Good Idea!
You would have to specify volume and surface area for the two aqueous
phases, and maybe volume of the vapor phase. To keep it simple
assume diffusion within each phase is fast compared to transfer
between, so you don't develop gradients within the liquid phase and
"unstirred layer" effects at the surface. The rate of water leaving
or entering the aqueous phase can be calculated from the vapor
pressure of the solution and the actual partial pressure of water,
since at equilibrium leaving = entering = rate of collisions of water
molecules with the surface. If water activity were proportional to
mole fraction the differential equations would be tractable.
Unfortunately solutes like PEG are far from ideal, you would have to
use look-up tables or empirical equations to give vapor pressure as a
function of PEG, and numerical integration (i.e. simulate the process)
to solve the differential equations. I'm not even sure the vapor pressure
data exists. So the first step is measure vapor pressure (or freezing point
depression, or boiling point elevation, whichever is easier; since all
these coacervative properties are related) for all the common precipitants,
to populate those lookup tables.
For acetate or ammonium salts, need to know the vapor pressure
(henry's law constant?) of dilute solutions of the volatile form,
and use henderson-hasselbach to calculate the concentration of
that form at the given pH. And pH may change in the process,
if the volatile salt is the major buffer. Not hard to simulate.
To measure vapor pressure as a function of solute concentration, equilibrate
a small known volume of a solution against large volume of several different
known humectants. Measure the drop volume after equilibrium, calculate solute
concentration, and plot vs relative humidity or vapor pressure of the standard.
google "Propylene Glycols - Hygroscopicity & Humectant Values" for the standards.
Jacob Keller wrote:
> Dear Crystallographers,
>
> Is anybody aware of a calculator for vapor diffusion experiments to plot
> concentrations of various solvent components as a function of time? For
> a simple example, what happens when I mix a protein solution containing
> 50mM NaCl 1:1 with a reservoir containing 50% MPD but no salt? Where is
> the vapor diffusion equilibrium, and how does the drop composition
> change as a function of time? More complicated would be experiments
> involving volatile components other than water, as I think, for example,
> ethanol would almost instantly equilibrate, then the water diffusion
> would kick in over a longer time scale. Even more complicated would be
> pH-dependent volatilities such as acetate. I don't think this would be
> impossible to figure out, but it would be nice if there were a
> pre-existing tool/server to do such.
>
> Regards,
>
> Jacob Keller
>
>
> *******************************************
> Jacob Pearson Keller
> Northwestern University
> Medical Scientist Training Program
> Dallos Laboratory
> F. Searle 1-240
> 2240 Campus Drive
> Evanston IL 60208
> lab: 847.491.2438
> cel: 773.608.9185
> email: [log in to unmask]
> *******************************************
>
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