## 1 Introduction  
With the ever-increasing emergence of renewable energy technologies in the overall worldwide energy production [1], it is now clear that energy storage solutions are needed to deal with natural fluctuations in the availability of renewables [2]. Knowing that a large percentage of energy end-use is in the form of thermal energy (space heating and cooling, domestic hot water, power generation, thermally driven industrial processes, etc. ), it appears logical that energy could be stored thermally in these instances, especially when it has been demonstrated that thermal energy storage (TES) is a less expensive option compared to electrical storage [3]. For example, storing heat in water (or other sensible storage media like rocks) is very inexpensive compared to electrical storage in Li-ion batteries. In contrast, it is very clear that the quality of energy stored in a Li-ion battery is much greater than that stored in a given mass of water (try charging your smartphone from a hot water tank). That is to say that TES solutions still face many challenges, of which the main one is designing a system that matches the need of a given application at a competitive market price [4]. Latent heat energy storage systems (LHESSs) use phase change materials (PCMs)to store heat with a much greater energy density than sensible heat, through their solid-liquid phase transition [5]. LHESSs also offer the advantage that the phase transition of the PCM happens over a small and well-defined temperature range, allowing for more efficient design of components linked to the LHESS [6; 7]. Both the selection of thermophysical properties of the PCM [8; 9] and the design of the heat exchange system [4; 10; 11; 12] are central parts in the design of a LHESS. The solid-liquid phase transition temperature often plays the most important role in the selection of a specific PCM for a given application, depending on the operating temperature range of that application. The latent heat and, to a certain extent, specific heat of a PCM are central to its ability to store thermal energy [13]. However, for the design of a LHESS based on transient operation, the (typically) very small thermal conductivity of PCMs (apart from metallic ones and exceptions [14]) are in the order of 0.2 to 0.4 W/m\(\cdot\)K [15], leading to limitations on how rapidly heat can be transferred in and out of the storage system, i.e., the \"rate problem\" [16]. The rate problem is currently more often addressed by designing the heat exchange system used in a LHESS to increase the heat transfer rate to a desired value, for example through the use of additional heat transfer fluid (HTF) passes [5; 17], the addition of fins [18; 19; 20], increasing the contact area [21; 22; 23], or by favoring close-contact melting during the charging phase [24; 25; 26]. These approaches aim to optimize the efficiency and performance of LHESSs by overcoming limitations posed by the PCM's thermal conductivity. Increasing the PCM's thermal conductivity could also directly affect that material's ability to move heat to and from the exchange media, increasing the system's heat transfer rate [27]. But by how much does the thermal conductivity of a PCM need to be increased to positively impact the design and performance of a LHESS? This question was asked by material scientists from the International Energy Agency (IEA) Annex 40/Annex 67 expert group on Compact Thermal Energy Storage. Optimizing PCM thermal conductivity holds the potential for cost benefits, offering a cheaper solution compared to relying on modifications to heat exchange systems. This increase in thermal conductivity has been attempted through the addition of conductive nanoparticles [28; 29; 30]. Numerous issues are impeding the widespread use of those nano-enhanced PCMs (NePCMs), including thermal limitations still stemming from the minimal thermal conductivity increase [31], the cyclability of those systems, the economics of higher NePCM costs, etc. [28].