Archival Journals Publications

2013
M. M. Sadeghi, Jo, I., and Shi, L., “Phonon-Interface Scattering in Multi-layered Graphene on an Amorphous Support,” Proceedings of the National Academy of Sciences, vol. 110, pp. 16321–16326, 2013. LinkAbstract
The recent studies of thermal transport in suspended, supported, and encased graphene just began to uncover the richness of two-dimensional phonon physics, which is relevant to the performance and reliability of graphene-based functional materials and devices. Among the outstanding questions are the exact causes of the suppressed basal-plane thermal conductivity measured in graphene in contact with an amorphous material, and the layer thickness needed for supported or embedded multilayer graphene (MLG) to recover the high thermal conductivity of graphite. Here we use sensitive in-plane thermal transport measurements of graphene samples on amorphous silicon dioxide to show that full recovery to the thermal conductivity of the natural graphite source has yet to occur even after the MLG thickness is increased to 34 layers, considerably thicker than previously thought. This seemingly surprising finding is explained by long intrinsic scattering mean free paths of phonons in graphite along both basal-plane and cross-plane directions, as well as partially diffuse scattering of MLG phonons by the MLG-amorphous support interface, which is treated by an interface scattering model developed for highly anisotropic materials. Based on the phonon transmission coefficient calculated from reported experimental thermal interface conductance results, phonons emerging from the interface consist of a large component that is scattered across the interface, making rational choice of the support materials a potential approach to increasing the thermal conductivity of supported MLG.
A. Weathers, Bi, K. D., Pettes, M. T., and Shi, L., “Reexamination of Thermal Transport Measurements of a Low-Thermal Conductance Nanowire with a Suspended Micro-Device,” Review of Scientific Instruments, vol. 84, pp. 084903, 2013. LinkAbstract
An increasingly used technique for measuring the thermal conductance of a nanowire is based on a suspended micro-device with built-in resistance thermometers. In the past, the technique has been limited to samples with thermal conductance larger than 1 × 10−9 W/K because of temperature fluctuations in the sample environment and the presence of background heat transfer through residual gas molecules and radiation between the two thermometers. In addition, parasitic heat loss from the long supporting beams and asymmetry in the fabricated device results in two additional errors, which have been ignored in previous use of this method. To address these issues, we present a comprehensive measurement approach, where the device asymmetry is determined by conducting thermal measurements with two opposite heat flow directions along the nanowire, the background heat transfer is eliminated by measuring the differential heat transfer signal between the nanowire device and a reference device without a nanowire sample, and the parasitic heat loss from the supporting beams is obtained by measuring the average temperature rise of one of the beams. This technique is demonstrated on a nanofiber sample with a thermal conductance of 3.7 × 10−10 W/K, against a background conductance of 8.2 × 10−10 W/K at 320 K temperature. The results reveal the need to reduce the background thermal conductance in order to employ the micro-device to measure a nanowire sample with the thermal conductance less than 1 × 10−10 W/K.
P. Jurney, Agarwal, R., Singh, V., Roy, K., Sreenivasan, S. V., and Shi, L., “Size-Dependent Nanoparticle Margination and Adhesion Propensity in a Microchannel,” Journal of Nanotechnology in Engineering and Medicine, vol. 4, no. 3, pp. 031002, 2013. LinkAbstract
Intravenous injection of nanoparticles as drug delivery vehicles is a common practice in clinical trials of therapeutic agents to target specific cancerous or pathogenic sites. The vascular flow dynamics of nanocarriers (NCs) in human microcapillaries play an important role in the ultimate efficacy of this drug delivery method. This article reports an experimental study of the effect of nanoparticle size on their margination and adhesion propensity in microfluidic channels of a half-elliptical cross section. Spherical polystyrene particles ranging in diameter from 60 to 970 nm were flown in the microchannels and individual particles adhered to either the top or bottom wall of the channel were imaged using fluorescence microscopy. When the number concentration of particles in the flow was kept constant, the percentage of nanoparticles adhered to the top wall increased with decreasing diameter (d), with the number of particles adhered to the top wall following a d−3 trend. When the volume concentration of particles in solution was kept constant, no discernible trend was found. This experimental finding is explained by the competition between the Brownian force promoting margination and repulsive particle–particle electrostatic forces retarding adhesion to the wall. The 970 nm particles were found to adhere to the bottom wall much more than to the top wall for each of the three physiologically relevant shear rates tested, revealing the effect of gravitational force on the large particles. These findings on the flow behavior of spherical nanoparticles in artificial microcapillaries provide further insight for the rational design of NCs for targeted cancer therapeutics.
