### Abstract

The effects of polydispersity on the linear viscoelastic properties of concentrated polymer solutions and melts are analyzed. Existing theories for the dynamics of linear polymers, based on the idea of each polymer confined in a fixed tube, are shown to be incapable of describing observed rheological response of polydisperse polymers. A model is proposed which, in a self-consistent manner, solves the many chain problem given the solution to the single chain problem. Two types of polymer relaxation are incorporated in the model. The first type is escape of a polymer from its tube by motion of the polymer itself. It includes all dynamic modes available to the single chain in a tube-those due to its reptation-as well as other modes, such as fluctuations in tube length. The second type is relaxation of a polymer chain by the motions of the surrounding polymers forming its tube (constraint release). The relaxation modulus is then the product of two functionsμ(t) and R(t). μ(t) is the fraction of tube occupied at time t = 0 that has not been evacuated at time t, thereby representing escape of the polymer from its tube (solution to the single chain problem). R(t) represents relaxation by the constraint release process, which is modeled by a Rouse chain with random bead mobilities. The probability distribution of these mobilities is determined, in a self-consistent way, from the disentanglement rates due to the tube evacuation processes of the surrounding chains. Thus R(t) is calculated from the spectrum of relaxation rates of the μ(t) processes for the surrounding chains. The predictions of the model with some single chain solutions μ(t) from the literature are compared with oscillatory shear data for binary blends of nearly monodisperse polybutadiene, in which both components are well entangled.

Original language | English (US) |
---|---|

Pages (from-to) | 5291-5306 |

Number of pages | 16 |

Journal | The Journal of Chemical Physics |

Volume | 89 |

Issue number | 8 |

DOIs | |

State | Published - Jan 1 1988 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*The Journal of Chemical Physics*,

*89*(8), 5291-5306. https://doi.org/10.1063/1.455620

}

*The Journal of Chemical Physics*, vol. 89, no. 8, pp. 5291-5306. https://doi.org/10.1063/1.455620

**Self-consistent theory of polydisperse entangled polymers : Linear viscoelasticity of binary blends.** / Rubinstein, Michael; Colby, Ralph H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Self-consistent theory of polydisperse entangled polymers

T2 - Linear viscoelasticity of binary blends

AU - Rubinstein, Michael

AU - Colby, Ralph H.

PY - 1988/1/1

Y1 - 1988/1/1

N2 - The effects of polydispersity on the linear viscoelastic properties of concentrated polymer solutions and melts are analyzed. Existing theories for the dynamics of linear polymers, based on the idea of each polymer confined in a fixed tube, are shown to be incapable of describing observed rheological response of polydisperse polymers. A model is proposed which, in a self-consistent manner, solves the many chain problem given the solution to the single chain problem. Two types of polymer relaxation are incorporated in the model. The first type is escape of a polymer from its tube by motion of the polymer itself. It includes all dynamic modes available to the single chain in a tube-those due to its reptation-as well as other modes, such as fluctuations in tube length. The second type is relaxation of a polymer chain by the motions of the surrounding polymers forming its tube (constraint release). The relaxation modulus is then the product of two functionsμ(t) and R(t). μ(t) is the fraction of tube occupied at time t = 0 that has not been evacuated at time t, thereby representing escape of the polymer from its tube (solution to the single chain problem). R(t) represents relaxation by the constraint release process, which is modeled by a Rouse chain with random bead mobilities. The probability distribution of these mobilities is determined, in a self-consistent way, from the disentanglement rates due to the tube evacuation processes of the surrounding chains. Thus R(t) is calculated from the spectrum of relaxation rates of the μ(t) processes for the surrounding chains. The predictions of the model with some single chain solutions μ(t) from the literature are compared with oscillatory shear data for binary blends of nearly monodisperse polybutadiene, in which both components are well entangled.

AB - The effects of polydispersity on the linear viscoelastic properties of concentrated polymer solutions and melts are analyzed. Existing theories for the dynamics of linear polymers, based on the idea of each polymer confined in a fixed tube, are shown to be incapable of describing observed rheological response of polydisperse polymers. A model is proposed which, in a self-consistent manner, solves the many chain problem given the solution to the single chain problem. Two types of polymer relaxation are incorporated in the model. The first type is escape of a polymer from its tube by motion of the polymer itself. It includes all dynamic modes available to the single chain in a tube-those due to its reptation-as well as other modes, such as fluctuations in tube length. The second type is relaxation of a polymer chain by the motions of the surrounding polymers forming its tube (constraint release). The relaxation modulus is then the product of two functionsμ(t) and R(t). μ(t) is the fraction of tube occupied at time t = 0 that has not been evacuated at time t, thereby representing escape of the polymer from its tube (solution to the single chain problem). R(t) represents relaxation by the constraint release process, which is modeled by a Rouse chain with random bead mobilities. The probability distribution of these mobilities is determined, in a self-consistent way, from the disentanglement rates due to the tube evacuation processes of the surrounding chains. Thus R(t) is calculated from the spectrum of relaxation rates of the μ(t) processes for the surrounding chains. The predictions of the model with some single chain solutions μ(t) from the literature are compared with oscillatory shear data for binary blends of nearly monodisperse polybutadiene, in which both components are well entangled.

UR - http://www.scopus.com/inward/record.url?scp=36549090668&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36549090668&partnerID=8YFLogxK

U2 - 10.1063/1.455620

DO - 10.1063/1.455620

M3 - Article

AN - SCOPUS:36549090668

VL - 89

SP - 5291

EP - 5306

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 8

ER -