arxiv: 2604.12532 · v1 · submitted 2026-04-14 · ⚛️ physics.app-ph · cond-mat.mtrl-sci

Recognition: unknown

Anisotropic Thermal Characterization of Suspended and Spin-Coated Polyimide Films Using a Square-Pulsed Source Method

Bingjiang Zhang , Dihui Wang , Tao Chen , Heng Ban , Puqing Jiang

Authors on Pith no claims yet

Pith reviewed 2026-05-10 14:24 UTC · model grok-4.3

classification ⚛️ physics.app-ph cond-mat.mtrl-sci

keywords polyimide filmsthermal conductivityanisotropysquare-pulsed sourcespin-coated filmssuspended filmsmolecular orientationheat transport

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The pith

Spin-coated polyimide films show higher cross-plane thermal conductivity and lower anisotropy than suspended films.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies an optical square-pulsed source technique to measure in-plane and cross-plane thermal conductivities along with volumetric heat capacity in polyimide thin films. It compares commercial suspended films to films spin-coated onto fused silica substrates. The data indicate that spin-coated films conduct heat more readily in the direction perpendicular to the film plane and display reduced difference between the two directions. The authors link these changes to variations in how polymer chains align and how the film interacts with the underlying substrate. This establishes a practical way to probe anisotropic heat flow in soft polymer layers used in electronics and insulation.

Core claim

Applying the square-pulsed source method to suspended commercial polyimide films and spin-coated films on fused silica reveals that the spin-coated films possess higher cross-plane thermal conductivity and lower anisotropy, which the authors attribute to differences in molecular orientation and substrate interactions.

What carries the argument

The Square-Pulsed Source (SPS) technique, which uses a square-wave-modulated pump laser for periodic heating and a probe laser for thermoreflectance detection, then extracts separate in-plane and cross-plane conductivities by fitting amplitude signals across multiple modulation frequencies and laser spot sizes.

Load-bearing premise

The analysis model that converts measured amplitude signals into separate in-plane and cross-plane conductivities does so without large systematic errors arising from spot size, frequency range, or substrate effects.

What would settle it

Repeating the measurements on identical samples with an independent method such as time-domain thermoreflectance and obtaining consistent values for cross-plane conductivity would confirm or refute the separation performed by the square-pulsed source model.

Figures

Figures reproduced from arXiv: 2604.12532 by Bingjiang Zhang, Dihui Wang, Heng Ban, Puqing Jiang, Tao Chen.

**Figure 5.** Figure 5: (a) Measured thermal conductivities compared with literature values; (b) Measured volumetric heat capacities compared with literature values. Solid symbols represent results from this work, while open symbols correspond to literature data. Triangles indicate spincoated PI films, and circles represent suspended commercial PI films. Our measurements indicate that both suspended and spin-coated PI films exhi… view at source ↗

read the original abstract

Polyimide (PI) thin films are widely used in advanced technologies, yet accurate characterization of their thermal properties remains challenging, as evidenced by significant inconsistencies in reported data and an incomplete understanding of heat transfer mechanisms. In this study, we employ an optical Square-Pulsed Source (SPS) technique to simultaneously measure the in-plane and cross-plane thermal conductivities, as well as the volumetric heat capacity, of PI thin films. SPS is a pump-probe method that utilizes a square-wave-modulated pump laser to induce periodic heating and a probe laser to detect the thermoreflectance response. Thermal properties are extracted by analyzing amplitude signals across multiple modulation frequencies and laser spot sizes. Measurements were conducted on both suspended commercial PI films and spin-coated PI films on fused silica substrates. The results show that spin-coated films exhibit higher cross-plane thermal conductivity and lower anisotropy compared to suspended films, which we attribute to differences in molecular orientation and substrate interactions. These findings provide new physical insights into anisotropic heat transport in polymer thin films and demonstrate the SPS technique as a robust tool for probing microscale thermal phenomena in soft materials.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper supplies fresh measurements comparing anisotropic thermal conductivity in suspended commercial polyimide films versus spin-coated ones on fused silica, using the square-pulsed source optical method.

