Reptate entangled

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Reptate entangled Powered By Docstoc
 Masayuki Okura
  Rheology of Entangled Polymers: Toolkit for Analysis of Theory & Experiment

Reptate is a software package for
viewing, exchanging and analysing
rheological data. Several of the
classical and latest theories of
polymer dynamics are included in
Reptate, so they can be tested and
fitted to the experimental data.

Reptate works under Windows and is provided for free. You can get
the installation package from the downloads page. If you want to
know more about the features of Reptate, or want to learn how to
use the software, check the documentation.
•   Data format
•   Time-Temperature Superposition
•   Linear theory
•   Rolie-Poly theory
•   Rubinstein-Colby theory
                 Data format
– angular frequency, G' and G" data (steady shear)
– text file, tab deliminated
– extension is “osc”

                        unit is °C        unit is kDa
         ang. frequency G'     G'' temperature   strain
         408.8      1.98E+06   2.83E+05 120 2.97E-03
         278.5      1.87E+06   3.10E+05 120 2.99E-03
         189.7      1.76E+06   3.50E+05 120 3.01E-03
         129.3      1.67E+06   4.00E+05 120 3.01E-03
         88.07      1.56E+06   4.60E+05 120 3.04E-03

                Sample.txt   <- double click to open
Time-Temperature Superposition
                                              click here to read data files

                          Input initial parameter
                          or choose data set
                                             then click here to start TTS
                          (for polyolefin and polystyrene)

                               optimized parameters
                          Then, click here to fit the data
   Also you can calculate (click the checkbox of C3 if
         you can calculate G’this G” at any temperature
   viscosity curve by clicking want to use vertical shift)

                                                    aT: shift parameter
                                                    C1, C2: WLF parameters
     |h*|: complex viscosity                        T: reference temperature
     w: angular frequency
                      Linear theory
• Simulate rheology of linear polymer
• Calculate relaxation times of linear polymers by using
  rheology data of low-polydisperse sample
• based on Reptation model by Doi-Edwards
• Correction for single chain problem
   – Contour Length Fluctuation
   – Constraint release

*Likhtman, A. E.; McLeish, T. C. B.
Macromolecules 2002, 35, 6332-6343.
Reptation (Doi-Edwards model )

R(s, t  t )  R(s   (t ), t )
 1-d diffusion along the tube contour
 Escape time from the tube ~M3
                                  Richard Graham 2006 for mupp2
Contour Length Fluctuations

                 Beads contract due to thermal
                 fluctuations (“breathe in”) and some
                 tube is lost.

                  When the beads expand (“breathe
                  out”) they are free to explore new

                     Richard Graham 2006 for mupp2
                    Constraint release
                                                                   •Constraints are not
                                                                   permanent objects.
                                                                   •Motion of the chain
                                                                   ends can release

Constraint release is a local jump motion. This is equivalent to Rouse-like motion of the
tube. The hop distance depends on the tube diameter.

                                                         Richard Graham 2006 for mupp2
                               Linear theory
                                Mw range: 1kDa – 5MDa

Likhtman, A.E. and McLeish, T.C.B., Quantitative Theory for Linear Dynamics of Linear Entangled
Polymers. Macromolecules, 2002. 35: p. 6332-6343.
Molecular weight                   Stress              vs             Time

                                Ge: Shear modulus of            e: Rouse relaxation
   Me: Molecular                a rubber with cross-            time of a free chain of
   weight between               linking density Me.             length Me.


                                                              Time for a chain of
                                                              length Me to diffuse its
All molecular weights                                         own radius.
                                 All stresses are
are scaled by Me to give
                                 proportional to Ge.          All timescales are
the number of
entanglements, Z.                                             proportional to e
                                                            Richard Graham 2006 for mupp2
             Constraint release parameter
          c controls the strength of constraint release.

                                                                        One CR event
Are entanglements
                                                                        causes a tube
binary interactions…
                                                                        (c =1)

 … or are they                                                         Several CR events
 from delocalized                                                      are needed for a
 interactions with                                                     tube hop
 many chains?                                                          (c <1)

                                    We suggest c =0.1
                                                            Richard Graham 2006 for mupp2
               Linear theory

Import data from TTS module
After the TTS procedure,
hPBD 442 kDa
Open Linear Viscoelasticity module
close Reptate and open viscoelastic module again

                                save the result to file
                                             load created data files
                            Input initial parameter
                            (or kDa
                     hPBD 147choose from the list)
                            Then, from data
             Choose Linear theory fit thedropdown box
             Then, click this

                                    fitted parameters

                                    You can find R and d from this box
     Calculation of Relaxation times
You can calculate the relaxation times of any Mw at any temperature.

                                              input LVE parameters

                                                 TTS parameters
                          Rolie-Poly theory
• estimate relaxation behavior in non-steady shear region
  by using rheology data of low-polydisperse sample

                  Mw = 1080 kDa

*Likhtman, A. E.; Graham, R. S. Journal of Non-Newtonian Fluid Mechanics 2003, 114, 1-12.
                   Rubinstein-Colby theory
  • Simulate rheology of the bimodal blend from
    LVE parameters.

                                      2 wt % 1700 kDa in 7 kDa

                                              2 wt % 1700 kDa
                                              in 18 kDa

            2 wt % 1700 kDa in 52 kDa
                        2 wt % 1700 kDa in 142 kDa

when the difference of Mw between long chains and short chains is big, it does not work.
Manual (Embedded)

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