A new ansatz for thermodynamics of confined systems

Harald Morgner Wilhelm Ostwald Institute for Physical and Theoretical Chemistry

Leipzig University, Linnéstrasse 2, D-04103 Leipzig, hmorgner@rz.uni-leipzig.de

Introduction to the phenomenon of adsorption hysteresis

Shortcomings of standard thermodynamics for confined systems

New concept Applications:•control of negative pressure (static, dynamic) molecular conformation, reaction rate, solvent properties, separation

CompPhys10, Leipzig, Nov. 25, 2010

N2 SBA-15

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P/P0

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Adsorption Hysteresis in Porous Material

R.Rockmann, PhD Thesis 2007, U Leipzig

Introduction Theoretical Applicationsadsorption from vapor phase

adsorption

desorption

Introduction Theoretical Applicationsadsorption from vapor phase

Adsorption Hysteresis in Porous Material adsorption isotherm, model calculation

0.E+00

1.E-09

2.E-09

3.E-09

4.E-09

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6.E-09

7.E-09

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P/P0

ad

so

rpti

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[m

ol/c

m^

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adsorption

desorption

low pressure

H.MorgnerJ.Phys.Chem.

C114 (2010) 8877-83

pore size distribution

0

0.05

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0.15

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0.25

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0.35

0 2 4 6 8

diameter [nm]

pro

bab

ility

Introduction Theoretical Applications computer simulation

shape of pore

isotherm of pores with two open ends

crossing of grand potential curves

gas reservoir

adjustedgas density

gas reservoir

adjustedgas density

treated explicitely in simulation

pore wall

adsorption isothermstraight pore with two open ends

0.0E+00

5.0E-10

1.0E-09

1.5E-09

2.0E-09

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reduced pressure P/P0

loa

d [

mo

l/c

m2]

adsorption

desorption

infinite pore length vs. finite pore length

0.E+00

1.E-09

2.E-09

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-72000 -70000 -68000 -66000 -64000 -62000 -60000

chem. potential [bar*cm^3/mol]

load

[m

ol/c

m^

2]

infinite pore (EOS)

adsorption

desorption

controlled volume increase

controlled volume decrease

Simulation: adsorption in cylindrical pore of infinite length EOS

Introduction Theoretical Applications computer simulation

pore with infinite length

-8E-12

-7E-12

-6E-12

-5E-12

-4E-12

-3E-12

-2E-12

-1E-12

-7200 -7000 -6800 -6600 -6400 -6200 -6000

chem.pot. [J/mol]

gra

nd

po

ten

tia

l pe

r u

nit

len

gth

[J

/cm

]

Simulation: adsorption in cylindrical pore of infinite length EOS

Introduction Theoretical Applications computer simulation

infinite pore length vs. finite pore length

0.E+00

1.E-09

2.E-09

3.E-09

4.E-09

5.E-09

6.E-09

-72000 -70000 -68000 -66000 -64000 -62000 -60000

chem. potential [bar*cm^3/mol]

load

[m

ol/c

m^

2] infinite pore (EOS)

adsorption

desorption

controlled volume increase

controlled volume decrease

adsorption isothermstraight pore with two open ends

0.0E+00

5.0E-10

1.0E-09

1.5E-09

2.0E-09

2.5E-09

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reduced pressure P/P0

loa

d [

mo

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high load

low load

Introduction Theoretical Applications shortcomings of TD

shape of pore

isotherm of pores with two open ends

crossing of grand potential curves

observations:

•switching points decoupled from grand potential crossing

•switching points reproducibly stable in experiment and simulation

•„metastable“ states are stable in simulation and in experiment for any trial time (up to > 6 weeks)

-2E-18

-1.5E-18

-1E-18

-5E-19

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reduced pressure P/P0

gra

nd

po

ten

tia

l [J

] grand potential

Introduction Theoretical Applications shortcomings of TD

Neimark&Vishnyakov

J.Phys.Chem. B110 (2006) 9403-12

LJ-model for N2

spherical pore with diameter 15.8

virtual interface to gas reservoir

Monte Carlo simulation

Introduction Theoretical Applications shortcomings of TD

Neimark&Vishnyakov

J.Phys.Chem. B110 (2006) 9403-12

explanation by Neimark et al:

•both branches contain a set of microstates

•these sets are subsets of one common state (equilibrium). Thus, both branches form only one state

•in actual simulation (and experiment) only one subset of microstates is accessible depending on history (constraint equlibrium).

