Supercritical fluids: Investigation of Supercritical fluids: Investigation of local density inhomogeneities and local density inhomogeneities and related properties using computer related properties using computer

simulations.simulations.Ioannis SkarmoutsosIoannis Skarmoutsos

In collaboration with: In collaboration with: Elvira Guardia (DFEN, UPC, Barcelona, Spain)Elvira Guardia (DFEN, UPC, Barcelona, Spain)

Dimitris Dellis (Chemistry Dept., Univ. Athens, Greece)Dimitris Dellis (Chemistry Dept., Univ. Athens, Greece)Jannis Samios (Chemistry Dept., Univ. Athens, Greece)Jannis Samios (Chemistry Dept., Univ. Athens, Greece)

What is a supercritical (SC) fluid?What is a supercritical (SC) fluid?

P – TPhase Diagrams

T – VPhase Diagram

P – VPhase Diagram

CriticalPoint

0

0

0

2

2

c

c

c

TT

PP

TT

VP

VT

VP

TVTVT P

VVcc

1lim

,,

PVTVT TV

Vcc

1lim,,

Isothermal Compressibility

Thermal Expansion

SF6 : Going from vapor liquid equilibrium to supercritical state and back!!

Characteristic Properties of SC fluidsClose to the critical point:

●VERY SMALL pressure changes cause VERY LARGE changes in density and dielectric constant

consequences

● Tuning of dissolving capability of SC solvents by adjusting the pressure

● Significant increase of the chemical reaction rates in SC solvents

Transport properties of SC fluids in comparison with liquids:

● Self Diffusion: 1 order of magnitude higher than in the liquid state

● Viscosity: 1 order of magnitude lower than in the liquid state

Applications of SC fluidsIndustrial Toxic Waste Treatment

Separation Processes: Supercritical ChromatographyFragmentation of macromolecules

Synthesis of fine metal particlesMaterial Science: Synthesis of nanoparticles

Synthesis of porous materials

Green Chemistry

See:Eckert, C.A., Knutson, B.L., Debenedetti, P.G., Nature, 383, 313 (1996)Tucker, S.C., Chem. Rev., 99, 391 (1999)Kajimoto, O., Chem. Rev., 99, 355 (1999)Akiya, N., Savage, P., Chem. Rev., 102, 2725 (2002) … etc

NO hazardous waste streams, NO harsh organic chemicalsRecyclable solvents

Characteristic Local Microstructure in SC FluidsMicrostructure in SC Fluids

Local Density Inhomogeneities(LDI)

Why are we interested in these Local Density Why are we interested in these Local Density Inhomogeneities?Inhomogeneities?

They affect significantly the properties of SC fluids

And the answer is:

The isothermal compressibility factor is directly related with these density fluctuations and their spatial extent (correlation length ξ)

WHY?

Close to the Critical Point: COMPRESSIBLE REGIME

Open problems:Open problems:

● Influence of thermodynamic parameters (P,V,T) on the formation of LDI

● Interrelation of these inhomogeneities with the bulkthermodynamic, structural and dynamic propertiesof molecular SC fluids

● Effect of intermolecular interactions on the behavior of LDI

● Dynamic behavior of LDI, Mechanisms of local environment reorganization

Theoretical Investigation of LDITheoretical Investigation of LDI

cR2

c c0

N (R ) 4 r g(r)dr

c ceff ,l c ref

c c ref

N (R , )(R , )N (R , )

Statistical Mechanics – Molecular Simulation

How can we calculate local densities? From the pair radial distributionfunction g(r)

Effective local density

cR2

c c0

N (R ) 4 r g(r)dr

ref cρ 2ρ

eff ,l c eff ,l c(R , ) (R , )

Liquid-like structure

Coordination number

Local density augmentation (LDA)

Local density enhancement (LDE)

eff ,l cenh c

(R , )F (R , )

SC Ethanol

Skarmoutsos, I., Samios, J., J. Phys. Chem. B., 110, 21931 (2006)

SC Water

Skarmoutsos, I., Guardia, E.,J. Phys. Chem. B, 113, 8887

(2009)

Influence of Intermolecular Interactions Influence of Intermolecular Interactions on LDA and LDEon LDA and LDE

•• LDE decreases with density.LDE decreases with density.

