The Kirkwood-Riseman Polymer Model of Polymer Dynamics is Qualitatively Correct

Phillies, George D. J.

doi:10.48550/arxiv.1801.06247

Cited by 1 publication

(4 citation statements)

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“…(4) Contrary to the Rouse model, under shear, the response of a chain is to rotate, not to distort affinely without rotation [ 18 ].…”

Section: Discussionmentioning

confidence: 99%

“…The statement that the modes are orthogonal at all times so that

arises from the forces in the Rouse model, and is not equivalent to the equally correct statement that the Rouse coordinates are orthogonal. It is straightforward to make a modest modification of the Rouse model such that some modes become cross correlated, namely, one applies to the molecule a time-independent external shear field [ 18 ].…”

Section: Models Of Polymer Dynamicsmentioning

confidence: 99%

“…For an isolated Rouse chain in a fluid with shear , this author previously showed from simulations that

can occur. In the presence of shear, one finds cross correlations for

and

[ 18 ].…”

Section: Models Of Polymer Dynamicsmentioning

confidence: 99%

“…To resolve this contradiction between the Rouse and Kirkwood–Riseman models, I made Brownian dynamics simulations on a single bead–spring polymer coil [ 18 ]. Hydrodynamic interactions were not included, so the random thermal forces on separate beads could be treated as being uncorrelated.…”

Section: General Tests Of the Rouse Modelmentioning

confidence: 99%

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Simulational Tests of the Rouse Model

Phillies

2023

Polymers

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An extensive review of literature simulations of quiescent polymer melts is given, considering results that test aspects of the Rouse model in the melt. We focus on Rouse model predictions for the mean-square amplitudes ⟨(Xp(0))2⟩ and time correlation functions ⟨Xp(0)Xp(t)⟩ of the Rouse mode Xp(t). The simulations conclusively demonstrate that the Rouse model is invalid in polymer melts. In particular, and contrary to the Rouse model, (i) mean-square Rouse mode amplitudes ⟨(Xp(0))2⟩ do not scale as sin−2(pπ/2N), N being the number of beads in the polymer. For small p (say, p≤3) ⟨(Xp(0))2⟩ scales with p as p−2; for larger p, it scales as p−3. (ii) Rouse mode time correlation functions ⟨Xp(t)Xp(0)⟩ do not decay with time as exponentials; they instead decay as stretched exponentials exp(−αtβ). β depends on p, typically with a minimum near N/2 or N/4. (iii) Polymer bead displacements are not described by independent Gaussian random processes. (iv) For p≠q, ⟨Xp(t)Xq(0)⟩ is sometimes non-zero. (v) The response of a polymer coil to a shear flow is a rotation, not the affine deformation predicted by Rouse. We also briefly consider the Kirkwood–Riseman polymer model.

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“…(4) Contrary to the Rouse model, under shear, the response of a chain is to rotate, not to distort affinely without rotation [ 18 ].…”

Section: Discussionmentioning

confidence: 99%

“…The statement that the modes are orthogonal at all times so that

Section: Models Of Polymer Dynamicsmentioning

confidence: 99%

“…For an isolated Rouse chain in a fluid with shear , this author previously showed from simulations that

can occur. In the presence of shear, one finds cross correlations for

and

[ 18 ].…”

Section: Models Of Polymer Dynamicsmentioning