Currently, when the necessary curing conditions for a coating are to be found, the coating is applied to test panels, which are then cured at different temperatures and for different periods of time. The different panels are then immersed in water and other chemicals of interest, at different temperatures. These experiments are time consuming to say the least, as one might have to wait up to a year to get adequate results. By using DMA to investigate the glass transition state (Tg) of the coating one can, with reasonable certainty, decide the needed curing conditions for a coating to be used at a given working temperature.
In addition to the pure temperature factor, it is widely known that postcuring of epoxy paints at elevated temperatures most often will improve a films chemical resistance. This can be explained theoretically, as elevated temperatures increase the reaction rate of curing. The molecules "trapped" at low temperatures can move more freely and therefore react more easily. This will result in a "tighter" polymer matrix and a tighter polymer matrix means less diffusion through the film. Diffusion of molecules through the film is often a problem, especially with small molecules like methanol and water. A tighter net will for epoxy films often result in a harder, and less flexible, film. This "tightening" of the polymer network can be measured by calculating the crosslink density using results from DMA.
It is also important to know how low we can go on initial curing temperature. Is curing the film for two weeks at 5�C tantamount to curing for two weeks at 23�C as long as one post cures the coating at a given elevated temperature? To know this would save one a lot of time required for testing.
Dynamic Mechanical Analysis Theory
Dynamic mechanical analysis (DMA) is a method involving application of an oscillating force to a sample and analysis of the material's response to that force. At right Figure 1 shows how by applying stress to a film results in a material response (strain) and a phase lag between the applied stress and resulting strain.
Where E′ is the storage modulus, E′′ is the loss modulus and tan δ is the loss tangent. Increase in this ratio relates to a harder and (often) more brittle polymer.
The crosslink density (Mc) is usually calculated from the minimum value of storage modulus E′ (also called the rubber modulus) in the rubbery plateau. The theoretical relation between molecular weight between two cross linking points (Mc) and the tensile storage modulus (E′) can be expressed as follows:
The oscillating force applied to the sample is most commonly sinusoidal as shown here. By measuring the amplitude of the deformation (material response) curve and the phase difference between applied stress and material response (strain), quantities like modulus, damping and Tg can be measured.
The glass transition temperature (Tg) can be found from the storage modulus curve, the loss modulus curve or the tan δ curve. This is shown below in Figure 2.
This figure shows how Tg can be found from any of the curves storage modulus (~97�C), loss modulus (~98�C) or tan δ (~108�C).
As seen from Figure 2 the Tg can vary quite a bit (up to 11�C in this case) depending on which function is used to decide Tg. One should therefore always keep in mind the degree of uncertainty when it comes to deciding Tg and always decide Tg from the same function within a set of experiments. Also, one should take into account that the glass transition for a polymer blend is never a set temperature but rather a temperature distribution, where Tg is the maximum.
Tg is the glass transition temperature maximum found from the tan δ curve. E'm is the minimum storage modulus while TE'm is the temperature at minimum storage modulus. Mc,min is the crosslink density at E'm. The "curing conditions" column gives the curing temperatures with number of days given in brackets.
Preparation of the Coating: The two-component coating was applied to smooth plastic polyester films using a 250 μm applicator. The panels were cured at different temperatures in climatic air chambers or in hot water/hot oil baths.
Dynamic Mechanical Analysis: A DMA 2980 analyzer from TA Instruments was used to determinate storage modulus, loss modulus and tan δ. The Tg was determined from the peak of the tan δ curve. The samples were heated from -50�C to 200�C with a heating rate of 4�C/min. The preload force was set to 0.020 N and the amplitude to 5 μm.
Results and Discussion
Calculated results from the primary experiments are given below in Table 1. All coated plates were cured at a given temperature for 14 days and then post-cured at an elevated temperature for a variable number of days (1-5 days).
Effect of Curing Temperature on Glass Transition Temperature
As expected, the glass transition temperature (Tg) increases with increasing post cure temperature. Figure 3 shows how varying the post cure temperature affects the tan δ curve and the Tg of the paint film.
The obvious trend seen from Figure 3 is the increase in glass transition temperature with increasing post cure temperature. As mentioned earlier on, tan δ is the relationship between storage modulus and loss modulus (see equation ). As post cure temperature is increased the film becomes less flexible and the value of storage modulus increases relative to the value of loss modulus. Consequently, the absolute value of tan δ decreases with increasing post cure temperature.
This graph shows tan δ of paint films cured at 5�C for 14 days and post-cured in hot air at different temperatures for five days.
