EVALUATION OF THERMOPHYSICAL PROPERTIES OF THERMAL CONDUCTIVE POLYMER COMPOSITES

by

Hakkı Serkan TEKÇE

January, 2004 İZMİR

EVALUATION OF THERMOPHYSICAL PROPERTIES OF THERMAL CONDUCTIVE POLYMER COMPOSITES

A Thesis Submitted to the Graduate School of Natural and Applied Sciences of Dokuz Eylül University In Partial Fulfillment of the Requirements for the Degree of Master of Science in Mechanical Engineering, Energy Program

by

Hakkı Serkan TEKÇE

January, 2004 İZMİR

M.Sc THESIS EXAMINATION RESULT FORM We certify that we have read this thesis and “EVALUATION OF THERMOPHYSICIAL

PROPERTIES

OF

THERMAL

CONDUCTIVE

POLYMER COMPOSITES ” completed by Hakkı Serkan TEKÇE under supervision of Asst. Prof. Dilek KUMLUTAŞ and that in our opinion it is fully adequate, in scope and in quality, as a thesis for the degree of Master of Science.

Asst. Prof. Dilek KUMLUTAŞ Supervisor

(Committee Member)

(Committee Member)

Approved by the Graduate School of Natural and Applied Sciences

Prof.Dr. Cahit HELVACI Director

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ACKNOWLEDGMENTS

Vital to my completion was my family, especially my parents, who I want to thank for their words of assurance and encouragement through my undergraduate and graduate education of which I partially had to carry out my studies as being very far away from them. Eminently worthy of thanks are my Ms.C. advisor Assistant Prof. Dr. Dilek Kumlutas who had immense impact on my choice of an academic career path and Prof. Dr. I. Hakki Tavman who is the president of Department of Energy in Dokuz Eylul University Mechanical Engineering Department-Turkey for their help and unique relief through the initiation and completion of my study. I would like to thank Prof. Dr.-Ing. Dr. h.c. G. W. Ehrenstein for providing me the opportunity to carry out my studies at “Lehrstuhl für Kunststofftechnik”, and also I would like to thank my co-advisor Dipl. Ing. Simon Amesoeder for his support and guidance

throughout

my

Ms.C.

project.

Help

from

the

Lehrstuhl

für

Kunststofftechnik staff in completion of my work has been irreplaceable. Everyone who gave guidance and encouragement throughout my time as a graduate student is especially worth of thanks.

ii

ABSTRACT

Thermally conductive polymer composites can replace metals in many applications. This technology is a substantial improvement since polymers are commonly used due to their thermal isolating properties. The advantages of thermally conductive polymers over metals are reduced density; increased corrosion, oxidation, and chemical resistance; increased processability; and properties are adjustable to fit the application. However, polymers have many disadvantages; for example, creep, thermal instability, and a limited number of processing techniques. The main application for thermally conductive polymers is heat sinks. Other possible benefits are faster injection molding cycle times and improved thermal stability. The main objectives of this project were to produce thermally conductive polymer composites and to investigate their thermal properties. Their thermal behaviors under heat loads to which they might be exposed to are also investigated numerically by finite element analysis using ANSYS university version. Spherical copper filler particles, prismatic copper filler particles, copper fiber, and Al2O3 powder were added to nylon 6 matrix. For this work, the transverse and longitudinal thermal conductivities of spherical copper filler particles, prismatic copper filler particles, copper fiber filled nylon 6 matrix composites were measured by Hot Disk method and Laser Flash technique. Special experimental set was designed for testing the temperature distributions within the Al2O3 filled nylon 6 composite. In addition, optical microscopy and image analysis were also performed to characterize the structure of the composites. From these studies, it was found that all three types of copper fillers positively affect the thermal conductivity.

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The results were used to examine the predictions of theoretical thermal conductivity models. These models include the particle geometry, thermal conductivity, and packing of the filler(s), and the thermal conductivity of the polymer. Also the results were used to conduct steady-state and transient thermal analysis with finite element software ANSYS in order to reveal the response of produced polymer composites to specific working conditions such as usage of them as an electronic system component.

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ÖZET

Termal olarak iletken polimer kompozitler günümüzde bir çok uygulamada metal malzemelerin yerini almaktadırlar. Polimerlerin genelde termal olarak yalıtkan bir malzeme oldukları için tercih edilmelerinden dolayı bu değişim oldukça önemli sayılmaktadır. Termal iletken polimer kompozitlerin metal malzmelere kıyasla avantajları düşük yoğunluk, daha fazla korozyon, oksidasyon dayanımı ve kimyasal direnç, daha kolay işlenebilirlik ve de istenilen kullanım alanına göre bazı fiziksel özelliklerinin ayarlanabilmesi olarak sıralanabilir. Bununla birlikte polimerlerin düşük sürünme dayanımı, aşınma, termal olarak kararlı bir malzeme olmamaları ve sınırlı sayıda işleme tekniğinin bulunması gibi dezavantajları vardır. Termal olarak iletken polimerlerin ana kullanım alanları ısı alıcılarının üretilmesidir. Üretimdeki avantajları ise arttırılmış termal kararlık ve daha hızlı injection molding çevrim zamanlarıdır. Bu projenin ana hedefleri termal olarak iletken polimer kompozitler üretmek ve bu kompozitlerin termal özelliklerini inclemektir. Polimer kompozitlerin çeşitli uygulamalarda maruz kalmaları muhtemel ısı yükleri altındaki termal davranışları da ayrıca ANSYS sonlu elemanlar analiz programıyla nümerik olarak incelenmiştir. Polimer kompozitler küresel, prizmatik ve kısa fiberler şekillerinde tane yapılarına sahip bakır tozları ile küresel yapıda taneciklere sahip Al2O3 tozları nylon-6 matris malzemesine eklenerek üretilmiştir. Bu çalışma için üretilen nylon-6 polimer kompozitlerden bakır katkılı olanlarının enine ve boyuna olan düzlemlerindeki ısı iletim katsayıları hot-disk ve laser-flash teknikleri kullanılarak ölçülmüştür. Al2O3 katkılı nylon-6 polimer kompozitin termal davranışlarını incelemek amacıyla da özel bir deney düzeneği tasarlanıp hazırlanmıştır. Bunlara ek olarak optik mikroskopi ve “image

analysis”

yöntemleri

kullanılarak

üretilen

kompozitlerin

yapısal

v

karakteristikleri de incelenmiştir. Bu çalışmaların neticesinde bakır katkılarının polimer kompozitin ısıl iletkenliğini pozitif yönde etkilediği görülmüştür. Elde edilen sonuçlar, ısı iletim katsayısı modelleriyle yapılan hesaplamalarla elde edilen ısı iletim katsayısı sonuçları ile karşılaştırılmıştır. Hesaplamada kullanılan bu modeller patikül geometrisi etkisi, ısı iletim katsayısı, ve katkı malzemesi doldurma oranı gibi parametreleri de içermektedir. Ayrıca elde edilen tüm sonuçlar, söz konusu polimer kompozitlerin elektronik sistem parçası olarak kullanımı gibi belli çalışma koşulları altındaki davranışlarını simüle etmek amacıyla statik ve zamana bağlı değişim şeklinde yapılan ANSYS sonlu elemanlar analizinde kullanılmıştır.

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CONTENTS

Page Contents …………………………………………………………………………... VI List of Tables……………………………………………………………………...XIII List of Figures....................................................................................................…...XV

Chapter One INTRODUCTION 1.1 .. Introduction…………………………….........………………………………….1 1.2 .. Thermal Conductivity……………...…………...………………………………3 1.3 .. Motivation…………………………..………………………………….……….4 1.4 .. Research Objectives..……………………………..……………...……………..9

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Chapter Two THEORETICAL BACKROUND 2.1 Polymer and Composite Background………………………...…………………11 2.1.1 Historical Perspective……………………………………………………..11 2.1.2 Classification of Polymers………………………………………………...18 2.1.3 Structure of Polymers……………………………………………………..19 2.1.4 Crystallinity...........................……………………………………………...21 2.1.5 Molecular Weight of the Polymers…………………………….………….22 2.2 Thermal Conductivity Background………………………..…………………….23 2.2.1 Heat Transfer Phenomena…………………………………………….…...24 2.3 Predictive Thermal Conductivity Models…………………………………….....28 2.3.1 Basic Thermal Conductivity Models……………………….……………..29 2.3.2 Advanced Models……………………………………...………………….31 2.4 Usage of Polymer Composites in Electronics……………………..…………….35 2.4.1 Electronic Packaging…………………………………...…………………36 2.4.2 Electrical Properties of Polymer Composites……………………………..37 2.4.2.1 Structure and Characteristic Parameters of the Conductive Polymer System……………………………………………………….………..38 2.4.3 Thermal Management……………………………………………………..41 2.5 Predictive Finite Element Thermal Analysis Background………………………42 Chapter Three MATERIALS 3.1 Materials…………………………………………………..…………………….44 3.1.1 Matrix……………………………………………………………….……..44 3.1.1.1 Nylon 6………………………………………………………..……….44 3.1.2 Fillers……………………………………………………………….……..49 3.1.2.1 Copper Fillers..................................................................................…...49 3.1.2.1.1 Copper Plate Filler Particles (Cubrotec 5000)….…………………49 3.1.2.1.2 Spherical Copper Filler Particles (Rogal GK 0/50)…………….....50

