5.4 Inorganic Polymers and Clusters

Silicon and Phosphorus Polymers

Inorganic polymers replace the carbon backbone found in organic polymers with chains built from elements like silicon, phosphorus, and nitrogen. This gives them access to properties that carbon-based polymers can't easily achieve, such as extreme thermal stability, flame resistance, and tunable flexibility. The three major families here are silicones, polysilanes, and polyphosphazenes.

Silicone-Based Polymers

Silicones (more precisely called polysiloxanes) have a repeating $\text{Si-O-Si}$ backbone with organic groups (typically methyl) attached to each silicon. Their general formula is $[\text{R}_2\text{SiO}]_n$.

The $\text{Si-O}$ bond is both strong (~452 kJ/mol) and more flexible than a $\text{C-C}$ bond because the $\text{Si-O-Si}$ bond angle is wide (~143°) and the barrier to rotation is low. This combination explains why silicones are thermally stable yet remain flexible over a broad temperature range. They're also hydrophobic, since the organic side groups point outward.

Synthesis follows two main steps:

1. Hydrolysis of organochlorosilanes (e.g., $\text{R}_2\text{SiCl}_2$) produces silanols ($\text{R}_2\text{Si(OH)}_2$) and HCl.
2. Condensation polymerization of the silanols eliminates water and builds the $\text{Si-O-Si}$ chain.

By varying the ratio of mono-, di-, and trifunctional silane monomers, you can control whether the product is a linear oil, a cross-linked rubber, or a rigid resin. Applications range from lubricants and sealants to medical implants and cookware coatings.

Phosphorus-Containing Polymers and Polysilanes

Polysilanes have an all-silicon backbone ($\text{Si-Si}$ bonds) with organic substituents. Unlike silicones, the interesting feature here is sigma-delocalization along the $\text{Si-Si}$ chain, which gives polysilanes UV absorption and semiconducting behavior. They're synthesized by Wurtz coupling: dichlorosilanes ($\text{R}_2\text{SiCl}_2$) react with sodium metal, which strips the chlorines and couples the silicon atoms together.

Polyphosphazenes have an alternating $\text{P-N}$ backbone with the general formula $[\text{NPR}_2]_n$, where R can be organic groups, alkoxides, or amines. The $\text{P-N}$ bonds have partial double-bond character due to $\text{p}_\pi\text{-d}_\pi$ interactions (or, in more modern treatments, negative hyperconjugation), which stiffens the backbone relative to silicones.

A common route to polyphosphazenes is ring-opening polymerization of the cyclic trimer $[\text{NPCl}_2]_3$ at ~250 °C, producing $[\text{NPCl}_2]_n$. The chlorines are then replaced with the desired substituent groups via nucleophilic substitution. This tunability makes polyphosphazenes useful as flame retardants, biomedical materials (some are biocompatible and biodegradable), and fuel cell membranes.

Polymerization Mechanisms

Polycatenation refers to chain formation through single covalent bonds between atoms of the same element (e.g., $\text{Si-Si}$ in polysilanes). Beyond that, the three key polymerization routes for inorganic polymers are:

• Condensation polymerization: Small molecules (typically water or HCl) are lost as monomers link. This is the standard route for silicones.
• Ring-opening polymerization (ROP): A cyclic precursor (like cyclic phosphazene trimers) opens and adds to a growing chain. ROP is the primary route for high-molecular-weight polyphosphazenes.
• Coupling reactions: Wurtz-type coupling with alkali metals joins atoms directly, as in polysilane synthesis.

Boron Hydrides and Boron-Containing Compounds

Boron has only three valence electrons but four valence orbitals, so it can't form enough conventional 2-center-2-electron (2c-2e) bonds to satisfy an octet. This electron deficiency forces boron hydrides into unusual bonding arrangements and polyhedral cage structures that have no real parallel in carbon chemistry.

Boron Hydrides and Their Structure

Boranes have the general formula $\text{B}_n\text{H}_m$. The simplest stable example is diborane, $\text{B}_2\text{H}_6$. Its structure can't be explained by classical bonding because there aren't enough electrons for six 2c-2e bonds. Instead, diborane uses two 3-center-2-electron (3c-2e) bonds: each bridging hydrogen sits between two boron atoms, and one electron pair is shared across all three nuclei (B-H-B).

Larger boranes adopt polyhedral cage geometries classified by how "complete" the polyhedron is:

• Closo ("closed"): A complete polyhedron with no missing vertices. Example: $\text{B}_{12}\text{H}_{12}^{2-}$ (icosahedron).
• Nido ("nest"): A polyhedron with one vertex removed, giving a more open, nest-like shape. Example: $\text{B}_5\text{H}_9$.
• Arachno ("web"): A polyhedron with two vertices removed, even more open. Example: $\text{B}_4\text{H}_{10}$.

