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- Herausgeber: Wiley-VCH
- Kategorie: Fachliteratur
- Sprache: Englisch
A one-of-a-kind exploration of the fundamentals of functional polymer foams, including their fabrication and a variety of their most common applications
In Functional Polymer Foams: Green Fabrication Methods, Performance and Applications, distinguished researcher Dr. Hao-Yang Mi delivers an up-to-date and incisive discussion of the fundamentals of functional polymer foams, as well as their fabrication methods and a diverse set of applications. The author covers a variety of the material’s applications, including energy absorption, acoustic absorption, superhydrophobic materials, tissue engineering scaffolding, flexible sensors, and solar steam generation.
Readers will find comprehensive summaries of the mechanisms, fabrication methods, and relative performance of various polymer foams, as well as:
- A thorough introduction to functional polymer foams, including the fundamentals of SCF foaming
- Comprehensive explorations of energy absorbing polymer foams, including mechanisms of action, testing, and characterization
- Practical discussions of functional polymer foams used in thermal insulation, including their fabrication
- Complete treatments of acoustic absorption polymer foams and superhydrophobic foams, including advanced applications
Perfect for polymer chemists, materials scientists, and researchers working in the sensor industry, Functional Polymer Foams will also benefit sensor developers and electronics engineers with an interest in the fabrication methods and applications of functional polymer foams.
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Veröffentlichungsjahr: 2024
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Table of Contents
Cover
Table of Contents
Title Page
Copyright
Author Biography
Preface
Acknowledgment and Dedications
1 Introduction
1.1 Overview of Polymer Foams
1.2 Polymer Foaming Methods
1.3 Fundamentals of SCF Foaming
1.4 Influencing Factors of Cell Structure in the Foaming Process
1.5 Previlant Foaming Methods for Microcellular Foams
1.6 Advanced Applications of Functionalized Polymer Foams
References
2 Energy-Absorbing Polymer Foams
2.1 Overview of Energy-Absorbing Foam
2.2 Energy Absorption Mechanism of Polymer Foams
2.3 Testing and Characterization of Energy-Absorbing Foams
2.4 Preparation Methods of Energy-Absorbing Polymer Foam
2.5 Applications of Energy-Absorbing Polymer Foams
References
3 Thermal Insulation Polymer Foams
3.1 Overview of Thermal Insulation Foams
3.2 Fundamentals of Thermal Insulation
3.3 Performance and Characterization
3.4 Fabrication of Thermal Insulation Polymer Foams
3.5 Other Thermal Insulation Polymer Foams
References
4 Acoustic Absorption Polymer Foams
4.1 Overview of Sound Absorption and Noise Reduction Foams
4.2 Fundamentals of Acoustic Absorption of Polymer Foams
4.3 Characterization and Influencing Factors for Sound
4.4 Types of Acoustic Absorption Foams
4.5 Fabrication of Acoustic Absorption Polymer Foams
References
5 Superhydrophobic Polymer Foams
5.1 Overview of Superhydrophobic Polymer Foams
5.2 Theoretical Basis of Superhydrophobicity
5.3 Characterizations of Superhydrophobic Foams
5.4 Superhydrophobic Foam Preparation Technology
5.5 Advanced Application of Superhydrophobic Polymer Foams
References
6 Electromagnetic Shielding Polymer Foams
6.1 Electromagnetic Pollution and Electromagnetic Interference Shielding
6.2 Conventional EMI Shielding Materials and Conductive Polymer Foams
6.3 Characterization of EMI Shielding Polymer Foams
6.4 Preparation of EMI Shielding Polymer Foams
6.5 Advanced Research on EMI Shielding Porous Composites
References
7 Polymer Foams for Tissue Engineering Scaffolds
7.1 Overview of Tissue Engineering
7.2 Fundamentals of Tissue Engineering
7.3 Characterization of Tissue Engineering Scaffolds
7.4 Preparation of Tissue Engineering Scaffolds by Gas Foaming
7.5 Application of Scaffolds in Tissues
References
8 Flexible Sensors Based on Porous Polymer and Polymer Foams
8.1 Overview of Flexible Strain Sensors
8.2 Fundamentals of Piezoresistive Sensors
8.3 Performance and Characterization of Piezoresistive Sensors
8.4 Preparation of Flexible Sensors Based on Porous Foams
8.5 Applications of Flexible Piezoresistive Sensors
References
9 Triboelectric Nanogenerators Based on Polymer Foams
9.1 Overview of TENG
9.2 Fundamentals of TENG
9.3 Performance and Characterization of Polymer Foam-Based TENGs
9.4 Fabrication of Polymer Foams for TENGs
9.5 Advanced Application of TENG
References
10 Porous Polymers for Solar Steam Generation
10.1 Overview of SSG
10.2 Energy Conversion in SSG
10.3 Characterization of Solar Steam Generator
10.4 Structural Design for Enhancing SSG Performance
10.5 Opportunity and Challenge of Porous Polymer for SSG
References
Index
End User License Agreement
List of Tables
Chapter 1
Table 1.1 Critical points of common supercritical fluids.
Chapter 3
Table 3.1 Classification of polymer foams depends on the cell size and cell ...
Chapter 5
Table 5.1 Surface energy of common polymers.
List of Illustrations
Chapter 1
Figure 1.1 Phase diagram of fluid: T, triple point; C critical point.
Figure 1.2 Schematic illustration of the five stages in the SCF foaming proc...
Figure 1.3 Two nucleation types in a polymer–gas system (a) homogeneous nucl...
Figure 1.4 Relationship between the free energy barrier and cell radius in h...
Figure 1.5 Comparison of the free energy barrier between homogeneous nucleat...
Figure 1.6 The single bubble growth model in the foaming process.
Figure 1.7
In situ
visualization investigating the evolution of nucleated ce...
Figure 1.8 Cell merging of adjacent cells due to the cell wall rupture.
Figure 1.9 Cell opening mechanism during the scCO
2
foaming of PBS/PLA blends...
Figure 1.10 Two cell-opening mechanisms for the system composed of (a) a hig...
Figure 1.11 Effect of cooling temperature on the volume expansion and cell s...
Figure 1.12 Solubility of gas in most molten polymers: (a) solubility change...
Figure 1.13 Proposed model of glass–liquid transition for a polymer–CO
2
mixt...
Figure 1.14 Temperature-induced batch foaming process.
Figure 1.15 Pressure-induced batch foaming process.
Figure 1.16 Schematic representation of foam extrusion on a tandem line.
Figure 1.17 Schematic representation of foam injection molding process.
Chapter 2
Figure 2.1 Different cell morphologies in polymer foams.
Figure 2.2 Typical compression strain–stress curve of polymer foams showing ...
Figure 2.3 Typical compression strain–stress curve of viscoelastic foams....
Figure 2.4 Illustration of cubic cell model for an open-cell foam.
Figure 2.5 Illustration of cubic cell model for a closed-cell foam.
Figure 2.6 Illustration of Kelvin model for a closed-cell foam.
Figure 2.7 A finite element micromechanical model of closed-cell polymer foa...
Figure 2.8 Compressive force response of a conventional foam and an auxetic ...
Figure 2.9 An auxetic concave hexagon monocell design.
Figure 2.10 3D-FS and its unit cell structure: (a) 2D star structure and thi...
Figure 2.11 The deformation phases of the unit cell: (a) the initial phase o...
Figure 2.12 Typical cyclic compression curves of polymer foams with differen...
Figure 2.13 Diagram of reversible formation–dissociation bonds between polym...
Figure 2.14 SEM characterization of cell size and cell density.
Figure 2.15 μ-CT scans and reconstructed models of original and stretched fo...
Figure 2.16 Energy absorption efficiency diagram of foams with different den...
Figure 2.17 The layout of the drop-hammer impact test setup.
Figure 2.18 Quasi-static (0.04 s
−1
) cushioning properties of PU foams:...
Figure 2.19 (a) Schematic illustration of the fabricating procedure for the ...
Figure 2.20 (a) Schematic illustration of the foaming of TPU filament during...
Figure 2.21 (a) Optical and SEM images of AMs; (b) Semirigid PU foam blocks ...
