Miscibility¶

This is an interface to calculate the miscibility of two compounds based on the Flory-Huggins theory. You will get the Flory-Huggins interaction parameter (χ) and the Gibbs free energy diagram of the mixture.

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¶

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
Flory PJ. J Chem Phys. 1942;10(1):51-61. https://doi.org/10.1063/1.1723621
Huggins ML. J Am Chem Soc. 1942;64(7):1712-1719. https://doi.org/10.1021/ja01259a068
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
Rubinstein M, Colby RH. Polymer physics. Oxford Academic; 2003:137-145. https://doi.org/10.1093/oso/9780198520597.001.0001
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 to select the compound from the dropdown list.

Degree of Polymerization¶

Default is 1 for small molecules and drugs (field will become invisible). For polymers, you need to specify the degree of polymerization.

Molar Fraction¶

You need to specify the molar fraction of the compounds. The sum of the molar fraction should be 1. When you type in the molar fraction, the system will automatically calculate the molar fraction of the other compound.

Note

Depending on the browser's locale, the decimal separator can be either a dot or a comma. The system will consider comma as a decimal separator. That means, if you type 0,5 in the molar fraction field, the system will consider it as 0.5. This applies to all the input fields.

Temperature¶

You can specify the temperature in Kelvin. The default value is 298.15 K.

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 P(Val-alt-G)(polymer) and BRP201 (drug) as the compounds, and set the degree of polymerization for P(Val-old-G) as 93. Set molar fraction of P(Val-alt-G) as 0.83, and the temperature is 298.15 K. Click on the Run button.: