Coarse-grained Models for Oligomer-grafted Silica Nanoparticles

Transcription

1 Modeling So+ Ma-er: Linking Mul3ple Length and Time Scales KITP Conference, Santa Barbara, June 4-8, 2012 Coarse-grained Models for Oligomer-grafted Silica Nanoparticles Bingbing Hong Alexandros Chremos Athanassios Z. Panagiotopoulos Department of Chemical & Biological Engineering Princeton Center for Complex Materials

2 Nanoscale ionic & organic hybrid materials Covalent grafting Ionic grafting -organosilane-peg Viscous liquids Solvent-free Ultra low vapor pressures Many functionalities from cores + chains SiO 2 J. L. Nugent, L. A. Archer, Adv. Mater. 22: (2010) P. Agarwal, L. A. Archer, Phys. Rev. E 83: (2011) A. B. Bourlinos,, L. A. Archer, E. P. Giannellis, J. Am. Chem. Soc. 126: (2004) R. Rodriguez,, L. A. Archer, E. P. Giannelis, Adv. Mater. 20: (2008)

3 Atomistic reference (PEO chains) Modified TraPPE potential for CH 3 O[CH 2 CH 2 O] n CH 3 Bond: FENE Angle: Modified 1 Dihedral: ( ) cos n U φ An ( φ) 5 = i= 1 n=2 Non-bonded: simulation Good agreement of transport properties with experiments (also see next page) experiment B. B. Hong, F. Escobedo, AZP, J. Chem. Eng. Data 50, , 2010

4 Transport properties of atomistic models for CH 3 O(CH 2 CH 2 O) n CH 3 Hong, Escobedo, AZP, J. Chem. Eng. Data, 55: (2010)

5 Coarse-Graining: PEO chains l Coarse-grained PEO [ ] CH O CH CH O CH [ CH 3 O CH ] CH O CH 2 [ 2 ] 3 n-mer (N+1)/2 bead chain l Bead-bead potential ( ) ( ) U + r = U r x k T 1 ln tgt i i B gi One CG bead g ( r) ( r) Iterative Boltzmann Inversion D. Reith, et al, J. Comput. Chem. 24, , 2003

6 Coarse-Graining: PEO chains Persistence length: ~ 0.46nm (~3.2 repeat units) l Harmonic bond potential bond Fitted equilibrated bond length between coarse-grained (CG) beads to the distance between two atomistic groups angle l Harmonic angle potential Determined from matching the end-to-end distance of long CG chains to atomistic simulations

7 End-to-end distance and structure of CG PEO chains 2 beads atomistic coarse-grained K 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). 2 beads 3 beads 5 beads g(r) K r/nm

8 Diffusivity of PEO chains 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 coarsegraining shortens the oligomer regime. Slope: ~ -2.5 (red squares) ~ -1.3 (others)

9 Coarse-graining: core particles Atomistic reference NOHMs: Integrated LJ 12 6 σ σ U( r) = ρρ dv 4ε dv ( ) U r ij ij i j I ij II i, j= Si, O r sphere I sphere II ij r ij 12 6 σ σ = ρ 4ε dv ij ij i ij I i= Si, O sphere I r ij r ij j = CH, CH, O 3 2 CH 3 CH 3 1 nm particle CH 3 2 nm particle CH 3

10 Semi-atomistic model: 1-center cores + full chains T (K) Red: 2 nm + 12x6-mer Blue: 2 nm + 12x12-mer Brown: 0.9 nm POSS +8x12mer (cp) simulations Experiments /T (K 1 ) x 10 3 Large number of interaction sites, slow relaxation Simulations only feasible at high T B. B. Hong, AZP, JPCB 116: (2012)

11 Core-bead CG interactions single core in atomistic and CG monomers. Iterative Boltzmann Inversion to fit core-bead g(r) at K

12 Core-core interactions also need to be adjusted coarse-grained atomistic 7 beads (13-mer) 3 beads (5-mer)

13 Corrected core-core interactions 3 beads (5-mer) 7 beads (13-mer) coarse-grained atomistic coarse-grained atomistic Smaller corrections for shorter grafted chains Poor transferability to different T s and chain lengths

14 Counter-intuitive core dynamics NOHMs with uncorrected potentials or short-chain NOHMs with corrected potentials diffuse more slowly 3 beads (5-mer) CG corrected atomistic CG uncorrected Cores grafted with longer chains CG diffuse faster 7 beads (13-mer) CG corrected atomistic CG uncorrected

15 Chain dynamics behave normally 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

16 Other possible causes for unexpected dynamics? 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 s bead ~ 0.65 nm atomistic segments rotate to fit; CG bead are too big

17 Cage escape dynamics ΔV b P. K. Depa and J. K. Maranas, J. Chem. Phys. 123: (2005). D. Fritz, K. Koschke, V. A. Harmandaris, N. F. A. van der Vegt, and K. Kremer, Phys. Chem. Chem. Phys. 13:10412 (2011) Softer potential faster cage escape

18 Integrand for acceleration factor Effects disappear after 2nd layer CG corrected CG uncorrected <ΔV b > > 0 for chains <ΔV b > < 0 for cores. Speedup or slowdown depends on core/chain content.

19 Ionic coarse-grained models Linear (NIMs-L) Stars (NIMs-S) Bead LJ parameters from T C & ρ C of CH 3 -O-CH 3 Electrostatic interactions : relative permittivity: κ = 4 (for SiO 2, PEG) V E (σ) = 35k B T

20 Core-core correlation functions 6 NOHMs NIMs L NIMs S g cc ( r ) r / nm

21 Dynamics: NIMs-S (chains not shown)

22 Diffusion of chains and cores MSD / nm NOHMs NIMs L core NIMs L chain NIMs S core NIMs S chain Unit Slope: D 10 8 cm 2 /s (NOHMs) 10 9 cm 2 /s (NIMs) η 0.1 Pa s (NOHMs) 1 Pa s (NIMs) t / ns

23 Canopy chain exchange

24 Canopy chain exchange kinetics 1 1 [n(t) n( )]/[n(0) n( )] 0.1 T [n(t) n( )]/[n(0) n( )] 0.1 chain length t (ns) t (ns) [n(t) n( )]/[n(0) n( )] 0.1 grafting density t (ns)

25 Conductivities < M J 2 >/6VkB T (S m 1 s) K 373 K 403 K 453 K < M J 2 >/6VkB T (S m 1 s) n = 5 n = 10 n = 20 < M J 2 >/6VkB T (S m 1 s) t (ps) g = 4 g = 8 g = t (ps) M J lim ΔM 2 J t t tc t (ps) ( t) = q i r c.m.i t i ( ) = lim ( ) [ ( )] 2 = 6Vk B Tσ( ω = 0) M J t t tc ( ) M J 0 [ ]t + 2 M J 2 simulated conductivity 2.5 times the value of polyoxometalates (POM(-)) grafted with two N(+)(CH 3 )(C 18 H 37 )[(EO) n ][(EO) m ] ( n+ m = 15) at 373 K.

26 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?