Figure 2.22 (a) Schematic illustration for the process of (a) fabrication of...
Figure 2.23 (a) Process for the preparation of NPR foam; (b) Schematic drawi...
Figure 2.24 (a) Schematic illustration of wrinkly TPU foams fabrication stra...
Figure 2.25 Diagram of an explosion experimental platform.
Chapter 3
Figure 3.1 Illustration of a vesicle composed of three phases. Phase I repre...
Figure 3.2 (a) Schematic diagram of the effect of various factors on thermal...
Figure 3.3 Thermal conductivity diagrams of closed cell foam: (a) cubic mode...
Figure 3.4 Schematic diagram of the heat transfer model consisting entirely ...
Figure 3.5 Schematic diagram of the simulated thermal radiation process thro...
Figure 3.6 Schematic diagram of the propagation characteristics of thermal r...
Figure 3.7 GHP device diagram for (a) two samples and (b) one sample.
Figure 3.8 Trend of thermal conductivity with porosity for different cell si...
Figure 3.9 Variation of thermal conductivity of PMMA foam with pore size at ...
Figure 3.10 Variation of thermal conductivity of PMMA foam with pore size fo...
Figure 3.11 Sketch of bubble pore formation of foam containing solid nanofil...
Figure 3.12 SEM images of PMMA foam with nanoparticles of: (a) 20 nm, (b) 80...
Figure 3.13 (a) Schematic illustration of the bimodal structure formation me...
Figure 3.14 Schematic illustration of the mechanism for the multiple soaking...
Figure 3.15 On-the-fly reconstruction model of closed cell insulation: (a) S...
Figure 3.16 Schematic diagram of the fabrication process of the honeycomb PP...
Figure 3.17 Schematic illustration of the high-pressure injection foaming pr...
Figure 3.18 Illustration of the nanocellular structure formation mechanism, ...
Figure 3.19 Scheme of the experimental setup used for the one-step batch foa...
Figure 3.20 Schematics of PI foam synthesis, the corresponding reactions, an...
Figure 3.21 Four kinds of aerogel particles added to the GFAR; the morpholog...
Figure 3.22 The photo and SEM images of PI aerogels synthesized by freeze-dr...
Chapter 4
Figure 4.1 (a) Active and passive noise control mechanisms, frequency respon...
Figure 4.2 Schematic illustration of (a,b) the piezo-conductor hybrid foams ...
Figure 4.3 (a) Sound absorption coefficients of the PVDF/SWCNT piezo-conduct...
Figure 4.4 Schematic of the sound absorption circular tube model.
Figure 4.5 (a) SEM micrographs of PLA foams with different percentages of PE...
Figure 4.6 Schematic diagram of sound absorption measurement system.
Figure 4.7 Schematic drawing of the effect of tortuosity on sound transmissi...
Figure 4.8 Airflow resistance measurement equipment illustration: (1) piston...
Figure 4.9 (a) SEM images of PU foams with different open-cell content, and ...
Figure 4.10 Illustration for acoustic wedge subjected to an impulsive pressu...
Figure 4.11 The sound absorption mechanism of slip-structured wedge cavity m...
Figure 4.12 (a) Schematic cross-sectional illustration of a unit cell of the...
Figure 4.13 Acoustic propagation through composite foams with: (a) low airfl...
Figure 4.14 (a) Optical microscope images of pure flex foam and composite fo...
Figure 4.15 (a) Schematic of particulate leaching technique to fabricate por...
Figure 4.16 (a) Schematic diagram of fabrication steps of micro-patterned au...
Figure 4.17 (a) Open-cell structure formation diagram and tortuosity illustr...
Figure 4.18 (a) Schematic demonstration of cell formation and pore-opening m...
Figure 4.19 (a) Schematic of the cracking behavior during the mold open foam...
Figure 4.20 (a) Schematic of the sequestering recycled scCO
2
torsion extrusi...
Figure 4.21 (a) Diagram of the fabrication of PFGA and a photograph of the P...
Figure 4.22 (a) Fabrication procedure of MF/CNF–FT composite foam, (b) TEM i...
Figure 4.23 (a) synthesis route of the CAP scaffold, (b) SEM images of PP fi...
