Coarse-grained Models for Oligomer-grafted Silica Nanoparticles

Bingbing Hong Alexandros Chremos

Athanassios Z. Panagiotopoulos

Department of Chemical & Biological Engineering

Modeling  So+  Ma-er:  Linking  Mul3ple  Length  and  Time  Scales  KITP  Conference,  Santa  Barbara,  June  4-­‐8,  2012    

Princeton  Center  for  Complex  Materials

Nanoscale ionic & organic hybrid materials

Covalent grafting

Ionic grafting

SiO2

-organosilane-PEG

J. L. Nugent, L. A. Archer, Adv. Mater. 22:3677-3680 (2010) P. Agarwal, L. A. Archer, Phys. Rev. E 83:041402 (2011)

A. B. Bourlinos, …, L. A. Archer, E. P. Giannellis, J. Am. Chem. Soc. 126:15358-15359 (2004) R. Rodriguez, …, L. A. Archer, E. P. Giannelis, Adv. Mater. 20:4353-4358 (2008)

•  Viscous liquids •  Solvent-free •  Ultra low vapor pressures •  Many functionalities from cores + chains

Atomistic reference (PEO chains)

Modified TraPPE potential for CH3O[CH2CH2O]nCH3

Non-bonded:

Bond: FENE

Angle: Modified Dihedral: ( ) ( )

51

1cosnn

iU Aφ φ−

=

=∑

Good agreement of transport properties with experiments (also see next page)

experiment

simulation

B. B. Hong, F. Escobedo, AZP, J. Chem. Eng. Data 50, 4273-4280, 2010

n=2

Transport properties of atomistic models for CH3O(CH2CH2O)nCH3

Hong, Escobedo, AZP, J. Chem. Eng. Data, 55: 4273-80 (2010)

l  Coarse-grained PEO

3 2 2 3CH O CH CH O CH− − − − −[ ] 3 2 2 3CH O CH CH O CH− − − − −[ ] [ ]

One CG bead

l  Bead-bead potential

( ) ( ) ( )( )1 ln tgt

i i Bi

g rU r U r x k T

g r+ = − ⋅

Iterative Boltzmann Inversion D. Reith, et al, J. Comput. Chem. 24, 1624-636, 2003

Coarse-Graining: PEO chains

n-mer → (N+1)/2–bead chain

l  Harmonic bond potential Fitted equilibrated bond length between coarse-grained (CG) beads to the distance between two atomistic groups

bond

angle

Persistence length: ~ 0.46nm (~3.2 repeat units)

Determined from matching the end-to-end distance of long CG chains to atomistic simulations

l  Harmonic angle potential

Coarse-Graining: PEO chains

303.15K

0 0.5 1 1.5 2 2.5 30

0.51

1.5

r/nm

00.51

1.5

00.51

1.5

g(r)

500K

2 beads

3 beads

5 beads

2 beads

3 beads

5 beads

•  Good transferability to other T’s, chain lengths

•  End-to-end distances at higher T are slightly smaller (chains less stiff).

End-to-end distance and structure of CG PEO chains atomistic coarse-grained

Slope: ~ -2.5 (red squares) ~ -1.3 (others)

•  Coarse-graining speeds up dynamics due to softer potentials which reduce the friction of cage escape.

•  Speed-up factors depend on T

•  Raising T or coarse-graining shortens the “oligomer” regime.

Diffusivity of PEO chains

Atomistic reference NOHMs: Integrated LJ ( )

12 6

, ,

d 4 dij ijI ij II

i j Si O ij ijsphere I sphi j

ere II

U r V Vr rσ σ

ερ ρ=

⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥= −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

∑ ∫ ∫

( )3 2

12 6

,, ,

4 dij iji ij I

i Si O ij ijsphere Ij CH CH O

U r Vr rσ σ

ρ ε==

⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥= −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

∑ ∫

CH3 – CH3

Coarse-graining: core particles

1 nm particle – CH3 2 nm particle – CH3

“Semi-atomistic” model: 1-center cores + full chains

10−2

100

102

104

T (K)

� (c

P)

1 1.5 2 2.5 3x 10−31/T (K−1)

1000 600 400 300

Experiments

simulations Red: 2 nm + 12x6-mer Blue: 2 nm + 12x12-mer Brown: 0.9 nm POSS +8x12mer

•  Large number of interaction sites, slow relaxation •  Simulations only feasible at high T

B. B. Hong, AZP, JPCB 116: 2385-2395 (2012)

single core in atomistic and CG monomers.

