Several papers and books point to the nucleation-growth behavior of zero-dimensional nanoparticles to be controlled by the free Gibbs energy available in the system. In that manner, the critical radius r* is defined as r* = -2 gamma / delta(Gv), where gamma is the surface energy per unit area and delta(Gv) is the change of Gibbs free energy per unit volume of the solid phase. Nuclei with radii smaller than r* will dissolve away to reduce the surface energy, whereas nuclei with r > r* will stabilize and continue to grow. Moreover, delta(Gv) is defined as = - k T * ln(sigma + 1) / ohmega, where k T is the thermal energy, sigma is the supersaturation state and ohmega is the atomic volume. Now, my question is, in a model synthesis involving only one salt and a reducing agent, let's say gold and citrate, if the only energy inlet to the system is heat/temperature (assuming no work and using The First Law), can we assume that delta(Gv) is due only to thermal increase? (Keeping all of the other variables constant: no variation in sigma, that is no feed lines - batch reaction.) If so, can I say that I might be able to control my seeds size only by temperature, if I keep the initial gold and citrate concentrations equal throughout experiments? If I overcome the energy barrier defined as delta(G*) = -16 pi gamma / (3 delta(Gv))^2 with heat, then will r = f(T) (radius be a function of temperature)? (References in the book Nanostructures and Nanomaterials, chapter 3.)
I guess, generally speaking, you need to study nonisothermal nucleation. There are different thermal effects of condensation, e.g.:
1). Molecules fall on droplet or nanoparticle with one temperature but evaporates or dissolves from it with another.
2). Condensation heat dependency on droplet radius also changes (Sreznevsky formula)
Depending on intensity of heat flux nonisothermal balance equation can be treated in two ways:
1). (simple) As quasi isothermal problem depending only on amount of molecules in droplets (when quasi-stationary distribution of droplets have enough time to settle during phase transition)
2). Otherwise you need to solve two-dimensional Becker-Doring-Zeldovich equation depending not only on amount of molecules in droplets but also on energies of droplets.
Anyway nonisothermal effects lead to different energy of droplet formation (its critical radius), different droplets flux in space of their sizes and their equillibrium distribution on sizes.
Hence, there is different mean droplets size over modified distribution and it has more complicated dependency on temperature.
Sorry, have no time to look for literature, I have only my handwritten Russian lecture notes on kinetics of nonisothermal nucleation (in attachment, detailed mass-energy balance equation on pages 18-19).
English articles on this theme of lecturer A. Shchekin you can find here on ResearchGate:
https://www.researchgate.net/profile/Alexander_Shchekin/publications/
Regards
I guess, generally speaking, you need to study nonisothermal nucleation. There are different thermal effects of condensation, e.g.:
1). Molecules fall on droplet or nanoparticle with one temperature but evaporates or dissolves from it with another.
2). Condensation heat dependency on droplet radius also changes (Sreznevsky formula)
Depending on intensity of heat flux nonisothermal balance equation can be treated in two ways:
1). (simple) As quasi isothermal problem depending only on amount of molecules in droplets (when quasi-stationary distribution of droplets have enough time to settle during phase transition)
2). Otherwise you need to solve two-dimensional Becker-Doring-Zeldovich equation depending not only on amount of molecules in droplets but also on energies of droplets.
Anyway nonisothermal effects lead to different energy of droplet formation (its critical radius), different droplets flux in space of their sizes and their equillibrium distribution on sizes.
Hence, there is different mean droplets size over modified distribution and it has more complicated dependency on temperature.
Sorry, have no time to look for literature, I have only my handwritten Russian lecture notes on kinetics of nonisothermal nucleation (in attachment, detailed mass-energy balance equation on pages 18-19).
English articles on this theme of lecturer A. Shchekin you can find here on ResearchGate:
https://www.researchgate.net/profile/Alexander_Shchekin/publications/
Regards
Dear Thiago, yes in theory you should be able to control the NP nucleation only by temperature in my opinion. Two notes: 1)you will find that the practice of NP nucleation is very different from Gipps Energy driven process and 2) I did not read the book you referred but I aware that many books on classical thermodynamic are full of errors and misconceptions, so be carefull
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