Below Figure 4 shows how varying initial cure temperature (using a fixed post-cure temperature) affects the tan δ curves and the Tg of the paint film.
This figure shows how tan δ and Tg are affected by varying the initial cure temperatures (5�C, 10�C, 23� and 40�C) using a fixed post cure temperature (60�C).
From Figure 4 one can see that as long as the sample is post cured at an elevated temperature the initial cure temperature is close to insignificant when it comes to influencing Tg. Even crosslink density changes little with the different initial cure temperatures (see Table 1). This tells us that we can cure this coating over the interval 5�C - 40�C as long as we post cure at a fixed elevated temperature. This is valuable information indeed, as seasonal changes in air temperature at application sites are substantial, and the coating can also be used at several different locations worldwide. One should note that these results are based on films that are post-cured only a few weeks after application. There is a time lag here that has to be taken into account. The desirable reaction is, of course, the curing of epoxy with the amine hardener. The competing reaction, between the amine hardener, carbon dioxide and water will cause problems over time, at least in poorly controlled humid environments. The product of this reaction is amine carbonates (amine blush). Amine blushing is described in detail by Rinker et al.  Due to this one has to make sure the coating is post-cured within a reasonable time limit (and at least within three months of application).
Effect of Curing Temperature on Storage Modulus
The general observed trend is an increase in storage modulus as the post-cure temperature is increased, as shown below in Figure 5. This is as expected since a higher cure temperature gives a higher crosslink density and, consequently, a less flexible film.
This graph shows storage modulus (E') of paint films pre-cured at 5�C for 14 days and post-cured at different temperatures for five days.
From Figure 5, looking at the interval between 0�C and 50�C, we clearly see that the film gets less flexible and more brittle with increasing post-cure temperature (the storage modulus curves are shifted upwards). There is little difference in flexibility, however, between the coating post cured at 60�C and the coating post-cured at 80�C. This tells us that we can safely increase the post-cure temperature without having to worry too much about brittleness and cracking of the film. Even though the coating films post-cured at 60�C and 80�C are less flexible than the film post-cured at 23�C, neither are what one would call a brittle coating. Especially at working temperatures above 50�C all the films can be considered quite flexible.
Glass Transition Temperature as Function of Post Cure Temperature
A plot of Tg versus post-cure temperature gives some very interesting curves as seen below in Figure 6.
This graph shows the effect of post curing temperature on the glass transition temperature, Tg. The paint film was first cured for two weeks at 5�C, 10�C, 23�C and 40�C, respectively. This was followed by a five day post-cure at 23�C, 50�C, 60�C and 80�C, respectively. Each curve represents an initial cure temperature.
As seen from Figure 6 the range between 50�C and 60�C is critical with a leap in the nearly linear Tg curve. Although hard to prove, a critical chemical change is probably the reason for this break in linearity. One hypothesis is that at temperatures above 60�C we start to see the effects of some homopolymerization between epoxy groups, causing a jump in Tg values. But then again, this is a hypothesis that needs to be studied further before any conclusion is drawn. We can, however, use what is seen here to argue that increasing post-cure temperature from 50�C to 60�C or above will make the coating more chemical resistant.
Effect of Curing Time on Glass Transition Temperature
Figure 7 shows how variation in post curing time affects Tg. It is of great value to know how long one has to post cure for the film to reach an optimal condition. For this specific coating a Tg of around 100�C is a satisfactory result.
This figure shows how Tg and tan δ are affected by varying post cure times and temperatures.
As the desired Tg for this coating is around 100�C we see from Figure 7 that post-curing for as long as five days is hardly necessary, neither at 60�C nor at 80�C. For a 60�C post-cure two days is suffcient and for an 80�C post-cure no more than one day is necessary to reach the desired Tg. The results are the same independent of the initial cure temperatures tested (5�C, 10�C, 23�C and 40�C).
The molecular crosslink density (Mc) can be calculated using equation . This method can be used to compare results within the same set relative to each other.
Looking at the results (see Table 1), one can see that the molecular crosslink density of the polymer film, M0c , decreases when the post-curing temperature is increased from 23�C to 50�C. Increasing the curing temperature above this, however, does not seem to affect M0c radically.
Glass Transition Temperature and Chemical/Corrosive Resistance
Chemical and corrosive resistance linked to Tg. The degree of blistering, discoloration and/or rust are considered. The curing condition is given together with Tg in the top row. The results recorded here are after six-months of exposure for chemical tests, 250 days for the rest (or until failure).
