Development of carbon nanofiber sheet for thermalinterface materials and its thermal and mechanicalproperties(カーボンナノファイバーを用い熱界面材料用シートの開発とその熱的特性と機械的特性の評価)

XIONG JIANGLING
March 2023

Development of carbon nanofiber sheet for thermalinterface material and its thermal and mechanicalproperties(カーボンナノファイバーを用い熱界面材料用シートの開発とその熱的特性と機械的特性の評価)

Dissertation for the Degree ofDoctor of Philosophy

Mechanical Engineering Program
Graduate School of Advanced Science and Engineering
Hiroshima University, Japan

Assoc. Prof. Choi Yong Bum, Advisor

XIONG JIANGLING
March 2023

CONTENTS
Contents
List of Figures
List of Tables
Chapter 1

Background and objectives

1.1 Introduction ........................................................................................................ 14
1.2 Types of tranditional thermal interface material(TIM) ..................................... 16
1.3 Development of advanced carbon TIMs............................................................. 21
1.3.1 Graphene TIMs ............................................................................................. 21
1.3.2 Carbon nanotube TIMs ................................................................................. 24
1.3.3 Carbon fiber TIMs......................................................................................... 26
1.4 Fabrication methods of TIMs ............................................................................. 27
1.5 Computer-assisted thermal simulation of TIMs ................................................. 30
1.6 Problems of previous studies and objective of this study ................................... 32
1.7 Outline of this study ........................................................................................... 33
References ................................................................................................................... 34
Chapter 2

Development of polyvinyl alcohol-based carbon nano fiber sheet

2.1 Introduction ........................................................................................................ 40
2.2 Experimental procedure ..................................................................................... 42
2.2.1 Raw materials................................................................................................ 42
2.2.2 Fabrication method of PVA-VGCF sheet ..................................................... 43
2.2.3 Evalution method and equipment .................................................................. 45
2.2.3.1 Observation of microstructure ................................................................. 45
2.2.3.2 Measurement of porosity, thickness, density and hardness ..................... 45

2.2.3.3 Periodic heating and infrared radiation thermometer method for thermal
conductivity .............................................................................................................. 45
2.2.3.4 High temperature and humidity test ......................................................... 47
2.3 Results and discussions ...................................................................................... 48
2.3.1 Microstructures and porosity of PVA-VGCF sheet ...................................... 48
2.3.2 Thickness, density and hardness of PVA-VGCF sheet .................................. 53
2.3.3 Thermal properties of PVA-VGCF sheet ...................................................... 55
2.3.4 High temperature and humidity test results .................................................. 59
2.4 Summary ............................................................................................................. 61
References ................................................................................................................... 62

Chapter 3

Effects of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

3.1 Introduction ........................................................................................................ 66
3.2 Experimental procedure ..................................................................................... 68
3.2.1 Raw materials................................................................................................ 68
3.2.2 Fabrication method of PVA-PTFE-VGCF sheet........................................... 69
3.2.3 Evaluation method and equipment ................................................................ 71
3.3 Results and discussions ...................................................................................... 72
3.3.1 Microstructures of PVA-PTFE-VGCF sheet ................................................. 72
3.3.2 Porosity, Thickness, density and hardness of PVA-PTFE-VGCF sheet ....... 74
3.3.3 Thermal properties of PVA-PTFE-VGCF sheet ........................................... 77
3.3.4 High temperature and humidity test results .................................................. 82
3.4 Summary ............................................................................................................. 88
References ................................................................................................................... 89
Chapter 4

Thermal simulation and analysis of fabricated PVA-VGCF sheet

4.1 Introduction ........................................................................................................ 92
4.2 Theory of thermal simulation ............................................................................. 95
4.3 Methodology of thermal simulation ................................................................... 98
4.3.1 Workflow ..................................................................................................... 98
4.3.2 Geometry ................................................................................................... 100

4.3.3 Model......................................................................................................... 103
4.3.4 Solution setup ............................................................................................ 105
4.4 Results ............................................................................................................ 106
4.4.1 Temperature distribution .......................................................................... 106
4.4.2 Heat flux distribution ................................................................................ 108
4.4.3 Thermal conductivity ................................................................................. 115
4.5 Summary ........................................................................................................... 118
References ................................................................................................................. 119

Chapter 5Conclusions ..................................................................................... 121

Acknowledgements .................................................................................................. 125
Published papers in regards to this thesis ............................................................. 126
Presentations ............................................................................................................ 127

List of Figures
Fig. 1.1 Schematic summary of traditional TIMs and their market share in 2023 U.S.
Fig. 1.2 Illustration of thermal conductivities of various carbon materials.
Fig. 1.3 SEM image of (a) vertically aligned CNTs(VACNTs) and (b) an elastic polyimide
copolymer and vertically aligned CNT TIM.
Fig. 1.4 Schematic of fabrication and microstructure of 3D carbon fiber skeleton/epoxy
resin composite TIM.
Fig. 1.5 Temperature distribution comparison of commercial TIM(XR-M) and developed
new graphene TIM(HLGP).
Fig. 1.6 Temperature distribution and cross-sectional view of Aluminum/polymer TIM
filled in a typical heating process.
Fig. 2.1 (a) FE-SEM image of VGCFs, and (b) Image and chemical formula of PVA.
Fig. 2.2 Schematic of the fabrication procedure of CNF sheet.
Fig. 2.3 Schematic of theory of periodic heating and infrared radiation thermometer
method: (a) In-plane direction (b) Through-plane direction.
Fig. 2.4 Images of 5 test points in thermal diffusivity measurement.
Fig. 2.5 Image of (a)device of high temperature and humidity test, (b) place method ofsamples.
Fig. 2.6 SEM images of upper surface of fabricated CNF sheets by different mass ratio of
PVA : VGCF, (a)1 : 0.100, (b)1 : 0.070, (c)1 : 0.050, (d)1 : 0.030, (e)1 : 0.025.
Fig. 2.7 SEM images of upper surface of fabricated CNF sheets by different mass ratio of
PVA : VGCF, (a)1 : 0.100, (b)1 : 0.070, (c)1 : 0.050, (d)1 : 0.030, (e)1 : 0.025.
Fig. 2.8 Effect of mass ratio of PVA:VGCF on porosity.
Fig. 2.9 Effect of mass ratio of VGCF on the thickness and density of fabricated sheets.
Fig. 2.10 Hardness of fabricated PVA-VGCF sheets by different mass ratio of PVA:VGCF.

Fig. 2.11 Effect of mass ratio of PVA and VGCF on the in-plane thermal conductivity.
Fig. 2.12 Effect of mass ratio of PVA and VGCF on the through-plane thermal
conductivity.
Fig. 2.13 In-plane thermal conductivity of specimens before and after high temperatureand humidity test.
Fig. 2.14 Through-plane thermal conductivity of specimens before and after hightemperature and humidity test.
Fig. 3.1 FE-SEM image(×6000) of: (a)PTFE powders of 120nm and (b)PTFE powders of
300nm.
Fig. 3.2 Schematic of the fabrication procedure of PVA-PTFE-VGCF sheet.
Fig. 3.3 SEM images (×6000) and microstructure schematics of fabricated VGCF sheets:(a) PVA-VGCF sheet*, (b) PPLV sheet and (c) PPTV sheet.
Fig 3.4 The porosity and thickness of fabricated PVA-VGCF, PPLV and PPTV sheets.
Fig 3.5 The density and shore hardness of fabricated PVA-VGCF, PPLV and PPTV sheets.
Fig. 3.6 In-plane thermal conductivities and thermal diffusivities of PVA-VGCF, PPLV
and PPTV sheet.
Fig. 3.7 Through-plane thermal conductivities and thermal diffusivities of PVA-VGCF,
PPLV and PPTV sheet.
Fig. 3.8 The schematic of microstructure near the surface of PVA-VGCF sheet and PVAPTFE-VGCF sheet.
Fig. 3.9 SEM images(×1000) of (a)PPLV sheet, (b)PPTV sheet in room temperature and(c)PPLV sheet, (d)PPTV sheet after high temperature and humidity test.
Fig. 3.10 The in-plane TC of fabricated VGCF sheet after high temperature and humidity
test.
Fig. 3.11 The in-plane TC of fabricated VGCF sheet after high temperature and humidity
test.
Fig. 3.12 The FT-IR analysis of fabricated VGCF sheets at room temperature and after
high temperature and humidity.
Fig. 3.13 The properties comparison of PVA-VGCF, PPLV and PPTV sheets.

Fig. 4.1 Schematic of 1D planar conduction.
Fig. 4.2 Schematic of heat conduction through multiple layers.
Fig. 4.3 A workflow for thermal simulation in this chapter.
Fig. 4.4 The schematic of basic unit of fabricated CNF sheet.
Fig. 4.5 Five types of geometry model: (a) pure PVA; (b) horizontally arranged VGCF
in PVA matrix; (c) vertically arranged VGCF in PVA matrix; (d) randomly
arranged VGCF in PVA matrix; (f) pure VGCF.
Fig. 4.6 Geometry model of Heater-Material-Cooler system in this thermal simulation.
Fig. 4.7 The images and statistics of mesh results of model: (a) pure PVA; (b)horizontally arranged VGCF in PVA matrix; (c) vertically arranged VGCF in
PVA matrix; (d) randomly arranged VGCF in PVA matrix; (f) pure VGCF.
Fig. 4.8 Image of temperature setup for simulation.
Fig. 4.9 Images of temperature distribution results of model: (a) pure PVA; (b)horizontally arranged VGCF in PVA matrix; (c) vertically arranged VGCF in
PVA matrix; (d) randomly arranged VGCF in PVA matrix; (f) pure VGCF.
Fig. 4.10 Images of heat flux distribution results of model: (a) pure PVA; (b) horizontal
arranged VGCF in PVA matrix; (c) vertical arranged VGCF in PVA matrix; (d)randomly arranged VGCF in PVA matrix and (f) pure VGCF.
Fig. 4.11 Detail images of heat flux distribution results of: (a) horizontally arranged
VGCF in PVA matrix; (b) vertically arranged VGCF in PVA matrix; (c)randomly arranged VGCF in PVA matrix.
Fig. 4. 12 Image of heat flux distribution results of only VGCF in the model of randomly
arranged VGCF.
Fig. 4.13 Schematic of steady-state method for thermal conductivity measurement.
Fig. 4.14 Image of temperature data of 9 points used for thermal conductivity calculationin pure PVA model.

List of Tables
Table 1.1 The summary of characteristics, advantages and disadvantages of traditional
TIMs.
Table 1.2 The summary of fabrication method of advanced carbon TIMs.
Table 2.1 Fabrication conditions of CNF sheets.
Table 2.2 Comparison of thermal conductivity of our CNF sheet with other polymer-basedcarbon TIMs.
Table 3.1 Fabrication conditions of PVA-PTFE-VGCF sheets.
Table 3.2 Comparison of thermal conductivity between this work and other paper-likecomposites.
Table 4.1 Typical thermal conductivity models for composite TIMs.
Table 4.2 Terms of thermal analogy used in the simulation.
Table 4.3 Major physical parameters used in the simulation.
Table 4.4 Statistics of total heat flux of each model.
Table 4.5 The summarized thermal conductivity of fabricated models.

Chapter 1. Background and objectives

Chapter 1

Background and objectives

1.1

Introduction ................................................................................................... 14

1.2

Types of traditional thermal interface material (TIM) .................................. 16

1.3

Development of advanced carbon TIMs ........................................................ 21

1.3.1

Graphene TIMs ....................................................................................... 21

1.3.2

Carbon nanotube TIMs ........................................................................... 24

1.3.3

Carbon fiber TIMs .................................................................................. 26

1.4

Fabrication methods of TIMs ....................................................................... 28

1.5

Computer-assisted thermal simulations of TIMs .......................................... 30

1.6

Problem of previous studies and objectives of this study .............................. 32

1.7

Outline of this study ....................................................................................... 33

References ................................................................................................................ 34

13

Chapter 1. Background and objectives

1.1 Introduction
Since the third industrial revolution, the electronics industry has emerged and quickly
developed. Especially in the years 1958 to 1975, the introduction of integrated
circuits(ICs) with superior capabilities of over several thousand components on a single
chip[1]. In the following years, being small in size and light in weight, the ICs has been
widely used in electronic components and devices. According to the Moore’ law, which
is used to predict the number of transistors in a dense ICs double about every two
years[2], which means the electronics device continue to show exponential growth incomplexity and performance. With rapid development of electronics industry, the sizeof electronic devices has decreased significantly, but on the contrary the power density
goes on increasing. High power, High frequency, high speed of electronic devices
greatly increases the overheating problem, the heat dissipation has become a major
concern which limited the development of electronics industry. For example, the latest
high-end CPU - Intel a Core i9-12900K can consume 125~241W power in a small sizeof 45mm × 37.5mm. its temperature can hit 373K easily with core-heavy workload,
which puts the CPU at risk of shortening and destroying the life of internal components.
Thus, the efficient heat dissipation of electronics device is very important, it determines
the life and working performance of device itself. In most instances, the electronics
device dissipates its heat by contacting metal heat sinks. However, when two solid
surfaces are clamped against each other under moderate loading, micro andmacroscopic surface defects resulting in the actual contact area being a very small
fraction of the apparent contact area[3], which is also called the air gaps. The presenceof air gaps results in high thermal resistance and severely reduce the heat dissipation
efficiency of the whole electronics device. The thermal interface materials (TIMs) areused to fill the air gaps between heat source and heat sinks, reducing the thermal contact
resistance and increasing heat conduction across the interface, which are considered
important for improving the heat dissipation efficiency of electronics devices.
Mechanically, TIMs must be flexible so that they can conform to mates with unevensurfaces. Meanwhile, the thickness of TIMs must be enough to comply with surface
14

Chapter 1. Background and objectives
irregularities and non-planarity. Thermally, TIMs should exhibit high thermal
conductivity and low thermal contact resistance[4]. There are many kinds of traditionaland commercially available TIMs, the most used ones are thermal grease, phase-changematerial, thermal pad and metal solder. However, the field of TIM is changing rapidly,
these traditional TIMs have many shortcomings and cannot adapt to the requirementsof advanced electronic products. Moreover, with the increasing range of humanactivities, from the land to the depths of the ocean or space, and from hot and dry deserts
to cold and humid forests, the use area of the TIMs is also becoming larger and larger.
The requirements for TIMs are not only the heat dissipation, but also other functional
properties. For example, for electronic equipment used in scientific research in
Antarctica, its TIMs need to endure the minimum temperature to 183K[5] and still
maintain a good flexibility and thermal conduction ability. For the electronic equipmentused in Amazon rainforest with a humid environment of a relative humidity high at an
average of 88% in the rainy season and 77% in the dry season[6], TIMs used in thisregion require a higher humidity resistance than usual. Thus, the development of new
TIMs become extremely significant for the heat management of advanced electronic
products over the world.

