Anisotropic Conductivity Research Articles

Anisotropic Heat Transfer in a Fibrous Membrane with Hierarchically Assembled 2D Materials.

Effective heat redistribution in specific directions is vital for advanced thermal management, significantly enhancing device performance by optimizing spatial heat configurations. We have designed and fabricated a hierarchical fibrous membrane that enables precise heat directing. By integrating hierarchical structure design with the anisotropic thermal conductivity of two-dimensional (2D) materials, we developed a fibrous membrane for anisotropic heat transfer. Such a structure is fabricated by aligning a 1D structured fiber in the 2D plane to achieve anisotropy at each scale level. The fiber units, where 2D nanosheets circumferentially and axially aligned, achieved a high axial thermal conductivity of 16.8 W·m-1·K-1 and advanced heat directing ability, confirmed by characterizations and simulations. The assembled membrane demonstrated an exceptional tensile strength (365 MPa) and high thermal conductivity (10.5 W·m-1·K-1) along the fiber axis. Our membranes are seen as a refined model for thermal management materials, combining the benefits of heat spreaders and thermal interface materials, thus being proficient in directing heat along programmed pathways. A practical wireless charging cooling demonstration illustrated this. Our methodology also proved versatile with different 2D fillers and various geometries. This research presents a method to achieve precise heat directing at the material's level, facilitating the systematic design of thermal management in electronics.

Abstract 4136863: Diffuse Functional and Structural Abnormalities in Fibrosis: Potential Structural Basis for Sustaining Atrial Fibrillation

Background: Structural remodeling is associated with atrial fibrillation (AF), but detailed structural and functional characteristics is not well defined. Goal: Using a novel transgenic goat model with cardiac-specific overexpression of TGF-β1 leading to increased cardiac fibrosis, we evaluated detailed structural and functional differences between fibrotic and healthy regions of the atria. Methods: Ex-vivo MRI and histology were used to evaluate fibrosis, fiber disarray, and structural anisotropy. Ex-vivo MRI intensity values were scaled to standard deviations around the mean. The functional analysis examined conduction speeds and direction heterogeneity. Conduction anisotropy was measured along the fiber direction obtained with diffusion tensor imaging. Results: The transgenic goats (n=12) had, on average, 21% of the left atria labeled as fibrotic determined from ex-vivo MRI. The histology samples taken from the labeled fibrotic regions had an increase in fibrosis percentage compared to labeled healthy regions (7.78±3.76% vs 2.80±1.86%, p<0.01). The structural anisotropy was lower in fibrotic regions (0.196±0.002 vs 0.244±0.002, p<0.01). Fiber disarray was greater in the fibrotic regions (20.3±0.2° vs 19.2±0.1°, p<0.01). The fibrotic regions had slower conduction speeds (0.78±0.02 m/s vs 1.12±0.02 m/s, p<0.01) and more aligned conduction directions (30.5±0.2° vs 31.6±0.1°, p<0.01), potentially developing unidirectional conduction block. Conduction anisotropy, measured on the fiber directions, was found to be lower in the fibrotic regions (1.86±0.05 vs 2.10±0.02, p=0.04). As scaled MRI intensity increased, the conduction speed, heterogeneity, and anisotropy all decreased. Conclusions: Functional and structural differences exist between fibrotic and healthy regions of the atria. Though statistically significant, the changes are not discrete. The correlation showed gradual functional abnormalities with MRI intensities. Fibrotic regions tended to have increased fiber disarray, slower conduction, and more unidirectional propagation with lower conduction and structural anisotropy. Diffuse functional and structural abnormalities may allow fibrotic regions to serve as a substrate to sustain AF.

Experimental and Theoretical Investigation of Anisotropic Proton Conduction in Two-Dimensional Metal-Organic Frameworks.

