Through-plane Conductivity Research Articles

Boosting through-plane electrical conductivity: chitosan composite films with carbon-sepiolite and multiwalled carbon nanotubes

Flexible and electrically conductive materials are gaining significant attention across various domains, notably in electronics, biomedicine and food industry. One promising strategy involves the integration of electrically conductive nanostructures into a polymeric matrix to fabricate composite materials. However, achieving uniform through-plane electrical conductivity remains a challenge due to the preferential alignment of carbon nanostructures in the in-plane direction. Herein, we report the development of electrically conductive chitosan (CS)-based biocomposite films incorporating a multicomponent filler system. By combining carbon supported on sepiolite clay (CARSEP) with multiwalled carbon nanotubes (MWCNT), it is aimed to facilitate an interconnected distribution in both in-plane and through-plane directions. The optimized film, featuring a CS/CARSEP/MWCNT mass ratio of 50/40/10, exhibited a maximum electrical conductivity of 55.5 S/m and 0.1 S/m in the in-plane and through-plane directions, respectively. Additionally, migration studies demonstrated the absence of harmful compounds upon heating the film up to 60 °C in air, ethanol, or hexane. These findings highlight the potential of these flexible and electrically conductive biocomposite films, primarily composed of biobased materials, for applications requiring through-plane electrical conductivity.

A New Numerically Improved Transient Technique for Measuring Thermal Properties of Anisotropic Materials

A new transient technique of the thermal conductivity and diffusivity measurement for anisotropic materials is presented and validated. It is based on measuring the through-plane properties using the extended dynamic plane source (EDPS) method and in-plane conductivity employing the transient plane source (TPS) and modified dynamic plane source (MDPS) methods. The key advantage of this technique is that only one pair of specimens is required for measurements. While the EDPS method is implemented on real measurements, the TPS and MDPS are applied to the finite elements method (FEM) simulation of the experiment. The accuracy of the results is enhanced by the application of the FEM and is better than 1% for materials with through-plane conductivity of less than 2 W m−1 K−1 and a specimen thickness of 9 mm.

Combined water electrolysis and 2D hydron separator for enhanced hydrogen isotope separation

This research presents the fabrication and analysis of a graphene/Nafion composite membrane designed to enhance the hydrogen separation performance of a water electrolyzer by leveraging the isotope effect in hydron transport through monolayer graphene, serving as a 2D hydron separator. The composite membrane exhibits lower proton conductivity than a Nafion membrane, leading to a 12 % decrease in water electrolysis cell efficiency at 75 °C. However, the incorporation of monolayer graphene substantially enhances the hardness of the membrane by a factor of 1.38, as measured by nanoindentation. The addition of monolayer graphene also increases the activation energy required for through-plane conduction of H+ and D+, with the graphene itself showing a twofold higher conductivity for H+ over D+. In electrolysis cells containing the composite membrane, the H/D and H/T separation factors improved by approximately 1.4 and 2 times, respectively, compared with those of a Nafion membrane, with a maximum H/T separation factor of ∼ 15 at 15 °C. Although increases in temperature reduce the separation factor, the operation time and the concentration of heavier isotopes in the feed water were found to minimally affect the separation efficiency.

Different functional groups cross-linked graphene oxide membranes for proton exchange membrane fuel cell

The graphene oxide (GO) membrane treated by ozone, GOL, exhibits a relatively high conductivity, but its mechanical strength cannot be maintained due to severe swelling. To further improve the conductivity while suppressing the swelling, the free-standing GO membrane was subjected to ozone treatment and subsequently modified by crosslinking agents with oxygen functional groups, i.e., glyoxal (GLX) and oxalic acid (OXA). The modified membranes, GLX/GOL and OXA/GOL, successfully reduced the swelling and increased the conductivity to provide an excellent power output of a fuel cell at 30 °C due to the increased oxygen functional groups and the carbon defects. Furthermore, OXA/GOL exhibited a significant stability at elevated temperatures. At 50 °C, the through-plane conductivity and power output increased to 23.5 mS cm−1 and 317 mW cm−2, respectively. This is considered to be due to the relatively high thermal stability of the carboxy group added by the OXA modification.