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3.1.2.1.3 Copper Fiber Fillers (Stax Cu99)…………….................................51 3.1.2.1.4 Aluminum Oxide (Al2O3) Filler Particles (CL 4400)…….…….....52 Chapter Four PRODUCTION TECHNIQUES AND PRODUCTS 4.1 Drying………………………………………………………….………………..54 4.2 Extrusion………………………………………………………...………………55 4.3 Injection Molding………………………………………….…………………….59 Chapter Five EXPERIMENTS AND TEST PROCEDURES 5.1 Thermal Behavior Testing of the PA6/Al2O3 Composite Specimens………….64 5.1.1 Experimental Design………………………………………………………65 5.1.2 Specimen Fabrication……………………………………………………...66 5.1.3 Test Method…………………………………………………….................67 5.1.4 Evaluation of the Results………………………………………………….72 5.2 Hot Disk Thermal Conductivity Measurement Method………………………...74 5.2.1 Hot Disk Thermal Constant Analyzer……………………………………..76 5.2.2 Hot Disk Sensor…………………………………………………………...77 5.2.3 Measuring Principle……………………………………………………….78 5.3 Laser Flash Method……………………………………………………………...79 5.3.1 Method Overview…………………………………………………………79 5.3.2 Features of the method…………………………………………………….83 5.4 Microscopy……………………………………………………………………...83 5.4.1 Determination of Orientation……………………………………...............83 5.4.2 Sample Preparation………………………………………………………..84 5.4.3 Polishing…………………………………………………………………..86 5.4.4 Optical Imaging Methods…………………………………………………87

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Chapter Six THERMAL ANALYSIS BY FINITE ELEMENT METHOD 6.1 Finite Element Method…………………….……………………………………88 6.1.1 Brief Information About the Application areas of FEM………………..…90 6.1.2 Details of FEM…………………………………………………….............93 6.1.2.1 Rules for Discretization of the Structure into Elements………………93 6.1.2.2 Types of Elements……………………………………..………………94 6.1.2.2.1 One-dimensional elements……………..………………………….94 6.1.2.2.2 Two-dimensional elements………………………………………..95 6.1.2.2.3 Three-dimensional elements…………………………....................96 6.1.3 Finite Element Analysis Procedure………………………………………..97 6.1.3.1 Geometry Creation…………………………………………………….97 6.1.3.2 Mesh Creation and Element Selection……………………………...…97 6.1.3.3 Boundary and Loading Conditions……………………………………98 6.1.3.4 Defining Material Properties…………………………………………..98 6.2 Steady-State Thermal Analysis……………………………………………….…99 6.2.1 Composites’ Thermal Analysis Overview………………………………...99 6.2.2 Model Development for Finite Element Analysis……………………….101 6.2.3 Numerical Analysis………………………………………………………106 6.2.4 Results and Discussion of the Analysis………………………………….107 6.3 Transient Thermal Analysis……………………………………………………112 6.3.1 Usage of Polymer Composites in Electronics Overview………………...112 6.3.2 Evaluation of Polymer Composites in Electronic Systems………………113 6.3.3 Numerical Approach……………………………………………………..115 6.3.4 Electronic Artifact………………………………………………..............117 6.3.5 Models of the Electronic Artifact………………………………………..119 6.3.6 Transient Thermal Analysis of PA6 (70 Vol.-%)/(30 Vol.-%) Cu (Rogal GK 0/50) Substrate………………………………………………………121 6.3.7 Conclusions of the Analysis……………………………………………...127

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Chapter Seven RESULTS AND DISCUSSION 7.1 Experimental Results…………………..………………………………………128 7.1.1 Thermal Conductivity…………………...……………………………….128 7.1.1.1 Hot Disk Thermal Conductivity Measurement Results……………...128 7.1.1.2 Laser-Flash Thermal Conductivity Measurement Results…………...130 7.2 Microscopy Orientation Results……………………………………………….135 7.2.1 PA6 Ultramid B3-Matrix with Copper-Rogal GK 0/50 Filler…………...135 7.2.2 PA6 Ultramid B3-Matrix with Copper-Cubrotec 5000 Filler……………138 7.2.3 PA6 Ultramid B3-Matrix with Copper Fiber Filler……………………...141 7.3 Theoretical Thermal Conductivity Models Calculation Results……………….142 7.3.1 Comparison of the Theoretical Models’ Predictions with the Experimental Data………………………………………………………………………142 Chapter Eight SUMMARY AND CONCLUSIONS 8.1 Effect of Conductive Fillers on the Thermal Conductivity……………...…….146 8.2 Effect of Conductive Filler Concentrations and Thickness on the Thermal Analysis of Copper Filled PA6 Composites as a Chip Substrate……………...147 Chapter Nine FUTURE WORK Future Work………………………………………………………………………..150

References…………………………………………………………………………152

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Appendices Appendix A Injection Molding….............................................................................156 A.1 Injection Molding Conditions…………………………..……………….156 A.2 Screw Scheme of the Injection Molding………………..……………….165 Appendix B Extrusion…………………………………………………..………….166 B.1 Scheme of the Zones….............................................................................166 B.2 Screw Design…………………………………………………………….167 Appendix C Experimental Results of PA6/Al2O3 Composite Thermal.Behavior Testing…….………………………………………………………..168 C.1 Results for Heat Imposing of 150 °C……………………………………168 C.2 Results for Heat Imposing of 190 °C……………………………………173 Appendix D Application of Theoretical Thermal Conductivity Models…………..181 D.1 Results of Theoretical Model Calculations for PA6/Cu Composites…...181 D.2 Comparison of the Theoretical Model Results with the Measured……… Thermal Conductivity Values………………………………..………….186 Appendix E 3D Steady-State Thermal Analysis Results…......................................188 E.1 Three Dimensional Thermal Analysis of PA/Cu Composites Filled with.Spherical Cu Particles with the Filler Concentration of 20% by Volume…………………………………………………………………188 E.2 Three Dimensional Thermal Analysis of PA/Cu Composites Filled with.Spherical Cu Particles with the Filler Concentration of 30% by Volume……………………………………...………………………….190 E.3 Three Dimensional Thermal Analysis of PA/Cu Composites Filled with.Spherical Cu Particles with the Filler Concentration of 40% by Volume……………………………...………………………………….191 E.4 Three Dimensional Thermal Analysis of PA/Cu Composites Filled with.Prismatic Cu Particles with the Filler Concentration of 30% by Volume……………………………………………...………………….192 Appendix F 3D Transient Thermal Analysis Results…………………..………….194

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F.1 Figures of Temperature Distributions During Load Step Time (600 sec). Through the PA6 (70 Vol.-%) / Cu (30 Vol.-%) Rogal GK 0/50 Composite Substrate with 2 mm Thickness………..……………………………….194 F.2 Figures of Temperature Distributions during Load Step Time (600 sec) Through the PA6 (70 Vol.-%) / Cu (30 Vol.-%) Rogal GK 0/50 Composite Substrate with 4 mm Thickness…………………………………………198 Appendix G Thermal Conductivity Measurement Results………………………...202

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LIST OF TABLES

Table 1.1: The thermal conductivity of some common materials are: (all the values are in W/mK)………………………………….………………………….3 Table 2.1: Maximum packing fractions of the selected fillers…………………...….34 Table 2.2: Shape Factor ‘A’ for Common Filler Types…………………….……….34 Table 3.1: Properties of PA-Ultramid® B3 (nylon 6)………………………………47 Table 3.2: Properties of Cubrotec 5000…………………………………….……….49 Table 3.3: Properties of Rogal Gk 0/50……………………………………………..50 Table 3.4: Properties of Al2O3………………………………………………...……52 Table 4.1: A Listing of Single Filler Composite Formulations………………….….54 Table 4.2: Produced compounds via extrusion process and their amounts...……….59 Table 4.3: Produced compounds via injection molding process and their quantities.63 Table 5.1: Fabricated composites formulations compositions for the experiment….66 Table 5.2: Polishing Procedure………………………………………………...……87 Table 6.1: Properties of the PA6 and Copper used in ANSYS for thermal analysis……………………………………………...………………..101 Table 6.2: Thermal Properties of the Electronic Artifact Model……………..……119 Table 6.3: Temperature dependent thermal conductivities of the substrate with different concentrations………………………………………………..120 Table 6.4: Transient thermal analysis results for the two different assumptions for temperature difference between the chip and the ambient while the chip is being deposited on the substrate………………………..……………...122 Table 7.1: Laser Flash measurement results…………………………………..…...131 Table 7.2: Thermal conductivity values according to two different methods for 30 Vol.-% PA6/Cu composite………………………………...…………...135