Two-dimensional (2D) materials are known for their potential to exhibit anisotropic transport properties due to their layered structures. However, the anisotropic ion conduction of 2D metal-organic frameworks (MOFs) has been rarely explored. In this study, we investigated the anisotropic proton conduction along the in-plane and stacking directions of two analogs of undulating 2D MOFs: [Mn(salen)]2[Pt(CN)4]·H2O (MnPt) and [Mn(salen)]2[PtI2(CN)4]·H2O (MnPtI). This investigation was conducted using both experimental methods, involving single crystals, and theoretical calculations. Compared to the relatively isotropic proton conduction of MnPt at 85 °C and 95% relative humidity (RH), with a stacking direction conductivity (σstacking) of 1.8 × 10-5 S/cm, which is approximately 2.9 times the in-plane conductivity (σin-plane), MnPtI exhibited highly anisotropic proton conduction. The σstacking of MnPtI under the same conditions (85 °C, 95% RH) was 1.5 × 10-4 S/cm, which is 83 times higher than its σin-plane. Additionally, the activation energy for proton conduction in MnPtI ranged from 0.65 to 0.73 eV, which is higher than the 0.48 eV observed for MnPt. Theoretical calculations confirmed that slight differences in local structures, including node distortions between MnPt and MnPtI, significantly influenced the activation energies for water migration. This was attributed to the formation of hydrogen bonds between layers and water molecules.

Research on the Anisotropy of the Thermal Conductivity of Sandstone Heritage via Digital Rock Physics Under Various Pore Media

ABSTRACT The thermal conductivity of sandstone heritage has been emphasized as one of the crucial factors affecting the weathering, in order to further investigate the anisotropy of the thermal conductivity of sandstone at the microscale. In this study, the thermal conductivity of the sandstone samples is measured using the laser flash method. Next, micro-CT images are utilized to reconstruct the digital rock, randomly selected different sizes of REVs (130 × 250 * 250, 100 × 100 * 100, 50 × 50 * 50 voxels) are taken from the reconstructed digital rock. Thermal simulations are then conducted on these REVs in different directions and under steady-state conditions for three pore-filling phases (air, water, and ice). An anisotropic model is introduced to evaluate the thermal conductivity anisotropy of the REVs. Finally, the overall analysis reveals that the pore-filled phase changes from air to water and finally to ice result in an increase of the thermal conductivity of the digital rocks; Additionally, as the thermal conductivity of the filling phase increases, the digital rock progressively transitions towards isotropy. As the porosity of the digital rocks increases, the thermal conductivity decreases and the thermal anisotropy factor diverse further from 1. Changes in REV size has an insignificant effect on the thermal conductivity; however, an increase in the REV size causes the anisotropy factor closer to 1. It is expected the innovative method reported in the present work can provide a feasible and reliable alternative for studying the thermal anisotropy and delaying weathering in stone heritage.

Anisotropic induced polarization modeling with neural networks and effective medium theory

Interpreting three-dimensional induced polarization (IP) data requires rock physics models that reflect the omnipresent anisotropy of the Earth’s crust. The Generalized Effective Medium Theory of Induced Polarization (GEMTIP) can model the IP signatures of rocks with polarizable mineral inclusions. However, it is computationally demanding because it requires numerically solving the depolarization tensors of each inclusion. We aim to streamline GEMTIP simulations by (1) integrating anisotropic background conductivity and triaxial ellipsoidal inclusions in the model and (2) estimating the depolarization tensors with a neural network. We validate the neural network predictions against known solutions for spherical and spheroidal inclusions, and we test our method using data from an actual rock sample. The neural network shows a relative sensitivity of 56% to inclusion shape and 44% to host rock anisotropy and is up to 100,000 times faster than numerical integration. We release the pre-trained neural network implementation as an open-source Python package, thereby providing a new method to interpret the IP signatures of anisotropic rocks.

