floryhugginsternary 0.0.0

package to find tie-lines, binodals and spinodals in a three-component mixture with flory-huggins free energy.

samternary

floryhugginsternary aids users in predicting phase diagrams for three component mixtures of small molecules. It does this by providing the equations of chemical equilibrium (i.e. equal chemical potentials) in a form which is fairly straightforward to implement into a numerical solver (e.g. scipy.optimize.root or similar).

For example, if I wanted to determine the binodal and spinodal lines of a three component mixture with two phases when the volume fraction of component one in phase A (phi_1A in the code below) is 0.07, with flory huggins parameters chi_11 = 1, chi_22 = 1, and chi_12 = 4, I would write

from floryhugginsternary.chemeq3 import ChemEq3_2phase

from scipy.optimize import root

ce = ChemEq3_2phase(phi_1A= 0.07,chi_12=3,chi_11=1,chi_22=-1)

phi_1B,phi_2A,phi_2B = 0.42,0.07,0.42 # a (good) guess for phi_2A, phi_1B, phi_2B

x0 = ce.phis_to_x(phi_1B,phi_2A,phi_2B)

solution = scipy.optimize.root(ce.rootfind_eqns,x0,jac=ch.rootfind_jacobian)

phi_1s,phi_2s = ce.get_phi1s_phi2s(solution.x) # get the volume fractions at phase coexistence

phi_1A,phi_1B = phi_1s[0],phi_1s[1]

phi_2A,phi_2B = phi_2s[0],phi_2s[1]

which would, if a solution existed, return the volume fractions of the two different phases for both components A and B (otherwise it would just return the trivial solution of component one being equal in both phases and component two being equal in both phases).

See the examples folder for a list of examples on how to use this package. Here is an example picture of a binodal curve at chi_12 = 4, chi_11 = chi_22 = 1, with tie-lines. Also shown is the spinodal curve. This picture was computed using this package along with matplotlib and scipy.optimize.