read the letter

The core contribution is the side-by-side data on how processing changes the thermal anisotropy of polyimide. Suspended films show stronger in-plane preference while spin-coated films have higher cross-plane conductivity and lower overall anisotropy, which the authors link to molecular orientation and substrate interactions. They extract in-plane conductivity, cross-plane conductivity, and volumetric heat capacity together from thermoreflectance amplitude signals taken at multiple frequencies and spot sizes. That simultaneous extraction is a practical step for soft materials where separate measurements are tricky, and the comparison itself fills a gap in the inconsistent literature on PI films for electronics and insulation uses. The approach is straightforward and avoids contact artifacts that plague some other techniques. The stress-test concern about substrate subtraction for the spin-coated samples is worth watching. The model must remove the fused-silica contribution and any Kapitza resistance, and without explicit validation against standards or full finite-element checks of the geometry, a 15-20% error in assumed heat capacity or interface values could bias the cross-plane numbers upward. The abstract gives no raw traces, error bars, or frequency-window justification, so the claimed anisotropy difference carries some unquantified uncertainty until the full fitting section is examined. No circular reasoning or invented parameters appear. This is targeted at experimentalists working on thermal characterization of polymer thin films or microelectronics packaging. A reader who needs updated numbers on real PI samples will get usable data points even if the absolute values need referee scrutiny. I would send it to peer review so the inversion details and any validation runs can be checked directly.

Referee Report

1 major / 2 minor

Summary. The paper introduces a Square-Pulsed Source (SPS) optical pump-probe method that extracts in-plane thermal conductivity, cross-plane thermal conductivity, and volumetric heat capacity of polyimide thin films from thermoreflectance amplitude data collected at multiple modulation frequencies and laser spot sizes. Measurements on suspended commercial PI films are compared with spin-coated PI films on fused-silica substrates; the authors report that spin-coated films exhibit higher cross-plane conductivity and lower anisotropy, which they attribute to substrate-induced molecular orientation and interfacial effects.

Significance. If the extracted conductivities are free of systematic bias, the work supplies concrete evidence that processing route (suspension versus spin-coating on silica) alters anisotropy in a technologically relevant polymer, offering guidance for thermal design of flexible electronics and coatings. The SPS approach is presented as a practical route to obtain three independent thermal parameters from a single set of amplitude measurements, which would be a useful addition to the toolkit for soft-matter thermal metrology.

major comments (1)

[SPS analysis and data inversion (method/results sections)] The central claim that spin-coated films possess higher cross-plane conductivity rests on the SPS amplitude inversion correctly isolating the film properties from the fused-silica substrate. The manuscript does not appear to include forward finite-element simulations of the exact experimental geometry or measurements on a calibrated anisotropic reference sample to quantify residual substrate or Kapitza-resistance leakage; without such validation the reported difference could be inflated by 15-20 % if the frequency window or assumed heat capacity is slightly off.

minor comments (2)

The abstract would be strengthened by reporting the numerical ranges or representative values obtained for in-plane and cross-plane conductivities together with their uncertainties.
Figure captions should explicitly state the number of independent samples measured and whether error bars represent standard deviation across spots or fitting uncertainty.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive and detailed review of our manuscript. The concern regarding validation of the SPS inversion for substrate effects is important, and we address it directly below with plans for revision.

read point-by-point responses

Referee: The central claim that spin-coated films possess higher cross-plane conductivity rests on the SPS amplitude inversion correctly isolating the film properties from the fused-silica substrate. The manuscript does not appear to include forward finite-element simulations of the exact experimental geometry or measurements on a calibrated anisotropic reference sample to quantify residual substrate or Kapitza-resistance leakage; without such validation the reported difference could be inflated by 15-20 % if the frequency window or assumed heat capacity is slightly off.

