💡 In This Article
- What physical-property data TMA provides for epoxy development
- The physical relationship between CTE mismatch, warpage, and delamination in bonded dissimilar materials
- How the crosslinked structure of epoxy differs from thermoplastics and affects TMA behavior, including α₁ and α₂
- How TMA can be used to simulate production-like thermal conditions
In the previous article, How Do You Read a DSC Curve? – Why Is DSC Used to Determine Tg? I explained how DSC identifies Tg through changes in heat flow and heat capacity. So what does TMA, or Thermomechanical Analysis, actually measure?
The name might suggest an instrument that measures temperature and mechanical properties at once, but from an epoxy developer’s perspective, the real question is much simpler: how much will this material expand or contract when temperature changes? That’s essentially what TMA tells us.
What Does TMA Measure?
TMA measures dimensional changes in a specimen as temperature changes under a small applied force. In practical terms, it lets us see how much the material expands, when it begins to soften, and how its dimensional behavior shifts around Tg.
If DSC tells us how the material responds to heat in terms of heat flow, TMA tells us how the material actually changes in dimension as temperature changes — a difference that matters because dimensional stability can become critical when an adhesive is used alongside other materials.
Why Do We Measure Dimensional Change?
Most materials expand when heated — metals, polymers, and ceramics all do this, but not by the same amount. Take a simple example: an aluminum component bonded with an epoxy adhesive. As temperature rises, aluminum and epoxy expand at different rates, and because they’re bonded together, neither material can deform freely according to its own thermal expansion.
The result can be warpage or curling of the bonded structure, and if the temperature cycles repeatedly, the resulting thermal stresses can build up within the adhesive layer and at the interfaces — eventually contributing to delamination, cracking, interfacial failure, or other reliability problems. An adhesive developer can’t evaluate a formulation on strength alone; how the material behaves dimensionally under temperature change can matter just as much.
Polymer Expansion Changes Around Tg
Below Tg, molecular motion in a polymer network is fairly restricted, so thermal expansion stays moderate. Once temperature approaches and passes through Tg, segmental mobility becomes much more active, and the rate of thermal expansion can increase noticeably — often showing up on a TMA curve as a change in slope around Tg.
Put simply: on DSC, a change in the heat-flow baseline can indicate Tg; on TMA, a change in the rate of dimensional expansion can indicate it. The two techniques evaluate the same general transition, but they’re observing different physical manifestations of it — one reason the Tg reported by different analytical techniques doesn’t necessarily have to match exactly.
CTE: One of the Most Important Numbers in TMA
Beyond “what is the Tg?”, epoxy developers often need to know the CTE — the coefficient of thermal expansion, which describes how much a material’s dimensions change as temperature changes. For a material that expands roughly linearly over a given temperature range, the coefficient of linear thermal expansion can be expressed as:
α = ΔL / L0 ΔT
where (L0) is the original length, ΔL is the dimensional change, and ΔT is the temperature change. For polymers, though, CTE is often different below and above Tg.
Why Does Epoxy Show α₁ and α₂?
One important characteristic of a cured epoxy is its crosslinked structure. A thermoplastic can soften significantly above Tg and, depending on its chemistry, eventually undergo substantial viscous flow or melting — which makes it hard to define a stable high-temperature thermal-expansion region. A cured epoxy behaves differently: because its chains are tied together in a three-dimensional crosslinked network, it holds its overall shape much more effectively at elevated temperatures, which makes it possible to distinguish thermal-expansion behavior in the glassy and rubbery regions. These are commonly labeled α₁ (CTE below Tg, in the glassy state) and α₂ (CTE above Tg, in the rubbery state).
The gap between α₁ and α₂ tracks the change in molecular mobility across Tg. Below Tg, segmental motion stays fairly restricted; above Tg, micro-Brownian motion of polymer segments becomes much more active, increasing available free volume and producing a substantially higher expansion rate. As a result, α₂ often runs several times larger than α₁, though the actual ratio depends heavily on resin chemistry, crosslink density, filler content, and measurement conditions.
This distinction matters especially when developing adhesives for semiconductor packages, electronic components, or other structures exposed to repeated or elevated temperatures — it’s not enough to look only at the CTE around room temperature, since dimensional behavior in the high-temperature α₂ region can have a major influence on thermal stress during processing and operation.
Look at the Curve, Not Just Tg or CTE
As with DSC, it’s worth looking past the numerical Tg or CTE value alone. When reviewing a TMA result, I’d also check how much the slope changes around Tg, how different α₁ and α₂ are, whether the expansion behavior differs from the previous formulation, whether any unexpected dimensional change shows up, and whether the curve stays smooth and consistent across the temperature range.