Flexible yet impermeable composites with wrinkle structured BNNSs assembling for high-performance thermal management

Efficient thermal management has become one of the most critical issues of electronics because of the high heat flux generated from highly integrated, miniaturized, and increased power. Here we report highly flexible composites with aligned and overlapping interconnected boron nitride nanosheets (BNNSs) assembled in wrinkle structures. Besides high in-plane thermal conductivity of more than 26.58 W m−1 K−1, such structure rendered enhanced through-plane conduction along with increasing pre-stain. As thermal interface materials (TIMs) of both rigid and flexible devices, the composites revealed an outstanding thermal cooling capability outperforming some commercial TIMs. During a record-long bending process of more than 3000 cycles, the maximum temperature fluctuation of the flexible device with 100%-prestrained composite was only within 0.9 °C, less than one-third of that with commercial thermal pad. Moreover, the composite revealed a superior impermeability for flexible seals. Our results illustrate that the composites could be an ideal candidate for the thermal management of emerging flexible electronics.

Anisotropic polyphenylene-based anion-exchange membranes with flexible side-chains via click reaction for high-performance water electrolysis

Anion-exchange membrane water electrolysis (AEMWE) represents a promising and cost-effective electrochemical energy conversion system for green hydrogen production owing to its utilization of earth-abundant metals for various cell components (catalysts, porous transport layers, bipolar plates) and the zero-gap design. However, the lack of high-performance anion-exchange membranes (AEMs) has hampered the advancement of AEMWE technology. Here, by using colon coupling and click reactions, the ether-free polyphenylene-based AEMs (QPPBTF-TMA-w) with flexible side-chains containing triazole linkers. The QPPBTF-TMA-w membranes stand out for their lower activation energy for hydroxide conduction which is attributed to the well-structured ion-conducting channels via distinct phase separation facilitated by the triazole linker, which optimizes hydrophilicity and ensures efficient ion transport within the membrane. In addition, the QPPBTF-TMA-w membranes exhibit unique anisotropic swelling and ion-conduction behaviors, such as lower in-plane swelling and higher through-plane conductivity, which are advantageous for practical cell applications. Therefore, despite having a modest ion exchange capacity (IEC) value of 2.0, the QPPBTF-TMA-w membrane delivers high-performance in anion-exchange membrane water electrolysis (AEMWE), achieving 6.4 A/cm2 at 2.0 V at 70 °C using a 1.0 M KOH solution.

Anisotropic Fourier Heat Conduction and phonon Boltzmann transport equation based simulation of time domain thermo-reflectance experiments

The anisotropic Fourier Heat Conduction Equation (FHCE) and the multidimensional phonon Boltzmann Transport Equation (BTE) were solved numerically in cylindrical coordinates and in time domain to simulate a Time Domain Thermo-Reflectance (TDTR) experimental silicon/aluminum substrate/transducer setup. The out-of-phase response of the probe laser was predicted at various beam offset distances for a pump laser pulse frequency of 80 MHz and modulation frequency of 10 MHz and compared against experimental measurements for a silicon substrate. The isotropic FHCE was also solved for comparison. Results show that the isotropic FHCE with bulk thermal conductivity of 145 W/m/K significantly underpredicts the out-of-phase temperature difference, particularly at smaller beam offsets. With an isotropic thermal conductivity of 105 W/m/K, the computed results match experimental data at smaller beam offsets well, but overpredicts the experimental data at larger beam offsets. An almost-perfect match is obtained by using an anisotropic thermal conductivity wherein the radial (in-plane) thermal conductivity is set to 85 W/m/K and the axial (through-plane) conductivity is set to 130 W/m/K. The multidimensional frequency and polarization dependent phonon BTE is next solved. The BTE results for the out-of-phase temperature difference match experimental observations well at small and intermediate beam offsets, but overpredicts the experimental data at larger beam offsets. FHCE results are fitted to the BTE predictions, and the extracted (best fit) thermal conductivity is found to be 110 W/m/K.