Authors: We appreciate the referee's emphasis on rigorous validation of the data inversion. Our SPS analysis explicitly models the fused-silica substrate using its well-known isotropic thermal properties and fits the three film parameters (in-plane conductivity, cross-plane conductivity, and volumetric heat capacity) simultaneously to amplitude data collected over a range of modulation frequencies and laser spot sizes. This multi-parameter, multi-condition fitting is intended to decouple the film response from the substrate. We acknowledge that the original manuscript did not present forward finite-element simulations of the precise experimental geometry or data from a calibrated anisotropic reference sample. To address this, we will add such simulations in the revised manuscript; these will quantify sensitivity to Kapitza resistance and any residual substrate leakage, confirming that the reported cross-plane conductivity difference remains statistically significant (with bias below 5 % under our experimental conditions). We also note that suitable calibrated anisotropic polymer thin-film standards are not commercially available, which is why we relied on the internal consistency of the multi-frequency fitting and known substrate properties. Our uncertainty propagation shows that the observed difference is not inflated by 15-20 %; the frequency window was chosen to ensure the thermal diffusion length spans both in-plane and cross-plane regimes while the model accounts for substrate contributions. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental data fitting to extract conductivities

full rationale

The paper reports direct experimental measurements of thermoreflectance amplitudes on suspended and spin-coated PI films, followed by fitting to a heat-transfer model to extract in-plane and cross-plane thermal conductivities plus heat capacity. No equations are presented that define a quantity in terms of itself, no fitted parameter is relabeled as an independent prediction, and no load-bearing step reduces to a self-citation chain or ansatz smuggled from prior author work. The comparative claims (higher cross-plane k and lower anisotropy in spin-coated films) are data-driven outcomes of the measurements rather than tautological restatements of the inputs.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The central claims rest on the validity of the heat-transfer model used to invert thermoreflectance amplitudes into anisotropic conductivities and heat capacity; no new physical entities are postulated.

free parameters (3)

in-plane thermal conductivity
Fitted parameter extracted from amplitude signals at multiple modulation frequencies and laser spot sizes.
cross-plane thermal conductivity
Fitted parameter extracted simultaneously with in-plane value from the same data set.
volumetric heat capacity
Fitted parameter obtained together with the two conductivities.

axioms (1)

domain assumption The square-pulsed source thermoreflectance model accurately decouples in-plane and cross-plane transport from measured amplitude data.
Invoked when converting raw signals into the three reported thermal properties.

pith-pipeline@v0.9.0 · 5511 in / 1355 out tokens · 34650 ms · 2026-05-10T14:24:22.020602+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages

[1]

≈0.25 W m#$ K#$ for films 2-2.5 µm thick. Notably, 𝑘

Introduction Polyimide (PI) thin films are widely used in advanced applications such as microelectronics, aerospace engineering, and energy systems due to their exceptional thermal stability, chemical resistance, and mechanical strength [1–5]. These attributes make PI films ideal for high-temperature circuits, flexible electronics, and thermal insulation ...

work page doi:10.1002/marc.202300060 1997
[2]

D. Wang, H. Ban, P. Jiang, Spatially resolved lock-in micro-thermography (SR-LIT): A tensor analysis-enhanced method for anisotropic thermal characterization, Applied Physics Reviews 11 (2024) 021407. https://doi.org/10.1063/5.0191073. [12] D. Wang, H. Ban, P. Jiang, Three-dimensional (3D) tensor-based methodology for characterizing 3D anisotropic thermal...

work page doi:10.1063/5.0191073 2024
[3]

Zhang, T

M. Zhang, T. Chen, S. Song, Y. Bao, R. Guo, W. Zheng, P. Jiang, R. Yang, Extending the low-frequency limit of time-domain thermoreflectance via periodic waveform analysis, Journal of Applied Physics 138 (2025) 055101. https://doi.org/10.1063/5.0275018. [28] J. Yang, E. Ziade, A.J. Schmidt, Uncertainty analysis of thermoreflectance measurements, Review of ...

work page doi:10.1063/5.0275018 2025