2.4 Intermolecular Forces and Crystal Structures

Chemical bonds hold atoms together within molecules, but intermolecular forces govern how those molecules interact with each other and organize into bulk materials. Understanding these forces and the crystal structures they produce is essential for predicting physical properties like melting point, hardness, and electrical conductivity.

Intermolecular Forces

Van der Waals and Hydrogen Bonding

Van der Waals forces is an umbrella term for weak attractions between molecules. They arise from temporary fluctuations in electron distribution and include both dipole-dipole interactions and London dispersion forces. Their strength increases with molecular size and polarizability, since larger electron clouds are easier to distort.

Hydrogen bonding is a special, stronger type of dipole-dipole interaction. It occurs when a hydrogen atom bonded to a highly electronegative atom (N, O, or F) interacts with a lone pair on another electronegative atom. Hydrogen bonds are stronger than typical van der Waals forces but still much weaker than covalent bonds. They're responsible for many of water's unusual properties (high boiling point, high surface tension) and play a critical role in the structure of DNA and proteins.

Dipole-Dipole and London Dispersion Forces

Dipole-dipole interactions occur between molecules that have permanent dipole moments. Polar molecules orient themselves so that the positive end of one molecule faces the negative end of another, minimizing potential energy. The strength of these interactions scales with the magnitude of the molecular dipole. Acetone, for example, has a relatively high boiling point for its molecular weight because of significant dipole-dipole forces.

London dispersion forces (LDFs) exist between all molecules and atoms, including nonpolar ones. They arise from instantaneous dipoles created by the random motion of electrons. A few key points:

• Strength increases with molecular size, surface area, and polarizability
• They're the only intermolecular force acting between noble gas atoms, which is why noble gases can still be liquefied at very low temperatures (e.g., liquid helium at 4.2 K)
• For large molecules like proteins or long-chain hydrocarbons, the cumulative effect of LDFs can be substantial

Types of Crystals

Ionic and Covalent Crystals

Ionic crystals are built from electrostatic attractions between oppositely charged ions arranged in a repeating lattice. Sodium chloride (NaCl) is the classic example. These crystals tend to have high melting points (801 °C for NaCl), are brittle (stress shifts ion layers into repulsive alignment, causing fracture), and conduct electricity only when molten or dissolved in water, since the ions must be free to move.

Covalent (network) crystals consist of atoms linked by covalent bonds extending in three dimensions. Because you'd have to break strong covalent bonds to disrupt the structure, these materials show extreme hardness and very high melting points. Diamond (all carbon, each atom bonded to four others) and quartz ($\text{SiO}_2$, a network of Si-O bonds) are prime examples. They're generally electrical insulators because there are no free electrons or mobile ions.

Metallic and Molecular Crystals

Metallic crystals feature positively charged metal cations surrounded by a "sea" of delocalized electrons. This electron sea model explains their defining properties:

• High electrical and thermal conductivity (delocalized electrons carry charge and heat)
• Malleability and ductility (layers of cations can slide past each other without breaking bonds, since the electron sea adjusts)
• Examples include pure metals like copper and alloys like steel

Molecular crystals are held together by intermolecular forces (van der Waals, dipole-dipole, or hydrogen bonds) rather than ionic or covalent bonds. Because these forces are relatively weak, molecular crystals generally have low melting points and are soft. They're poor electrical conductors. Ice ($\text{H}_2\text{O}$, held by hydrogen bonds, mp 0 °C) and dry ice ($\text{CO}_2$, held by London dispersion forces, sublimes at −78.5 °C) are common examples.

Crystal Structure

Lattice and Unit Cell

A crystal lattice is the three-dimensional, periodic arrangement of points representing atom or ion positions. It defines the overall symmetry of the crystal and can be described mathematically by a set of translation vectors.

The unit cell is the smallest repeating unit that, when stacked in all three dimensions, reproduces the entire lattice. It contains all the structural information of the crystal. A unit cell is defined by six lattice parameters: three edge lengths ($a$, $b$, $c$) and three angles ($\alpha$, $\beta$, $\gamma$). These parameters give rise to seven crystal systems: cubic, tetragonal, orthorhombic, hexagonal, trigonal (rhombohedral), monoclinic, and triclinic.

Coordination and Packing

The coordination number is the number of nearest neighbors surrounding a given atom or ion. It directly influences properties like density and hardness. For example, each $\text{Na}^+$ ion in NaCl is surrounded by 6 $\text{Cl}^-$ ions (coordination number = 6), while each carbon in diamond is bonded to 4 neighbors (coordination number = 4).

Packing efficiency measures what fraction of the unit cell volume is actually occupied by atoms (treating them as hard spheres). To calculate it:

1. Determine how many atoms belong to the unit cell (accounting for shared atoms at corners, edges, and faces)
2. Calculate the total volume of those atoms using $V_{\text{atom}} = \frac{4}{3}\pi r^3$
3. Divide by the unit cell volume

Common packing efficiencies:

• Simple cubic: ~52%
• Body-centered cubic (BCC): ~68%
• Face-centered cubic (FCC) and hexagonal close-packed (HCP): ~74% (the theoretical maximum for identical spheres)

Polymorphism and Structure Analysis

Polymorphism occurs when a single substance can crystallize in more than one crystal structure. Different polymorphs have the same chemical composition but distinct physical properties. Carbon is the textbook example: diamond (tetrahedral network, extremely hard) and graphite (layered sheets, soft and conductive) are both pure carbon. Calcium carbonate similarly exists as calcite and aragonite. Polymorphism matters enormously in the pharmaceutical industry, where different crystal forms of the same drug can have different solubilities and absorption rates.

X-ray crystallography is the primary technique for determining crystal structures. It works by directing X-rays at a crystal and analyzing the resulting diffraction pattern. Because X-ray wavelengths (~0.1 nm) are comparable to interatomic distances, the scattered waves produce constructive and destructive interference patterns governed by Bragg's law: $n\lambda = 2d\sin\theta$, where $d$ is the spacing between lattice planes, $\theta$ is the angle of incidence, and $n$ is an integer. From these patterns, you can extract bond lengths, bond angles, and the overall molecular packing arrangement. This technique is indispensable in structural biology, mineralogy, and materials science.