The horizontal dashed line is representative of the thermal conductivity of neat epoxy (Moisala et al. 2006). 44 Figure 2-11: Thermal circuit diagram for steady-state DC thermal bridge measurement setup.
Introduction
Effective Medium Approximations
As a result, numerous models have been developed to estimate the thermal conductivity of the composite systems. Here κc, κm and κf are the thermal conductivity of the composite material, polymer medium and filler, respectively, and φ is the volume fraction of the filler material.
Thermal Boundary Resistance
Plots illustrating the effects of the non-dimensional parameter α on the thermal conductivity of a theoretical zinc sulfide-diamond composite material for both the updated Maxwell Garnett and Bruggeman models are shown in Figure 1-5a and 1-5b, respectively (Every et al. 1992). In addition to providing useful insight into the relative effects of decreasing filler diameter, it should be noted that if the thermal conductivities of the filler, matrix, and composite material are known, the only remaining unknown in both the Maxwell Garnett and Bruggeman models is the nondimensional parameter a.
Thermal Boundary Resistance in Polymer Nanocomposites
- Nanotube Composites
- Two Dimensional and Layered Materials
- Metallic Nanofillers
- Binary Filler Systems
Nevertheless, certain metallic nanofillers have demonstrated significant ability to improve the thermal conductivity of polymer composites. Similarly, the thermal conductivity of the epoxy-BNNS-BNNT composite outperformed both an epoxy-BNNS and an epoxy-BNNT composite at the same total filler volume fraction (Su et al. 2013).
Summary
Furthermore, EMA modeling suggests that both the lower thermal boundary resistance and the larger geometric dimensions of AgNWs may contribute to a much greater improvement in the thermal transport properties of AgNW composites compared to base composites. CNT. Thermal measurements of the bulk thin films demonstrate a significant improvement in the in-plane thermal transport properties and provide further evidence that silver is able to bond effectively to the polymeric matrix material.
Sample Preparation and Experimental Setup
Suspended, Micro-Fabricated Thermal Bridge Approach
- Measurement Devices
- Sample Transfer
- Measurement Setup
- Effects of Radiation Shields
- Background Thermal Conductance and Calculation
A portion of this heat, Q2, passes through the sample, bridging the suspended membranes and raising the temperature of the sensing side membrane. Finally, the temperature rise on the touch side can be calculated according to Eq. The difference between the measured temperature on the DIP and the set temperature is depicted in Figure 2-7c.
Another important consideration in improving the resolution of the microdevice for thermal measurements is the background thermal conduction between the suspended membranes and the support beams.
Steady-State DC Thermal Bridge Approach
- Experimental Setup
- Radiation Effects
- Measurement Validation
- Sample Preparation
This change in the output AC voltages of the lock-in amplifier is monitored by. Figure 2-11 shows a thermal circuit diagram for the steady-state DC thermal bridge measurement scheme. Because of this, it is important to determine the contributions of the metal layer to the measured thermal conductivity of the thin film assembly according to Eq.
4𝜅𝑠𝑡 is less than ~0.015 to ensure that radiation losses do not exceed 10% of the thermal conduction through the sample.
Summary
This is small compared to the ∼200 Ω measured for the gold heater film deposited on the suspended, composite samples.
Contact Thermal Resistance Between Silver Nanowires with
Sample Preparation and Measurement Method
Previous studies have shown that electric field strength plays a key role in the thermal conductivity of electrospun polymer nanofibers (Ma et al. 2015, Zhang et al. 2018), so the electrospinning voltage was fixed at 20 kV. After placing the AgNWs of interest, we dropped a small amount of reagent alcohol on each membrane to completely cover the nanowires, as the alcohol evaporation process could help the nanowires to be in close contact with the measuring device and thus reduce the contact resistance (Yang et al. 2012 , Yang et al. 2017). To transfer these composite wires into a thermal measurement microdevice, a drop of PVP-AgNW-ethanol solution was cast onto a piece of PDMS.
In this setup, a Wheatstone bridge circuit is used to cancel the baseline cryostat temperature fluctuation, allowing a thermal conductivity measurement resolution of 85 pW/K at room temperature with the selected instrument settings (Wingert et al. 2012).
Polyvinylpyrrolidone (PVP) Thermal Conductivity
The background thermal conductivity between the suspended membranes is measured and subtracted from the total thermal conductivity to further increase the accuracy of the measurements. However, it has been shown that for polymers with high molecular weight side groups or large degrees of asymmetry, the effect of chain alignment on the thermal conductivity of electrospun nanofibers is negatively affected (Zhang et al. 2018). Due to the heavy and complex side group of PVP (Figure 3-2b), the effect of electrospinning on its thermal conductivity is marginal, and the measured thermal conductivity of PVP nanofibers is treated as the value for PVP in all calculations, regardless of what form the polymer is in.
Bare Silver Nanowire Thermal Conductivity
To reduce the contact resistance between the AgNW sample and the suspended membranes, EBID of Pt/C was performed on the wire-membrane contacts, and Figure 3-3b shows the extracted thermal conductivity of a bare 89 nm AgNW after one and two rounds of EBID. The good agreement of the extracted thermal conductivity indicates that the thermal contact resistance becomes negligible compared to the intrinsic resistance of the nanowires (Hochbaum et al. 2008). The measured thermal conductivity after the first and second rounds of EBID largely overlaps (with <2% difference).
By demonstrating that the thermal contact resistance for bare AgNWs is reduced to a negligible level, the measured thermal conductivities of bare AgNWs are treated as intrinsic properties of the nanowires and used directly in determining the contact resistance for AgNWs coated with PVP as discussed in the next section.
Contact Thermal Resistance between PVP-Coated AgNWs
Here, Rt,s and Rt,c denote the measured total thermal resistance of the single continuous wire and the contact sample, respectively. Rw,s and Rw,c represent the intrinsic resistance of the nanowire in the continuous wire and the contact sample, respectively. Now the contact width of the 84 nm diameter wire is 58 nm and using the intrinsic thermal conductivity of AgNWs from Zhao et al.'s measurement, Lc,min is estimated to be 2.03 µm.
However, for the 91 nm sample, the two AgNW segments in the contact sample are slightly longer than for the continuous sample, 29 µm versus 27 m.
Effective Medium Approximation (EMA) Model
This difference in thermal boundary resistance in the polymer–AgNW and polymer–CNT composites may contribute to an improved thermal conductivity enhancement. Interestingly, despite the lower thermal conductivity used for silver, AgNW-PVP composites drastically outperform previously measured CNT composites, and as shown by the red shaded region in Figure 3-12, the uncertainty associated with the calculation of 𝑅𝑖′′ has a limiting effect on the predicted increase in their thermal conductivity. Here the shaded region corresponds to that of Figure 3-11 and represents the upper and lower bounds of the EMA forecasts.
An examination of the model parameters shows that the larger d and L of AgNW (84 nm and 80 µm, respectively) and the relatively lower 𝑅𝑖′′ correspond to a higher equivalent heat of the filler.
Summary
As a result, considerable efforts have been made to improve the thermal performance of bulk polymer structures, often by introducing fillers with high thermal conductivity into a polymer matrix. In particular, metallic nanofillers whose transport properties are dominated by the flow of electrons have shown considerable promise in improving the thermal conductivity of polymer composites. In light of these interesting results, this chapter reports on measurements of the thermal conductivity of bulk, PVP-AgNW composite films prepared using a layered approach.
As a result of this alignment and the low thermal boundary resistance that exists at the PVP-AgNW boundary, the resulting composite films were measured to have an in-plane thermal conductivity as high as 27 W m-1 K-1.
Composite Thin Film Fabrication
A single layer is insulated, and a mister spray bottle is used to gently coat and partially dissolve the top surface of the composite layer. In both cases, once a layer is isolated to serve as the composite base, a spray bottle is used to apply a small amount of ethanol to the surface of the base layer. This is mainly achieved because the length of the AgNW fillers (40 µm) is significantly larger than the individual composite layer thickness (~10 µm).
The enlarged images show the residual effects of the PVP welding and demonstrate the degree of AgNW alignment with respect to the in-plane direction.
Measurement Details
Finally, the thermal conductivity of the samples, κs, including the combined thermal conductivity of the layered composite, insulating PVP layer and gold heater layer can be determined according to Eq. To accurately quantify the thermal conductivity of the samples, it is important to consider the effects of the contact thermal resistance that exists between the sample and sample container. The contact conductance per unit area, h, can be estimated from the reported thermal conductivity of the paste as ℎ = ( 𝑡 . 15.7)−1 where t is the thickness of the contact layer.
Here, a simple parallel model can be used to calculate the thermal conductivity of the composite according to 𝜅𝑐 = 𝜅𝑠− 𝐴𝑟𝜅𝑃𝑉𝑃.
Thin Film Thermal Conductivity
For composite structures it has been shown that the effects of thermal boundary resistance on thermal conductivity are proportional to the dimensions of the filler (Every et al. 1992). As α decreases, it can be shown that the effects of thermal boundary resistance on thermal transport also decrease, resulting in a higher composition of thermal conductivity (Every et al. 1992). This would further reduce the magnitude of α and allow an increase in the thermal conductivity of the composite film.
Finally, since the AgNWs are aligned in the in-plane direction, the thermal conductivity of the composite films is expected to exhibit a similar degree of anisotropy.
Binary Filler Composites
The measured thermal conductivity of the PVP-AgNW-FWCNT is plotted in Figure 4-7 and compared with the thermal conductivity measured for the PVP-AgNW composite films. However, despite the exceptionally high thermal conductivity of CNTs, adding an equal volume of AgNWs and FWCNTs to a composite film resulted in a ∼55% decrease in the measured thermal conductivity relative to the composite containing only AgNWs. However, in the binary PVP-AgNW-FWCNT composite, the FWCNTs contributed to a disproportionate reduction in the measured thermal conductivity compared to a composite containing only AgNWs.
This suggests that, in addition to not being able to contribute significantly to the enhancement of the thermal conductivity of the binary composite, the FWCNTs also interfere with thermal transport through the embedded AgNW network.
Summary
Tunable Young’s Modulus and Reactive Ion Etching Rates for
- Experimental Details
- Young’s Modulus Measurements
- Etch Rate Characterization
- Relevance to Practical Applications
- Summary
The dependence of Young's modulus on the curing time is straightforward based on the above understanding. The etch rate shows an inverse dependence on the weight ratio of prepolymer to curing agent and curing time in relation to Young's Modulus. In fact, comparison of Figure 5-3 and Figure 5-4 suggests that the etch rate shows an exact opposite trend from Young's modulus as a function of mix ratio and cure time.
An established relationship between etch rate and Young's modulus of PDMS would allow better tuning of the RIE etching process.
Summary
Enhancing the thermal conductivity of polymer composites by reducing the thermal boundary resistance between boron nitride nanotubes. Measurement of the intrinsic thermal conductivity of a multi-walled carbon nanotube and its thermal contact resistance with the substrate. Several features of electron-phonon coupling observed in the lattice thermal conductivity of NbSe3 nanowires.
The thermal conductivity of the measured samples is given by Eq. 3.5) and depends on the dimensions of the sample (L and A), the sensitivity of the device to the applied power (I and V) and the electrical properties of the gold heater layer (β, R0 and Rm).
