Materials for the short course

“Entangled polymer dynamics”

Alexei Likhtman, January 5-9, 2009

 

Lectures 1-2 : Introduction and Experimental techniques

 

lecture1_exp_handouts.pdf– slides for review of experimental techniques

rheology.pdf – Introduction to rheology

mcleish_review.pdf – review of Tom Mcleish, 2002

watanabe_review.pdf – Review of Hiroshi Watanabe, 1999

 

Lecture1 video (reduced size) – right click on the link and save to your computer.

Lecture2 video (reduced size)

 

Lectures 3-4 : Rouse model and computer simulations techniques

 

rouse.pdf – Detailed Rouse model description

RepTate.zip – installation of Reptate software – unpack it into \program files\reptate folder and run reptate.exe. You can associate *.gt, *.osc, *.tts and *.shear files with it.

uview.zip – universal viewer – to view simulation data, associate a particular extension with uview.exe and have ini file in the same directory as the data.

rouse.zip – Rouse Brownian dynamics simulation program – updated at 3.02pm on Tuesday – now all 4 methods

(Euler’s (step_bd), predictor-corrector (step_pc), Monte-Carlo (step_mc) and smart Monte-Carlo (step_smc) are working and produce identical results in the limit of dt->0. However the convergence is very different.

lecture3sm.wmv– Video

lecture4sm.wmv- Video

Problems: 

1.      Calculate center of mass mean square displacement in Rouse model and compare with simulation results

2.      Calculate middle monomer displacement in Rouse model and compare with simulation results – consider three regimes of time

3.      Read the note rouse.pdf (above) and study derivation of stress relaxation. Correct mistakes.

4.      Run the simulations with different bond potential U(i,i+1)=k/2(|R|-1)^2 and analyze the results: what difference can you see, what are the dependences on N and k (do not forget to reduce your timestep dt~1/k)

5.      Same, but for potential for semiflexible chain, where force on particle i is
f_i=3(R[i+1]+ R[i-1]-2*R[i])+3k_b*( R[i+2]-4R[i+1]+6 R[i]-4 R[i-1]+ R[i-2])

6.      (Advanced: Jing, Bart, Shukor, Tim – you can attempt this). Calculate Rouse modes and Introduce correlators for them, show that slow modes (p=1,2,3) are still uncoupled even for complicated potentials. You can calculate for example <X_1(t) X_3(0)>, <X_2(t) X_4(0)> and compare them with <X_N(t) X_{N-2}(0)>. Use cross-correlators to compute these.

7.      Investigate convergence of 4 different algorithms in the program by plotting some particular value as a function of dt or dt^2. Which algorithm is the best?

 

Lectures 5-6: Tube theory: pure reptation model

 

md_results.pdf – slides with molecular dynamic results, showing regimes where Rouse model is valid, and where entanglements have to be modeled.

Problems: 

In simulation program rouse.cc, add this step for pure reptation and investigate all observables as a function of molecular weight.

void step_rep()    // pure reptation step

{ int i,j;tp3 f,v; double s3i=1/sqrt(3.);   

     dt=(n+1);

    ntt++;//=int(floor((n+1)/dt));

     for(j=0;j<nc;j++){

           if(mtrand1.randExc(1)<0.5){  //step to the left

                for(i=n;i>0;i--)r[j][i]=r[j][i-1];

                addgau(r[j][1],&r[j][0],s3i);

           }else{                               //step to the right

                for(i=0;i<n;i++)r[j][i]=r[j][i+1];

                addgau(r[j][n-1],&r[j][n],s3i);

           }

     }

     if(ntt%ndt==0) calc();

}

 

lecture5sm.wmv Video

lecture6sm.wmv Video

Lectures 7-8: Tube theory: contour length fluctuations (CLF) and constraint release (CR)

 

rouse_clf.cc – simulation program of reptation+CLF model

clf_results.zip  - results of simulations of reptation+CLF model

clf_rep.pdf – slides from the presentation

Problems: 

1.      Analyze CLF results – different N, dt, Ne. Summarize dependence of observables in different regimes on N and Ne in a table.

2.      Change the model to allow variable tube segment length by modifying add_u() function (just do not divide by modulus). Which observables change?

Do not forget that now you need to do more sophisticated algorithm for projection onto the tube – one more loop to find which monomer will sit on which tube segment. Try to do it in an efficient way.

lecture7sm.wmv- Video

lecture8sm.wmv– Video

Lectures 9-10: Slip-links, non-linear deformations

ccr.pdf – non-linear theory slides

slip-links.pdf – slides

 

lecture9sm.wmv Video

lecture10sm.wmv Video

 

 

 

my papers can be found here by clicking on the dot at the end of each reference.

 

Any questions – e-mail: A.Likhtman@reading.ac.uk