Thermal Analysis Labs


Using Thermal Effusivity to Investigate the Thermal Performance of PCMs and PCM Composites

Phase change materials (PCMs) are substances with a high latent heat (typically of fusion) which may be used to store a large degree of heat energy by melting and crystallizing at a certain temperature. PCMs can be organic, inorganic, eutectics, and hydroscopics (where the phase change is not a change of fusion but rather of absorption and desorption of water vapor). A key performance metric of a PCM is its ability to exchange heat with its surroundings – a metric which is often referred to as “thermal inertia” or, more commonly, “thermal effusivity.” A higher thermal effusivity allows a material to be thermally activated in a more rapid manner – and therefore more thermal load can be stored during a dynamic thermal process. In short: PCMs with higher thermal effusivity can absorb or release more thermal energy, faster.

Thermal effusivity is governed by the following equation:

e = (k p Cp)1/2

Where e is the thermal effusivity, p (rho) is density, Cp is the mass specific heat capacity at constant pressure, and k is the thermal conductivity. Thermal effusivity may be expressed equivalently in units of Ws1/2/m2K or J/s1/2m2K.


Figure 1. Thermal inertia (effusivity) of gypsum board with an embedded paraffin-based PCM. (Source: )

How thermal effusivity describes the ability of a material to exchange heat with its surroundings is a large part of why not only k is important to PCM performance, but also the volumetric heat capacity, or . Given density information as a function of temperature, thermal conductivity information as a function of temperature, and a DSC curve which provides specific heat data, it is possible to calculate the thermal effusivity of a material as a function of temperature, which Korean scientists recently did in a paper published in the Journal of Adhesion Science and Technology. Their results are seen above in Figure 1.

However, this approach may be difficult, as it is often hard to obtain accurate density and thermal conductivity data during a phase transition – which can introduce error to the process and is time-consuming as it requires collection of thermal expansion and thermal conductivity data as well as DSC data. Researchers are increasingly benefitting from the ability to directly measure the thermal effusivity instead of calculating it – and thus reduce the error introduced by assumptions of constant density or thermal conductivity.

The C-Therm TCi Thermal Conductivity Analyzer is primarily known for its ability to measure the thermal conductivity of materials – however, it also directly measures the thermal effusivity of materials. It is compliant with existing standards for the measurement of thermal effusivity via the Modified Transient Plane Source method (ASTM Standard D7984).

A sample of paraffin wax, a commonly used base for many organic phase-change materials, was obtained and its thermal effusivity was monitored as a function of temperature on cooling through the phase change. The resulting data is plotted below in Figure 2:


Figure 2. Measured thermal effusivity of paraffin as a function of temperature

At the highest point, the measured thermal effusivity is 1.49 x 103 Ws1/2/m2K. Aside from the phase transition highlighted in pink, the data plotted also exhibits a peak near 40°C and another near 22°C – it is fairly common for paraffins to exhibit crystal-crystal transitions in the latter, and the former is explainable by the melt of a minor component with a shorter chain length than the bulk of the wax. The performance of paraffin in this metric is best illustrated by comparison to the results obtained by the Korean group, whose shape-stabilized PCM exhibited a thermal effusivity at its peak of 103.19 x 103 Ws1/2/m2K – nearly two full orders of magnitude larger. As expected from the well-known thermal performance issues of pure paraffin in phase-change applications, this suggests that paraffin has difficulty exchanging heat with its surroundings, which limits its utility as a PCM.

Performance Characterization of Thermal Interface Materials: Rapid Thermal Conductivity Testing

Thermal interface materials (TIMs) are widely used to reduce thermal resistance at the interface between two materials (often called the thermal contact resistance). There are many different types of TIMs, ranging from thermal greases to thermal glues, thermal gap pads, and thermal adhesive pads. Of these, thermal greases (Figure 1) are popular because they tend to be easy-to-use, non-toxic, and non-permanent solutions to the thermal contact resistance problem.


Figure 1. A thermal grease compound being tested in the Small Volume Test Kit (SVTK)

Thermal greases are difficult for many traditional methods of thermal conductivity testing to analyze: They are highly viscous, resulting in a very slow pour rate. As a result, air can become entrapped within the material and artificially deflate its thermal conductivity.