Chapter 5
Figure 5.1 (a) Microstructure of lotus leaf in different scales, and (b) Mic...
Figure 5.2 Schematic illustration of the modified foam surface microstructur...
Figure 5.3 Fabrication of silicon nanowires via top-down etching and its sup...
Figure 5.4 (a) Schematic illustration of the fabrication of the porous and h...
Figure 5.5 (a) Illustration of the preparation process of the bionic gradien...
Figure 5.6 Schematic illustration of the liquid contact states described by ...
Figure 5.7 Wetting performance of water droplets on the substrate surface.
Figure 5.8 Schematic illustration of the contact state of the Wenzel model....
Figure 5.9 Schematic illustration of the contact state of the Cassie–Baxter ...
Figure 5.10 Schematic model of a water bead in contact with circular structu...
Figure 5.11 Schematic illustration of liquid droplets in contact with (a) sm...
Figure 5.12 Effects of the concentrations of TiO
2
sol gel and PDMS solution ...
Figure 5.13 (a) Schematic illustration of the bidirectional freeze-drying fa...
Figure 5.14 Schematic diagram (a) and morphology, and (b) of the micro-nanos...
Figure 5.15 (a) Schematic diagram of hydrophobicity and lipophilicity of the...
Figure 5.16 (a) Schematic diagram of as-spun self-assembled 3D TEOS/PVA fibe...
Figure 5.17 (a) SEM images of the UHMWPE nanocomposite foam and the modified...
Figure 5.18 Illustration of the fabrication process of entirely superhydroph...
Figure 5.19 Schematic illustration of the fabrication process of skinless ce...
Figure 5.20 Schematic illustrations of the fabrication processes and propert...
Figure 5.21 Illustration for the fabrication of superhydrophobic nanohybrid ...
Figure 5.22 Schematic diagram of the preparation process of UHMWPE coated sp...
Figure 5.23 (a) SEM images of Fe
3
O
4
microspheres, water contact angle and sl...
Figure 5.24 Schematic illustration of the preparation of PLA aerogels and th...
Figure 5.25 The porous micro-nanostructured PTFE with superhydrophobicity an...
Chapter 6
Figure 6.1 Illustration of electromagnetic shielding mechanism.
Figure 6.2 The interaction between incident EM waves and porous structure....
Figure 6.3 (a) VNA pictures. (b) The measurement principle of VNA scattering...
Figure 6.4 (a) Illustration of the fabrication process of T/C/MG/Ag composit...
Figure 6.5 (a) Illustration of the electric and magnetic waves and their dir...
Figure 6.6 (a) Measured and calculated
SE
T
,
SE
A
, and
SE
R
of PLA/MXene multil...
Figure 6.7 (a) Schematic for the fabrication of epoxy/NCCFs composite foams;...
Figure 6.8 (a) illustration of the fabrication process of PVDF/PE composite ...
Figure 6.9 (a) Experimental flow chart of preparation of auxetic composite f...
Figure 6.10 (a) Preparation process for the oriented CNT/NFC foams; (b) TEM ...
Figure 6.11 (a) Schematic showing the fabrication process of segregated TPU/...
Figure 6.12 (a) Schematic of EM wave dissipation in the PMMA/MWCNTs nanocomp...
Figure 6.13 (a) The fabrication process of the MXene coated gradient composi...
Figure 6.14 (a) Illustration of the fabrication process of the layered foam ...
Figure 6.15 (a) Schematic illustrating the fabrication process of the BMF/Ag...
Figure 6.16 (a) Illustration of the fabrication process of the TPU-/AgNW-lay...
Chapter 7
Figure 7.1 Steps in a typical tissue engineering process: (a) a small number...
Figure 7.2 Factors to consider in the design of advanced tissue engineering ...
Figure 7.3 (a) Images of different nHA containing chitosan–agarose scaffolds...
Figure 7.4 (a) SEM images of TPU/PLA scaffolds with different TPU to PLA rat...
Figure 7.5 (a) SEM images of the PLA/PEG/NaCl blends before and after leachi...
Figure 7.6 (a) Illustration of the fabrication process of the interconnected...