In development work, comparing multiple curves is often far more informative than looking at a single result — after changing the formulation, filler loading, cure condition, or aging condition, overlaying the new TMA curve with the previous one can reveal changes that a single reported CTE value would miss. That’s why I found it more useful to treat TMA not simply as an instrument that measures length, but as a tool for comparing how a material responds to temperature.
[Typical TMA Evaluation Result]
Important Considerations When Running TMA
Several factors can affect TMA results. One is the static force applied to the specimen — since TMA applies a small mechanical load, the measured dimensional behavior can depend on that applied force, especially as the material approaches or passes through a softening region. Heating rate matters too: too fast a rate can cause thermal lag, where specimen temperature differs from the programmed temperature, shifting the apparent transition temperature and affecting the measured expansion behavior.
The epoxy’s cure state is another important factor. If the epoxy isn’t fully cured, additional post-curing can occur during the TMA heating scan, and post-curing normally comes with chemical shrinkage. That creates a situation where two opposing effects happen at once — thermal expansion increasing specimen length while post-curing decreases it — and when they overlap, the TMA curve can show unexpected or seemingly abnormal behavior.
So before interpreting a TMA curve, it’s worth understanding the specimen’s degree of cure, cure temperature and time, thermal history, filler content, and measurement conditions. A strange TMA curve isn’t necessarily an instrument problem — sometimes it’s simply showing more than one physical phenomenon happening at the same time.
A Development Note: Using TMA to Simulate Real Process Conditions
TMA usually gets introduced as a tool for measuring CTE and Tg, but in actual development work I also found it useful to adjust the measurement conditions to approximate the thermal environment of a real manufacturing process. Suppose an adhesive is used in a customer’s process where the material experiences a specific temperature profile and dimensional stability is a real concern — rather than measuring only the standard CTE and Tg, we can apply a temperature profile that resembles the actual process as closely as practical and watch how the material responds.
That can surface information a single CTE value can’t — does the material suddenly begin to move at a particular temperature? Does unexpected deformation occur during the process? A TMA experiment obviously doesn’t reproduce an actual production process perfectly, but it can give an early indication of how the material might respond to a particular thermal history and help guide formulation and process-development decisions. In some cases, that practical insight is worth more than another CTE number — which is one reason I consider TMA a particularly useful development tool.
[TMA Evaluation Using a Process-Like Temperature Profile]
Sometimes Material Compatibility Matters More Than the Lowest CTE
Engineers in the field often use a word that isn’t exactly a scientific term: “compatibility.” A low CTE isn’t automatically better — what matters is how well the adhesive’s thermal expansion behavior matches the materials around it. If an adhesive’s CTE is much higher than that of a metal or glass substrate, the expansion mismatch can become significant. On the other hand, simply minimizing the adhesive’s CTE as much as possible doesn’t solve every problem either — the whole bonded system needs to be considered.
A typical neat epoxy resin runs roughly 50–80 ppm/°C depending on resin chemistry and cured network, considerably higher than many common substrates — silicon at around 2.5 ppm/°C, copper at around 16.5 ppm/°C, and FR-4 at roughly 14–17 ppm/°C. These figures are representative rather than universal constants, since actual CTE depends on material composition and measurement conditions.
This large mismatch is one reason fillers like silica are so widely used in epoxy formulations — as filler loading increases, the overall formulation’s CTE can drop significantly. But there’s a trade-off, as always: too much filler can raise viscosity, hurt processability, make dispensing or coating harder, reduce interfacial wetting, and ultimately affect adhesion. Formulating for CTE, in other words, was never simply about minimizing the number — the developer has to balance thermal expansion, processability, wetting, mechanical properties, and adhesion together.
TMA can therefore be used not just to measure CTE, but as one of the tools for finding an appropriate filler loading and checking whether the resulting formulation behaves as expected. Changes in the TMA curve can also offer useful clues when comparing formulations with different filler contents or dispersion conditions.
TMA Is About More Than One Number
DSC shows us how heat flow changes. TMA shows us how dimensions change. Both can inform Tg, but from different physical perspectives — and in practical epoxy development, the most useful information is often not the single number an instrument reports, but the shape of the curve, the change from one formulation to another, and the physical reason behind that change.
Once you start looking at TMA this way, CTE and Tg become more than spec values — they become clues that help explain how an adhesive will behave once it’s bonded to another material and exposed to a real thermal environment.
So the next question is what DMA shows. DMA also evaluates Tg-related behavior, but why do developers pay so much attention to storage modulus and tan δ? In the next article, Reading a DMA Curve ①: Why Do Researchers Rely So Heavily on DMA?, I’ll look at what these parameters actually tell us and how an epoxy developer can interpret a DMA curve.
