The temperature profile for the melting and solidification (crystallization) of sugar alcohols and their thermophysical properties have been evaluated based on the temperature-history (T-history) method. Although conventional calorimetric methods using differential scanning calorimetry (DSC) and differential thermal analyses (DTA) are available, they are complex and expensive and often the samples are too small for the supercooled PCMs to even demonstrate its supercooling properties as shown in bulk samples. In addition, the limitation of the test in terms of visual observation also creates additional barriers to the investigation (Shao et al. 2018). The T-history was investigated by recording the temperature profile of the samples during heating and cooling with a reference sample with known heat capacity following the work of (Sandnes and Rekstad 2006). In the setup as presented in Fig. 1a test tube at 3 cm diameter and 2 cm height of sample has been used. It is worth noting that the temperature sensors were fully immersed in the sample and hence minimizing temperature gradients along the axial direction within the sample. During the testing, the temperatures were measured and logged every 5 s.

The process of seeding is one of the most fundamental methodologies for instigating nucleation in supercooled substances. This process involves the introduction of a stable solid crystal congruent with the material, which serves to expedite the crystallization of the adjacent liquid phase. The resultant structural transformation enhances the stability of the system and facilitates the liberation of latent heat. Due to its reproducibility and efficacy in heat dissipation, seeding has been the subject of extensive empirical investigations. However, a notable challenge associated with seeding is maintaining the persistent availability of solid seed crystals during the melting of the predominant phase change material (PCM). Moreover, the mechanism of 'seeding' introduction itself presents opportunities for various innovations and investigations. For instance, questions arise about whether seeding should be introduced onto the surface of supercooled phase change materials (PCMs), injected into their core, or released concurrently with bubbles. In the current study, as illustrated in Figure 2, seeding was effectively achieved by simply introducing sugar alcohol crystals by injecting them into the core of the PCMs.

The basic process behind nucleation induction through localized cooling is based on starting the nucleation. This start happens when the material's temperature is lowered to its crystallization point, thus creating nucleation sites. Cooling sodium acetate trihydrate (SAT) in its liquid state down to its crystallization temperature can lead to heterogeneous nucleation (Englmair et al. 2018a). Therefore, it is understood that localized cooling effectively initiates nucleation when the local temperature reaches the crystallization point. Studies on the effect of localized cooling on supercooled phase change materials (PCMs) have found that local cooling methods, like carbon dioxide evaporation and Peltier modules, are effective in thermally triggering and managing the crystallization process on SAT. As shown in Figure 3, this study uses the TEC Peltier module to provide localized cooling for selected sugar alcohol PCMs to assess its capability in triggering the sample. In this investigation, as depicted in Figure 3, a Peltier cooler was utilized to achieve low temperature to initiate crystallisation in conjunction with a heat sink. Although the Peltier cooler is capable of reaching subzero temperatures, the thermal gain from the surrounding environment and its low capacity limited the heat sink tip to a minimum temperature of approximately 5 °C. In comparison, previous research as in (Englmair et al. 2018a), achieved average temperature as low as -31 °C when triggered by the Peltier cooler at high capacity. As a result, crystallisation was observed in their study, highlighting the limitation of the current study.

Meanwhile, for electrical mechanism, among the researchers who investigate the triggering mechanism are (Dong et al. 2024) and (Chen et al. 2023) who applied low-voltage fields (1.0–1.5 V) to crystallize supercooled SAT composites. Dong et al. demonstrated sub-second triggering (0.5 s) with dendritic growth observed, while Chen et al. achieved stable control over 100 cycles using structured electrodes. Despite these advances, surface degradation and electrode oxidation over time present challenges to durability. Nevertheless, as illustrated in Figure 4, we investigated its potential as a crystallisation mechanism by conducting tests using a pair of cylindrical copper electrodes with a 1 mm diameter under 4.5 V low voltage supply.

Mechanical agitation in crystallization is a triggering method in which physical disturbance such as stirring, vibration, or bubble injection is applied to a supercooled phase change material to promote nucleation. In this approach, the movement of the liquid and introduction of bubbles or solid seeds create local fluctuations in temperature and structure, breaking the metastable state and providing active sites where crystals can start to form. This enhances the reliability of crystallization, reduces the degree of supercooling, and shortens the time required for the material to solidify. In some systems, mechanical agitation is combined with seeding particles or additives (e.g. nanoparticles) to further stabilise nucleation, although this can introduce practical challenges related to flow control, dispersion, and system sealing in larger-scale applications (Jarimi et al. 2025). In this study, a simple manual stirring procedure was implemented, consisting of continuous agitation for 1 minute for each sample. However, due to the viscosity of the sample at 30 °C, the effective stirring rate for the lower-temperature phase change material (PCM) was reduced by approximately 25%.

A review of various triggering methods reported in the literature revealed that, at low temperatures, the crystallization kinetics of the sample are significantly hindered. We therefore propose combining these triggering approaches with a cold-crystallisation method. Cold crystallization denotes an exothermic crystallization process that takes place upon reheating at temperatures below the melting point, allowing the controlled release of stored latent heat from a supercooled PCM. In long-term latent heat storage schemes, the PCM is first charged by melting, then cooled to form a supercooled state for storage, and the stored energy is later extracted by inducing crystallization. A reheating-based thermal triggering strategy (cold-crystallization upon heating) has been shown for supercooled sugar alcohol systems, where crystallization is deliberately activated during the reheating phase instead of during the cooling and storage stage (Puupponen & Seppälä, 2018; Turunen et al., 2023; Yazdani et al., 2020). The cold-crystallisation technique has demonstrated the operational feasibility of thermal energy storage as studied in (Turunen et al. 2023). This level of efficiency is achieved by exploiting the latent heat associated with the phase transition of melting for extended storage durations, and the sensible heat resulting from supercooling for shorter storage periods. The prototype facilitated the determination of a previously unidentified critical cooling rate, above which premature crystallization is inhibited during supercooling, notwithstanding the inherent unpredictability of supercooling and crystallization phenomena (Turunen et al. 2023).

The cold-crystallization process, as illustrated in Figure 5, comprises several steps. Initially, the samples undergo a melting process in an oil bath maintained at 130 °C. Upon complete melting, the samples are subjected to a controlled ambient temperature of 20 °C and subsequently cooled to 30 °C (step 2). At this cooled state, the samples are in a supercooled state, below their glass transition temperature. The samples were then momentarily pre-heated at the specified rate to the cold-crystallisation temperature (step 3), after which seeding, TEC localised cooling, electrode triggering, or mechanical agitation was introduced to initiate crystallisation. TEC heat sink, Electrode and mechanical agitation was introduced to initiate crystallisation. The momentary heating enhances molecular mobility due to the increased kinetic energy. This kinetic enhancement contributes to the formation of crystal nuclei, a process requiring energy. As crystallization progresses, exothermic heat release reaches a peak, as illustrated in the temperature curve in Figure 5.

Subsequently, the samples are exposed to an ambient temperature of 20 °C (step 4). During this phase, the sample temperature rises to reach the peak temperature, and even though crystallization is underway, the rate of heat release diminishes, leading the system to a quasi-stable state. As crystallization nears completion and equilibrium is approached, heat release continues to decrease, resulting in a temperature decline. It is important to note that for samples with a high potential for self-crystallization, the controlled progression of steps 3 and 4 may not be applicable.

Avrami-type relations are widely reported for phase-transformation progress curves (Shirzad and Viney 2023), therefore, in this study, we report Avrami-form fits as a benchmark for comparing different triggering mechanisms. The Avrami (Johnson–Mehl–Avrami–Kolmogorov, JMAK) expression is commonly written as:

where is the fraction of material that is transformed as a function of time, and k and n are constants that are extracted from the model. As discussed in (Shirzad and Viney 2023), it is originated in classical nucleation theory (CNT) and represents the convergence of analyses performed independently by Johnson & Mehl (Johnson 1939) (Avrami 1940; Avrami 1941). This kinetic analysis clarifies how mixture composition and triggering methodology jointly regulate controllable heat release in supercooled sugar alcohol PCMs. Nucleation arises unintendedly from random fluctuations in the atomic (or molecular) arrangement of the parent phase (Sosso et al. 2016) and occurs in two forms: homogeneous nucleation, in which free-standing nuclei form without external sites, and heterogeneous nucleation, which is assisted by crystal defects or foreign surfaces (Karthika et al. 2016; Callister Jr and Rethwisch 2020). In practical supercooled PCM systems, crystallisation is typically initiated by heterogeneous nucleation on container walls, impurities/particles, or deliberately added nucleation sites (seeds/nucleating agents), while homogeneous nucleation is rarely observed. Therefore, controlled heat release commonly relies on introducing nucleation centres or external triggering methods (e.g., seeding, bubbling/agitation, ultrasonication) to initiate crystallisation on demand (Englmair, Moser, et al. 2018).

Based on the literature, Table 2 summarises studies on polyol-based thermal energy storage systems that employed Avrami-type equations to analyse crystallisation kinetics of the polyols sample. Only two studies were identified on polyol-based PCMs. Note that, in principle, crystallisation of supercooled polyols is non‑isothermal due to the release of latent heat and the associated sensible temperature rise. In this work, we nevertheless use Avrami‑type correlations, derived for isothermal conditions, as an empirical benchmark to compare crystallisation behaviours. The model is not intended to capture the full non‑isothermal thermodynamic coupling, but to provide a consistent phenomenological comparison across different triggering mechanisms with and without cold crystallisation via heating.

For the present image-based analysis, crystallisation was quantified at discrete times (5, 15, 30 and 40 min). To enable consistent comparison across triggering methods using the same fitting approach, the Avrami exponent n was fixed rather than fitted simultaneously with k. In selecting the best n value, we have conducted a sensitivity check for the mechanical agitation crystallisation mechanism as a complete crystallisation was achieved via the triggering method. In order to conduct the sensitivity analysis, the n value was varied in the range of 0.1-2 at the interval of 1 decimal point. To conduct the sensitivity analysis, we conducted first Sum of Squared Errors (SSE) given in Equation (3), and to further verify the analysis. However, given the limited number of data we have, we have also employed the leave-one-out cross-validation root-mean-squared error (LOOCV-RMSE) statistical method.

For each simulated n, we estimated the LOOCV-RMSE for each model by iteratively omitting one 𝑋-data point from model fitting, predicting its log-transformed concentration, and computing the difference between observed and predicted values. We then calculated the RMSE as the square root of the mean of these squared differences across all data. Values closer to 0 indicate better model performance, and we ensured the chosen model did not have an excessively large LOOCV-RMSE given the small sample size.

As illustrated in Figure 6b the best SSE and LOOCV was obtained when n = 0.5, provided the closest agreement with the measured trends across the datasets.

From the analysis, the crystallisation progress was then fitted using the reduced Avrami-type form when n = 0.5:

In Eq. (4), the exponent must be dimensionless; therefore k has units of . The parameter k was estimated by least-squares regression of Eq. (2) against the experimental values. Worth noting that, in this analysis, the parameter k governs the time scale of the crystallisation progress curve of which, higher k indicates faster crystallisation under the same experimental and image-processing condition.

To report the pointwise mismatch between the measured data and the fitted curve (as a fit residual rather than experimental uncertainty), the absolute residual at each time point was calculated as:

where is the image-derived crystallised fraction and is the fitted value from Eq. (2).

Because n was fixed at 0.5, k has units of in Eq. (4). For interpretability, a characteristic half-crystallisation time was also reported in which lower indicates faster crystallisation. From Eq. (2), set :

Figures 12 and 13 present the crystallization behaviour of the selected supercooled phase change materials (PCMs), induced by a crystallization seed, under two thermal conditions: cooling to 30 °C and pre-heating to 60 °C, hereafter referred to as case A and case B, respectively. Comparative analysis reveals that the elevated viscosity and reduced internal energy of the PCMs when triggered in case A, led to a markedly slower crystallization process. After 40 minutes, the samples that were triggered in case B which was subjected to cold crystallisation with seeding pre reached approximately 75% crystallization after 40 minutes of triggering, whereas the sample which was maintained at 30 °C in case A attained only about 30% crystallization. These observations indicate that seeding alone, without the application of cold crystallization, is not an effective approach, primarily due to the high viscosity of the supercooled material, which substantially impedes crystallization (Aladool et al. 2017). In addition, this observation may also be attributed by the increased viscosity which diminishes molecular mobility and mass transfer rates, thereby restricting diffusion and hindering the orderly molecular rearrangement required for crystal lattice formation.

Image-processing-based analysis further shows that the Avrami-type progress model provides a satisfactory representation of crystallisation under both thermal conditions. For the case B, the absolute residuals were 3.20 %, 0.10 %, 2.72 % and 1.20 % at 5, 15, 30 and 40 min, respectively, indicating close agreement after the earliest time point. For case B, residuals remained within 1.56–10.07 % over 5–40 min, with the maximum deviation at 5 min, suggesting that a significant portion of crystallisation occurred rapidly immediately after seeding and was not fully resolved by the discrete imaging times. These trends are consistent with viscosity-controlled behaviour: under case A, higher viscosity reduces molecular mobility and diffusion, slowing growth from the seed, whereas under case B reduced viscosity enhances transport and promotes faster crystallisation propagation.

Consistent with these observations, the fitted kinetic parameter for the case B is (RMSE = 5.74 %), corresponding to a rapid increase in crystallised fraction from 48.3 % (5 min) to 69.6% (40 min). In contrast, the case A dataset yielded a much smaller kinetic parameter, (RMSE = 2.18 %), consistent with the lower crystallised fraction of 10.1–19.4 % between 5 and 40 min. Overall, pre-heating to 60 °C in case B increased the apparent crystallisation kinetics by a factor of approximately 6.8 relative to 30 °C, in agreement with the substantially larger crystallised fraction observed in Figure 13 compared with Figure 12 over the same 40 min interval. Meanwhile, using the characteristic half-crystallisation time , seeding corresponds to ≈ 474min (≈ 7.9 h) in case A but only ≈ 10.3min in case B, confirming a strong acceleration when the PCM was pre-heated to 60 °C.

Figure 14 shows the crystallisation response of the supercooled PCM to a localised cooling shock introduced using a thermoelectric cooler (TEC) under case B (60 °C). The image-derived crystallised area fraction increased only marginally from 5.3% (5 min) to 9.8% (15 min) and then progressed slowly to 10.3% (30 min) and 13.2% (40 min). The crystallisation maps indicate that transformed regions remained spatially localised and did not propagate substantially through the bulk during the observation window, demonstrating that the TEC-induced perturbation did not create a sufficiently strong or sustained nucleation-and-growth process.

This weak response is consistent with practical limitations of the current TEC implementation. Commercial TEC modules are typically planar and square, which constrains the achievable cooling intensity at a local “tip” and limits the formation of steep temperature gradients within the PCM. In addition, the effective cooling at the contact point can be reduced by thermal contact resistance, lateral heat spreading through the heat sink, and rapid heat replenishment from the warm bulk PCM. Consequently, the local undercooling may remain below the threshold required to reliably initiate heterogeneous nucleation. Even if transient nuclei form near the cooled region, growth may be impeded by insufficient driving force and by the balance between local cooling and heat inflow from the surrounding PCM.

Consistent with the visual and map-based observations, the reduced Avrami-type fit with fixed exponent n = 0.5 yielded a small kinetic parameter, . Using Eq. (2), the fitted curve predicts crystallised fractions of approximately 3.34%, 5.72%, 7.99% and 9.17% at 5, 15, 30 and 40 min, respectively. The corresponding absolute residuals (measured – fitted) are therefore 1.96%, 4.08%, 2.31% and 4.03%, indicating that the model captures the slow-progress trend but underestimates the measured fractions, likely due to early localised crystallisation and segmentation artefacts that are not fully resolved by discrete imaging times. A characteristic half-crystallisation time derived from the fitted parameter, , is approximately 2079 min (~34.6 h), reinforcing that TEC triggering is extremely slow and ineffective for rapid, on-demand crystallisation with the present setup.

Figures 15 and 16 present crystallisation initiated by electrification (4.5 V applied for 1 min) under case A (30 °C) and case B (60 °C, following cold-crystallisation condition). A strong thermal dependence is evident. Under case A, crystallisation remains limited and appears to plateau within the 40 min observation window. The image-derived crystallised area fraction increases only modestly from 5.9% (5 min) to 7.8% (15 min), reaching 9.0% (30 min) and remaining at 9.0% (40 min). The processed crystallisation maps show nucleation primarily localised around the electrode region with little subsequent propagation into the bulk, indicating that although the applied potential can initiate local nuclei, bulk growth remains strongly hindered.

In contrast, electrification under case B produces rapid and extensive crystallisation throughout the sample volume. The crystallised area fraction increases from 37.6% (5 min) to 57.2% (15 min), reaching 81.6% (30 min) and 95.5% (40 min). The crystallisation maps confirm fast propagation and coalescence of crystallised regions, culminating in near-complete conversion by the end of the measurement period. This behaviour is consistent with viscosity-controlled kinetics of which at the lower temperature in case A, elevated viscosity suppresses molecular mobility and diffusion-limited growth, whereas at the higher temperature in case B, reduced viscosity supports both growth and the spread of crystallisation once nucleation was initiated. In addition, electrification may promote heterogeneous nucleation at the electrode surface and in its vicinity (e.g., through interfacial effects and local field-induced perturbations), but the extent to which this leads to bulk conversion is ultimately governed by transport and growth conditions.