Electrospun green fluorescent-highly anisotropic conductive Janus-type nanoribbon hydrogel array film for multiple stimulus response sensors

A new strategy aimed at significantly enhancing the anisotropic conductivity of hydrogel materials, along with a simple construction technology and design concept, are proposed. Anisotropic conductive hydrogel materials have attracted much attention from researchers in the field of flexible electronics for their inherent excellent properties. However, the anisotropic conductivity of the existing conductive hydrogels is not high and the preparation methods are complex. Herein, fluorescent-highly conductive anisotropic Janus-type nanoribbon hydrogel array film (named JNHAF) is successfully prepared using a combination of parallel electrospinning and post-polymerization as an example of the study. Highly oriented [2,7-dibromo-9-fluorenone (DF)/gelatin (GE)]//[carbon black (CB)/GE] Janus-type nanoribbon is used as the building block. The composition as well as the arrangement of Janus-type nanoribbons are microscopically designed and regulated to effectively separate the conductive and insulating materials, so that the samples can achieve highly anisotropic conductivity and obvious green fluorescence. When the mass ratio of GE to CB is 1:0.1, the conductive anisotropy ratio of JNHAF can reach 1.12 × 105. The degree of anisotropic conductivity of JNHAF is significantly improved compared with existing reported anisotropic conductive hydrogels, and the preparation method is simple. JNHAF responds quickly to light, tensile strain, and temperature, making it suitable for assembling multi-stimulus responsive sensors. JNHAF has excellent flexibility, degradability, mechanical properties and a certain degree of sensitivity (gauge factor of 4.29), and is used for human joint motion detection with an obvious response signal. The design idea and construction technology of this hydrogel breaks through the technical bottleneck of the low degree of anisotropy of conductive hydrogels, which will lead and expand the scientific frontiers of anisotropic conductive hydrogel materials, and provide novel design ideas and theoretical values for new hydrogel materials.

Multi-directional deformation and hydraulic conductivity of expansive soils subjected to freeze-thaw cycles from three distinct initial saturation levels

Infrastructure construction in seasonally frozen regions, covering 23% of total land, faces challenges from freeze-thaw (F-T) induced damages. Expansive soils, as an important problematic soil undergo major hydromechanical properties changes influenced by F-T cycles. Sand-bentonite mixtures are extensively used for constructing earthen hydraulic barriers in cold regions. This study investigates the influence of F-T cycles on multi-directional strains and anisotropic hydraulic conductivity of different sand-bentonite mixtures prepared at optimum water content and experienced three distinct saturation levels. Results indicate that saturation level and bentonite content significantly influence volumetric strain under F-T cycles. The simultaneous effect of ice lens formation, expanding micro-voids, and suction generated by freezing processes cause different volumetric behaviors at varying saturation degrees. The dry specimen exhibits no strain under F-T cycles, while optimum and saturated specimens experienced final volumetric strains of 1.02% and 3.03%, respectively. Notably, during freezing, the specimen at optimum water content shrank, while the saturated specimen expanded. Increasing bentonite content from 40% to 70% developed freezing-induced shrinkage, from 1.73% to 4.72%, with higher thaw strain attributed to increased specimen plasticity. Also, dimensional variations revealed the cross-anisotropic nature of specimens, highlighting direct influence of water content on the shrinkage ratio. F-T cycles also increased hydraulic conductivity along both orthogonal directions by two orders of magnitude, while the anisotropy ratio decreased by about 3 after 9 F-T cycles, indicating altered pore structures. F-T cycles induce reduced swelling potential and compressibility over subsequent cycles. Microstructural observations also confirmed the F-T effects on the enhancement of porosity.

Lightning Damage Evaluation in Carbon Fiber Composite Polymer Structure

While metallic aircraft structures are largely unaffected by lightning strikes, not the same statement could be made about carbon fibre reinforced polymer (CFRP) ones. CFRPs have low electrical conductivity and high anisotropy, and for this reason they are covered with metallic meshes, generally of aluminium or copper, to redistribute the electrical charge when the plane encounters lightning events. During these phenomena, electrical discharges could lead to physical damage, called direct effects, such as: ablation, erosion, explosion, structural weakening and degradation. Although relatively rare, when aircraft is affected by lightning strikes, structural inspections are necessary to determine the need and magnitude of repairs. Since the extent of lighting strike damage on laminated composite is difficult to determine and quantify visually, other non-destructive evaluation (NDE) techniques must be used. In this work, we complement established techniques, such as pulse-echo ultrasonics, X-ray radiography, eddy currents, and thermography with a novel investigative approach, based on planar capacitive sensing and imaging. This has the advantage of being non-contact, and requiring only single-side access to the part. The technique’s capabilities to detect dielectric changes and breakages in conductive layers make it an ideal candidate for the investigation of CFRP aircraft structure for lightning effects. The outcomes of capacitive imaging inspections on laboratory introduced lightning damage on CFRP panels are discussed along the advantages and disadvantages of the technique compared to more established ones.

