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					Lecture 4:

Solvation Forces

Intermolecular Forces
6

Interaction F orce/R adius (m N /m )

5 4 3 2 1 0 -1 -2 0

v an d er W aals E lectro static S teric D ep letio n H y d ro p h o b ic S o lv atio n

Repulsive Forces (Above X-axis) Attractive Forces (Below X-axis)
10 20 30 40 S ep aratio n D istan ce (n m ) 50

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
Electrostatic Forces: - Interaction dictated by surface charge & solution ionic strength - Scales with interacting body size ( r2) - Long range forces - Usually repulsive between like bodies

The System So Far
+ Surfaces: Surface Charge, Hamaker Constant, Geometry Fluids: Dissolved ions, Hamaker Constant, Temperature + + + What’s Missing? Solvent-Solvent & Solvent-Surface interactions

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

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.

Oscillatory Solvation Pressure
δ= 0

σ

2σ

3σ

Pressure (P)

Repulsion 0 σ 2σ 3σ Attraction

Molecular Distances !!!
0
δ = Separation Distance

Oscillatory Solvation Pressure
δ= 0

σ

2σ

3σ

ρs(δ) = 0

>ρ∞

<ρ∞

>ρ∞

>ρ∞

<ρ∞

>ρ∞

Pressue (P)

0

σ

2σ

3σ

0

Results from solvent density fluctuations between approaching surfaces

ρs(δ) = Surface Density of Solvent Molecules; ρ∞= ρs(∞)

Calculating Solvation Interactions
A starting point: The Contact Value Theorem
P ( )  kT  s ( )   s (  ) 

P(δ) – Pressure at separation δ kT – Boltzmann Constant times Temperature ρs(∞) – 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:
PV  nkT

Calculating Solvation Interactions (contd.)
The simplest case:

P(δ) = -kTρs(∞) cos(2πδ/σ)e-δ/σ
P(δ) – Pressure at separation δ kT – Boltzmann Constant times Temperature ρs(∞) – Density of surface solvent molecules at infinite separation σ – 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.

Solvation Contributions to Interaction Energy
Neglecting solvent-surface interactions for two flat surfaces assuming ρs(∞) ≈ ρbulk and an idealized close packed system, then
i 
1 2 W (0)  kT  s (  ) 8
2

Taking :  

2



3

for a FCC close-packed system
kT  8
2

i 

2



3



0 . 02 kT



2

How does this compare to van der Waals interactions?
Israelachvilli, Page 267

vdwls Contributions to Interaction Energy
For van der Waals:
1 A  i   2  12 
2 0

   

Continuum Approach not strictly valid at inter-atomic distances

Using a molecular approach:
i 
1 3w 3A 0 .1 A     2  2 2 2 2   sin 60   2   
6

3 w  3 C /  = binding energy gained by surface contact
2  sin 60  = surface area occupied by each atom

A   C
2

2

 

2



3

Israelachvilli, Page 203; recall

Simplified Solvation vs. van der Waals
Simplified Solvation van der Waals
i 
0 .1 A

i 

0 . 02 kT



2



2

Equating the two interfacial energies & solving for A, we find that the contributions are equivalent when A ≈ 0.2kT ≈ 110-21J

Indicates that without taking in account solvent-surface interactions, solvation forces can dominate van der Waals interactions in systems where A < 110-21J
- Many biological interactions (e.g., cell-cell; protein folding) - Refractive index matched suspensions, etc.

How can solvent-surface interactions modify this effect?

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

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)

What ultimately defines the interaction?
If the last layer of solvent molecules is removed, the interaction will result in adhesion

Pressue (P)

0

σ

2σ

3σ Ultimate interaction can be defined by Surface-Solvent Affinity

0

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

MD Simulations: Influence of Solvophillicity
n-Decane – Small Spheres
1.0 0.0

F·σ/kT

-1.0 -2.0 -3.0 Solvophilic Solvophobic van der Waals -4.0 0.5 2.5 4.5 6.5 8.5 10.5

Weak Solvophilic Forces

Step-Like Solvophobic Forces

δ/σ

Kristen A. Fichthorn and Darrell Velegol; Department of Chemical Engineering, Penn State University

Interactions for Spheres, Cubes
600.0 400.0 200.0
F·σ/kT

10.0 5.0 0.0
F·σ/kT

-5.0 -10.0 -15.0 -20.0 -25.0 -30.0

0.0 -200.0 -400.0 -600.0 1.5 2.0 2.5 3.0 δ/σ 3.5 4.0 4.5

Large Sphere
Solvophilic Solvophobic van der Waals
1.0 1.5 2.0 2.5 δ/σ 3.0 3.5 4.0

Cube

van der Waals Solvophilic

• 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

Influence of Molecular Roughness
6.0 5.0 Left Center Right

Force (kT/σ)

4.0 3.0 2.0 1.0 0.0 -1.0 -2.0 0.0 0.5 1.0 1.5 2.0 2.5

3.0

3.5

Separation (σ)

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

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.

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

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

Calculating Hydration Repulsion
Empirically, the work of hydration repulsion between two hydrophillic surfaces appears to follow the following equation:
W flt  flt ( )  W 0 e
  / 0

Where,

λ0≈ 0.6 - 1.1nm for 1:1 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 λ0

Hydration Interactions: What’s 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

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
A121=210-20 J

Electrolyte can modify the Hydration Interaction
(Israelachivilli and Pashley (1983))

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+ > Ca2+ > Li+ ~ Na+ > K+ > Cs+

Ions can be used to disperse or coagulate suspensions

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: -2.5×10-21 J Across water: -14×10-21 J

Contact Angle, q – Some Guidance
LG SG SL q

At least two general classes of hydrophobic forces are identified - q < 90° short range attraction (~10-20 nm) - q > 90° long range attraction (> 20 nm)

Long Range Attraction -- q > 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

LONG RANGE ATTRACTION -- effect of dissolved gas -Air

Saturated Argon

Rabinovich and Yoon, Colloids and Surfaces A, (1994)

Calculating Hydrophobic Attraction
Short or Long Range

W flt

/ flt

  A 1e

 H / 1

 A 2e

H / 2

 A 3e

H / 3

A = Constant (mJ/m2),  = decay length (nm) 1 from 1-2 nm; 3 from 10-20 nm H = surface separation distance (nm)
W flt / flt  K 132 12  H
2

Yoon et al.

K132 = hydrophobic force constant (may be 5 to 10 x greater than Hamaker Constant), (mJ) May be applied between dissimilar surfaces

K 132 

K 131  K 232

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.

•

•


				
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