Layer Thickness and Dose Scaling of the Required Dose (UV Curing)

What this is about

UV-curing datasheets do not give the "required dose" of an adhesive or coating as a universal constant. Instead, they specify it against a particular reference layer thickness. Adhesive manufacturers typically spec the required dose against a 100 µm or 200 µm layer. If you apply a thicker or a thinner layer than that reference, you cannot carry the datasheet dose over one-to-one.

Concrete illustration: an adhesive specified at 1000 mJ/cm² for a 100 µm layer raises an immediate question once you coat 200 µm — do you still need only 1000 mJ/cm², or more?

The physics behind it (short version)

UV passes through the still-uncured coat layer and is absorbed along the way — by the photoinitiator (intended: that is the curing reaction) and by the binder and any pigments (parasitic). The Beer-Lambert law describes this attenuation:

I(z) = I₀ × exp(-α × z)

Here α is the substrate-specific absorption coefficient and z is the depth into the layer. The bottom face of a 200 µm layer sees less UV than the bottom face of a 100 µm layer of the same coat — so you need more dose at the surface for enough to reach the bottom for full crosslinking. Light intensity falls off exponentially with depth into an absorbing medium, which is why a thicker bond line can leave the surface over-cured while the bottom stays under-cured.

Linear scaling as an approximation

A strict Beer-Lambert model needs α values per substrate and per wavelength. Where those coefficients are not available, a conservative linear approximation is a reasonable first estimate:

effectiveDose = referenceDose × (selectedThickness / referenceThickness)

Examples:

• Reference 1000 mJ/cm² at 100 µm; coat 200 µm → effectiveDose = 1000 × (200/100) = 2000 mJ/cm²
• Reference 1000 mJ/cm² at 100 µm; coat 50 µm → effectiveDose = 1000 × (50/100) = 500 mJ/cm²

Why the linear approximation is "conservative"

In the middle range of a manufacturer's specified window (often around 50–200 µm) linear scaling produces values in the same order of magnitude as a Beer-Lambert estimate. For very thick layers (beyond the manufacturer maximum) linear scaling underestimates the true required dose, because exponential absorption grows faster than a straight line — outside the recommended range you should always consult the datasheet directly.

For very thin layers (below the manufacturer minimum) linear scaling overestimates, because surface oxygen inhibition becomes a problem in its own right. Atmospheric oxygen quenches the photoinitiator triplet state and scavenges propagating free radicals, forming a poorly cured surface layer. This surface-cure penalty does not scale down one-to-one with falling dose, so thin layers behave differently than the linear model assumes.

When linear scaling is wrong

• Heavily pigmented or filled coatings (high parasitic absorption): linear scaling gives too low a dose — use the datasheet values instead.
• Depth-of-cure-critical applications (optical bonds, medical-grade joints): do not extrapolate linearly — always follow the datasheet and the manufacturer's recommendation.
• Substrates with no reference thickness on record: no scaling is applied and the spec dose is used as-is.

Manufacturer practice (what the datasheet tells you)

Fields that are worth capturing systematically from technical datasheets:

Field	Example	Meaning
referenceThicknessUm	100	Layer thickness the required dose is specified against
thicknessRangeUmMin	50	Lower bound of valid application
thicknessRangeUmMax	250	Upper bound of valid application
requiredDose	1000 mJ/cm²	Dose required at the reference thickness

The following are representative examples drawn from manufacturer technical datasheets — they illustrate the spread of reference thicknesses and ranges across product classes, and should be re-checked against the current datasheet before use:

• Glass-bonding / potting / sealing adhesive: dose specified in the low-thousands mJ/cm² range against a 100–200 µm reference, valid roughly over a 50–500 µm window, 320–410 nm.
• LED-cure adhesive (dual-wavelength profile): dose in the mid-thousands mJ/cm² range against a ~100 µm reference, tested for 365 + 405 nm dual-LED curing.
• Dome / high-build novelty coating: dose specified against a multi- millimetre reference (e.g. 5 mm), valid over a 1–10 mm range — a very different regime from thin bond lines.
• Multi-cure adhesive (UV plus heat or activator backup): dose against a ~100 µm reference, valid across a wide 50–1000 µm window.

One manufacturer's datasheet cure table is instructive: it lists a much larger increase in layer thickness against a far smaller increase in required dose — i.e. the real dose-versus-thickness relationship for that product is sub-linear, not proportional. That is consistent with Beer-Lambert exponential attenuation and confirms that a purely linear scaling rule tends to overestimate the dose needed for thick layers, erring on the safe side.

Where this is heading

The next refinement step is a full Beer-Lambert model with a substrate × wavelength α-coefficient table. That requires systematic measurement of the absorption coefficients of the most common substrates — drawing on photoinitiator-manufacturer datasheets and UV-coating literature. A further step is a depth-profile visualisation (a "dose at depth z" view for a chosen substrate and lamp spectrum), which extends the surface-geometry model with a depth axis.

Cross-references

• Lambert's Cosine Law — geometric incidence, orthogonal to the layer-thickness question
• UV System Type Taxonomy — where the surface model later extends to a depth axis