Dissipative Particle Dynamics: Perspective, Framework and Applications Meenakshi Dutt Chemical & Biochemical Engineering April 7, 2016 Guest lecture Chemical Engineering North Carolina State University
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
F. Aydin, G. Uppaladadium and M. Dutt. Biointerfaces
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.
" Dissipative Particle Dynamics (DPD)
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”)
" Dissipative Particle Dynamics (DPD)
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?
R. Groot and P. Warren, J. Chem. Phys., 107: 4423 (1997)
" 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
R. Groot and P. Warren, J. Chem. Phys., 107: 4423
(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
R. Groot and P. Warren, J. Chem. Phys., 107: 4423
(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
R. Groot and P. Warren, J. Chem. Phys., 107: 4423 (1997)
! Mesoscale phenomena of interest
" Self-assembly, coarsening dynamics, activated processes
" Applications of DPD
F. Aydin, G. Uppaladadium and M. Dutt. Biointerfaces
2016
Interfacial Adsorption Self-Assembly
F. Aydin, G. Uppaladadium and M. Dutt. Biointerfaces
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.