•  Iterative Boltzmann Inversion to fit core-bead g(r) at 303.15 K

Core-bead CG interactions

7 beads (13-mer)

3 beads (5-mer)

Core-core interactions also need to be adjusted

atomistic

coarse-grained

7 beads (13-mer) 3 beads (5-mer)

Smaller corrections for shorter grafted chains

Poor transferability to different T’s and chain lengths

Corrected core-core interactions

atomistic

coarse-grained

atomistic

coarse-grained

CG corrected

CG uncorrected

CG corrected

CG uncorrected

3 beads (5-mer)

7 beads (13-mer)

NOHMs with uncorrected potentials or short-chain NOHMs with corrected potentials diffuse more slowly

Cores grafted with longer chains CG diffuse faster

Counter-intuitive core dynamics

atomistic

atomistic

Particle + 13-mer

Particle + 5-mer

Core + 7-bd, corrected U Core + 3-bd, corrected U

Core + 7-bd, uncorrected U

Core + 3-bd, uncorrected U

•  Coarse-graining speeds up chain relaxations – chain motions are not the cause for core slow-down

•  Core potentials have little effect on chain relaxation

Chain dynamics behave normally

l  Chain extensions – no different

3-­‐bead  NOHMs   7-­‐bead  NOHMs  

Uncorrected  U   5  %  longer   4  %  longer  

Corrected  U   4  %  longer   Within  errors  

l  Grafting topology •  g(r) data: space between neighbor cores (s) ~ 0.4 nm atom ~ 0.3 nm bead ~ 0.65 nm

atomistic segments rotate to fit; CG bead are too big

s

Other possible causes for unexpected dynamics?

Softer potential → faster cage escape

ΔVb

Cage escape dynamics

P. K. Depa and J. K. Maranas, J. Chem. Phys. 123: 094901 (2005). D. Fritz, K. Koschke, V. A. Harmandaris, N. F. A. van der Vegt, and K. Kremer, Phys. Chem. Chem. Phys. 13:10412 (2011)

•  <ΔVb> > 0 for chains •  <ΔVb> < 0 for cores. •  Speedup or slowdown depends on core/chain content.

Effects disappear after 2nd layer

Integrand for acceleration factor

CG corrected

CG uncorrected

Bead LJ parameters from TC & ρC of CH3-O-CH3

Electrostatic interactions :

relative permittivity: κ = 4 (for SiO2, PEG) ⇒VE(σ) = 35kBT

Ionic coarse-grained models

Stars (NIMs-S) Linear (NIMs-L)

0 2 4 60

2

4

6

r / nm

g cc( r

)

NOHMsNIMs−LNIMs−S

Core-core correlation functions

Dynamics: NIMs-S (chains not shown)

0.1 1 10 100 1000

0.01

0.1

1

10

t / ns

MSD

/ nm

2

Unit Slope:

NOHMsNIMs−L coreNIMs−L chainNIMs−S coreNIMs−S chain

D ≈ 10–8 cm2/s (NOHMs) 10–9 cm2/s (NIMs) η ≈ 0.1 Pa s (NOHMs) 1 Pa s (NIMs)

Diffusion of chains and cores

Canopy chain exchange

0 20 40 60 80 1000.01

0.1

1

t (ns)

[n(t)−n

(�)]/

[n(0

)−n(�

)]

0 20 40 60 80 1000.01

0.1

1

t (ns)

[n(t)−n

(�)]/

[n(0

)−n(�

)]

0 50 100 1500.01

0.1

1

t (ns)

[n(t)−n

(�)]/

[n(0

)−n(�

)]

T ↑

chain length ↑

grafting density ↑

Canopy chain exchange kinetics

101 102 103 10410−11

10−10

10−9

10−8

t (ps)

<�MJ2 >/

6Vk BT

(S�m

−1�s

)

101 102 103 10410−11

10−10

10−9

t (ps)

<�MJ2 >/

6Vk BT

(S�m

−1�s

)

101 102 103 10410−12

10−11

10−10

10−9

10−8

t (ps)

<�MJ2 >/

6Vk BT

(S�m

−1�s

)343 K 373 K 403 K 453 K

n = 5 n = 10 n = 20

g = 4 g = 8 g = 13

�

MJ t( ) = qirc.m.i t( )i∑

�

limt≥tc

ΔMJ2 t( ) = lim

t≥tcMJ t( )−MJ 0( )[ ]2 = 6VkBTσ ω = 0( )[ ]t +2 MJ

2

•  simulated conductivity 2.5 times the value of polyoxometalates (POM(-)) grafted with two N(+)(CH3)(C18H37)[(EO)n][(EO)m] ( n+ m = 15) at 373 K.

Conductivities

Summary & discussion points

Bulk PEO chains •  structural properties in good agreement with atomistic models •  diffusion coefficients increase by a nearly constant factor at high T only •  non-trivial scaling at low T NOHMs (non-ionic) Diffusion of nanoparticles can be slower in coarse-grained models under some conditions NIMs (ionic) •  insights on mechanism for fluidity + conductivity •  reasonable agreement with experiments using simple “thermodynamic”

CG models Open question Is there a way to obtain dynamic scaling of CG models for complex nanoparticle / chain systems?