K. Davami, Weathers, A., Kheirabi, N., Mortazavi, B., Pettes, M. T., Shi, L., Lee, J. S., and Meyyappan, M., “Thermal Conductivity of ZnTe Nanowires,” Journal of Applied Physics, vol. 114, pp. 134314, 2013. LinkAbstract
The thermal conductivity of individual ZnTe nanowires (NWs) was measured using a suspended micro-bridge device with built-in resistance thermometers. A collection of NWs with different diameters were measured, and strong size-dependent thermal conductivity was observed in these NWs. Compared to bulk ZnTe, NWs with diameters of 280 and 107 nm showed approximately three and ten times reduction in thermal conductivity, respectively. Such a reduction can be attributed to phonon-surface scattering. The contact thermal resistance and the intrinsic thermal conductivities of the nanowires were obtained through a combination of experiments and molecular dynamic simulations. The obtained thermal conductivities agree well with theoretical predictions.
E. Fleming, Wen, S., Shi, L., and da Silva, A. K., “Thermodynamic Model of a Thermal Storage Air Conditioning System with Dynamic Behavior,” Applied Energy, vol. 112, pp. 160–169, 2013. LinkAbstract
Highlights •We developed an automotive thermal storage air conditioning system model. •The thermal storage unit utilizes phase change materials. •We use semi-analytic solution to the coupled phase change and forced convection. •We model the airside heat exchange using the NTU method. •The system model can incorporate dynamic inputs, e.g. variable inlet airflow. A thermodynamic model was developed to predict transient behavior of a thermal storage system, using phase change materials (PCMs), for a novel electric vehicle climate conditioning application. The main objectives of the paper are to consider the system’s dynamic behavior, such as a dynamic air flow rate into the vehicle’s cabin, and to characterize the transient heat transfer process between the thermal storage unit and the vehicle’s cabin, while still maintaining accurate solution to the complex phase change heat transfer. The system studied consists of a heat transfer fluid circulating between either of the on-board hot and cold thermal storage units, which we refer to as thermal batteries, and a liquid–air heat exchanger that provides heat exchange with the incoming air to the vehicle cabin. Each thermal battery is a shell-and-tube configuration where a heat transfer fluid flows through parallel tubes, which are surrounded by PCM within a larger shell. The system model incorporates computationally inexpensive semi-analytic solution to the conjugated laminar forced convection and phase change problem within the battery and accounts for airside heat exchange using the Number of Transfer Units (NTUs) method for the liquid–air heat exchanger. Using this approach, we are able to obtain an accurate solution to the complex heat transfer problem within the battery while also incorporating the impact of the airside heat transfer on the overall system performance. The implemented model was benchmarked against a numerical study for a melting process and against full system experimental data for solidification using paraffin wax as the PCM. Through modeling, we demonstrate the importance of capturing the airside heat exchange impact on system performance, and we investigate system response to dynamic operating conditions, e.g., air recirculation.
2012
C. Baker, Vuppuluri, P., Shi, L., and Hall, M. J., “Model of Heat Exchangers for Waste Heat Recovery from Diesel Engine Exhaust for Thermoelectric Power Generation,” Journal of Electronic Materials , vol. 41, pp. 1290–1297, 2012. LinkAbstract
The performance and operating characteristics of a hypothetical thermoelectric generator system designed to extract waste heat from the exhaust of a medium-duty turbocharged diesel engine were modeled. The finite-difference model consisted of two integrated submodels: a heat exchanger model and a thermoelectric device model. The heat exchanger model specified a rectangular cross-sectional geometry with liquid coolant on the cold side, and accounted for the difference between the heat transfer rate from the exhaust and that to the coolant. With the spatial variation of the thermoelectric properties accounted for, the thermoelectric device model calculated the hot-side and cold-side heat flux for the temperature boundary conditions given for the thermoelectric elements, iterating until temperature and heat flux boundary conditions satisfied the convection conditions for both exhaust and coolant, and heat transfer in the thermoelectric device. A downhill simplex method was used to optimize the parameters that affected the electrical power output, including the thermoelectric leg height, thermoelectric n-type to p-type leg area ratio, thermoelectric leg area to void area ratio, load electrical resistance, exhaust duct height, coolant duct height, fin spacing in the exhaust duct, location in the engine exhaust system, and number of flow paths within the constrained package volume. The calculation results showed that the configuration with 32 straight fins was optimal across the 30-cm-wide duct for the case of a single duct with total height of 5.5 cm. In addition, three counterflow parallel ducts or flow paths were found to be an optimum number for the given size constraint of 5.5 cm total height, and parallel ducts with counterflow were a better configuration than serpentine flow. Based on the reported thermoelectric properties of MnSi1.75 and Mg2Si0.5Sn0.5, the maximum net electrical power achieved for the three parallel flow paths in a counterflow arrangement was 1.06 kW for package volume of 16.5 L and exhaust flow enthalpy flux of 122 kW.
R. Agarwal, Singh, V., Jurney, P., Shi, L., Sreenivasan, S. V., and Roy, K., “Scalable Imprinting of Shape-Specific Polymeric Nanocarriers using a Release Layer of Switchable Water Solubility,” ACS Nano, vol. 6, no. 3, pp. 2524–2531, 2012. LinkAbstract
There is increasing interest in fabricating shape-specific polymeric nano- and microparticles for efficient delivery of drugs and imaging agents. The size and shape of these particles could significantly influence their transport properties and play an important role in in vivo biodistribution, targeting, and cellular uptake. Nanoimprint lithography methods, such as jet-and-flash imprint lithography (J-FIL), provide versatile top-down processes to fabricate shape-specific, biocompatible nanoscale hydrogels that can deliver therapeutic and diagnostic molecules in response to disease-specific cues. However, the key challenges in top-down fabrication of such nanocarriers are scalable imprinting with biological and biocompatible materials, ease of particle-surface modification using both aqueous and organic chemistry as well as simple yet biocompatible harvesting. Here we report that a biopolymer-based sacrificial release layer in combination with improved nanocarrier-material formulation can address these challenges. The sacrificial layer improves scalability and ease of imprint-surface modification due to its switchable solubility through simple ion exchange between monovalent and divalent cations. This process enables large-scale bionanoimprinting and efficient, one-step harvesting of hydrogel nanoparticles in both water- and organic-based imprint solutions.
L. Shi, “Thermal and Thermoelectric Transport in Nanostructures and Low-Dimensional Systems,” Nanoscale and Microscale Thermophysical Engineering, vol. 16, pp. 79–116, 2012. LinkAbstract
Significant progress has been made in recent studies of thermal and thermoelectric transport phenomena in nanostructures and low-dimensional systems. This article reviews several intriguing quantum and classical size effects on thermal and thermoelectric properties that have been predicted by theoretical calculations or observed in experiments. Attention is focused on the Casimir limit in phonon boundary scattering and the effect of phonon confinement on the lattice thermal conductivity of semiconductor nanowires (NWs) and nanomeshes; the effects of thickness, lateral size, and interface interaction on the lattice thermal conductivity of carbon nanotubes (CNTs) and graphene; and the phonon-drag thermopower and quantum size effects on the thermoelectric power factor in semiconductor NWs. Further experimental and theoretical investigations are suggested for better understanding of some of these nanoscale transport phenomena.
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M. M. Sadeghi, Pettes, M. T., and Shi, L., “Thermal Transport in Graphene,” Solid State Communications, vol. 152, pp. 1321–1330, 2012. LinkAbstract
The recent advances in graphene isolation and synthesis methods have enabled potential applications of graphene in nanoelectronics and thermal management, and have offered a unique opportunity for investigation of phonon transport in two-dimensional materials. In this review, current understanding of phonon transport in graphene is discussed along with associated experimental and theoretical investigation techniques. Several theories and experiments have suggested that the absence of interlayer phonon scattering in suspended monolayer graphene can result in higher intrinsic basal plane thermal conductivity than that for graphite. However, accurate experimental thermal conductivity data of clean suspended graphene at different temperatures are still lacking. It is now known that contact of graphene with an amorphous solid or organic matrix can suppress phonon transport in graphene, although further efforts are needed to better quantify the relative roles of interface roughness scattering and phonon leakage across the interface and to examine the effects of other support materials. Moreover, opportunities remain to verify competing theories regarding mode specific scattering mechanisms and contributions to the total thermal conductivity of suspended and supported graphene, especially regarding the contribution from the flexural phonons. Several measurements have yielded consistent interface thermal conductance values between graphene and different dielectrics and metals. A challenge has remained in establishing a comprehensive theoretical model of coupled phonon and electron transport across the highly anisotropic and dissimilar interface.
M. T. Pettes, Ji, H. X., Ruoff, R. S., and Shi, L., “Thermal Transport in Three-Dimensional Foam Architectures of Few-Layer Graphene and Ultrathin Graphite,” Nano Letters, vol. 12, no. 6, pp. 2959–-2964, 2012. LinkAbstract
At a very low solid concentration of 0.45±0.09 vol %, the room-temperature thermal conductivity (κGF) of freestanding graphene-based foams (GF), comprised of few-layer graphene (FLG) and ultrathin graphite (UG) synthesized through the use of methane chemical vapor deposition on reticulated nickel foams, was increased from 0.26 to 1.7 W m–1 K–1 after the etchant for the sacrificial nickel support was changed from an aggressive hydrochloric acid solution to a slow ammonium persulfate etchant. In addition, κGF showed a quadratic dependence on temperature between 11 and 75 K and peaked at about 150 K, where the solid thermal conductivity (κG) of the FLG and UG constituents reached about 1600 W m–1 K–1, revealing the benefit of eliminating internal contact thermal resistance in the continuous GF structure.
X. Chen, Weathers, A., Moore, A. L., Zhou, J. S., and Shi, L., “Thermoelectric Properties of Cold-Pressed Higher Manganese Silicides for Waste Heat Recovery,” Journal of Electronic Materials, vol. 41, pp. 1564–1572, 2012. LinkAbstract
Polycrystalline higher manganese silicide (HMS) samples with different grain sizes have been obtained by cold-pressing HMS powder under high pressure of about 3 GPa and postprocessing annealing. It was found that the cold-pressing process can reduce the grain size of HMS to 120 nm. The cold-pressed pellets were then annealed at different temperatures to obtain a series of samples with different grain sizes. For comparison, an additional sample was prepared in a regular die under low pressure of 300 MPa, which resulted in lower density and higher porosity than the high-pressure process. For these samples, the effect of grain size and porosity on Seebeck coefficient was not as apparent as that on electrical conductivity and thermal conductivity. The electrical conductivity of the cold-pressed samples increases as the grains grow, and the grain boundary connection is improved during the postprocessing annealing. A significant reduction in the thermal conductivity of the cold-pressed samples was observed. The sample prepared with the low-pressure pressing shows the lowest thermal conductivity of 1.2 W m−1 K−1 at 300 K, which can be attributed to its high porosity of 34% and low phonon transmission coefficient through the grain boundaries. The low-temperature thermal conductivity data of all samples were analyzed to obtain the phonon transmission coefficient and the Kapitza resistance at the grain boundaries.
H. X. Ji, Zhang, L. L., Pettes, M. T., Li, H. F., Chen, S. S., Shi, L., Piner, R., and Ruoff, R. S., “"Ultra-Thin Graphite Foam: A Three-Dimensional Conductive Network for Battery Electrodes,” Nano Letters, vol. 12, pp. 2446–2451, 2012. LinkAbstract
We report the use of free-standing, lightweight, and highly conductive ultrathin graphite foam (UGF), loaded with lithium iron phosphate (LFP), as a cathode in a lithium ion battery. At a high charge/discharge current density of 1280 mA g–1, the specific capacity of the LFP loaded on UGF was 70 mAh g–1, while LFP loaded on Al foil failed. Accounting for the total mass of the electrode, the maximum specific capacity of the UGF/LFP cathode was 23% higher than that of the Al/LFP cathode and 170% higher than that of the Ni-foam/LFP cathode. Using UGF, both a higher rate capability and specific capacity can be achieved simultaneously, owing to its conductive (1.3 × 105 S m–1 at room temperature) and three-dimensional lightweight (9.5 mg cm–3) graphitic structure. Meanwhile, UGF presents excellent electrochemical stability comparing to that of Al and Ni foils, which are generally used as conductive substrates in lithium ion batteries. Moreover, preparation of the UGF electrode was facile, cost-effective, and compatible with various electrochemically active materials.
2011
I. K. Hsu, Pettes, M. T., Aykolc, M., Chang, C. C., Hung, W. H., Theiss, J., Shi, L., and Cronin, S. B., “Direct Observation of Heat Dissipation in Individual Suspended Carbon Nanotubes Using a Two-Laser Technique,” Journal of Applied Physics, vol. 110, pp. 044328, 2011. LinkAbstract
A two-laser technique is used to investigate heat spreading along individual single walled carbon nanotube(SWCNT) bundles in vacuum and air environments. A 532 nm laser focused on the center of a suspended SWCNT bundle is used as a local heat source, and a 633 nm laser is used to measure the spatial temperature profile along the SWCNT bundle by monitoring the G band downshifts in the Raman spectra. A constant temperature gradient is observed when the SWCNT bundle is irradiated in vacuum, giving direct evidence of diffusive transport of the phonons probed by the Raman laser. In air, however, we observe an exponentially decaying temperature profile with a decay length of about 7 μm, due to heat dissipation from the SWCNT bundle to the surrounding gas molecules. The thermal conductivity of the suspended carbon nanotube(CNT) is determined from its electrical heatingtemperature profile as measured in vacuum and the nanotube bundle diameter measured via transmission electron microscopy. Based on the exponential decay curves measured in three different CNTs in air, the heat transfer coefficient between the SWCNTs and the surrounding air molecules is found to range from 1.5 × 103 to 7.9 × 104 W/m2 K, which is smaller than the 1 × 105 W/m2 K thermal boundary conductance value calculated using the kinetic theory of gases. This measurement is insensitive to the thermal contact resistance, as no temperature drops occur at the ends of the nanotube. It is also insensitive to errors in the calibration of the G band temperature coefficient. The optical absorption is also obtained from these results and is on the order of 10−5.
A. L. Moore and Shi, L., “On Errors in Thermal Conductivity Measurements of Suspended and Supported Nanowires using Micro-thermometer Devices from Low to High Temperatures,” Measurement Science and Technology, vol. 22, pp. 015103, 2011. LinkAbstract
For micro-thermometer devices developed for thermal conductivity measurements of nanowires, it is found using finite element analysis that radiation heat transfer can cause nonlinear temperature profiles in the long supporting beams of the thermometers when the sample stage temperature is considerably higher or lower than room temperature. Although the nonlinearity alone does not introduce errors in the measured thermal conductance, it can cause errors in the measured temperature coefficient of resistance of the thermometers and needs to be minimized with additional radiation shields. For a design where the sample is supported on a silicon dioxide bridge between two micro-thermometers, the numerical analysis reveals that a two-dimensional temperature distribution can cause a 25% error in the sample thermal conductance obtained from a one-dimensional heat conduction analysis for a high-thermal-conductance thin film sample covering only the center part of the oxide bridge. This systematic error is reduced considerably for a low-thermal-conductance nanowire sample. However, care must be taken to ensure that the random uncertainties in the two measured thermal conductance values of the bridge with and without the nanowires are much smaller than the thermal conductance of the nanowires.
M. T. Pettes, Jo, I., Yao, Z., and Shi, L., “Influence of Polymeric Residue on the Thermal Conductivity of Suspended Bi-Layer Graphene,” Nano Letters, vol. 11, no. 3, pp. 1195–1200, 2011. LinkAbstract
The thermal conductivity (κ) of two bilayer graphene samples each suspended between two microresistance thermometers was measured to be 620 ± 80 and 560 ± 70 W m−1 K−1 at room temperature and exhibits a κ T1.5 behavior at temperatures (T) between 50 and 125 K. The lower κ than that calculated for suspended graphene along with the temperature dependence is attributed to scattering of phonons in the bilayer graphene by a residual polymeric layer that was clearly observed by transmission electron microscopy.
I. Jo, Hsu, I. K., Lee, Y. J., Sadeghi, M. M., Kim, S., Cronin, S., Tutuc, E., Banerjee, S. K., Z, Y., and Shi, L., “Low-Frequency Acoustic Phonon Temperature Distribution in Electrically Biased Graphene,” Nano Letters, vol. 11, pp. 85–90, 2011. LinkAbstract
On the basis of scanning thermal microscopy (SThM) measurements in contact and lift modes, the low-frequency acoustic phonon temperature in electrically biased, 6.7−9.7 μm long graphene channels is found to be in equilibrium with the anharmonic scattering temperature determined from the Raman 2D peak position. With 100 nm scale spatial resolution, the SThM reveals the shifting of local hot spots corresponding to low-carrier concentration regions with the bias and gate voltages in these much shorter samples than those exhibiting similar behaviors in the infrared emission maps.
