Interpretation of density profiles and pair correlation functions

Transcription

1 Interpretation of density profiles and pair correlation functions Martin Horsch and Cemal Engin Paderborn, 22 nd June 12 IV. Annual Meeting of the Boltzmann Zuse Society

2 Surface tension of nanodroplets Tolman (1949): Size dependence of γ is due to curvature, coupled by the length δ 0. New consensus emerging today: δ 0 is too small to describe the dominating effect 2

3 Liquid slab size effect on interfacial profiles density / σ -3 ( p N - p T ) / εσ LJ ( r c = 2.75 σ ) T = 0.9 ε /k coordinate normal to the interface / σ cutoff correction: Janecek with MIC γ = εσ -2 γ = εσ -2 γ = εσ -2 γ = εσ coordinate normal to the interface / σ 3

4 Mode of the long-range cutoff correction ρ / σ -3 ρ / σ -3 ρ / σ MIC PBC semi-infinite boundary condition site i site i site i y / σ y / σ y / σ 4

5 Heterogeneous or fluctuating systems Objective: Simulation of systems with an arbitrary heterogeneous structure significant long-range fluctuations (e.g., near T c ) cutoff radius r c 5

6 Heterogeneous or fluctuating systems hierarchy of longrange corrections short-range correction cutoff radius r c 6

7 Modelling polarity and hydrogen bonding Stockmayer model extended by an elongation parameter d LJ concentric with point charge LJ concentric with dipole 7

8 Modelling polarity and hydrogen bonding Stockmayer model extended by an elongation parameter d LJ concentric with point charge LJ concentric with dipole density / σ -3 Fluid properties determined by the dipole moment (undesired!) temperature / εk -1 temperature / εk -1 8

9 Modelling polarity and hydrogen bonding monomer fraction electrostatic pair potential π π elongation d / σ -π -π Further objectives on the basis of the present parameter study: SAFT-like equation of state for the elongated Stockmayer model Prediction of VLE for multi-site models of hydrogen bonding fluids 9

10 Industrially important reactive systems Objective: Simulation of transition states Here: EOX+ (based on reliable EOX model) Correlation function controlling the S N 2 reaction of protonated EOX with water: methylene (EOX + ) oxygen (H 2 O) ethylene oxide H + (catalysis) O H + H H High economic interest Difficult experiments Few reliable data ethylene glycol Need for predictive modelling and simulation 10

11 Transient radial distribution function 11

12 Discussion Could it be that the diameter effect (rather than the curvature effect) determines the influence of droplet size on the surface tension? How should we implement the cutoff correction for anisotropic or fluctuating systems in (long-term!) future releases of ls1 mardyn? For modelling a chemical reaction: How does the relaxation time of the fluid phase, during which the correlation function for the transition state are established, relate to its average life time? Does it make sense as a perspective to work on methods for reactive ensembles with classical force fields? (E.g., with reaction probabilities speficied as a function of kinetic energy and orientation.) 12