15

Chapter 1. Background and objectives

1.2 Types of traditional thermal interface materials (TIMs)
Currently, Thermal grease, phase-change material (PCM), thermal pad and metal
solder are the most used traditional TIMs in the world.
Thermal greases, also called thermal pastes or thermal compounds, are the first
generation of TIMs and the most widely used in electronics device[7]. Greases havegood wetting property, low cost, low assembly pressure. In general, there are types ofthermal grease: non-conductive and conductive. Non-conductive thermal greaseusually consists of a polymerizable liquid matrix and a large volume fraction ofelectrically insulating but thermally conductive fillers. Silicone or hydrocarbon oils areoften used as matrix material due to their good combination of fluidity and viscosity,
allowing more precise filling of air gaps. SiC, Al2O3, ZnO and other inorganic material
are widely used as thermal conductive filler[8]. The filler loading can be added to 7080mass% and raise the low thermal conductivity (~0.5 W·m-1·K-1)[9] of matrix up to
about 5 W·m-1·K-1[10] for commercial thermal grease. Non-conductive thermal greases
have a low price with limited thermal conductivity. Conductive thermal grease types
include silver-based, copper-based and aluminium-based thermal grease. These metalbased thermal greases can achieve a higher thermal conductivity than non-conductive
thermal grease, Uppal et al. introduced a silicone-oil-based thermal grease throughusing liquid metal as the filler and micro silver needles to connect the liquid metal
droplets[11]. The thermal conductivity of this multiphase thermal grease can reach to 17
W·m-1·K-1. But the metal-based thermal greases must be used carefully due to theirelectronically conductive. They can cause electrical shorts and destroy the electronics
if some of them leaks into the ICs. Moreover, all of thermal grease do exhibit various
failure mechanisms that can severely impair the functionality of the electronic devices
after a long period of use. When two surfaces are subjected to the thermomechanicalstress, thermal grease is easily pumped out through the gaps due to its high fluidity andpollute the electronic components. Moreover, at high temperature, the fillers and matrix
in thermal grease will be separated, which results in a reduction of thermal
16Chapter 1. Background and objectives
conductivity[12].
PCMs has been widely studied due to their excellent ability to store and release
thermal energy[13-15]. PCMs are usually in form of solid state at room temperature andbecome liquid when the temperature reaches the melting temperature, which caneffectively fill the air gap and improve the compliance of TIMs. Moreover, the pumpout problem can also be solved due to the operating temperature of electronics is usually
lower than the melting temperature of PCMs in practical applications[16,17]. However,
PCMs required a moderate contact pressure to bind surfaces together and their physicaland chemical properties are unstable in processes during their long-term usage[18].
Moreover, the high costs, non-electrical insulation and limited heat conduction in solidstate are also the disadvantages of PCMs in practical applications.
Typical thermal pads are a kind of thermally conductive silicone elastomer. They are
fabricated by directly mixing silicone rubber with thermal conductive fillers or
reinforcements depending on the performance requirements, such as ceramic or boron
nitride. Due to metal particles are rarely used as fillers, thermal pads are particularly
suitable for applications which require an electrical insulation between contact surfacesof electronic devices and heat sinks. Meanwhile, thermal pad could provide better
workability and easier assembly process compared to thermal grease, without theconcern for pump-out and flexible maintenance during long-term usage. In addition,
thermal pad can also act as a vibration damper and protect the electronic devices inmobile state. However, thermal pads usually have a thickness in a range of 200-1000µm [16,19], which is much higher than other types of TIM. Thus, thermal pads also require
high contact pressure(~700kPa)[20] to conform to mating surfaces. Previous researchshowed that thermal pads should be compressed to at least 25% of their total thickness
to deal with the existence of some large air gaps[19]. Other shortcomings of thermal pads
are their low thermal conductivity and high thermal contact resistance. A thermal padwith a thermal conductivity of 3 W·m-1·K-1 is considered to be the medium quality on
the market. Although there are also some commercial thermal pads with a thermal
conductivity of 14 W·m-1·K-1, they are super high grade and quite expensive[21] that isdifficult to apply widely.
Due to compliance in both molten state and solid state, metal solders are widely used
17

Chapter 1. Background and objectives
as TIM to enhance the heat conduction between mating surfaces[22-27]. Typical metal
solders are low melting-temperature alloys such as bismuth, tin and indium, which have
low melting point(333~573K), chemical stability and high thermal conductivity(>30
W·m-1·K-1)[28]. In molten state solder can properly fill into the air gap between two
mating surfaces, thus, using metal solders with high thermal conductivity can improve
the thermal contact conduction efficiently. However, the cost, stress crack and operatecomplexity involved in metal solders have limited its application for TIM[29].
In addition to the traditional used thermal grease, PCMs, thermal pad and metal
solders, there are some other commercially TIMs on the market, such as thermal gels,thermal conductive adhesives and thermal tapes. Fig. 1.1 shows the schematic summaryof traditional TIMs and their share market in U.S 2023. Table 1.1 gives the summary of
the characteristics, advantages, disadvantages and thermal conductivities of these
traditional TIMs.

18

Chapter 1. Background and objectives

Fig. 1.1 Schematic summary of traditional TIMs and their market share in 2023
U.S.[33]

19

Chapter 1. Background and objectives
Table 1.1 The summary of characteristics, advantages and disadvantages of traditional
TIMs[16,17,19,29-32].
TIM type

Characteristics

Advantages

Disadvantages

greaseSilicone or Good wettinghydrocarbon oils +property

fillers

 Low assemblypressure

Phase-changematerial

Polyolefin or low
molecular weight
polymer + fillers

silicone rubber +Thermal pad

fillers or
reinforcements

requiredthan grease No electrical Reusable

insulation

 No pump-out
 Easy application
 Electricalpaste

conductive
adhesives

Silicone or epoxy +fillers

Acrylic or siliconebased pressure
Thermal tapes

sensitive adhesive
loaded withthermally conductive
fillers

 High thickness
 High pressureduring installation

1-6.5

than grease No pump-out

 Reusable Good wetting
property High temperaturestability

Thermal1-5 More expensive

insulation

 No pump-out

form a low module

1-5 Hard to Easy application

attachment

Thermal gelsthickness

 Compressive force Mechanical

Silicone + fillers to Difficult to control

 No pump-out

conductivity
Low-melt metal alloyand dry out

maintenance High thermal
Metal solder[λ/W·m-1·K-1]

 Pump-out effect Low cost
ThermalThermal conductivity

 High cost
 Difficult to install Corrosion
 Void concern
 Low thermal
conductivity Cure need
concern Cure need

 Low contact

 Delamination

resistanceconcern

 Mechanical Low thermal

attachment

conductivity

 No pump-out
 Easy to use Mechanicalattachment

20

1-3.5

 Delamination

 No pump-out

 Low cost

30-86

1-2

 Low thermal
conductivity
 Hard to fill large
air gap efficiently

0.15-0.25

Chapter 1. Background and objectives

1.3 Development of advanced carbon TIMs
1.3 1

Graphene TIMs

Due to the high thermal conductivity, flexibility and high stability of raw materials,
developments on TIM through using carbon materials such as graphene and carbon
nanotubes has been widely studied. Graphene, discovered in 2004 by Andre Geim andKonstantin Novoselov, an atomic layer thick carbon with a sp2 hybrid structure[34]. This
material is considered a 21st century materials because of its unique properties andpotential for practical application and has attracted researchers from all fields. As
showed in Fig. 1.2, graphene has high thermal conductivity (~5300 W·m-1·K-1), highmechanical strength (breaking strength of ~42 N·m-1 and Young’s modules of ~1TPa),high elasticity, flexibility and lightweight properties(Theoretical density of 2.267g·cm3 [34, 36-38]). Although graphene has such excellent properties, it is hard to use it directly

due to its 2D structure. Thus, composite with other material such as polymer or metal
to fabricate graphene composites is widely studied in recent year. Graphene papers
fabricated by stacking graphene nanosheets have been widely reported that have apotential for efficient thermal materials for advanced electronic device[39,40]. Although
the graphene bulk composite may achieve a better thermal property, many researchers
have turned their attention to the development of graphene paper as TIMs due to its low
thickness and flexibility. Graphene paper as a TIM can be used to attach meting surfaceof heat source and heat sink, achieving a direct contact between the graphene and metal.
Based on the ultrahigh in-plane thermal conductivity of graphene paper, feasibility oflarge-scale preparation and low production cost, the possibility of TIMs for practicalapplication in academia and industry is rising up rapidly[41-43]. In common, according
to the types of materials added, graphene TIMs can be simply divided into 4 types:
graphene/polymer composite, graphene/metal composite, graphene/other caronmaterial composite, graphene/ceramic composite.
Graphene/polymer composite TIM can achieve a great enhancement of high thermal
conductivity at low graphene content, and not significantly affect the intrinsic properties
21

Chapter 1. Background and objectivesof the polymer matrix[44,45]. However, due to the bad dispersion of graphene in thepolymer and the low thermal conductivity of polymer, although in-plane thermal
conductivity is very high to reach 23.5 W·m-1·K-1[46], the through-plane thermal
conductivity of graphene/polymer composite TIM cannot meet the ideal value(~3 W·m1

·K-1)[47].
The use of metal particles with high thermal conductivity to fabricate graphene/metalcomposite TIM is studied to enhance the through-plane thermal conductivity of TIMs.
For example, J. Wang et al. obtained PDA-graphene complexed with metal irons
graphene/metal composite, which has a high through-plane thermal conductivity of
3.48 W·m-1·K-1[48]. Although metal materials have ultra-high thermal conductivity, theinteraction between metal and graphene is relatively weak, resulting in limited throughsurface thermal conductivity of composite paper[43].
Enhancing the interaction between the fillers is important to improve the thermal
conductivity of graphene TIMs. Compared with other materials, there is no doubt thatcarbon materials interact better with graphene. An interesting hybrid graphene
composite with cellulose nanocrystal added in are reported recently[49]. During the
fabricate process, cellulose nanocrystals are carbonized into nanorods after hightemperature annealing. These carbon nanorods connect with graphene nanosheet andfill the air gaps in the fabricated composite, which raise the through-plane thermal
conductivity to 4.6 W·m-1·K-1. However, this graphene/nanorods composite material
needs an annealing temperature ranging from 1073K to 1773K to achieve the reductionof graphene oxide and carbonization of cellulose nanocrystals[49], which demand a highcost and energy waste during the fabrication process and is hard for practical application.
This is also the disadvantages for most graphene/other caron material composite TIMs.
Similar with graphene/metal composite TIM, ceramic materials also can be used
as a filler in graphene TIM. Ceramic materials have good thermal conductivity, which
is no worse than metal materials. For example, SiC has a thermal conductivity of 80300 W·m-1·K-1 and that of Al2O3 is about 30-35 W·m-1·K-1[50]. C. P. Feng et al.
developed a composite with robust graphene nanoplatelets and large size Al2O3 forTIM[51], in which only a single-layer Al2O3 particles are distributed in the through-plane
direction of this composite and Al2O3 particles are covered by graphene nanoplatelets
22Chapter 1. Background and objectives
via simple vacuum-assisted self-assembly method. This graphene/ceramic composite
TIM show an excellent through-plane thermal conductivity of 9.09 W·m-1·K-1.
However, this single-layer structure lack of flexibility and is difficult for large scale
production, which is also limited its practical application for TIMs.

Fig. 1.2 Illustration of thermal conductivities of various carbon materials[35].

23Chapter 1. Background and objectives

1.3 2

Carbon nanotube TIMs

As showed in Fig. 1.2, Carbon nanotube(CNT) can be defined as a rolled-up
graphene sheet. Since the discovery of multi-walled CNT(MWCNT) in 1991 by
Iijima[52] and single-walled CNT(SWCNT) in 1993 by Iijima and Ichihashi[53], the CNT
is considered one of an ideal choice for thermal materials, because of its high thermal
conductivity(2800-6000 W·m-1·K-1) and mechanical reliability[47,54]. There are manyfactors There are many factors that affect TC, such as atomic structure, defects, thepurity, length and diameter and of the CNTs, especially the length of the CNTs isimportant for phonon transport and is considered to its increase would contribute to anincrease of mean free path for phonons. Heat transfer is carried out by electrons andphonons in solid[55,56]. In common, SWCNT have a longer cylindrical structure andhigher purity compared to MWCNT, which contribute to a higher thermal
conductivity[57,58].
Many works have been carried out in developing carbon nanotube TIMs. In the First
period, researcher just combine CNT and other traditional TIM to seek for a remarkable
improvement of thermal conductivity. X. J. Hu et al. introduced a kind of CNT TIM
that CNT into a silicone composite filled with metal particles[59]. The thermal
conductivity (1.3 W·m-1·K-1) of this CNT TIM is about 7 times higher than that of thesilicone matrix and 2 times higher than traditional TIMs. Though the thermal
conductivity can be improved by adding CNT fillers, many studies have demonstrated
that the properties of CNT TIMs cannot be completely exploited[60-63]. The low
efficiency is the first reason, due to the random dispersion and discontinuity of CNTs,
the heat conduction actually only goes through a small number of CNTs. Thus, heatcannot be conducted directly from a side to the other side through CNTs and the heat
conduction would be influenced by matrix with a lower thermal conductivity.
Meanwhile, the presence of defects, high thickness, high thermal interface resistanceand low purity of CNT is also the reason for low thermal conductivity of CNT TIMs.
Since then, the researchers have explored other way to fabricated CNT TIMs, using24

Chapter 1. Background and objectives
CNT array is considered to be one of the most promising methods. As shown as Fig.
1.3(a), the CNT array, which also call vertically aligned CNTs(VACNTs), is expected
provide an efficient thermal conduction because of its highly ordered and verticallyaligned structure and a relatively high thermal conductivity of 15~267 W·m-1·K-1[63].
M. Wang et al. developed a vertically aligned CNT/epoxy resin composite, which hasa high thermal conductivity of 8.23 W·m-1·K-1 and good flexibility[64]. As shown as Fig.
1.3(b), H. T. Yu et al. introduced a high thermal conductive and self-healing CNT TIM
by using a forest of VACNTs covered by elastic polyimide copolymer[65], which exhibitsa high thermal conductivity at 10.83 ± 0.22 W·m-1·K-1 and low thermal resistance at
6.83 ± 0.15 K·mm2·W-1. However, there are still some disadvantages for the usage of
CNT array. Firstly, poor thermal/mechanical contact between CNT array andsurrounding surfaces resulting in an increasement of thermal contact resistance between
CNT array and mating surfaces. In addition, due to the low self-supporting strength of
CNT array, they are easily damage during fabricating process(>973K, harsh chemical,
long exposure time) or external working environment, such as complex mechanicalenvironment and humid environment[66-68]. Thus, to fully use the excellent thermal
properties of CNT array, more research is needed.

Fig. 1.3 SEM image of (a) vertically aligned CNTs(VACNTs)[69] and (b) an elastic
polyimide copolymer and vertically aligned CNT TIM[65].

25Chapter 1. Background and objectives

1.3 3

Carbon fiber TIMs

Among the carbon materials, carbon fiber(CF) is the oldest one which discovered in
the mid-1800s by J. W. Swan[70]. Similar to graphene and CNT, CF has many excellent
properties like high strength, high thermal and chemical stabilities, low density andgood thermal and electrical conductivities. However, , CF is often used to composite
with metal materials and seldom to be studied for TIM application due to its structure
limitations and low relative thermal conductivity(190-220 W·m-1·K-1) compared tographene and CNT. As shown in Fig. 1.4, the group of J. K. Ma et al. developed a 3D
network of CFs composited in epoxy polymer where CFs is randomly dispersed[71]. This
CF/epoxy TIM provided an enhanced through-plane thermal conductivity(2.84 W·m1

·K-1) compare with epoxy matrix(0.19 W·m-1·K-1). However, the thermal conductivity

is still lower than commercial TIM and further improvement is needed. And then,similar to VACNT, to solve the low thermal conductivity of CF composite, verticallyaligned CFs are also used for developing new TIM. Recently, Q. Wu et al. reported thata kind of CF reinforced elastomeric TIM. In the fabrication process, on the basis ofconventional alumina/silicone rubber, mesophase pitch CFs are added as fillers and theCFs are oriented in the matrix by a strong magnetic field during the fabrication
process[72]. In their report, the composite with 20 vol% CFs shows an outstanding
thermal conductivity of 26.49 W·m-1·K-1. However, due to the flexible fabrication
process and the necessity to use magnetic field treatments, it is difficult for the practicalapplication. Improving the thermal conductivity is not the only requirement fordeveloping a new TIM, reducing the cost, simplifying the fabrication process andallowing for big scale industrial production are also important issues for researchers toconsider. As a type of carbon nanofiber, vapor grown carbon fiber(VGCF, CNF) has
excellent mechanical properties such as high thermal conductivity, high specificstrength, and high corrosion resistance and is commercially available at a low cost.
VGCF can be incorporated in a wide range of matrices, including thermoplastics andthermosets, for the formation of thin and flexible sheets. Thus, VGCF is considered an
26

Chapter 1. Background and objectives
ideal material for TIM development in this study.

Fig. 1.4 Schematic of fabrication and microstructure of 3D carbon fiberskeleton/epoxy resin composite TIM.