High corrosion resistance and through-plane electrical conductivity of C/Ti and C/Cr coated metal bipolar plates used in PEMFC

To improve the corrosion resistance and enhance the electrical conductivity in a simulated proton exchange membrane fuel cell, carbon bound SS316L stainless steel plates were modified with titanium (Ti) or chromium (Cr). The SS316L interfacial contact resistance of 312.38 mΩ·cm2 was reduced to 1.59 mΩ·cm2 when modified with Ti and to 1.32 mΩ·cm2 when modified with Cr. The increase in potential enhanced the shedding of C films and the oxidation and dissolution of Ti and Cr buffer layers. The corrosion current density in the C/Ti coating was lower than C/Cr coating under high voltage polarization. The oxidation of Ti and Cr buffer layers led to poor appetency between the C film and the SS316L and to degradation of the through-plane electrical conductivities in the C/Ti and C/Cr coated metal bipolar plates.

An intrinsic electrical conductivity study of perovskite powders MAPbX3 (X = I, Br, Cl) to investigate its effect on their photovoltaic performance.

An investigation into the intrinsic electrical conductivity of perovskite powders MAPbX3, where X represents iodine (I), bromine (Br), or chlorine (Cl), was conducted to explore its impact on their photovoltaic performance. Results revealed that MAPbCl3 demonstrated light absorption ability in the ultraviolet and visible regions, while MAPbBr3 showed capacity for light absorption at longer wavelengths in the visible spectrum. On the other hand, MAPbI3 exhibited good absorption at longer wavelengths, indicating its ability to absorb light in the near-infrared region. The optical bandgap of each perovskite was determined to be 2.90 eV for MAPbCl3, 2.20 eV for MAPbBr3, and 1.47 eV for MAPbI3. The electrical conductivities of these powders were measured in-plane using the four-probe method and through-plane by electrochemical impedance spectroscopy (EIS). Electrochemical impedance spectroscopy (EIS) studies revealed a significant change in the conductivity of the MAPbI3 perovskite at temperatures between 80 °C and 100 °C. This change could be attributed to structural modifications induced when the temperature exceeds these values. The through-plane conductivity changed from 3 × 10-8 S cm-1 at 60 °C to approximately 6 × 10-5 S cm-1 at 120 °C and around 2 × 10-3 S cm-1 at 200 °C. Meanwhile, the sheet conductivity (in-plane conductivity) measurements performed at ambient temperature reveal that sheet conductivities are 489 × 103 S m-1, 486 × 103 S m-1 and 510 × 103 S m-1 for MAPbBr3, MAPbCl3 and MAPbI3, respectively. This study provides valuable insights for optimizing the performance of perovskite solar cells. Understanding how dopants influence the electrical conductivity and photovoltaic properties of the perovskite material, this work will enable researchers to design and engineer more efficient and stable solar cell devices based on MAPbX3 perovskites.

Preparation and Optimization of Novel Anisotropic Proton-Exchange Membranes with Enhanced through-Plane Conductivity

Maximizing through-plane (TP) conductivity, as opposed to in-plane (IP), is desired for proton exchange membranes (PEMs) in fuel cells, electrolysis and electrodialysis. Nafion, the benchmark PEM material, owes conductivity to randomly oriented ion-channels. Channel alignment in electrospun nanofibers was shown to enhance conductivity along the fibres by an order of magnitude, but it proved challenging to convert this to desired stable TP conductance. Another challenge is that orientation proves unstable and returns to random after nanofiber consolidation.Previously, we reported fabrication of electrospun nanofiber-based membrane with a stable anisotropic TP alignment of proton conducting channels prepared by co-spinning, buckling and fusion of Nafion and PVDF nanofibers (Odess, Li et al, ACS Appl Mat Interfaces, 2021), as shown in Figure 1. PVDF nanofibers serve as a mechanical reinforcement as well as a stabilizing component to safeguard Nafion TP alignment during annealing and swelling, akin to a solid template. However, the prepared 50% Nafion membrane still showed a TP conductivity slightly inferior to Nafion.In this report, we systematically optimized the Nafion content in the 50-80% range, as well as buckling and consolidation procedure and its temperature regime, to achieve a maximal and sustained conductance, exceeding that of pure Nafion. It was found that the TP proton conductivity of the membrane with 60% Nafion already exceeded that of Nafion 117 and further increased with Nafion content (Figure 1), with decrease in anisotropy (TP/IP conductance ratio). As another attractive feature, compared with Nafion 117, the TP conductivity of aligned membranes decreased less at lower humidity, i.e., was less sensitivity to dehydration, apparently due to better channel connectivity. Anisotropic structure and nanoscopic alignment were further confirmed by TEM and SAXS. The results demonstrate the potential of the new buckling approach for making novel nanofiber-based anisotropic membranes with significantly improved performance in electromembrane applications. Figure 1

