Q&A: Which is more important irradiance or exposure?
By R.W. Stowe, UV Applications Engineering Consultant
Heraeus Noblelight America LLC
They are both important, but the relative effectiveness depends on the physical chemistry of an ink, coating, adhesive or paint as well as on the optical thickness of the UV-curable material and the properties required of the end application.
A higher flux rate, or irradiance, intitiates a higher rate of simultaneous radical generation, and consequently, more short polymer chains usually characteristic of harder, less flexible and more resistant properties. Noting that exposure* is the time-integral of irradiance, a longer duration of lower irradiance may yield the same degree of exposure, but the resulting longer chains may exhibit different physical properties, such as flexibility or lower resistance. At increased depth within an optically thick material, a higher effective irradiance (greater than a minimum threshold) can affect adhesion.
A high intensity or peak irradiance will have a beneficial effect on the depth of cure of most UV-curable materials. The effective irradiance, or photon flux rate, at any depth within the film to be cured follows a definite relationship between irradiance at the surface and the spectral absorbance of the film (at any specific wavelength), according to the Bouguer-Lambert law:
Io is the incident irradiance (flux rate) at wavelength λ. Ia is the flux rate at depth d, Aλ is absorbance at wavelength λ, and d is the depth from the surface or film thickness.
The optical thickness of a UV-curable material is a combination of the physical thickness and the opacity of the film at specific wavelengths of interest. It also may be represented by the ratio of the photon flux rate at the bottom of the film (adhesion interface) compared to that measured at the top.
A cure ladder** of a material can reveal the relative benefits of irradiance and time of exposure for a specific curable film and substrate by identifying the upper and lower limits of the two and assessing the process window of successful cure. This, of course, is essential to process and equipment design of curable systems. Figure 1 illustrates the concept of different process windows for several classes of applications. Of course, the spectral distribution of the source is a fundamental variable of UV exposure, but cure ladders can explore the response of the UV-curable material with a specific selected type of UV lamp by varying power, distance and speed to find the irradiance and exposure process limits. Power and energy ladder analyses can be conducted with wavelength distribution nearly constant.
Radiometers measure only the instantaneous value of irradiance (mW/cm² in a specific wavelength band), while integrating radiometers can calculate exposure (mJ/cm² in the same band). An electronic sample-and-hold type of electronic memory can report the maximum (or peak) irradiance observed during a dynamic pass under a lamp or lamps. Integrating radiometers will sample irradiance at an internal clock rate and will sum all the instantaneous irradiance measurements to calculate exposure.
Although peak irradiance is an important component of exposure, the irradiance profile is more significant. This is because differing regions of the irradiance profile will have different effects on cure and depth of cure. Irradiance and peak irradiance may fall into any one of these useful categories:
VERY LOW:1 to 100 mW/cm2
LOW:100 mW/cm² to 1 W/cm2
HIGH:1 W/cm² to 10 W/cm2
VERY HIGH:More than 10 W/cm2
The illustration in Figure 2 shows a comparison of different peak irradiance curves of a typical 385 nm UV-LED array (without optics) at several distances.
Most UV LEDs will have a soft irradiance profile, and the irradiance very close to the face window of the lamp has become an important primary measure of the output of the UV-LED products. Figure 3 is the characteristic irradiance profile of many UV-LED arrays.
The peak of irradiance of medium-pressure mercury UV lamps is affected by such factors as power input to the bulb, bulb diameter, lamp focus, type of reflector and distance from the lamp. The higher the peak of focus, the narrower it may be; and the time of exposure at the peak can be short, so the precision of measuring it becomes less important. The general or average irradiance may be important to curing, but most radiometers cannot measure that.
Exposure is a measure of the total photon flux delivered to the work surface, and most instruments will calculate it with an accuracy and repeatability of ±10 percent. Essentially, it is represented by the area under the irradiance profile curve. It is the time-integral of irradiance.
A measurement of UV exposure (mW/cm²) is the integration of the irradiance profile over time, but information about neither irradiance nor speed can be extracted from it. A specification of exposure alone can be misleading or insufficient in terms of material cure dynamics. Most UV-curable materials do not exhibit exposure reciprocity or linearity.***
A simple specification of exposure may not be sufficient because it does not provide enough information for the selection or design of the most effective UV exposure or process configuration. Further, often a material suppliers data sheets do not provide sufficient information. That fact, however, may be a practical necessity, owing to the fact that there is no way to know at the supply level what type of UV lamp, film thickness, substrate or production speed will be required in a users application. For this reason, the process development step of production design must include a series of test exposures to determine the optimum exposure as well as verification of the achievement of all specific physical and chemical properties of the final cured material. Accordingly, a suppliers specification of exposure can be, at least, useful to provide some guidance and approximation of optimum exposure.
*Note: Exposure is the optical term for radiant energy density at a plane. Dose is a term defined for high-energy and ionizing radiation, for example X-ray and electron beam energy. In electron beam technology, the units are Mrads or kGy. See Is there a technique to evaluate the performance of low-voltage electron beam processors? in this issue.
**See What is a Cure Ladder and How is it Used in UV Curing? UV+EB Technology, Issue 3, 2015; pp 8-9.
***See Non-Reciprocity of Exposure of UV-Curable Materials and the Implications for System Design, RadTech 2016.