27

Chapter 1. Background and objectives

1.4 Fabrication methods of TIMs
There are many fabrication methods for different types of TIMs, and researchers arestill exploring some new method now. To traditional TIMs like thermal grease, PCM
and thermal pad, direct incorporation method is most widely to be used in industrial
production which described as mixing the fillers into matrix directly, then follows thepelletize, compress, dry and heating process if it is necessary[73]. Metal solders isapplied on the mating surface by soldering. To carbon TIMs, the fabrication method canbe much more diverse and selective thanks to the flexibility and chemical and thermal
stability of carbon material, such as vacuum filtration(VF), solution casting, layer-bylayer assembly, chemical vapor deposition(CVD), electro-spray deposition(ESD),
freeze casting and so on. Among these fabrication methods, VF and solution casting are
the most commonly used and relatively simple ones. In the VF process, thehomogeneous dispersion of carbon material, other fillers and solvent is vacuum filtrated
by using a filter. After removing the filter and drying under the right conditions, a TIM
film will be obtained. And solution casting is an easier and low-cost method to fabricate
TIMs, which can also be applied to large scale TIM products in practical applications.
Table 1.2 shows a simple summary of fabrication method of advanced carbon TIMs.

28

Chapter 1. Background and objectives

Table 1.2 The summary of fabrication method of advanced carbon TIMs.
Thermal conductivity

Fabrication

SamplemethodBN nanosheet/cellulose nanofiber
CNF/RGO
CNTs/RGO
AgNPs@BC/Al2O3/GNPs
RGO paper
PVDF/BN/GNPs
Cellulose/GNP[λ/W·m-1·K-1]
In-planeThrough-plane

22.67

1.08

2018[74]

7.3

0.13

2017[75]

977

0.38

2014[76]

27.78

9.09

2022[51]61

0.09

2015[77]

unknown

0.72

2018[78]800

5.5

2018[79]

12.6

0.042

2017[80]

Vacuumfiltration
Vacuumfiltration
Vacuumfiltration
Vacuumfiltration
Solution
casting
Solution
casting

Year [Ref]Solution
casting
Layer by

NFC/RGO

layer
assembly

Epoxy/VACNTs

CVD

unknown

1.65

2019[81]

SiC/CF

CVD

unknown

16.8

2017[82]

Epoxy/CNT

CVD

1

4.87

2011[83]

unknown

2.13

2016[44]

1.7

2.84

2020[71]

Epoxy/Graphene network
Epoxy/Carbon fiber network
BN: Boron nitride
BC: Bacterial cellulose

FreezecastingFreezecasting

RGO: Reduced graphene oxide

GNP: Graphene nanoplatelet

PVDF: Polyvinylidene fluoride

29

AgNPs: silver nanoparticles

Chapter 1. Background and objectives

1.5 Computer-assisted thermal simulations of TIM.
As a new trend of current science research, combining computer simulation andpractical experiments together become an important way to study new things anddemonstrate new ideas. Compared to experiments, simulations can help researchers togenerate new knowledge and thoughts about unknown territory by a simpler and moreintuitive way. Recently, computer-assisted thermal simulations of advanced TIM using
finite element analysis(FEA) software begin to appear commonly in research. FEA is acomputerized method for predicting the how real objects will respond to force, heat,vibration and other physical effects under the specified conditions set by people. The
working principle of FEA is to break down real objects into a large number of finite
elements and use mathematical equations help predict the behavior of each element.
And in final, the results of each element will be summed up to predict the behavior of
the whole object[84]. Using thermal simulation by FEA could contribute to a significant
reduction of development circles, avoidance of material waste and lower research cost.
For example, as shown as Fig. 1.5, W. Dai et al. build an evaluation system of HeaterTIM-Heat sink to investigate and compare the cooling performance between theirdeveloped new graphene TIM and state-of-the-art TIMs in real case[85]. However, likemost thermal simulation of TIM, the microstructure of their developed TIM and thearrangement of graphene are not considered, the model of TIM is created as anequivalent to a single-phase material with uniform internal structure. As anotherexample, Q. Q. Ma et al. develop an aluminum/polymer TIM and through the usage of
FEA to study the uniform temperature distribution along the heat transfer path of thisTIM[86], which is showed in Fig. 1.6. In the reported studies, the computer-assisted
thermal simulation and analysis of fiber reinforced composite materials is seldom to bestudied, due to the complicated and different arrangement of fibers in each research.

30

Chapter 1. Background and objectives

Fig. 1.5 Temperature distribution comparison of commercial TIM(XR-M) anddeveloped new graphene TIM(HLGP)[88].

Fig. 1.6 Temperature distribution and cross-sectional view of Aluminum/polymer TIM
filled in a typical heating process.[89].

31Chapter 1. Background and objectives

1.6 Problem of previous studies and objectives of this study
As mentioned above, traditional TIMs cannot meet the requirements of electronic
devices with a high-speed development, due to their low thermal conductivity and otherpoor properties, such as the pump-out of thermal grease and the poor stability duringlong-term usage of PCMs. In the previous studies, although advanced carbon TIMs aredeveloped

successfully with higher thermal conductivity, light-weight property, better

physical and mechanical stability compared to traditional TIM, the properties ofdeveloped carbon TIMs still cannot not be completely exploited and failed to meet thedesign value temporarily. Besides, the balance between performance and cost of TIM
should concerned as another key. Using high-cost material and complicated fabrication
process may contribute to a higher thermal conductivity or other important propertiesof advanced carbon TIM, but it is unfavorable to practical application and industrial
production.
In this study, VGCF and polyvinyl alcohol(PVA) were fabricated to CNF sheetsthat exhibit high thermal conductivity through a simple fabrication method. PVA, acommercial resin, is expected to bind VGCFs and impart high flexibility to fabricatedsheets through its high adhesion strength and high malleability. The microstructure wasobserved, and the thermal and mechanical properties of fabricated sheets were
investigated. Moreover, as an attempt to increase the functionality of fabricated CNF
sheets for practical application, polytetrafluoroethylene (PTFE) was added to fabricated
PVA-PTFE-VGCF sheets for an improvement in hydrophilicity. The effect of PTFE
addition on microstructure and properties of CNF sheet were discussed. In addition, thethermal simulation was also carried out with the purpose of investigating the heattransfer path in CNF sheet. Our purpose was to fabricate a CNF sheet that exhibit highthermal conductivity by a simple and low-cost fabrication process for advanced TIM
applications.

32

Chapter 1. Background and objectives

1.7 Outline of this study
In Chapter 1, types of traditional TIMs were introduced and the development ofadvanced carbon TIMs was reviewed. The requirements properties of TIM and the
problems of the existed TIM were also discussed.
Chapter 2 introduced the fabrication of the PVA-based CNF sheet for TIM bysolution casting method. The microstructure, porosity, thickness, density, hardness andthermal conductivity were discussed. In addition, high temperature and humidity test
was measured in this chapter.
Chapter 3 introduced the fabrication of PVA-PTFE-VGCF sheet. By using two types
of PTFE with different size, the effect of PTFE addition on microstructure, thermal
conductivity and other properties of CNF sheet were investigated.
In Chapter 4, the thermal simulation of PVA-VGCF sheet is measured by using FEA
ANSYS student software. 5 types of microstructure models were created as: pure PVA,
horizontally arranged VGCF in PVA, vertically arranged VGCF in PVA and randomly
arranged VGCF in PVA, respectively. The heat transfer path inside the models is briefly
evaluated and the thermal conductivity of them was calculated through using thesimulation results.
As last, the results from the above-mentioned studies are summarized in Chapter 5.

33

Chapter 1. Background and objectives

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38

Chapter 2

Development of polyvinyl alcohol-based carbon
nano fiber sheet

2.1

Introduction ................................................................................................... 40

2.2

Experimental procedure................................................................................. 42

2.2.1

Raw materials ......................................................................................... 42

2.2.2

Fabrication method of PVA-VGCF sheet ............................................... 43

2.2.3

Evalution methods and equipments .......................................................... 45

2.2.3.1

Observation of microstruture ............................................................. 45

2.2.3.2

Measurement of porosity, thickness, density and hardness .............. 45

2.2.3.3

Periodic heating and infrared radiation thermometer method forthermal conductivity .......................................................................................... 45
2.2.3.4
2.3

High temperature and humidity test .................................................. 47

Results and discussion ................................................................................... 48

2.3.1

Microstructures and porosity of PVA-VGCF sheet ................................. 48

2.3.2

Thickness, density and hardness of PVA-VGCF sheet ............................ 53

2.3.3

Thermal properties of PVA-VGCF sheet ................................................ 55

2.3.4

High temperature and humidity test results ............................................ 59

2.4

Summary ........................................................................................................ 61

References ................................................................................................................ 62

39

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

2.1 Introduction
With the continually development of electronic industry, the heat density is
increasing rapidly on the electronic components. Without efficient heat dissipation,
malfunctions would be happened in junctions or modules of electronic component
caused by heat concentration[1]. Therefore, efficient heat dissipation threatens to limit
not only the working performance but also the service life of electronic component.
Thermal interface materials (TIMs), which is used to fill the air gaps between electronic
component and heat sink, are generally considered as an important part to improve theheat dissipating efficiency of electronic device by increasing the thermal conductive
and reducing the thermal contact resistance on the contact surface between electronic
component and heat sink. There are many types of TIM materials such as thermal pad,phase change materials, graphite sheets and metal sheets[2]. Grease is generally used as
TIM at present, but there were problems such as the difficulty of uniform spread andthe inclusion of voids in the grease. If grease is not properly spread, heat conduction
from the heat source to the heat sink could not be efficiently performed. The phasechange materials require a moderate contact pressure to keep mating surfaces together,in addition, the physical and chemical properties of the phase change materials are notstable during long term use[3]. In recent years, new TIM development has beenpromoted by carbon material, like Graphene, Carbon nanotube (CNT), Carbon
nanofiber (CNF) and others. Carbon materials such as graphene and CNTs, have been
widely studied as the fillers of TIMs, because of their high thermal conductivity andexcellent mechanical properties[4-8]. However, due to 2-dimensional structure, graphene
TIMs have a strongly anisotropic thermal conductivity. For example, Jeon et al.
developed a new cellulose-graphene-based TIM papers[9]. According to their report,
although the in-plane thermal conductivity of the cellulose-graphene-based TIM paper
was 7.32 W·m-1·K-1, the maximum through-plane thermal conductivity was very low
which was only 0.14 W·m-1·K-1. Huang et al. reported thermal conductivities of current
advanced graphene-based polymer composites. The thermal conductivities of most40

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet
reported graphene-based polymer nanocomposites were under 10 W·m-1·K-1, usinggraphene to enhance thermal conductivity did not show significant effect due to thehigh aspect ratio of graphene materials[7]. As for CNT TIMs, many studies havedemonstrated that it is hard to reach the expected properties, because of defects,
thickness, interface thermal resistance and purity[10]. Hong et al. fabricated a new
CNTs/polymethylmethacrylate (PMMA) composite by using single-walled carbon
nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs). The maximum
thermal conductivity of SWCNT/PMMA and MWCNT/PMMA composites were only
2.43 W·m-1·K-1 and 3.44 W·m-1·K-1. Their reports stated that the thermal conductivityof CNT TIMs was significantly affected by the purity and defects of CNT[11]. Moreover,the commercialization of most advanced TIMs is difficult due to the complexity inlarge-scale manufacturing method and their high cost. As for another carbon material,
CNF are discontinuous, highly graphitic, highly compatible with most polymer
processing techniques, and they can be dispersed in an isotropic or anisotropic mode.
As a type of CNF, vapor grown carbon fiber (VGCF) has excellent mechanicalproperties, such as high thermal conductivity, high specific strength, corrosion
resistance, and it is a commercially available carbon material with low price. VGCF
can be imparted to a wide range of matrices including thermoplastics and thermoset toform thin and flexible sheets. Therefore, carbon nanofiber was chosen as thermallyconductive fillers instead of other carbon materials. As a resin, PVA is expected to bind
VGCFs together and provide a good flexibility to CNF sheet, due to a goodadhesiveness and film-forming property.
The objective of this chapter is to fabricate PVA-based CNF sheets that exhibit
high thermal conductivity and good workability by a simple and low-cost fabrication
process. The microstructure of the PVA-VGCF sheets was determined through scanningelectron microscopy (SEM), and their porosity was calculated by using an image
analysis software. The thickness, density, and hardness of the PVA-VGCF sheets werealso investigated. A periodic heating and infrared radiation thermometer method wasused to measure the thermal conductivities of the PVA-VGCF sheet. In addition, a hightemperature and humidity tests was measured to investigate the long-term performanceof PVA-VGCF sheet, the test condition was set as 358 K and 85% RH for 500 h.
41

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

2.2 Experimental procedure
2.2.1

Raw materials

In this study, VGCFs with a diameter of 150nm and length of 10-20µm (Showa
Denko Co., Ltd.) were used for enhancing the thermal conductivity of fabricated sheet,
and a commercial PVA solution(Yamato Co., Ltd) with a concentration of 13 mass%
sold was used as the binder. SEM image of as-received VGCF and general chemical
formula of PVA are shown in Fig. 2.1. It should be noted that although the VGCFs wasreadily aggregates, the VGCFs were used under as-received condition directly, nodispersion medium was used in this study. Because the aggregation of VGCFs cancontribute to provide a 3D net-like structure during the fabrication process, which is
expected to improve the isotropic thermal conductivity of fabricated sheets.

(a)

(b)

Fig. 2.1 (a) FE-SEM image of VGCFs, and (b) Image and chemical formula of PVA.
42

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

2.2.2 Fabrication method of PVA-VGCF sheet
The fabrication procedure of CNF sheet is shown in Fig. 2.2. First, in order to obtaina TIM sheet with an isotropic thermal conductivity, the as-received VGCFs was poured
into PVA binder directly without any dispersion medium. After mixing by a silicone bar
with 20 rpm for 1 minute, spread the VGCF-PVA mixture on a PET ((C10H8O4)n) film
which is A4 paper size. Then, dried at room temperature (RT) for 48hours, the CNF
sheet can be separated from PET film. In this study, to investigate the influence ofamount of VGCF on thermal conductivity, five types of CNF sheets were fabricatedwith different the weight ratio of VGCF under fixed PVA amount. The fabrication
conditions of CNF sheets are shown in Table 2.1.

Fig. 2.2 Schematic of the fabrication procedure of CNF sheet.

43

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

Table 2.1 Fabrication conditions of PVA-VGCF sheets.
Samples

PVA: VGCF(mass%)VGCF(mass%)

VGCF(vol.%)

a1:0.100

43.48

17.04

b

1:0.070

33.90

12.85

c

1:0.050

27.78

10.15

d

1:0.030

20.41

8.18

e

1:0.025

16.13

7.95

44

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

2.2.3 Evaluation methods and equipment
2.2.3.1 Observation of microstructure
The microstructure of PVA-VGCF sheets were characterized by field mission
scanning electron microscopy (FE-SEM, HITACHI, S-5200).

2.2.3.2 Measurement of porosity, thickness, density and hardness
The porosity of each sheet was calculated by image analysis using the Image Pro Plus
6.0, and 5 random areas with a size of 250μm2 in each PVA-VGCF sheet was used forimage analysis. The density was calculated by mass and volume of each fabricated sheet.
The hardness of PVA-VGCF sheets was also tested by a shore durometer. According to
ASTM D2240 procedure, the PVA-VGCF sheets with a total thickness of 5 mm wereused for hardness measurement.

2.2.3.3 Periodic heating and infrared radiation thermometer method
for thermal conductivity
The thermal diffusivities of the PVA-VGCF sheets were evaluated by using periodic
heating and infrared radiation thermometer method at room temperature, with athermophysical analyzer (Thermowave Analyzer TA, BETHL). Fig. 2.3 shows theschematic of measurement theory. As showed in Fig. 2.4, 5 random points were chosen
to measure the thermal diffusivity of a simple with a size of 2500mm2. The specific heat
capacities of CNF sheets were measured by differential scanning calorimetry(DSC, XDSC7000, HITACHI). After getting all these values, TC was calculated with theequation:
𝜆 = 𝛼 × 𝜌 × 𝐶!

(2.1)

where 𝜆 is thermal conductivity (W·m-1·K-1), 𝛼 is thermal diffusivity(×10-6m2·s-1), 𝜌
is density(×106g·m-3) and 𝐶! is specific heat capacity(J·g-1·K-1) of samples,
respectively.
45

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet(a) In-plane direction(b) Through-plane direction

Fig. 2.3 Schematic of theory of periodic heating and infrared radiation
thermometer method: (a) In-plane direction (b) Through-plane direction.

