Answer to the Referee.
First of all we would like to thank the Referee for a thorough analysis of our manuscript! The
comments given are highly appreciated and we tried to improve the text accordingly. Please, find
below the list of changes and corrections done.
RC: (1) Page 4, line 4. It's probably fair to point out more recent work on the putative "ferromagnetic
liquid" phase, some of which is by J.-J. Weis…
We added the suggested references: see Refs. [41-43] and Ref. [45].
RC: (2) Page 4, equation (1.2). As defined, S(q) for an uncorrelated fluid is zero. Shouldn't S(q) =
I(q)/I0(q), so that for an uncorrelated fluid S(q)=1?
Absolutely correct. The expression was corrected in the text.
RC: (3) Page 4, equation (1.4). g(r) is introduced as the radial distribution function, which has
the property that g(r)->1 when r->infinity. Therefore, equation (1.4) should carry an additional
factor of 1/[4*pi*(r^2)].
In equation (1.4) we take the ensemble average, so the factor is not needed there. It appears only
after spherical averaging in the case of the field being absent. This fact is also used in Eq. (2.1).
RC: (4) Page 5, equation (2.2). Should the minus sign be there at the front? The excess part of the free
energy should be F ~ -kTlnQ, and the ideal part should go like F ~ kTh[ln(h)-1].
Correct, we fixed the typo.
RC: (5) Page 7, line 22. "loose" -> "loss".
Corrected.
RC: (6) Page 7, equation (2.6). There should be an additional term in the denominator. For an observable
A, the ensemble average should be <A*exp(-U/kT)>/<exp(-U/kT)> if the <...> means an average over
angles and also the radial distance between the particles (as per equation (5.1) in Appendix 1).
The angular brackets mean here to take the proper statistical average, i.e., with normalization.
This is also used and defined in the appendix.
RC: (7) Page 13, line 34. "The magnetic field" is spurious.
RC: (8) Page 13, line 38. The reduced dipole moment (squared) should be
mu^2/(epsilon*sigma^3).
RC: (9) Page 14, line 40. Why choose T=297K, or is this a typo?
Corrected. Temperature typo was also corrected. T = 293.
RC: (10) Page 16, line 11. "Since the first peak of the structure factor corresponds to large wave vectors,
meaning short wave lengths, it reflects short-range ordering. Therefore the growth of the peak height can
be treated as a sign that the aggregate number increases." I can understand the basis for this comment,
but it is not unambiguous. All simple fluids will show the same trend (with increasing density or
decreasing temperature) due to the increase in near-neighbor correlations, with q~2*pi/(effective
diameter).
We modified the text:
Since the first peak of the structure factor corresponds to large wave vectors, meaning short
wave lengths, it reflects short-range ordering. Therefore the growth of the peak height can be
treated as a sign that the aggregate number increases. However, the same kind of behaviour will
be exhibited by any simple fluid due to the increase of short-range correlations. Looking only at
the first peak, however, it is not possible to describe uniquely neither the density of these
aggregates, nor their topology.
RC: (11) Pages 16, line 30 onwards to the end of the section: the discussion of power-law scaling of S(q).
Does the theory predict a power law, too, over a finite range of q? Regarding the analysis of (simulated)
S(q): what were the fitting ranges of the power law? What are associated uncertainties? In figures 6(d)-(i),
it seems that the power-law behavior is only apparent in the simulation results between q=1 and, say,
q=0.3 or so. What about the range 1 < q < 2? In Phys. Rev. E 62, 5403 (2000), P. J. Camp and G. N.
Patey offered some sort of rationale for the observable range of power-law behavior: the lower limit
q(min)=2*pi/l corresponds to the persistence length l=6-7 (as also seen by Weis and Levesque); and the
upper limit q(max)=pi corresponds to the shortest possible chain of 2 particles.
Our theory does not predict a power-law of S(q). We also considered the paper of Camp and Patey and
replotted Fig. 6. Error bars of fitting are added in the legend of the plot. Fitting is now done from 0 < q < 3.
RC: (12) Page 18, line 6. Does "correlation scale" mean some sort of mean spacing, rather than a
correlation length?
We decided to remove the sentence, not to puzzle the readers.
(13) Page 18, line 18 onwards. In equation (4.1) why is the total S(q)written in this form. For a binary
mixture, S(k) = (x1^2)*S11(k) +2*x1*x2*S12(k) + (x2^2)*S22(k) (see Hansen and McDonald). It is
therefore not so surprising that the simple linear combination in equation (4.1 )doesn't match up with the
simulations.
It is commonly considered that the interaction between small and large particles are too weak and not
worth extending the model since they make the theory more complicated. In the present paper we wanted
also to underline that it is not the case for the systems under study. That is why we decided to use an
ideal binary mixture, in which particles from different fractions are totally indifferent to each other, so the
linear combination was used for the “ideal” binary mixture.
(14) References: the complete lists of authors should be given for references 2, 3, 6, 8, 9, 11, 22-25, 4649, 52-54, 61, 63, 64, and 67; the proper journal abbreviations should be given in references 1 and 24;
the correct author names should be given in references 15 and 26; and reference 27 is mainly about
dipolar hard spherocylinders and cut spheres, and not so much about model ferrofluids - Phys. Rev. E 48,
3728 (1993) could be added to the list.
The complete list of authors is given now. The abbreviation for the journal in Ref. 1 is taken from the website of Molecular Physics, the abbreviation for PCCP is changed to Phys. Chem. Chem. Phys. Names are
corrected. The reference is replaced.
(15) Could the authors comment on the likely accuracy of the theory in terms of thermodynamics
properties? For instance, the compressibility is linked to S(q) at q=0.
As for the compressibility in our theory, it has a finite value. Since our theory is based on a noninteracting gas of aggregates, we expect that thermodynamic properties will be correct as long as
this limiting assumption holds. We decided not compare our values with simulation results, and
are also not aware of any experimental data. We would like to thank the Referee for the idea, and
will surely look at it in the future.
An additional acknowledgement to JJW is added also to the paper.
Sincerely yours, Sofia S. Kantorovich for all authors.