Complex Mechanical Behavior of Thermal Interface Materials: Silicone and Polyurethane Foams

The demand for thermal interface materials (TIMs) is growing due to increasing applications in industries such as batteries and electronics. A common class of TIMs are polymer-based foams that are generally composed of either polyurethane or silicone rubber. Variants of these foams are produced by integration of additives to yield different properties and performance. Materials characterization of TIM foams can be a challenge since their microcellular structure gives rise to complex mechanical responses such as anisotropic properties, rate dependency, and spectra of relaxation behavior. To capture this behavior, a testing platform with multiple deformation and rate capabilities must be used. This note examines the complex mechanical behavior of two commercial silicone and polyurethane foams utilizing the TA Instruments™ Discovery™ Dynamic Mechanical Analyzer (DMA) 850. The TIMs foams are examined under monotonic and transient compression along with dynamic linear compression and shear profiles. The material response to these various deformation profiles is discussed in relation to the applications each foam is suited for.

Thermal interface materials (TIMs) are a class of materials that serve to enhance heat transfer between two components such as a microprocessor (heat generator) and a heat sink (heat dissipator). The global demand for these materials has seen rapid growth due to the proliferation and advancement of compact electronic devices, thermal management in electric vehicles, and technological advances in the electronics industry. The increase in demand is anticipated to continue with growth predictions from 4.13 billion (USD) in 2023 to 9.91 billion by 2032, with a compound annual growth rate (CAGR) of 10.2 % [1]. Due to this expected growth, it is necessary to identify characterization methods of TIMs for materials processing and optimization.

From a materials perspective there are four categories of TIMs: polymer-based, metal-based, carbon-based, and phase change materials [2]. Within the polymer-based systems (the focus of this note) are thermal interface pads or foams. The base material of these foams is generally silicone or polyurethane (PU) with variants produced for specific applications by addition of additives. Benefits of foams over other TIMs are conformability to various gaps and irregular volumes, efficient thermal conductivity with adequate electrical insulation, vibration damping, workability, and relatively low cost. This makes them suitable for applications such as battery packs, consumer electronics, and flexible electronics.

During use, polymer TIMs are consistently exposed to various stresses such as compression, shear, or dynamic loading profiles. For example, when processing and assembling a consumer electronic or battery pack, the foam can experience shear or be placed under compression. If stress exceeds the material limits, then failure such as tearing or non-recoverable strain can be induced. This will lead to failure or unpredictable performance of the final product. Mechanical testing provides a means of determining key foam properties and limits for optimization of the material processing and performance.

Due to their microcellular structure, these foam systems can be challenging to characterize. Depending on the microstructure, foams can exhibit complex mechanical behavior such as anisotropy, deformation rate dependent properties, and complex densification / compressive behavior [3] [4] [5]. Common tests such as isothermal linear compression tests at a fixed rate only capture a snapshot of the foam’s diverse mechanical responses. To fully capture the unique properties of foams, a testing platform must be used that can apply variable deformation profiles on the material. These deformations include monotonic, transient, and dynamic compression along with dynamic shear deformations. Coupled with rate and temperature control, these deformation profiles can help provide a complete picture of the complex behavior of the foams.

For this application note, the TA Instruments Discovery Dynamic Mechanical Analyzer (DMA) 850 was used to investigate the mechanical properties of commercial silicone and PU foams. Specifically, this work will examine the materials response to monotonic compressive, dynamic compressive, transient compressive, and dynamic shear deformations. In addition, the upper functioning temperature limit of the two materials will be explored. The versatility of the DMA 850 is highlighted as these various deformation modes are performed on one instrument with two easily interchangeable clamps along with a small sample requirement. The discussion will focus on how the determined properties dictate the specific applications the different foams are best suited for. Throughout the discussion there will be fundamental insights given into the different deformation modes and how the DMA 850 can be utilized to extract a plethora of material property information.

The TIM foams used in this work were commercially available silicone and PU foams that will be referred to as SF and PUF, respectively. Figure 1 shows the DMA 850 along with the compression and shear sandwich clamps that were used for monotonic and dynamic compression and dynamic shear, respectively. The SF and PUF samples were cut into 10×10 mm squares with thicknesses of 3.1 and 2.8 mm, respectively. The standard furnace connected to the TA Instruments Gas Cooling Accessory (GCA) was used for temperature control.

Monotonic Compression

Monotonic compression tests were performed at 25 °C with rates of 1 and 10% strain/min. TA Instruments TRIOS™ Software was used to analyze the resulting stress versus strain curves and determine the Young’s modulus, compressive strength at 25 % strain, and yield at 0.02 strain offset. The latter analysis creates a line parallel to the linear portion of the stress versus strain curve and horizontally shifts the line to intersect at 0 kPa and 0.02 strain. This method was chosen to standardize the yield stress determination between the materials.

Dynamic Compression and Shear

Strain sweeps were run under compression and shear at 1 Hz to determine the linear viscoelastic region (LVR) at 25 °C of the foams. For all deformations a strain below 0.1 % was within the LVR of the materials.

Frequency sweeps were run under compression and shear at 0.05 % strain to examine complex viscoelastic behavior at 25 °C. Temperature ramps were run under compression and shear from 20 °C to 100 °C at 3 °C/min at 1 Hz and 0.05 % strain. By convention, E is used to represent dynamic linear compression moduli and G for dynamic shear moduli.

Transient Compression

Creep experiments were performed by applying a 1 N load to the sample and monitoring the sample compliance versus time. Stress relaxation experiments were performed by applying a 25 % strain to the samples and monitoring the time dependent modulus. Both experiments were run at 25 °C.

Monotonic Compression

Figure 2 shows the monotonic compression profiles of SF and PUF at 10 % strain/min. Table 1 details the analysis of the stress versus strain curves. The Young’s modulus was determined from the slope of the initial linear portion of the respective curves. The larger modulus of SF compared to the PUF identifies the SF as a stiffer and more elastic material. The higher strength of SF is also observed in the higher yield strength at 0.02 strain offset and compressive strength at 25 % strain. This classic mechanical analysis identifies key differences between the materials, but only with a single deformation profile and rate.

Table 1. TGA Data

Sample	Young’s Modulus (kPs)	Compressive Strength at 25 % strain (kPa)	Yield at 0.02 strain offset (kPa)
SF	310	34	20
PUF	94	3.3	2

The rate dependent response of the foams was examined by applying a slower linear compression rate of 1 % strain/min in addition to the 10 %/min condition. These results are shown in Figures 3A and 3B for SF and PUF, respectively. Both curves show a rate dependence behavior where a lower Young’s modulus (Figure 3 insets) is observed along with a lower compressive strength at 25 % strain with a reduced rate. This rate dependency is characteristic of viscoelastic foams where faster rates allow less relaxation and manifest in higher stresses at lower strains.

Dynamic Compression and Shear

The above results identify how foams behave to a linear monotonic compressive deformation. In processing and application, these materials will experience more than simple linear compressive stresses. Examples of this include flexible and wearable electronics where bending, twisting, and stretching are applied to the material [6]. In automotive and aerospace there will also be a presence of thermal cycling, which will apply dynamic stresses to TIMs [7]. The foams’ frequency-dependent response to dynamic loading was evaluated by frequency sweeps within the linear viscoelastic region (LVR) of the respective foams. [8]. Figure 4 shows the frequency sweeps under dynamic compression.

The dynamic compression data show the SF and PUF have similar storage moduli (E’), but different loss moduli (E”) behavior. The PUF has nearly parallel E’ and E”, while the SF has similar E’ behavior but with the E” decreasing with decreasing frequency. Physically this translates to greater damping capacity at higher frequency compared to lower frequencies. The inset of Figure 4 shows the Tan delta (loss factor) of the SF and PUF and identifies how SF has a frequency-dependent loss factor in comparison to the nearly frequency-independent PUF.