In addition to chemical testing the paints are also subjected to accelerated corrosion tests including hot water testing, salt spray (ASTM B 117), prohesion (ASTM G 85), continuous condensation (ISO 6270), cathodic disbondment (ASTM G8, ASTM G42) and seawater immersion. The plates tested in salt spray, prohesion and seawater are scribed to see how well the paint system can handle damage in the film.
As seen from Table 2 the 60�C post-cured coating does not differ much from the coating cured at 23�C. A few exceptions are seen with acetic acid, ethanol diamine, tetrahydrofuran, cathodic disbondment and condensation, in which the 23�C cured coating shows some blistering while the post-cured coating is performing better. It should be noted that the panels in these tests were post cured using hot air and that one might get completely different results with a hot water or hot oil cure.
Hot Air Post Curing Versus Hot Liquid Post Curing
In practice a tank coating is often post cured using a hot cargo instead of or in addition to hot air. It was therefore of interest to use DMA to study some paint cured using hot liquid instead of hot air. The results are given in Table 3.
The results given in Table 3 are very interesting, but their interpretation is not straight-forward. The Tg is about a factor of 7�C-14�C higher for hot water post cure than for hot air post cure. And the crosslink density roughly double.
Tg is the glass transition temperature maximum found from the tan δ curve. E'm is the minimum storage modulus while. TE'm is the temperature at minimum storage modulus. Mc,min is the crosslink density at E'm. The "curing conditions" column gives the curing temperatures with number of days in brackets.
One might argue that not all the water leaves the film, but some molecules remain, acting as a softening agent. This is why we see an increase in the molecular crosslink density, calculated from storage modulus (see equation ).
Of course, these are only mere hypotheses, which need further study to accept or reject. However, if one assumes these hypotheses to be valid, further study is needed to see if the painted steel is affected by the uptake of water into the paint film.
In actual application oil is often used for post curing and as seen from Table 3 this differed to some extent from post curing with hot water. The molecular crosslink density, M0c, is almost half that seen for the water immersed panels.
One possible explanation for this effect is that both water and oil work as a softening agent, but oil to a lesser degree than water due to the obvious difference in molecular size.
The storage modulus curves of the coating post cured in different media are shown below in Figure 8.
This figure shows how storage modulus are affected by varying the post cure medium.
From Figure 8 it can be seen that post curing the coating in hot water or hot oil gives a softer/less brittle film than curing the coating in hot air at the same temperature. Indeed, the storage modulus is more than double up to 50�C. This confirms the hypothesis that both water and oil is taken up to by the coating, to some extent, working as a softening agent. The danger of this, however, is that depending on what chemicals are transported, this higher flexibility might only be temporary. If one were to load a hot water cured tank with for example hydroxide slurry (which is very hygroscopic in nature) all the remaining water could possibly be drawn out of the coating leaving behind a highly stressed coating full of "gaps". This could in turn leave to cracking and, consequently, corrosion of the underlying steel structure.
A novolac epoxy-based tank coating was analyzed using dynamic mechanical analysis resulting in a greater understanding of the coating system and how it is affected by varying post curing time, temperature and medium. As expected, Tg was found to increase with post curing time and/or post curing temperature. A suffciently good Tg value (~100�C) was achieved by curing at 60�C for two days or 80�C for one day, regardless of cure medium. Tg was also found to be nearly independent of initial cure temperature (5�C - 40�C) as long as the coating was post cured at an elevated temperature.
Good correlations were found between mechanical properties of the coating and real life testing. The post-cured film was denser and its glass transition occurred at a higher temperature, which resulted in a more protective coating that could withstand higher working temperatures and more corrosive chemicals.
Research into the effect of different post curing media showed that post curing in either hot water or hot oil resulted in a more flexible coating with a higher glass transition temperature compared to the coating post cured in hot air. This heightened flexibility might however only be temporary and so this needs to be studied further.
First of all, I would like to thank Vivian Farstad for introducing me to DMA as a valuable method for deciding coating properties. Secondly, I could not have written this article had it not been for the encouragement from my manager, St�le Nordlien.
 Menard, Kevin P. Dynamic Mechanical Analysis: A practical introduction; 1st ed., CRC Press LLC, Florida 1999.
 Hill, Loren W. J. Coat. Tech., 64, 1992, 29-40.
 Rinker, E. B., Ashour, S.S. and Sandall, O.C. Ind. Eng. Chem. Res., 39, 2000, 4346-4356.