Τhe role of surface energy in the apparent solubility of two different calcite crystal habits

The interplay between polymorphism and facet-specific surface energy on the dissolution of crystals is examined in this work. It is shown that, using cationic additives, it is possible to produce star-shaped calcite crystals at very high supersaturations. In crystallization processes following the Ostwald rule of stages these star-shaped crystals appear to have higher solubility than both their rhombohedral counterparts and needle-shaped aragonite crystals. The vapour pressures of vaterite, aragonite, star-shaped calcite and rhombohedral calcite crystals are measured using thermogravimetric analysis and the corresponding enthalpies of melting are obtained. Using inverse gas chromatography, the surface energy of the aforementioned crystals is measured as well and the surface energy of the main crystal facets is calculated. Combining the effect of facet-specific surface energies and the enthalpies of melting on a modified version of the classical solubility equation for regular solutions, it is proved that the star-shaped calcite crystals can indeed have higher apparent solubility than aragonitecrystals.


Comments to the Author(s)
In this work, the authors have successfully made different shapes and polymorphs. It is interesting to report these different shapes and investigate the facet of these crystals. Then, the solubility was linked to the surface energy of different shapes and polymorphs, and the influence of different facets on solubility was discussed.
Some comments: In the introduction, it is not clear if any other researchers have investigated the relation solubility with the surface energy in this system or other systems? why Ni2+ was introduced?
any of these conditions repeated in experiments? Figure 3 shows the obvious translation happening from 5 min to 24h? any date to show the transaction progress? Table 1, the peak values of XRPD are dependent on many factors? how authors minimize the influences? Table 2, for facet 1 or 2, is that possible to mark them in the real crystal images?
Any polymorph change during the crystal growth or testing in TGA? the work starts with an equation for dissolution, but the equation was not used in the discussion, will this equation help to understand the phenomena?
For other equations, such as Equ 4, will this equation help to make a quantity-comparison? rather than quality-comparison?

Comments to the Author(s)
This is an interesting and detailed work on crystallization of calcium carbonate polymorphs in controlled conditions with design of morphology of calcite the stable morph to have high dissolution/ solubility in star shaped crystals. The applicability of this result is widespread and publication is recommended. A few comments to improve/ correct the MS 1. Experimental -was de-aerated for 3 h with a N2 stream (h is missing) 2. The additive NiCl2.6H2O which gives the desired morphology for stable calcite polymorph. A possible chemical binding or catalytic and templating effect may be added to make the rationale clear for readers how / why the morphology of calcite crystals changes from rhombohedral to star shaped.

Review form: Referee 3
Is the manuscript an original and important contribution to its field? Excellent

Is the paper of sufficient general interest? Excellent
Is the overall quality of the paper suitable? Good Can the paper be shortened without overall detriment to the main message? Yes Do you think some of the material would be more appropriate as an electronic appendix? No

Recommendation?
Accept with minor revision (please list in comments)

Comments to the Author(s)
This work discusses an interesting experimental study of vapor pressures and surface energies of a series of calcium carbonate polymorphs. The work highlights the importance of surface energy as a factor in polymorph solid state behaviour, and indeed how the design of high surface energy solids can infer improved solubility behaviour of crystal solid state material. A topic which should be of significant interest to the pharmaceutical world where the solubility of solid state dosage forms, especially hydrophobic molecules, is especially challenging, and this new insight could provide an interesting new strategy. The vapor pressure study of the polymorphs is particularly interesting in Figure 6. The precise methodology is not mentioned, I assume it is Knudsen effusion. But I would like to see details included in the manuscript, including how the orifice size was determined as well as the sample temperature measurement if this was the method used. I think a Table reporting these heats of vaporisation should be included, as well as some comparison with literature values. The legend comment for Figure 6 "A plot similar to the previous one" does not seem very informative. The authors had included a detailed surface energy analysis of the crystal surfaces using IGC. This is a very comprehensive and informative data set. However, the methodology for deconvoluting this total surface energy data into facet specific surface energies is not explained at all, beside the cryptic comment -in silico. Please provide a proper explanation of this important step in estimating the face specific data.

26-May-2021
Dear Dr Hadjittofis, On behalf of the Editor, I am pleased to inform you that your Manuscript RSPA-2021-0200 entitled "Τhe role of surface energy on the apparent solubility of two different calcite crystal habits" has been accepted for publication subject to minor revisions in Proceedings A. Please find the referees' comments below.
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We welcome submissions of images for possible use on the cover of Proceedings A. Images should be square in dimension and please ensure that you obtain all relevant copyright permissions before submitting the image to us. If you would like to submit an image for consideration please send your image to proceedingsa@royalsociety.org In this work, the authors have successfully made different shapes and polymorphs. It is interesting to report these different shapes and investigate the facet of these crystals. Then, the solubility was linked to the surface energy of different shapes and polymorphs, and the influence of different facets on solubility was discussed.

