stability of the Cassie-Baxter state and its effect on liquid water...

Mauro ChinappiCenter for Life Nano Science

IIT@Sapienza

Superhydrophobic surfaces: stability of the Cassie-Baxter state andits effect on liquid water slippage

Talks outline

Wetting and slippage: atomistic and continuum approaches M. Chinappi

●Water slippage on rough surfaces

●Effect of meniscus curvature on slippage

Water

Defected OTS-SAM

SolidTalk 1: Molecular Dynamics application to nanofluidics

Talk 2: Cassie-Wenzel transition

●Wetting on rough surfaces

●Cassie-Baxter/Wenzel transition

●Free-energy profile and transitionmechanism

Wetting on rough surfaces(A. Giacomello, S. Meloni, C.M. Casciola)


Liquid

Vapour

Cassie-Baxter Wenzel

Transition

Motivation: super-hydrophobic surfaces


●Multiscale rough surfaces

●Hydrophobic wax

●A drop does not wet the whole surface

Self-cleaning and super-hydrophobicity

Barthlott and Neinhuis 1997, Bhushan and Jung 2010

Motivation: super-hydrophobic surfaces


●The water does not wet cauliflowers

●The oil does !!

Combination of chemical and geometrical features

Drop on smooth and rough surfaces


cosθ=γSV−γSL

γLV

Young equation for contact angle

Cassie-Baxter (CB)Wenzel (W)

Rough surfaces of hydrophobic materials show a contactangle larger than smooth surfaces

< 90° hydrophilic

> 90° hydrophobic

CB state iscrucial for applications(self cleaning,liquid slippage)

(fakir)

Wetting of a rough surface


Given a certain geometry and a thermodynamic condition, what is the wetting state? Cassie-Baxter or Wenzel? (or other)

Metastabilities


Presence of long lived states less stable than the system's most stable state.

Diamonds are metastable!

Operative meaning

In wetting?In several actual cases CB (or W)

state is metastable

free-energy profile

Metastable statesLafuma and Quéré (2003)

Our aim


Analyze wetting of structured surfaces by molecular dynamics and continuum approach

●Simple geometry (groove)

●Characterize metastable states(Molecular dynamics)

●Reconstruct the free-energy profile(CB/W transition barrier)

●Extend the approach to continuumsystems

Highlights:

Collective variables and free-energy profile


Collective variables

●A proper set of variables able to describe the process

●Our collective variable: number ofparticles in the groove region z = z(r)

z = Number of atoms in the groove region

PZ ∝∫ dr dpZ− z r , pr , p

Probability of a given state

F (Z )=−kBT ln P(Z )Free-energyprofile

Low P(Z) High F(Z)High P(Z) Low F(Z)

F (Z1)−F (Z2)=−k BT lnP(Z1)

P(Z2)

Free-energy profile from Molecular Dynamics


… run a long enough MD simulation and calculate free energy profile F(Z)

… in principle …

Remember metastabilities!! Presence of long lived states less stable than the system's most stable state.

Not possible !!Dedicated techniques

●Restrained Molecular Dynamics(RMD)

●Umbrella sampling●Parallel tempering●...

Molecular dynamics (MD) allows to sample correctly a statistical ensemble, i.e. in principle you have the correct ρ(r,p)

Umbrella potential


Method: Restrained Molecular Dynamics

U (r )=12

k (Z−z (r ))2

Target valueUmbrella potential

Current value

Reconstruction of F(Z) from “mean force”

d Fd Z

=⟨k (Z−z (r))⟩ Average estimated via RMD

Derivative of free-energy

Our system


Collective variable

System set-up●100k atoms●Lennard-Jones model●Possibility to control contact angle●Small groove in large system●3D, periodic in x and z●NPT (or NVT) ensemble

z (r)=atoms in the groove

z (r)∼2000→Wenzel

z (r)∼1000→Cassie-Baxter

Number of atoms in the groove region

Results I: Free-energy


1000Cassie-Baxter

2000Wenzel

Results I: Free-energy profiles


Evidences●Large F(Z) barriers

●High T. Wenzel

●Low density. Cassie-Baxter

●Presence of one other metastable state

Results II: Free-energy barriers


1000Cassie-Baxter

2000Wenzel

Results III: asymmetric path


Liquid

Vapour

Cassie-Baxter WenzelTransition

Configuration obtained from RMD suggests an asymmetric transition path

Z = 1000 Z = 2000

A. Giacomello et al Langmuir (2012)

Cassie-Baxter/Wenzel transition


Analyze wetting of structured surfaces by molecular dynamics and continuum approach

●Simple geometry (groove)

●Characterize metastable states

●Reconstruct the free-energy profile(CB/W transition barrier)

●Extend the approach to continuumsystems

Highlights

XXX

Extension to microscale: continuum model


Molecular dynamics

Add umbrella potential on Z

Add a constraint to enforce the value of Z (Lagrange multiplier)

Continuum

Select an ensemble(NVE, NVT or NPT)

Select a thermodynamic state

Select a propercollective variable Z

Select an order parameter Z (filling level)

Calculate F(Z) from “mean force”

Calculate F(Z) from constrained minimization of the thermodynamic potential

2

1

3

4

Extension to microscale: continuum model


Continuum restrained thermodynamic integration


Bulk Interface

I=ΩTOT

−λ(V L−Z) Target value

δ I=∫ΣLV

( pL−pV+λ−J γLV )δ xN dS+∮∂ ΣSL

(γLS−γSV +γ LV cos θ)δ x tl dl

cosθ=γSV−γSL

γLV

Young equation

pL−pV+λ−J γLV=0

Modified Laplace equation

Curvature LV interface

Solid interface fixedΩL=−pLV L

ΩL=−pV V V

ΩTOT

(μ ,V ,T )=ΩL+ΩV +γLV ALV +γSV ASV +γLS A LS

Grand potential (µVT)

δV L=∫ΣLV

x N dS

Meniscus surface



I=ΩTOT

−λ(V L−Z) Target value

δ I=∫ΣLV

( pL−pV+λ−J γLV )δ xN dS+∮∂ ΣSL

(γLS−γSV +γ LV cos θ)δ x tl dl

cos =SV− SL

LV

Young equationpL−pV−J LV=0

modified Laplace equation

Curvature LV interfaceMeniscus surface

λ=∂Ωeq

∂ZΩeq (Z)

Free energy profile



●Given z, different interface configurations are possible●Calculate the grand potential ω for each one of the possible interface●Select the state with smallest ω

Methodology

Cassie Wenzel

Pres

s ure

Dimensionless grand potential



●Continuum approach to metastabilities

●Result in agreement with MD(asymmetric path !!)

●No implicit assumption on mechanism

●Assumption: succession of thermodynamic states (quasi static)

Results

Giacomello et al. PRL (2012) Cassie-Baxter Wenzel

Open issues and ongoing work


Open issues:

●General approach to transition path (Molecular Dynamics)

●Vapor (not gas)

●Complex geometries (numerical approach required)

=> ●string method●Committor analysis

Talks outline


●Water slippage on rough surfaces

●Effect of meniscus curvature on slippage

Water

Defected OTS-SAM

SolidTalk 1: Molecular Dynamics application to nanofluidics

Talk 2: Cassie-Wenzel transition

●Wetting on rough surfaces

●Cassie-Baxter/Wenzel transition

●Free-energy profile and transitionmechanism

Thanks !!

stability of the Cassie-Baxter state and its effect on liquid water...

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