Derive the Gibbs-Thomson relation (Equation 1) between vapor pressure and the size of a spherical nanodroplet...

 

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Derive the Gibbs-Thomson relation (Equation 1) between vapor pressure and the size of a spherical nanodroplet (pictorially, assume the nanodroplet is adhered to a solid surface). Equation 1: In() = 2yvm RTr The following will be helpful: AP = Pin - Pext = 2 and dGin = Vin dPin; dGext Vext dPext Where: Pin pressure inside of droplet Pext pressure outside droplet Pr vapor pressure at a given droplet size = Po equilibrium vapor pressure y= surface energy/tension Vm molar volume R = gas constant T = temperature r = radius of droplet = Derive the Gibbs-Thomson relation (Equation 1) between vapor pressure and the size of a spherical nanodroplet (pictorially, assume the nanodroplet is adhered to a solid surface). Equation 1: In() = 2yvm RTr The following will be helpful: AP = Pin - Pext = 2 and dGin = Vin dPin; dGext Vext dPext Where: Pin pressure inside of droplet Pext pressure outside droplet Pr vapor pressure at a given droplet size = Po equilibrium vapor pressure y= surface energy/tension Vm molar volume R = gas constant T = temperature r = radius of droplet =