Download You obtained your required density profile data

June 17, 2010 - Questions by GA Mansoori:
You obtained your required density profile data in nanoslit pore using the perturbative
fundamental measure density functional theory.
1. Could the normal pressure tensor be also derived using the perturbative fundamental
measure density functional theory?
2. If it is possible to calculate the normal pressure tensor using the perturbative
fundamental measure density functional theory then what is the advantage of the analytic
theory presented here?
3. If the answer to question 1 is positive and you have a good reason to say we need the
analytic theory also then the question is: Shouldn't we also report in Figures 2-7 (or in
some other figures) the results of the perturbative fundamental measure density
functional theory along with the present analytic theory?
June 18, 2010 - Answers by Ms. Fatemeh Heidari:
Dear Prof. Mansoori
Thank you for e-mail. My responses to your question are as follows:
1 ,2) The Gibbs equation, dE, for a system in which pressure has tensorial character is:
3
dE  TdS   pii dVi  dN
i 1
In confined fluid in nano pore pressure has tensorial character and Gibbs equation
assumes this format.
In nanoslit pores the pressure tensor is a diagonal tensor with pii (i =x, y, z) components.
By using the Legendre transformation we can get the grand potential for an open system:
  E  TS  N  
3
d   SdT   pii dVi  Nd
i 1
In the Cartesian coordinate we have
d   SdT  pxx dVx  p yy dVy  pzz dVz  Nd
Where pxx and pyy are the lateral and pzz is the normal pressure components. In naoslits the
lateral pressures are equal to each other , pxx  p yy and since
V  Lx Ly Lz  A  H
therefore
,
dVx  Lz Ly dLx , dVy  Lz Lx dLy , dVz  Lx Ly dLz
d  SdT  pzz dVz  pxx H Lx dLy  Ly dLx   Nd

dA
d  SdT  pzz AdH  pxx HdA  Nd
Therefore the pressure components may be obtained via
p zz  
1   


A  H T ,  ,, A
p xx  
1   


H  A T ,  , , H

represents an average transverse pressure
V
acting parallel to the confining walls [J. Chem. Phys, 126, 244708 (2007)].
Also, the negative grand potential density 
Both of two components of pressure tensor in all above equations are average quantities.
Therefore we can calculate just the average pressure using DFT.
3)Also figures 2-7 have been plotted using the derived equation although in which the
results of the local densities results of the perturbative fundamental measure density
functional theory have been used.
Finally, I have calculated the average normal and lateral pressure components for
different thermodynamics states (H,T, bulk density) using DFT recently via the grand
potential. In this case we are able to predict thebehavior of average pressure components
in a nanoslit with H ,T and bulk density. Also using the average pressure we are going to
study validity of some regularity in confined fluids.
June 18, 2010 - Comments by GA Mansoori:
Thank you for your quick response. From your answers above it is obvious to me that
normal pressure tensor data can be derived from the perturbative fundamental measure
density functional theory (PFM-DFT). If we send the manuscript as it is (calculating
density profile from PFM-DFT but not the normal pressure tensor the reviewers of
manuscript will raise a RED FLAG and will probably say “why haven’t the authors
calculated normal pressure tensor also from PFM-DFT and compared their results with
their analytic solution?”.
Ms. Heidari - Please note that we could publish Paper 1 (without calculating the hardsphere normal pressure tensor) because we quoted density profile data from Kamalvand’s
paper. Actually Kamalvand should have calculated hard-sphere normal pressure tensor
using FM-DFT (am I right?).
Anyway, I like to hear from you what we must do now:
1. Are you willing to calculate the normal pressure tensor from PFM-DFT and report
them on the same graphs as your analytic theory?
2. If that (#1) is not possible then what aspect of the pressure tensor could be calculated
using PFM-DFT and your analytic theory to compare the two methods in either tabular or
graphical forms?
June 19, 2010 - Dear Prof. Mansoori
1) In DFT approach for a confined fluid at constant T and ρ(r), H, we have a unique value
for the grand potential, In fact it is not defined locally, and therefore we can not get the
local pressure from it by its derivative with respect to dvi.
2) As you know, Ω(ρ( r )) in different versions of DFT is function of the local density and
when we minimize it with respect to ρ( r ) at constant T and µ we get the equilibrium
local density. Such a functionality of the grand potential to ρ(r) is based of the DFT in
quantum mechanics. For your purpose we should have the grand potential as a function
of local pressure, Ω(p( r )). To our konwledge there isn’t such functionality. Therefore in
such a way we can not get the local pressure from DFT.
3) Also you know that the definition of the pressure for an inhomogeneous system is
arbitrary and it can be formulated based on on your definition, for example via our
equation, by using the values of T and ρ( r ), H. It means that ρ( r ) is as one of the initial
parameter to obtain the local pressure. In this paper such a parameter has been obtained
From DFT.