Imagine you have two particles or molecules, alone in an empty space. At first glance, there seems to be no interaction between them, but if we zoom in enough with our microscopic lens and look closely, something incredible begins to happen: an invisible dance begins to connect them.
No, it's not magic, but fundamental forces of nature playing their role in the most everyday things, from the simple act of you grabbing a glass of water without it slipping through your fingers, to the behavior of materials at an atomic level.
What really happens between those molecules and how does this influence our daily lives?
Well, it's time to delve a little deeper into the fascinating world of physics.
Today we talk about the forces of Van der Waals.
Johannes Diderik van der Waals
Johannes Diderik van der Waals (1837-1923) was a Dutch physicist famous for his work on the theory of gases and liquids. His major contribution was the formulation of the state equation that bears his name, the Van der Waals equation, which describes the behavior of real gases, taking into account the volume of the molecules and the forces of attraction between them. This was a crucial advancement over the laws of ideal gases, which did not consider such factors. For this work, Van der Waals received the Nobel Prize in Physics in 1910.
He is also credited with the discovery of the Van der Waals forces, which we discuss in this article and which are featured in his Nobel Prize-winning work, as they are very important in explaining the behavior of gases.
What are Van der Waals forces?
Van der Waals forces are short-distance attractive or repulsive interactions that act between molecules or atoms. Although much weaker than other types of interactions, such as covalent or ionic bonds, their significance is enormous in nature, as they are responsible for the cohesion between molecules and affect phenomena such as the adhesion between surfaces, the behavior of gases, and the structure of solids and liquids.
To better understand these interactions, it is useful to know the concept of dipole. A dipole occurs when there is a separation of charges within a molecule. This means that one part of the molecule has a slight positive charge and another part has a slight negative charge. A good example of a dipole is the water molecule (H₂O). In it, the oxygen atom attracts electrons more than the hydrogen atoms, causing the region near the oxygen to have a partial negative charge and the region near the hydrogens, a partial positive charge. This difference in charge distribution is what creates the dipolar moment.
Now that we understand what a dipole is, we can break down the types of Van der Waals forces:
Dispersion Forces (or London Forces):
These forces are the most general and occur between all molecules, regardless of whether they are polar or not, even if they do not have a permanent dipole. How is it possible that there is an attraction between them? Quantum mechanics gives us the answer. Electrons within a molecule are constantly moving, and at any moment, this movement can cause an asymmetric distribution of electrons, generating a temporary dipole. This instantaneous dipole can induce a dipole in a nearby molecule, creating an attraction between the two. Although a molecule may be electrically neutral on average, at any given moment, a temporary dipole can form due to an imbalance in the electron cloud. This momentary dipole can induce a dipole in a neighboring molecule, creating a mutual attraction.
Technically, dispersion forces are inversely related to the sixth power of the distance between the molecules, meaning that the attraction rapidly decreases as the separation between them increases. These interactions also depend on the polarizability of the molecules, that is, the ease with which the electron cloud around an atom or molecule can be distorted.
Example: In noble gases, like helium (He) or argon (Ar), dispersion forces are responsible for these gases being able to liquefy at extremely low temperatures. Although these atoms do not have permanent dipoles, the temporary dipoles induced by quantum fluctuations allow them to attract each other enough to form a liquid when the temperature is low enough.
Dipole-Dipole Forces:
These forces act between molecules that have permanent dipoles, those in which the charge distribution is asymmetric, i.e., molecules where charges are not distributed uniformly.
Dipole-dipole forces act in such a way that the areas of opposite charge of different molecules attract each other.
These forces are especially important in substances where polar molecules predominate. The strength of the dipole-dipole interaction depends on the dipolar moment of the molecules and decreases with the increase in the distance between them. Moreover, these interactions are influenced by the medium in which they are located, as the dielectric constant of the environment can dampen the attraction.
Example: Water molecules (H₂O) are polar and align in such a way that the hydrogen atoms, which have a partial positive charge, are oriented towards the oxygen atoms of other molecules, which have a partial negative charge.
When several water molecules are close, the areas of opposite charges attract each other, generating an interaction that is stronger than dispersion forces, although still weaker than covalent bonds.
This interaction between the permanent dipoles of water molecules is responsible for many of its unique behaviors, such as its unusually high boiling point compared to other similarly sized molecules.
Induced Dipole-Dipole Forces
In this case, a polar molecule (with a permanent dipole) can induce a dipole in a nearby non-polar molecule. The polar molecule distorts the electron cloud of the non-polar molecule, generating a temporary separation of charges in the latter, allowing the two molecules to attract each other.
An example can be seen in the dissolution of oxygen (O₂) in water. Although oxygen is a non-polar molecule, the permanent dipole of water can induce a dipole in oxygen molecules, allowing them to interact weakly.
This type of interaction is weaker than dipole-dipole interactions or dispersion forces, but it is still important in certain phenomena. The magnitude of these forces depends both on the polarizability of the non-polar molecule and on the strength of the permanent dipole of the polar molecule.
Example: A good example is the interaction between water molecules (H₂O) and molecular oxygen (O₂). Oxygen, being a non-polar molecule, would not have a strong interaction with other molecules. However, in contact with water, the polarity of H₂O molecules induces a temporary dipole in O₂ molecules, allowing these to dissolve in water in small amounts. Without Van der Waals forces, there would be no oxygen in the water, and therefore, no animals in the sea.
Lennard-Jones Model
To mathematically describe these interactions, the Lennard-Jones model is very useful. This equation represents the potential energy between two molecules as a function of the distance between them, and is widely used to model the Van der Waals interaction forces (attractive) and the repulsive forces that appear at very short distances, due to the repulsion between the molecules' electrons.
The equation is expressed as follows:
\(V(r) = 4 \varepsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6} \right]\)
Where:
- V(r): Represents the potential energy as a function of the distance r between two particles.
- r: Is the distance between the two particles.
- ε (epsilon): Represents the depth of the energy well, that is, the amount of energy at which the two molecules strongly attract each other. This parameter is related to the intensity of the Van der Waals attraction.
- σ (sigma): Is the distance at which the potential energy between the two molecules is zero. In other words, it is the distance at which the repulsion and attraction balance each other out.
- The term \(\left(\frac{\sigma}{r}\right)^{12}\): Represents the repulsive force, which increases rapidly when the atoms or molecules are very close together due to electron repulsion.
- The term \(\left(\frac{\sigma}{r}\right)^{6}\): Represents the attractive force (Van der Waals forces), which acts when the molecules are at a certain distance and decreases more slowly.
Interpretation of the equation:
- At very short distances (r less than σ), the repulsion between atoms dominates, causing the potential energy to increase rapidly due to Pauli exclusion.
- At intermediate distances (close to σ), a balance between attraction and repulsion is reached, where the potential energy is minimal, indicating that the particles are in a stable position.
- At greater distances (r greater than σ), the Van der Waals attraction dominates, but this decreases rapidly with distance, reducing the potential to zero.
Graph of the Lennard-Jones potential:
In a graph of V(r) versus r, the curve has a characteristic shape: a sharp drop in the attractive region followed by a rapid increase in the repulsive region. The minimum potential energy occurs at a point where the molecules are at an optimal distance from each other.
This equation is fundamental in the simulation of molecular systems and is widely used in fields such as computational chemistry and materials physics.
Conclusions:
Although Van der Waals forces may seem weak and trivial compared to other molecular interactions, they are of enormous importance in the design and study of materials, structural biology, and chemistry. These interactions are key in understanding the molecular world and although we do not see them, their presence is constant, maintaining balance in everything around us.
Where do we find these forces in the real world?
- Geckos: These small reptiles can walk vertically or even upside down on smooth surfaces such as glass, using Van der Waals forces to adhere to these surfaces. The pads of their feet are covered by millions of tiny hairs called setae, which increase the contact area with the surfaces, allowing the Van der Waals forces between the gecko's molecules and the surface to provide strong adhesion.
- Condensation of noble gases: Noble gases like neon (Ne), argon (Ar), and helium (He) do not have permanent dipoles, but can still be liquefied at low temperatures due to the dispersion forces discussed earlier. These weak interactions are sufficient for the atoms of the noble gases to attract each other and condense into liquids when the temperature is low enough.
- Interaction between proteins and DNA: Proteins bind to DNA through weak interactions such as Van der Waals forces. These interactions help proteins recognize and bind to certain amino acids of DNA, crucial for processes such as replication and transcription and essential for stabilizing their three-dimensional structure.
- Adhesion of polymers (adhesives): In plastics and synthetic materials, polymer chains can interact through Van der Waals forces, contributing to their cohesion and strength. This is key in the manufacture of plastic products and adhesives, where these forces help keep the layers of material together.
- Interaction between graphene sheets: In the field of nanoscience, Van der Waals forces are crucial for the stability of materials like graphene, an extremely thin form of carbon, as previously discussed in this article. The individual sheets of graphene are bound together by Van der Waals forces, allowing these materials to maintain their layered structure and be useful in the manufacture of electronic devices.
- Molecular solids like iodine: Iodine is a molecular solid at room temperature. Its molecules are held together in a crystalline structure thanks to Van der Waals forces. Although iodine molecules do not have permanent dipoles, the dispersion forces between them are strong enough to keep the solid in its crystalline form.
- Interactions in non-polar liquids: In liquids like hexane, a non-polar hydrocarbon, the molecules do not have permanent dipoles, but still attract each other through dispersion forces (London). These forces allow hexane to be a liquid at room temperature and explain many of its physical properties, such as its boiling point and viscosity.
- When we grab glass objects: When you hold a glass, Van der Waals forces help create a slight adhesion between the molecules of your skin and those of the glass material. Although friction and muscle strength play the main role in keeping the glass in your hand, Van der Waals forces contribute to preventing it from slipping, establishing subtle interactions between the contacting surfaces.
- Naphthalene crystals (C₁₀H₈): Naphthalene, commonly used in products like mothballs, is a molecular solid that is held together by Van der Waals forces. Its molecules are non-polar, but they cluster due to dispersion forces that allow the material to form a solid at room temperature. These same forces are what allow naphthalene to slowly sublime, passing from solid to gas without going through the liquid state.
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