Tailoring Binder Systems for LiNi0.6Mn0.2Co0.2O2-Based Positive Electrode by Investigating Various Polyvinylidene Difluorides for Different Active Material Morphologies

Polyvinylidene difluoride (PVdF) is the state-of-the-art binding agent for positive electrodes (cathodes) consisting of Ni-rich materials such as LiNi0.6Mn0.2Co0.2O2 (NMC622) and a conductive additive, which are processed with the organic solvent N-methyl-pyrrolidone. Processing and composition of the positive electrode strongly influence the specific energy and electrochemical performance of the corresponding lithium ion batteries (LIBs). Various binder systems were studied for state-of-the-art positive electrodes, however, a deeper understanding of the impact on the electrode properties is yet to be acquired.1,2 Besides the electronical and mechanical properties of the positive electrode, the binding agent additionally affects the charge/discharge cycling stability and rate capability of the battery cell. An important factor is the ratio of binder content to surface area of the solid components.3 For instance, using a low binder coverage (ratio of binding agent to solid components) can lead to weak adhesion between composite electrode and current collector, resulting in a decrease in cycling stability. This is due to mechanical degradation upon prolonged charge/discharge cycling, as altering volume extension and reduction leads to mechanical stress and therefore in particle cracking and contact loss. On the contrary, extensive binder coverage leads to high internal resistance, due to hindered lithium mobility and potentially reduced electronical conductivity of the composite electrode.The properties of binding agents vary depending on chain length and the degree of polymerization, hence affecting intermolecular stability, swelling rate, and adhesion to the current collector. While the morphologies of active materials are predetermined (primary/secondary particles) and the variation of the conductive additive can influence the pore structure and conductivity of the electrode, the binding agent is essential for the distribution of the conductive additive and the adhesion to the current collector. Binding agents make up a comparably small part in the electrode composition, however, it is the electrode component that can essentially enhance the lifetime of a battery.Thus, it is crucial to understand the influence of the binder characteristics on the electronical, mechanical, and electrochemical properties of the cathode. To understand how binder coverage can enhance or impair these properties, primary particles (high surface area) and secondary particles (comparably low surface area) of NMC622 were processed with various polyvinylidene difluoride binding agents differing in molecular weight. Experiments regarding the physical electrode properties such as adhesion and electronic through-plane conductivity, as well as the electrochemical properties concerning rate capability and long-term charge/discharge cycling were compared and evaluated for the two active material variants. Additionally, aging studies with one of the binding agents were carried out to investigate the influence of the active material surface on the aging products found in the electrolyte and by that gaining a deeper understanding for the aging mechanisms in different NMC622 cell set ups. The combination of the mentioned experimental techniques enables the determination of a tailored binder system for a specific active material morphology and the associated electrode composition for the intended LIB application.[1] Gordon, R.; Kassar, M.; Willenbacher, N., ACS omega 2020, 5 (20), 11455–11465.[2] Chen, H.; Ling, M.; Hencz, L.; Ling, H. Y.; Li, G.; Lin, Z.; Liu, G.; Zhang, S., Chemical reviews 2018, 118 (18), 8936–8982.[3] Weichert, A.; Göken, V.; Fromm, O.; Beuse, T.; Winter, M.; Börner, M., Journal of Power Sources 2022, 551, 232179.

Polyethyleneimine-confined halloysite nanotubes for poly(2,5-benzimidazole) composite membranes with phosphoric acid retention and proton conductivity via ion pairs for wide-temperature PEMFCs

To prevent phosphoric acid (PA) from leaching and harming traditional polybenzimidazole-based proton exchange membranes, polyethyleneimine-confined halloysite nanotubes (PEI@HNTs) were embedded in poly (2,5-benzimidazole) membranes to construct rich ion pairs that stably conducted protons. With the aid of supercritical carbon dioxide, PEI oligomers with basic groups were confined in HNTs. Then, through in-situ synthesis, highly-dispersed PEI@HNT enhanced the mechanical stability of composite membranes, whose basicity improved the absorption and retention capacity of PA. The PEI@HNTs/ABPBI composite membrane exhibited excellent mechanical strength and electrical performance over a temperature range of 40–180 °C. The through-plane proton conductivity of the 5%PEI@HNTs/ABPBI composite membrane was 0.061 S cm−1 at 98% relative humidity and 90 °C and 0.049 S cm−1 under anhydrous conditions at 180 °C. This performance was attributed to strong hydrogen bonding between PEI and PA, as well as the excellent retention of bound water within the HNTs. The peak power density of PA-doped 5%PEI@HNTs/ABPBI composite membrane reached 0.235 W cm−2 and 0.418 W cm−2 at 120 °C and 180 °C under anhydrous conditions, respectively, which were 1.68 and 1.96 times higher than those obtained with the pristine PA-ABPBI membrane. These results highlight the potential of this composite membrane for applications requiring a wide temperature range.

Optimization of Filler Compositions of Electrically Conductive Polypropylene Composites for the Manufacturing of Bipolar Plates.

In this research, polypropylene (PP)-graphite composites were prepared using the melt mixing technique in a twin-screw extruder. Graphite, multi-walled carbon nanotubes (MWCNT), carbon black (CB), and expanded graphite (EG) were added to the PP in binary, ternary, and quaternary formations. The graphite was used as a primary filler, and MWCNT, CB, and EG were added to the PP-graphite composites as secondary fillers at different compositions. The secondary filler compositions were considered the control input factors of the optimization study. A full factorial design of the L-27 Orthogonal Array (OA) was used as a Design of Experiment (DOE). The through-plane electrical conductivity and flexural strength were considered the output responses. The experimental data were interpreted via Analysis of Variance (ANOVA) to evaluate the significance of each secondary filler. Furthermore, statistical modeling was performed using response surface methodology (RSM) to predict the properties of the composites as a function of filler composition. The empirical model for the filler formulation demonstrated an average accuracy of 83.9% and 93.4% for predicting the values of electrical conductivity and flexural strength, respectively. This comprehensive experimental study offers potential guidelines for producing electrically conductive thermoplastic composites for the manufacturing of bipolar fuel cell plates.

Interfacial Effects in Conductivity Measurements of Block Copolymer Electrolytes.

The ionic conductivity in lamellar block copolymer electrolytes is often anisotropic, where the in-plane conductivity exceeds the through-plane conductivity by up to an order of magnitude. In a prior work, we showed significant anisotropy in the ionic conductivity of a lamellar block copolymer based on polystyrene (PS) and a polymer ionic liquid (PIL), and we proposed that the through-film ionic conductivity was depressed by layering of lamellar domains near the electrode surface. In the present work, we first tested that conclusion by measuring the through-plane ionic conductivity of two model PIL-based systems having controlled interfacial profiles using impedance spectroscopy. The measurements were not sensitive to changes in interfacial composition or structure, so anisotropy in the ionic conductivity of PS-block-PIL materials must arise from an in-plane enhancement rather than a through-plane depression. We then examined the origin of this in-plane enhancement with a series of PS-block-PIL materials, a P(S-r-IL) copolymer, and a PIL homopolymer, where impedance spectra were acquired with a top-contact electrode configuration. These studies show that enhanced in-plane ionic conductivities are correlated with the formation of an IL-rich wetting layer at the free surface, which presumably provides a low-resistance path for ion transport between the electrodes. Importantly, the enhanced in-plane ionic conductivities in these PS-block-PIL materials are consistent with simple geometric arguments based on properties of the PIL, while the through-plane values are an order of magnitude lower. Consequently, it is critical to understand how surface and bulk effects contribute to impedance spectroscopy measurements when developing structure-conductivity relations in this class of materials.

