Dynamics of polyelectrolytes and living polymers in shear flow P. - - PowerPoint PPT Presentation

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Dynamics of polyelectrolytes and living polymers in shear flow P. - - PowerPoint PPT Presentation

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Dynamics of polyelectrolytes and living polymers in shear flow P. B. Sunil Kumar Department of Physics, IIT Madras. 1 Tuesday 10 August 2010 Hydrophilic Hydrophobic (a) Spherical Micelle, (b) Cylindrical Micelle, (c) Reverse Micelle, (d)

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SLIDE 1

Dynamics of polyelectrolytes and living polymers in shear flow

  • P. B. Sunil Kumar

Department of Physics, IIT Madras.

1 Tuesday 10 August 2010

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SLIDE 2

Hydrophilic Hydrophobic

(a) Spherical Micelle, (b) Cylindrical Micelle, (c) Reverse Micelle, (d) Bilayer, (e) Hexagonal phase, (f) Vesicles

2

Cylindrical micelles also called living polymers Can undergo scission/recombination under thermal fluctuations

Tuesday 10 August 2010

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SLIDE 3

Shear banding

Lerouge et al. PRL, 81, 5457 (1998)

Shear induced gelation

Liu et al. PRL, 77, 2121 (1996)

Oscillating solid sphere

Jayaraman et al. PRE, 67, 65301 (2003)

Micellar solutions are examples of living polymers

Rheocaos : R. Bandyopadhyay, G. Basappa, and A. K. Sood, Phys. Rev. Lett. 84, 2022 (2000).

Tuesday 10 August 2010

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SLIDE 4

4

[8] Padding J T and Boek E S 2004 Europhys. Lett. 66 756 [9] Padding J T and Boek E S 2004 Phys. Rev. E 70 031502 [10] Kr¨

  • ger M and Makhloufi R 1996 Phys. Rev. E 53 2531

Padding and Boek (2004): Atomistic MD simulations erucate than for EHAC surfactants to compute the mechanical properties of atomistic micelles such as persistence length, elastic modulus and scission energy

[16] Boek E S, den Otter W K, Briels W J and Iakovlev D 2004 Phil. Trans. R. Soc. A 362 1625 [17] den Otter W K, Shkulipa S A and Briels W J 2003 J. Chem. Phys. 119 2363

MD simulations of micelles consisting of coarse-grained (CG) mode surfactants to optimize the CG model with respect to the structure factor S(q) of the atomistic micelle at large values of the wavevector q. The CG model is used to extrapolate the structure factor for small q in order to obtain reliable values for the micelle bending rigidity and persistence length . Padding, Boek and Briels ((2005): a mesoscopic model of wormlike micelles, represented by chains which can break and recombine and can be subjected to shear flow. For this model, where the smallest length-scale is the persistence length, the elastic modulus , scission energy and persistence length are taken as input parameter from the atomistic and CG MD.

Tuesday 10 August 2010

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SLIDE 5

Dissipative Particle Dynamics ( DPD) is a particle based “meso-fluid” model

Molecular Dynamics (MD) Special (DPD-)thermostat, #0&*+0+3(+."-2"0+%3$"1@ ! dissipative pair @1')+$ ! stochastic pair @1')+$

DPD (mesoscopic)

MD with special thermostat 8:1'A$"43.+'"+64#*#-'#40"B 313,+64#*#-'#40")13.#(#13$/ +C=C/"$5+%'#3=?

