Solvation Forces

1
Lecture 4
Solvation Forces
2
Intermolecular Forces
3
Interaction Forces A Brief Review
van der Waals Forces

• Interaction dictated by dielectric succeptability
• Scales with interacting body size (? r )
• Short range forces
• Usually attractive between like bodies

4
The System So Far
- - -
Surfaces Surface Charge, Hamaker Constant,
Geometry
-

Fluids Dissolved ions, Hamaker Constant,
Temperature


Whats Missing?

5
Importance of Solvent Interactions

• At short separation distances (a few molecular
  layers) solvation interactions can dominate
  van der Waals forces.
• Influence becomes more dominant as van der Waal
  forces become weaker (e.g., systems with closely
  matched refractive indices)

Some phenomena strongly influenced by solvent
interactions

• Nanoparticle Dispersion
• Self-Assembly
• Biological Systems
• Protein Conformation

6
Solvation Interactions

• Structural interactions induced by solvent
  molecules at short separation distances (i.e.,
  when solvation spheres overlap)
• Arises when there is a change of solvent molecule
  density as two surfaces approach.
• Why?

Versus
Confinement!

• Can be oscillatory or monotomic.

7
Oscillatory Solvation Pressure
Repulsion
Pressure (P)
0
s
3s
2s
Attraction
Molecular Distances !!!
0
d Separation Distance
8
Oscillatory Solvation Pressure
3s
2s
0
s
d
Pressue (P)
0
3s
s
2s
0
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Calculating Solvation Interactions
A starting point The Contact Value Theorem
P(d) Pressure at separation d kT
Boltzmann Constant times Temperature ?s(8)
Density of surface solvent molecules at infinite
separation
Recall that
kT thermal energy magnitude of energy required
to win out against the disorganizing effects of
thermal motion
And, for a hard sphere system
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Calculating Solvation Interactions (contd.)
The simplest case
P(d) -kT?s(8) cos(2pd/s)e-d/s
P(d) Pressure at separation d kT
Boltzmann Constant times Temperature ?s(8)
Density of surface solvent molecules at infinite
separation s solvent molecule diameter
Note The above equation is based on a hard
sphere model between atomically smooth surfaces.
Solvent-surface interactions are not included.
Also assumes spherical solvent molecules.
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Solvation Contributions to Interaction Energy
Neglecting solvent-surface interactions for two
flat surfaces assuming ?s(8) ?bulk and an
idealized close packed system, then
for a FCC close-packed system
Taking
How does this compare to van der Waals
interactions?
Israelachvilli, Page 267
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vdwls Contributions to Interaction Energy
For van der Waals
Continuum Approach not strictly valid at
inter-atomic distances
Using a molecular approach
binding energy gained by surface contact
surface area occupied by each atom
Israelachvilli, Page 203 recall
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Simplified Solvation vs. van der Waals
Simplified Solvation
van der Waals
Equating the two interfacial energies solving
for A, we find that the contributions are
equivalent when A 0.2kT 1?10-21J
How can solvent-surface interactions modify this
effect?
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Solvent Structuring at Interfaces

• Solvent-Surface interactions ultimately lead to
  solvent structuring at the surface.
• Modification of the solvent structure as two
  surfaces approach results in solvation
  interactions.

Structuring
Solvation forces
No structuring No Solvation forces
To appropriately describe solvation interactions
liquid structuring at interfaces and transitions
thereof must be taken in account. -Not a
trivial task! -Currently not well
understood! -Modern Approach Experiment MD
Simulations
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Influence of Molecular Structure
Irregularly shaped molecules (e.g., assymetric or
branched chain molecules) are less likely to
order in discrete layers.
Leads to monotonic rather than oscillatory
solvation forces.
(Christenson and Horn, 1983)
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What ultimately defines the interaction?
Pressue (P)
0
3s
s
2s
0
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Basic Solvent-Surface Interactions
Solvophillic Surface likes the solvent
molecules.

• Difficult to remove the last layer of solvent
  molecules.
• Surface strongly interacts with solvent molecules.

