Intermolecular forces, surface forces&

the Atomic Force Microscope (AFM)

Reading suggestion: J. N. Israelachvili, Intermolecular and surface forces,

Academic Press 2011

The four forces of nature

• Strong interactionHolds neutrons and protons together in atomic nuclei.

• Weak interactionβ and elementary particle decay

• ElectromagnetismAll intermolecular forces can be derived from electromagnetic interactions!

• GravitationCan be ignored in molecular interactions, but might be significant for particles of sice ~ µm or larger.

+ -r

Molecule

Surface

ion - ion

Baspar

Guanine-cytosine base pair

N

N

N

N

O

N H

H

N

N

O

NHH

HBackbone

Backbone

Force and energy in molecular interactions

Bonds in molecules ~ 100-500 kJ/mol

Bonds between molecules 10 kJ/mol<~

Force- and potential curves

( )( )

W rF r

r

∂= −∂

The equilibrium distance re is at thepotential minimum, where the force between particles is zero!

( )F r = Force

Interaction between two particles

( )W r = Potential

Forces between atoms and molecules

• Polarization forcesIon - induced dipoleDipole - induced dipole (Debye)

• Dispersion forces (van der Waals)Induced dipole - induced dipole

(London)

Dispersion forces, van der Waals forces

• Quantum mechanical ”forces”Covalent bondsMetal bindingBorn repulsion

• Electrostatic forcesIon – ion (Coulomb)Ion – dipoleDipole - dipole (Keesom)

• Hydrogen bondsSpecial case of dipole-dipole interaction

Forces betweenatoms andmolecules

{{

{Q charge (C)u dipole moment (Cm)α polarizability (C2m2/J)r distance (m)ν elektronic absorption

frekvens (Hz)

200

10

3

2

0.5

kT

Coulomb-interaction

For two particles with charges q1 and q2 :

1 2

0

( )4

q qW r

rπε ε= −

Ex: For Na+ and Cl- separeted by the distance r = 2.8 Å,

W(r) = - 8 × 10-19 J ≈ 200 kT

Strong interaction, which decays slowly with the separation; ~ 1/r.

Dipole-interactionsIon-dipole Dipole-dipole

Of relevance only for very polar molecules at normal temperatures.(Hydrogen bonds!)

>> kT at typical interatomic distances, strong enough to bind ions to polar molecules, and to orient them, at RT. (Hydration of ions!)

Hydration of ions

Cations Anions

Apparent dynamic hydration numbers (ADHN), versus the Jones-Doleviscosity B coefficients (a measure of the affinity of ions for water).

0

11B

c

ηη

= −

Zavitsas, Curr Opin Colloid Interface Sci, 23 72–81 (2016).

η0 is the viscosity of pure water,

η is the viscosity at the concentration c.

Hydrogen bonds

Electronegativehydrogen bonddonor

Electronegative acceptorwith unpaired (non-binding) electron pair. Typically O, N or F.µ

Dipole moment

δ+δ−

D — H … A

• NB! A hydrogen bond acceptor is an electron donor!• A dipole-dipole bond, with covalent contribution.• May create short-range order in liquids,

which are then termed associated.• Of considerable importance for the very special

physical and chemical properties of water.

See http://www.lsbu.ac.uk/water/anmlies.html for a list of anomalous properties of water!

Hydrogen bonds in waterSome bond strengths in water (kJ/mol):O-H covalent bond 492Hydrogen bond 23.3van der Waals-attraction 1.3

• Hydrogen bonds have some covalent character, but it is debatedto which extent.

• Hydrogen bonds are directed, but small deviations from linearity(up to approx +/- 20 degrees) have little influence, but the strengthdecays exponentially with the separation.

• Water molecules are well separated in condensed phases(water and ice) so there is plenty of room for bending andstretching of the bonds.

Dispersion forces(London-, van der Waals-, electrodynamic- or fluctuation forces)

• Caused by temporary dipoles in atoms or molecules,which generate temporary dipoles in the surroundings,which in turn attrach each other.

• Always present, therefore of great importance fora number of molecular phenomena.

• Effective rage ~ 0.1–10 nm; w(r) ~ 1/r6

• Non-additive; the forces between two moleculesis affected by the presence of a third molecule.