Highly thermally conductive and negative permittivity epoxy composites by constructing the carbon fiber/carbon networks

The geometry of electronic devices is shrinking, while electronic components are moving towards miniaturization, integration and high frequencies. Polymer composites with high thermal conductivity, low cost and light weight are urgently needed for thermal management areas such as clean energy, 5G mobile phones, artificial intelligence and so on. In this paper, pre-oxygenated fibers (POF) are firstly prepared into POF felt using air-flow netting and needling. The POF felts are graphitized to form carbon felts (CF). Finally, the CF/C felt are prepared by vacuum impregnation-lamination cured-carbonization-graphitization-purification. Epoxy resin/carbon fiber/carbon (EP/CF/C) composite prepared by a simple vacuum encapsulation method. Test results show that the prepared epoxy composites have a thermal conductivity of up to 2.83 W/mK and 0.57 W/mK in-plane and through-plane with 8.94 vol% CF/C. The maximum thermal conductivity enhancement of the epoxy composites is 1389% and 202% compared to the pure epoxy resin. The composite's maximum in-plane and through-plane conductivity can reach 0.17 S/cm and 0.04 S/cm respectively. Composites show a certain negative dielectric behavior. With increasing of graphitization, the negative permittivity appears in the low frequency region. Infrared imaging shows that the prepared epoxy composites have excellent thermal management properties. The carbon fiber thermally conductive composites prepared in the above manner may have promising applications in advanced thermal management.

Modification of sulfonated poly(arylene ether nitrile) proton exchange membranes by poly(ethylene-co-vinyl alcohol).

The modification of the physicochemical properties of sulfonated poly(arylene ether nitrile) (SPAEN) proton exchange membranes was demonstrated by poly(ethylene-co-vinyl alcohol) (EVOH) doping (named SPAEN-x%). By controlling the temperature during membrane preparation, the side reactions of the sulfonic acid groups to form sulfonic acid esters were effectively prevented, greatly reducing the proton conductivity of the membranes. Due to the flexible chain of EVOH, SPAEN-8% showed a relatively high elongation of 30.2%, which enhanced the aromatic polymers' flexibility. The SPAEN-2% membrane exhibited proton conductivity of 166, 55, and 9.6 mS cm-1 at 95%, 70%, and 50% relative humidity, respectively, higher than those of the other SPAEN-x% membranes and even comparable to that of Nafion 212. The water uptake, morphological study, and through-plane proton conductivity of the membranes were studied and discussed. The results suggest that EVOH doping can be used as an effective strategy to improve SPAEN-based proton exchange membranes' performance.

Enhancing the ionic conductivity and mechanical properties of PEO-based solid electrolytes through thermal pre-stretching treatment.

Pre-stretching as a method for directing polymer crystallization offers a promising solution for addressing the limitations of solid polymer electrolytes in flexible batteries at ambient temperatures. In this study, we have investigated the ionic conductivity, mechanical behaviour, and microstructural and thermal properties of polyethylene oxide (PEO)-based polymer electrolytes with varying pre-strain levels. The results indicate that thermal stretching-induced pre-deformation can significantly increase the through-plane ionic conductivity, in-plane strength, stiffness of solid electrolytes, and cell-specific capacity. However, modulus and hardness decrease for pre-stretched films in the thickness direction. Notably, applying 50-80% pre-strain to the PEO matrix composites through thermal stretching may be preferred for improving the electrochemical cycling performance, as it can increase through-plane ionic conductivity by at least 1.6 times while maintaining compressive stiffness at 80% compared to their unstretched counterparts, while the in-plane strength and stiffness can be boosted by 120-140%. Besides, adding nanoceramics contributes to lithiated PEO exhibiting a higher enhancement coefficient than the pristine sample. This positive effect is because the pre-strain and nano-inorganic filler decrease crystallinity and increase the free volume size of pre-stretched PEO-based electrolytes.

Comparison of the Thermal and Mechanical Properties of Poly(phenylene sulfide) and Poly(phenylene sulfide)-Syndiotactic Polystyrene-Based Thermal Conductive Composites.

