dissipative particle dynamics: perspective, framework and

Dissipative Particle Dynamics: Perspective, Framework and Applications

Meenakshi Dutt

Chemical & Biochemical Engineering

April 7, 2016 Guest lecture

Chemical Engineering North Carolina State University

! Phenomena spanning large length and time scales

" Self-assembly, coarsening dynamics, activated processes

" Mesoscale Phenomena

F. Aydin, G. Uppaladadium and M. Dutt. Biointerfaces

2016

Activated Processes Self-Assembly


2015

Coarsening Dynamics

F. Aydin, G. Uppaladadium and M. Dutt. J Phys. Chem. B

2015

! Phenomena spanning extensive length and time scales

" Development and use of multiple computational methods

" Mesoscale Phenomena and Computational Methods

We are here

! Microscale phenomena: Molecular Dynamics " All atom simulations ideal for capturing chemical

specificity, molecular structure

" Computationally VERY EXPENSIVE for phenomena

occurring over large spatiotemporal scales

! Mesoscale phenomena: Dissipative Particle Dynamics " Each particle represents a collection of atoms/molecules " Particles that move off-lattice through prescribed forces " Conserves momentum

! Macroscale phenomena: Navier-Stokes " Continuum fluid mechanics

" Dissipative Particle Dynamics (DPD)

Atomistic chain DPD representation

! DPD bridges atomistic and continuum approaches

" Allows simulation on mesoscale

" Captures effects of molecular architecture (lipid structure) and hydrodynamics

" DPD allows the capture of supramolecular organization in membranes.


Atomistic chain DPD representation

We are here

R. Groot and P. Warren, J. Chem. Phys., 107: 4423 (1997)

" History: We Stand on the Shoulder of Giants …

! New scheme for studying mesoscale phenomena in complex fluids " Hoogerbrugge and Koelman, 1992

! Refinement of method " Fluctuation-dissipation relation (Espanol & Warren, 1995) " Further development of methodology

" Polymers (Groot & Warren, 1997) " Electrostatics (Groot, 2003) " Others

! State-of-Art

" DPD used to study amphiphiles, polymers, colloids, lipid bilayer membranes & vesicles, nucleic acids, fluids.

! Similar to Molecular Dynamics (MD) " Study Newtonian time evolution of many-body system

! Numerical integration of Newton’s 2nd Law:

" Forces due to collisions, viscous interactions and random fluctuations

! Departure from MD: " Soft conservative interaction potential " Coarse grained in time and space (“fluid elements”)


Atomistic chain (Avanti Polar, Inc.) DPD representation

" Forces in DPD

! Soft repulsive force:

! Dissipative drag force:

! Stochastic force:

" Forces are pair-wise and central " Conserve angular and linear momentum, preserve hydrodynamics

R. Groot and P. Warren, J. Chem. Phys., 107: 4423

(1997)

" Conservative Forces in DPD

! Soft repulsive force: " Pairwise and central

! Soft repulsive interaction parameter aij

! Soft potentials arise from averaging molecular field over rapidly fluctuating motions of atoms during short time intervals

! Class exercise: compare forces arising from DPD and MD " Use Lennard-Jones 12-6 potential for pair potentials in MD " Compare functional forms of force (repulsive component) " What is more repulsive? What are the implications?


" Repulsive Parameter aij

! Soft repulsive force: " Compressibility of system set wrt real system via soft repulsive

parameter aij

! Virial theorem provides system pressure P " Requires radial distribution function g(r) " g(r) describes how density behaves as a function of distance from

reference particle " Question: what is the g(r) for simple liquid?

! System pressure

! Comparison between results from all atom simulations or experiments

! If density is too high or temperature is too low, DPD fluid will freeze. €

P = ρkBT +2π3ρ2 rfc (r)g(r)r

2dr0

rc∫P = ρkBT +αρ2

€

α ~ 0.1aijrc4

R. Groot and P. Warren,

J. Chem. Phys., 107: 4423 (1997)

" Repulsive Parameter aij

! Dimensionless compressibility:

" From equation of state for high density fluid

" For water κ-1~16

" NO liquid-vapor coexistence on account of purely repulsive force " DPD can capture liquid-liquid and liquid-solid interfaces

! Relation between aij and Flory Huggins theory

€

κ−1 =1kBT

∂p∂ρ

=1kBT

∂p∂n

∂n∂ρ

€

κ−1 =1+ 0.2aijρkBT

€

aij = 75 kBTρrc

4


(1997)

" Random and Dissipative Forces in DPD

! Dissipative drag force: " Reduces relative velocity of pair of particle, acts like a frictional force

! Stochastic force: " Accounts for reduced degrees of freedom

! Dissipative and random forces form DPD thermostat

! Magnitude of dissipative and random forces determined by fluctuation-dissipation theorem


(1997)

" DPD Integration Scheme

! Basic Verlet algorithm " Velocity not generated directly " Numerically inaccurate

! Velocity Verlet Algorithm " Particle position, velocity and

acceleration obtained directly " Numerically accurate

! Modified Velocity Verlet Algorithm " DPD force depends upon

velocity " How to select λ?

! Value of λ at which time step of 0.06 gives good temperature control " λ = 0.65


! Mesoscale phenomena of interest

" Self-assembly, coarsening dynamics, activated processes

" Applications of DPD


2016

Interfacial Adsorption Self-Assembly


2015

Coarsening Dynamics

F. Aydin, G. Uppaladadium and M. Dutt. J Phys. Chem. B

2015

" Resources ! Groot and Warren, J. Chem. Phys. 107: 4423 (1997) ! F. Aydin, G. Uppaladadium and M. Dutt, J. Phys. Chem. B 2015,

DOI: 10.1021/acs.jpcb.5b02239 . ! F. Aydin, G. Uppaladadium and M. Dutt, Biointerfaces 2015,

DOI: 10.1016/j.colsurfb.2015.01.049. ! F. Aydin, G. Uppaladadium and M. Dutt, Biointerfaces 2016,

DOI: 10.1016/j.colsurfb.2016.01.061.

dissipative particle dynamics: perspective, framework and

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