An improved goal-oriented adaptive finite-element method for 3-D direct current resistivity anisotropic forward modeling using nested tetrahedra

We developed a novel adaptive finite element method (FEM) to address the problem of 3-D direct current (DC) resistivity forward modeling with complex surface topography and arbitrary conductivity anisotropy. The tetrahedra-based FEM and secondary virtual potential algorithm are first used to handle arbitrary complex geo-models. Then, to ensure the accuracy of the simulation solution, an improved goal-oriented adaptive mesh refinement (AMR) algorithm is proposed to realize an optimized mesh density distribution. To avoid the drawback of the traditional goal-oriented AMR algorithm for the DC forward modeling problem, we incorporate a volume-based weighting factor into the posterior error estimation procedure to further optimize the density distribution of the forward modeling grid. In addition, instead of traditional open source mesh generation software, we propose using the longest-edge bisection (LEB) algorithm to perform the mesh refinement process, which can preserve the topological structure between different-level meshes. Finally, the comprehensive test using a two-layered model and two complex 3-D models demonstrate the capability of our newly developed code to obtain highly accurate solutions even on relatively coarse initial grids. By incorporating the volume factor, our novel AMR algorithm achieves a more uniform and reasonable mesh density distribution during these experiments. The LEB refinement technique can generate a series of nested tetrahedral elements and provide fewer tetrahedral elements compared to the traditional Delaunay-based AMR method. The proposed 3-D DC forward modeling method has been implemented into an open source C++ code, which will contribute to the advancement of the 3-D DC resistivity imaging field.

Reconstruction of intra- and extra-neurite conductivity tensors via conductivity at Larmor frequency and DWI data patterns

The developed magnetic resonance electrical properties tomography (MREPT) techniques visualize the internal conductivity distribution at Larmor frequency by measuring the B1 transceive phase data. In biological tissues, electrical conductivity is influenced by ion concentrations and mobility. To visualize the anisotropic conductivity tensor of biological tissues, we use the Einstein–Smoluchowski equation, which links the diffusion coefficient to particle mobility. By assuming a correlation between ion mobility and water diffusivity, we aim to decompose the internal isotropic conductivity at Larmor frequency into anisotropic conductivity tensors within the intra- and extra-neurite compartments. The multi-compartment spherical mean technique (MC-SMT), utilizing both high and low b-value diffusion-weighted imaging (DWI) data, characterizes the diffusion of water molecules within and across the intra- and extra-neurite compartments by analyzing the microstructural intricacies and the foundational architectural arrangement of the brain’s tissues. By analyzing the relationships between the measured DWI data, the microscopic diffusion signal, and the fiber orientation distribution function, we predict the DWI data for the intra- and extra-neurite compartments using spherical harmonic decomposition. Using the predicted DWI data for the intra- and extra-neurite compartments, we develop a conductivity tensor imaging method that operates specifically within the separated compartments. Human brain experiments, involving four healthy volunteers and a brain tumor patient, were performed to assess and confirm the reliability of the proposed method.

Muscle‐Inspired Robust Anisotropic Cellulose Conductive Hydrogel for Multidirectional Strain Sensors and Implantable Bioelectronics