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Table 8.1: Transient thermal analysis results for the two different assumptions for temperature difference between the chip and the ambient while the chip is being deposited on the substrate………………………..……………...148

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LIST OF FIGURES

Figure 1.1: Applications for plastics in the U.S during 1998 (and % change compared to 1997)…………………………………………………………………5 Figure 1.2: Production of different materials in the western world starting after 1950 and world wide starting after 1990……………………………………..6 Figure 1.3: Worldwide plastic productions in 1999………….……………………….7 Figure 2.1: Representation of Polymer Chains in an Amorphous Polymer………....20 Figure 2.2: 2D Representation of Polymer Chains in a Semi-Crystalline Polymer…21 Figure 2.3: Two-Dimensional Array of Atom Connected by Springs…………...….25 Figure 2.4: Filler Configurations [(a) spherical filler in a vacuum (b) spherical filler in polymer matrix]…………………………………………..………...28 Figure 2.5: Typical dependence of electrical conductivity (logarithm) on conductive filler volume content…………………………………………………..39 Figure 3.1: Chemical structure of nylon 6…………………………………………..45 Figure

3.2:

Linear

expansion

of

Ultramid

grades

as

a

function

of

temperature…........................................................................................46 Figure 3.3: Graphical expression of glass transition phenomenon………….………48 Figure 3.4: REM picture of Cubrotec 5000…………………………………………50 Figure 3.5: REM picture of Rogal GK 0/50………………………………...………51 Figure 3.6: REM picture of Copper Fiber…………………………………………...51 Figure 4.1: Gecco Type TTM 4/50 Dryer…………………………………………...55 Figure 4.2: 27mm diameter Twin Screw Leistritz ZSE 27 HP 40 D Model Extruder………………………………………………………………..57 Figure 4.3: A view of the screws and the grinder of the Leistritz ZSE 27 HP 40 D Model Extruder………………………………………………………..57 Figure 4.4: Demag Ergotech 25/280-80 System Injection Molding Machine…….….61

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Figure 4.5: One-cavity mold used in injection molding process………...………….61 Figure 5.1a: An image of the Al2O3 fillers……………………………...…………..65 Figure 5.1b: An image of the Al2O3 fillers……………………………...…………..65 Figure 5.2: Prepared sample for test………………….……………………………..67 Figure 5.3: Representation of heat generation disk with the thermocouple connected to the power tuner……………………….…………………………….68 Figure 5.4a: View of the heat generation disk device and measurement substrate....68 Figure 5.4b: Computer set used for acquiring data from the samples…………..…..69 Figure 5.4c: Aluminum substrate with an initiation switch………………….……...69 Figure 5.5: Illustration of the test conditions with the insulating wooden plate on the Al substrate with an initiator switch for data acquisition……………..70 Figure 5.6: Experimental designs of the specimens with thermocouples (T1, T2, T3, and T4)…………………………………………………………………71 Figure 5.7: Test Graph of PA6/80 Vol.-% Al2O3 (4 layers with 2mm thicknesses)………………………………………...………………….72 Figure 5.8: Test Graph of pure PA6 (4 layers with 2mm thicknesses)…….………..73 Figure 5.9: Test Graph of PA6/80 Vol.-% Al2O3 (4 layers with 1mm thicknesses)………………………………………………………...….74 Figure 5.10: Hot Disk measurement principal illustration…………..………………75 Figure 5.11: Hot Disk thermal conductivity measurement set…………...…………76 Figure 5.12: Hot Disk sensor…………………………………………..……………77 Figure 5.13: Time evaluation versus temperature rise………………………………80 Figure 5.14: Laser Flash thermal diffusivity measurement device………………….82 Figure 5.15: Diagram of image analysis specimens………………………...………85 Figure 5.16: Orientation of image analysis specimens………………………...……86 Figure 6.1: Truss element………………………………………………………..….95 Figure 6.2: Two-dimensional FEM element………………………………………...95 Figure 6.3: Three-dimensional FEM element………………………………….……96 Figure

6.4a:

Three-dimensional

finite

element

model

for

the

PA6/Cu

microstructure………………………………………………………..102 Figure 6.4b: 3D-Finite element model for the filler dispersion in the in the matrix material………………...…...………………………………………..102

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Figure 6.5a: 2D-Finite element model for the PA6/Cu microstructure……………103 Figure 6.5b: A view of meshed model of Figure 2a with a demonstrative temperature distribution…………………………………………………………...103 Figure 6.6a: 2D Microstructure Assumption for PA6/Cu………………..………...105 Figure 6.6b: 2D Microstructure Assumption for PA6/Cu……………….………...105 Figure 6.7: 3D Microstructure Assumption for PA6/Cu…………………………..105 Figure 6.8: Definition of the Problem with Assumed Microstructural Model….....107 Figure 6.9a: Finite Elements Model of PA6/Cu (20% by volume)……..…………108 Figure 6.9b: Temperature Distribution for the Model in Figure 6.9a……...………108 Figure 6.10a: Finite Elements Model of PA6/Cu (45% by volume)………………109 Figure 6.10b: Temperature Distribution for the Model in Figure 6.10a…………...109 Figure 6.11a: Finite Elements Model of PA6/Cu (38% by volume)………………110 Figure 6.11b: Temperature Distribution for the Model in Figure 6.11a…………...110 Figure 6.12a: Finite Elements Model of PA6/Cu (38% by volume)……………....111 Figure 6.12b: Temperature Distribution for the Model in Figure 6.11a…………...111 Figure 6.13: Solid model representation of the electronic artifact in ANSYS….....115 Figure 6.14a: FEM model showing view of electronic artifact without air covering………………………………………………………………116 Figure 6.14b: FEM model with air covering over the chip and the substrate……...117 Figure 6.15: FEM model of the electronic artifact with the applied loads………...118 Figure 6.16: Representation of the data source for the expressions in Fig. 6.17 a-b-cd………………………………………………………………………124 Figure 6.17a: Temperature distribution at the lower surface of the substrate with 2 mm thickness………………………………………………………...125 Figure 6.17b: Heat flux distribution at the lower surface of the substrate with 2 mm thickness………………………………...…….……………………...125 Figure 6.17c: Temperature distribution at the lower surface of the substrate with 4 mm thickness………………………………………………………...126 Figure 6.17d: Heat flux distribution at the lower surface of the substrate with 4 mm thickness……………………………………………………………...126 Figure 7.1: Hot Disk complete thermal conductivity measurement……………….130

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Figure 7.2: Laser-Flash thermal conductivity measurement results for PA6 Ultramide B3/Cu 30 Vol.-% (Cubrotec 5000, Rogal GK 0/50, Fiber) according to the injection direction…………………………………………...……..132 Figure 7.3: REM picture of PA6/Cu 30 Vol.-% (Rogal GK 0/50)…………...……133 Figure 7.4: REM picture of PA6/Cu 30 Vol.-% (Cubrotec 5000)…………………133 Figure 7.5: REM picture of PA6/Cu 30 Vol.-% (Copper Fiber)………………..…134 Figure 7.6: Image of PA6 Ultramid B3/30 Vol.-% Cu Rogal GK 0/50 in the counter direction to injection direction (2.5x magnification)……………...…...135 Figure 7.7: Image of PA6 Ultramid B3/30 Vol.-% Cu Rogal GK 0/50 in the perpendicular direction to injection direction (2.5x magnification)…136 Figure 7.8: Image of PA6 Ultramid B3/30 Vol.-% Cu Rogal GK 0/50 in the perpendicular direction to injection direction (10x magnification)….137 Figure 7.9: Image of PA6 Ultramid B3/30 Vol.-% Cu Cubrotec 5000 in the counter direction to injection direction (2.5x magnification)………………...138 Figure 7.10: Image of PA6 Ultramid B3/30 Vol.-% Cu Cubrotec 5000 in the perpendicular direction to injection direction (2.5x magnification)....138 Figure 7.11: Image of PA6 Ultramid B3/30 Vol.-% Cu Cubrotec 5000 in the counter direction to injection direction (10x magnification)………………....140 Figure 7.12: Image of PA6 Ultramid B3/30 Vol.-% Cu Cubrotec 5000 in the perpendicular direction to injection direction (10x magnification)….140 Figure 7.13: Image of PA6 Ultramid B3/30 Vol.-% Cu Fiber in the counter direction to injection direction (2.5x magnification)…………….…………….141 Figure 7.14: Image of PA6 Ultramid B3/30 Vol.-% Cu Fiber in the counter direction to injection direction (10x magnification)…………………………...141 Figure 7.15 Comparison of theoretical results with experimental results for PA6B3/Cubrotec 5000 composites……………………………………….143 Figure 7.16: Comparison of theoretical results with experimental results for PA6 B3/Rogal GK 0/50 composites………………………………………144 Figure 7.17: Comparison of theoretical results with experimental results for PA6 B3/Copper-Fiber composites………………………….……………..145

