Re: [Towhee-users] Chemical potential calculation with multicomponents

[Thaer Al-J. <tha...@po...>]

Dear Seunghwan Baek,

I prefer to see your files ( input and force fields) to be more accurate in my answer.
I believe there is a mistake in your force field files. I would suggest you to check it.


Best regards
Thaer Al-Jadir
PhD Student and Teaching assistant at the School of Chemical Engineering and Analytical Science | The University of Manchester | The Mill (B9) | Oxford Road | Manchester | M13 9PL | Tel: 07473889191



________________________________
From: 백승환 <kar...@na...>
Sent: 04 February 2017 03:34:29
To: tow...@li...
Subject: [Towhee-users] Chemical potential calculation with multicomponents


Dear all,



Hello, I am trying to calculate chemical potential for multi-component molecules.

I ran NPT for 10,000 cyles with 7 components having methane, ethane, propane, butane, pentane, hexane, and dodecane.



The results are,

 u (Gibbs Total)                K    1   1    -4205.520       11.451

 u (Gibbs Total)                K    2   1    -5189.762       40.365

 u (Gibbs Total)                K    3   1    -4799.743       76.045

 u (Gibbs Total)                K    4   1    -3745.663      196.951

 u (Gibbs Total)                K    5   1    -2728.364      480.996

 u (Gibbs Total)                K    6   1    -1632.444      214.713

 u (Gibbs Total)                K    7   1     6518.731      622.668



First, what does the positive value of the chemical potential mean? As far as I know, the chemical potential is negative.

Shown in the manual,

μtotal(i) = μresidual(i) + μdensity(i) + μisolation(i)
μresidual(i) = μNpT Insertion(i) - μIsolation(i).

Since there is no isolation, only μNpT Insertion(i) +μdensity(i)  needs to be considered.
μtotal(i) = - kB T ln[ < W * V / ( [N(i)+1] * Λ3(i) ) > ]
μdensity(i) = - kB T ln[ < V / N(i) > / Λ3(i)) ]
μNpT Insertion(i) = - kB T ln[ < V W > / < V > ]

Secondly, I do not understand the following,
μtotal(i) = μdensity(i) + μNpT Insertiona(i)
- kB T ln[ < W * V / ( [N(i)+1] * Λ3(i) ) > ] = - kB T ln[ < V / N(i) > / Λ3(i)) ]  - kB T ln[ < V W > / < V > ] = - kB T ln[< V / N(i) > / Λ3(i))*< V W > / < V >]
<=>  < W * V / ( [N(i)+1] * Λ3(i) ) >   =   < V / N(i) > / Λ3(i))*< V W > / < V >

According to Martin and Siepmann 1998 (TCA)<http://towhee.sourceforge.net/references.html#martin_siepmann_1998_tca>.
The term W  is <W+>/Wideal where W+ ‡and Wideal are the Rosenbluth weights of the ghost chain and of an ideal chain.
Is this the weighted average insertion probability in Molecular Physics, 1990, 70, 6, 1145-1158, which is equation 6 in page 1150?
Otherwise, how can I calculate this? Which source file I should refer to related to this?

I see, as the number of carbon (length of the molecules) increases, the value of u (NpT Insertion) also increases.
For example,

 u (Density)               K    6    -5886.576
 u (NVT Insertion)         K    6     4189.927
 u (NpT Insertion)         K    6     4189.927
 u (Den. + NVT Insert)     K    6    -1696.649
 u (Den. + NpT Insert)     K    6    -1696.649
 u (Gibbs Total)           K    6    -1698.935
 u (Density)               K    7    -5523.402
 u (NVT Insertion)         K    7    11449.852
 u (NpT Insertion)         K    7    11449.852
 u (Den. + NVT Insert)     K    7     5926.450
 u (Den. + NpT Insert)     K    7     5926.450
 u (Gibbs Total)           K    7     5419.709

I simply assume that the positive value of chemical potential of component-7 comes from this large u (NpT Insertion).

μNpT Insertion(i) = - kB T ln[ < V W > / < V > ]
ln[ < V W > / < V > ]  < 0  to get positive μNpT Insertion(i)
then,
[ < V W > / < V > ]  < 1

In conclusion, the longer molecules may have smaller W. So I need additional explanation of this W, please.
Moreover, the chemical potential deviation of my simulation is large. Give me suggestion for this and normally, how small they should be?
I would appreciate your help!

*A few days ago, I emailed with similar question as a non-member. You are able not to post the email from this email address. Sorry for that.

Seunghwan Baek




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