaffect the relaxation starting at the intermediate length scales around Ne. The extent of the effect depends on N as Weff decreases graduallywith N/p in the KG model, whereasit is constant in the CC model. For large N/p, the plateau in Weff for theCC model shows that it better satisfies the assumptions inherent inthe Rouse model than the KG model. The much lower plateau values of Weff for the entangled chains clearly show thatthe presence of topological constraints serve to significantly slowdown chain motion.

Bottom Line: We analyze the resulting trajectories using the Rouse modes of the chains and find that entanglements strongly affect these modes.The monomeric relaxation rates of longer modes vary approximately inversely with chain length due to kinetic confinement effects.None of these trends are found in models that allow for chain crossing.

View Article: PubMed Central - PubMed

Affiliation: Department of Chemical Engineering, Columbia University , New York, New York 10027, United States.

ABSTRACT
We use molecular dynamics simulations of the Kremer-Grest (KG) bead-spring model of polymer chains of length between 10 and 500, and a closely related analogue that allows for chain crossing, to clearly delineate the effects of entanglements on the length-scale-dependent chain relaxation in polymer melts. We analyze the resulting trajectories using the Rouse modes of the chains and find that entanglements strongly affect these modes. The relaxation rates of the chains show two limiting effective monomeric frictions, with the local modes experiencing much lower effective friction than the longer modes. The monomeric relaxation rates of longer modes vary approximately inversely with chain length due to kinetic confinement effects. The time-dependent relaxation of Rouse modes has a stretched exponential character with a minimum of stretching exponent in the vicinity of the entanglement chain length. None of these trends are found in models that allow for chain crossing. These facts, in combination, argue for the confined motion of chains for time scales between the entanglement time and their ultimate free diffusion.

No MeSH data available.