Hi! The Davson-Danielli model proposed that the cell membrane was made of a phospholipid bilayer with proteins distinguished on the top and the bottom of it - like the bread on a sandwich. This was disproven because of fluorescent tagging which proved that the proteins were mobile, as you stated. Florescent tagging is a mechanism or technique that scientists use to illuminate proteins inside a cell to see where they are located and their structure. Florescent tagging basically "lights up" the proteins. They found that proteins are mobile, which means they can move around. They are not fixated in one distinct spot above or below the phospholipid bilayer.
Freeze fracturing is exactly as it sounds - it means that the scientists froze cells and fractured them, or broke them, to expose the cell membrane. This allows scientists to look under a microscope to see the distribution of proteins, which they found are located inside the phospholipid bilayer, instead of the outside as the sandwich model proposed.
Please let me know if you have any more questions! Hopefully this cleared some things up! :)
