Presentation on theme: "Entanglements and stress correlations in coarsegrained molecular dynamics Alexei E. Likhtman, Sathish K. Sukumuran, Jorge Ramirez Department of Applied."— Presentation transcript:
Entanglements and stress correlations in coarsegrained molecular dynamics Alexei E. Likhtman, Sathish K. Sukumuran, Jorge Ramirez Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
Hierarchical modelling in polymer dynamics Constitutive equations –Tube theories Single chain models –Coarse-grained many-chains models »Atomistic simulations > Quantum mechanics simulations Kremer-Grest MD, Padding-Briels Twentanglemets, NAPLES Well established coarse- graining procedures, force-fields, commercial packages Traditional rheology Traditional physics CR Tube Model? The weakest link
The missing link Many chains system + self-consistent field One chain model The ultimate goal: Stochastic equation of motion for the chain in self-consistent entanglement field
Is there a tube model? Best definition of the tube model: one-dimensional Rouse chain projected onto three-dimensional random walk tube. Open questions: Can I have expression for the tube field, please? How to “measure” tube in MD? Is the tube semiflexible? Diameter = persistence length? Branch point motion How does the contour length changes with deformation? Tube parameters for different polymers? Tube parameters for different concentrations?
Rubinstein-Panyukov network model Rubinstein and Panyukov, Macromolecules 2002, 6670
Construction of the model
Constraint release Hua and Schieber 1998 Shanbhag, Larson, Takimoto, Doi 2001
A.E.Likhtman, Macromolecules 2005
2k 6k 12k M w mat Rouse Relaxation of dilute long chains (36K) in a short matrix: constraint release M.Zamponi et al, PRL 2006 labeled
Molecular Dynamics -- Kremer-Grest Polymers – Bead-FENE spring chains With excluded volume – Purely repulsive Lennard-Jones interaction between beads k = 30 / 2 R 0 =1.5 Density, = 0.85 Friction coefficent, = 0.5 Time step, dt = Temperature, T = /k K.Kremer, G. S. Grest JCP (1990)
g1(t) from MD for N=100, /4 0.5 ee dd RR
g1(i,t)/t 0.5 from MD for N=350 g1(i,t)/t 0.5 ends middle t
G(t) from MD for N=50,100,200,350 (Ne~50) ee
G(t) from MD for N=50,100,200,350 (Ne~70) ee G(t) from MD for N=50,100,200,350 (Ne~50)
Questions for discussion Binary nature of entanglements? –Can one propose an experiment which contradicts this? Non-linear flows: – do entanglements appear in the middle of the chain? Is there an instability in monodisperse linear polymers?