Final answer:
The fracture plane passes through the center of cell membranes because it takes the path of least resistance, which is between the hydrophobic fatty acid tails in the membrane's phospholipid bilayer during the freeze-fracture process.
Step-by-step explanation:
The reason the fracture plane tends to pass through the center of cell membranes has to do with the structure of the phospholipid bilayer that makes up the membrane. Plasma membranes consist of two layers of phospholipids, comprised of hydrophilic heads and hydrophobic tails. When subjected to the freeze-fracture technique for examination under a scanning electron microscope, the membranes tend to split along the middle of the bilayer because this is the area of least resistance, where the hydrophobic fatty acid tails face each other and easily separate.
The fracture plane does not select this path due to an attraction or repulsion to specific substances, but rather due to the physical properties of the membrane. The tails are hydrophobic and prefer to avoid interactions with water. When the cell membrane is frozen and then fractured, it breaks along the line of least resistance, which is between the layers of closely packed hydrophobic tails, revealing the distinct inner structures of the plasma membrane.