Figure 7.7 (a) SEM images of TPU/HA composite scaffolds containing micro HA ...
Figure 7.8 (a) The architecture of the natural osteochondral unit and the HA...
Figure 7.9 (a) SEM images of the random fibrous scaffolds and aligned fibrou...
Figure 7.10 (a) Schematic of preparation of vascular grafts using assembled ...
Figure 7.11 (a) The fabrication process of triple-layered vascular grafts (T...
Figure 7.12 (a) SEM images of electrospun scaffolds: from i to v are the sca...
Figure 7.13 (a) Schematic diagram of the fabrication of the four-channel con...
Chapter 8
Figure 8.1 The fields where flexible electronic products are currently appli...
Figure 8.2 Schematic diagram of reducing resistivity by pressing through a c...
Figure 8.3 Schematic diagram of tunneling effect in CPCs.
Figure 8.4 Change of contact resistance based on interface contact resistanc...
Figure 8.5 (a) Δ
R
/
R
0
results of conductive polymer foam with increased compr...
Figure 8.6 Compression resistance changes of three graphene foams with diffe...
Figure 8.7 (a) Optical side-view images during compression of the microstruc...
Figure 8.8 The Schematic diagram of (a) GF and (b) sensitivity with the incr...
Figure 8.9 Diagram of response time and recovery time for a piezoresistive s...
Figure 8.10 The diagram shows the hysteresis for a piezoresistive strain sen...
Figure 8.11 The diagram of linearity for a piezoresistive strain sensor.
Figure 8.12 The diagrams show the: (a) operation stability [48], and (b) the...
Figure 8.13 (a) Schematic diagram illustrating the preparation process for s...
Figure 8.14 (a) Foaming principle of porous GNP/SR composite and (b) diagram...
Figure 8.15 Schematic of the preparation of a CNF/PEDOT:PSS composite foam, ...
Figure 8.16 The dip coating fabrication process of piezoresistive sensors th...
Figure 8.17 Schematic diagram showing the fabrication process of graphene fo...
Figure 8.18 The template sacrificial fabrication process of piezoresistive s...
Figure 8.19 Application of graphene-PDMS foam sensors in human gait monitori...
Figure 8.20 (a) Schematic illustration of the skin sensor for texture roughn...
Figure 8.21 The application of the CB-coated auxetic PU-foam-based pressure ...
Figure 8.22 (a) Schematic illustration of microstructural changes in CB/CPPC...
Chapter 9
Figure 9.1 Various new renewable energy sources have frequently been used so...
Figure 9.2 (a) Displacement current model of TENG in contact-separation mode...
Figure 9.3 Four basic operating modes of triboelectric nanogenerators: (a) v...
Figure 9.4 Working principle of triboelectric nanogenerator in vertical cont...
Figure 9.5 Working principle of the horizontal sliding mode TENG.
Figure 9.6 Working principle of TENG in single-electrode mode.
Figure 9.7 Working principle of triboelectric nanogenerator with the indepen...
Figure 9.8 The tribological power generation schematic diagram of TENGs base...
Figure 9.9 Schematic diagram of single-hole power generation process of cond...
Figure 9.10 The triboelectric sequence of common materials.
Figure 9.11 Schematic diagram illustrating the working principle of KPFM....
Figure 9.12 Standards and optimal values (FOMs) for evaluating the performan...
Figure 9.13 (a) Schematic illustration of the fabrication process of skinles...
Figure 9.14 (a) Fabrication process and (b) SEM images of the composite TPU ...
Figure 9.15 (a) Schematic diagram of the preparation process for silicon/CNF...
Figure 9.16 (a) Schematic illustration of the manufacturing process for the ...
Figure 9.17 (a) Schematic illustration of the TENG made of CNF/PEI aerogel f...
Figure 9.18 (a) The schematic preparation process of the polyimide (PI) aero...
Figure 9.19 The schematic diagram and electrical output performance of TENG ...
Figure 9.20 Roadmap for the development of TENGs from 2017 to 2027.
Figure 9.21 Applications of TENG micro and nano energy: (a) a coexistent pac...
Figure 9.22 TENG spherical structure for collecting multidirectional water w...