• London’s approximation:

(α = polarizability, Ι = ionisation energy)

21

216

21

3

2)(

II

II

rrW

+−= αα

Field off

Field on

Atomic and molecular polarizability, α0

Wvdw ∝ α0E

b

Example: Surface tension componentsSurface tension is caused by intermolecular forces (or the absence of them acrossthe interface), and surface tension can be divided into contributions from these:

Dispersive contributionsLW = Lifshitz/van der Waals

Polar contributionsAB = Acid/Base

2ABlγ γ γ+ −=

γ+ = Acceptor contributions (Lewis acid) γ− = Donator contributions (Lewis base)

γ = γ LW + γ AB

Forces between surfaces

• Electrostatic• Dispersion (vdW)• Steric – Undulation• Structural – Hydration• Entropic – Bridging • Osmotic – Depletion• Capillary forces• Hydrodynamic• Hydropfobic forces• Casimir forces• ...

Forces between particles or surfaces cannot be considered only as the sum of the forces acting between individual molecules:

Interactions which depend on molecular sizesolvent structureentropic effects andosmotic pressure are apparent, and are ofparticular importance inaqueous solutions.

van der Waals forcesbetween surfaces / particles

NB! The relations in the figure yield the potential W. A can be determined either by Hamaker’s (A constant) or Lifshitz’ (Adistance dependent) method.

There are two routes from van der Waals forces between individual molecules to vdW-forces between surfaces:

• Hamaker’s additive method:Assume that the force between surfaces can be considered a sumof the forces between individual atoms. (Does not work well with amedium between the surfaces.)

• Lifshitz’ continuum method:Consider the electric fields betweentwo polarizable surfaces, and sum the energies from all these contributions.

vdW-forces between atoms/molecules are always attractive, but might be repulsive between macroscopic surfaces (rarely!).

van der Waals forces between surfaces / particles II

i

j

ΣΣ−Fiji j

12

Hamaker constant versus oxide thickness for silicon-silicon oxide-contacting material systems

Langmuir 2015, 31, 4862−4867.DOI: 10.1021/acs.langmuir.5b00251

Thickness versus time for oxide growth incontact with various media.

A native silicon oxide film will grow on silicon if left exposed to air. This native oxide is self-limiting. In dry oxygen, the film will only grow to ∼1 nm, whereas in humid air, the film will grow to ∼2 nm.

Casimir interactionTwo conducting plates in vakuum attract each other due to the absence of electromagnetic fields with λ > d between them, while these are present on the outside, causing a radiation pressure from the outside!

A phenomenom of relevance for e.g. cosmology, atomic spectroscopy and particle physics, but also of relevance for micromechanical structures which are predicted to become more and more important for chemical analysis and biosensing!

2

4

( )

240

F d c

A d

π= − h

The electrostatic double layer

A surface in water is almost always charged:

• Ionization of acids or bases on the surface• Adsorption of ions (ex. OH– ).• Asymmetric dissociation from the surface.

Surface charges create a surplus of counter-ionsnear the surface, more strongly bound nearer the surface.

Electrostatic double layer forcesTwo equally charged surfaces repel each other; in air this is a purely electrostatic effect, while in water, where counter-ions screen the surface charges, the charges at the surfaces do not interact directly with each other.

In water the repulsion is primarily an effect of repulsion between the counterions: As the surfaces are brought closer together, the available volume for each ion is reduced, this increases electrostatic interaction, reduces the entropy, and increases the total free energy.

DLVO-forces

The sum of van der Waals and electrostatic forces (=DLVO) is of great importance in water-based systems, where both always are present, and it decides the stability of colloidal systems.

The total force can be modulated e.g. by varying the salinity, or the surface charge.

(Derjaguin-Landau-Verwey-Overbeek)

Forces caused by solvent structureMolecules near a smooth interfaces tend to order themselves in layers; the order reaches a few molecular diameters from the surface.

An oscillating force appearbetween the surfaces.(Of relevance e.g. for lubrication!)

P85 is a polymer which formesaggregates near room temperature.

Pluronics P85 (EO27PO39EO27)

Forces between SiO2 surfaces in P85:

Thormann, Phys. Chem. Chem. Phys., 12, 10730 (2010)

Hydration

Strong hydrogen bonds in water increases the tendency to molecular order, especially near charged interfaces.

Force measurements between micasurfaces in water with 1 mM KCl(inset shows a theoretical calculationfor the same system), showing the removalof layers of adsorbed hydrated ions.

Water is often strongly bound to surfaces or ions...

Steric stabilization with polymers

Compression Interpenetration

Polymers with molecular weight > 10 kDa have a size typically extending beyond the range of van der Waals forces.

Such a polymer can prevent two surfaces from coming close enough for attraction to be significant if it is adsorbed to the surfaces, and if the solvent is good enough so that the chains do not attract each other.

~

Poly(etylene glycol)-modified surfaces are frequently used to preventnon-specific protein adsorption, by steric repulsion.

Attractive ”bridging”of polymersLong polymers which adsorb to two surfaces result in attraction since it is entropically unfavourable for the chains to be stretched.