A. J. Heltzel, Shi, L., and Howell, J. R., “Microsphere Coupler for a Nanowire Waveguide Plasmonic Probe for Molecular Imaging,” Nanotechnology, vol. 22, pp. 045203, 2011. LinkAbstract
Highly forward scattering of light by a silica microsphere is predicted by Mie theory. Finite-difference time-domain simulations are used to examine the use of a silica microsphere for coupling light into a ZnO nanowire terminated with a gold nanoparticle (NP) tip, intended for near-field imaging of single molecules immobilized on a gold substrate or gold nanoparticle-labeled cell membranes. The results show that plasmonic coupling at the Au tip is dependent on the incident angle of the excitation. Pre-conditioning the signal with the microsphere amplifies the coupling while reducing background energy levels, significantly boosting the signal-to-noise ratio.
S. S. Chen, Moore, A. L., Cai, W. W., Suk, J. W., An, J., Mishra, C., Amos, C., Magnuson, C., Kang, J., Shi, L., and Ruoff, R. S., “Raman Measurements of Thermal Transport in Suspended Monolayer Graphene of Variable Sizes in Vacuum and Gaseous Environments,” ACS Nano, vol. 5, no. 1, pp. 321–328, 2011. LinkAbstract
Using micro-Raman spectroscopy, the thermal conductivity of a graphene monolayer grown by chemical vapor deposition and suspended over holes with different diameters ranging from 2.9 to 9.7 μm was measured in vacuum, thereby eliminating errors caused by heat loss to the surrounding gas. The obtained thermal conductivity values of the suspended graphene range from (2.6 ± 0.9) to (3.1 ± 1.0) × 103 Wm−1K−1 near 350 K without showing the sample size dependence predicted for suspended, clean, and flat graphene crystal. The lack of sample size dependence is attributed to the relatively large measurement uncertainty as well as grain boundaries, wrinkles, defects, or polymeric residue that are possibly present in the measured samples. Moreover, from Raman measurements performed in air and CO2 gas environments near atmospheric pressure, the heat transfer coefficient for air and CO2 was determined and found to be (2.9 +5.1/−2.9) and (1.5 +4.2/−1.5) × 104 Wm−2K−1, respectively, when the graphene temperature was heated by the Raman laser to about 510 K.
M. C. Moore, Kang, M. K., Moore, Z., Singh, V., Sreenivasan, S. V., Shi, L., Huang, R., and Roy, K., “Swelling Behavior of Nanoscale Shape- and Size-specific Hydrogel Particles Fabricated using Imprint Lithography,” Soft Matter, vol. 7, pp. 2879–2887, 2011. LinkAbstract
Recently a number of hydrogel-based micro- and nanoscale drug carriers have been reported including top down fabricated, highly monodisperse nanoparticles of specific sizes and shapes. One critical question on such approaches is whether in vivo swelling of the nanoparticles could considerably alter their geometry to a point where the potential benefit of controlling size or shape could not be realized. Little has been reported on experimental characterization of the swelling behavior of nanoscale hydrogel structures, and current theoretical understanding is largely based on bulk hydrogel systems. Using atomic force microscopy (AFM) and environmental scanning electron microscopy (ESEM) capsules, we have characterized the swelling behavior of nano-imprinted hydrogel particles of different sizes and aspect ratios. Our results indicate a size-dependent swelling which can be attributed to the effect of substrate constraint of as-fabricated particles, when the particles are still attached to the imprinting substrate. Numerical simulations based on a recently developed field theory and a nonlinear finite element method were conducted to illustrate the constraint effect on swelling and drying behavior of substrate-supported hydrogel particles of specific geometries, and compared closely with experimental measurements. Further, we present a theoretical model that predicts the size-dependent swelling behavior for unconstrained sub-micron hydrogel particles due to the effect of surface tension. Both experimental and theoretical results suggest that hydrogel swelling does not significantly alter the shape and size of highly crosslinked nanoscale hydrogel particles used in the present study.
J. H. Seol, Moore, A. L., Jo, I., Yao, Z., and Shi, L., “Thermal Conductivity Measurement of Graphene Exfoliated on Silicon Dioxide,” Journal of Heat Transfer, vol. 133, pp. 022403, 2011. LinkAbstract
We have developed a nanofabricated resistance thermometer device to measure the thermal conductivity of graphene monolayers exfoliated onto silicon dioxide. The measurement results show that the thermal conductivity of the supported graphene is approximately 600 W/m K at room temperature. While this value is lower than the reported basal plane values for graphite and suspended graphene because of phonon leakage across the graphene-support interface, it is still considerably higher than the values for common thin film electronic materials. Here, we present a detailed discussion of the design and fabrication of the measurement device. Analytical and numerical heat transfer solutions are developed to evaluate the accuracy and uncertainty of this method for thermal conductivity measurement of high-thermal conductivity ultrathin films.

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