Figure 9.23 (a) Illustration of flexible TENG, (b) digital photographs of a ...
Figure 9.24 Applications of TENG-based high voltage power sources: (a) schem...
Chapter 10
Figure 10.1 Structural comparisons of conventional solar evaporation-based d...
Figure 10.2 The role of porous polymer absorber and substrate in the develop...
Figure 10.3 The energy balance of an SSG system includes solar input, conduc...
Figure 10.4 Schematic illustration of the solar steam generation test system...
Figure 10.5 (a) UV−vis absorption spectra of MB and MO solutions before evap...
Figure 10.6 Infrared images show the surface temperature change of different...
Figure 10.7 The ability of an SSG system to eliminate salt granules during o...
Figure 10.8 (a) Solar spectral irradiance, (b) the light absorption of carbo...
Figure 10.9 (a) Preparation process of PACMPs and the structure design of PA...
Figure 10.10 (a) The one-way fluidic photo-electro-thermal evaporator for al...
Figure 10.11 (a) Schematic illustrations of the fabrication process of PP no...
Figure 10.12 (a) Flow chart for the fabrication of Janus absorber and schema...
Guide
Cover
Table of Contents
Title Page
Copyright
Author Biography
Preface
Acknowledgment and Dedications
Begin Reading
Index
End User License Agreement
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Functional Polymer Foams
Green Fabrication Methods, Performance and Applications
Haoyang Mi
Author
Professor Haoyang MiZhengzhou UniversityZhengzhou 450003China
Cover Design: Wiley
Cover Image: © Polygraphus/Shutterstock
All books published by WILEY-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
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Print ISBN: 978-3-527-35295-1ePDF ISBN: 978-3-527-84458-6ePub ISBN: 978-3-527-84459-3oBook ISBN: 978-3-527-84460-9
Author Biography
Haoyang Mi received his BS and PhD degrees from South China University of Technology in 2010 and 2015, respectively. He served as a visiting scholar at the University of Wisconsin-Madison from 2011 to 2014. Subsequently, he worked as a postdoctoral researcher at the Wisconsin Institutes for Discovery, University of Wisconsin-Madison, from 2016 to 2018, and as a research fellow at Hong Kong Polytechnic University from 2018 to 2019. In 2019, he joined the National Engineering Research Center for Advanced Polymer Processing Technology, Zhengzhou University, as an associate professor.
Dr. Mi has amassed over 15 years of experience in the field of polymer composite foams, specializing in the fabrication and application of multifunctional porous polymer composites. His work has contributed to advancements in various domains, including energy absorption, self-cleaning surfaces, oil–water separation, thermal insulation, solar steam generation, electromagnetic interference shielding, tissue engineering scaffolds, flexible sensors, and energy harvesting devices. Notably, he has been an advocate for the environmentally friendly technique of supercritical carbon dioxide foaming in advanced applications.
Dr. Mi directs three grants funded by the National Natural Science Foundation of China and many regional and corporate projects within the realm of polymer processing and polymer foams. He also holds the role of associate editor for international journals such as Bio-design and Manufacturing and Scientific Reports. His academic contributions include over 100 SCI journal papers, where he served as either the first author or corresponding author. His work has received significant recognition with a total of over 8500 citations and an impressive h-index of 52 according to Google Scholar. Furthermore, he holds 20 invention patents, serving as the first inventor for 16 of them.
Preface
This book delves into the world of advanced polymer foams, which have evolved into functional materials and integral components within cutting-edge fields. Three-dimensional porous foams are at the forefront of advanced functional materials, driving innovations in diverse cutting-edge applications. The microstructure and material composition of these polymer foams play pivotal roles in defining their unique functional properties. Crafting polymer and polymer composite foams with precise and desirable structures poses a formidable challenge, yet is essential for unlocking their full potential across a range of applications. This book seeks to bridge the existing gap by introducing readers to the manifold applications of functional porous polymer foams, elucidating the underlying fundamentals that drive their functionality, and providing insights into their fabrication processes.