Fig.2.4 Images of 5 test points in thermal diffusivity measurement.

46

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

2.2.3.4 High temperature and humidity test
To evaluate the long-term performance of CNF sheets under extreme condition, thehigh temperature and humidity test was also measured. The experiment device and theplace method are showed in Fig. 2.5. The size of samples is 20mm×20mm. The sample
under a net was place on a petri dish. The experimental conditions were set up as:
temperature was 358K, relative humidity (RH) was 85% and holding time was 500
hours.

(a)(b)

Size: 20mm×20mm
Fig. 2.5 Image of (a)experimental device of high temperature and humidity test, (b)place method of samples.
47

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

2.3 Results and discussion
2.3.1

Microstructures and porosity of PVA-VGCF sheet

Fig. 2.6 and Fig. 2.7 shows the photograph and SEM images of the PVA-VGCF
sheets. The fabricated sheet was soft and flexible with two surfaces: upper surface andbottom surface, due to the difference in the contact condition. The upper surface wascontact with air. Fig. 2.6 (a)~(e) show the SEM images of the upper surface
microstructure by different mass ratio of PVA:VGCF (1:0.100, 1:0.070, 1:0.050,
1:0.030, 1:0.025). All of sheets was shown that VGCFs were arranged in random
directions and connected with each other via PVA aggregates. In Fig. 2.6(a), a lot ofpores were observed between VGCFs. At the PVA:VGCF ratio of 1:0.100, due to therelatively low ratio of PVA, PVA can neither effectively infiltrate the VGCFs nor
construct a uniform surface; thus, there were a large number of obvious pores exhibit
in surface of PVA-VGCF sheet. As shown in Fig. 2.6(b) ~ (e), with the reduction of
VGCF ratio and the increasement of PVA ratio, the pore between VGCFs has been filled
by PVA and the porosity of fabricated sheet was decreased. Porosity of each PVAVGCF sheets was calculated by using image analysis software Image Pro, the result isshown in Fig. 2.8. The porosity of the 5 types of PVA-VGCF sheets decreases from 25%
to 22%, 18%, 17%, 13%, by decreasing the amount of VGCFs, which was considered
due to the numbers of intersection between VGCFs. Decreasing the amount of VGCFs
would also decrease the intersections between VGCFs. Because of these intersections,the PVA-VGCF sheets obtained a cellulose-like structure, through which the PVA
infiltration between VGCFs was hindered during the mixing process, thereby leading
to pore formation in the fabricated sheet. Therefore, decreasing the amount of VGCFs
lead to a lower porosity in CNF sheet. Fig. 2.7 showed the SEM images of bottom
surface of fabricated CNF sheets. The bottom surface was in contact with PET film
holder which was relatively flat and had a lower surface roughness. For the same reason,
due to the low content of PVA, Fig. 2.7 (a) showed a lot of large pores existed in the
microstructure of fabricated sheet. As shown in Fig. 2.7(b) ~ (e), with the reduction of48

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet
VGCF ratio and the increasement of PVA ratio, the pore between VGCFs has been
totally filled by PVA.

49

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

PVA-VGCF sheet

PET film holder

Upper surface

(a)

VGCF
Pore

Bottom surface

PVA

Upper surface

5μm

(c)

(b)

VGCF

VGCF
PVA

Pore
PVA

Pore

5μm

5μm

(d)

(e)

VGCF

PVA
VGCF

PVA

5μm

5μm

Fig. 2.6 SEM images of upper surface of fabricated CNF sheets by different mass
ratio of PVA : VGCF, (a)1 : 0.100, (b)1 : 0.070, (c)1 : 0.050, (d)1 : 0.030, (e)1 : 0.025.

50

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet(a)

PVA-VGCF sheet

PET film holder

Bottom surface

VGCF
Pore

PVA

Upper surface
(b)

5μm

PVA

(c)
VGCF
VGCF
PVA

5μm

5μm

(e)

(d)
VGCF

VGCF
PVA

PVA

5μm

5μm

Fig. 2.7 SEM images of bottom surface of fabricated CNF sheets by different mass
ratio of PVA : VGCF, (a)1 : 0.100, (b)1 : 0.070, (c)1 : 0.050, (d)1 : 0.030, (e)1 : 0.025.

51

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

Fig. 2.8 Effect of mass ratio of PVA:VGCF on porosity.

52

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

2.3.2

Thickness, density and Shore hardness of PVA-VGCF sheet

In order to evaluate the possibility of the fabricated PVA-VGCF sheets for practical
TIM application, thickness, density and Shore hardness of PVA-VGCF sheets were
measured. Fig. 2.9 shows the relationship between thickness and density by amountratio of VGCF and PVA. Average thickness of each PVA-VGCF sheet was 56, 52, 47,
35 and 30µm, it was showed that the fabricated sheets are become thicker by decreasing
amount of VGCFs. Considering the flat and smooth surface between semiconductor
and heat sink, it is better to keep the thickness of TIM to be about 0.5mm or less. It
should be noted that the air gaps between the semiconductor and heat sink could not beeffectively filled in wafer-thin TIMs. The thickness of sheet b (PVA:VGCF=1: 0.07)
and sheet c (PVA:VGCF=:0.05), which was 52µm and 47µm, were thought to be theideal thickness for TIM, because the thinner TIM could not to fill air gaps effectively
and the thicker TIM would increase the thermal resistance between semiconductor andheat sink. The density of each PVA-VGCF sheet was calculated by mass and volume,
the results was 1.10×106g·m-3, 1.06 ×106g·m-3, 1.03 ×106g·m-3, 1.15 ×106g·m-3, 1.12×106g·m-3. It was found that the fabricated sheets keep a relative constant density,
although fabricated by different mass ratio of PVA and VGCF and the density results
showed the lightweight property of PVA-VGCF sheets compared to some commerciallyavailable TIMs (1.44 ~ 3.6 × 106 g·m-3)[12]. In hardness test, according to ASTM D2240
procedure, each PVA-VGCF sheet was superimposed into the same thickness (6mm)and measured by Shore hardness. The result is shown in Fig. 2.10. The hardness of each
PVA-VGCF sheet was 83.4HS, 84.4HS, 82.2HS, 83.6HS, 83.8HS. There was not
obvious difference between fabricated sheets in Shore hardness, a constant hardness
was thought to be obtained successfully. It is interesting that the fabricated sheets
obtained a similar Shore hardness to that of commercial soft lining material[13], it was
implied the great softness and flexibility of fabricated PVA-VGCF sheets for practicalapplication of TIM.

53

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

Fig. 2.9 Effect of mass ratio of PVA:VGCF on the thickness and density of fabricatedsheets.

Fig. 2.10 Hardness of fabricated PVA-VGCF sheets by different mass ratio of
PVA:CNF.

54

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

2.3.3

Thermal properties of PVA-VGCF sheet

Fig. 2.11 and Fig. 2.12 shows the effect of mass ratio of PVA and VGCF on in-plane
and through-plane thermal conductivities of PVA-VGCF sheet, respectively. As weknown, the pure PVA resin has low thermal conductivity of about 0.28 W·m-1·K-1, andVGCF used in this study has a high thermal conductivity of 1200.00 W·m-1·K-1 at room
temperature[14]. As shown in Fig.2.11, the PVA-VGCF sheets were fabricated byamount of VGCFs: 1:0.1(17.04 vol.%), 1:0.07(12.85 vol.%), 1: 0.05 (10.15 vol.%), 1:
0.03 ( 8.18 vol.%), 1: 0.025 (7.95 vol. %), and the corresponding in-plane thermal
conductivity was shown as 3.40, 1.34, 6.44, 3.25 and 1.51 W·m-1·K-1, and though-plane
thermal conductivity was obtained as 12.94, 8.87, 14.30, 8.90, and 5.29 W·m-1·K-1,
respectively. Among all fabricated sheets, PVA-VGCF sheet c had the max thermal
conductivities as 6.44 W·m-1·K-1 in plane and 14.30 W·m-1·K-1 throughout plane.
Moreover, both of in-plane and through-plane thermal conductivities showed a nonlinear relationship with different VGCF content, it can be suggested that the thermal
conductivity was not only influenced by amount of VGCFs. Although VGCF was usedas thermally conductive material in this study, as mentioned above, the porosity offabricated sheet would also increase by increasing the amount of VGCF. The pores infabricated sheet were like air gaps, will decrease thermal properties apparently andcause a low density. This was the reason why sheet a and sheet b appeared lower thermal
conductivities. Moreover, overloading of VGCFs may also result in a deterioration of
mechanical properties of PVA-VGCF sheet. Therefore, minimizing the amount of
VGCFs while keeping high thermal properties is preferable for sheet fabrication[15]. In
addition, there was a large thermal conductivity error of sheet a as shown in Fig. 2.12,
it was also caused by the high porosity. Because the thermophysical properties of thefabricated sheets were measured using periodical heating radiation-temperature
measuring method in this study, the laser diameter was 100 ~ 150µm, which means theresult was easily affected by the surface condition and roughness of sample. Meanwhile,
due to the high porosity of sheet a, a large number of pores can readily structure an
undulating surface. Considering the thickness of sheet a was only 56µm, some large
pores shown in Fig. 2.6(a) would also lead to an obvious reduction of thickness in this55

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet
area. The undulating surface and uneven thickness of sheet a can have a strong influenceon heat radiation and the calculation of thermal conductivity. Therefore, there was alarge thermal conductivity error of PVA-VGCF sheet a. As for PVA-VGCF sheet d andsheet e, the low thermal conductivity was caused by low VGCF content, and theirregularity of surface which has mentioned above. Table 2.2 lists previously reported
thermal conductivity of other polymer-based carbon TIMs. As shown in this table, thethrough-plane thermal conductivity of CNF sheet in this study is significantly higher
than those of previous studies. Although the in-plane thermal conductivity of CNF sheet
is not the best, but it is still higher than the most of reported thermally conductive
materials. By using a simple and cost-effective process, the integration of high thermal
conductivity, lightweight and super flexibility makes the CNF sheets highly promisingfor heat management of advanced electronic device.

56

Thermal conductivity, λ/ W·m-1·K-1

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

16

In-plane

14

c

12
10
8
6

d

b

a

e

4
2
0
1:0.1

1:0.07 1:0.05 1:0.03 1:0.025
Mass ratio of PVA : VGCF

Thermal conductviity, λ/ W·m-1·K-1

Fig. 2.11 Effect of mass ratio of PVA and CNF on the in-plane thermal conductivity.

16

Experimental data
Theoretical calculation

14

Through-plane

12
10

c

8
6
4

d

a

e

b

2
0
1:0.1

1:0.07

1:0.05

1:0.03

1:0.025

Mass rate of PVA:VGCF

Fig. 2.12 Effect of mass ratio of PVA and CNF on the through-plane thermal
conductivity.

57

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

Table 2.2 Comparison of thermal conductivity of our PVA-VGCF sheet with otherpolymer-based carbon TIMs.
Thermal conductivity
Material

CNF

MatrixFractionThickness[λ/W·m-1·K-1][t/µm]
In-planeThrough-plane

Reference

PVA

10.15 vol%

47

14.30

6.44

This study

Epoxy

13 vol%Unknown

1.70

2.84

16

Epoxy

16.7 vol%Unknown

1.00

4.87

17

PVDF

2.5 wt%50

Unknown

0.72

9

Epoxy

0.92 vol%Unknown

0.63

2.13

18

Epoxy

8.3 wt%Unknown

8.80

2.00

19

27.48 vol%

71

39.27

1.50

20

3D-Carbon
fibersnetwork
CNT
Graphite
nanoplatelet
Graphene
aerogelTemplatedgrapheneframework
Graphene

Naturenanoplateletrubber58

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

2.3.4

High temperature and humidity test results

In this chapter, the PVA-VGCF sheet (PVA:VGCF=1:0.050), which had the highest
value of thermal conductivities among the fabricated sheets, was cut into 4 specimens
with a size of 20×20mm for high temperature and humidity test. Each specimen washeld at the temperature of 358K and relative humidity (RH) of 85% for 500 hours. Afterthe high temperature and humidity test, the average of in-plane and through-plane
thermal conductivity of 4 specimens was measured. As shown in Fig. 2.13 and Fig. 2.14,
it was indicated that before test the in-plane thermal conductivity had a high value as
14.30 W·m-1·K-1, but after test the average in-plane thermal conductivity of 4 specimens
decreased to 9.85 W·m-1·K-1, with a reduction of 31%. As the same, before test thethrough-plane thermal conductivity was 6.44 W·m-1·K-1, and after test the averagethrough-plane thermal conductivity decreased to 2.71 W·m-1·K-1, which was reducedby nearly 57%. It was considered that the reduction of thermal conductivity was causedby the hydrophilic property of PVA. The water in PVA increased porosity and decreased
thermal properties of fabricated sheet. The water molecules in the environment would
be absorbed into fabricated sheets by PVA. The absorbed water in PVA not only disruptshydrogen bonding, but also contributes more free volume and lubrication. The PVA
segments in fabricated sheets become readily mobile and rapidly responding to the loadchange[21], which may lead to a movement of PVA from surface to center part of PVAVGCF sheet. A large number of pores would be generated in surface of fabricated sheet.
Therefore, absorbed water in PVA increased the porosity and degraded the thermal
properties of the PVA-VGCF sheets.

59

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

Fig. 2.13 In-plane thermal conductivity of specimens before and after the hightemperature and humidity test.

Fig. 2.14 Through-plane thermal conductivity of specimens before and after the hightemperature and humidity test.

60

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

2.4 Summary
In this chapter, an innovative thermal interface material based on a composite of PVA
and VGCF was fabricated successfully, by a simple and cost-efficient procession
method. 5 kind of CNF sheets have been fabricated with different mass ratio of
PVA:VGCF, the in-plane and through-plane thermal conductivities were measured. The
mechanical properties of each CNF sheet also have been tested. From this work, theimportant results are list below:(1) The VGCFs in fabricated sheets were arranged in random directions and connectedwith each other via PVA aggregates. A lot of pores existed between VGCFs due tothe evaporation of water. The porosity of CNF sheets decreased by decreasing theamount of VGCF.
(2) The thickness of CNF sheets increased by increasing the amount of VGCF. The
density and hardness of CNF sheets had not apparent difference between eachfabricated sheet.
(3) The highest value of thermal conductivity was 6.44 W·m-1·K-1 in-plane and 14.30
W·m-1·K-1 through-plane. Reducing the amount of VGCF would decrease thethermal conductivity apparently. However, increasing the amount of VGCF
excessively could also bring an increase of porosity in CNF sheet and reducing thethermal conductivity.
(4) The in-plane and through-plane thermal conductivities had obvious reductions after
the high temperature and humidity test due to the hydrophilic property of PVA.

61

Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet

References[1]

Y. L. Ji, H. L.Yan, X. Xiao, J, T. Xu, Y, T. Li, C. Chang: Appl. Therml. Eng. 166(2020) 114649.

[2]

J. W. Zhao, R. Zhao, Y. K. Huo, W. L. Cheng: Int. J. Heat Mass Transf. 140 (2019)705-716.

[3]

Y.C. Li, G. L. Sang, H. W. Shi: J. New Mater. Electrochem. Syst. 17 (2014) 123127.

[4]

Y. X. Fu, Z. X. He, D. C. Mo, S. S. Lu: Int J Therm Sci. 86 (2014) 276-283.

[5]

L. Peng, Z. Xu, Z. Liu: Advanced Material 29 (2017) 1700589.

[6]

H.Y Sun et al.: Chem. Mater. 29 (2017) 7808-7815.

[7]

J. Khan, S. A. Momin, M. Mariatti: Carbon 168 (2022) 65-112.

[8]

Y. Gogotsi: Nanotubes and Nanofibers (CRC Press, New York, 2006) pp. 51-58.

[9]

Q. S. Song, W. Zhu, Y. Deng, D. L. He, J. J. Feng: Compos. Sci. Technol. 168(2018) 381-387.

[10] N. D. Greef, L. X. Zhang, A. Magrez, L. Forrό, J. P. Locquet, I. Verpoest, J. W.
Seo: Diam Relat Mater. 51 (2015) 39-48.
[11] W. T. Hong, N. H. Tai: Diamond Relat. Materi. 17 (2008) 1577-1581.
[12] C. P. Feng: Compos. Commun. 22 (2020) 100528.
[13] I. M. Meththananda, S. Parker, M. P. Patel, M. Braden: Dent. Mater. 25 (2009)956-958.
[14] Y. M. Et al.: J. Mater. Chem. C. 24 (2018) 6469-6501.
[15] H. F. Song et al.: Joule 2 (2018) 442-463.
[16] J. K. Ma et al.: Chem. Eng. J. 380 (2020) 122550.
[17] A. Marconnet, N. Yamamoto, M. A. Panzer, B. L. Wardle: ACS Nano 5 (2011)4818-4825.
[18] G. Lian et al.: Chem. Mater. 28 (2016) 6069-6104.
[19] X. Shen et al.: Mater. Horizons 5 (2018) 275-284.
[20] C. P. Feng et al: Compos. Commun. 12 (2019) 80-85.
62Chapter 2. Development of polyvinyl alcohol-based carbon nanofiber sheet[21] R. M. Hodge, T. J. Bastow, G. H. Edward, G. P. Simon, A. J. Hill:
Macromolecules 29 (1996) 8137-8143.

63

64

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

Chapter 3

Effects of polytetrafluoroethylene addition on
microstructure and thermal properties of PVA-VGCF
sheet

3.1

Introduction ................................................................................................... 66

3.2

Experimental procedure................................................................................. 68

3.2.1

Raw materials ........................................................................................ 68

3.2.2

Fabrication method of PVA-PTFE-VGCF sheet.................................. 69

3.2.3

Evaluation method and equipment ....................................................... 71

3.3

Results and discussion ................................................................................... 72

3.3.1

Microstructures of PVA-PTFE-VGCF sheet ........................................... 72

3.3.2

Porosity, Thickness, density and hardness of PVA-PTFE-VGCF sheet . 74

3.3.3

Thermal properties of PVA-PTFE-VGCF sheet ..................................... 77

3.3.4

High temperature and humidity test results ........................................ 82

3.4

Summary ........................................................................................................ 88

References ................................................................................................................ 89

65

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

3.1 Introduction
The thermal interface materials (TIMs) are used to fill the air gaps between a heatgeneration device and a heat-dissipation thrust for heat distribution. With the rapid
development of the electronics industry, the rising higher power density in electronics
presents an increasing requirement for heat dissipation, because electronics are
becoming intelligent, miniaturized, and integrated. Thus, the development of TIMs
become extremely significant for the heat management of advanced electronic products.
Besides of thermal properties, the functional property of TIM is also required now. For
example, for electronic equipment used in scientific research experiments in Antarctica,
its TIMs need to endure the minimum temperature to 183K[1] and maintain a certain
degree of flexibility and thermal conduction ability. For the electronic equipment usedin Amazon rainforest with a flexible environment of a relative humidity high at an
average of 88% in the rainy season and 77% in the dry season[2], TIMs used in thisregion require a higher humidity resistance than usual.
In chapter 2, we reported an efficient and simple method to fabricate polyvinyl
alcohol (PVA)-based VGCF sheet with a mass ratio of VGCF:PVA = 1:2.6, which highTC of 6.44 W·m-1·K-1 in the through-plane direction and 14.30 W·m-1·K-1 in the inplane direction. The PVA-based VGCF sheet also has a lightweight property with adensity of 1.03×106 g·m-3 and is as soft as commercial soft lining materials with a Shore
hardness of 82.2HS. However, the thermal conductivities were significantly reduced
after the high temperature and humidity test, due to the hydrophilic property of PVA.
Polytetrafluoroethylene(PTFE) consisting of carbon and fluorine, has excellent
hydrophobicity and good dispersibility, and high chemical stability[3,4], which isconsidered to be an excellent filler to enhance the hydrophobicity of composite material
for practical application. Moreover, dispersed nanometric scale reinforcement
significantly increases the tortuosity of the path for the permeation of water molecules.
However, it should be noted that excessive addition of PTFE powders would
significantly reduce the thermal conductivities of the fabricated sheet, due to the low
66

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet
TC of PTFE (~0.3 W·m-1·K-1). Considering all the above, it is believed that thehydrophobicity of the PVA-VGCF sheet will be enhanced by adding PTFE nanopowders, while keeping the mass ratio of VGCF : resin (PVA and PTFE) the same asthat of previous PVA-VGCF sheet.
This chapter has focused on understanding the full influence of the use of an
optimized mass ratio of PTFE (VGCF:PVA:PTFE=1:1.3:1.3) as a filler in the VGCF
sheet, for guaranteeing an improvement in hydrophilicity. All the experimental resultsof the VGCF:PVA:PTFE sheet were compared with the PVA-VGCF sheet of theprevious report to evaluate the influence of added PTFE powders on their properties.

67

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

3.2 Experimental procedure
3.2.1

Raw materials

The VGCFs were purchased from SHOWA DENKO K.K. and have an excellent
thermal conductivity of 1200 W·m-1·K-1 and a length of 10 - 20 µm. Commercial PVA(Yamato Co., Ltd.) with a concentration of 13 mass% was used as a binder. As showed
in Fig. 3.1, two types of PTFE particles with different size: L173JE(120nm) andTF9207Z(300nm) were used to improve the hydrophobicity of the PVA-VGCF sheet,
which were supplied by 3M Japan Ltd., and AGC Chemical Company, respectively.

Fig. 3.1 FE-SEM image(×6000) of: (a)PTFE powders of 120nm and (b)PTFE
powders of 300nm.

68Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

3.2.2

Fabrication method of PVA-PTFE-VGCF sheet
The preparation process of the PVA-PTFE-VGCF sheet is shown in Fig. 3.2.

Based on solution mixing, a simple but industrial method was adopted to fabricate the
VGCF sheet. To make PTFE powders dispersed evenly in a fabricated sheet, PTFE
powders were mixed PVA binder by an agitator at 100 rpm for 1 hour. After that, theVGCFs were poured into the PVA-PTFE mixture and mixed with a silicon bar at 20rpm for 1 minute, the PVA-PTFE-VGCF mixture was spread on a PTFE film of A4
paper size. At last, after drying this at room temperature (RT) for 48 hours, the PVAPTFE-VGCF sheet was separated from the PTFE film. In this study, two types of PVAPTFE-VGCF sheets: PVA-PTFE L173JE-VGCF sheet (PPLV) and PVA-PTFE
TF9207Z-VGCF sheet (PPTV) were fabricated by using different PTFE particles of
L173JE (120nm) and TF9207Z (300nm). The fabrication condition is listed in table 3.1.

Fig. 3.2 Schematic of the fabrication procedure of PVA-PTFE-VGCF sheet.

69

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

Table 3.1 Fabrication conditions of PVA-PTFE-VGCF sheets.
Samples

VGCF:PVA:PTFE(mass%)

Particle size of
PTFE
(nm)

PPLV

1:1.3:1.3

120

PPTV

1:1.3:1.3

300

70

VGCF
(mass%)

27.78%

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

3.2.3

Evaluation method and equipment

The dispersion of PTFE powders in the PVA matrix and the morphology offabricated sheets were checked by FE-SEM. The porosity of each VGCF sheet wascalculated by using the image analysis software Image-Pro Plus 6.0, which used fiverandom areas with a size of 1.28×10-3 mm2 from each VGCF sheet. The thickness of
fabricated sheets was measured by using a digital micrometer (MonotaRo Co., Ltd.).
Density was calculated from the mass and volume of each fabricated VGCF sheet.
According to the ASTM D2240 procedure[5], the fabricated VGCF sheets with a total
thickness of 6 mm were used for the Shore hardness test by using a Shore hardness
durometer. The thermal diffusivity (α) of fabricated sheets at RT was evaluated using aperiodic heating and infrared radiation thermometer method (Thermowave Analyzer
TA). Specific heat capacity (Cp) was measured by using DSC (X-DSC 7000, HITACHI,
Japan). After getting all these values, TC was calculated by equation (2.1). To evaluate
the long-term performance of the fabricated sheets, the high temperature, and humidity
test was performed at a temperature of 358K and relative humidity (RH) of 85% for
500 hours. The infrared spectra of the fabricated PVA-PTFE-VGCF sheet were
measured by using a Fourier transform infrared spectrometer (FT-IR) in the range of4000 cm-1 to 600 cm-1. FT-IR is a technique that is used to obtain infrared spectrum ofabsorption, emission and photoconductivity of solid, liquid and gas[6], which is often
used to identify organic and polymeric materials.

71

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

3.3 Results and discussions
3.3.1

Microstructures of PVA-PTFE-VGCF sheet

Fig. 3.3 shows the SEM images and microstructure schematics of referred PVAVGCF sheets and fabricated PVA-PTFE-VGCF sheets. All of the sheets were shownthat VGCFs were arranged in random directions and connected with each other via PVA
aggregates. Because of the aggregation of as-received VGCFs, a 3D net-like structure
was built by VGCFs, which contribute high through-plane TC and good physicalstability to fabricated sheets. On the other hand, as shown in Fig3.3 (a), the intersectionsof the 3D network structure also led to the difficulty for PVA to enter inside during
mixing and created many pores in the reference PVA-VGCF sheet, resulting in asignificant decrease in TC. In Fig. 3.3(b) and 3(c), the microstructures showed that theaddition of PTFE powder can effectively filled these pores. However, partial
aggregation of PTFE particles was also observed due to the intermolecular forces ofPTFE particles. Especially for 120nm PTFE, some large collections of 120nm PTFE
particles and unfilled pores were observed in Fig. 3.3(b). This poor dispersion of 120nm
PTFE powder will adversely affect the efficiency of heat dissipation in the fabricatedsheet. On the contrary, it can be clearly seen from Fig. 3.3(c) that the 300nm PTFE
particles were still well distributed and compatible in the fabricated PPTV sheet due tothe smaller aggregates, and the pores between VGCFs were almost filled by 300nm
PTFE particles. Furthermore, the schematic diagram of the microstructure showed thatthe different dispersion of 120nm and 300nm PTFE powders leads to different
microstructures in the fabricated sheets. Smaller PTFE particles were more likely toaggregate and form uneven surfaces, while 300 nm PTFE particles can be relatively
uniformly dispersed among VGCFs and filled the pores effectively.

72

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

Fig. 3.3 SEM images (×6000) and microstructure schematics of fabricated VGCF
sheets: (a) PVA-VGCF sheet*, (b) PPLV sheet and (c) PPTV sheet.

73

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

3.3.2

Porosity, Thickness, density and hardness of PVA-PTFE-VGCF

sheet
To evaluate the possibility of a fabricated VGCF sheet for practical application for
TIM, the porosity, thickness, density, and Shore hardness was measured. As shown in
Fig. 3.4, the porosity of the reference PVA-VGCF sheet was as high as 18%. Afteradding PTFE particles, although the concentration of PVA decreased, which means
more pores should be produced theoretically[7], the porosity of PPLV sheet and PPTV
sheet are reduced to 9% and 6% respectively due to the pores were filled by PTFE
particles. And due to the aggregation of 120nm PTFE particles, the porosity of PPLV
sheet was higher than that of PPTV sheet.
As the same, the average thickness of the VGCF sheet was also decreased from 47µm
for the PVA-VGCF sheet to 31.2µm and 28.2µm for PPLV and PPTV sheets
respectively, due to the lower content of the PVA matrix. It is considered that
agglomeration of 120nm PTFE particles were much larger than that of 300nm PTFE
particles and cannot fill the pores of fabricated VGCF sheets. Agglomeration of 120nm
PTFE particles caused surface unevenness and increased the thickness of the fabricatedsheet. In addition, the thickness of TIM has a great influence on the absolute thermal
resistance across the TIM. From Fourier’s Law for heat conduction, the absolute
thermal resistance Rθ of TIM is calculated by using the equation:18):#

𝑅" = $×&(3.1)

where t is the thickness of TIM, A is the cross-sectional area perpendicular to the pathof heat flow, and λ is the thermal conductivity of TIM. Therefore, the absolute thermal
resistance of a TIM will decrease by using thinner material. The lower absolute thermal
resistance means this material is a better thermal conductor in practical applications.
Therefore, the TIMs with lower thickness such as PPLV and PPTV sheets have greater
potential in the application in advanced precision instruments, which have become
miniaturized and complex in recent years. However, it should be noted that the air gaps
74

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet
cannot be efficiently filled in wafer-thin TIMs. In this case, increasing the total mass of
PVA, PTFE, and VGCF during the preparation process could increase the thickness ofthe fabricated VGCF sheet to solve the problem. The density of PPLV and PPTV sheet
were calculated using mass and volume, as shown in Fig. 3.5, the values were 0.79×106
g·m-3 and 0.91 × 106 g·m-3 respectively. Compared with the PVA-VGCF sheet, PPLV
and PPTV sheets had a lower density, which showed a greater lightweight property of
PPLA and PPTV sheet compared to some commercially TIMs (1.44-3.6×106 g·m-3).
PPLV and PPTV sheets were superimposed to the same thickness as 6mm to measure
their Shore hardness according to ASTM D2240 procedure. The result was shown in
Figure 3.5. The average Shore hardness of PVA-VGCF sheet, PPLV and PPTV sheet
was 82.2HS, 86.0HS and 85.4HS, respectively. PPLV and PPTV sheets became slightly
stiffer than PVA-VGCF sheets due to lower PVA matrix content. Even so, thecontinuous 3D-net like structure composed of VGCFs allows the fabricated sheets totake advantage of the high elasticity of the PVA matrix to generate large deformationand low stiffness, which suggesting that PPLV and PPTV have great softness andflexibility for practical applications as TIMs.

75

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

30

65
60
55

20

50
15

45
40

10

Thickness, t/μm

Porosity, %25

70
Porosity
Thickness

35
30

5

25
0

20
PVA-VGCF*

PPLV

PPTV

Fig 3.4 The porosity and thickness of fabricated PVA-VGCF*, PPLV and PPTV
sheets.

2

88

1.6

86

1.4

84

1.2

82

1

80

0.8

78

0.6

76

0.4

74

0.2

72

0

Shore hardness

Density, ρ/×106g·m-3

1.8

90Density
Hardness

70
PVA-VGCF*

PPLV

PPTV

Fig 3.5 The density and shore hardness of fabricated PVA-VGCF*, PPLV and
PPTV sheets.

76Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

3.3.3

Thermal properties of PVA-PTFE-VGCF sheet
Fig. 3.6 and Fig. 3.7 show the effect of the addition of PTFE powder on the in-plane TC, through-plane TC, and the thermal diffusivities of the fabricated sheets. As
shown in Fig. 3.6, with the addition of the PTFE powders, the in-plane TC of PPLV and
PPTV sheet had a reduction of 46% and 31% respectively, which decreased from 14.30
W·m-1·k-1 to 7.66 W·m-1·k-1 of PPLV sheet and 9.81 W·m-1·k-1 of PPTV sheet. As
shown in Fig. 3.7, the through-plane TC also had a reduction of 72% and 67% after the
addition of PTFE powders, which decreased from 6.44 W·m-1·k-1 to 1.79 W·m-1·k-1 and2.11 W·m-1·k-1, respectively. The thermal diffusivities on the in-plane and throughplane directions of fabricated sheets have similar reduction trends with TC.
In theory, thermal conduction of VGCF, PVA and PTFE is achieved mainly by thevibration of atoms and molecules near their equilibrium position[8]. VGCF has a highTC of 1200.00 W·m-1·k-1. On the other hand, due to the low crystallinity of polymer,
the PVA and PTFE have very low thermal conductivities, the TC of pure PVA isapproximately 0.21 ~ 0.76 W·m-1·k-1 and the that of PTFE powders is less than 0.3
W·m-1·k-1. Thus, the thermal conduction in PVA-PTFE-VGCF sheet mainly depends
on the high thermal conductivity via VGCF networks. The thermal conductive
mechanisms in this study include thermal conductive path theory and surface
microstructure of fabricated sheet. Through the thermal conductive path theory[9,10], thethermal paths were formed by the contact of VGCFs in the fabricated sheet. The heat
flux mainly transferred along the 3D network of VGCF with lower thermal resistance.
The PVA and PTFE increased the thermal interface resistance and formed thermal
barrier to the thermal paths. This is the first reason for the reduction of TC with theaddition of PTFE powders. The surface microstructure was another reason for the
reduction of TC, which was shown in Fig. 3.8. Without the filling of PTFE powders,
the surface of the PVA-VGCF sheet had a surface wave, which was caused by the bulge
of VGCFs. With the addition of PTFE powders, this wave can be filled and reformed
into a relatively smooth surface, consisting mostly of PTFE particles and a small part77

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheetof bulging VGCFs. When the front surface of the PVA-VGCF sheet was heated by alight pulse, the heat can reach the rear face quickly through the heat paths as shown in
Fig. 3.8(a), which is indicated that the PVA-VGCF should have a good thermal
diffusivity and TC. As shown in Fig. 3.8(b), due to the low TC of PTFE, adding PTFE
powder resulted in forming a thermal barrier, and the heat can only reach the rear facethrough the small part of bulging VGCFs, which lead to the lower TC of PPLV and
PPTV sheet. Table 3.2 lists the previously reported thermal conductivity of other paperlike thermally conductive composites. As shown in this table, the through-plane thermal
conductivity of PPLV and PPTV sheet in this study was significantly higher than thoseof previous studies,while the in-plane thermal conductivity of the fabricated sheet

still maintains a higher level among all these paper-like thermally conductive
composites.

