Membrane structure and permeability
Membranes are dynamic mixtures of lipids and proteins. The nonpolar interior impedes charged ions and many large polar solutes. Small nonpolar molecules such as O2 and CO2 can diffuse through the bilayer. Water can cross, but aquaporins often greatly increase its rate of movement. Membrane proteins can serve as channels, carriers, receptors, enzymes, and anchors. Saturation, tail length, and cholesterol influence membrane properties. In animal membranes, cholesterol tends to buffer fluidity: it limits phospholipid movement at higher temperatures and interferes with tight packing at lower temperatures. Selective permeability depends on molecular chemistry as well as size.
A sodium ion is small but charged, so it crosses the bare lipid interior poorly. Oxygen is small and nonpolar, so it crosses much more readily. “Smaller” is not a complete permeability explanation.
A membrane protein is not automatically a pump. Channels can support passive movement without directly using ATP.