The correct answer is C. montmorillonite.
Montmorillonite is a smectite clay mineral with a very high cation exchange capacity (CEC) and a high swelling potential. It is a 2:1 layer silicate with a tetrahedral sheet of silica and an octahedral sheet of alumina. The tetrahedral sheet is linked to the octahedral sheet by shared oxygen atoms. The interlayer space is filled with water and exchangeable cations.
The swelling and shrinkage characteristics of montmorillonite are due to the nature of the interlayer space. The interlayer space is negatively charged, which attracts water molecules and exchangeable cations. The water molecules and exchangeable cations can move in and out of the interlayer space, which causes the clay to swell and shrink.
Kaolinite is a 1:1 layer silicate with a tetrahedral sheet of silica and an octahedral sheet of alumina. The tetrahedral sheet is linked to the octahedral sheet by shared oxygen atoms. The interlayer space is filled with hydroxyl groups.
Illite is a 2:1 layer silicate with a tetrahedral sheet of silica and an octahedral sheet of alumina. The tetrahedral sheet is linked to the octahedral sheet by shared oxygen atoms. The interlayer space is filled with water and exchangeable cations. However, the interlayer space in illite is much smaller than the interlayer space in montmorillonite. This is because the tetrahedral sheet in illite is bonded to the octahedral sheet by potassium ions, which are much larger than the water molecules and exchangeable cations in montmorillonite. The smaller interlayer space in illite limits the swelling and shrinkage of the clay.
Therefore, the clay mineral with the largest swelling and shrinkage characteristics is montmorillonite.