The unique planar, one-sided and one-directional thermal conductivity measurement provided by the C-Therm TCi Thermal Conductivity Analyzer provides a useful tool for the performance verification of thermal grease compounds, as the grease may be applied directly to the sensor surface, minimizing the formation of bubbles and enabling a uniform sample distribution over the sensor. Additionally, the small sensor surface area, short test time, and the optional small volume test kit result in a very small sample volume (< 2 mL) required to obtain good data, reducing the wastage in quality-control applications and the synthetic demand in research applications.

Figure 2. Thermal Conductivity Testing of a Thermal Grease

The C-Therm TCi Thermal Conductivity Analyzer was used to test the thermal conductivity of a thermal grease compound. The observed value was referenced to the manufacturer’s specification for the grease’s thermal conductivity performance. The grease was found to test within 2% of the manufacturer’s specification on all tests. The mean of three tests of five measurements each was 0.727 W/mK. The relative precision for each of the three tests was 0.4%, 0.3%, and 0.2%, respectively, and the relative standard deviation across the three tests was 0.5%.

Characterizing the Thermal Conductivity Performance of Aerogel Samples

Aerogels are a relatively new class of ultralight, porous materials, typically derived from a gel. In an aerogel, the liquid component of the gel has been replaced by a gas (typically air). Owing to the very light nature of most aerogels, most aerogel samples have a transluscent, blueish appearance. Porosity of aerogels is generally in excess of 98% (meaning that, per unit volume, >98% of an aerogel’s volume is pore volume). Aerogels can be made of a variety of chemical compounds.

Aerogel Figure 1

Image Source: NASA/JPL-Caltech

Aerogels (above) are known for their extremely low thermal conductivity, which is often lower than that of air. In this respect, the thermal conductivity of an aerogel material is typically identified as a critical performance specification. This low thermal conductivity makes aerogel materials exciting in the field of insulation research, where engineers are continually looking to improve energy efficiency without adding excessive weight.

Three commercially-available aerogel samples were recently provided by a client seeking performance data on them in comparison to the specification sheet. The samples were analyzed with the C-Therm TCi Thermal Conductivity Analyzer using the Modified Transient Plane Source (MTPS) technique. The results are displayed below:

It can be seen that the thermal conductivity performance measured is in good agreement with the specified thermal conductivity of these commercially-available aerogel samples. Agreement with the specified value in all three cases was better than 4%.

Thermal Conductivity Enhancement of Biodegradable Thermoplastic Blends

Increasingly, work is being devoted to replacing heavy and expensive metallic heat sinks with lower cost, lighter organic-based heat sinks. One way in which to do this is to mix a polymer material with some thermally conductive additive to improve its thermal conductivity. Such a material is referred to as a thermally-conductive polymer composite (TCPC) material. The field of TCPC research is an emerging and highly competitive one – however, historically, such materials have historically possessed very high percolation thresholds – the percolation threshold being the point at which an additive in such a mixture begins to have an appreciable and scalable effect upon the thermal conductivity of the mixture, before which there is little, if any appreciable improvement in thermal conductivity upon successive additions of additive (Figure 1).

TCPC Figure 1

Figure 1. Left: Below the percolation threshold, no pathway exists for effective heat conduction. Right: Above the percolation threshold, a pathway for conduction exists

As a result of the high percolation threshold, very high loadings of additives (30 wt% or more) have been needed to achieve the desired thermal conductivity. The issue with such a high loading is that it sacrifices the mechanical properties, and sometimes the electrical properties, of the composite for the thermal conductivity, and it makes the composite denser, resulting in a heavier consumer good. Research in recent years has therefore focused on ways of reducing the required additive loading.

Scientists from the Chinese Academy of Forestry and the Chinese Academy of Sciences recently published work in the Journal of Composites Science and Technology detailing thermal conductivity improvement of a polylactic acid (PLA)/polycaprolactone (PCL) blend by addition of graphene, a type of elemental carbon one layer thick with an extremely high thermal conductivity. This work is unique, as the additive doping requirement was substantially reduced by trapping the graphene material at the interface of the polymer blend.

TCPC Figure 2

Figure 2. Thermal conductivity of PLA/GE, PCL/GE, and PCL/PLA/GE composite materials as a function of GE loading.