Furthermore, this book will mainly focus on the polymer foams that are prepared by physical foaming where the technique is applied, especially the foaming process using supercritical carbon dioxide (scCO2) as the foaming agent, since the scCO2 foaming is an environmentally friendly, cost-effective, and scalable technique that is promising for large-scale production of multifunctional polymer foams for advanced applications. The content of this book transcends the conventional, showcasing innovative applications of polymer foams in energy absorption, acoustic absorption, superhydrophobicity, electromagnetic interference shielding, tissue engineering scaffolds, flexible sensors, triboelectric nanogeneration, and solar steam generation.
Comprising 10 comprehensive chapters, this book embarks on a journey through the multifaceted realm of functional polymer foams and their advanced applications in recent years. Our journey begins in Chapter 1, where we establish the foundational principles of scCO2 foaming, its classifications, and its significance. We then venture into a spectrum of applications in subsequent chapters. Chapter 2 offers an in-depth examination of functional polymer foams in the realm of energy absorption. We uncover the fundamental theories, the impact of foam structure, methods for fabricating energy-absorbing foams, and applications of energy-absorbing foams. In Chapter 3, the focus shifts to thermal insulation, elucidating the mechanism behind foams’ insulation properties, their structural influence, fabrication techniques, and pertinent advanced research. Chapter 4 brings us to the world of acoustic absorption, where we unravel the intricacies of basic theories, influential factors, fabrication approaches, and advanced sound-absorbing foams reported in the literature. Chapter 5 introduces us to superhydrophobic polymer foams, indispensable in self-cleaning and oil absorption applications. We delve into superwetting theories, influential factors, fabrication methods, and the relevant literature and applications. In Chapter 6, we explore composite polymer foams designed for electromagnetic interference (EMI) shielding, deciphering the shielding mechanism, influential factors, and advanced EMI shielding foam fabrication methods. Biomedical foams for tissue engineering are introduced in Chapter 7, outlining the requirements for tissue engineering scaffolds, the primary biodegradable polymers, scaffold fabrication methods, and applications of the polymer-based scaffolds. Chapter 8 steers us toward composite polymer foams for flexible piezoresistive pressure sensors, unveiling their sensing mechanisms, factors affecting sensing properties, common materials, fabrication methods, and relevant literature. The journey continues in Chapter 9, as we investigate polymer foams tailored for triboelectric nanogenerators (TENG) in energy generation. We probe into TENG working mechanisms, factors influencing output performance, innovative fabrication methods, and advanced TENGs developed using polymer foams. Chapter 10 ushers us into the world of polymer foams for solar steam generation, shedding light on solar steam generation mechanisms, the impact of material and porous structure on performance, fabrication methods, and pertinent literature.
We believe that this book will serve as a bridge between environmentally friendly polymer foam fabrication methods and their limitless potential in advanced functional applications. Readers will not only expand their knowledge of foam development but also gain insights into enhancing their performance and extending the applicable areas of polymer foams to potential cutting-edge fields.
Welcome to a journey through the world of advanced polymer foams.
10 Aug 2024
Haoyang Mi
National Engineering ResearchCenter for Advanced PolymerProcessing TechnologyZhengzhou UniversityZhengzhou, China
Acknowledgment and Dedications
I would like to express my heartfelt gratitude to my advisors, Professor Xiang-Fang Peng, Professor Lih-Sheng Turng, Professor Han-Xiong Huang, Professor Shaoqin Gong, Professor Heng Li, and Professor Xiaoming Tao, for their unwavering support, invaluable guidance, and enduring patience throughout the journey of my research career. Your wisdom, expertise, and mentorship have been instrumental in shaping the content and direction of this work.
I am also indebted to my dedicated graduate students for their diligent efforts in collecting data, conducting experiments, and providing critical insights. Your contributions have been indispensable in ensuring the accuracy and depth of the information presented within these pages. Specifically, Chengzhi Yuan helped with Chapter 1, Qingli Tian helped with Chapter 2, Zemian Zuo helped with Chapter 3, Miaomiao Zhang helped with Chapter 4, Lin Wang and Xiao Li helped with Chapter 5, Jinghao Qian helped with Chapter 6, Yi Yang helped with Chapter 7, Xiaoyue Ren helped with Chapter 8, Ruixue Li helped with Chapter 9, and Shuangjie Sun helped with Chapter 10.
