# Evidence: combinatorial entropy of mixing

Parent: entropy of mixing · class: thermodynamics · names merged here: combinatorial entropy of mixing

2 papers measured or used it, 0 only mentioned it (of 207 kept papers). Papers in year order; each section heading ends with the paper's category / subcategory. Generated by tools/build_evidence.py from registry/concepts.csv and the cards; do not edit.

## 2009 Marsac — Estimation of Drug–Polymer Miscibility and Solubility in Amorphous Solid Dispersions Using Experimentally Determined Interaction Parameters · Solid state stability / Miscibility and drug-polymer interactions

[2009-marsac-drug-polymer-miscibility-solubility-asd-interaction-parameters](../../../cards/2009-marsac-drug-polymer-miscibility-solubility-asd-interaction-parameters/paper.html) · Solid state stability / Miscibility and drug-polymer interactions · used · as: combinatorial entropy of mixing

| id | kind | content | locator |
|---|---|---|---|
| E8 | equation | Flory–Huggins scaling of an activity coefficient from a liquid analogue to the polymer: ln γ_drug^PVP = (MV_drug/MV_lattice)[(1/m_drug) ln(Φ_drug/x_drug) + (1/m_drug − 1/m_PVP)Φ_PVP] + ln γ_drug^EP | p.143 |
| E10 | equation | Flory–Huggins free energy of mixing: ΔG/RT = (Φ_drug/m_drug) ln Φ_drug + (Φ_polymer/m_polymer) ln Φ_polymer + χΦ_drug Φ_polymer | p.146 |
| C24 | claim, mechanism, authors: asserted ("easily rationalized") | Predicted solubility falls drastically from EP to PVP K12 and then only slightly with higher PVP molecular weight (indomethacin 0.396, 0.144, 0.134, about the same for K90); this is easily rationalized because (1/m_drug − 1/m_polymer) quickly approaches 1/m_drug as m_polymer grows [rests on: R9] | p.145 |
| C26 | claim, generalisation, authors: asserted | Because API and polymer molecular weights fall in fixed ranges (R13), the entropy contribution to drug–polymer mixing is relatively fixed and favourable, any pair can tolerate a certain maximum unfavourable enthalpy of mixing, and predicting miscibility therefore requires the magnitude of χ [rests on: R13; cited: ref 39] | p.146, p.148 |
| C31 | claim, generalisation, authors: asserted ("illustrate") | The free-energy simulations illustrate that differences between compounds come from the magnitude of χ rather than from the entropy term, which (if purely combinatorial) is virtually constant across systems; for immiscible systems the enthalpy of mixing cannot be accessed and the entropy goes to zero [rests on: R10] | p.147 |

## 2012 Eerdenbrugh — Molecular Weight Effects on the Miscibility Behavior of Dextran and Maltodextrin with Poly(vinylpyrrolidone) · Solid state stability / Miscibility and drug-polymer interactions

[2012-van-eerdenbrugh-dextran-maltodextrin-pvp-molecular-weight-miscibility](../../../cards/2012-van-eerdenbrugh-dextran-maltodextrin-pvp-molecular-weight-miscibility/paper.html) · Solid state stability / Miscibility and drug-polymer interactions · measured · as: combinatorial entropy of mixing

| id | kind | content | locator |
|---|---|---|---|
| R15 | record, simulated (E5, P6) | entropic part of the free energy of mixing per lattice site (plotted as 10^23 ΔGmix in J per lattice site) versus DEX weight fraction; curve minima — 20 DEX-PVP combinations, 25 °C, no enthalpic term (P6) — sub-table below; text: for DEX450-PVP90 the entropic contribution becomes virtually zero | Fig. 7, p.2763; text p.2763-2764 |
| E5 | equation | Flory-Huggins combinatorial entropy of mixing per lattice site: −TΔS_mix = kT[(φ1/N1) ln φ1 + (φ2/N2) ln φ2] | p.2762-2763 |
| C34 | claim, conclusion, authors: "in line with" | DEX1 systems have similar entropic free energies of mixing for all PVP grades, more negative than for the other DEX grades owing to the low DEX MW, in line with their complete miscibility and extensive hydrogen bonding [rests on: R15, R13, R14] | p.2763 |
| C35 | claim, conclusion, authors: "in agreement with"; "in line with" | DEX6 systems give less negative entropic terms and larger differences between PVP12 and the higher grades, in agreement with complete miscibility of DEX6-PVP12 and a gap for higher grades; the trend extends to DEX40 and DEX450, in line with the higher miscibility and hydrogen bonding of PVP12; for DEX450-PVP90 the entropic contribution becomes virtually zero [rests on: R15, R13, R14] | p.2763-2764 |
| C39 | claim, mechanism, authors: conclusions: "it was surmised"; abstract: "was observed"; "thought to accompany" | From the mixing thermodynamics the authors surmise that the mixing enthalpy is positive and that the entropy of mixing becomes rapidly less favourable with increasing MW and cannot offset it; abstract: the combinatorial mixing entropy "was observed to decrease" with MW, giving a reduced counterbalance to the unfavourable enthalpy "thought to accompany" this polymer pair, and the thermodynamics "supported these findings" [rests on: R15, C32, C36] | p.2754, p.2764 |