Effective Medium Theory for Multi-Component Materials Based on Iterative Method

Round 1

Reviewer 1 Report

In this manuscript, the authors  proposed an iterative effective medium theory for multi-component materials. Recent advances in materials require to create EMT models for the description of multi-component composite. A clear “point by point” method has been shown in the manuscript. Either the theory has been applied to three different composite materials.

Following points should be addressed by the authors before the manuscript can be accepted from my side:

1. At the end of the introduction, the word “popular” is not applicable to EMT models
2. Why are these three composites chosen to confirm the method validity? (Chapter 4 Validation)
3. Which particle shape was used on model 2 (gelatin, water, glycerin, starch, bentonite)? (4.2.)
4. Figure 2 and figure 4 both consist of four graphs, but only picture (a) and (b) are signed. It would be better to sign the upper and lower ones.
5. In the manuscript an iterative effective medium theory  for a multi-component mixture is based on Bruggeman (BG) model. Is it correct to use a “stacking dolls” approach to another model, for example,  Polder-van Santen formula or Coherent Potential formula?

Author Response

Please see the attachment

Author Response File: Author Response.docx

Reviewer 2 Report

The manuscript “Effective Medium Theory for Multi-component Materials based on Iterative Method” by Nazarov, Zhang, and Khodzitsky discusses Bruggeman Effective Medium Theory in the THz spectral range. The novelty of the work is that the Bruggeman equation is solved step by step instead of using the generalized multicomponent equation. The paper is written in good English, however some nouns are missing articles (the/a). I can recommend the manuscript for publication after revision. In particular, the examples need to explained in more detail. What input parameters were used? Spectrally resolved or simply a static value? The authors are also sometimes stating that the inclusion is modeled as a spherical particle, but not every time. The authors should be more explicit when this assumptions is made. Furthermore:  

1. The authors present in their introduction a fine situation of THz in the field of bio-applications. However, not a single citation is given for these examples. I urge the authors to cite the appropriate literature.
2. In the introduction the authors mention that the LLL model has “strong restrictions on the component concentrations”. I suggest that the authors explicitly state what restrictions these are.
3. The authors should also mention the used accent convention. In particular, I assume ^ is used to denote complex? If so the authors should mention it, and also point out that all vectors seem to be complex.
4. The authors state in line 54: “in practice the simulation result of these models are not accurate for multi-component composites”. This should be supported by examples or citations. Furthermore, the statement is a bit strong, several groups used BG successfully for mixtures….
5. I assume LDPE stands for low density polyethylene? If so, please add the written-out explanation of this acronym in the manuscript.
6. I am puzzled by equation (18). The authors spent a full page on deriving simple well-established electrodynamics (equation 1-12). Why not split (18) in the two steps to allow the reader to follow it? Furthermore, I suggest to keep v in the equation instead of using the value (1/3) here.
7. The authors use the “standard” Bruggeman Model as comparison in their figures. Was BM used with geometrical expansion or not? Either way it should be explicitly stated.
8. Regarding the second examples:
   1. What values were used for the different components? Please state the values and cite the source.
   2. What geometrical factors were used? And for which materials? The authors state 1/3 for sphere but it is only mentioned after referring to the usual BG. Is this factor also used for the iterative method? And if so, for which of the components?
   3. Why was this iteration direction chosen? What happens if I would start with Water+glycerol for example?
   4. Furthermore, what about water solvation shells? What about interaction between water and other materials?
   5. The authors mention a resonant feature that is not considered in the simulation? Why is this not considered? The equations present here can be solved broad band. So if the absorption of the components has a resonance, so should the mixture, or?
9. Regarding the Third example
   1. The authors state that spherical geometry was assumed. What is the reason for this? Is there any indication that either of the materials forms a spherical droplet?
10. In general ,I am missing an explanation or discussion; For example in the last example, why is LLL fine despite being completely of in the previous examples? Or further scientific insight.
11. The authors use a small delta (δ) for the “error” between model and experiment, as well as in the derivation of the equations. In the derivation it is the difference between host and inclusion material. I strongly urge the authors to single use the variables, as it potentially confuses a reader if the same symbol is used for different things.  

In conclusion, the authors should explicitly state which geometrical assumptions are used, and also justify them! I am skeptical on whether the sub-wavelength size Ag in the first example should be a sphere and even more confused by the final example. Why is the gelatin/water a sphere in the oil?

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 3 Report

The paper reports a new computational approach which allows to estimate the complex permittivity of multi-component composite materials, demonstrating improved accuracy. It may be of interest and use to readers employing such calculations. The paper requires English editing.

Author Response

The quality of language was improved