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Variation along liquid isomorphs of the driving force for crystallization
by Ulf R. Pedersen, Karolina Adrjanowicz, Kristine Niss, Nicholas P. Bailey
This is not the current version.
|As Contributors:||Nicholas Bailey|
|Arxiv Link:||http://arxiv.org/abs/1702.01010v1 (pdf)|
|Date submitted:||2017-02-06 01:00|
|Submitted by:||Bailey, Nicholas|
|Submitted to:||SciPost Physics|
We investigate the variation of the driving force for crystallization of a supercooled liquid along isomorphs, curves along which structure and dynamics are invariant. The variation is weak, and can be predicted accurately for the Lennard-Jones fluid using a recently developed formalism and data at a reference temperature. More general analysis allows interpretation of experimental data for molecular liquids such as dimethyl phthalate and indomethacin, and suggests that the isomorph scaling exponent $\gamma$ in these cases is an increasing function of density, although this cannot be seen in measurements of viscosity or relaxation time.
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Reports on this Submission
Anonymous Report 2 on 2017-3-10 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1702.01010v1, delivered 2017-03-10, doi: 10.21468/SciPost.Report.94
1) Novel approach to understand better how the crystallization dynamics depends on the state point.
1) No discussion on the theoretical concepts used to describe crystallization
2) Basically no discussion on other numerical approaches to get the crystallization rate
3) No discussion of previous numerical results that predicated crystallization rate
4) The mechanism for crystallization is not really understood. In the present work the authors
only calculate the difference in free energy. This is not enough to predict the crystallization
4) Introduction to isomorphs is way too long
5) Reference list is too strongly biased towards citations of the group of the authors.
6) The simplest system for crystallization is the hard sphere system. What
can we learn from the present results for HS?
Crystallization is not only an important process in many applications but
also a challenging scientific problem since it is not trivial at all to
come up with a reliable theoretical description for this phenomenon. The
most popular approach is probably the classical nucleation theory
(CNT), in which the crystallization rate is connected to the free
energy difference between the two phases and the diffusion constant of
the particles. Quite a few studies have been carried out to test this
idea (see, e.g. Auer and Frenkel 2001, Kawasaki and Tanaka 2010) but
none of these papers are cited. These studies have also shown that in
order to get the crystallization rate, it is not sufficient to know the
difference in the free energy between the two phases since the kinetics
plays also an important role. Furthermore these studies have also
shown that sometimes the liquid crystallizes by first forming (locally)
a phase that is different from the one of the target crystal, i.e. the free
energy difference between the liquid and the final crystal is not even
a good indicator for the driving force.
In the present manuscript the authors use the approach of the isomorphs
to calculate the free energy difference between the liquid and crystalline
phase. Unfortunately they do not explain at all why this is the relevant
quantity for the crystallization process since they do not even mention
CNT. They do discuss results of experiments in which the crystallization
dynamics has been studied as a function of temperature and pressure. But
at the end, see section 4.4, not much insight can be gained from the
present theoretical approach to rationalize the experimental findings.
More convincing are the direct comparison between the theoretical
results and computer simulations by means of which the authors that have
determined directly the free energy difference. The agreement between
theory and simulations is good once the second order correction terms
have been taken into account.
-Is it really useful to give such a long introduction to the ideas of the
-The authors cite 26 papers (out of 36 references) in which
they are coauthors or that are authored by members of their group. Doesn't
this indicate that either the citations are not balanced or that outside
this group nobody work on the approach with the isomorphs? There is,
e.g. the recent paper by Maimbour and Kurchan that have worked on this
subject as well. Also, Tolle (Rep. Prog. Phys. 2001) has studied the
dynamics of glass-formers as a function of pressure and temperature and
found that one can generate master curves.
p. 11, 3 lines after Eq. 17: What is the meaning of the sum over R?
In summary, it is to some extent interesting that the approach with the
isomorphs is able to give insight to the free energy difference between
the liquid and the crystalline phase. But as argued above, this does not
help much to advance our understanding of the crystallization dynamics.
Therefore I find it misleading that the authors use data from experiments
that probe the crystallization dynamics to motivate their calculations.
As it is the message of the paper is too confusing and hence I do not
recommend it to be accepted.
1) Make a much stronger point why this work is relevant for crystallization. If this is not
possible refocus the message.
2) Add references
3) Take care of the items that are mentioned in the report
Anonymous Report 1 on 2017-2-22 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1702.01010v1, delivered 2017-02-22, doi: 10.21468/SciPost.Report.86
1- The article is written in a transparent, pedagogical way.
2- The article attempts to relate the perturbative approach of isomorphs to experimental measurements.
1 - Some typos.
In their work "Variation along liquid isomorphs of the driving force for crystallization" the authors illustrate a case study of application of the isomorphs theory to the calculation of the driving force to crystallisation for a simple liquid (Lennard-Jones fluid) and in the context of a selection of experimental results.
Proceeding from a previous work, [Pedersen, Ulf R., et al. "Thermodynamics of freezing and melting." Nature communications 7 (2016): 12386.] the authors discuss the details of a chemical potential calculation for a simple system, extend it to a class of isomorphic liquids and attempt a prediction for the experiments. From their discussion, it appears that the hypothesis of simple scaling does not apply to the considered experimental system, as the predictions are contradicted.
The article is well written and requires only minor modifications. There are, however, three aspects that could be explained by the authors more:
1- in Figure 3 (both left and right panel), the thermodynamic integration calculations appear to be overestimated for T>2 and underestimated for T<2 by the isomorphs theory. Can this be more explicitly rationalised?
2- related to the previous question, one could approximate the high temperature limit of Figure 3 by a suitably scaled system of hard spheres. How different would the estimate of the driving force be? Does the isomorph prediction converge to the hard sphere limit?
3-the discussion of the experimental data concludes, by exclusion, that $\gamma(\rho)$ should be a strong function of the density. What is the implication of this observation, in physical terms, on the nature of the interactions? Can the author propose a list of experimentally viable systems where they expect a milder dependence of $\gamma$ on the density, such that the predictions of the theory could be verified?
1-In the caption of Figure 2 a sentence is worded incorrectly: " but the for a given temperature...."
2-At page 10, the quantity "W" appears for the first time in the main text. Since it can be mistaken for other quantities, I suggest to modify the sentence as follows: "The resulting densities can be used in Eq.915) and Eq.(27) to find the $potential$ $energy$ U and the $virial$ W".
3-At page 14, the IPL (inverse power law) acronym appears without previous definition.