Reverse Coarsening and the Control of Particle Size Distribution through Surfactant

Round 1

Reviewer 1 Report

A very interesting study and I would recommend it for publication. I only have a few requests as to the presentation of the results and methods used.

Check Reference on line 25
Unless developed specifically for this study and stated as such please include the source of formulae used in the calculations in both the main text and the appendices.
Please detail the method used to realise the calculations conducted for this study. If they were conducted on a general PC please detail the software used and any additional treatments utilized on the generated data. If you utilised a specialist computational system please also detail the model and specifications of the hardware used.
Please also, with appropriate references, add more detail in the discussion section on how this study will help add to the understanding of the mechanism of nanoparticle formation. Please also add more detail as to forms of synthetic set-up where this form of reverse coarsening may be predicted to occur.

Author Response

Reviewer 1

Comments and Suggestions for Authors

A very interesting study and I would recommend it for publication. I only have a few requests as to the presentation of the results and methods used.

R1: Check Reference on line 25

A: Corrected

R1: Unless developed specifically for this study and stated as such please include the source of formulae used in the calculations in both the main text and the appendices.

A: The formulae used in the study and not accompanied with appropriate references have been obtained by the authors by standard statistical mechanics methods.

R1: Please detail the method used to realise the calculations conducted for this study. If they were conducted on a general PC please detail the software used and any additional treatments utilized on the generated data. If you utilised a specialist computational system please also detail the model and specifications of the hardware used.

A: We have added the text with Ref [53]

To confirm this effect, we conduct numerical simulations using Kinetic Monte Carlo technique [53].

 (see lines 141-142 in the revised manuscript) for a general description of the Kinetic Monte Carlo method and also the text with Ref [51]

Using Eqs (4)-(7) we introduced molecular absorption and emission probabilities by the particle (Eqs (16)-(17) in Ref [51]) and implemented them in the original Fortran code to simulate the evolution of 10⁴ particle ensemble.

(see lines 173-174 in the revised manuscript) where this technique is implemented to similar problems. All simulations have been carried out using our own Fortran code on a standard PC.

R1: Please also, with appropriate references, add more detail in the discussion section on how this study will help add to the understanding of the mechanism of nanoparticle formation. Please also add more detail as to forms of synthetic set-up where this form of reverse coarsening may be predicted to occur.

A: The discussion section has been amended with

 

The value of  in our simulations is chosen for illustration purpose without reference to any particular material’s surface or binding molecule. Determining  in practice is difficult, as it requires measuring the particle’s surface energy  in solution. In our case it is reasonable to demand that  is low enough for the surfactant molecules not to affect the particle shape during its growth or dissolution [58]. Note that the fine tuning of the coarsening process, which is determined by the value of the effective surface energy , can be easier achieved by varying the bulk concentration of surfactant molecules  and the system temperature T rather than  using different surfactant molecules.

 

lines 205-212 in the revised manuscript describing the strength of the surfactant-surface interaction in terms of the effective surface energy for nanoparticle and how this interaction can be tuned in practice. Unfortunately, without having appropriate expertise in nanoparticle synthesis we are not able to specify particular synthetic set-ups. However, we are sure that the proposed conceptual mechanism of controlling the coarsening effect is relevant to any thermodynamically driven solution-processed generation of nanoparticles, as articulated in

the last sentence of Conclusions

 

This reverse coarsening effect is a new paradigm for the thermodynamically controlled solution-processed generation of mono-sized nano-particulate arrays of various materials.

 

Reviewer 2 Report

The authors have done some interesting work on particle reverse coarsening by manipulation of surface energy. The study is sound, however has certain faults and is lacking in some aspects which need to be addressed before it can be published in an archival journal like MDPI Applied sciences.

1. The references: [1-7] [Error! Reference source 25 not found.-10], need to be reinserted properly.
2. In introduction, regarding particle coarsening and deagglomeration the authors talk about equilibrium-based methods. However, such nanoparticle configurations can be generated efficiently with discrete sized binning on bypassing equilibrium based considerations by employing undercooling (ACS Appl. Nano Mater.2020, 3, 6, 5178–5188; Applied physics letters 89, no. 3 (2006): 033123) and dewetting (Nanotechnology 21, no. 15 (2010): 155601; MRS Communications, 8(2), 533-540) principles in the nonequilibrium regime.
3. The motive behind choosing the parameters in data for Figure 2 needs to be mentioned. Are these arbitrary parameters, or relevant to some particular case. If they are, they need to be mentioned in the manuscript.
4. For the characteristic energy given by _AB, from the chosen values the critical condition of _AB* value of 0.06 is established. The authors need to mention how this value compares to surfactants in the experimental conditions.
5. Are there experimental evidences that follow authors’ hypothesis. If there are any with even close resemblance, they need to be mentioned in the discussion.
6. The authors need to also mention that the interfacial energies shall change with particle surface roughness. And the fact that the surfactant stickiness coefficient changes with temperature, while mentioning their mechanism to impart a sense of realism with experimental considerations.

Author Response

We are very grateful to the Reviewer for valuable comments!

Reviwer 2

Comments and Suggestions for Authors

The authors have done some interesting work on particle reverse coarsening by manipulation of surface energy. The study is sound, however has certain faults and is lacking in some aspects which need to be addressed before it can be published in an archival journal like MDPI Applied sciences.

R2: The references: [1-7] [Error! Reference source 25 not found.-10], need to be reinserted properly.

A: Corrected

R2: In introduction, regarding particle coarsening and deagglomeration the authors talk about equilibrium-based methods. However, such nanoparticle configurations can be generated efficiently with discrete sized binning on bypassing equilibrium based considerations by employing undercooling (ACS Appl. Nano Mater.2020, 3, 6, 5178–5188; Applied physics letters 89, no. 3 (2006): 033123) and dewetting (Nanotechnology 21, no. 15 (2010): 155601; MRS Communications, 8(2), 533-540)  principles in the nonequilibrium regime.

A: We have added a new paragraph

Besides the quasi-equilibrium fabrication methods when the system is thermodynamically driven, narrow PSDs are also successfully generated using discrete size selection by undercooling [39-41] and dewetting [42-43] in non-equilibrium regime. Here, we study the role of surfactants, or surface binding molecular ligands [44-50] in controlling PSDs.

(lines 54-58 in the revised manuscript) mentioning the non-equilibrium fabrication methods with the corresponding references [39-43]. We have also explicitly mentioned there the ligand-assisted fabrication routes relevant to our study -Refs [44-50].   

R2: The motive behind choosing the parameters in data for Figure 2 needs to be mentioned. Are these arbitrary parameters, or relevant to some particular case. If they are, they need to be mentioned in the manuscript.

A: We have mentioned in lines 176-177 in the revised manuscript that the parameter values used for calculating the curves in Fig. 2 have been chosen for illustration purposes and from the realistic range

The results shown in Fig. 2 correspond to some realistic values of known model parameters, chosen for illustrative purpose.

R2: For the characteristic energy given by _AB, from the chosen values the critical condition of _AB* value of 0.06 is established. The authors need to mention how this value compares to surfactants in the experimental conditions.

A: We added lines 205-212 in the revised manuscript discussing the value of the surfactant-surface interaction energy _AB­­­* and its relevance to experimental conditions – see the added Ref [58]

The value of  in our simulations is chosen for illustration purpose without reference to any particular material’s surface or binding molecule. Determining  in practice is difficult, as it requires measuring the particle’s surface energy  in solution. In our case it is reasonable to demand that  is low enough for the surfactant molecules not to affect the particle shape during its growth or dissolution [58]. Note that the fine tuning of the coarsening process, which is determined by the value of the effective surface energy , can be easier achieved by varying the bulk concentration of surfactant molecules  and the system temperature T rather than  using different surfactant molecules.

 

R2: Are there experimental evidences that follow authors’ hypothesis. If there are any with even close resemblance, they need to be mentioned in the discussion.

A: The main hypothesis in our theory is that there can be surfactant molecules, which relatively weakly bind to nanoparticle surfaces such that their concentration on these surfaces can be tuned by varying their bulk concentration and the system temperature. The energetics of surfactant binding to nanoparticles is described in the review Ref. [58].

R2: The authors need to also mention that the interfacial energies shall change with particle surface roughness. And the fact that the surfactant stickiness coefficient changes with temperature, while mentioning their mechanism to impart a sense of realism with experimental considerations.

A: We have added a sentence

With such a generic form, this equation can effectively account also for the contributions to the surface energy coming from possible roughness of particle surfaces.

 lines 168-169 in the revised manuscript - indicating that the role of surface roughness in the particle surface energy can effectively be taken into account within the same approach.

A: In our approach the surface concentration of surfactant molecules is determined by the surfactant-surface binding energy, surfactant concentration in the bulk and the temperature. Therefore, the surfactant stickiness coefficient, if it is defined using the surface concentration of surfactant molecules, is intrinsically temperature dependent.

We have to point out that we have discovered a sign mistake in the previous version of the manuscript, which is corrected in the revised version. As a result the Eqs (2), (A6) and (A8) and the values of the energy parameter in the caption to Fig.2 have been corrected

Figure 2. a) Time evolution of the mean  and maximum  radii calculated for ensemble of 10⁴ particles with Gaussian initial distribution ( =1.5 and standard deviation  =0.25) obtained via numerical solution of Eqs (4) - (7) for T=0.032 eV (100^o C), ,  and . The values of , respectively are (eV units): 1) 0.24 and 0; 2) 0.21 and 0; 3) 0.21 and 0.01; 4) 0.196 and 0; 5) 0.18 and 0. b) PSD corresponding to the curves 3) at the time moments indicated by arrows in a).

 All the simulation results remain unchanged. For clarity we have also slightly extended the description of Fig. 1

 The same figure also shows the surface concentration of surfactant  as a function of  illustrating an increase in surface concentration  and a decrease in  with increasing bulk concentration  of the surfactant molecules.

Reviewer 3 Report

This is an important paper that extends our fundamental understanding of nanoparticle growth in the presence of a surfactant. This reviewer recommends acceptance in Applied Sciences.

Author Response

No review

Round 2

Reviewer 2 Report

The authors have made appropriate corrections to their study and have provided satisfactory responses to my queries. I recommend publication.