AbstractIntegrating superior mechanical performance, anisotropic conductivity, and biocompatibility into conductive hydrogels as all‐in‐one human‐machine interaction device remains challenging. Herein, by mimicking the anisotropic structures of human muscles, a robust anisotropic conductive hydrogel is developed by initially aligning polyvinyl alcohol with polypyrrole decorated cellulose nanofibrils to form an anisotropically oriented polymer networks, followed by post‐crosslinking with tannic acid (TA). Introducing TA into hydrogel network permanently secures its hierarchically anisotropic structure through multiple hydrogen bonds, thus endowing the hydrogel with exceptional mechanical properties (tensile strength of 11.41 MPa, toughness of 12.44 MJ m−3), anisotropic adhesive property, and direction‐dependent conductivity. With these attributes, a hydrogel strain sensor with excellent multidirectional sensitivity is developed, enabling stable monitoring of multi‐degrees of freedom joint movements in the human body and facilitating the control of a multiaxial virtual robot manipulator. Moreover, the in vitro/vivo tests demonstrate exceptional biocompatibility and anti‐biofouling properties of the as‐prepared hydrogel sensor, maintaining stable electronic response signals for over 14 days after successful implantation into the Achilles tendon of mice. Overall, this study presents a promising approach for designing conductive hydrogels with superior mechanical properties and anisotropic functionality for emerging applications in both in vitro and in vivo human‐machine interface materials.

Rapid fabrication of gold microsphere arrays with stable deep-pressing anisotropic conductivity for advanced packaging

Smooth metal microspheres with uniform sizes are ideal for constructing particle-arrayed anisotropic conductive films (ACF), but synthesis is hindered by challenges in controlling anisotropic metal growth. Here, we present a positioned transient-emulsion self-assembly and laser-irradiation strategy to fabricate pure gold microsphere arrays with smooth surfaces and uniform sizes. The fabrication involves assembling gold nanoparticles into uniform colloidosomes within a pre-designed microhole array, followed by rapid transformation into well-defined microspheres through laser heating. The gold nanoparticles melt and merge in a layer-by-layer manner due to the finite skin depth of the laser, leading to a localized photothermal effect. This strategy circumvents anisotropic growth, enables tunable control of microsphere size and positioning, and is compatible with conventional lithography. Importantly, these pure gold microspheres exhibit stable conductivity under deep compression, offering promising applications in soldering micro-sized chips onto integrated circuits.

Control of Orientation and Periodicity of Laser‐Induced Surface Structures on Metals

AbstractLaser‐induced periodic surface structures (LIPSS) can be created on various materials, and they hold an exceptional potential for surface nanopatterning, enabling new industrial applications in medicine, biology, optics and other fields. However, LIPSS formation is typically restricted to a specific orientation and periodicity. In this work, a novel approach is demonstrated for full control of the LIPSS periodicity and orientation on metallic surfaces using a 1064 nm nanosecond laser. Analytical expressions and experimental verification are presented to show that by simultaneously manipulating three parameters of the laser beam, such as the polarization, angle of incidence, and direction of the laser scan along the surface, LIPSS can be formed with the desired geometrical configuration. This enhanced control opens vast possibilities for laser processing technologies as a flexible and highly competitive solution for advanced applications relying on surface modifications in the fields of anisotropic surface wettability, thermal and electrical conductivity, structured colors, diffraction gratings, and many others.

Corrosion-Resistant Polymer Composite Tubes with Enhanced Thermal Conductivity for Heat Exchangers

The heat transfer surfaces of heat exchangers are usually made of metals which may suffer from severe corrosion. When corrosive fluids are present, highly corrosion-resistant metals, graphite or ceramics are used, resulting in high costs. This study presents measured data on the thermophysical and mechanical properties of recently developed corrosion-resistant polymer composite tubes for use in heat exchangers. Extruded polymer composite tubes based on polypropylene or polyphenylene sulfide filled with graphite flakes were investigated. The anisotropic thermal conductivities of the polymer composite tubes were measured at various temperatures. The through-wall thermal conductivity of the tubes made of polypropylene filled with 50 vol.% graphite is increased by a factor of 30 compared to pure polypropylene, resulting in a thermal conductivity of 6.5 W/(m K) at 25 °C. The tubes composed of polyphenylene sulfide filled with 50 vol.% graphite have a through-wall thermal conductivity of 4.5 W/(m K) at 25 °C. The mechanical properties of the polymer composites were measured using tensile and flexural tests at different temperatures. The composite materials are more rigid and keep their mechanical properties up to a higher temperature level compared to the unfilled polymers. Surface roughness measurements show the very smooth and sealed surface of the composite tubes. The results contribute to establishing the viability of using polymer composites for heat exchanger applications with corrosive fluids.

