Effect of Size Polydispersity on the Pitch of Nanorod Cholesterics

Round 1

Reviewer 1 Report

The authors analyze the effect of polydispersity of chiral nanorod colloidal particles on the cholesteric phase formed by a suspension of such particles.  The approach is based on the Onsager-Straley theory with included length polydispersity and on using an algebraic approximation. The increase of the twist elasticity and decrease of the helical twist is observed. The approach certainly contributes to the better understanding of mechanisms relevant for the chirality of such cholesteric phases. The paper is well written but a bit too formal for the broad audience of Crystals. Before supporting the publication in Crystals, I suggest that the authors improve the paper to become more attractive for the audience this journal.

Particular remarks:

1  It would be good to choose how to call these systems! Often the term “colloidal liquid crystals” is used.

2 The term "twist elastic resistance" is not commonly known and should not appear in the abstract without explanation.

31-33  When listing studies of related systems the review of Dierking should be included. What about chiral doped chromonics, DNA systems, viruses, etc?

36  It would be good to stress why algebraic approach is useful, although numerical approaches are no more severely restricted by available computer facilities.

57-58  A figure with an illustration of the excluded volume chiral interaction should be added! The energy cost associated with a non-uniform director field needs more explanation.

69 The meaning of the terms “chiral amplitude” and “twist elastic resistance” should be explained, particularly in relation to the above introduced helical amplitude and twist elastic modulus.

71  How does the simple chiral potential acting between two freely rotating rods relate to the excluded volume approach.

77  The Fig 1 should be positioned where the  log-normal and Schulz-distributions are introduced . The introduction of the log-normal function should be accompanied by the reference.

85   Also the weakly bimodal size distribution should be illustrated on a graph.

99  The term “isotropic-nematic phase gap” is not commonly used!

125-137  The algebraic approach has quite a number assumptions so that it can provide the basic understanding of the chirality in these systems but for the fine tuning of their properties one needs a serious numerical approach. 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

This work aims to study the effect of polydispersity on suspensions of chiral rods exhibiting cholesteric ordering. The topic is interesting and well fits within the scope of the issue. It was quite instructive to learn the number of approximations needed to arrive to a tractable semi-analytical theory. Within this framework, the main results are that the dependence of the cholesteric pitch on concentration is insensitive to polydispersity (for unimodal distributions) and doping the system with longer rods decreases the macroscopic chirality of the system. These results are definitely dependent on the significant approximations used but nevertheless the paper represents an interesting contribution to the field. The paper is written in a reasonably concise way, that is both positive since the main points are clearly highlighted but also it makes difficult to follow all the derivation. Nevertheless all the main formulas are clearly presented and the references on the previous works on which part of the theory is based are clearly reported. Overall, I have only minor comments, as detailed below, and I can recommend publication.

To me, it is confusing to call the quantity “q” the “pitch”, since this term is usually associated to a “length” and not its inverse.

In the abstract at line 9 I would specify “helical twisting power” and perhaps because of the ambiguity that I mentioned above, it would be more clear to add the symbols K2, Kt and q directly after the corresponding terms in the abstract as well.

It should be clearly stated throughout the text when the dopants are achiral (section 4.1?) 

To improve readability, I would also specify in the paragraph between lines 102-110 that the point at x_chol=0 is termed I-C cloud point and the one at x_chol=1 is the C-I cloud point. 

In the conclusions, in addition to the three main assumptions of the theory, I would also state that to arrive at the asymptotic results also assumptions on the inter-particle potential were made. 

In general, the fact that the theory only predicts q ~ concentration  seems quite a strong limitation since many (most/all?) colloidal systems show different dependence.  

Some typos:

- page 3 line 66 “complication” -> “complicate” ?

-page 4 below eq (10) “orderi” -> order

-page 8 line 130, the sentence does not read nicely, perhaps it should be “algebraic form. The determination”

- line 132 “to determine the dependence on the length..”

Author Response

Please consult pdf

Author Response File: Author Response.pdf