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Last Update

Properties Estimation: Critical Temperature (Tc) Estimation


Lecture note of Dr. Hiroshi Yamamoto

The program that Pirika provide.

Pirika neural network method (JAVA version 2004.11.14)
Joback method (JAVA version 2004.11.14)
Joback method(HTML5 version 2011.4.16, with Other Properties)
PirikaLight(JAVA version 2009.9.15, with Other Properties)
Temperature-Vapor Pressure relationship (HTML5 version 2011.6.13)
YMB simulator (HTML5 version 2011.6.10, need pass code to use full function)

Newest version is implemented into HSPiP ver.4(Y-Predict). If the corporate visitor want to use full version, please buy HSPiP. The Abstract of HSPiP (2013.1.18)
How to buy HSPiP

Critical temperature ( Tc ), critical pressure ( Pc ), and critical volume ( Vc ) represent three widely used pure component constants. These critical constants are very important properties in chemical engineering field because almost all other thermo chemical properties are predictable from boiling point and critical constants with using corresponding state theory. So precise prediction of critical constants are very needed.

There are several methods to predict critical constants.

Every these methods need normal boiling point to predict critical temperature and the accuracy of Tc estimated value is strongly depend on inputted normal boiling point. So for completely unknown molecule case, it needs to estimate of boiling point, then to calculate Tc, this means multiply two errors. On the contrary, our neural network method predict critical temperature directly from molecular structure and need not boiling point.

For critical pressure estimation, summation of group contribution factors with molecular weight (or number of heavy atom) lead to good correlation. But it is said that both Tc and Pc estimation with group contribution method, it can not introduce bi-functional interaction, so multifunctional compounds case, the result error become approximately 5%. Our neural network method takes bi-functional interaction and/or hydrogen bonding effect into account, so accuracy of estimation is much higher than conventional method.

Experimental Critical volume or Critical density ( molecular weight / critical volume ) data can not be available so much compare to Tc and Pc. Some data book listed not experimental values but estimated values. Actually, this property is not so sensitive to its structure, but uncertainty of experimental/estimated problem is so serious when applying Vc to estimate liquid density. My neural network method introduce correction factor from absolute molecular volume calculated from optimized structure by Molecular Orbital.

Estimation Method

There are many methods to estimate Critical Temperature. The most popular method is Joback method. This method calculate Critical Temperature with this scheme. (Please refer to Wiki page)

Tc = Tb[0.584 + 0.965ΣΔTc - (ΣΔTc)2]-1

This method seems accurate enough. But I think it is not true. If you can use experimental boiling point, Joback method is accurate enough. But if you use estimated boiling point, the result become so worse. And Joback group factors are so limited. Then problem is that "how can we expand group factor for Joback method" like boiling point case? For boiling point case, we can use a lot of experimental data so we can expand functional groups. I have checked the popular thermo-chemical Dipper 801 database. Experimental Critical Temperature is so limited.

From only 420 compounds, i need to build new scheme to estimate Tc. The measurement of Tc is very hard for larger molecule because Tc become very high, and thermal stability of compounds prevent from accurate experiment. So we can not expect much data. In pirika site I use neural network method to predict properties, and NN need a lot of data to learn something. So it is very hard to apply for Tc estimation.

What can I do for this?

There is one empirical scehme Tc=1.5*BP.

I checked this scheme for the data listed in "The properties of Gases & liquids".

Statistically, it is true. Iif you are Mathematics or Statistic teacher, you can teach like that. But if you are Chemical teacher, you can not teach like that. You should teach further chemistry.

I extract only hydrocarbon, Aromatics and Olefine compounds from dataset and plot with molecular volume. I got this result.

I can easily understand from this chart that small molecule have large Tc/BP and large molecule have small Tc/BP. If I introduce volume effect, how the Tc=1.5*BP*f(volume) scheme improve?

Almost all case, this volume correction work very well. The exception is Alcohol and Carboxylic acid. The chemist easily find out the reason. The hydrogen bonding play other role. So, I extract only alcohol compounds.

There are 2 groups in alcohol. One is mono alcohol and one is multifunctional alcohol. The chemist know the reason. the multifunctional alcohol have inner hydroge bonding and reduce the effect.

Now I have new thread of Tc estimation scheme. That is completely different from Joback method and I can apply cross check for new compounds.

I always use this cross check method when I build new estimation scheme. For Tc estimation, I build 3rd scheme withusing vapor pressure.


If I plot vapor pressure to Cox temperature, vapor pressure curve become line and critical point come on the line. So I can build QSPR scheme to estimate critical temperature from Antoine parameters.