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)
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
(Eulers
(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?
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
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
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