what does brownian movement have to do with diffusion
Brownian motion There are two parts to Einstein's theory: the first part consists in the formulation of a diffusion equation for Brownian particles, in which the diffusion coefficient is related to the mean squared displacement of a Brownian particle, while the second part consists in relating the diffusion coefficient to measurable physical quantities.[5] In this way Einstein was able to determine the size of atoms, and how many atoms there are in a mole, or the molecular weight in grams, of a gas.[6] In accordance to Avogadro's law this volume is the same for all ideal gases, which is 22.414 liters at standard temperature and pressure. The number of atoms contained in this volume is referred to as Avogadro's constant, and the determination of this number is tantamount to the knowledge of the mass of an atom since the latter is obtained by dividing the mass of a mole of the gas by Avogadro's constant.
Facilitated diffusion Polar molecules and large ions dissolved in water cannot diffuse freely across the plasma membrane due to the hydrophobic nature of the fatty acid tails of the phospholipids that make up the lipid bilayer. Only small, non-polar molecules, such as oxygen and carbon dioxide, can diffuse easily across the membrane. Hence, no nonpolar molecules are transported by proteins in the form of transmembrane channels. These channels are gated, meaning that they open and close, and thus deregulate the flow of ions or small polar molecules across membranes, sometimes against the osmotic gradient. Larger molecules are transported by transmembrane carrier proteins, such as permeases, that change their conformation as the molecules are carried across (e.g. glucose or amino acids). Non-polar molecules, such as retinol or lipids, are poorly soluble in water. They are transported through aqueous compartments of cells or through extracellular space by water-soluble carriers (e.g. retinol binding protein). The metabolites are not altered because no energy is required for facilitated diffusion. Only permease changes its shape in order to transport metabolites. The form of transport through a cell membrane in which a metabolite is modified is called group translocation transportation.