First-principles calculations of the elastic anisotropy, thermal conductivity, and optical properties of MAX-phase M2AlC (M = V, Nb, Ta) series carbides

Materials from the MAX phase, such as the M2AlC (M = V, Nb, Ta) series carbides, exhibit superior mechanical, electronic, and thermodynamic properties, making them highly promising for research. Density functional theory (DFT) has been employed to study the elastic anisotropy, thermal conductivity, electronic, and optical properties of these carbides. The results indicate that the formation enthalpies of the M2AlC (M = V, Nb, Ta) series are negative and the phonon spectra do not exhibit imaginary frequencies, confirming the thermodynamic and dynamic stability of these carbides. Additionally, the calculated Poisson's ratios and B/G ratios suggest that these materials are brittle and contain covalent and ionic bonds—a conclusion further corroborated by analyses of electronic structures. The elastic anisotropy is illustrated through anisotropy indices, three-dimensional (3D) surface configurations, and two-dimensional (2D) projections, with the sequence of anisotropy being: Nb2AlC > Ta2AlC > V2AlC. Further investigations into the sound velocities, Debye temperature, anisotropy of sound velocity, thermal conductivity, and optical properties of the M2AlC (M = V, Nb, Ta) series provide substantial theoretical support for the research on MAX phase M2AlC (M = V, Nb, Ta) series carbides.

A simple, effective and high-precision boundary meshfree method for solving 2D anisotropic heat conduction problems with complex boundaries

A simple, effective and high-precision boundary meshfree method called virtual boundary meshfree Galerkin method (VBMGM) is used to tackle 2D anisotropic heat conduction problems with complex boundaries. Temperature and heat flux are expressed by virtual boundary element method. The virtual source function is constructed through the utilization of radial basis function interpolation. Calculation model diagram and discrete model diagram of real boundaries, and schematic diagram of VBMGM are demonstrated. Using Galekin method and considering boundary conditions, the integral equation and the discrete formula of VBMGM are given in detail. The benefits of the Galerkin, meshfree, and boundary element methods are all presented in VBMGM. Seven numerical examples of general anisotropic heat conduction problems (including three numerical examples with complex boundaries and four numerical examples with mixed boundary conditions) are computed and contrasted with precise solutions and different numerical methods. The computation time of each example is given. The number of degrees of freedom used in many examples is half or less than that of the numerical method being compared. The suggested method has been demonstrated to be effective and high-precision for solving the 2D anisotropic heat conduction problems with complex boundaries.

Bio‐inspired graphene oxide/epoxy coating with ordered stacking for anticorrosion/wear protection of Mg alloy

AbstractThe random arrangement of graphene oxide (GO) nanosheets within the organic coating forms a conductive network, thereby accelerating galvanic corrosion and exacerbating metal deterioration. Inspired by ordered layered structure of natural nacre, this study has successfully fabricated a biomimetic GO/epoxy coating on Mg alloy to prevent corrosion and reduce wear. By polymerizing polyaniline (PANI) and dopamine (PDA) on the GO, GO/PANI/PDA sheets with good dispersibility and impermeability are obtained. Subsequently, the bio‐inspired coating (I‐GO/PANI/PDA‐WEP) with “nacre‐like” structure is prepared via alternately spraying GO/PANI/PDA layers with epoxy layers. The anisotropic electrical conductivity of the coating is derived from the ordered distribution of GO/PANI/PDA layers to the Mg substrate, which can conduct electricity more efficiently in‐plane while suppressing longitudinal electron transport. The enhanced physical barrier effect by the “nacre‐like” structure and the electron suppression effect can improve anticorrosion performance. The coating reduces the corrosion rate by 6.3 × 105 times in comparison to Mg alloy. Moreover, this coating shows excellent wear resistance, which protects Mg alloy from friction and wear with a reduction in wear rate by approximately 96%. This bio‐inspired approach offers a unique strategy for fabricating GO composite coatings with exceptional performance.Highlights The corrosion/wear resistance of I‐GO/PANI/PDA has greatly improved. GO/PANI/PDA coating exhibits excellent anisotropic conductivity. Galvanic corrosion is inhibited due to the addition of GO/PANI/PDA. “Nacre‐like” structure shows high labyrinth effect. The ordered orientation of GO/PANI/PDA suppresses out‐plane electron transport.

