Dynamics of chains grafted on solid wall during polymer melt extrusion

M.A. Tchesnokov, J. Molenaar, J.J.M. Slot

Research output: Book/ReportReportProfessional

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Abstract

The objective of the present work is the mathematical modeling of the dynamics of polymer molecules grafted on a solid boundary during polymer melt extrusion. This topic is closely related to the long-standing problem of polymer flow instabilities encountered in industry when extruding melts. In order to describe the behavior of the tethered chains, we introduce the bond vector probability distribution function (BVPDF) which appears to be a simple, yet effective mathematical 'tool'. The bond vector, i.e. the tangent vector to a polymer chain depending on the position along the chain and on time, describes the local geometry via its direction and the local stretching of the chain via its length. The BVPDF contains all information about the geometry of the ensemble of chains. Via averaging over the BVPDF we can calculate all interesting macrsocopic quantities, e.g. the thickness of and stress in the layer of tethered molecules. The time dependence of the BVPDF yields the time evolution of the system. We derive the equation of motion for the BVPDF taking into account all important mechanisms, such as reptation and (convective) constraint release. Besides that, we show that all macroscopic quantities of practical interest can be expressed via second order moments of this distribution function.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages17
ISBN (Print)0169-2690
Publication statusPublished - 2003

Publication series

NameMemorandum
PublisherDepartment of Applied Mathematics, University of Twente
No.1673
ISSN (Print)0169-2690

Keywords

  • MSC-35K55
  • IR-65858
  • METIS-211690
  • MSC-35Q35
  • MSC-76D10
  • MSC-65P40
  • MSC-60G15
  • EWI-3493
  • MSC-76A10

Cite this

Tchesnokov, M. A., Molenaar, J., & Slot, J. J. M. (2003). Dynamics of chains grafted on solid wall during polymer melt extrusion. (Memorandum; No. 1673). Enschede: University of Twente, Department of Applied Mathematics.
Tchesnokov, M.A. ; Molenaar, J. ; Slot, J.J.M. / Dynamics of chains grafted on solid wall during polymer melt extrusion. Enschede : University of Twente, Department of Applied Mathematics, 2003. 17 p. (Memorandum; 1673).
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Tchesnokov, MA, Molenaar, J & Slot, JJM 2003, Dynamics of chains grafted on solid wall during polymer melt extrusion. Memorandum, no. 1673, University of Twente, Department of Applied Mathematics, Enschede.

Dynamics of chains grafted on solid wall during polymer melt extrusion. / Tchesnokov, M.A.; Molenaar, J.; Slot, J.J.M.

Enschede : University of Twente, Department of Applied Mathematics, 2003. 17 p. (Memorandum; No. 1673).

Research output: Book/ReportReportProfessional

TY - BOOK

T1 - Dynamics of chains grafted on solid wall during polymer melt extrusion

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PY - 2003

Y1 - 2003

N2 - The objective of the present work is the mathematical modeling of the dynamics of polymer molecules grafted on a solid boundary during polymer melt extrusion. This topic is closely related to the long-standing problem of polymer flow instabilities encountered in industry when extruding melts. In order to describe the behavior of the tethered chains, we introduce the bond vector probability distribution function (BVPDF) which appears to be a simple, yet effective mathematical 'tool'. The bond vector, i.e. the tangent vector to a polymer chain depending on the position along the chain and on time, describes the local geometry via its direction and the local stretching of the chain via its length. The BVPDF contains all information about the geometry of the ensemble of chains. Via averaging over the BVPDF we can calculate all interesting macrsocopic quantities, e.g. the thickness of and stress in the layer of tethered molecules. The time dependence of the BVPDF yields the time evolution of the system. We derive the equation of motion for the BVPDF taking into account all important mechanisms, such as reptation and (convective) constraint release. Besides that, we show that all macroscopic quantities of practical interest can be expressed via second order moments of this distribution function.

AB - The objective of the present work is the mathematical modeling of the dynamics of polymer molecules grafted on a solid boundary during polymer melt extrusion. This topic is closely related to the long-standing problem of polymer flow instabilities encountered in industry when extruding melts. In order to describe the behavior of the tethered chains, we introduce the bond vector probability distribution function (BVPDF) which appears to be a simple, yet effective mathematical 'tool'. The bond vector, i.e. the tangent vector to a polymer chain depending on the position along the chain and on time, describes the local geometry via its direction and the local stretching of the chain via its length. The BVPDF contains all information about the geometry of the ensemble of chains. Via averaging over the BVPDF we can calculate all interesting macrsocopic quantities, e.g. the thickness of and stress in the layer of tethered molecules. The time dependence of the BVPDF yields the time evolution of the system. We derive the equation of motion for the BVPDF taking into account all important mechanisms, such as reptation and (convective) constraint release. Besides that, we show that all macroscopic quantities of practical interest can be expressed via second order moments of this distribution function.

KW - MSC-35K55

KW - IR-65858

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KW - MSC-35Q35

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KW - MSC-65P40

KW - MSC-60G15

KW - EWI-3493

KW - MSC-76A10

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BT - Dynamics of chains grafted on solid wall during polymer melt extrusion

PB - University of Twente, Department of Applied Mathematics

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Tchesnokov MA, Molenaar J, Slot JJM. Dynamics of chains grafted on solid wall during polymer melt extrusion. Enschede: University of Twente, Department of Applied Mathematics, 2003. 17 p. (Memorandum; 1673).