1

CHAPTER ONE

INTRODUCTION

1.1 Introduction Since their earliest development, composite materials have primarily been used for structural applications. However, polymer composite materials have been found to be extremely useful for heat dissipation applications in electronic packaging (Chen Yu-Mao & Ting Jyh-Ming, 2002). Polymer composites filled with metal are of interest for many fields of engineering. This interest arises from the fact that the thermal characteristics of such composites are close to the properties of metals, whereas the mechanical properties and the processing methods are typical for plastics (Bigg D. M., 1986, Hansen D. & Bernier G. A., 1972). The achievement of metallic properties in such composites depends on many factors, and it is just the possibility of controlling the thermal and physical characteristics which determines the variety of ranges of their application. The transfer conditions of the heat flow determine thermal conductivity level in the heterogeneous polymer-filler system, in which dispersed metallic or carbon filler forms the conductive phase. The influence of the type of polymer matrix and filler on the thermal characteristics of the composite has been studied in many works (Sundstrom D. W. & Lee Yu-Der, 1972, Agari et al., 1991). Although in some publications it was observed that the percolation behavior of the conductive composite depends on both filler particle shape and spatial distribution within the polymer matrix, as a rule, the equations and models used do not contain any parameters linked with the filler particle shape and conductive phase topology. Concerning the thermal conductivity of such composites, in spite of several models

2

for two phase systems, there are only a few publications on the study of the correlation between the structure and thermal properties (Fried, J. R., 1995, Mamunya et al., 2002) Engineering design requires both mechanical and thermal properties to define material behavior adequately and accurate analysis techniques to predict generic part performance based on those data. Increasingly, plastic materials are being considered for use in electronic applications where the heat management and removal of the heat is required, and the ability to apply thermal analysis effectively to design for performance continues to grow in importance. In order to foster this technology growth, issues specifically relevant to the thermal behavior and analysis of plastic parts must be identified. Thermally conductive polymer composites can replace metals in many applications. This technology is a substantial improvement since polymers are commonly used due to their thermal isolating properties. The advantages of thermally conductive polymers over metals are reduced density; increased corrosion, oxidation, and chemical resistance; increased processability; and properties are adjustable to fit the application. However, polymers have many disadvantages; for example, creep, thermal instability, and a limited number of processing techniques. The main application for thermally conductive polymers is heat sinks. Other possible benefits are faster injection molding cycle times and improved thermal stability. The increasing demand for smaller, lighter, and faster machines and electronics has created a need for new materials. In addition, industry has a growing need to tailor the properties of materials, including thermal conductivity, to desired applications. Composites are often used to fill these needs. Composites are a mixture of two or more types of materials (polymer, metal, ceramic, etc.) that form a new material with properties that are a combination of the constituents. Many composites are used in everyday life, such as concrete for roads and fiberglass in cars’ body panels. Copper and Al2O3 filled thermoplastic polymer composites are investigated in this study and their thermal behaviors and conductivities will be the central focus.

3

Conductive composites are often formed by the addition of thermally conductive fillers to a polymer matrix. Many studies have investigated the addition of single fillers to increase the thermal conductivity of polymer-based composites (Bigg D. M., 1986). For instance, various copper and Al2O3 fillers are often used to increase a composite’s thermal and electrical conductivity. The addition of the copper and Al2O3 fillers increases the composite’s thermal conductivity beyond that of the neat resin alone, but not to the level of the copper or Al2O3 fillers. 1.2 Thermal Conductivity Thermal conductivity has been and is critical to human existence. Significant portions of the world’s population inhabit the temperate and colder portions of the earth where keeping warm is necessary for existence. The use of materials with low thermal conductivities, such as wool and animal skins, has kept people warm for millennia. The use of heat shields with extremely low thermal conductivities in returning space vehicles is critical during re-entry into the atmosphere. One can see that the thermal conductivity of materials has been important for humans from the Stone Age through the space age and beyond. Table 1.1 The thermal conductivity of some common materials are (all the values are in W/mK) (WEB_10, 2003)

Thermally conductive polymer composite’s potential uses are in heat sink applications such as computers, laptop cases, and transformer housings. Polymer

4

composites with thermal conductivities between 1 and 30 W/mK can be used in heat sink applications. This technology could also be used in applications such as heat exchangers and radiators. In all of these applications, the thermal conductivity of a material is an important property to understand and reliably predict. With the ability to predict the thermal conductivity of the composites, large scale testing would not be needed to tailor it to an application. 1.3 Motivation The demand for conductive polymer composites continues to grow in the United States. In 1995, the demand for conductive polymer composites was 221 million lbs. It is projected to grow 6.1 percent annually to 565 million pounds (including both resins and additives) by 2004. Its value will reach $1.5 billion by 2004, consisting of the cost of resins and additives, as well as labor and other overhead costs incurred during the production of the conductive compound. Modern plastics are lightweight, though, corrosion resistant, and can be easily molded into complex components with various functions and features. These desirable features have influenced the applicability of plastics within several US markets as shown in Figure 1.1. Historically, the largest market has been the packaging industry, which comprises over 26% of the consumption of all plastics within the US. Though the total volume of plastics used in packaging applications in staggering, the yearly increase in consumption figures is approaching a plateau. This is due to innovative techniques developed in recent years that allow for the minimization of the total plastic volume while maintaining the stringent packaging design requirements (Ehrenstein, G. W., 2001).

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Figure 1.1 Applications for plastics in the U.S during 1998 (and % change compared to 1997) Sectors that have seen improved growth in comparison to packaging include consumer goods as well as building and construction. Export of resins from the US has seen rapid growth; however recent investments by resin producers in manufacturing facilities in foreign markets will significantly influence this trend. It is anticipated that both the consumer goods and construction industries will continue to grow as plastics continue to be introduced as a replacement material for conventional engineering materials such as wood, stone, glass, and metal (Ehrenstein, G. W., 2001). Historically, the production in comparison with steel and aluminum has made major strides since 1950 as shown in Figure 1.2. The graph in terms of volumetric production is not meaningful since the most important engineering calculations, such as tension and elastic modulus, are based on the part geometry. In the last 25 years, the quantity of steel production has remained stable while the production of plastics has almost quadrupled. Although the production of aluminum has increased to approximately 50%, production levels remain relatively low even today (Ehrenstein, G. W., 2001).

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Figure 1.2 Production of different materials in the western world starting after 1950 and world wide starting after 1990 The industrially important plastics consist of 30 to 40 different types of polymers that are offered in approximately 13000 variations under approximately 25000 different trade names. Plastics can be subdivided into roughly three overlapping groups according to their application, prize, and quantity of use:

1. Commodity resins or bulk resins •

polyvinyl chloride (PVC)

•

polyethylene (PE)

•

polypropylene (PP)

•

styrene-based polymers (PS, PS-HI)

2. Technical resins or engineering resins

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•

polyamide (PA)

•

polyoxymethylene (POM)

•

polycarbonate (PC)

•

polyethylene terephthalate (PET)

•

polybutylene terephthalate (PBT)

•

styrene copolymers (ABS ASA, SAN, etc.)

•

blends such as ABS+PC and PBT+PC

3. High-performance resins •

aramid, polysulfone (PSU, PPSU, PAS etc.)

•

polyetherketone (PEK, PEEK, and PEEKK)

•

polyimide (PI, PAI, PEI)

•

polyphenylene sulfide (PPS)

•

liquid crystalline polymers (LCP) and fluoropolymers (PTFE)

The world wide consumption of the commodity resins totaled 95.6 million tons in 1996, a 12.5% increase from 1994. The country that has dominated the consumption of thermoplastics remains the US with approximately 25% of the market as shown in Figure 1.3. However, the largest potential for growth over the next several years will be with the Southeast Asian countries, followed closely by developing Eastern European and South American countries (Ehrenstein, G. W., 2001).

Figure 1.3 Worldwide plastic productions in 1999

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Although plastics possess the crucial advantage of a low specific weight and relatively straightforward processing techniques compared to other materials, disadvantages do exist. It should be noted that the actual characteristics, e.g. stiffness and strength, for the bulk material are only a fraction of what was predicted from the theory. While row material production takes place almost exclusively in the chemical industry, the processors are either medium sized companies or integrated enterprises, such as steel or other major manufacturing companies. The potential for processing innovation is tremendous, compared to metals and other conventional materials. Therefore, plastics open the doors to new and inexpensive processing methods. Developments in this area have achieved extraordinary success. Multi-component processing is only one example. This process directly connects plastics with other materials during the processing procedure. The materials can be several different types of plastics, from which adhesive or anti-friction systems can be produced. Multi-component processing allows for the integration of different colored, soft and hard, decorative and functional components, as well as permanent connections between films, fabrics, leathers, and other components via injection molding. Plasticmetal-hybrids have also been successful for applications in which the highly loaded laminar metal parts are connected to the plastic. In this case, the plastic represents a complex load-carrying structure and functional structure at the same time. Considering the substantial number of mergers between companies since the end of the 1980s, the selling prize of plastics is relatively constant in the US over the last ten years. The prize of plastics in Europe, in comparison, has undergone major cost fluctuations with an overall slight decrease in prize over the same period. The indicated values refer to the cost of the materials in medium sized quantities. The decrease in the prize of technical and, in particular, commodity plastics will allow the substitution of expensive plastics and thus offer price incentives compared to conventional materials (Ehrenstein, G. W., 2001).