78

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

Thermal conductivity,λ/ W·m-1·K-1

18

20

Thermal conductivity

18

Thermal diffusivity

16

16

14

14

12

12

10

10

8

8

6

6

4

4

2

2

0

Thermal diffusivity,𝛼/x10-6·m2·s -1

20

0
PVA-VGCF*

PPLV

PPTV

Fig. 3.6 In-plane thermal conductivities and thermal diffusivities of PVA-VGCF,
PPLV and PPTV sheet.

Thermal conductivity,λ/ W·m-1·K-1

18

20

Thermal conductivity
Thermal diffusivity

18

16

16

14

14

12

12

10

10

8

8

6

6

4

4

2

2

0

Thermal diffusivity,𝛼/x10-6·m2·s- 1

20

0
PVA-VGCF*

PPLV

PPTV

Fig. 3.7 Through-plane thermal conductivities and thermal diffusivities of PVAVGCF, PPLV and PPTV sheet.
79

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

Fig. 3.8 The schematic of microstructure near the surface of PVA-VGCF sheet and
PVA-PTFE-VGCF sheet.

80Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

Table 3.2 Comparison of thermal conductivity between this work and other paper-likecomposites.

Materials

Amount rate ofreinforcement[wt.%]

Thermal conductivity[λ/W·m-1·K-1]
In-planeThroughplane

Ref.

PPLV

27.78

7.66

1.79

This
work

PPTV

27.78

9.81

2.11

This
work

Graphene paper

Unknown

7.32

0.14

11

Cellulose/Ag
composite film

2

6

0.8

12

Cellulose/Graphene
Nanosheets Hybrid
Films

1

12.6

0.042

13

Boron nitride
nanosheet/cellulose
nanofiber film

25

22.67

1.08

14

Graphene oxide/cellulose nanofiber
composite films

50

7.3

0.13

15

81

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

3.3.4

High temperature and humidity test results
To evaluate the long-term performance, the PPLV and PPTV sheets were cut into

specimens with a size of 20 × 20 mm for high temperature and humidity test. Eachsample was kept at 358K and 85% RH for 500 hours. After the high temperature andhumidity test, the in-plane and through-plane TC of each specimen were also measured.
In Fig. 3.9, the SEM images of PPLV and PPTV sheets before and after the hightemperature and humidity test was showed. It was clear to seen that the PVA in surface
was partially disappeared after the test. As shown in Fig. 3.10, prior to testing, the inplane TC of the PVA-VGCF sheet, PPLV sheet, and PPTV sheet were 14.30, 7.66, and9.81 W·m-1·k-1, respectively; After testing, the TC of PVA-VGCF sheet wassignificantly reduced by 31% to 9.85 W·m-1·k-1. However, the TC of PPLV and PPTV
sheets were increased to 9.02 and 10.81 W·m-1·k-1, with an increase of 18% and 10%.
Similarly, as shown in and Fig 3.11, the through-plane TC of the PVA-VGCF sheet was
decreased by 57% from 6.44 W·m-1·k-1 to 2.71 W·m-1·k-1 after the high temperatureand humidity test. The TC of PPLV and PPTV sheets were increased from 1.79 and 2.11
W·m-1·k-1 to 2.21 and 2.49 W·m-1·k-1, with an increase of 23% and 18% respectively.
In order to find out the reasons for the increased TC in PPLV and PPTV sheets, FT-IR
analysis was performed on the surfaces of PPLV and PPTV sheets. The FT-IR result
was shown in Fig. 3.12. Two IR detection bands were marked in this figure, 1211 cm-1
to 1154 cm-1 representing the entire C-F stretching of PTFE and a narrow band at 1734
cm-1 to 1717 cm-1 representing the C=O stretching of PVA. Before the high temperatureand high humidity test, PVA and PTFE were detected on the surface of the fabricated
VGCF sheet. However, after the high-temperature and humidity test, the C=O peak
disappeared, which means that the PVA disappeared from the surface of the fabricatedsheet. It is considered that due to the strong hydrophilicity of PVA, water molecules in
the high-temperature and humidity test environment will be absorbed into the VGCF
sheet by PVA. Water absorbed in PVA not only breaks hydrogen bonds but also provides
more free volume and lubricity[16,17]. As a result, the PVA segments in the VGCF sheet
82

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet
become easily mobile and respond quickly to load changes, which may cause the PVA
to move from the surface to the central part of the VGCF sheet and lead to thedisappearance of the C = O stretch in the FT-IR analysis. As a result, a large number ofpores was generated on the surface of the VGCF sheet, resulting in a reduction of TC.
Unlike PVA-VGCF sheets, the pores generated by PVA movement in PPLV and PPTV
sheets can be effectively filled by PTFE particles. Therefore, due to the rearrangementof PVA and PTFE particles, PPLV and PPTV sheets obtained a uniform surface andhigher density after high temperature and humidity tests. A TIM with a uniform surface
tends to have a lower absolute thermal resistance, while a higher density helps increase
the TC of the TIM. Therefore, the TC of PPLV and PPTV after high temperature andhumidity test were increased. This phenomenon provides innovative ideas for
improving the stability and long-term performance of TIMs in practical applications.
The properties of each VGCF sheet were measured, and a comparison with referred
PVA-VGCF sheet was shown in Fig. 3.13.

83

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

(a)

(b)

(c)

(d)

Fig. 3.9 SEM images(×1000) of (a)PPLV sheet, (b)PPTV sheet in room temperatureand (c)PPLV sheet, (d)PPTV sheet after high temperature and humidity test.

84

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

20

PVA-VGCF*
PPLV
PPTV

Thermal conductivity,λ/ W·m-1·K-1

18
16
14
12
10
8
6
4
2
0

Room temperature

High temperature andhumidity

Fig. 3.10 The in-plane TC of fabricated CNF sheets after high temperature andhumidity test.

20
Thermal conductivity, λ/ W·m-1·K-1

18
16

PVA-VGCF*
PPLV
PPTV

14
12
10
8
6
4
2
0
Room temperature

High temperature andhumidity

Fig. 3.11 The in-plane TC of fabricated CNF sheets after high temperature andhumidity test.

85

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

C-F Stretching
High temperature and humidity

Absorbance

C=O Stretching

Room temperature

Wavenumber (cm-1)

Fig. 3.12 The FT-IR analysis of fabricated CNF sheets at room temperature andafter high temperature and humidity.

86

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

Fig. 3.13 The properties comparison of PVA-VGCF, PPLV and PPTV sheets.

87Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

3.4 Summary
A comparison with referred PVA-VGCF sheet was shown in Fig. 3.12. In all,novel PVA-PTFE-VGCF thermal interface materials were successfully developed by asimple and cost-effective process. Two types of VGCF sheets were fabricated by using
120nm and 300nm PTFE particles, the conclusions were summarized as follows:(1) the microstructure observation revealed that the VGCFs were arranged in random
directions and interconnected via PVA aggregates. 300nm PTFE particles were welldistributed and compatible within the PPTV sheet, while partial aggregations of
120nm PTFE particles and unfilled pores were observed in the PPLV sheet.
(2) With the addition of PTFE particles, the thermal conductivities of fabricated CNF
sheets were decreased. The fabricated PPTV sheet with PTFE size of 300nm has
higher thermal conductivities of 9.81 W·m-1·k-1 in the in-plane direction and 2.11
W·m-1·k-1 in the through-plane direction.
(3) After the high temperature and humidity test, the in-plane and through-plane TC of
PVA-PTFE-VGCF sheets were increased. According to the FT-IR analysis result,it was considered that the increase in TC was caused by the hydrophobic propertyof PVA and rearrangement of PVA and PTFE particles.

88

Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet

References[1]

Encyclopædia Britannica, Inc., USA, Available at. https://www.britannica.com/
place/Antarctica/Plant-life (Accessed 2022-11-26).

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World Wide Fund For Nature, Switzerland, Available at. https://wwf.panda.org/
discover/knowledge_hub/where_we_work/amazon/about_the_amazon/(Accessed 2022-11-26).

[3]

J. H. Ki, J. O. Hyun, E. Hyeonjin, K. Yeonsang, H. J. Jae: Sci. Total Environ. 783(2021) 147083.

[4]

M. G. Shi, F. M. Miyazawa, S. G. Tobe, T. A. Stolarski: Mater. Trans. 46 (2005)[5]84-87.
ASTM International. ASTM D2240-15 Standard test method for rubber propertydurometer hardness (2015).

[6]

R. Sindhu, P. Binod, A. Pandey: Industrial Biorefineries & White Biotechnology[7](Elsevier B.V. 2015) pp. 575-605.
J. L. Xiong, S.R. Chen, Y. B. Choi, K. Matsugi: Sci. Rep. 11 (2021) 17183.

[8]

F. Zhang, Y.Y. Feng, M.M. Qin, L. Gao, Z.Y. Li, F.L. Zhao, Z.X. Zhang, F. Lv, W.
Feng: Adv. Funct. Mater. 29 (2019) 1901383.

[9]J. Gu, G. Liang, X. Zhao, B. Gan, H. Qiu, Y. Guo, X. Yang, Q. Zhang, D.Y. Wang:
Compos. Sci. Technol. 139 (2017) 83-89.

[10] C. P. Feng, L.Y. Yang, J. Yang, L. Bai, R.Y. Bao, Z.Y. Liu, M.B. Yang, H.B. Lan,
W. Yang: Compos. Commun. 22 (2022) 100528.
[11] D. Jeon, S.H. Choi, W. Byon: Int. J. Heat Mass Transfer 132 (2019) 944-951.
[12] Z. M. Shen, J. C. Feng: ACS Appl. Mater. Interfaces 10 (2018) 24193-24200.
[13] N. Song, D. J. Jiao, S. Q. Cui, X. S. Hou, P. Ding, L.Y. Shi: ACS Appl. Mater.
Interfaces 9 (2017) 2924-2932.
[14] Z. R. Hu, S. Wang, G. K. Chen, Q. Zhang, K. Wu, J. Shi, L.Y. Liang, M. G. Lu:
Compos. Sci. Technol. 168 (2018) 287-295.
[15] W. X. Yang, Z. D. Zhao, K. Wu, R. Huang, T. Y. Liu, H. Liang, F. Chen, Q. Fu: J.
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Chapter 3. Effect of polytetrafluoroethylene addition on microstructure andthermal properties of PVA-VGCF sheet
Mater. Chem. C 5 (2017) 3748-3756.
[16] R. J. Fong, A. Robertson, P. E. Mallon, R. L. Thompson: Polymers 10 (2018)1036.
[17] R.M. Hodge, T.J. Bastow, G.H. Edward, G.P. Simon, A.J. Hill: Macromolecules
29 (1996) 8137-8143.

90

Chapter 4. Thermal simulation of PVA-VGCF sheet.

Chapter 4

Thermal simulation of PVA-VGCF sheet

4.1 Introduction ..................................................................................................... 92
4.2 Theory of thermal simulation ............................................................................ 95
4.3 Methodology of thermal simulation ................................................................ 98
4.3.1 Worl flow .................................................................................................. 98
4.3.2 Geometry ................................................................................................ 100
4.3.3 Model ...................................................................................................... 103
4.3.4 Solution setup ......................................................................................... 105
4.4 Results ........................................................................................................... 106
4.4.1 Temperature distribution ........................................................................ 106
4.4.2 Heat flux distribution.............................................................................. 108
4.4.3 Thermal conductivity .............................................................................. 115
4.5 Summary.......................................................................................................... 118
References .............................................................................................................. 119

91

Chapter 4. Thermal simulation of PVA-VGCF sheet.

4.1 Introduction
In the past, researchers typically use equation calculations to predict the thermal
properties of materials. As showed in Table. 4.1, there are many typical thermal
conductivity models to predicting the thermal conductivity of composite TIMs. Except
of cumbersome calculations, these typical models also have limitations in usage case.
For example, Maxwell-Eucken model is only valid in low volume fraction of fillers in
TIM. And Eshelby model requires the fillers has no interacts between each other.
Recently, many researchers have used the thermal simulation to demonstrate thethermal properties of their developed materials to obtain a more direct and clear
expression with a relatively simple method than certified only by equation calculations.
For example, W. Dai et al. build an evaluation system of Heater-TIM-Heat sink toinvestigate and compare the cooling performance between their developed newgraphene TIM and state-of-the-art TIMs in real case[1]. C. P. Feng et al. also used thesystem of Heater-TIM-Heat sink to certify the thermal performance of paper like TIM
fabricated by single layer Al2O3 and graphene nanoplatelets[2]. Many studies using
thermal simulation to provide good results in predicting the thermal properties of TIM.
Unsuitable concepts or fabrication condition can be discarded quickly without big costof materials. A lot of features and options of the simulation system also reduce thetemporary and apparatuses efforts compared to practical experiments. However, inthese thermal simulations, the microstructure of developed TIM was seldom to beconsidered, the model of TIM is created as an equivalent to a single-phase material withuniform internal structure. Especially for fiber reinforced composite materials due to its
complicated and randomly arrangement of fibers, studies are seldom focused on its
thermal simulation based on the microstructures.
In this chapter, we prepared 5 types of three-dimensional model to present different
arrangement of VGCFs in the fabricated CNF sheets through the CAE software ANSYS
student. The goal of this chapter was to investigate the effect of VGCF arrangement on
92

Chapter 4. Thermal simulation of PVA-VGCF sheet.
the heat transfer in the fabricated sheets and develop a method using simulation data to
predict the thermal conductivity of TIM.

93

Chapter 4. Thermal simulation of PVA-VGCF sheet.
Table 4.1 Typical thermal conductivity models for composite TIMs.

Model

FormulaCharacteristics

Reference

Used for continuous anduniformly distribution particles𝜆#𝜆− 2𝑉" '1 − # )𝜆"𝜆"𝜆! = 𝜆"𝜆𝜆2 + # + 𝑉" '1 − # )
𝜆"
𝜆"
2+

Maxwell andMaxwell-Eucken

fillers in TIM.
Inclusions of reinforcements
isolated and dispersed in a

𝜆$ + 2𝜆" − 2𝑉$ (𝜆" − 𝜆$ )𝜆! = 𝜆" *𝜆$ + 2𝜆" + 𝑉$ (𝜆$ − 𝜆" )3-5continuously homogeneous
matrix; it is only valid in low
volume fraction of fillers
Dilute suspension of spheres in

Bruggeman

1 − 𝑉$ =a homogeneous medium; It can

𝜆$ − 𝜆! 𝜆% &( )'𝜆$ − 𝜆% 𝜆!

be applied for high volume6

fraction of fillers.
This model is based on
Hasselman andJohnson𝐾$
𝐾$
𝐾$ 2𝐾$
2'−− 1) 𝑉$ +++2
𝐾" 𝑎ℎ!
𝐾" 𝑎ℎ!
𝐾($$ = 𝐾"𝐾$
𝐾$
𝐾$ 2𝐾$
'1 −
+
)𝑉 +
+
+2
𝐾" 𝑎ℎ! $ 𝐾" 𝑎ℎ!

