ROLE OF THE RANGE OF INTERMOLECULARINTERACTIONS IN FLUIDS (TOWARDS A UNIFIED VIEW OF FLUIDS)

Ivo NEZBEDAE. Hala Lab. of Thermodynamics, Acad. Sci., Prague, Czech Rep.andInst. of Theoret. Physics, Charles University, Prague, Czech Rep.

COLLABORATORS:J. Kolafa, M. Lisal, M. Predota, Acad. Sci., PragueA. A. Chialvo, P.T. Cummings, ORNL, Oak RidgeM. Kettler, U of Leipzig, Leipzig

workshop on

SHORT RANGE INTERACTIONS IN SOFT CONDENSED MATTER

… You are invited to provoke a lively discussion with your ideas. Werner Kunz

Excerpts from referee’s reports:

…This result may generate some controversy, as it is at odds with the conventional wisdom.

…The results are provocative and will likely generate interest and discussion.

…This is an interesting study and presents useful results. However, some of their results are rather unusual and defy the conventional wisdom.

QUESTION:

What are the main driving forces that determine the observed macroscopic behavior of fluids?

WHY?

An answer to this question is an indispensable first step towards - more complete understanding of the behavior of fluids- the development of simple theoretically-based models, and hence molecular-based workable expressions for the thermodynamic properties of fluids

HISTORICAL BACKGROUNDAccounting for the overall electroneutrality of molecules, physical considerations identify four main types of interactions acting between the molecules of pure fluids:

1. Short-range repulsions that reflect, roughly, the shape and size of molecules (excluded-volume effects);2. Relatively weak and fast decaying (as 1/R^6 and faster, where R is the intermolecular separation) attractive interactions (called dispersion or van der Waals interactions);3. Long-range electrostatic interactions (e.g. dipole-dipole) having their origin in the permanent multipoles of molecules;4. Strong short-range and strongly orientation-dependent attractions identified as hydrogen bonding interactions (H-bonding).

It has thus been common to write approximate intermolecular interaction models accordingly,

)2,1()2,1()2,1()2,1()2,1( bondHmultipolemultipolevdWrep uuuuu

HISTORICAL BACKGROUND (cont.d)

Starting from the above form of u(1,2), it is tempting to express (explain) the properties of a more complex fluid in terms of an excess over a less complex (simpler) fluid, pointing to a perturbation treatment as a suitable tool for both theory and applications.

CONSEQUENTLY, the observable differences in the behavior of different substances (classes of fluids) seem thus to reflect differences in the relative strengths of the individual contributions to the total u(1,2), and the properties of fluids belonging to different classes seem to be determined by the different types of predominant interactions.

If this is true, problems for theory and applications immediately arise(and they do!).

)2,1()2,1(||

),(),,(,

)2()1(,

)2()1(2112 Coulombelnon

lk lk

lk

lklkLJ uu

rr

qqrruRu

Accepting the pair potential in this form, one immediately loses the clear (and simple) physical picture of intermolecular interactions.

Potentials for different compounds differ only in the geometrical arrangement of the sites and in the strengths of the individual site-site interactions.

Nonetheless, there is one general property which might be useful for the characterization of the interactions: their rate of decay with increasing intermolecular separation or, equivalently, the range over which they operate.

STATE-OF-THE-ART It is assumes that molecules contain interaction sites which may, but need notnecessarily, coincide with the location of the individual atoms.

The sites are the seat of two types of interactions:(1) non-electrostatic [short-range repulsions and medium-range attraction](2) long-range Coulombic charge-charge interaction

Effective pair potentials are of the site-site form:

To this end, we may define trial potentials of variable range,

)2,1();'','()2,1()2,1( CoulurRRSuu ccT ; S=0 for rcc<R’ and S=1 for rcc>R’’

and examine changes in the structure as the switching range (R’,R’’) varies.

ACETONE: C-C

r [Å]

2 4 6 8 10 12

g ij

0.0

0.5

1.0

1.5

ACETONE: O-C

r [Å]

2 4 6 8 10

g ij

0.0

0.4

0.8

1.2

ACETONE: O-O

r [Å]

2 4 6 8 10

g ij

0.0

0.4

0.8

1.2

TIP4P WATER: O-O

r [Å]

2 4 6

g ij

0

1

2

3

TIP4P WATER: H-H

r [Å]

2 4 6

g ij

0.0

0.5

1.0

TIP4P WATER: O-H

r [Å]

0 2 4 6

g ij

0.0

0.5

1.0

1.5

(4,6) (5,7) (7,9)

(3.1,4.1) (3.5,5.0) (4.0,6.0)

WORKING HYPOTHESIS: Provided that the trial potential uT(1,2) includes the firstcoordination shell, then the structure of the systems definedby u(1,2) and uT(1,2) is very similar (nearly identical).

In other words (and rather provocatively) the hypothesis claims thatthe long range part of the Coulombic interactions has onlymarginal effect on the structure of (pure) fluids.