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The actual number of universities, colleges, and technical centers concentrating on plastics and their engineering application is small in comparison with other materials and engineering disciplines. This applies not only the number of institutions but also the supply of educators in the field of plastics engineering. An increase in the knowledge base and new applications for plastics in the future will result in a steady increase of usage of plastic engineering materials. Due to the increasing demand, continual development, and research into conductive polymers is required. This research and development will not only allow materials to be produced, but also reduce the cost of producing the materials. Currently, the main applications for conductive polymer composites are for electromagnetic and radio frequency interference (EMI/RFI) shielding and electrostatic dissipation (ESD). With greater understanding of other properties, such as thermal conductivity, the same composites used for EMI/RFI shielding and ESD could take advantage of other properties and become multifunctional. A possible example of this is EMI/RFI shielding that is both chemically and oxidative resistant and thermally conductive. Such a material could be used as a combined EMI/RFI shield and heat sink in a harsh environment. 1.4 Research Objectives The objectives of this project were to: 1. Create thermally conductive composites 2. Characterize and analyze copper and Al2O3 filled polymer composites 3. Determine the effects of conductive filler combinations on the thermal conductivity of the resulting composite 4. Conduct thermal analyses by FEM (finite element method) under certain virtual loads to get information on the thermal behavior of copper-filled or Al2O3-filled polymer composites in the case they are employed in such systems which are possible to impose loads to polymer composites emulating to virtual FEM loads.

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These objectives have been reached through two different studies where data were collected and analyzed. The first study centered on the production and testing of filled conductive resins. This study examined polymer composites filled with copper and Al2O3. This study also examined polymer, polyamide (Ultramide B3)-nylon 6. Their thermal conductivities were determined by conventional measurement techniques such as “hot disk” and “laser-flash”. The knowledge gained from this study forms the foundation for the FEM modeling and analysis work. This foundation allowed the modeling to focus on the important factors. The second study centered on the determination of the behaviors of combinations of conductive filler on the thermal conductivities of filled polymer composites. This study examined the same two fillers as in the first study.

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CHAPTER TWO

THEORETICAL BACKGROUND

2.1 Polymer and Composite Background The word polymer is derived from the classical Greek words poly meaning “many” and meres meaning “parts”. Simply stated, a polymer is a long chain molecule that is composed of a large number of repeating units of identical structure. Certain polymers, such as proteins, cellulose, and silk, are found in nature, while many others, including polystyrene, polyethylene, and nylon are produced only by synthetic routes. In some cases, naturally occurring polymers can also be produced synthetically. An important example is natural rubber (i.e., Hevea), which is known as polyisoprene in its synthetic form (Fried, J. R., 1995). 2.1.1 Historical Perspective The first plastic to be produced commercially was Celluloid polymer. The history of this material can be traced back to written records attributed to J. Pelouze in 1835 and the German chemist Schonbein in 1845 that document observations of an interesting new material derived from mixing wood fibers or paper with concentrated nitric acid. In spite of the lack of understanding of the basic chemistry of this material, a 19th-century English materials technologist named Alexander Parkes was able to initiate commercial production of a material he called “Parkesine”, which was related to the earlier recordings of Pelouze and Schonbein. Parkes had no formal education in chemistry but had experienced considerable success in processes related to both metallurgy and rubber. He exhibited his material at the Great International Exhibition of 1867 in South Kensington, England and was awarded a bronze medal

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for excellence in quality. Visitors to the exhibition were impressed with the low cost and formability of this new material as well its hardness once completely processed. In 1866, Parkes launched the Parkesine Company, an enterprise to use the Parkesine polymer for production of commercial products such as combs, umbrella handles, tableware handles, and jewelry. However, for a variety reasons including extreme efforts to minimize production cost, the quality of these products was less than acceptable and the company was liquidated in 1868. During the same period of time, another imaginative inventor in the United States named John Wesley Hyatt had started pursuing the production of a very similar material. Like Parkes, Hyatt had no formal education in chemistry. As a result of a growing shortage of ivory, the billiard-ball manufacturing enterprise of Phelan and Collander in Albany, New York had offered a $10,000 prize for the invention of a replacement material for the ivory in their product. It was in pursuit of this prize that Hyatt initiated his investigation. Hyatt’s first patents in this area appeared in 1865, but it was not until 1870 that the patent covering his discovery of the contribution of camphor in processing celluloid appeared. This discovery eventually allowed Hyatt to solve most of the problems that had plagued Parkes in England. In 1872, Hyatt and his brother formed the Celluloid Manufacturing Company and embarked on a very successful commercial introduction of this material and products made from it. The business grew and eventually moved to Newark, New Jersey. Its name evolved to the American Celluloid and Chemical Corporation and it was eventually absorbed by the Calanese Corporation, which has more recently been acquired by Hoeschst to become Hoeschst Calanese. The commercial plastics industry had achieved its first success. In spite of the success of Celluloid polymer as a material, other plastics did not rapidly appear. The continued lack of understanding regarding the basic structure and chemistry of this new class of materials proved to be a major impediment to the introduction of additional materials of a similar nature. In fact, it was not until 1877, five years after the establishment by Kekule as relevant to the very special properties associated with certain natural organic substances like cellulose.

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It was approximately 41 years after the discovery of Celluloid polymer that the second plastic material was developed by Dr. Leo Bakeland in the United States and named Bakalite polymer. Although Bakeland had developed the material as a synthetic electrical insulator, John Hyatt, who had also founded the Hyatt-Burroughs Billiard Ball Company, applied it to billiard balls once again. While Celluloid polymer was the first plastic, it was really only semi-synthetic since it was made of natural materials. Bakalite polymer was the first truly synthetic plastic. The introduction of new plastic materials still did not accelerate with the discovery of Bakalite polymer. By 1930, almost 60 years after the commercial introduction of the first plastic, the annual production of these materials in the United States was only 23,000 metric tons, almost all of which was Celluloid and Bakalite polymers. A fundamental understanding of the basic chemistry relevant to plastics was still the most significant technological issue impeding progress toward new polymeric materials with a wider range of potential applications. That situation was soon to change. The scientist who is generally honored for having led the way in founding polymer chemistry is Hermann Staudinger. Staudinger wrestled with basic issues relevant to the size of the molecules of which natural and synthetic polymers were made and the character of the forces that held them together and gave them their peculiar properties. In contrast to the majority of investigators dealing with such issues in the 1920s, Staudinger did not subscribed to the concept that these materials consisted of small molecules, clustered in aggregates and held together by some electrical or yet-to-be-defined force of molecular attraction. Instead, Staudinger was a proponent of the idea that atoms comprising polymers were bound together by the same covalent bonds understood to exist in normal organic compounds. His experiment led him to believe that the only significantly distinctive feature of polymeric materials was the immense size of their molecules. In 1924, Staudinger proposed that polystyrene and natural rubber had linear structures with extremely large molecular weights-about 20,000 for polystyrene-made up of identical, repetitively linked, basic chemical units. He went on to explain that unlike other

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compounds such as water, which has a fixed and identical molecular weight associated with all its molecules, the molecular weight of a polymer was merely an average. In 1953 Staudinger received the Nobel Prize for his pioneering work in polymer chemistry, but his work in understanding the basic structure of polymers helped fuel the expansion of polymer technology well before his award. As the molecular structure of polymers became better understood, there was also progress in defining mechanisms by which these polymers could be produced. The work of Dr. Wallace H. Carothers was particularly important in this area. Carothers’ contributions to the science of polymer synthesis include emphasis on the concept of “functionality” in polymeric reactions as well as the distinction between the two important classes of polymerization: namely addition and condensation. Beyond his fundamental contributions to polymer science, Carothers is also remembered for his management of the Du Pont Company research laboratory, where he invented the synthetic rubber, neoprene, as well as the thermoplastic polymer, nylon. The next impetus in the development of polymer technology was rooted in international history as much as in science: during World War II it was necessary to find new synthetic materials to replace inaccessible natural resources such as rubber. Coupled with the newly acquired knowledge of polymer chemistry, these immense new demands created the new surge in plastic materials invention. Beginning in the years just prior to World War II, a number of today’s familiar plastics began to appear. Many of the first applications were related to the outstanding electrical insulation properties of these new materials. Polyvinyl chloride, for example, was widely used as cable insulation. The dielectric properties of polyethylene made it another attractive material for use in electric equipment, and it became especially critical in the radar used by the English during the Battle of Britain. Polystyrene not only saw use in electrical equipment, but it was also associated, in one form or another, with the artificial rubbers developed for use as tires for most of the military vehicles. Clear and light in weight, polymethyl methacrylate was used extensively for cockpit canopies. Nylon, on the other hand, saw application in a very different form. Drawn into fibers, it was heavily used for parachute material, tow ropes, and

