Introduction
Introduction to transient grating spectroscopy
Fundamentals
An example of confirming the lattice period of the deionized (DI) water is illustrated in Fig. Figure 2.2B shows the measured frequency of the oscillation versus the grating period on the sample, which agrees with the calculation from Equation 2.8.
Signal monitoring via heterodyne detection
Note that the attenuation factor is determined by the optical density (OD) of the ND filter. Another advantage of the heterodyne signal is the presence of an attenuation factor (𝑡𝑟) in the heterodyne signal.
Thermal signal traces and fitting
The attenuation factor significantly increases the signal-to-noise ratio while not saturating the detector. 2.29). First, the initial signal magnitude is linearly proportional to the injected optical energy, which is related to the transition temperature of the sample.
TG arrangements
A representative TG signal trace for crystalline silicon measured at 𝐿 = 8.3 𝜇m (A) The signals at each heterodyne phase. The corresponding value of the thermal conductivity for a 1 𝜇m thick membrane agrees with the literature data given in Fig.2.5B.
Summary
All glassy materials show that the thermal conductivity trend decreases monotonically with decreasing temperature. The cylindrical conduction resistance is 𝑅 =ln(𝑟2/𝑟1)/(2𝜋 𝜅 𝑑)where𝜅 is the thermal conductivity of the membrane.
In-plane elastic and thermal properties of Molybdenum disulfide 21
Ultrafast transient grating
Also, free focusing from the third lens significantly reduces the risk of non-linear optical effect compared to tight focusing. This is mainly caused by the effect of the combination of non-idealities in the phase mask and optics that were used.
Material: Molybdenum disulfide
We obtain the frequency of the oscillation by performing both the Fourier transform and the sinusoidal curve fitting. Silicon-on-insulator (SOI) wafers were wet etched to create rectangular openings approximately 1 - 2 mm in size on the device side of the wafer.
TG experiments on MoS 2
The measured frequency of oscillation can be related to the elastic properties of the MoS2. To illustrate this, the literature data of the ab-initio calculation of the in-plane phonon distribution in Ref.
Summary
With temperature, the thermal conductivity exhibits a monotonic increase, characteristic of the phonon domain boundary scattering. The dotted (solid) lines correspond to the calculation using 95 % credible interval (mean) of the MFP distribution described in the main text. The grating period dependence of the thermal conductivity provides constraints on the frequency dependence of the MFPs from sub-THz excitations.
Heat-carrying phonons with micron-scale mean free paths in
Background
Various methods have been employed to understand the origin of the increased thermal conductivity in aligned polymers. Consequently, the microscopic properties of heat-carrying phonons and the origin of the high thermal conductivity of highly oriented polyethylene remain a subject of debate. The mean free paths exceed those in smaller draw ratio samples by an order of magnitude, indicating that the high thermal conductivity of the present samples mainly results from reduced structural scattering in the crystalline phase.
Bulk thermal property of PE
Since the purpose of the drawing is to make the fiber oriented in a certain direction, we characterized the fiber alignment using scanning electron microscope (SEM) and helium-ion microscope (HIM). For comparison, an SEM image of partially oriented sample (DR7.5 with ZnO nanoparticles) is shown in Fig. 4.2, where we do not see obvious alignment of the fibers. As mentioned in the previous chapter, it is important to avoid surface instability when applying TG to thin films.
TG application on highly oriented PE
Corresponding ratio between the thermal conductivity (𝜅k/𝜅⊥) is shown in Fig.4.6B. The𝜅⊥ decreases and approaches the bulk value as the draw ratio increases, which is attributed to the heat conduction by interchain van der Waals interactions as in bulk [129]. First, the thermal conductivity versus temperature for two samples with similar DRs is shown in Fig.4.7AB. Thermal conductivity along the chain versus temperature at a lattice period 𝐿 = 9.8 𝜇𝑚. The thermal conductivity was calculated using reported heat capacities for linear PE in Ref. 135].
Grating period dependent thermal conductivity
The measured decay rate is close to that predicted from the large thermal conductivity at 𝑞2≤ 0.3𝜇𝑚−2, above which the decay rate is slower by up to a factor of 5 at the smallest grating period. The thermal conductivity is almost constant at large grating period (𝐿 ≥ 10 𝜇𝑚), below which a dependence on the grating period is observed. Note that the lattice period dependence in DR 196 is much stronger than that reported in partially oriented PE [131] , indicating the presence of heat-carrying phonons with longer MFPs in the present highly oriented samples.
Ballistic transport of the heat-carrying phonons in DR196
In Figure 4.14, the intensity of the shaded area is the calculation obtained using the MFP profiles, enclosed by 95% credible intervals (dashed line). On the other hand, the percentage of heat carried by MFP below 100 nm is less than 1%. The intensity of the shaded area is the calculation using the MFP profiles obtained from the Bayesian inference.