•thus, postulated equilibrium state does not show up in (computer) experiment

true GCE isotherm

„….the true GCE isotherm cannot be sampled in practical simulations….“

Introduction Theoretical Applications new concept, confined TD

COS and concept of applying canonical boundary conditions

COS allow to retrieve isotherm

curves of statesstraight pore with two open ends

0.0E+00

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1.5E-09

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reduced pressure P/P0

loa

d [

mo

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COS(alfa)

COS(beta)

adsorption isothermstraight pore with two open ends

0.0E+00

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reduced pressure P/P0

loa

d [

mo

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adsorption

desorption

grand canonical boundary conditions

canonical boundary conditions

Introduction Theoretical Applications new concept, confined TD

isotherm finite pore length

1.E-09

2.E-09

3.E-09

4.E-09

5.E-09

-66000 -65000 -64000 -63000 -62000 -61000 -60000

chem. pot.

adso

rpti

on

[m

ol/c

m^

2] two IF

one IF

COS() two IF

COS() one IF

curves of states (COS)

rules of new concept:

•system is fully described by COS

•change within COS is always reversible

•switching between different COS is always irreversible, occurs only if required by boundary conditions

•all states of a system can be visited in simulation and experimentally

Introduction Theoretical Applications new concept, confined TD

isotherm finite pore length

1.E-09

2.E-09

3.E-09

4.E-09

5.E-09

-66000 -65000 -64000 -63000 -62000 -61000 -60000

chem. pot.

adso

rpti

on

[m

ol/c

m^

2] two IF

one IF

contr. chem. pot.

contr. volume

contr. amount

curves of states (COS)

COS() two IF

COS() one IF

Transitions between curves of states (COS)

Introduction Theoretical Applications new concept, confined TD

Standard TD:

one EOS exists

states depend on actual boundary conditions, not on history

rules involving TD potentials predict all equilibrium states

hysteresis requires ad hoc assumptions

Confined TD:

one or more COS exist

changing between states of same COS reversible

change between COS irreversible

TD potentials loose predictive power

hysteresis natural consequence of concept

Introduction Theoretical Applications negative pressure

negative pressure states

curves of statesstraight pore with two open ends

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reduced pressure P/P0

loa

d [

mo

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COS(alfa)

COS(beta)

expanded liquid: -140bar !

Introduction Theoretical Applications control of negative pressure

negative pressure: exerts pull onto embedded molecule

negative pressure is known for macroscopic systems, but metastable (e.g. A. R. Imre On the existence of negative pressure states, Phys. Stat. Sol. (b) 244 (2007) 893-9)

in the nanoworld negative pressure states are stable and can be controlled, homogeneous negative pressure is taken on in volumes large enough to handle big (bio-)molecules

for comparison: positive pressure of ~80bar turns CO2 into polar solvent!

what can -140bar do to influence molecular properties?

•molecular conformation

•reaction rate (large reaction volume)

•solvent properties•separation of mixtures by inducing phase separation at neg. pressure Indirect methods to study liquid-liquid miscibility in binary liquids under negative pressure Imre, Attila R. et al. NATO Science Series, II: Mathematics, Physics and Chemistry  (2007), 242 (Soft Matter under Exogenic Impacts), 389-398

Introduction Theoretical Applications negative pressure in stationary flow?

for high throughput: continuous flow of solvent desirable

can situation of negative pressure exist under stationary flow?

the answer requires the ability to handle a velocity field

Introduction Theoretical Applicationsgeneralized diffusion

Transport of Matter

Common Treatment of Diffusion and Convection by generalized Diffusion

vgradT

LJ

vgrad

Ma

1

vgradxgradx

Ma BBAA

1

vgradT

LJ AAA

vgrad

T

LJ BBB

single component:

binary system:

only one common driving force

Introduction Theoretical Applications negative pressure in stationary flow

the answer:

negative pressure can be held up under stationary flow!

curves of statesstraight pore with two open ends

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reduced pressure P/P0

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d [

mo

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COS(alfa)

COS(beta)

v=0.018cm/s => residence time in 100nm pore is ~500s

Thank you !

comments or criticism welcome !!!

Introduction Theoretical Applicationsadsorption from vapor phase

exp. adsoption isotherm, Ar / SBA-15, 77.35K

0.E+00

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0 0.2 0.4 0.6 0.8 1P/P0

adso

rpti

on

[m

ol/c

m^

2]

R.Rockmann PhD Thesis

2007U Leipzig

Adsorption Hysteresis in Porous Material

SBA-15:

silica pores with two open ends

narrow pore size distribution

Introduction Theoretical Applicationsbehavior of fluids in mesopores

natural phenomena •hydrology of ground water•natural purification and pollution

industrial activities •oil extraction•mixture separation, filtering•catalysis•sensor development

basic research •bioanalytics

Introduction Theoretical Applications new concept, confined TD

Pore with bottom,narrow mouth

isotherm, pore with bottle neck

1.E-09

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4.E-09

-70000 -65000 -60000

chem.pot.

ad

so

rpti

on

[m

ol/c

m^

2] two IF

one IF

curves of states (COS)

homogeneous volume 3nm x31nmexpanded liquid

neg. pressure, P< -100 bar

Introduction Theoretical Applications new concept, confined TD

more complex pore shape

five COS!

if done correctly, full control over all states in all COS!

large volume with neg. pressure

P< -140bar in 13nm x 18nm

COS (Curves of States)

0.0E+00

2.0E-09

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P/P0

adso

rpti

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[m

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m2]

COS(alfa)

COS(beta)

COS(gamma)

COS(delta)

COS(epsilon)

Adsorption in Porous Material

N2 SBA-15

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adsorption

R.Rockmann, PhD Thesis 2007, U Leipzig

Introduction Theoretical Applicationsadsorption from vapor phase

N2 SBA-15

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Desorption in Porous Material

desorption

R.Rockmann, PhD Thesis 2007, U Leipzig

Introduction Theoretical Applicationsadsorption from vapor phase