DC"E1..+0%33/"9C"FG3:+=/"%3."HC"H'+0+'/

  • Phys. Rev. E 68 8IJJK?"JLMNJI"

OP2.'1.23%0#) #3(+'%)(#13$Q 8@*1:"+@@+)($?"%'+"@4**2 (%A+3"#3(1"%))143(>

DPD beadsR '+&'+$+3(")*4$(+'$"1@" %(10$;01*+)4*+$/"1'" @*4#. +*+0+3($ ! !"#"$%&&'()*)+''($,-.$#"/"0"1"$2&(34,-5$Europhys. Lett. !" 67889:$7;; ! !"$<=>,?&3 ,-.$!"$@,))(-5$Europhys. Lett. #$ 6788;:$787

S'10"%"(+)53#)%* &1#3("1@"7#+:"CCC

Soft-repulsive +@@+)(#7+"con- servative pair @1')+$"-+(:++3" 313,-13.+."8F[F,?"-+%.$

Tuesday 10 August 2010

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SLIDE 6

DPD-­‑ ¡ ¡Basic ¡model

N "dpd" particles interacting via conservative, dissipative and random pair wise interactions

Dissipative & random forces related through fluctuation-dissipation theorem Pair-wise random and dissipative forces conserve momentum Resulting in correct description of hydrodynamics Soft interactions allow for longer time steps, and therefore much longer times can be probed via DPD as opposed to MD

  • P. J. Hoogerbrugge and J. M. V. A. Koelman, Europhys. Lett. 19, 155 (1992)

Tuesday 10 August 2010

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SLIDE 7

For, W – W, W – I W – A, I – I, I – A

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DPD model for living polymers ( LP)

For, A-A

r1 r3 r5

Tuesday 10 August 2010

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SLIDE 8

Uijk = k3(1 − ˆ rij · ˆ rjk)

The three-body bending potential

For LP For solvent

I1 – A’1 – A2 & A’1 – A2 – I2

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Three body potentials

  • Simulation box size L = 40 , Periodic Boundary Condition
  • density ρ = 3 , number of particles 192000
  • Resting length A-I = 1.0 , A-A = 2.0
  • Spring constant k = 200
  • Time step = 0.01 τ, with τ of the order of 10-6 sec

U3body = k3 2 (1 − rjk/r3)2(1 − ˆ rij.ˆ rjk)

for A1I1A1’ and A2I2A2’

  • S. Thakur et al Soft Matter 6, 489, 2010

Tuesday 10 August 2010

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SLIDE 9

Fluid-gel transition

C -- % ratio of number of monomers to the total number of particles Phase behavior was characterized by diffusivity of trimers

11

  • Fluid phase at low C
  • Gel phase at higher C
  • Transition point C = Cp = 3.5
  • Branched point ---- coordination number of particle is > 2

Tuesday 10 August 2010

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SLIDE 10

Organization of polymers

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C = 2 C = 3 C = 4 C = 5

Fluid Gel

Increasing C

Tuesday 10 August 2010

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SLIDE 11

Segment length distribution

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  • M. E. Cates and S. J. Candau, J. Phys 2,6869 (1990)

l Average polymer length Φ Monomer concentration

Branching reduces the average segment length

Cluster size distribution

  • Exponential distribution at low C <

Cp

  • Power law distribution at C = Cp:

random percolation

  • Gel phase contains spanning clusters

and small segments

branching of polymers lead to random percolation

Tuesday 10 August 2010

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SLIDE 12

Self-intermediate scattering function

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Diffusive at low q: Zimm dynamics at large q:

N: total number of monomers Relaxation time

  • S. Thakur et al Soft Matter 6, 489, 2010

Tuesday 10 August 2010

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SLIDE 13

First recombination time τR = scission time (t2 )–recombination time (t1 )

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td td td ts

Two classes of recombination kinetic: Mean field (MF) and Diffusion controlled (DC)

  • Ben O’ Shaughnessy and Jane Yu, PRL, 74, 4329 (1995)

Tuesday 10 August 2010

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SLIDE 14

0.01 0.1 1 10 0.1 1 10 100 G(t) t 0.01 0.1 1 10 0.1 1 10 100 G(t) t

stress relaxation

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  • G(t) decays as:
  • G. Faivre and J. L. Gardissat,

Macromolecule, 19, 1988 (1986)

  • We find a residual stress is due to the spanning clusters with stretched bonds
  • Early time oscillation is the result of bond potential within a trimer