•• LDA maximum in range 0.6LDA maximum in range 0.6--0.8 0.8 ρρcc..

•• LDE and LDA higher in polar, Hydrogen bonded LDE and LDA higher in polar, Hydrogen bonded fluids.fluids.

•• Amplitudes of LDE and LDA :Amplitudes of LDE and LDA :•• Xe < CO2, N2, CH4 < NH3 < MeOH < H2O Xe < CO2, N2, CH4 < NH3 < MeOH < H2O

•• No significant differences in LDE and LDA No significant differences in LDE and LDA between nonbetween non--dipolar systems.dipolar systems.

•• For Hydrogen Bonding fluids, Water LDE and For Hydrogen Bonding fluids, Water LDE and LDA sufficiently higher than those of MeOH and LDA sufficiently higher than those of MeOH and NH3.NH3.

benh

eF

0

1

11)(

Skarmoutsos, I., Dellis, D., Samios, J., J. Phys. Chem. B.,113,2783 (2009)

T/Tc = 1.03

Representative SnapshotsMethanol Ammonia

Xenon Water

First Shell of sc ethanol going from low to high densities

Nc = 2

Nc = 7

Nc = 4

Nc = 10

Local Density ReorganizationLocal Density Reorganization

l l l(t) (t)

l

l lρ 2

l

ρ (0) ρ (t)C (t)

ρ (0)

l l0

C (t) dt

Local Density Reorganization time

Length Scale Effects on theLength Scale Effects on theMechanisms of Local Density ReorganizationMechanisms of Local Density Reorganization

3 length scale regions with different density dependence oflocal reorganization times (and different time decay)

00

1

R3

R1

Second ShellFirst Shell

g (r

)

r

First Peak

R2

Region 1 : r --> 0 – R1

Region 2 : r --> R1 – R2

First Shell : r --> 0 – R2

Second Shell : r --> 0 – R3

At very short intermolecular distances:

‘Direct’ Potential induced mechanism

Goodyear, G., Maddox, M. W., Tucker, S.C., J. Phys. Chem. B, 104, 6240-6266 (2000)

At higher length scales: Collective effects start to affect thelocal density reorganization

As the length scale increase

The Local Density Reorganization timeis maximized in the density range close

to the critical density

Effect of critical slowing down on local density dynamics

Density Dependence of local reorganization Density Dependence of local reorganization timestimesSC Ethanol

Skarmoutsos, I., Guardia, E., J. Phys. Chem. B. 113, 8887 (2009)

Local density reorganization as a function of densityand length scale

The Local Density Reorganization timeis indeed maximized

at higher lengthscales in the density range close

to the critical density

WHAT DO WE PREDICT?

Benzene

D. Dellis, I. Skarmoutsos, J. Samios, J. Mol. Liq. , 153, 25 (2010)

Local density reorganization processes Local density reorganization processes inside the first solvation shellinside the first solvation shell

‘Direct-Pair Potential’ and ‘Collective’ contributions:

212

0

22

1

1

44 NNdrrgrdrrgrRNR

R

R

cc

Skarmoutsos, I., Guardia, E., J. Phys. Chem. B. 113, 8887 (2009)

00

1

R1

First Shell

g (r

)

r

First Peak

R2

Length scale contributions on the reorganization mechanism

SC Ethanol

21 )1()()( 21tt

tt

leccetCtCtC

2121 )1( tctcl

First Solvation Shell

Second Solvation Shell

The time decay is differentespecially at higher densities

Another indication ofthe change in the relaxation

mechanism at larger length scalesSkarmoutsos, I., Samios, J., J. Chem. Phys., 126, 044503 (2007)

Time scale contributions

Residence DynamicsResidence Dynamics

ji ij

tijijres

h

thhtC

,20

0 *

dttCresres

0

● hij (t) = 1, if molecule j is inside the solvation shell of molecule i at times 0 and t and the molecule jhas not left in the meantime the shellfor a period longer than t*.

