Chemical Potential difference across the cell membrane Chemical potential difference due to osmotic pressure osmotic pressure on the cell membrane -RTIn a π= Le cell Vw:partial molar volume of H2O H,O(osmosis) aw:H2O molar fraction difference RT In ae-RTIn aw.i π；-πe=
cell H2O (osmosis) w w V RT ln a Chemical Potential difference across the cell membrane , , ln ln we wi i e w w RT a RT a V V difference
Chemical difference due to extracellular ice formation △G(T)=G(T)-G,(T) 兰△T△S(Tr) =LATIT Total chemical potential difference △Π=π，-π。+△G(T)
Chemical difference due to extracellular ice formation Total chemical potential difference () () () ( ) / L s f f f GT G T G T T ST L TT ( ) i e G T
Volume flux of water leaving the cell J= dV cet dt =PA△Π =[π，-π。+△G(T)] B Water permeability
Volume flux of water leaving the cell [ ( )] cell w w i e dV J dt P A G T Pw Water permeability
Cell response during freezing Seeding of External Ice Solution effect -1t0-4℃ Slow Cooling 1104℃ s Rapid Cooling <.10℃ Lethal
Solution effect Lethal Cell response during freezing
The freeing process of biological t tissue 3 Supercooling 2 1 0 A C Supercooling -2 Release D 3 of energy from latent -4 heat Ice formation -5 B E 0 1 2 3 4 5 Time(minutes)
The freeing process of biological tissue