Maximum Possible Cooling Rate in Ultrafast Chip Nanocalorimetry: Fundamental Limitations Due to Thermal Resistance at the Membrane/Gas Interface

Round 1

Reviewer 1 Report

In this manuscript authors investigate the fundamental limitations of cooling rate in ultrafast membrane-based nanocalorimetry. The work is interesting and outcome is potentially useful for the development of a new generation of calorimetric sensors. In my opinion, the article could be accepted after authors conveniently address the following comments.

• Introduction should include a wider overview of the current state of the art regarding membrane-based nanocalorimetry. Authors could briefly describe a few investigations among those already cited in ref. 1-20.
• Problem conceptualization (mainly presented in section 2 and 3, as well as Annexe A) is described in detail. Even so, some sentences should be supported by convenient references (take “typically, nitrogen…”, as an example).
• Provide appropriate references for the thermal and contact parameters of gases gathered in Tables 1 and 2.
• The article is, in general, well written and described in a comprehensive manner. However, some more contrast and comparison with previous studies should be desirable. Particularly in the second half of section 4.
• Figures are well presented and relevant to display the outcome of the investigation. Even so, Figures 3-5 could be improved by increasing the number of ticks in x-axis of inserted graphs (3a, 4a and 5a). Likewise, authors should also improve the readability of normalized heating rate in those same figures.
• Conclusions should not make references to figures. They would better summarize major findings of the article.

Some other minor remarks are: i) units are presented using “slash” (/) and negative powers (compare Table 1 and nomenclature section, for instance), ii) revise words unnecessarily presented in italics (nomenclature, for instance) and iii) some subscripts were not included in the nomenclature (for example: r and c, standing for radiative and convective contributions of heat transfer coefficients, respectively).

Author Response

The authors are grateful to the reviewers for their valuable comments. The corrections have been done and all changes are marked in the revised manuscript.

Author Response File: Author Response.docx

Reviewer 2 Report

There are numerous papers address the method to enhance the cooling rate of materials. The method is relevant in the material processing industry to manufacture nano-crystal and amorphous materials. The theoretical investigation focuses on the contact with cold solid metals to attain the maximum coolability possible which falls in a few 10⁷ K/s and much greater. The derived theory was validated against the experimental results already.
In turn, the authors could calculate such a high cooling rate with gases. This is because the authors assume that characteristic heat loss is associated to the lateral distance, r₀ in place of L in z-coordinate which is perpendicular to the lateral. In fact, the maximum cooling rate must be calculated by conduction theory in both membrane and gas domains for such a short time and distance. The author assumes the convective heat transfer and gap conductance in this conduction problem with wrong assumptions. If the cooling rate exceeds 10⁹ K/s, you need to consider the terms of velocity of light to solve a relativistic heat conduction equation. The following article tells you how. 

Reference
Juan A. López Molina, María J. Rivera, Enrique Berjano, ”Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study,” Proc. Royal Society A470 (2014), doi: 10.1098/rspa.2014.0547

Minor comment:
Figure 4 (a): When the scanning rate is normalized, the unit must be nondimensional.

Author Response

The authors are grateful to the reviewers for their valuable comments. The corrections have been done and all changes are marked in the revised manuscript.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Authors have carried out the changes suggested by this Reviewer. In my opinion the article may be accepted in the persent form.