Maxwell model, and it
considers the interfacial thermal

7

resistance and the fillers size.
Applied for InhomogeneousEshelbyspheres and the fillers don’t𝐾($$ = 𝐾) + 𝑐& (𝐾& − 𝐾) )𝑇interact with each other; Only

8

valid in low volume of fillers
This model is used for more($$

Tavangar

𝐾! = 𝐾"𝐾#(1 + 2𝑉# ) + (2 − 2𝑉# )𝐾"

than two components in TIM

𝐾#(1 − 𝑉# ) + (2 + 𝑉# )𝐾"

and can be applied for high($$9volume fraction of fillers.
This model considers theMori Tanaka𝑐) 𝐾) + 𝑐& 𝐾& 𝑇
𝐾($$ =𝑐) 𝐼 + 𝑐& 𝑇interactions of fillers and can be

10,11

used for up to 20Vol% of fillers.
Applied for cylindricaldispersed dispersions in a 3D
randomly oriented occasion.
The model considers theCe-Wen Nan

3 + 2𝑓[𝛽* (1 − 𝐿* ) + 𝛽+ (1 − 𝐿+ )]𝐾($$ = 𝐾"
3 − 𝑓(2𝛽* 𝐿* + 𝛽+ 𝐿+ )anisotropy in thermal
conductivity, the aspect ratio
and volume fraction of thefillers as well as the interfacial
thermal resistance.

94

12,13

Chapter 4. Thermal simulation of PVA-VGCF sheet.

4.2 Theory of thermal simulation
The main governing equation of the thermal simulation in this chapter is heatdiffusion equation for conductive heat transfer. Solving this equation can achieves themain goal of conduction analysis, which is to predict the temperature distribution andheat flux in the TIM. In ANSYS system, the diffusion equation follows from theconservation of energy presented in three conditions: neglecting advection, assuming
no mechanical work by surroundings and using internal energy in terms of enthalpy[14].
The diffusion equation can be described as:𝜕(𝜌ℎ)= 𝛻 ∙ (𝑘𝛻𝑇) + 𝑆'
𝜕𝑡

(4.1)

This equation can be simplified by assuming constant density and specific heat capacity:𝜕𝑇𝜌𝑐!
= ∇ ∙ (𝑘∇𝑇) + 𝑆'
(4.2)
𝜕𝑡where 𝜌 is the density, 𝑐! is the specific heat capacity, 𝑇 is the temperature, 𝑡 is
time, k is the thermal conductivity and 𝑆' is the heat generation source or heat sink.
The physical meanings of heat diffusion equation are the rate of energy transfer into aunit volume by heat conduction, and plus the volumetric rate of heat generation is equal
to the rate of change of heat stored within the volume. Then, the Cartesian form of theheat equation (4.2) can be described as[14]:
𝜕𝑇
𝜕
𝜕𝑇
𝜕
𝜕𝑇
𝜕
𝜕𝑇
𝜌𝑐!
=
;𝑘 < +;𝑘 < + ;𝑘 < + 𝑆'𝜕𝑡 𝜕𝑥 𝜕𝑥
𝜕𝑦 𝜕𝑦
𝜕𝑧 𝜕𝑧

(4.3)

()

In this form of heat equation, 𝜌𝑐! (# represents the rate of change of heat stored,
*
*+

()

*

()

*

()

@𝑘 (, A + *- @𝑘 (.A + */ @𝑘 (0 A represents the rate of transfer by conduction and 𝑆'

is the rate of heat generation source. Furthermore, in the case of constant thermal
conductivity, equation (4.3) can be reduced to[15]:1 𝜕𝑇 𝜕 1 𝑇 𝜕 1 𝑇 𝜕 1 𝑇 𝑆'
=
+
+
+
(4.4)
𝛼 𝜕𝑡 𝜕𝑥 1 𝜕𝑦 1 𝜕𝑧 1 𝑘
where the property 𝛼 = 𝑘/𝜌𝑐 is the thermal diffusivity of the material. Equation (4.4)
is also known as Fourier-Biot equation. Besides, this equation reduces to these forms
95Chapter 4. Thermal simulation of PVA-VGCF sheet.
under specific conditions, Poisson equation for steady-state condition:
𝜕 1 𝑇 𝜕 1 𝑇 𝜕 1 𝑇 𝑆'++
+ =0
𝜕𝑥 1 𝜕𝑦 1 𝜕𝑧 1 𝑘
Diffusion equation for transient and no heat generation condition:
1 𝜕𝑇 𝜕 1 𝑇 𝜕 1 𝑇 𝜕 1 𝑇=++
𝛼 𝜕𝑡 𝜕𝑥 1 𝜕𝑦 1 𝜕𝑧 1
Laplace equation for steady-state and no heat generation condition:
𝜕1𝑇 𝜕1𝑇 𝜕1𝑇++=0𝜕𝑥 1 𝜕𝑦 1 𝜕𝑧 1

(4.5)

(4.6)

(4.7)

practical case of planar conduction as showed in Fig. 4.1, the heat conduction equation
is:
𝑥
(4.8)
𝐿
The heat transfer rate 𝑞, and heat flux 𝑞,33 can be derived from Fourier’s Law:
𝑑𝑇 𝑘𝐴
(𝑇 − 𝑇2 )𝑞, = −𝑘𝐴
=
(4.9)
𝑑𝑥
𝐿 2
𝑞, 𝑘
𝑞,33 == (𝑇2 − 𝑇2 )(4.10)𝐴
𝐿
𝑇(𝑥) = 𝑇2 − (𝑇2 − 𝑇2 )where 𝐴 is wall area normal to the heat transfer direction. And thermal resistance ofplanar conduction is:
𝑅# =

𝐿
𝑘𝐴

(4.11)

Furthermore, for the heat conduction in multiple layers of composite walls as shownas Fig. 4.2, thermal resistance is additive by a linear increase. The heat transfer throughmultiple layers can be derived from the sum of thermal resistance:
𝑅#4#56 = N 𝑅#7(4.12)

𝑇2 − 𝑇8
𝑅#4#56(4.13)𝑞, =It should be noted that in this chapter, the steady-state condition was chosen forthermal simulation, therefore the heat transfer under transient and unsteady condition
was not discussed.

96Chapter 4. Thermal simulation of PVA-VGCF sheet.

qx
T1
T2
0

L
x

Fig. 4.1 Schematic of 1D planar conduction.

Fig. 4.2 Schematic of heat conduction through multiple layers.

97Chapter 4. Thermal simulation of PVA-VGCF sheet.

4.3 Methodology of thermal simulation
4.3.1 Workflow
As showed in Fig. 4.3, a simplified workflow for thermal simulation in this chapter
was introduced. There were totally 7 steps need to finish during the thermal simulations.
In table 4.2, terms of thermal simulation and its units was listed. Table 4.3 showed the
major physical parameters used in this thermal simulation. The 𝜆2 , 𝜆1 , 𝜆9 , 𝜌2 , 𝜌1 ,
𝜌9 and 𝑐!2 , 𝑐!1 , 𝑐!9 represent the thermal conductivity, density and specific heat
capacity of PVA, VGCF and Copper, respectively. The 𝑇: , 𝑇; represent the set
temperature of heater, cooler, respectively. The 𝑇<= is ambient set temperature.
Analysis type
Steady-state thermalEngineering data
Choose materials andinput material data

Geometry• Set up coordinate System• Create structures

Model• Assign materials properties• Set up boundary conditions• Set up mesh conditions andgenerate mesh

Loads

Check the results• Specify initial temperature• Set up temperature loads

If results is incorrect, check thegeometry and model step

Solutions
Run thermal simulation

Fig. 4.3 A workflow for thermal simulation in this chapter.
98

Chapter 4. Thermal simulation of PVA-VGCF sheet.

Table 4.2 Terms of thermal analogy used in the simulation.
Thermal analysis item, [units], symbol
Temperature [K], T
Temperature gradient [K·m-1], ∇𝑇
Heat Flux [W·m-2], qHeat source for point, line, surface, volume[W], [W·m-1], [W·m-2], [W·m-3], Q
Thermal conductivity [W·m-1·K-1], 𝜆Specific heat capacity [J·kg-1·K-1], 𝑐!
Density [kg·m-3], 𝜌Table 4.3 Major physical parameters used in the simulation.
Major physical parameters
𝜆2 =0.5 W·m-1·K-1
𝜌2 =1250 kg·m-3
𝑐!2 =2.5 J·kg-1·K-1
𝑇: =373K

𝜆1 =1200 W·m-1·K-1
𝜌1 =2100 kg·m-3
𝑐!1 =700 J·kg-1·K-1
𝑇; =293K99

𝜆9 =386 W·m-1·K-1
𝜌9 =8960 kg·m-3
𝑐!9 =384 J·kg-1·K-1
𝑇<= =293K

Chapter 4. Thermal simulation of PVA-VGCF sheet.

4.3.2 Geometry
In the geometry step of thermal simulation, the PVA-VGCF sheet was chosen as
simulate object firstly and the porosity was not considered. As showed in Fig. 4.4, we
divided the CNF sheet into many small basic units and created geometry of basic unit.
The size of a small basic unit was set up as 15um×15um×15um to keep the aspect ratioof VGCF(diameter:0.15um,average length:15um, aspect ratio:100 ). The reason forusing basic unit instead of the whole CNF sheet was it is impossible to create a TIM
model directly with countless VGCFs in it. Too many objects in the geometry cansignificantly increase the difficulty of the solution step. If it is necessary in the future
research, TIM can be formed by stacking these basic units together. The size of TIM
also can be controlled through adding or reducing the number of basic units. In Fig. 4.5
To evaluate the effect of the arrangements of VGCFs on the thermal conduction of
fabricated PVA-VGCF sheet, 5 types of microstructure models were designed: pure
PVA, horizontally arranged VGCF in PVA matrix, vertically arranged VGCF in PVA
matrix, randomly arranged VGCF in PVA matrix and pure VGCF. For the cases where
VGCF was added, the number of added VGCF was 100 and the volume fraction ratioof VGCF was about 3.13 vol%. Especially for the models of horizontally arranged
VGCF in PVA, vertically arranged VGCF in PVA, the VGCFs was set up as a diameterof 0.15um, length of 15um and 1.67um apart from each other. Furthermore, as shownas Fig. 4.6, those 5 models were inserted respectively between a heater and cooler withsame size of 15um×15um×15um in geometry step. The Heater-material-Cooler system
was created to investigate the heat transfer path and thermal conductivity for 5 models
consisting of PVA and VGCF. The cooper was set up as the material of heater and cooler.

100Chapter 4. Thermal simulation of PVA-VGCF sheet.

m

15um

15u

15um

PVA-VGCF sheet

1 basic unit

Fig. 4.4 The schematic of the basic unit of fabricated CNF sheet.

Fig. 4.5 Five types of geometry model: (a) pure PVA; (b) horizontally arranged
VGCF in PVA matrix; (c) vertically arranged VGCF in PVA matrix; (d) randomly
arranged VGCF in PVA matrix; (f) pure VGCF.

101

Chapter 4. Thermal simulation of PVA-VGCF sheet.

Fig. 4.6 Geometry model of Heater-Material-Cooler system in this thermal
simulation.

102

Chapter 4. Thermal simulation of PVA-VGCF sheet.

4.3.3 ModelIn this thermal simulation, the boundary condition was set up as bonded without
considering the existence of pores in models, which means the PVA and VGCF weretightly bonded together in the contact surface. Other boundary conditions such as
formulation and thermal conductance, were set up to controlled by the software
program.
During the mesh step, the mesh size was used to control the mesh equality of models.
Mesh size determine the size of elements, it is one of the most common problems insimulation. Too big elements give bad results, but too small elements make computing
so long and give the risk of failing in solution step. Usually, reducing the element sizein places where the main thermal conduction existed is an efficient way for set up meshsize. Therefore, in this simulation, since the heater and cooler were not very criticalparts in the heat transfer process and reducing the number of elements can reduce thetime and difficulty of the solution step, the mesh size of the heater and cooler was set
to 1.5um. The mesh size of PVA was decreased to 0.5um and mesh size of VGCF wasrefined to 0.15um to increase accuracy of heat conduction results. The image andstatistics of mesh results is showed in Fig. 4.7.

103

Chapter 4. Thermal simulation of PVA-VGCF sheet.

(a)Nodes: 126203
Element: 29000

(b)

(c)

Node: 1799156
Element: 368975

Node: 2159965
Element: 452718

(d)

(f)

Node: 1614047
Element: 433226

Nodes 126203
Elements 29000

Fig. 4.7 The images and statistics of mesh results of model: (a) pure PVA; (b)horizontally arranged VGCF in PVA matrix; (c) vertically arranged VGCF in PVA
matrix; (d) randomly arranged VGCF in PVA matrix; (f) pure VGCF.

104

Chapter 4. Thermal simulation of PVA-VGCF sheet.

4.3.4 Solution setup
In this simulation, the solution setup includes loads setup and analysis results setup.
As showed in Fig. 4.8, the top face of heater was set up to 373K and bottom face ofcooler was set up to 293K in loads setup. The initial temperature and the ambient
temperature were assumed to be equal as 293K. The fixed time stepping method wasused in the simulation. The time step size and number of time steps were 1 s and 1000,
respectively. The analysis results were set to temperature distribution and heat flux
distribution.

Fig. 4.8 Image of temperature setup for simulation.

105

Chapter 4. Thermal simulation of PVA-VGCF sheet.

4.4 Results
4.4.1

Temperature distribution

Fig. 4.9 shows the images of temperature distribution results of 5 models. The models
of pure PVA, horizontally arranged VGCF in PVA and vertically arranged VGCF in
PVA showed a similar distribution of temperature. The temperature decreased fromheater to cooler, while the change of temperature was mainly concentrated on the regionof the test material which dropped from 363K to 303K. As for the material of randomly
arranged VGCF in PVA, the temperature also had a significant drop in the test material
region and the temperature distribution had obvious fluctuations along the VGCF
direction which was showed in Fig. 4.9(d). To material of pure VGCF, the temperature
distribution exhibited a uniform distribution from top of heater to bottom of cooler, andthe temperature of test materials region only dropped from 338K to 325K. The betterthe thermal conductivity of the TIM is, the easier for TIM to help the heat source
transfer heat to the heat sink and forms a more uniform temperature distribution ofwhole system.

106

Chapter 4. Thermal simulation of PVA-VGCF sheet.

(a)

(b)

(d)

(f)

(c)

Fig. 4.9 Images of temperature distribution results of the model: (a) pure PVA; (b)horizontally arranged VGCF in PVA matrix; (c) vertically arranged VGCF in PVA
matrix; (d) randomly arranged VGCF in PVA matrix; (f) pure VGCF.
107

Chapter 4. Thermal simulation of PVA-VGCF sheet.

4.4.2

Heat flux distribution

Fig. 4.10 shows the images of heat flux distribution of 5 models and Table 4.4 gives
the statistics of heat flux of them. Pure PVA and pure VGCF models had the constantheat flux distribution value respectively due to their single-phase microstructure. But
because of the huge difference of thermal conductivity(PVA:0.5 W·m-1·K-1, VGCF:
1200 W·m-1·K-1), the average heat flux in pure PVA model was just 2.66 W·m-2 , whilethat in pure VGCF model was as high as 886.64 W·m-2, which also demonstrated thatheat transfer was very slow in pure PVA model and need much time to reach the steadystate condition. As for the left 3 models: horizontally arranged VGCF, verticallyarranged VGCF and randomly arranged VGCF in PVA matrix, Fig. 4.11 provide moredetails about heat flux distribution and vectors pictures which shows the transfer
direction of heat. Due to lacking efficient heat transfer path, the model of horizontallyarranged VGCF showed very low heat flux data, which was almost similar to pure PVA.
As for the model of vertically arranged VGCF, each single vertical VGCF connectedheater and cooler, which provided many efficient heat transfer paths for the materials.
Thus, there were high value of heat flux results. Neither like model of horizontallyarranged VGCF which completely lacked effective heat transfer paths, nor similar tomodel of vertically arranged VGCF which had many paths, from the Fig. 4.12 it was
showed that the efficient heat transfer paths in model of randomly arranged VGCF werecreated only by the interleaved VGCFs and connected to each other. Also, the directionof heat transfer was severely affected by the VGCF alignment direction as showed inFig. 4.11(c). Thus, increasing the amount of thermally conductive fillers would
contribute to an increasement of thermal conductivity by increasing the number ofintersections between fillers. Overall, heat transfer in TIM with randomly arranged
fillers mainly depends on the efficient heat transfer path created by interactions ofthermally conductive fillers. Without efficient heat transfer paths, the heat transfer
would not follow the direction from the heat source to the heat sink as we hoped but
108

Chapter 4. Thermal simulation of PVA-VGCF sheet.
may towards other directions disorderly, or even almost stop.