Solvophobic Surface dislikes the solvent
molecules.
-Easy to remove the last layer of solvent
molecules.
-Surface structures but does not strongly
interact with solvent molecules
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MD Simulations Influence of Solvophillicityn-Dec
ane Small Spheres
Step-Like Solvophobic Forces
Weak Solvophilic Forces
Kristen A. Fichthorn and Darrell Velegol
Department of Chemical Engineering, Penn State
University
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Interactions for Spheres, Cubes
Large Sphere
Cube

• Shape influences interaction profile.
• Solvophilic solvation forces are oscillatory and
  often comparable to van der Waals forces
• Solvophobic solvation forces are attractive

Kristen A. Fichthorn and Darrell Velegol
Department of Chemical Engineering, Penn State
20
Influence of Molecular Roughness
Particle orientation significantly affects the
force profile Particles will Rotate in Solution
Kristen A. Fichthorn and Darrell Velegol
Department of Chemical Engineering, Penn State
University
21
Interim Summary

• Solvation forces occur when the solvation sphere
  of two approaching surfaces overlap resulting in
  structural modifications of surface-solvent
  molecules.
• Solvent type, solvent-surface interactions, and
  interacting geometries can have a significant
  influence on the overall interaction.
• Solvation interactions are often comparable to
  van der Waals interactions.

22
Solvation Interactions in Water

• Water is a unique solvent
• Tetrahedral Coordination ability to form 3-D
  networks
• Hydrogen bonding capability

Solvophillic ? Hydrophillic Interactions
(Hydration Forces)
- Additional monotonic repulsive force
Solvophobic ? Hydrophobic Interactions
- Additional monotonic attractive force -
Unusually long range attractive forces often
observed
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Solvation Interactions in Water (contd.)
In Water

• Hydrophillic Surfaces have an additional
  monotonic repulsive force range can be twice
  that of oscillatory forces in H20 (i.e., 3-5nm)
• Hydrophobic Surfaces have an additional monotonic
  attractive force

In simpler liquids

• Solvation interaction follows van der Waals,
  oscillating above and below

Israelachvili, p. 268
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Calculating Hydration Repulsion
Empirically, the work of hydration repulsion
between two hydrophillic surfaces appears to
follow the following equation
Where,
?0 0.6 - 1.1nm for 11 electrolytes
(characteristic decay length)
W0 depends on the hydration of the surface but is
usually below 3-30 mJ m-2 higher W0 value are
asssociated with lower ?0
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Hydration Interactions Whats Known

• Hydration forces may be the most important yet
  the least understood of all interaction forces.
  First principle theories are effectively
  non-existent.
• What has been observed
• Two general types of hydration interactions
• Intrinsic induced from native surface-water
  interactions
• Regulated induced from added electrolyte

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Hydration Forces A Classical Example
Forces between Mica surfaces in KNO3

• low salt Interaction follows conventional DLVO
• Higher salt (10-3 to 1M) oscillatory force
  appears with periodicity of 0.22 0.26 nm,
  monotonic component has a decay length of 1nm

A1212?10-20 J
Electrolyte can modify the Hydration Interaction
(Israelachivilli and Pashley (1983))
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Dissolved Cations and Hydration Interactions

• Enhanced hydration forces in the presence of salt
  believed to be related to the adsorption of
  hydrated cations.
• Enhanced repulsion thought to be due to the
  energy associated with dehydrating the cations.
• Strength of hydration force increase with
  hydration number of cations
• Mg2 gt Ca2 gt Li Na gt K
  gt Cs

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Hydrophobic Forces -- molecular interactions
with water --
Water tends to structure around but not with
hydrophobic moieties
-Favorable Enthalpy - Very Unfavorable Entropy
Hydrophobic moieties have unusually strong
interactions across water.
An Example
van der Waals interaction energy for two
contacting methane molecules
Free space -2.510-21 J Across
water -1410-21 J
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Contact Angle, q Some Guidance
gLG
?
gSG
gSL
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Long Range Attraction -- q gt 90 --

• At a specific distance, dependent on
  hydrophobicity (contact angle), surfaces
  attracted due to coalescence of nano-bubbles.
• - Force linked to type and concentration of
  dissolved gas

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LONG RANGE ATTRACTION -- effect of dissolved gas
--
Air
Saturated Argon
Rabinovich and Yoon, Colloids and Surfaces A,
(1994)
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Calculating Hydrophobic Attraction
Short or Long Range A Constant (mJ/m2), l
decay length (nm) l1 from 1-2 nm l3 from 10-20
nm H surface separation distance (nm)
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Concluding Remarks -- hydrophobic and hydration
forces --

• Due to the number of fitting parameters (y0,
  A132, spring constant, I.S.) and uncertainty in
  force laws (C.C. vs C.P., retardation)
  hydrophobic / hydration forces often invoked to
  explain differences between theory and
  experiment.
• Because solvation forces involve the structure of
  the solvent, the number of molecules to be
  considered in the interaction is large and
  computer simulation have only begun to approach
  this problem.
• Widely accepted phenomenological models of
  hydrophobic and hydration forces still need to
  be developed.