15

tire chords. The technology and practical application of polymeric materials had obviously achieved a new and much more rapid growth rate. By 1949, the annual production of plastic in the United States had reached 517,000 metric tons (517,000 tons). After World War II, the rate of discovery and introduction of new polymers continued to accelerate. This growth helped stimulate the development of the other technologies that were essential to the effective use of plastics. Processing technology in particular had to improve to meet the efficiency demands of a peace time economy. The original Celluloid products were manufactured with a variety of techniques including injection molding and extrusion. However, the limited use of plastic did not merit any extensive work to refine these processing methods. That situation changed with the rapid introduction of new materials during the 1930s and 1940s. As material suppliers began looking for new peacetime applications for their plastics, there was new impetus for improving processing technology as well. Some of the new polymers were difficult to process, with narrow windows of temperature available for molding parts. Commercial efficiency became an increasingly important goal as the new plastics competed with older materials as well as each other for market share. Innovations in the existing processes such as preplasticizing systems began to appear rapidly. Although injection molding and extrusion remained the highest volume plastic processing methods, new techniques such as blow molding also appeared. Another technology that began to develop and mature in response to the rapid expansion of the plastic industry was polymer materials science. Materials science might be defined as focusing upon the relationship between material properties and material form and structure. One example of the significance of this technology is the effect of molecular weight on plastic material properties. Reduced molecular weight is associated with lower viscosity at processing temperatures and can often make a plastic easier to mold. However, reducing a polymer’s weight also has negative effects on the impact resistance of the polymer, which In turn could make the performance of the molded component unacceptable. Understanding and controlling

16

such effects is crucial to the success of a plastic component. Materials science has also helped industry come to understand that modifying or manipulating any one property usually also affects other properties. For instance, the addition of small rubber particles to the polymer will improve impact resistance, especially at lower temperatures when materials are stiffer. However, the presence of those particles also affects the flame-retardant properties of the material. The more rubber added to increase impact performance, the lower the fire resisting properties of the polymer. And generally, the grater the amount of flame-retardant additives in the polymer matrix, the poorer the resulting material’s impact resistance will be. Progress in the materials science technology area has also been very influential in expanding the application opportunities for plastic materials. At this point, it is worthwhile to mention one additional element of the history of plastics. Although seemingly insignificant in comparison to some of the previously mentioned events, it is highlighted because of its significance with respect to the development of mechanical technology for plastics. In the Story of the Plastics Industry, published by the Society for the Plastics Industry (SPI) in 1977, the appearance of a subgroup of plastics identified as “engineering thermoplastics” are mentioned during a brief discussion of relevant events occurring during the 1950s. Acetal (introduced in 1956) and polycarbonate (1957) are listed as examples, along with nylon which was developed much earlier. In describing the nature of this plastic subgroup SPI singles out superior impact strength and thermal and dimensional stability, which allowed these materials to compete more closely with metals in loadbearing environments. Many other plastics that fall into this somewhat ambiguously defined subgroup have appeared since. This material evolution placed new pressure upon mechanical technology to meet the challenge of performance in structural applications. Furthermore, since these materials generally cost more than other plastics, there was also new pressure for mechanical and processing technology to be more efficient in the use of these materials. With a solid basis established in polymer chemistry and rapidly evolving technologies in polymer processing and materials science, the annual production of

17

plastic in the United States reached 2,476,601 metric tons (2,730,000 tons) in 1959 and swelled to 17,263,420 metric tons (19,000,000 tons) by 1978. In 1979, production of all plastics in the United States surpassed the production of steel on a volume basis. At this stage in the development of plastic as a material, mechanical technology began to play a more significant role, continuing the success and expansion of plastic technology. Effective mechanical engineering and design was not always an important ingredient for success in many of the first applications of plastic that have been mentioned. It is not necessary to design a billiard ball. No geometry or structure must be defined for insulation used in an electrical cable. However, from their rather modest initial applications, plastic materials have evolved toward much more demanding applications that require sophisticated engineering analysis and design. For example, plastics are now being used to manufacture automotive bumpers, which must be able to survive 8-km/h impacts without damage and without deflecting so much that other parts of the car are damaged. In applications such as electronics packaging and thermal management requiring processes, geometries and microstructure must be defined to fulfill thermal and mechanical performance requirements. In order for geometric definition to be most efficient, it must be possible to predict thermal and mechanical performance as a function of geometry based on the fundamental thermal and mechanical properties of the materials being considered. If this is not possible, then the mechanical design process can only fall back on the time-consuming and inefficient trial-and–error or build-and-test process, something that today’s highly competitive and global economy can rarely cost justify. Despite their large volume of use, polymers are still a relatively new class of engineering materials. In fact, the use of the term polymer dates back only to 1832 when it was applied by the Swedish chemist Berzelius. Whenever a new class of materials enters engineering use, there is a necessary period of technology development and adjustment before a well-structured and logical process of design with such materials reaches maturity. Before such a logical process can evolve, several much more fundamental developments must occur. For example, elemental structure of the material must be well understood in order to facilitate material

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invention and fundamental evolution. Furthermore, the processes used for forming the material into useful shapes must become routine and well controlled, and an understanding of the relationship between the material’s morphology and its thermal and mechanical properties must also develop. As these technologies mature, it becomes possible to recognize whether the material’s properties and manufacturing processes offer specific advantages for achieving the functional requirements of a part. Out of these technologies arises a framework for conceiving potential approaches for application of the material and manufacturing processes to achieve a functional goal (Tarantine G. & Nimmer R., 1994). 2.1.2 Classification of Polymers Polymers are classified •

Thermosets

•

Elastomers

•

Thermoplastics

Thermosets are cross-linking polymers in which the final macro-molecules are formed by chemical reaction under the influence of heat and pressure. Once this reaction is complete, thermosets can not be altered from this state by further application of heat and pressure. Phenol (PF), Urea (UF), Melamine (MF) formaldehyde resins, Polyester (UP) resins and epoxy (EP) resins are typical Thermosets. Elastomers are plastics or modified natural substances with a limited degree of cross linking capability. They deform readily under stress but recover their original shape as soon as this stress is removed. Thermoplastics consist of long chain macromolecules which are not interlinked. Their characteristics property is that they may be moulded when the temperature is increased beyond their softening range, and on cooling revert to the solid state in its

19

new moulded shape. This process may be repeated indefinitely, but it is in fact limited by the ageing stability of the particular material. This means that after undergoing a certain number of processing operations, the original properties of the material are altered as a result of excess thermal stress. HDPE, LDPE, PP, PS, ABS, NYLON, PVC, PMMA, PBT, etc are thermoplastics. 2.1.3 Structure of Polymers Polymeric materials are called homogenous if all macroscopic parts of the material have the same properties, i.e. if any differences in properties due to the different types of macromolecules that may be present in the material can not be macroscopically observed. Homogenous does not mean that the polymer exists in only one phase, i.e. solid, rubber-elastic, or as a melt. The macromolecules of a thermoplastic polymer may take the form of highly ordered crystallites in either a solid or viscous (rubber-elastic) state, or in a glassy solidified state as disordered amorphous regions between the crystallites. In such a case, the material is defined as a two-phase homogenous polymeric material (Ehrenstein, G. W., 2001). Polymers are extremely long chained molecules that have repeating units (Fried, J. R., 1995). In many polymers, very few interactions exist between the chains except van der Waals forces. If van der Waals forces were the only forces holding the chains together, little cohesion would exist between chains. The resulting material would likely be a liquid or a gel, which is not the case. Polymers are generally solids and this is due to entanglements of the long molecules. To have stable entanglements that restrict the flow of the polymer chains polymers must have a critical molecular weight that is dependent on the flexibility of the backbone and the steric hindrance within the molecule. The importance of the entanglements on the cohesion can be seen in an illustration. If an assortment of different length strings are mixed into a ball the short pieces of string could be easily removed. The intermediate length pieces of string could be removed only with some effort but it would take a substantial amount of

20

effort to remove the longest strings. These entanglements influence the viscoelasticity, melt viscosity, and mechanical properties of the polymer (Fried, J. R., 1995). Polymers are significantly less crystalline than other crystalline materials, such as metals or low-molecular-weight compounds, and many are amorphous (Fried, J. R., 1995). Figure 2.1 is a representation of how polymer chains arrange in an amorphous (non-crystalline) polymer matrix. A good way to think of the amorphous polymer matrix is as a plate of cooked spaghetti. Some characteristics of amorphous polymers are that they have good mechanical properties and good dimensional stability. Amorphous polymer also shrinks consistently during cooling, as well as being inherently transparent.