A key finding of their work is summarized in Figure 1. With a C-Therm TCi Thermal Conductivity Analyzer, Huang et al were able to study the effect of graphite content on the various polymer blends. The graphene loading improves the thermal conductivity of the PLA and PCL, but only marginally. However, once it becomes trapped at the interface of the polymer blend, the thermal conductivity of the material substantially improves, resulting in a four-fold improvement of the thermal conductivity of the material with merely a 0.5 volume % doping of graphene into the material. Remarkably, the percolation threshold of the PCL/PLA/GE blend (circled) was 0.11 vol%, representing the lowest percolation threshold for TCPC yet discovered.

Determining Glass Transition Temperature of PET

Polyethylene Terathalate (PET or PETE), is among the most used types of plastics in industry. It is used in drink and frozen food packaging and as a synthetic fibre under the common name “polyester.” As a result of its wide application, particularly in food applications, strict quality control is needed over batches. Measurement of glass transition temperature is one way in which quality of a batch of PET may be assessed.

Glass transition temperature (Tg) is a characteristic of some amorphous materials, including plastics. At the glass transition temperature, the material converts from a hard and brittle “glassy” state to a soft and rubbery, semi-molten state. At temperatures above this point, the plastic has a compromised ability to retain form and structure, unless it undergoes a recrystallization at a higher temperature. A literature survey for PET’s glass transition temperature shows it to be between 69°C and 85°C, depending on the grade examined.1 The C-Therm Dilatometer (DiL), which uses a horizontal Linear Variable Displacement Transducer (LVDT)-based technology compliant to ASTM E228 can be used to observe this phenomenon.


Figure 1. C-Therm DiL High Precision Dilatometer

The glass transition of a polymer is evident via dilatometry as an inflection point in the thermal expansion curve, in between two regions of linear thermal expansion – the exact temperature of the transition is then determined using the two-line method. For added convenience, consistency and confidence, an advanced software package such as CALISTO data processing software may be used to automate analysis of the Tg point, thus eliminating possible user bias.

Measurement of Glass Transition Temperature
A 50mm piece of PET was cut from a thin rod, and the end surfaces were polished to achieve a smooth contact between the sample and the pushrod. A tipped pushrod was used with a cross-sectional area of 1 mm2. The minimal force employable by the DiL was used upon the sample to minimize contact force and reduce the risk of sample deformation.

The operation of the dilatometer was conducted in compliance with known measurement standards for thermal analysis.2 When thermally analyzing thermoplastics, one must be mindful of the effect of thermal history of the sample. This may be addressed by pre-conditioning the sample at a temperature above its glass transition temperature, taking care not to exceed the dilatometric softening point or recrystallization temperature, depending on the thermoplastic in question. The heating rate should not exceed 5°C/min. This preconditioning process normalizes the thermal history of the sample, enabling repeatable data collection. The measurement may then be conducted either upon the cooling from the temperature above the glass transition temperature, or with a second heating cycle.

PET is a material which is widely known to have morphology and thermal properties which are sensitive to its thermal history. Therefore, for this work, the sample was allowed to soak for 30 minutes at this 30°C to normalize the initial condition of the measurements. The sample was then heated at a rate of 5°C/min to 130°C then cooled. Measurement was conducted on the cooling cycle. The resulting measurement profile on the cooling part was obtained and analyzed using the Calisto software. Figure 2 shows the profile obtained and the glass transition temperatures on the first test.


Figure 2. Glass Transition Temperature Determination: First run Tg=75°C

To assess repeatability of the analysis, the test was repeated upon the same sample material, using identical testing parameters and temperature profile. Figure 3 shows the data from this second test.


Figure 3. Glass Transition Temperature Determination: Second run Tg=75.7°C

The repeatability is remarkable with an RSD of 0.7%. The average of the two measurements, at 75.35°C falls well within the expected range of 69°C-80°C.

In conclusion, glass transition temperature can be measured in a repeatable manner using horizontal pushrod dilatometry, provided the thermal memory of the sample is normalized through the heating profile.

1“Crystallization Behaviour of PET Materials”, Demirel B., et al, BAU Fen Bil. Enst. Dergigi C.H., Vol 13(1), pp 26-35, 2011; Polímeros vol.23 no.3 São Carlos 2013 Epub May 28, 2013; Misumi Corporation, “Glass transition temperature of plastics,” Plastic Moulding Tutorial,; Sepe, Michael. “Know How: PBT & PET Polyester: Part 2 The Performance Factor”Plastics Technology, November 2012.;
2“Standard Test Method for Linear Expansion of Solid Materials with a Push Rod Dilatometer”, ASTM E228-11