Figure 5 shows the dynamic shear frequency sweeps of the SF and PUF. Both foams show well separated G’ and G” with a slight frequency dependency with decreasing moduli at lower frequency. As opposed to dynamic compression, the G’ for SF is noticeably larger compared to PUF. In addition, the G” is lower, which indicates SF is stronger and has greater elasticity under shear. From an application perspective, this indicates the SF can withstand greater shear or twisting deformations during processing or in application use.

Figures 4 and 5 also show how the E’ in dynamic compression is greater compared to the dynamic shear for both foams. This is an expected result for microcellular structured foams since deformation mechanisms in compression (such as bending and buckling) resist higher loads compared to sliding and angular distortion mechanisms in shear [9]. The relative strength of the material for the given deformations plays a critical role in material choice where processing and application stresses need consideration.

In addition to variable deformation modes and stresses, TIM foams are commonly used in environments with changing temperatures. Therefore, understanding the thermo-mechanical behavior of these materials within their application temperature is important. Figure 6A and 6B show the dynamic temperature ramps of the SF (red curves) and PUF (blue curves) foams under compression and shear. Both foams show no significant thermal transition within the experimental temperature range from the compressive (E) and shear (G) storage and loss moduli curves. The SF exhibits a temperature independent shear modulus throughout the entire range. The absence of transitions along with little thermal softening is advantageous for applications where adequate interface integrity is required.

Transient Compression

As previously discussed, the TIM foams can undergo transient compressive loads during processing and application use. An example of this is using the foam between components in a layered electronic assembly. The TIM’s response to this imposed deformation will impact the overall assembly’s properties and performance. Replicating or mimicking these transient compressive deformations can be performed on the DMA through either stress controlled (creep) or strain controlled (stress relaxation) experiments.

Figure 7 shows the creep behavior of the SF and PUF when placed under a 1 N load. Under this constant load the PUF is almost two orders of magnitude more compliant compared to the SF. This is the expected result as the monotonic linear compression tests identified SF as the stiffer material. Both foams exhibit a viscoelastic response where an initial elastic portion is observed followed by a viscoelastic region. Following the blended viscoelastic response, a viscous response is observed up to the experiment termination at 10 minutes. The insets in Figure 7 have re-scaled y-axes to clearly show the overall viscoelastic response.

Figure 8A and 8B show the time-dependent relaxation modulus E(t) versus time for the SF and PUF foams when transiently deformed to 25% strain. Both samples exhibit a viscoelastic response with an initial high modulus followed by stress relaxation. Polymer foams, such as the ones in this study, tend to exhibit complex time-dependent relaxation behavior. Therefore, a simple stress relaxation model such as the classic Maxwell model is not sufficient to capture the multiple relaxation time-scales [10].

To capture the complex behavior of these foams, a generalized Maxwell model can be applied that expresses the relaxation modulus as a sum of exponential terms. Modelling these systems as discrete Maxwell modes gives rise to a Prony series as follows:

Where:
E_∞ : Infinite modulus after full relaxation
E_t : Relative modulus for the i-th term
t_i : Relaxation time for the i-th term
N : Number of terms in the series

The tabulated results of the Prony series fitting are shown as insets for SF and PUF in Figure 8A and 8B, respectively. The relative contribution to stress relaxation can be assessed by the magnitude of the relative moduli and are expressed as E₁, E₂, and E₃. These are also termed the Prony coefficients. E₁ and E₂ represent the faster decay processes present in the material as seen by the corresponding decay times of t₁ and t₂. The third Prony coefficient (E₃) represents the long-term decay process and its associated time (t₃). For PUF, the initial decay is relatively fast compared to SF, as seen in the shorter time t₁ and t₂, and apparent by the steep initial modulus decrease in Figure 8B. However, the longer time scale relaxation captured by E₃ is greater for PUF compared to SF. Physically this translates to SF being a stiffer material with slower initial relaxation compared to PUF, but faster long-term relaxation.

The transient results indicate the SF is a stiffer material but has relatively faster relaxation times compared to the PUF. As opposed to this, the PUF is a more compliant material with longer-term relaxation mechanisms. From an application standpoint the SF will be ideal when a more robust interface is needed between components, whereas the PUF can be used for applications where flexibility and irregular volume filling is needed.