Figure 2.1 Representation of Polymer Chains in an Amorphous Polymer Semi-crystalline polymers generally orient themselves in a lamellae structure (Fried, J. R., 1995). An example of lamellar structures is the gills of a fish or mushroom. For a polymer to crystallize, the conditions during the cooling of a polymer melt have to allow the polymer chains to arrange themselves. The crystal sheets may be as thin as 100 to 200Å; between these crystalline sheets, there are amorphous regions (Fried, J. R., 1995). It was found that as the lamellar structure’s thickness increased, the thermal conductivity of polyethylene did as well (Hansen D. & Bernier G. A., 1972). Figure 2.2 is an illustration of how polymer chains orient in a lamellae structure. This figure illustrates three possible ways the chains could

21

orient in two dimensions, which can be expanded into three dimensions. Semicrystalline polymers have anisotropic shrinkage, very good electrical properties, and are chemically resistance to some harsh environments.

Figure 2.2 2D Representation of Polymer Chains in a Semi-Crystalline Polymer Thermal conductivity has been experimentally shown to increase with increasing crystallinity or orientation of polymer chains. This can be extrapolated to show that amorphous polymer will be less conductive then semi-crystalline polymers. It was also experimentally shown that filled amorphous polymers are less thermally conductive then filled semi-crystalline polymers (Sundstrom D. W. & Lee Yu-Der, 1972). 2.1.4 Crystallinity During the solidification process, some polymers are able to form an internal structure consisting of regular shapes with surfaces in an even arrangement. This internal arrangement of macromolecules is called the crystalline structure. Whether polymers are able to crystallize or not depends on their molecular structure. In general, the unbranched macromolecules with no or only a very few regularly spaced

22

constituents crystallize more easily. In all cases, the crystalline structure covers only a part of the entire volume, while the rest of it is formed by the polymer in the amorphous state. Polymers that contain both crystalline and amorphous regions are called semi-crystalline polymers (Ehrenstein, G. W., 2001). Inter-molecular order refers to the geometric arrangements of adjacent polymer molecules in the solid mass. There are three types of inter-molecular order. •

Amorphous random coils are isotropic and entangled and their properties depend

primarily

on

molecular

flexibility,

polystyrene,

acrylic,

polyphenylene oxide, polysulphane, and polycarbonate are amorphous polymer. •

Crystalline polymers have their molecules arranged in a very regular repeating lattice structure, so precise that every section of the polymer molecule must recur at very specific points in the repeat structure. No polymer is completely crystalline. Highly crystalline polymers are HDPE, PP, Acetal, Thermoplastic Polymer, and Nylon.

•

Oriented polymers - orientation produces anisotropic properties, i.e., different in different direction.

2.1.5 Molecular Weight of the Polymers Polymers (as thermoplastics) are molecules that are chains of 500 or more carbon atoms. The distance between adjacent carbon atoms are being 1.5 x 10-8 cm. All the molecules may not contain same number of monomers. However, some control over the length of polymer chain is ensured during polymerization. The polymer is classified or specified by its average molecular weight. This also gives rise to molecular weight distribution of particular grade. Most monomers are gases. A short polymer chain of low molecular weight will be liquid. Large molecular chain gives solid material. Higher molecular weight results in increased strength and stiffness. Higher molecular weight also increased viscosity

23

of melt. Hence higher molecular weight melt requires higher power (pressure) to fill the mould. Higher the molecular weight are difficult to process. Ultra high molecular materials are not moldable. High molecular weight material is accompanied by a very high melt viscosity. To reduce the viscosity the processing temperature must be increased, but this results in degradation of polymer. Therefore while processing the thermal stability of the polymer dictates the processing temperature and residence time of melt in the plasticizing unit of the machine. Limitation of residence time dictates the speed of cooling to avoid the degradation of polymer. Many thermoplastics are deteriorated by prolonged exposure to oxygen and ultraviolet radiation in sunlight. Resistance to such deterioration is improved by higher molecular weight. It means few molecules with fewer terminal monomers (which are reactive) in the carbon chain. Longer molecules are less mobile. Even if high molecular weight degrades it results in medium molecular weight with acceptable properties instead of a low molecular weight. 2.2 Thermal Conductivity Background Polymers filled with metal powder have better electrical and thermal conduction properties and extend their uses in technological applications. This adds to the mechanical properties with these kinds of material, making them useful for specific requirements. In the literature there are several reports of the thermal behavior of polymers filled with different types of metal powder (Goyannes et al., 2001). The low thermal conductivity of polymers is a decisive factor affecting the use of these materials as thermal insulators. However, composites of a polymer matrix with inorganic fillers increase the coefficient of thermal conductivity. This condition is interesting in several applications and also from the point of view of optimizing heat input into the processing of thermoplastic and thermosetting polymers. On the other hand molded plastic packages made of composite materials are being used

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increasingly in electronic systems owing to their ease of manufacturing, light weight and customizable properties (Goyannes et al., 2001). Several investigation of polymer composites with dispersed fillers show the absence of percolation behavior of the thermal conductivity with increasing dispersed filler concentration (Fried, J. R., 1995). It should be pointed out that, in order to explain the steeper rise of thermal conductivity with increase of filler concentration then was predicted by the equations used. The reason for the percolation threshold absence is due to the fact that the thermal conductivities of dispersed filler and of the polymer matrix are comparable to each other, their ratio not being more than 103, whereas the filler electrical conductivity is 1010-1020 times larger than the polymer conductivity. The model predicts the percolation threshold appearance only if the ratio of the filler conductivity to polymer conductivity is larger than 105. In fact, the percolation theory is applied only to systems having conductive sites (or bonds) in a non-conductive medium (Mamunya et al., 2002). 2.2.1 Heat Transfer Phenomena Heat transfer is an important property of a material, so it should be incorporated into the design of new or existing applications. Heat transfer occurs through three mechanisms: radiation, convection, and conduction. Heat conduction is the main mechanism of heat transfer within solids and is the focus of this work. Heat conduction is calculated using Equation 2.1 (Lienhard J. H. IV & V, Prof., 2002).

hi = −k ij

∂T ∂xi

(2.1)

From this equation, one can see that heat transfer (hi) depends on the thermal conductivity (kij) and a temperature gradient. The thermal conductivity in Equation 2.1 is assumed to be constant; in reality, the thermal conductivity of a material varies with temperature. Thermal conductivity as defined by Equation 2.1 is a macroscopic

25

view with different methods of transporting the heat summed together to produce the material thermal conductivity. In solids two main methods of heat transport exist: electron transport and phonon transport. In pure metals, electron transport is the dominant transport mechanism. Both electron and phonon transport of the heat energy can be significant in metal alloys. In dielectric materials, like polymers, the dominant method of heat conduction is by phonons. Phonons are the quanta frequency of atomic vibrations. Phonons transfer heat energy through interactions with themselves and subatomic particles (Bigg D. M., 1986). A perfect crystal can be thought of as an array of atoms connected by springs. A graphical representation can be seen in Figure 2.3. The transfer of heat energy by phonons can be simplistically envisioned by exciting one or more atoms by twisting, pulling, or pushing. This energy would propagate through the array in a manner similar to phonons.

Figure 2.3 Two-Dimensional Array of Atom Connected by Springs

26

The effectiveness of heat transfer by phonons depends on the scattering of phonons as they propagate through the material (Bigg D. M., 1986). Again, looking at Figure 2.3 one can imagine how a different atom or a missing atom could alter the propagation of the vibration energy through the array. These are two very simple illustrations of causes of phonon scattering, though many more exist. The longer distance between scattering incidents results in greater thermal conductivity of the material. This concept is illustrated by the Debye model for heat conduction in dielectric solids (Hansen D. & Bernier G. A., 1972).

k = 1 .c.u.λ 3

(2.2)

In this model, ‘k’ is the thermal conductivity, ‘c’ is the volumetric heat capacity, ‘u’ is the velocity of sound in the material, and ‘ λ ’ is the mean free path of the phonons in the material. Typically, the speed of sound is approximately 5x105 cm/s and is material dependent, although it is relatively independent of temperature. The mean free path decreases with an increase in temperature. The mean free path is about 10 nm at room temperature and 104 nm near 20K. The heat capacity of a material can be calculated using the Debye model as found in Equation 2.3. In this equation, ‘c’ is the volumetric heat capacity, ‘kB’ is the Boltzmann’s constant, ‘No’ is Avogadro’s Number, ‘T’ is the absolute temperature in Kelvin, ‘ θ D’ is the Debye temperature in Kelvin, ‘ h ’ is Planck’s Constant, ‘ ω ' is the frequency of vibration, and ‘ ω D’ is the Debye frequency of vibration.

