In models for the description of the spinodal decomposition, the concept of uphill diffusion is used. Uphill diffusion tends to assemble the molecules into a single whole, which leads to the appearance of the nucleus of a new phase. The term association is also used in this context. What is the difference between an uphill diffusion from an association? Can the micelle formation of the surfactant be a spinodal decomposition? I ask the specialists of phases separation to begin a discussion on this issue.
Uphill diffusion indeed leads to the formation of associates, but an association (micellization included) process can occur following less peculiar mechanisms such as the most common normal (downhill) diffusion followed by a chemical or physicochemical barrier rate process. Uphill diffusion requires mixture at the vicinity of the critical point, with mixture composition on the unstable side of the spinodal where d(mu)/dC < 0 - this is a very special case of association.
I don't see a problem making micelles by starting with a critical mixture of surfactant and solvent, and using uphill diffusion as a step of the process. If you let the spinodal decomposition do its job, however, you'll end up not with a micellar solution but with two phases, i.e., you should somehow prevent the complete spinodal decomposition, I guess.
The fundamental problem is that Fick's laws, which are normally used to define the diffusion constants, are based on a misconception: The driving force of diffusion is not a concentration gradient, but a gradient of the chemical potential. Between two ideal mixtures of different composition x'i, x"i (i. component index) one has Delta mui proportional to ln(x"i/x'i), which for small concentrations differences yields Fick's 1st Law. In this sense, there is no uphill diffusion. Describe your problem in terms of chemical potentials, and most points of confusion will disappear.
“Association” is a term normally used for chemical reactions. Again a chemical reaction equilibrium is characterized by a balance equation for chemical potentials. If the process you have in mind leads to an equilibrium state containing micelles, the chemical reaction formalism can be applied. If the micelles are merely a transition state on the way to a large-scale phase separation, the term “association” should perhaps better be avoided.
In my humble opinion (I'm not consider myself an expert in this field), the micellization is usually treated as the new phase formation, governed both by enthalpy and entropy changes. The equilibrium concentration of surfactant monomers in micellar solution should be approximately equal to CMC, so I guess no uphill diffusion can be observed in regular micellization process.
@Andrei:
The equilibrium concentration of surfactant monomers in micellar solution should be approximately equal to CMC.
This is approximately true for non-ionic surfactants. At them the binodal almost coincides with a spinodal, as at hydrocarbons. Before the CMC of ionic surfactants, a surfactant dimer is first formed. The phase transition is stretched from the binodal (the onset of dimer formation) to the CMC2. The CMC is the middle part of the phase transition or the spinodal. See our work.
@Radomir,
@Ulrich :
Uphill and downhill diffusion are opposite in sign. How to define experimentally uphill diffusion? The sum of two diffusions is determined experimentally. The coefficients of diffusion by different methods for ionic surfactants differ by an order of magnitude. Uphill diffusion coefficient is binary and it includes the effect due to the correlation of the movement of the different diffusing species (water and surfactant). There may be a special case of spinodal decomposition. The system will remain in a self-oscillating state and will not reach large-scale phase separation.
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