OBSERVATIONS:1. When the potential is switched off at too short separations then too much of the Coulombic interactions is missing Differences in the structure become even qualitative

2. Close agreement is found for not too large RrangeR’’

Examination of validity of the hypothesis:

Properties examined:- complete sets of the site-site c.f. gss

- dipole-dipole c.f. Gk - radial slices through g(1,2)- dielectric constant- thermodynamic properties

homogeneous phaseliquid in equilibrium with its vapor

Compounds considered:carbon dioxide

acetoneacetonitrile

methanolwaterhydrogen fluoride

r [Å]

4 8 12

g ij

0.0

0.5

1.0

1.5

r [Å]

4 8 12

g ij

0.0

0.5

1.0

1.5

r [Å]

4 8 12

g ij

0.0

0.5

1.0

1.5

r [Å]

4 8 12

g ij

0

1

2

CH3-CH3C-C

N-NCH3-N

ACETONITRILE

r[Å]

3 5 7

g ij

0

2

4

6

r[Å]

4 6 8 10

g ij

0

2

4

r[Å]

4 6 8 10

g ij

0

2

4

r[Å]

2 4 6

g ij

0

2

4

6

C-C

O-C O-H

548

498

398

298

548548

498498

398

398

298

298

398

498

548

O-O

298

METHANOL

F-F

r [Å]

2 4 6 8

gij

0

1

2

3

F-H

r [Å]

2 4 6 8

gij

0

1

2

H-H

r [Å]

2 4 6 8

gij

0

1

2

HYDROGEN FLUORIDE

Contribution of the electrostatic interactions to the total configurational energy(in dependence on the switching range)

ACETONITRILE

r [Å]

4 8 12

<co

s

12>

-0.6

-0.4

-0.2

0.0

0.2

ACETONE

r [Å]

4 8 12 16

<co

s

12>

-0.6

-0.4

-0.2

0.0

0.2

HYDROGEN FLUORIDE

r [Å]

2 4 6 8

<co

s

12>

-0.25

0.00

0.25

0.50

0.75

1.00

1.25

1.50

TIP4P WATER

r [Å]

2 4 6 8 10

<co

s

12>

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

700/0.328

373/0.958

297/0.997

500/0.5

500/0.3

350/1.2

Dielectric constants of the full and short-range modelsat a number of thermodynamic conditions

(εmin, εmax) … range at the 95% confidence level

SUMMARY OF THE RESULTS:

From all the results obtained so far for pure fluidsone can unambiguously conclude that the primary driving force determining the structure of pure fluids are short-range interactions (which may be both repulsive and attractive) and thatthe long-range part of electrostatic interactions plays the roleof a mere perturbation only.

POTENTIAL LIMITS:

thermodynamic conditions - validity seems to extend to lower densitiesinhomogeneous fluids - a large body of simulation data available;

short-range models follow even such trends asflip over of the water molecules with decreasingcurvature of the (hydrophobic) interface

kinetic properties - shear viscosity and auto-diffusion coefficients of the full- and short-range models of water perfectly agree

TWO QUESTIONS IMMEDIATELY ARISE: (i) what are the limits of the drawn conclusions, and (ii) what are implications of the findings for theory and applications.

WATER

T [K]

300 400 500

B2

[cm

3 /mol

]

-5000

-3000

-1000

ACETONE

T [K]

400 600 800 1000

B2

[cm

3 /mol

]

-1200

-800

-400

0

POTENTIAL LIMITS:

thermodynamic conditions - validity seems to extend to lower densitiesinhomogeneous fluids - a large body of simulation data available;

short-range models follow even such trends asflip over of the water molecules with decreasingcurvature of the (hydrophobic) interface

kinetic properties - shear viscosity and auto-diffusion coefficients of the full- and short-range models of water perfectly agree

zO-wall

0 5 10

0

1

zH-wall

0 5 10

0.0

0.5

1.0

zO-wall

2 4 6

-0.4

-0.2

0.0

0.2

cut4_z vs cut4_alpha full_z vs full_alpha

<co

s

g H-w

all

g O-w

all

full- and short-range TIP5P-E waterat a flat Lennard-Jones 9-3 carbon wall

T=298 K, density=1.0 g/cm3

circles … full modellines … (4,6) short-range model

POTENTIAL LIMITS:

thermodynamic conditions - validity seems to extend to lower densitiesinhomogeneous fluids - a large body of simulation data available;

short-range models follow even such trends asflip over of the water molecules with decreasingcurvature of the (hydrophobic) interface

kinetic properties - shear viscosity and auto-diffusion coefficients of the full- and short-range models of water perfectly agree

OPEN PROBLEM: MIXTURES

Due to polarizibility and other possible effects brought about by electrostatic interactions between unlike species, the pair interaction, and hence the local and, particularly, orientational arrangement may be changed. The most difficult mixtures will evidently be solutions of electrolytes. Nonetheless, even in this case there is at least a piece of indirect evidencethat the same conclusions may be correct at least for dilute electrolytes

IMPLICATIONS FOR THEORY AND APPLICATIONS

Once the long-range part of electrostatic interactions may beignored at the zeroth level of approximation, then - one can immediately devise a perturbation expansion about a suitably chosen short-range reference. - the way for theoretically-based modeling of complex problems is open

For accomplishing the expansion, the so called primitive models (counterparts of hard spheres for non-simple fluids) are employed.

A theoretical method has been developed enabling one to derive a primitive model as a direct descendant of a realistic parent model.

Primitive models reproduce, even (semi)quantitatively, the structure of therealistic fluids and their main field of applications is thus- in modeling of complex problems, and - in both theoretical and computer simulation studies of details of molecular mechanisms governing the behavior of fluids.

THANK YOU :-):-)