C=3.0 C=4.0

Tuesday 10 August 2010

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SLIDE 15

Shear

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  • Density of wall = 20* Density of fluids
  • Periodic boundary in x & y directions
  • Results were verified using Lees-Edward method to rule out wall effect

V*

  • V*

x y z

Tuesday 10 August 2010

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SLIDE 16

Shear induced Lamellar phase

  • First layer forms near the

shear boundaries

  • All the polymers within a

range of r5 is pulled towards the boundary

  • Next layer forms exactly at a

distance r5 from the first

  • 19
  • S. Thakur et al Soft Matter 6, 489, 2010

Tuesday 10 August 2010

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SLIDE 17

Shear induced structures

18

y x z y x

  • Lamellar phase in the system with C = 5

Tuesday 10 August 2010

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SLIDE 18

Shear induced structures

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y x

  • Columnar phase in the system with C = 5
  • Layer spacing is decided by r5

y x z

Tuesday 10 August 2010

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SLIDE 19

Stress and viscosity

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  • Alignment of polymers leads to decrease in viscosity

Tuesday 10 August 2010

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SLIDE 20

0.01 0.1 1 10 100 1000 1 10 100 1000 10000

n(s) s

2% 2.5% 2.6% 2.75% 3% 4% 0.01 0.1 1 10 100 1000 1 10 100 1000 10000

n(s) s

2% 2.5% 3% 4% 5%

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Cluster size distribution for a tetramer building block. Percolation at 3% concentration Cluster size distribution for a pentamer building block. Percolation at 2.75% concentration For larger segments the percolation is at a lower concentration

Tuesday 10 August 2010

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SLIDE 21

1e-05 0.0001 0.001 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

D 1/C wt %

Trimer Tetramer Pentamer

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Diffusion coefficient as a function of concentration for different building blocks

Tuesday 10 August 2010

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SLIDE 22

a1 = a2 = 0.1

a1 = a2 = 0.1

a1 = a2 = 0.5

a1 = a2 = 1.0

a1 = a2 = 1.0

a1 = a2 = 1.0

Trimer Tetramer Pentamer

˙ γ = 1

Tuesday 10 August 2010

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SLIDE 23

!"#$%& '(()"'*+,-!"#$./01$)&$0,2+$)3"&2'24,5

!"#$%&'()*$ +,-.%'/)01-%$('")2$-2$(34)")$5-63%-7'%")4($-7')%5-6%3&-'-8'9/$((-.)5"%)+:")30; '((3/5-)0-7%)04)7($-"3-'.<:5"-"#$-=)0$&'")4-2)5435)",-53-"#'"-"#$-*"))$*2,6*+3722,0839$) >Sc :,;<= 63%-'-()?:).@-)5-3+"')0$.A

5,BC-DC-E3/$F-Europhys. Lett. >? !GHHHA-GIJ

@A0'37*'B,(')'3$2$) ! 'BB"#&,2",280$,2+$,C7&*"&72A

Higher Sc fluid ? Sc of DPD fluid is around 1 , while that for a real fluid is about 1000 !!

Tuesday 10 August 2010

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SLIDE 24

Sc=7, =1

˙ γ

E a r l y s t a g e s t e a d y s t a t e

Tuesday 10 August 2010

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SLIDE 25

Summary of living polymer results

  • A coarse grained model was developed for studying the dynamics of living

polymer solutions

  • The model, based on Dissipative Particle Dynamics, predicts a fluid to gel

transition as the concentration of polymer is increased

  • The self intermediate scattering function, scission and recombination kinetics

and stress correlation function shows that the model reproduces expected results.

  • We show the emergence of lamellar and columnar phase when the solution is

subjected to simple shear

  • The gelation point ( as evident from the cluster size distribution) shifts to lower

monomer concentration as the size of the basic building block ( molecular weight) is increased.

  • For larger molecular weight, higher shear stress was required to obtain the

layering transition

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We now switch to polyelectrolytes

Tuesday 10 August 2010