Placement
The placement procedure
Placement under TDA Logic runs in two passes. Each ingredient is assigned a destination using four criteria; the finished formula is then checked against four loading budgets and the cross-cutting constraint of pH.
What does TDA Logic assign each ingredient to?
Every ingredient goes to one of four destinations, described on the overview: the water phase, the nanomicellar domain, the nanoliposomal (bilayer) domain or the nanocolloidal (oil-core) domain. The assignment is derived from physicochemical properties, so it is a design specification, not a measured location.
Polarity gives the starting point, solubility can confirm or override it, charge can rule an ingredient out, and molecular size is a secondary check.
Criterion 1: which governs placement, logP or logD?
logP is the octanol–water partition coefficient of the neutral species. logD, the distribution coefficient, counts every species present at a stated pH, ionised and neutral together (Leo, Hansch & Elkins 1971). For an ingredient that does not ionise the two are identical. For one that does ionise in the relevant range, logD at the finished pH is the number that governs placement.
The broad pattern is: a high logP points to the oil core; a polar head joined to a lipid tail points to the bilayer; a low logD points to the water phase or, for surface-active or solubilised species, to the nanomicellar domain.
Worked example: a weak acid whose logD falls as pH rises
For a monoprotic acid, and assuming that the neutral form is the species that partitions into octanol, the Henderson–Hasselbalch relation gives:
logD = logP − log10(1 + 10(pH − pKa))
Fraction un-ionised = 1 / (1 + 10(pH − pKa))
Benzoic acid is a convenient textbook case, with logP ≈ 1.87 and pKa ≈ 4.2. Values in the table are calculated from these two inputs and rounded to one decimal place.
| pH | pH − pKa | Un-ionised fraction | logD |
|---|---|---|---|
| 3.2 | −1 | 91 % | 1.8 |
| 4.2 | 0 | 50 % | 1.6 |
| 5.2 | +1 | 9 % | 0.8 |
| 6.2 | +2 | 1 % | −0.1 |
| 7.2 | +3 | 0.1 % | −1.1 |
The qualitative lesson is what matters. Well below the pKa, logD is close to logP. At the pKa it sits log102 ≈ 0.3 below logP. Above the pKa it drops by close to one unit for every pH unit. The same ingredient at the same percentage is a modest lipophile in an acidic formula and an anion in the water phase two pH units higher. Placement is therefore done at the finished pH, and pH drift during shelf life can move an ingredient between destinations. Ionisation also brings a counterion, which is why criterion 3 and the ionic-strength budget follow directly.
Caveats: the simple relation ignores ion-pair partitioning and assumes one pKa, and octanol is a proxy for neither a bilayer nor an oil core. For a monoprotic base the exponent becomes (pKa − pH). The table illustrates the equation; it sets no routing thresholds, and TDA Logic publishes none.
Criterion 2: when does solubility override polarity?
Partition estimates are checked against the ingredient’s actual solubility in water and in oil. Where the two disagree, solubility takes precedence.
The important case is esters and light oils with slight water solubility. Polarity sends them to the oil core, yet their molecules can still travel through the water phase from smaller particles to larger ones. This is Ostwald ripening, and its rate scales with the dispersed component’s solubility in the continuous phase (see Colloid science). Such ingredients are flagged even when their logP points clearly to the oil core. Hansen solubility parameters can serve as an additional input when judging compatibility with a domain’s lipid (Hansen 2007).
Criterion 3: how does charge at the formula pH decide compatibility?
The architecture’s particle surfaces are specified as anionic. Anionic and nonionic ingredients are, as a rule, compatible with that stabilisation. Three groups are not:
- Cationic surfactants, including quaternary ammonium conditioners, which adsorb on the anionic surface and neutralise its charge.
- Polycations, which neutralise charge and can bridge neighbouring particles.
- Multivalent metal ions such as calcium, magnesium, zinc and aluminium, which bind to anionic head groups and can bridge particles.
These are minimised or excluded whatever domain their polarity might suggest. Charge is judged at the finished pH, because an ingredient that is neutral at one pH can be charged at another. The check covers ions hidden inside supplier blends, and ingredients that change over time; a lactone, for example, hydrolyses slowly to its acid and should be counted as that acid.
Criterion 4: does molecular size matter?
Size is a secondary criterion. Small molecules distribute freely among destinations. Large polymers that stay free in the continuous phase can cause depletion flocculation, and the amount that can be tolerated falls as molecular weight rises (Asakura & Oosawa 1954). Thickeners and film formers are therefore dosed against a free-polymer budget, not chosen on rheology alone.
What budgets must the whole formula stay within?
Once every ingredient has a destination, totals are compared with the limits for each destination.
- Oil-core budget. Added oil is carried on interface that the particles already have; it brings no new emulsifier with it. The allowance for added oil therefore scales with the proportion of architecture in the finished formula.
- Bilayer budget. Lipidated ingredients compete for a finite number of anchoring sites in the phospholipid bilayer, so this budget is counted in moles. At the same weight percentage, a lipidated peptide with twice the molar mass of another occupies half as many sites.
- Ionic-strength budget. Dissolved electrolytes compress the electrical double layer, shortening the Debye length and lowering the DLVO repulsive barrier (Verwey & Overbeek 1948). Everything ionic counts: inorganic salts, salt forms of actives, humectant salts, chelators, neutralising counterions and pH adjusters. Multivalent ions weigh more than their molar concentration suggests.
