Van der Waals force

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Up: Nonbonded interactions

This page is not going to discuss the origin and nature of the VdW force but is focusing on practical applications and an intuitive understanding.

Practical usage

Getting an intuitive feel for this force that does not occur at the macroscale in everyday life

Bond trustworthiness, bond area and temperature (energy)

The question: VdW forces are "weak", so are they sufficient to hold stuff trustworthily together?

At room temperature a C-C bond practically does not break due to thermal motions. So a VdW bond with an area big enough to provide the same bonding energy will too practically not break at room temperature. As it turns out, this area is not all that big (relative of the area of a single C-C bond), so one might rely on VdW forces for reliably holding things together quite early on in the size scales of crystolecules.

So to prevent thermal motion from knocking VdW bonds open it might not be necessary to do some clever form closure designs (that are then strongly locked at a bigger size scale) except maybe for very small parts at very high temperatures. (TODO: ckeck that)

VdW bonds – stronger than expected (force = energy per length)

Two coplanar atomically flat surfaces attract each other quite a lot.
The attractive pressure from VdW forces is in the low nN range per square nm.
Here are two quite different values:

  • ~1nN per square nm. Note that this equates to no less than around ~10,000 bar.
    Original Source: (Nanosystems 9.7.1.)
    indirect source: [1] (beware: the noted binding energy is mistakenly taken from a covalent interface - Nanosystems 9.7.3.)
    double indirect source: [2]
  • ~2.7nN per square nm. Note that this is about 1/20 of the tensile strength of diamond
    Source: (Nanosystems 3.5.1.b) (And this is more than titanium and low grade steel. These are just two flat surfaces contacting. VdW forces are by no means weak from an intuitive pespective)

Especially if there is superlubrication a flat surfaces can still slide effortlessly on each other (that is - in case of small parts - relative motion may even be triggered by thermal motion) so depending on the use case male protrusions penetrating female indents may be needed to prevent that random 2D diffusion motion.
(related: intuitive feel)

(stiffness = force per length)

The stiffness of VdW bonds is substantially lower than the stiffness of bulk diamondoid material.

Infos from Nanosystems 9.7.1 (reformulated):
(30N/m)/nm^2 is a lower bound for the expectable stiffness of a VdW bond between two complementary diamondoid surfaces.
A slab of diamond must be increased in thickness up to 30nm thick (about 150 C atom diameters) such that this slabs stiffness decreases down to the same value of stiffness the VdW bond features. (wiki-TODO: illustrate this equivalence comparison)

(wiki-TODO: Retrace derivation & present more clearly.)
(wiki-TODO: Comparison with stiffness of singular C-C bond. Which VdW area is needed for equivalent stiffness?)

Comparison in energy, force and stiffness

Note: Force is the first spacial derivative of energy and stiffness is the second.

(wiki-TODO: Make a proper table comparing energy, force and stiffness of a single covalent C-C bond to a surface to surface contact VdW bond by showing the areas that are necessary such that the VdW bond can provide the equivalent values than the single C-C bond. Note that these are three different areas.)

Bonding energies - Tensile strengths - Stiffnesses

To get a better feel it can be helpful to compare energy strength and stiffness of VdW bonds to the strength of material that is solidly covalently "welded" together. This way it becomes clear that while VdW bonds are considered weak in comparison to they are still very strong in an intuitive sense.

(TODO: Add the same info table as on VdW force page)
[Todo: Add table - make it visualizable for covalent bonds and VdW bonds]
[Todo: show surface area thats VdW ashesion is energetically equivalent to one covalent bond - related: Form locking]


Please use external sources - there are plenty out there.
Wikipedia: [3]

In Nanosystems

  • Part I – Physical Principles > 3 Potential Energy Surfaces > ...
    ... 3.3. Molecular mechanics > 3.3.2. The MM2 model > e. Nonbonded interactions. – (page 48)
    ... 3.5. Continuum representations of surfaces > ... – (page 63)
  • Part II – Components and Systems > 9 Nanoscale Structural Components > ...
    ... 9.7. Adhesive interfaces > 9.7.1. Van der Waals attraction and interlocking structures – (page 270)


External links