109

Chapter 4. Thermal simulation of PVA-VGCF sheet.

110Chapter 4. Thermal simulation of PVA-VGCF sheet.

(f)Fig. 4.10 Images of heat flux distribution results of model: (a) pure PVA; (b)horizontal arranged VGCF in PVA matrix; (c) vertical arranged VGCF in PVA matrix;(d) randomly arranged VGCF in PVA matrix and (f) pure VGCF.

111

Chapter 4. Thermal simulation of PVA-VGCF sheet.

Table 4.4 Statistics of total heat flux of each model.
Model

Pure PVA
horizontally arranged
VGCF+PVA
Vertically arranged
VGCF+PVA

randomly arranged
VGCF+PVA
Pure VGCF

Heat flux [q/W·m-2]
Minimum

Maximum

Average

2.65982.65982.65980.009522.8

3.5

1.79436820.22780.80.0171

19209.0

624.3

886.64886.64886.64112

Chapter 4. Thermal simulation of PVA-VGCF sheet.

Fig. 4.11 Detail images of heat flux distribution results of: (a) horizontally arranged
VGCF in PVA matrix; (b) vertically arranged VGCF in PVA matrix; (c) randomly
arranged VGCF in PVA matrix.

113

Chapter 4. Thermal simulation of PVA-VGCF sheet.

Fig. 4. 12 Image of heat flux distribution results of only VGCF in the model ofrandomly arranged VGCF.

114

Chapter 4. Thermal simulation of PVA-VGCF sheet.

4.4.3

Thermal conductivity

As showed in Fig. 4. 13, the steady-state method was used to calculate the thermal
conductivity of 5 models. Assuming that the temperature gradients of heater, materialand cooler are ah, as, ac, they are expressed by the following equations:
9

9

9

9

1
1
𝑎> = N(𝑧7 − 𝑧> )(𝑇7 − 𝑇> )/ N(𝑧7 − 𝑧> )1 , 𝑧> = N 𝑧7 , 𝑇> = N 𝑇7
3
3
7?2

7?2

A

A

7?2

7?2

A

A

1
1
𝑎@ = N(𝑧7 − 𝑧> )(𝑇7 − 𝑇> )/ N(𝑧7 − 𝑧> ) , 𝑧> = N 𝑧7 , 𝑇> = N 𝑇7
3
3
1

7?8

7?8

C

C

7?8

7?8

C

C

1
1
𝑎B = N(𝑧7 − 𝑧> )(𝑇7 − 𝑇> )/ N(𝑧7 − 𝑧> ) , 𝑧> = N 𝑧7 , 𝑇> = N 𝑇7
3
3
1

7?D

7?D

7?D

(4.14)(4.15)(4.16)

7?D

where 𝑧7 and 𝑇7 are the distance and temperature of the number i thermal couple fromheating plate. Effective thermal conductivity λx can be calculated by the following
equation:λx =λR (ah +as )ac(4.17)For the example showed Fig. 4.14, the temperature data of 9 point was taken from thesurface of pure PVA model by a same distance of 4.5um. Through equation(4.14)~(4.17), the thermal conductivity of pure PVA model can be calculated as 0.497
W·m-1·K-1, which was almost the same as the reference value of 0.5 W·m-1·K-1. The
thermal conductivity of 5 models was summarized in table 4.5. By compared thethermal conductivity of pure PVA and pure VGCF to the reference data(PVA:0.5 W·m1

·K-1, VGCF:1200 W·m-1·K-1), it was obvious that using thermal simulation results topredict the thermal conductivity of materials is feasible and the results is deserved to betrust. From the table, it can be seen that due to the lack of heat transfer path,microstructure model of horizontally arranged VGCF exhibited the almost the same low
thermal conductivity(0.509 W·m-1·K-1) as pure PVA. For the model with vertically arranged115

Chapter 4. Thermal simulation of PVA-VGCF sheet.
VGCF, its thermal conductivity was as high as 8.238 W·m-1·K-1, which had an ideal

arrangement of conductive fillers for TIM. As mentioned in Chapter 1, this verticalarrangement of fillers requires complex manufacturing process and high cost, which is
hard to achieve in practical application. As for the microstructure model of randomly
arranged VGCF, although the thermal conductivity of it was relatively lower(4.600
W·m-1·K-1) than that of vertically arranged VGCF model, the thermal conductivity canbe improved significantly by increasing the amount of VGCF. The increasement of
VGCF would contribute to more VGCF interactions and provide additional heattransfer paths in the materials. In general, from the microstructure to the macroscopic
performance, the number of efficient heat transfer paths was determined by thearrangement of the conductive fillers in TIM, meanwhile the thermal conductivity of
the whole material was determined by the heat transfer paths in it.

Fig. 4.13 Schematic of steady-state method for thermal conductivity measurement.

116

Chapter 4. Thermal simulation of PVA-VGCF sheet.

Fig. 4.14 Image of temperature data of 9 points used for thermal conductivity
calculation in pure PVA model.

Table 4.5 The summarized thermal conductivity of fabricated models.
Thermal conductivity

Model[λ/W·m-1·K-1]

Pure PVA

0.497

Horizontally arranged VGCF+PVA

0.509

Vertically arranged VGCF+PVA

8.238

Randomly arranged VGCF+PVA

4.600

Pure VGCF

1193.749

117

Chapter 4. Thermal simulation of PVA-VGCF sheet.

4.5 Summary
In this chapter, 5 types of simulation models were created successfully: pure PVA,
horizontally arranged VGCF in PVA matrix, vertically arranged VGCF in PVA matrix,
randomly arranged VGCF in PVA matrix and pure VGCF. To investigate the heattransfer path and thermal conductivity of them, they were combined with a heater anda cooler to measure the thermal simulations, the main conclusions are as follows:(1) Material models of pure PVA, horizontally arranged VGCF and vertically arranged
VGCF in PVA showed a change of temperature mainly concentrated on the regionof the test material. Temperature distribution of randomly arranged VGCF model
had obvious fluctuations along the VGCF direction. The temperature distributionof pure VGCF model exhibited a uniform distribution from top of heater to bottomof cooler.
(2) Heat transfer was severely affected by the VGCF arrangement in material models.
To the material model of randomly aligned VGCF in PVA, increasing the amountof VGCF would contribute to an increasement of thermal conductivity byincreasing the number of intersections between VGCFs.
(3) An attempt on predicting thermal conductivity of material by using thermal
simulation results was succeeded. Compared with the horizontally and randomly
arrangement of VGCF, the vertically arrangement of VGCF has been shown tocontribute significantly to the enhancement of thermal conductivity. If there were
no efficient heat transfer paths, the thermal conductivity would be as low as PVA
matrix.

118

Chapter 4. Thermal simulation of PVA-VGCF sheet.

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W. Dai et al.: ACS Nano 13 (2019) 11561-11571.

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C. P. Feng et al: Chem. Eng. J. 392 (2020) 123784.

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119Chapter 4. Thermal simulation of PVA-VGCF sheet.

120

Chapter 5. Conclusions

Chapter 5Conclusions
With the rapid development of electronic device, traditional TIMs cannot meet therequirements of advanced electronic devices due to their low thermal conductivity andother poor properties. In the previous studies, although advanced carbon TIMs weredeveloped

successfully with better physical properties and characteristics like higher

thermal conductivity, light-weight property, better physical and mechanical stability
compared to traditional TIMs, the properties of these carbon TIMs still cannot not becompletely exploited and required complex manufacturing process and high cost, which
was too difficult to be applied in practical applications due. The object of this thesis is
to fabricate CNF sheets by using conductive fillers VGCF and PVA binder that exhibit
high thermal conductivity by simple and low-cost fabrication process. Furthermore, as
an attempt to increase the functionality for practical application, PTFE particles wereadded to fabricated PVA-PTFE-VGCF sheets for an improvement in hydrophilicity.
The thermal simulations were measured to evaluate the heat transfer paths in CNF sheet
and develop a method for predicting thermal conductivity by using data of thermal
simulation. The conclusions of this thesis are summarized as follows:(1)

An innovative TIM consisting of PVA and VGCF was fabricated successfully,

by a simple and simply and cost-efficient solution casting method (Chapter 2). 5 kindof CNF sheets were fabricated with different mass ratio of PVA:VGCF: 1:0.1(17.04
vol.%), 1:0.07(12.85 vol.%), 1: 0.05 (10.15 vol.%), 1: 0.03 ( 8.18 vol.%), 1: 0.025 (7.95
vol. %). Microstructure observation revealed that the VGCFs were arranged in random
directions and interconnected via PVA aggregates. Numerous pores existed between the
VGCFs due to water evaporation. The porosity of the CNF sheets decreased bydecreasing the VGCF amount. The thickness of the CNF sheets was between 30 - 56
µm and increased with increasing the VGCF amount. Moreover, the CNF sheets did not
121Chapter 5. Conclusions
exhibit considerably different density and hardness: the average density of the CNF
sheet was about 1.00 × 106 g·m3, the Shore hardness of the CNF sheets was between 82- 85 HS. It is indicated CNF sheets was fabricated with suitable thickness, lightweightproperty and great flexibility for practical application of TIM.
The highest value of thermal conductivity was obtained for the CNF sheet
fabricated at the PVA:VGCF mass ratio of 1:0.050, with the in-plane and through-plane
thermal conductivities being 14.30 and 6.44 W·m-1·K-1, respectively. Reducing the
VGCF amount decreased the thermal conductivity. Furthermore, an excessive increasein the VGCF amount increased the number of pores in the CNF sheet, which led tothermal conductivity reduction. The in-plane and through-plane thermal conductivities
were significantly reduced after the high-temperature and humidity tests. It isconsidered that due to the hydrophilic property of PVA, the water molecules in theenvironment would be absorbed into CNF sheet by PVA, which led to high porosity
and thermal conductivity reduction.
(2)

For an improvement in hydrophilicity, PPVL and PPTV sheets were fabricatedby using 120nm and 300nm PTFE particle (Chapter 3). The microstructure observationof PPLV and PPTV revealed that the VGCFs were arranged in random directions andinterconnected via PVA aggregates, which similar to PVA-VGCF sheet. 300nm PTFE
particles were well distributed and compatible within the PPTV sheet, while partial
aggregations of 120nm PTFE particles and unfilled pores were observed in the PPLV
sheet. As the pores on the surface were filled by PTFE powders, the porosity of thefabricated sheet was reduced. The average thickness of the fabricated sheets was also
decreased from 47µm for the PVA-VGCF sheet to 31.2µm and 28.2µm for PPLV and
PPTV sheets respectively, due to the lower content of the PVA matrix.
With the addition of 300nm PTFE particles, the fabricated sheet has higher thermal
conductivities of 9.81 W·m-1·k-1 in the in-plane direction and 2.11 W·m-1·k-1 in thethrough-plane direction. The in-plane and through-plane TC of PVA-PTFE-VGCF
sheets were decreased by 31% ~ 46% and 67% ~ 72% compared with referred PVAVGCF sheet, due to the thermal barrier of PTFE particles. In the high temperature andhumidity test under the condition of 358K and 85% RH, the in-plane and through-plane
122Chapter 5. Conclusions
TC of PVA-PTFE-VGCF sheets were increased by 10% ~ 18% and 18% ~ 23%.
According to the FT-IR analysis result, it is considered that the increase in TC wascaused by the hydrophobic property of PVA and rearrangement of PVA and PTFE
particles.
(3)

5 types of materials models were created successfully: pure PVA, horizontallyarranged VGCF in PVA matrix, vertically arranged VGCF in PVA matrix, randomly
arranged VGCF in PVA matrix and pure VGCF (Chapter 4). To investigate the heattransfer path and thermal conductivity of them, these material models were combinedwith a heater and a cooler to measure the thermal simulations. Material models of pure
PVA, horizontally arranged and vertically arranged VGCF in PVA showed a similar
distribution of temperature. The change of temperature was mainly concentrated on theregion of the test material which dropped from 363K to 303K. Temperature distributionof randomly arranged VGCF model had obvious fluctuations along the VGCF direction.
To material model of pure VGCF, the temperature distribution exhibited a uniform
distribution from top of heater to bottom of cooler.
Pure PVA and pure VGCF models had the constant heat flux distribution value
respectively due to their single-phase microstructure. Due to lacking efficient heattransfer path, the material model of horizontally arranged VGCF showed very low heat
flux data, which was almost similar to pure PVA. As for the model of vertically arranged
VGCF, each single vertical VGCF connected heater and cooler, which provided many
efficient heat transfer paths for the materials. The efficient heat transfer paths in material
model of randomly arranged VGCF were created only by the interleaved VGCFs andconnections of each other.
In the calculation of thermal conductivity by using thermal simulation results, thematerial models of pure PVA and pure VGCF exhibited the lowest thermal
conductivity(PVA: 0.497 W·m-1·K-1) and the highest thermal conductivity(VGCF:
1193.749 W·m-1·K-1), respectively. The material model of horizontally arranged VGCF
exhibited the almost the same low thermal conductivity(0.509 W·m-1·K-1) as pure PVA.
The material model of vertically arranged VGCF, its thermal conductivity was as highas 8.238 W·m-1·K-1 due to efficient heat transfer paths. As for the material model of123

Chapter 5. Conclusions
randomly arranged VGCF, which had a similar microstructure with fabricated PVAVGCF sheet, the thermal conductivity of 4.600 W·m-1·K-1, and the thermal conductivityof this model can be improved significantly by increasing the amount of VGCF.

124

Acknowledgements
I would like to dedicate my paper to all those who have offered me tremendous
assistance.
First of all, my heartiest thanks flow to my supervisor, Associate Professor Choi, for
his helpful guidance, valuable suggestions, and constant encouragement both in mystudy and in my life. His profound insight and accurateness about my paper taught me
so much that they are engraved on my heart. He provided me with beneficial help andoffered me precious comments during the whole process of my writing, without which
the paper would not be what it is now.
Also, I would like to express my sincere gratitude to Professor Matsugi, who havetaught me in this university that greatly broadened my horizon and enriched myknowledge in my study. His inspirational and conscientious teaching have provided mewith a firm basis for the composing of this paper and will always be of great value tomy future academic research. In addition, I would like to express my heartfelt thanks
to Professor Inumaro and Professor Akebono for their technical advice and assistanceto my doctoral thesis.
My thanks also go to the members of my lab whose monographs and academic ideas
have enlightened me in my whole research life.
Finally, I would like to extend my deep gratefulness to my family and friends,
especially my fiancée Siran Chen, who encouragement and support have made myaccomplishments possible.

125Published papers in regard to this thesis
1. J. L. Xiong, S. R. Chen, Y. B. Choi*, K. Matsugi. Development of polyvinyl
alcohol-based carbon nano fiber sheet for thermal interface material. Scientific reports.
2021(11) 17183. (Chapter 2)
2. J. L. Xiong, T. Kinoshita, Y. B. Choi*, K. Matsugi, Y. Hisazato, N. Fujiwara.
Thermal Properties of Carbon Nanofiber Sheet for Thermal Interface Materials underHigh Temperature and Humidity. Materials transactions. 2023 (64): in press. (Chapter
3)

126

Presentations
1. Jiangling Xiong, Siran Chen, Yongbum Choi, Kazuhiro Matsugi. Fabrication ofcarbon nano fiber sheet for thermal interface material. 2021 2nd Japan-Korea
collaborative Symposium in Advanced Composite Materials. Sep. 10, 2021, Hiroshima,
Japan; Hiroshima University.
2. Jiangling Xiong, Siran Chen, Tomoo Kinoshita, Yongbum Choi, Kazuhiro
Matsugi, Yuuji Hisazato, Nobuto Fujiwara. Performance evaluation of carbon
nanofiber interface material. May 22-26, 2022, Matsue, Janpan.

127