- Free-polymer budget. High-molecular-weight polymer that is not adsorbed raises the risk of depletion flocculation.
- pH, the cross-cutting constraint. The charge on an anionic surface depends on pH, as do the logD of ionisable ingredients and the charge state of many others. pH therefore acts on every criterion and every budget at once.
When is a formula acceptable?
A formula passes only when all three checks succeed at once: each ingredient has been placed somewhere, every budget total sits within its limit, and the finished pH falls within the range specified for the architecture. The numeric limits are architecture-specific.
What does the formulator not do under TDA Logic?
- No required-HLB calculation.
- No emulsifier selection.
- No solubiliser added to clarify oils.
- No hot, high-shear processing to rebuild the carrier.
Any further emulsifier or solubiliser would contend with the existing interface for adsorption and could weaken stability, so the procedure leaves such materials out instead of tuning their levels. The decisions HLB is designed to support have already been taken upstream.
How are common ingredient classes routed?
| Ingredient class | Deciding criteria | Expected destination | Budget drawn on | Watch-point |
|---|---|---|---|---|
| A plant oil (triglyceride) | Polarity; solubility | Oil core | Oil-core | Very low water solubility, so little tendency to ripen |
| A light ester with slight water solubility | Solubility override | Oil core, flagged | Oil-core | Prone to Ostwald ripening; slowed when a much less soluble oil shares the core (Kabalnov & Shchukin 1992) |
| An oil-soluble vitamin such as tocopherol | Polarity | Oil core | Oil-core | Counts as added oil; sensitive to oxidation |
| A palmitoyl peptide | Polar head with lipid tail | Bilayer | Bilayer, in moles | Molar mass sets how many sites a given percentage uses; check the head group’s charge at the finished pH |
| Glycerin | Polarity | Water phase | Water-soluble load | Nonionic, so no ionic-strength cost |
| Sodium PCA | Polarity; charge | Water phase | Water-soluble load; ionic strength | A 1:1 salt; it counts towards ionic strength in proportion to its molar concentration |
| A lipophilic weak-acid active, such as salicylic acid | logD at the finished pH; charge | Shifts with pH: towards lipid destinations below the pKa, the water phase above it | Ionic strength once neutralised | pH drift relocates it; the neutralising base adds counterions |
| A nonionic surface-active ingredient included for its own function | Polarity; solubility | Nanomicellar | Micellar solubilisation capacity | Added surfactant competes with the built interface; it is not used to clear oils |
| A quaternary ammonium conditioner | Charge | None: minimised or excluded | Not applicable | Cationic; neutralises the anionic surface charge |
| A preservative blend containing a calcium or zinc salt | Charge | None: minimised or excluded (or chelated) | Not applicable; any residue counts heavily towards ionic strength | A divalent cation can bridge anionic surfaces; read the blend’s full composition |
| A chelator such as disodium EDTA | Polarity; charge | Water phase | Ionic strength | A salt in its own right, but it binds trace multivalent metals; count it rather than ignore it |
| A high-molecular-weight gum such as xanthan | Size class | Water phase, as free polymer | Free-polymer | Anionic and so compatible by charge; depletion risk rises with molecular weight |
| pH adjusters and buffers (sodium hydroxide, citric acid, a lactate buffer) | Charge | Water phase | Ionic strength | Counterions and buffer salts all count |
The case studies apply these questions, on paper, to failures in other people’s conventional formulas.
Can the placement procedure be run in software?
Yes. Formulators can apply the procedure on paper, as described above, and no software is needed. For teams that work with AI formulation assistants, NanoBase Labs, part of the lab that defined TDA Logic, has released a free API that encodes the same placement rules in machine-readable form.
According to its developer, the API takes a submitted formula and assigns each ingredient a destination. It then checks the formula against the loading budgets described on this page and returns a domain-loading verdict with suggested adjustments. The free tier covers a monthly allowance of formula checks, a loading-envelope calculator, ingredient search, a draft ingredient (INCI) list and preservation guidance. It connects over the Model Context Protocol (MCP) or REST. Its numeric thresholds are specific to one architecture and are applied inside the tool rather than published; as with any design aid, results need review by a qualified formulator and bench testing. Documentation is at api.nanobaselabs.com.
References
- Pensive Beauty® Nanoscience Labs (2026). TDA Logic: The Tri-Domain Placement Logic Succeeding 1940s HLB Logic in Nanoscale Cosmetic Formulation (Version 1.0) [Preprint]. Zenodo. doi:10.5281/zenodo.23384911
- Leo A, Hansch C, Elkins D (1971). Partition coefficients and their uses. Chem Rev 71(6):525–616. doi:10.1021/cr60274a001
- Hansen CM (2007). Hansen Solubility Parameters: A User’s Handbook, 2nd ed. CRC Press.
- Asakura S, Oosawa F (1954). On interaction between two bodies immersed in a solution of macromolecules. J Chem Phys 22:1255–1256.
- Kabalnov AS, Shchukin ED (1992). Ostwald ripening theory: applications to fluorocarbon emulsion stability. Adv Colloid Interface Sci 38:69–97.
- Verwey EJW, Overbeek JThG (1948). Theory of the Stability of Lyophobic Colloids. Elsevier.