T c = 9.k B .N 0  θD

where x =

  

3 θD

T

x 4 .e x

∫ (e 0

x

− 1)

2

dx

(2.3)

h.ω D h.ω and θ D = kB k B .T

Heat conduction by phonons is the main conduction method in polymers and their composites. Polymers are dielectric materials so they generally follow the Debye

27

model. Many copper and Al2O3 fillers (including all the copper and Al2O3 fillers used in this project) are electrically conductive, but their thermal conductivity is essentially due to phonon transport. Thermal conductivity in copper/polymer and Al2O3/polymer composites is a bulk property, unlike electrical conductivity, which is path dependent. Previous experimental research review has shown thermal conductivity increases continuously over the whole concentration range, whereas electrical conductivity increases by as many as 10 orders of magnitude over a small range of concentration commonly known as the “percolation threshold” (Agari et al., 1991, Ni F. et al., 1997). At the percolation threshold, the fillers get close enough to conduct current with little resistance. Thermal conductivity does not show large sudden jump over the same range, demonstrating that closeness and touching are not significant in thermal conduction. This shows that thermal conductivity is a bulk property. Another way of looking at this phenomenon is through the scattering of phonons involved with touching fillers. One possible configuration is a line of spherical fillers surrounded by a vacuum touching each other along one side (see Figure 2.4a); another involves the same arrangement but with matrix surrounding around the spherical fillers (see Figure 2.4b). For this exercise, it is assumed that no heat transfer by radiation occurs; therefore, all heat transfer is through conduction. Looking at the first case (Figure 2.4a), phonons are scattered at each interface, and energy is not passed except at the point location where the spheres touch. In the second case, the same phonon scattering occurs at each interface; however, at each interface of spherical filler particles with other spherical fillers or the polymer matrix heat is also transferred. Due to the presence of the polymer matrix, the second configuration (Figure 2.4b) allows appreciably more heat to be transferred. If heat conduction is a path property, the first and second cases would conduct the same amount of heat. These two instances show that thermal conductivity is a bulk property and not a path property like electrical conductivity.

28

View of Spherical Fillers

View of Spherical Fillers Figure 2.4 Filler Configurations [(a) spherical filler in a vacuum, (b) spherical filler in polymer matrix]

2.3 Predictive Thermal Conductivity Models

For conductive resins, heat is transferred by two mechanisms, lattice vibrations (major contributor) and electron movement. Several important factors affect the thermal conductivity of a material. These include the thermal conductivity of its constituents (filler and matrix) and the crystallinity of the polymer (increasing crystallinity improves polymer thermal conductivity). The filler size, shape, concentration, dispersion (degree of mixing), orientation, and bonding between the filler and the matrix greatly affect the thermal conductivity. The orientation of the fillers is important since carbon-based fillers are often anisotropic. For example, the thermal conductivity across the basal planes of graphite is approximately 60 W/mK compared to 600 W/mK along the basal planes. Thermal conductivity is a bulk property and is analogous to viscosity, tensile modulus, and shear modulus. Equation 2.4 demonstrates the numerical relationship between the composite and the pure polymer (Bigg D. M., 1986). This equation uses the subscripts ‘c’ for the composite property and ‘p’ for the pure polymer property. This equation uses ‘k’ for thermal

29

conductivity, ‘η ’ for the viscosity, ‘E’ for the elastic modulus, and ‘G’ for the shear modulus. kc ηc E G = = c = c k p η p Ep Gp

(2.4)

2.3.1 Basic Thermal Conductivity Models

The most basic thermal-conductivity models start with the standard mixture rule (Equation 2.5) and inverse mixture rule (Equation 2.6). These equations use ‘K’ for the thermal conductivity of the composite, ‘n’ for the number of constituents in the composite, ‘i’ for the Index variable for the composite constituents, ‘ φ ’ for the volume fraction of constituents, and ‘ki’ for the thermal conductivity of the ith constituent. n

K = ∑ Qi .K i

(2.5)

i =1

n

K =∑ i =1

Qi Ki

(2.6)

The composite thermal conductivity in the filler direction is estimated by the rule of mixtures. The rule of mixtures is the weighted average of filler and matrix thermal conductivities. This model is typically used to predict the thermal conductivity of a unidirectional composite with continuous fibers. In the direction perpendicular to the fillers (through plane direction), the series model (inverse mixing rule) is used to estimate composite thermal conductivity of a unidirectional continuous fiber composite. In this project, spherical copper particles ( ≈ 50 µm), copper particles in the form of plates ( ≈ 45 µm), copper fibers ( ≈ 300-400 µm), and Al2O3 powder (4.5-8.5 µm) were used as the conductive filler (WEB_2, 2003, WEB_4, 2003, WEB_5, 2003,

30

WEB_9, 2003). Hence, this project studies conductive resins of discontinuous short fiber/particle composites. Another model similar to the two standard-mixing rule models is the geometric model shown in Equation 2.7. In Equation 2.7 ‘K’ refers to the thermal conductivity of the composite, ‘n’ to the number of constituents in the composite, ‘i’ to the index variable for the composite constituents, ‘ φ ’ to the volume fraction of constituents, and ‘k’ to the thermal conductivity of the constituents. n

K = ∑ K iφi

(2.7)

i =1

More simply, for a two component composite, the simplest alternatives would be the materials arranged in either parallel or series with respect to heat flow, which gives the upper or lower bounds of effective thermal conductivity (Tavman I. H., 1998). For the parallel conduction model: k c = φ .k f + (1 − φ ).k m

(2.8)

and for series conduction model:

1 φ 1−φ = + kc k f km

(2.9)

where, k c , k m and k f are thermal conductivities of composite, matrix and filler, respectively and φ is the volume fraction of filler.

In case of geometric mean model, the effective thermal conductivity of the composite is given by:

kc = k φf .km(1−φ )

(2.10)

31

2.3.2 Advanced Models

Many models have been proposed for filler matrix systems. The Maxwell Theoretical Model is the basis of many of these models. This model uses potential theory to obtain an exact solution for the conductivity of a system with spherical, non-interacting particles in a continuous matrix (Tavman I. H., 1997). This model is not applicable to many systems since it was designed for non-interacting spheres. Maxwell’s model can be found in Equation 2.11.

kc = km

k f + 2.k m + 2.φ .(k f − k m ) k f + 2.k m − φ .(k f − k m )

(2.11)

This model predicts well effective thermal conductivities at low filler concentrations; whereas for high filler concentrations, particles begin to touch each other and form conductive chains in the direction of heat flow, so that this model underestimates the value of effective thermal conductivities in this region. According to Tsao’s probabilistic model, Cheng and Vachon, assumed a parabolic distribution of the discontinuous phase. The constants of the parabolic distribution were evaluated as a function of the discontinuous phase volume fraction. The equivalent thermal conductivity of a unit cube of the mixture is derived in terms of the distribution function, and the thermal conductivity of the constituents (Tavman I. H., 1996). The effective thermal conductivity is given for the case k f > k m :

k m + B.(k f − k m ) + B / 2 C.(k f − k m ) 1 − B 1 1 = ln + kc km C.(k f − k m )(k m + B.(k f − k m )) k m + B.(k f − k m ) − B / 2 C.(k f − k m )

(2.12)

where,

B=

2 3.φ , C = −4. 3.φ 2

(2.13)

32

For two phase materials for which the thermal conductivity of the continuous phase is much smaller than the thermal conductivity of the discrete phase, k m 100, as long as φ k m km + B.(k f − km ) + B/ 2 C.(k f − km ) 1− B 1 1 = + ln kc C.(k f − km )(km + B.(k f − km )) km + B.(k f − km ) − B/ 2 C.(k f − km ) km

CHENG and VACHON

B=

3.φ 2

C = −4.

2 3.φ

0,707530312

AND IF k m 100, as long as

φ

k m km + B.(k f − km ) + B/ 2 C.(k f − km ) 1− B 1 1 = + ln kc C.(k f − km )(km + B.(k f − km )) km + B.(k f − km ) − B/ 2 C.(k f − km ) km

CHENG and VACHON

B=

3.φ 2

C = −4.

2 3.φ

0,972113683

AND IF k m 100, as long as

φ

k m km + B.(k f − km ) + B/ 2 C.(k f − km ) 1− B 1 1 = + ln kc C.(k f − km )(km + B.(k f − km )) km + B.(k f − km ) − B/ 2 C.(k f − km ) km

CHENG and VACHON

B=

3.φ 2

C = −4.

2 3.φ

1,306034191

AND IF k m 100, as long as

φ

k m km + B.(k f − km ) + B/ 2 C.(k f − km ) 1− B 1 1 = + ln kc C.(k f − km )(km + B.(k f − km )) km + B.(k f − km ) − B/ 2 C.(k f − km ) km

CHENG and VACHON

B=

3.φ 2

C = −4.

2 3.φ

1,419677335

AND IF k m 100, as long as

φ

k m km + B.(k f − km ) + B/ 2 C.(k f − km ) 1− B 1 1 = + ln kc C.(k f − km )(km + B.(k f − km )) km + B.(k f − km ) − B/ 2 C.(k f − km ) km

CHENG and VACHON

B=

3.φ 2

C = −4.

2 3.φ

1,79355947

AND IF k m 100, as long as

φ