Image-processing-based analysis shows that the reduced Avrami-type progress model with fixed exponent n = 0.5 provides a reasonable comparative description of the electrification datasets. Using Eq. (2) with , the fitted values are approximately 3.83%, 6.54%, 9.13% and 10.46% at 5, 15, 30 and 40 min, giving absolute residuals of 2.07%, 1.26%, 0.13% and 1.46%, respectively (case A). For case B (), the fitted values are approximately 45.57%, 65.13%, 77.46% and 82.10%, giving absolute residuals of 7.97%, 7.93%, 4.14% and 13.40%, respectively. The larger deviations in case B are consistent with the observed rapid conversion (especially at later times) and indicate that a single fixed exponent (n = 0.5) may under-represent the accelerating, bulk-propagating behaviour under electrification at elevated temperature. Nevertheless, the fitted kinetic parameters clearly capture the strong enhancement between the two conditions: kincreases from 0.01747 to 0.272 (approximately 15.6 higher), consistent with the transition from weak, localised crystallisation in case A to near-complete conversion in case B.

In addition, based on the reduced Avrami-type fit (n = 0.5), the characteristic half-crystallisation time t_50 computed using Eq. (5) was 1574 min (26.2 h) for electrification in case A (), but only 6.49 min in case B (), confirming a strong temperature-dependent acceleration for this triggering method.

Figures 17 and 18 show crystallisation initiated by mechanical agitation under case A (30 °C) and case B (60 °C, following the cold-crystallisation condition). Mechanical agitation produced the most rapid and spatially widespread crystallisation among the triggering strategies examined, with high crystallised fractions achieved even under case A. Under case A, the image-derived crystallised area fraction increased from 49.4% (5 min) to 59.9% (15 min) and 61.8% (30 min), reaching 72.8% (40 min). The crystallisation maps indicate that agitation generates distributed nucleation sites throughout the sample volume rather than relying on localised initiation, enabling comparatively rapid bulk conversion despite the higher viscosity at 30 °C.

Under case B, agitation further accelerated crystallisation and produced near-complete conversion within the 40 min window. The crystallised area fraction rose from 63.4% (5 min) to 80.4% (15 min) and 87.6% (30 min), reaching 99.1% (40 min). The processed maps show extensive propagation and coalescence of crystallised regions, consistent with reduced viscosity at elevated temperature supporting faster growth and more effective heat/mass transport during crystallisation.

The reduced Avrami-type progress model with fixed exponent n = 0.5 was fitted to both datasets to enable direct comparison across triggering methods. For case A, the fitted parameter was , giving fitted values of approximately 39.04%, 52.52%, 65.41% and 71.19% at 5, 15, 30 and 40 min, respectively. The corresponding absolute residuals are 10.36%, 7.38%, 3.61% and 1.61%, showing that deviations are largest at the earliest time point, likely reflecting very rapid crystallisation immediately after stirring that was not fully resolved by the discrete observation times. For case B, yields fitted values of approximately 62.69%, 81.85%, 91.20% and 93.81%, with absolute residuals of 0.71%, 1.45%, 3.60% and 5.29%. Overall, the fit captures the fast, saturating behaviour well, with slightly increased mismatch at later times as conversion approaches completion.

A characteristic half-crystallisation time derived from the fitted kinetics, from Eq. (5) further highlights the effectiveness of agitation. Under case A, ≈ 9.79 min, indicating rapid crystallisation even without pre-heating. Under case B, ≈ 2.47 min, confirming that agitation combined with the elevated-temperature condition provides the fastest overall conversion. From kinetics point of view, agitation is expected to enhance crystallisation by disrupting the metastable supercooled structure, increasing collision frequency and molecular rearrangement, and inducing secondary nucleation via shear, thereby reducing the nucleation barrier and enabling rapid growth throughout the bulk volume. These results demonstrate that mechanical agitation is the most promising method for achieving reliable, high-fraction crystallisation of the selected supercooled sugar-alcohol PCM within short time windows.