Syndiotactic polystyrene (SPS) has attracted considerable attention recently due to its high melting temperature, low cost, and relatively low density value. The aim of the study is to reveal whether a blend of PPS and SPS (PPS-SPS) can be used instead of PPS for high thermal stability, high mechanical performance, and high thermal conductive material applications. For this aim, poly(phenylene sulfide)/syndiotactic polystyrene-based carbon-loaded composite materials were prepared using a twin screw extruder. Two carbon-based materials, carbon fiber (CF) and synthetic graphite (SG), were used to improve the mechanical properties and thermal conductivity of the PPS-SPS blends. Through-plane conductivity values of PPS-30SG-10CF and PPS-SPS-30SG-10CF were obtained to be 13.67 and 12.92 W/mK, with densities of 1.55 and 1.50 g/cm3, respectively. It was demonstrated that PPS-SPS blend-based carbon-loaded composites have great potential to be used in thermal management applications with the advantages of relatively low cost and lightweight compared to PPS-based composites.

A Transient Resistance/Capacitance Network-Based Model for Heat Spreading in Substrate Stacks Having Multiple Anisotropic Layers

Abstract Heat spreading from local, time-dependent heat sources in electronic packages results in the propagation of temperature nonuniformities through the stack of material layers attached to the chip. Available models either predict the chip temperatures only in the steady-state or a single substrate for transient analysis, without the ability to predict the transient response in compound substrates having multiple anisotropic layers. We develop a transient resistance/capacitance network-based modeling approach capable of predicting the spatiotemporal temperature fields for this chip-on-stack geometry, accounting for in-plane heat spreading, through-plane heat conduction, and the effective convection resistance boundary conditions. The transient heat spreading resistance for an anisotropic substrate has been formulated by converting it to an effective isotropic substrate for which there is an available half-space solution. The transient heat spreading model for a step heat input to a single substrate is subsequently extended to any arbitrary transient heat input using a Fourier series and extending the half-space formulation from a step heat input to sinusoidal heat input. For obtaining the transient spreading resistance for heat inputs into multiple stacked substrates, a method has been outlined to convert the multisubstrate stack to a single substrate with effective isotropic properties by properly accounting for the in-plane and through-plane thermal conductivities, and the heat capacity. The estimates from the present model are validated with direct comparison to a finite volume numerical model for three-dimensional heat conduction. Case studies are presented to demonstrate the capabilities of the proposed network-based model and compare its estimates with the numerical conduction solution. In the presence of a step heat input, the results demonstrate that the model accurately captures the transient temperature rise across the multisubstrate stack comprising layers with different anisotropic properties. For a case where the rectangular stack is exposed to a sinusoidally varying heat input, the model is able to capture the general trends in the transient temperature fields in the plane where the heat source is applied to the multisubstrate stack. In summary, the developed resistance/capacitance network-based transient model offers a low-computational-cost method to predict the spatiotemporal temperature distribution over an arbitrary transient heat source interfacing with a multilayer stack of substrates.

Characterization of Commercial Polymer–Carbon Composite Bipolar Plates Used in PEM Fuel Cells

Bipolar plates represent a crucial component of the PEM fuel cell stack. Polymer-carbon composites are recognized as state-of-the-art materials for bipolar plate manufacturing, but their use involves a compromise between electrical and heat conductivity, mechanical strength and costs. Thus, all key parameters must be considered when selecting a suitable plate satisfying the demands of the desired application. However, data relevant to commercial materials for such selection are scarce in the open literature. To address this issue, 13 commercially available polymer-carbon composites are characterised in terms of the following parameters: through-plane conductivity, hydrogen permeability, mechanical strength, water uptake, density, water contact angle and chemical stability. None of the materials tested reached the DOE target for electrical conductivity, while five of the materials met the target for flexural strength. The overall best-performing material showed a conductivity value of 50.4 S·cm-1 and flexural strength of 40.1 MPa. The data collected provide important supporting information in selecting the materials most suitable for the desired application. In addition, the key parameters determined for each bipolar plate supply important input parameters for the mathematical modelling of fuel cells.