Some comments:
In the introduction, it is not clear if any other researchers have investigated the relation solubility with the surface energy in this system or other systems?
any of these conditions repeated in experiments? Figure 3 shows the obvious translation happening from 5 min to 24h? any date to show the transaction progress? Table 1, the peak values of XRPD are dependent on many factors? how authors minimize the influences? Table 2, for facet 1 or 2, is that possible to mark them in the real crystal images?
Any polymorph change during the crystal growth or testing in TGA? the work starts with an equation for dissolution, but the equation was not used in the discussion, will this equation help to understand the phenomena?
For other equations, such as Equ 4, will this equation help to make a quantity-comparison? rather than quality-comparison?
Referee: 2 Comments to the Author(s) This is an interesting and detailed work on crystallization of calcium carbonate polymorphs in controlled conditions with design of morphology of calcite the stable morph to have high dissolution/ solubility in star shaped crystals. The applicability of this result is widespread and publication is recommended. A few comments to improve/ correct the MS 1. Experimental -was de-aerated for 3 h with a N2 stream (h is missing) 2. The additive NiCl2.6H2O which gives the desired morphology for stable calcite polymorph. A possible chemical binding or catalytic and templating effect may be added to make the rationale clear for readers how / why the morphology of calcite crystals changes from rhombohedral to star shaped.
Referee: 3 Comments to the Author(s) This work discusses an interesting experimental study of vapor pressures and surface energies of a series of calcium carbonate polymorphs. The work highlights the importance of surface energy as a factor in polymorph solid state behaviour, and indeed how the design of high surface energy solids can infer improved solubility behaviour of crystal solid state material. A topic which should be of significant interest to the pharmaceutical world where the solubility of solid state dosage forms, especially hydrophobic molecules, is especially challenging, and this new insight could provide an interesting new strategy. The vapor pressure study of the polymorphs is particularly interesting in Figure 6. The precise methodology is not mentioned, I assume it is Knudsen effusion. But I would like to see details included in the manuscript, including how the orifice size was determined as well as the sample temperature measurement if this was the method used. I think a Table reporting these heats of vaporisation should be included, as well as some comparison with literature values. The legend comment for Figure 6 "A plot similar to the previous one" does not seem very informative. The authors had included a detailed surface energy analysis of the crystal surfaces using IGC. This is a very comprehensive and informative data set. However, the methodology for deconvoluting this total surface energy data into facet specific surface energies is not explained at all, beside the cryptic comment -in silico. Please provide a proper explanation of this important step in estimating the face specific data.

22-Jul-2021
Dear Dr Hadjittofis I am pleased to inform you that your manuscript entitled "Τhe role of surface energy on the apparent solubility of two different calcite crystal habits" has been accepted in its final form for publication in Proceedings A.
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Sincerely, Raminder Shergill proceedingsa@royalsociety.org on behalf of Dr Andy Sutherland Board Member Proceedings A Figure 3 shows the obvious translation happening from 5 min to 24h? any date to show the transaction progress?
Detailed SEM imaging suggest that the star-shaped calcite crystals shrink with increasing time. Similarly, needle shaped aragonite crystals dissolve as well. On the other hand, rhombohedral calcite crystals appear later on and they grow. This pattern combined with the XRD results suggest that the crystallization is determined by the Ostwald rule of stages. This is in-line with the theory suggesting that the Ostwald rule is triggered at relatively high supersaturations. It is not clear yet, whether star-shaped calcite crystals shrink to a certain minimum size and then they regrow as rhombohedral crystals. It is true that the peak quality can be influenced by numerous factors. The presence of amorphous and/or nanoparticles is one of those. The SEM investigation did not reveal the presence of such particles. A large amount of sample was used, in a back-loaded sample holder. As the material was relatively free flowing and fine, no mechanical force was exerted on it, to assist in the packing. Thanks to the fine nature of the particles, the surface of the sample can be considered flat with respect to the sample holder. For the crystals produced at 3 and 5 mins, in the presence of Ni2+, the material was unloaded from the sample holder, mixed with the mother batch and then a new sample was taken for a second measurement. The same procedure was repeated once again. The three measurements were identical. This point was also amended in the document. Table 2, for facet 1 or 2, is that possible to mark them in the real crystal images?
Crystals are faceted entities, with each facet corresponding to a different crystallographic plane. The authors were not able to grow a macroscopic single crystal of star-shaped calcite, to perform the appropriate studies required to confidently provide the requested drawing. The authors assumed two crystal facets as this number was allowing better fitting of experimental and simulated results. The use of a single major crystallographic plane was not going to change the outcomes of the discussion drastically.
Any polymorph change during the crystal growth or testing in TGA? This is an excellent point that the authors have considered; albeit it was not mentioned in the text for brevity. The enantiotropic relationship, between calcite and aragonite, is a very important research question. Therefore, it may be the case that the TGA measurement may be impacted by a potential in situ transformation of calcite to aragonite. During the TGA experiments, the material was exposed at a temperature gradient in an open pan connected to a mass spectrometre. The existing phase diagrams show that, for the range of temperatures used, the pressures required for an enantiotropic transition are orders of magnitude higher than those encountered in the TGA set-up. Therefore, the possibility of enantiotropic transformation is minimum.
(1) Zimmermann, H.D. Equilibrium Conditions of the Calcite/Aragonite Reaction between 150°C and 350°C Nature Physical Science, 1971, 231, 203-204 the work starts with an equation for dissolution, but the equation was not used in the discussion, will this equation help to understand the phenomena?
This equation (Eq. 1) provides the mathematical framework to understand why the difference in surface energy anisotropy can alter the apparent solubility sequence. To address this, the authors amended the document to compare the results of Eq. 1 with those of Eq. 4 (Eq. 5 in the revised manuscript) quantitatively.
For other equations, such as Equ 4, will this equation help to make a quantity-comparison? rather than quality-comparison?
A more quantitative approach will substantially elevate the quality of the manuscript. An appropriate amendment was done to address this.