Fluctuation-induced piezomagnetism in local moment altermagnets

It was recently discovered that, depending on their symmetries, collinear antiferromagnets may break spin degeneracy in momentum space, even in the absence of spin-orbit coupling. Such systems, dubbed altermagnets, have electronic bands with a spin-momentum texture set mainly by the combined crystal-magnetic symmetry. This discovery motivates the question of which novel physical properties derive from altermagnetic order. Here we show that one consequence of altermagnetic order is a fluctuation-driven piezomagnetic response. Using two Heisenberg models of d-wave altermagnets, a checkerboard one and one for rutiles, we determine the fluctuation-induced piezomagnetic coefficients considering temperature-induced transversal spin fluctuations. We establish in addition that magnetic fluctuations induce an anisotropic thermal spin conductivity. Published by the American Physical Society 2024

Thermal spreading in a multilayer geometry with convective cooling along the side wall of each layer

Two-dimensional thermal conduction between a source/sink and a body of larger size results in thermal spreading and constriction, which are of much technological importance in problems such as semiconductor thermal management. While the traditional analysis of thermal spreading and constriction assumed adiabatic side walls, there is growing interest in convective heat removal from the side walls, such as in multilayer three-dimensional integrated circuits (3D ICs) and stacked Li-ion cells in a battery pack. This work presents theoretical analysis of thermal spreading in a multilayer body with distinct convective heat transfer coefficients along the side wall for each layer, in addition to anisotropic thermal conductivity in each layer and thermal contact resistance at interfaces between layers. A series solution for the temperature distributions in each layer is derived, with a unique set of eigenvalues for each layer. A set of linear algebraic equations that govern the coefficients of the series solutions is derived. Results are shown to agree well with past work for special cases, as well as with numerical simulations for general problems. The impact of source size, thermal anisotropy and Biot numbers of various layers is analyzed in detail. In particular, the interplay between Biot numbers along the sidewall and at the sink plane in determining total thermal resistance is investigated in detail. This work contributes towards a fundamental understanding of theoretical thermal conduction in problems of practical relevance, such as advanced microelectronics and Li-ion cells. Results may find application in the design and optimization of these and other engineering systems where thermal spreading or constriction play an important role.

Impact of anisotropic conduction and premature atrial contraction on the fractionated atrial potentials

AbstractBackgroundFractionated atrial potential (FAP) during sinus rhythm (SR) may be a new target for ablation of atrial fibrillation (AF). However, the effects of the direction of activation and premature atrial contraction (PAC) on FAP is unknown. Therefore, we examined the impact of anisotropic conduction and PAC on the distribution and areas of FAP.MethodsFAP map in the left atrium was created in 40 patients with AF before ablation. The distribution and areas of FAP were compared during SR, distal coronary sinus (CS) pacing (S1) and extrastimulus (S2), and paced PAC after SR. FAP was defined as a potential with four or more fragmented deflections.ResultsFAPs during SR were found in the right and mid‐anterior walls and septum in most patients. During S1 compared to SR, FAPs significantly decreased in the right and mid‐anterior walls, appendage, septum, and right inferior wall, while significantly increased in the lateral wall. During S2 compared to S1, FAPs significantly increased in the mid anterior and right and mid posterior walls. During PAC compared to SR, FAPs significantly decreased in the right and mid anterior walls and roof, while significantly increased in the left anterior, left inferior and lateral walls. A rotational activation pattern at the FAP area during CS pacing was observed in 12 patients (30%), mostly in the left inferior wall.ConclusionsThe distribution and areas of FAP vary with anisotropic conduction and extrastimulus. Therefore, FAP should be evaluated not only during SR but also during extrastimulus from the distal CS.