Requires low surface concentration of the polymer, so that a chain has a reasonable chance to bind to both surfaces.

At high surface concentration (forcing chains into the solution) long polymers with high affinity will form ”bridges”.

Interactions with a polymer chain gives more possible configurations than what is possible for interactions with the solvent alone, increasing entropy.

Effect of surface concentrationand solvent quality on forcesbetween surfaces with adsorbedpolymers.

T < θ Interaction between monomers is attractive.

T > θ Repulsion betweenmonomerers.

Depletion forces

If the two large surfaces come close enough, small particles are excluded from the volume between them, resulting in a lower osmotic pressure between the surfaces, forcing the large particles closer to each other.

Rayleigh-instability

A water jet breaks up in droplets through (Plateau-)Rayleigh instability, driven by the surface tension.

The same effect has been observed in falling streams of powders!

Cluster formation through van der Waals forces and capillary bridges between nm-sized roughness on the surfaces.

These forces correspond to an equivalent surface tension about five orders of magnitude weaker than in water.

Royer, Nature 459, 1110 (2009)

Measurement of forces between surfaces

• Indirect methods, e.g.– Adsorption isotherms– Contact angle measurements– Rheology or sedimentation rate (colloids)

• Direct methods, e.g.– Adhesion tests – Surface force measurements, R ~ cm– Atomic force microscope, R ~ nm-µm

Scanning Probe Microscopy, SPM

• A family of methods for ”imaging” of surfaces, where a probe is scanned over a surface in a regular pattern.

• The probe can be sensitive to topography, surface elasticity, electron density, surface charge, hydrophobicity, heat conductivity, specific chemical interactions (e.g. gen-antigen), magnetism etc.

Topographic image of a DVD master

Magnetic image ofa hard disk storage

The atomic force microscope (AFM)• Topographic images of surfaces over dimensions from 1 nm to 100 µm.

• Commonly used method for direct measurement of forces between surfaces.

• Sensitivity ~10-12 N, (covalent bonds have strengths of ~ 10-9 N).

A sharp tip is mounted on a spring (cantilever) and scanned over the surface. The deflection is recorded, and is assumed to reflect the topography of the surface.

In force measurements, the tip is only moved vertically, and the deflection vs separation is recorded. The spring stiffness then gives the force via Hooke’s law.

Functionalization of probes• Colloidal particles

5 µm

(M. Rutland)

Gives the probe a well-defined radius, for quantitative force measurements.

Chemical modification of the probe to vary thesurface charge, surface energy, polarity, etc.

Molecules for specific interactions or recognition, e.g. antibodies, oligonucleotides for DNA recognition, or other ligands.

• Molecules

• Surface coatings

Mechanical strength in proteins

Rief m.fl. J. Mol. Biol. 286, 553 (1999)

Proteins with mechanical functions (e.g. muscles) can be investigated by AFM to provide information about their function or mechanisms.

Unfolding of immunoglobulin domains in the muscle protein titin, ~ 200 pN/domain.

Avidin-biotin bindning

Moy, Science 266, 257 (1994)

Ligand-receptor F (pN) ∆H (kcal/mol) ∆G (kcal/mol) Avidin-iminobiotin � 85 -11.6 -14.3 Avidin-destiobiotin � 94 -13.5 -16.5

Streptavidin-iminobiotin + 135 ? -12.2

Avidin-biotin � 160 -21.5 -20.4 Streptavidin-biotin � 257 -32.0 -18.3

Adhesive forces are proportional to ∆H but not ∆G, implying that the separation is adiabatic (isoentropic). Entropic changes occur after the separation of the ligand-receptor pair.

Protein-membrane receptor recognition

Luckham, Faraday Discuss., 111, 307 (1998)

Enzyme activity: Lipid hydrolysis via Phospholipase A2

Grandbois, Biophys. J. 74, 2398 (1998)

Före 2 min

4 min 6 min Soft Matter 2014, 10, 7769DOI: 10.1039/c3sm52785a

(1) Prior to moving together,(2) compressed during thin film drainage,(3) adhering due to depletion attraction,(4) being stretched during separation, and(5) after separation while they are still moving apart. DOI: 10.1039/c3sm52785a

See video in the Supporting Information!

(contact radius)

Cell adhesion

Evans, Biophysical Chemistry 82, 83 (1999)

Real cells or model membranes (above) on micropipettes can be used to measure cell adhesion or the strength in membrane bound molecules.

Histogram for the force inone biotin-streptavidinbond.

(Biotin is a vitamin, and streptavidin a proteinreceptor. This pair forms one of the strongest non-covalent bonds in biology.)