Modified Catalysts and Their Fractal Properties

Round 1

Reviewer 1 Report

This paper can be accepted after solving below issues.

1. The quality of the figures should be improved. Most of the figures are unclear.
2. The English language should be checked.
3. Since there are a lot of small mistakes in references, the format of references should be checked carefully.
4. More related papers should be cited (Materials & Design 2021, 210, 110040)

Author Response

R1. The quality of the figures should be improved. Most of the figures are unclear.

A1. According to the recommendation of the reviewer, the quality of all figures has been improved. Please see pages 5-8, 10 and 12-14.

R2. The English language should be checked.

A2. According to the reviewer`s advice, the English language has been improved to the best of our knowledge.

R3. Since there are a lot of small mistakes in references, the format of references should be checked carefully.

A3. At the reviewer suggestion, the format of references has been checked carefully.

R4. More related papers should be cited (Materials & Design 2021, 210, 110040).

A4. At the reviewer`s recommendation, more papers were added in the manuscript, as can be seen on the bibliography. The suggested reference is also available (Materials & Design 2021, 210, 110040) [15].

Reviewer 2 Report

The authors summarized some scientific results related to oxide catalysts, such as lanthanum cobaltites and ferrites with perovskite structures, and nanoparticle catalysts (such as Pt, Rh, Pt-Cu, etc). Some methods to compute the fractal dimension of the catalysts (micrographs fractal analysis, the adsorption isotherm method) and the computed fractal dimensions are also presented and discussed.

Overall, the analyses of the data are adequate for the problem under study. The conclusions are relevant and supported by the results. The conclusions of this work should be of interest to the readership of catalyst. Thus I think this manuscript met the standard of the Catalysts. Nevertheless, I have some comments that should be addressed before publication.

1. In the section “Introduction”, the authors described the fractal geometric features and the scaling law in catalysts. In fact, the self-similarity, as well as scaling law, exist in many fields, for example, in cell biology, where it has been reported that the self-similarity in cell structure leads to scalar-law rheological behavior of cells very recently (Nature Communications, 2021, 12:6067). The fractal properties and the self-similarity should not be limited to the catalyst, which will limit the influence of this paper.

2. There is an error in Equation 4. Check it carefully and correct it. There are two in the numerator and P₀ is missing from the denominator. Otherwise, the formulae are not written correctly that the numbers should not be written in italics, please check all formulae carefully.

3. In Figures 7-10, the number of basic centers span several orders of magnitude so that the usual linear coordinate system cannot well describe their variation with the fractal dimension of the system/support. The mentioned paper (Nature Communications, 2021, 12:6067) has proposed a self-similar hierarchical model to study the universal power-law rheological behavior of cells. They used a double-logarithmic coordinate system to compare creep responses with values spanning multiple orders of magnitude. It might be better to use a double logarithmic coordinate system to show the relationship between the number of basic centers and the fractal dimension of the system/support.

Author Response

Overall, the analyses of the data are adequate for the problem under study. The conclusions are relevant and supported by the results. The conclusions of this work should be of interest to the readership of catalyst. Thus I think this manuscript met the standard of the Catalysts. Nevertheless, I have some comments that should be addressed before publication.

R1. In the section “Introduction”, the authors described the fractal geometric features and the scaling law in catalysts. In fact, the self-similarity, as well as scaling law, exists in many fields, for example, in cell biology, where it has been reported that the self-similarity in cell structure leads to scalar-law rheological behaviour of cells very recently (Nature Communications, 2021, 12:6067). The fractal properties and the self-similarity should not be limited to the catalyst, which will limit the influence of this paper.

A1. We thank the reviewer for the valuable comment. The former Introduction section has been modified and the new references were added in the manuscript. Thus, the following paragraphs have been introduced in the revised paper:

Paragraph no. 1: “The power of self-similarity, as fractal`s property, was first emphasized in 1975 by B.B Mandelbort [1,2]. After that, a lot of processes and phenomena were analyzed leading to fractal behavior: light scattering on rough surfaces [3], fractal antenna [4], diffusion-limited aggregation [5], fracture [6], reaction kinetics [7], even tumors diagnosis and cancer therapy [8,9] and recently, mechanical response of cell membrane [10].”

Paragraph no. 2: “Tailoring catalysts with high activity in specific reactions is a challenging field of interest. Strategies implying the influence of particle size on catalytic properties [27] or metal-support interaction [28] or morphological controlling, metal deposition and chemical treatment [29] are largely exposed in literature. In the following, we shall focus only on the influence of fractal behaviour self-similarity on catalytic properties.”

Please see on page 1.

R2. There is an error in Equation 4. Check it carefully and correct it. There are two in the numerator and P0 is missing from the denominator. Otherwise, the formulae are not written correctly that the numbers should not be written in italics, please check all formulae carefully.

A2. We thank the reviewer for this observation. The equation 4 has been check it and corrected.

Please see on page 16.

R3. In Figures 7-10, the number of basic centers span several orders of magnitude so that the usual linear coordinate system cannot well describe their variation with the fractal dimension of the system/support. The mentioned paper (Nature Communications, 2021, 12:6067) has proposed a self-similar hierarchical model to study the universal power-law rheological behavior of cells. They used a double-logarithmic coordinate system to compare creep responses with values spanning multiple orders of magnitude. It might be better to use a double logarithmic coordinate system to show the relationship between the number of basic centers and the fractal dimension of the system/support.

A3. We thank the reviewer for the helpful advice and recommendation. Therefore, the figures 7-10 were redrawn by using double logarithmic scale. Please see on pages 12-14. The suggested reference  ((Nature Communications, 2021, 12:6067) is also cited as [10].