The progression closo → nido → arachno corresponds to increasingly open structures and increasing numbers of hydrogen atoms relative to boron.

Carboranes and Electron-Deficient Compounds

Carboranes are borane cages in which one or more boron atoms have been replaced by carbon. The most well-known is $\text{C}_2\text{B}_{10}\text{H}_{12}$ (ortho-carborane), which has an icosahedral structure. Because carbon brings one more electron than boron, carboranes are generally more electron-rich and thermally robust than the parent boranes. They find use in medicine (boron neutron capture therapy), heat-resistant polymers, and as ligands in coordination chemistry.

Electron deficiency is the unifying theme across boron chemistry. With fewer valence electrons than needed for classical bonding, boron compounds rely on multicenter bonding (3c-2e bonds for B-H-B bridges and B-B-B faces of polyhedra) to hold their structures together.

Wade's Rules and Structural Predictions

Wade's rules let you predict the shape of a borane or carborane cluster from its electron count. The method uses skeletal electron pairs (SEPs), which are the electron pairs available for holding the cage together (after accounting for B-H or C-H terminal bonds).

How to apply Wade's rules:

1. Count the total number of valence electrons from all atoms in the cluster, plus any charge.
2. Subtract 2 electrons per vertex atom for terminal B-H or C-H bonds. The remaining electrons are the skeletal electrons.
3. Divide by 2 to get the number of skeletal electron pairs.
4. Compare to the number of vertices, n:
   • n + 1 SEPs → closo (complete polyhedron with n vertices)
   • n + 2 SEPs → nido (based on a polyhedron with n + 1 vertices, one removed)
   • n + 3 SEPs → arachno (based on a polyhedron with n + 2 vertices, two removed)

Quick example: $\text{B}_6\text{H}_6^{2-}$ has 6 BH units. Each BH contributes 2 skeletal electrons (boron has 3 valence e⁻, minus 1 for the terminal B-H bond = 2). Total skeletal electrons = 12 + 2 (from charge) = 14, giving 7 SEPs. With n = 6 vertices, 7 = n + 1, so the structure is closo: an octahedron.

Metal Clusters and Cage Compounds

Metal Clusters and Their Properties

Metal clusters contain three or more metal atoms connected by direct metal-metal bonds, usually stabilized by bridging or terminal ligands (CO, phosphines, etc.). Bonding within the cluster core involves delocalized electrons spread across multiple metal centers, somewhat analogous to bonding in bulk metals but on a molecular scale.

Clusters are described by their nuclearity (the number of metal atoms):

• Low-nuclearity clusters (3–12 metal atoms) behave like discrete molecules with well-defined geometries. Example: $\text{Os}_3(\text{CO})_{12}$, a triangular cluster.
• High-nuclearity clusters (13+ metal atoms) begin to show properties that bridge molecular and bulk-metal behavior, making them useful models for understanding surfaces and nanoparticles.

Metal clusters are studied extensively for catalysis (they can activate small molecules at multiple metal sites simultaneously) and as precursors to nanomaterials.

Zintl Ions and Their Structures

Zintl ions are polyatomic anions formed by post-transition metals and metalloids (Sn, Pb, Ge, Bi, Sb, etc.) when combined with highly electropositive metals like sodium or potassium. The electropositive metal donates electrons to the p-block element, which then forms homoatomic clusters.

Examples include $\text{Sn}_5^{2-}$ (trigonal bipyramidal), $\text{Pb}_5^{2-}$, and $\text{Bi}_5^{3-}$. Their structures often follow Wade's rules, since the bonding is analogous to that in boranes. For instance, $\text{Sn}_5^{2-}$ has the same electron count as a closo cluster and adopts a trigonal bipyramidal geometry.

Zintl phases are the solid-state compounds that contain these ions (e.g., $\text{Na}_4\text{Sn}_9$). They're being explored for thermoelectric materials and as anodes in lithium-ion batteries.

Cage Compounds and Polyhedral Structures

Cage compounds extend beyond boron chemistry to include several other important families:

• Fullerenes ($\text{C}_{60}$, $\text{C}_{70}$) are all-carbon cages. $\text{C}_{60}$ has a truncated icosahedral structure (the "buckyball") with 12 pentagonal and 20 hexagonal faces.
• Clathrates are cage structures (often built from water or silicon frameworks) that physically trap guest molecules inside without covalent bonding. Gas hydrates (methane clathrates) on the ocean floor are a well-known example.
• Polyoxometalates (POMs) are anionic metal-oxide clusters, typically built from early transition metals (Mo, W, V) in high oxidation states. The Keggin ion $[\text{PW}_{12}\text{O}_{40}]^{3-}$ is a classic example. POMs are used in catalysis, medicine, and materials science.

These cage structures generally form through self-assembly, where thermodynamic and geometric factors drive the components into the most stable polyhedral arrangement, though template-directed synthesis can also be used to target specific cage sizes.