● hij (t) = 0 , otherwise

● t* = 0

● t* = 2 ps

Continuous

Intermittent- Like

Ethanol

The residence dynamics are also different atshort length scales, but not the same

with local density dynamics

Relation of HB network with LDIRelation of HB network with LDI

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 2,20,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

< n HB > Nc

c

< n H

B >

0

2

4

6

8

10

12

NC

Similar non-linear density dependence

with the coordination number

Ethanol

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 2,20,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

T / Tc = 1.03

sc H2O

< n H

B >

ρ / ρc

Water

Higher deviation from linearity

Possible reason for higher LDA valuesin SC water

Relation of spectral shifts with the local densityRelation of spectral shifts with the local density

Libration Bands in SCW

Now some experimentalists doubt previous assumptions that:

cmax

INDEEDWe observe a clearnon-linear behavior!

e.g. see Song, W., Maroncelli, M. , Chem. Phys. Lett., 378, 410 (2003)

Skarmoutsos, I., Guardia, E.J. Chem. Phys, 132, 074502 (2010)

HB Dynamics

ji ij

tijijHB

h

thhtC

,20

0 * dttCHBHB

0

● hij (t) = 1, if molecule j is hydrogen bonded with molecule i at times 0 and t and the bond has not been brokenin the meantime for a period longer than t*.

● hij (t) = 0 , otherwise

● t* = 0

● t* = ∞

Continuous

Intermittent

Effect of mutual diffusion and reorientation on HB Dynamics

ji ijd

ij

tij

dijd

HB hh

thhtC

, 00

0 *

● ifat times 0 and t and this bond length has not been largerin the meantime for a period longer than t*.

● , otherwise

Mutual Diffusion

dttC dHB

dHB

0

●

at times 0 and t and this angle has not been largerin the meantime for a period longer than t*.

● , otherwise

Intermittent Case

Mutual Reorientation

Skarmoutsos, I., Guardia, E., J. Phys. Chem. B. 113, 8898 (2009)

Effect of mutual diffusion - reorientation on HB Dynamics

Especially forContinuous dynamics

Mutual reorientation mechanism seemsto be more

important than mutual diffusionin the case of HB dynamics

Similar behavior with residence dynamicsat short length scales

Ethanol

Skarmoutsos, I., Guardia, E., J. Phys. Chem. B. 113, 8898 (2009)

What about single molecule dynamics?

Single Reorientational Dynamics

Legendre Reorientational tcfs

Skarmoutsos, I., Samios, J., J. Chem. Phys., 126, 044503 (2007)

Different density dependence for reorientational modes related withstronger interactions (e.g. O-H in methanol)

MeOH

Plateau

SC Ethanol

DifferentBehavior of1st, 2nd order

Legendre dynamics

3 groups of vectorsexhibiting similar

density dependence

Plateau for 2nd ordercorrelation times

related with weakerinteractions

Skarmoutsos, I., Guardia, E., J. Phys. Chem. B. 113,

8898 (2009)

Effect of the HB network on single reorientational dynamics

The HB network aroundeach molecule affectssignificantly its single

reorientational dynamics

Plateau for 2nd ordercorrelation timesare observed for

free (non-HB) moleculesAnd for modes relatedto weak interactions

● 1st order Legendre reorientational dynamics more affected by thelocal environment

● Modes related with weak interactions are not affected by LDI inthe case of 2nd order Legendre reorientational dynamics

Effect of the HB network on single translational dynamics

SCW (SPC/E)

Significant influence of the HB network on single translational dynamics!

The libration band peaks are shifted towards higher ω values for more strongly H Bonded water molecules

Skarmoutsos, I., Guardia, E.J. Chem. Phys, 132, 074502 (2010)

Bulk Density Dependence of librational modes as a function of H. Bonds

As the bulk density increases

the peaks shift towards higherfrequencies. Plateau behavior in the caseof more strongly H-Bondedmolecules (e.g. nHB = 3)

Dependence of the local HB network on the C.O.M. motion

Effect of the HB network on single O-H reorientational dynamics

Density Dependence HB Dependence

Further work in progress…..

FIN

Muchas gracias !Muchas gracias !