Phase Diagram

This is an interface to visualize the variation of the Gibbs Energy not only against the volume fraction, but also against the temperature.

Theory

The FH interaction parameter χ can be calculated based on differences in Hildebrand solubility parameters δ, which provides a straightforward approach for predicting miscibility. Here, χ is calculated based on the Hildebrand solubility parameters of pure substances as ^[1]

\[ \chi = {V_m \over RT}(\delta_1-\delta_2)^2 \tag{1} \]

where \(V_m\) is the molar volume of the lattice segment in FH theory, approximated here as the molar volume of each chain unit, and δ is the Hildebrand Solubility parameter which is defined as:

\[ \delta = \sqrt{CED} = \sqrt{\Delta H_{vap}-RT \over V_m} \tag{2} \]

where \(\Delta H_{vap}\) is the heat of vaporization or enthalpy of vaporization.

Based on the lattice model, Flory-Huggins (FH) theory^[2,3] describes the mixing behavior of binary systems through a combination of enthalpic and entropic contributions.^[4] This approach allows for straightforward calculations of the Gibbs free energy of mixing^[5,6]

\[ \Delta G_{mix} = RT \Big[ {\phi_1 \over x_1}\ln \phi_1 + {\phi_2 \over x_2}\ln \phi_2 + \phi_1 \phi_2 \chi \Big] \tag{3} \]

where \(R\) is the gas constant, \(T\) denotes the temperature, \(\phi_1\) and \(\phi_2\) are the volume fractions of compound 1 and compound 2 respectively, \(x\) represents the degree of polymerization, and \(\chi\) is the FH interaction parameter.

References

1. Erlebach A, Muljaew I, Chi M, Bückmann C, Weber C, Schubert US, Sierka M. Adv Theory Simul. 2020;3:2000001. https://doi.org/10.1002/adts.202000001
2. Flory PJ. J Chem Phys. 1942;10(1):51-61. https://doi.org/10.1063/1.1723621
3. Huggins ML. J Am Chem Soc. 1942;64(7):1712-1719. https://doi.org/10.1021/ja01259a068
4. Huynh L, Grant J, Leroux JC, Delmas P, Allen C. Pharm Res. 2008;25(1):147-157. https://doi.org/10.1007/s11095-007-9412-3
5. Rubinstein M, Colby RH. Polymer physics. Oxford Academic; 2003:137-145. https://doi.org/10.1093/oso/9780198520597.001.0001
6. Hu W. Polymer physics: a molecular approach. Springer; 2014:150-156. https://doi.org/10.1007/978-3-7091-0670-9

Compounds

You can search the compounds you want to mix by clicking on the field and selecting from the dropdown list.

You can search the compounds you want to mix by clicking on the field and selecting from the dropdown list.

You can also select the compounds using SMILES, either by typing the SMILES into the field or by using the Ketcher instance to draw the molecule. by clicking the aromatic cicle icon.

From Ketcher, you can use the buttons Get SMILES or Predict, the first of which gets the SMILES from the drawn molecule and pastes it into the form field, while the second one makes the prediction if the other compound is selected.

Degree of Polymerization

The default is 1 for small molecules and drugs. For polymers, you need to specify the degree of polymerization.

Temperature

You can specify the temperature range in Kelvin. The default values are from 273 to 373K.

Clear

You can click on the Clear button to clear all the content.

Run

Click on the Run button to calculate with the entered compounds and the conditions.

Example

Enter 4,4-dimethyl-2-pentanol and Acetic acid as the compounds, leaving the DOPs as 1. Make the temperature range 50-500K, and click on the Run button: