From two materials laid one on top of the other (adhesive + PVC flooring, plasterboard + paint, wood flooring + varnish), their thickness and their emission measured at 28 days — the value on the health label —, the i4o model computes the emission of every regulated pollutant from the assembly, and its evolution from 28 days to 10 years.
Indoor air quality simulation needs, for every surface, an emission factor per pollutant (µg/m²/h). Yet standardised tests (ISO 16000-9 chamber) and labels characterise each product on its own, on a glass plate — never the assembly as actually installed, never beyond 28 days, and most often at two measurement points only. These are the gaps this model closes.
"The level comes from the measurement; physics supplies the evolution over time and the interaction between layers."
A floor is an adhesive + covering system; a wall, board + paint. The assembly is not characterised by the tests, and its emission is not the sum of its parts: the top layer resists the diffusion coming from the layers beneath.
Tests run for 28 days; the target service life is several years. Extrapolating is not trivial: formaldehyde barely decays, and some adhesives generate new compounds several weeks after installation.
For roughly three materials out of four, the database holds not a curve but two measurement points — typically at 3 and 28 days. Anywhere else, the data simply does not exist: naively reading the database at 1 year returns "zero", which is not a zero emission but a missing measurement.
Correlations exist that estimate the transport coefficients (diffusion, material/air partition) from the material type and the pollutant. We combine this information with the value measured at 28 days (the label). The correlations between these data serve two purposes:
A material holds a finite reservoir of emittable compound that migrates to the surface by diffusion: emission is high at first, then decreasing. The kinetics depend on the material's permeability to the pollutant and on its thickness (the thicker it is, the longer the reservoir takes to escape).
This is the heart of the model, developed below. The level comes from the measurement, physics supplies the relative dynamics — this anchoring is what makes the model robust despite the uncertainty of the correlations.
And when there are two points, we use them for the shape too. If the database provides two measurements (3 and 28 days, say), we don't just anchor the amplitude: we fit the diffusion rate so the model reproduces the decay actually observed between those two dates. The difference is decisive. A paint that loses 95% of its emission in 25 days is a nearly exhausted reservoir: it will be practically silent after a few months. A particle board that loses only 7% over the same period is a deep reservoir, still emitting ten years on. Those two opposite fates are already written into the two measurement points — they just have to be read.
And when the product datasheet already contains an emission curve over time (a common case), we use it directly: a measurement beats a correlation. The physical model steps in when only a single point is available, and above all to handle the assembly.
A PVC floor laid over an emitting adhesive behaves, at first, like a barrier: at 28 days the adhesive's contribution is near zero and the assembly emits like the PVC alone. One might conclude the adhesive is neutralised.
That would be a mistake. The top layer adds a resistance to diffusion: it delays and attenuates the flux coming from below, but does not cancel it. Over time, the adhesive's compounds make their way through the PVC and re-emerge — this is breakthrough, well documented for PVC floors (plasticiser migration).
| Age | Share of emission coming from the adhesive |
|---|---|
| 28 days | ~0% (held back by the vinyl) |
| 6 months | 6% |
| 1 year | 24% |
| 5–10 years | ~46% |
Consequence: an assembly cannot be judged on its 28-day value alone. The ranking of solutions can reverse over time: a layer "masked" at the start can become the dominant source within a few years. The breakthrough delay is driven by the thickness and density of the covering (it scales as L²) — for a 2 mm PVC, a few days to a few weeks, consistent with measurements.
In wood-based panels (MDF, plywood), some adhesives and plasters, formaldehyde is not a reservoir that depletes: it is continuously regenerated by hydrolysis of the resins (urea- and melamine-formaldehyde) under the effect of humidity. Its emission is therefore quasi-steady-state and persists for years. A "finite reservoir" model would give a wrong result here (extinction within months). Formaldehyde is therefore treated as a permanent source that the covering attenuates at steady state without ever extinguishing. On MDF under vinyl, the model gives an emission that is stable over 10 years, reduced to a few percent by the vinyl.
Some adhesives and PVC floors generate new compounds after installation (2-ethylhexanol, acetic acid, aldehydes…) through a slow reaction — typically the alkaline hydrolysis of plasticisers in contact with the substrate's moisture. These compounds are absent initially, appear after a few weeks, pass through a maximum between 1 and 4 months, then decline over several years. The model reproduces this kinetics (delayed onset → peak → decay) — otherwise the database would drop the compound to zero right after 28 days, which is incorrect.
| Age | Emission (µg/m²/h) |
|---|---|
| 28 days | 3.0 |
| 4 months | 4.7 (peak) |
| 1 year | 4.2 |
| 10 years | 0.7 |
Wood flooring and its adhesive go down together. Plasterboard, on the other hand, gets painted weeks later. This is no detail: a bare board sheds most of its surface stock within hours. By the time the paint arrives a month later, there is almost nothing left to hold back.
The model therefore takes an installation date per layer and chains two computations: the board first ages bare, and the paint starts on the board's genuinely depleted profile — not on a fictitious substrate still full.
| Painted at | 28 days | 1 year | 10 years |
|---|---|---|---|
| D0 (straight away) | 111 | 18.5 | 5.6 |
| D30 | 38 | 15.4 | 5.5 |
| never | 38 | 16.9 | 5.5 |
Painting straight away triples the emission at 28 days: you seal a board that is still full, and add the paint on top. Painting a month later lets the board purge itself first.
At 10 years, though, the gap is gone. The schedule moves emissions in time without changing the reservoir. In other words: it is a first-order lever for air quality at handover — hence for regulatory measurements and flush-out — and it has no effect on the building's life.
⚠️ One honest caveat: in the 28 days following a layer's installation, the model says nothing. It is anchored on 28-day tests; below that it would extrapolate the off-gassing of fresh paint that nobody has measured. That window is displayed as the "construction phase", not as a value.
Input: two materials from the database, their thicknesses, their installation date, the target age. Output: the emission of every regulated pollutant (toluene, formaldehyde, benzene…), in the format expected by the i4o solver.
"Floor = adhesive (0.5 mm) + vinyl flooring (2 mm), laid together, emission at 1 year."
The model was checked against independent measurements, notably a reference study on complete floor structures (concrete + adhesive + covering), Wilke et al. (2002), and a calibration set on plasterboard (Bhoonah et al., 2023).
"Complete structures with PVC/linoleum emit like the covering alone": the model gives ~0% breakthrough at 28 days.
An adhesive compound passes through the 2 mm PVC from ~3 weeks: the model predicts the same time scale.
The measured "onset → peak → decay" kinetics match the model; the generation rates were calibrated on these measurements.
The complete structure emits less than the sum of its parts (absorption by the concrete), consistent with the model.
The model works at fixed conditions (23 °C, 50% RH): neither temperature nor humidity is accounted for yet, although formaldehyde is sensitive to them — the first planned improvement. Compounds that appear only after 28 days (some acids, ~7 weeks) escape the test as they do the database: this is a limitation of the test data, not of the model. Symmetrically, the model does not answer during the 28 days following an installation (the "construction phase"): here again it is the test window that limits it. Finally, in the very long term (> 1 year) on classic pollutants, the model is conservative (it slightly underestimates the tail at 10 years).
Two acknowledged approximations, finally: classification by pollutant — the same compound can be primary or secondary depending on the material, and the model decides per pollutant —, and unmodelled reactive sinks: acetic acid is in reality neutralised by alkaline concrete, so the model would overestimate it in a complete structure with a screed.
None of these limitations touches the structure of the model: they are extensions of data and of the validity range.
The level comes from the 28-day measurement; physics supplies the evolution over time and the interaction between layers.
A covering layer delays and attenuates, it does not block: an assembly cannot be judged at 28 days — the ranking can reverse within a few years.
Formaldehyde is a regenerated source, quasi-steady-state, not a reservoir that depletes.
Adhesives can generate secondary compounds after installation, with a delayed peak at 1 to 4 months.
The installation schedule moves emissions without changing the reservoir: decisive at handover, irrelevant at 10 years.
The model is validated against independent measurements and integrated into the existing simulation tool.
Describe a floor or a wall by its two layers and their thicknesses — i4o returns the emission of every regulated pollutant, from 28 days to 10 years. No credit card required.
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