Molecular Dynamics Simulations and Neutron Scattering: Polymer Melt and Solution Dynamics

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1 Molecula Dynamics Simulations and Neuton Scatteing: Polyme Melt and Solution Dynamics Gant D. Smith Depatment of Mateials Science and Engineeing Univesity of Utah Polyme Dynamics and Relaxation Richad H. Boyd and Gant D. Smith ambidge Univesity Pess 007 1

Smith Depatment of Mateials Science and Engineeing Univesity of

2 Bill Gate s Opinion MD simulation = dissimulation the act of deceiving deception, dissembling, deceit misepesentation, falsification - a willful pevesion of facts fakey - the act of faking o the poduct of faking indiection - deceitful action that is not staightfowad Outline Molecula Dynamics Simulations Foce Fields and Foce Field Paametization MD Simulations and Neutons: The onnection Local Melt Dynamics: Polyethylene Local Solution Dynamics: PEO/wate Solutions hain Dynamics: Polybutadiene Glass and Sub-glass Pocesses: Polybutadiene

Outline Molecula Dynamics Simulations Foce Fields and Foce Field Paametization MD Simulations and Neutons: The onnection Local Melt

3 MD Backgound: Scales of Modeling continuum mesoscale Time Scale 10-4 S 10-6 S 10-8 S 10-1 S quantum chemisty Ηψ = Εψ molecula dynamics F = MA Monte alo exp [- E/kT] domain M 10-8 M 10-6 M 10-4 M Length Scale MD Backgound: lassical Equations of Motion NE H = K + = total enegy = constant K= i 1 m iv i, = U i, j d j dt = H = v p j, dpj j dt = - H =- = F j j j NT H = K + + Ks + s = constant Ks = ½ Qps s = f + 1k B T lns ps = conjugate momentum of themostat Q = conjugate mass s = genealized coodinate of the themostat f = numbe of degees of feedom 5000 atoms, 4 nm 3

constant K= i 1 m iv i, = U i, j d j dt = H = v p j, dpj j dt = - H =- = F j j j NT H = K + + Ks + s = constant Ks = ½ Qps s = f + 1k B T lns

4 4 tosional intemolecula inteactions intamolecula nonbonded bond stetch valence angle bend Foce fields Intamolecula and Intemolecula Inteactions j i N j i POL NB q q B A 0 6 1, 4 exp 1 πε + + = = = = REP DIS A σ σ ε kl dihedals TORS k bends BEND bonds BOND NB ϕ θ =

Inteactions j i N j i POL NB q q B A 0 6 1, 4 exp 1 πε + + = = = = 6

5 Foce fields: Whee do they come fom? Geneic e.g., Deiding: Roughly descibe a wide ange of mateials, not paameteized o validated Tained e.g., AMBER, OMPASS, HARMM, OPLS Paameteized to epoduce the popeties of a boad set of molecules such as small oganics, peptides o amino acids Specialized e.g., Atomistic Polaizable Potential fo Liquids, Electolytes and Polymes APPLE&P aefully paameteized and validated potentials designed to epoduce popeties of a small class of specific molecules Foce Field Paametization: Intemolecula Inteactions hydophobic path binding kcal/mol 3 quantum chemisty foce field OW Å hydophilic path 5

Roughly descibe a wide ange of mateials, not paameteized o validated Tained e.g., AMBER, OMPASS, HARMM, OPLS Paameteized to epoduce the popeties of a boad set of molecules such as small oganics, peptides o amino acids Specialized e.

6 Foce Field Paametization: Intamolecula Inteactions E kcal/mol 6 t-φ -t, foce field 4 t-φ -t, quantum chemisty φ, degees Polybutadiene confomational enegy kcal/mol Q FF β dihedal angle H H H H H H H H H H H H 6

degees Polybutadiene confomational enegy kcal/mol 7 6 5 4 3 1 0 Q

7 Foce Field Paametization: alidation: Static Stuctue Facto Sq Neuton Diffaction MD q, Å -1 Foce Field Paametization: alidation: Time oelation Functions TAF t = θ t θ 0 θ 0 θ 0 θ 0 7

5 1 3 4 5 6 7 8 9 10 q, Å -1 Foce Field Paametization:

8 Foce Field Paametization: alidation: Dynamic Stuctue Facto fo PEO Melt Iq,t QENS, q=0.718 Å -1 QENS, q=0.913å -1 QENS, q=1.095 Å time ps Incoheent Dynamic Stuctue Facto, QENS and MD oheent Dynamic Stuctue Facto, NSE and MD MD-Neuton onnection: Dynamic Stuctue Factos Simulation yields intemediate dynamic stuctue factos time domain diectly oheent scatteing s coh N N 1 q, t = < exp iq k t j0 >=< sin q k t j0 / q k t j0 > N j, k Incoheent scatteing N N 1 s inc q, t = < N Simulation time scales fom femtoseconds to micoseconds Expeimental time scales fom picoseconds to nanoseconds A Fouie-Laplace to fequency domain o an invese tansfom of QENS data is equied fo compaison Diect compaisons can be made with NSE data j, k expiq k t k 0 > =< sinq k t k 0 / q k t k 0 > k k 8

stuctue factos time domain diectly oheent scatteing s coh N N 1 q, t = < exp iq k t j0 >=< sin q k t j0 / q k t j0 > N j, k Incoheent scatteing N N 1 s inc q, t = < N Simulation time scales fom

9 Example: Local Dynamics is a Polyethylene Melt: MD simulations povide data ove a wide ange of time MD simulations ae in good ageement with QENS Libations o onfomational Tansitions? s inc q, t = q < > H t exp 6 9

simulations ae in good ageement with QENS Libations

10 PEO/Wate Solutions: Local Dynamics Polyme Dynamics q = 0.4 A -1 Mw = 500 q =.4 A -1 Low molecula weight PEO exhibits a minimum in local dynamics with concentation This is due to slowing confomational dynamics and inceasing tanslational/otational dynamics with dilution time ps τ DSFq=0.58 Å -1 time ps 1000 τ DSFq=0.91 Å -1 τ DSFq=1.57 Å τ TRANS - τ TRANS -O τ H vecto

confomational dynamics and inceasing tanslational/otational dynamics with dilution time ps 10000 τ DSFq=0.

11 PEO/Wate Solutions: Local Dynamics Wate Dynamics Iq,t wp=0.53, 98 K q=0.90 Å -1 q=0.57 Å q=1.6 Å -1 q=.4 Å time ps Wate quasi-confinement 1.0 =0.17, q c =0.95 Å -1 =0.5, q c =1.34 Å -1 =0.78, q c =1.58 Å =0.17 =0.5 =0.78 Γ ps go-o q, Å - sepaation Å 11

0 0 10 0 30 time ps Wate quasi-confinement 1.0 =0.17, q c =0.95 Å -1 =0.5, q c =1.

12 Lage Scale Dynamics: Single chain coheent dynamic stuctue facto fo PBD 353 K S'q,t = Sq,t/Sq = <sin[qr mn t]/qr mn t> / <sin[qr mn 0]/qR mn 0> m,n m,n q = 0.05 Å -1 H H H H S'q,t q = 0.4 Å -1 q = 0.08 Å -1 q = 0.10 Å -1 H H H H q = 0.30 Å -1 q = 0.0 Å -1 q = 0.14 Å time ns H H H H Why does the Rouse model povide such a poo desciption of Sq,t? S'q,t hain stiffness? Intenal viscosity? Non-Gaussian displacements? time ns Figue 5 1

0.0 q = 0.30 Å -1 q = 0.0 Å -1 q = 0.14 Å -1 0 5 10 15 0 time ns H H H H Why does the Rouse model povide such a poo desciption of Sq,t?

13 an dynamic neuton scatteing tell us about the bifucation of the glass and subglass pocesses? 10 8 dielectic elaxation αβ log 1/τ s α β - T s /T T g MD Simulations and Dynamic Neuton Scatteing in Polymes --Natual patnes ovelapping time and length scales --DNS expeiments ae impotant fo validation of simulations --Simulations can diect expeiment --Simulations can help povide mechanistic insight into expeimental esults --Simulations can help povide sanity checks fo conclusions based on limited but expanding! DNS capabilities 13

--Natual patnes ovelapping time and length scales --DNS expeiments ae impotant fo validation of simulations --Simulations can diect

14 14

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