Low energy Debye model
Modeling
The previous data provided limitations to our modelling. the thermal conductivity versus the lattice period. As shown in Fig.4.17A, the calculated thermal conductivity versus temperature at 𝐿 = 9.8 𝜇m agrees with our measurement up to about 100 K, below which a significant deviation was observed. Under the same constraints, we found that the frequency-dependent mean free path,Λ(𝜔) =𝑣𝐿 𝐴𝜏∼ 80 nm best explains the thermal conductivity versus lattice for DR8.
Discussion
In semi-crystalline polymers, the heat capacity of the amorphous fraction for temperatures 100 - 300 K has been reported to be higher than that of crystalline fraction [143], with a maximum difference by a factor of 1.5 - 2 near 250 K. according to the theory of the phonon boundary scattering, it is well known that the long wavelength phonons are more likely to scatter specularly, leading to a coherent thermal conductivity in PE. Second, as mentioned earlier, the understanding of the thermal transport properties in PE is only limited in a perfect microstructure (a repeated coil structure), which is far from real materials.
Summary
Minimum thermal conductivity is one of the empirical approaches to explain thermal transport in glassy substances. 196], Δ𝑇𝑝𝑢 (Δ𝑇𝑝𝑟) is the transient temperature rise due to the pump (probe), and Δ𝑇𝑡 𝑜𝑡 𝑎𝑙 is the overall transient temperature rise of the sample. Measurement of the anisotropic thermal conductivity of molybdenum disulfide with the time-resolved magneto-optical kerr effect.
Origin of acoustic excitations in amorphous silicon
Motivation
Consequently, studies of acoustic excitation in aSi have relied on numerical simulations based on normal mode analysis. Feldman and Allen classified the excitations in aSi as propagons, diffusons, and locons based on the properties of the normal mode eigenvectors [14]. Combined with picosecond acoustics and inelastic X-ray scattering for the low and high frequency limits of the attenuation coefficient, respectively, TG measurements could constrain the frequency dependence of the attenuation in the sub-THz frequency band and thus eliminate the discrepancy.
Anomalous thermal properties observed in amorphous materials
From a high frequency above 0.1𝜔𝐷 the MFP is of the order of sub-nm with frequency independence due to an atomic disorder. In this temperature range, the damping of the vibration is strongly dependent on the frequency [148] and the chemical composition [184]. For temperatures lower than 1 K the temperature dependence of the internal friction again shows a clear temperature dependence.
Prior empirical models
The minimum thermal conductivity assumes the heat transfer process as a random step of the heat energy. In the following, we briefly describe the frequency dependence of the MFP induced by resonant absorption. The density fluctuation is based on the structural inhomogeneity as a primary mechanism for the scattering of the acoustic excitations [182].
Picosecond sound acoustics (PSA) on aSi
Next, we consider the selection of the optimal optical energy and pump modulation frequency. While the average signal magnitude increases with increasing pump power, the corresponding SNR value saturates at 10 mW. The aSi film thickness was determined from the time difference between the echoes and the known LA sound speed.
Thermal characterization of aSi
This requirement, the PSA and IXS measurements, and the measured thermal conductivity versus lattice period at the five temperatures in this study place severe constraints on the frequency dependence of the attenuation in the sub-THz frequencies. We find that only profiles consistent with profile 2 can explain the magnitude and lattice period dependence of the thermal conductivity. Measured thermal conductivity versus lattice period (symbols) and predicted value from optimized profile 2 (total, yellow dashed line; LA, blue dashed line; TA, red dashed line) for (C) 315 K, (D) 225 K, (E) 150 K, and (F) 80 K. Good agreement is observed at all temperatures with MFPs that are temperature independent. the Ioffe-Regel crossover frequency ~ 10 THz for LA and ~ 5 THz for TA [174]) was derived.
Unusually weak damping of acoustic excitation in aSi
The heat capacity of excitations in the former frequency range is larger by a factor of (𝜔𝑎 𝑆𝑖/𝜔𝑆𝑖 frequency band for glassy silica are smaller by an order of magnitude The second discrepancy is the prediction from the normal mode analysis of the frequency dependence (𝑛 =2) and the anharmonic origin of the damping in the few THz frequency range.
Summary
Measurement of lateral and interfacial thermal conductivities of single and double layer MoS2 and MoSe2 using refined optothermal raman technique. Thermal conductivity of polyethylene: The effects of crystal size, density and orientation on the thermal conductivity. Vibrational Mean Free Paths and Thermal Conductivities of Amorphous Silicon from Non-Equilibrium Molecular Dynamics Simulations.
Conclusion and future works
Summary
Next, we presented our measurements of the mean free path of heat-carrying acoustic phonons in the present samples of highly oriented polyethylene. Our results provide insights into the current upper limit of thermal conductivity in highly oriented polymers that will prove useful for the development of thermally conductive polymers. In Chapter 5, we described the microscopic origin of heat-carrying acoustic excitation in amorphous materials.
Outlook and future insight
Metallic thermal conductivity in a lightweight insulator: Solid-state processed ultra-high molecular weight polyethylene tapes and films. Thermal conductivity and thermal boundary resistance of Si film on Si substrate determined by photothermal displacement interferometry.