Furthermore, I extend my gratitude to all the colleagues, collaborators, and peers who have shared their knowledge and experiences, enriching the scope of this book. This endeavor would not have been possible without the support and encouragement of my family and friends. Your unwavering belief in my pursuits has been a constant source of inspiration.
Last but not least, I extend my heartfelt appreciation to the readers of this book. It is my hope that the knowledge and insights shared within the book will be of value to the scientific community and beyond.
Haoyang Mi
1Introduction
1.1 Overview of Polymer Foams
Foam materials, characterized by highly porous structures, are prevalent in both natural and synthetic forms [1]. Examples in nature include natural sponges with open cellular structures and wood, which humans have used for millennia. Polymer foams are defined as a kind of polymer material formed by a large number of microcellular cells containing a gas medium uniformly dispersed in the polymer matrix. Almost all polymers can be made into polymer foams. In the twentieth century, with the growth of the polymer industry, various types of polymer foam products emerged. The introduction of the gas phase makes polymer foams possess excellent performance in material weight reduction, heat insulation, sound absorption and noise reduction, shock absorption, etc. As a gas phase and solid phase mixed material, polymer foams possess special properties. It is widely used to prepare various packaging materials, automotive and aircraft parts, sports equipment, building materials, etc.
Traditional polymer foams are mainly prepared by direct mixing of molten polymer and gas. The foams usually have large cell diameters and low cell density, and the average cell size is generally larger than 100 μm. These large cells often become the starting point of cracks, which become one of the factors restricting the performance improvement of traditional polymer foams.
With the continuous development of human society and the enhancement of people’s pursuit of a higher quality of life, the performance of traditional polymer foams has gradually entered a bottleneck that cannot meet the new requirements in the fields of automobile, aircraft, aerospace, electronic devices, and medical devices. To address this problem, Professor N P Suh from MIT and colleagues first proposed the microcellular foaming technology and defined the cell size and density range. The average cell size and cell density in modern microcellular foam are in the range of 0.1–100 μm and within 109–1015 cells cm−3. The microsized cells in the foamed part could blunt the crack tip and block the crack propagation when the cell size is smaller than the crack size, which greatly improves the mechanical properties of the polymer foams compared with traditional large cell foams [2].
Microcellular foaming enhances mechanical properties compared to traditional foams, offering more than fivefold improvements in impact strength, toughness, and fatigue life, with density reductions ranging from 5% to 95% [3]. In addition, microcellular foaming leads to lower dielectric constants and thermal conductivities [4] expanding its range of applications. Owing to their low density and high toughness, robust shock strength, and fatigue resistance, these materials are suitable for packaging, as well as shock-absorbing buffers.
In applications requiring lightweight and high-strength soundproofing, such as aircraft and automobiles, microcellular foams are preferred due to their high specific strength and effective soundproofing. Their low dielectric constant, thermal conductivity, and excellent electromagnetic shielding/absorption properties, arising from their unique vesicular structure, make microcellular foams desirable for aerospace and electronics industries. Moreover, adjusting foaming process conditions, such as temperature and pressure, allows for control over the final material structure and properties.
Beyond these properties, microcellular foams with high open porosity find applications in various fields, including biological tissue scaffolds, filtration adsorption, catalyst carriers, and sustained drug release. Traditional chemical blowing agents, like chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs), have environmental limitations due to the emission of chlorinated pollutants. In contrast, microcellular foaming with supercritical CO2 as the foaming agent is environmentally friendly and offers excellent performance making it highly promising for various applications. To delve into the advanced applications of polymer foams, it is crucial to first grasp the fundamental principles of polymer foaming technology.
1.2 Polymer Foaming Methods
The basic process in polymer foaming contains the blending of a polymer matrix with a foaming agent, separating gas from the polymer, and fixing the polymer matrix to form a unique uniform cellular structure. According to the gas introduction methods, polymer foaming can be roughly divided into three categories, namely, mechanical foaming, physical foaming, and chemical foaming.
1.2.1 Mechanical Foaming
Mechanical foaming is a method in which air is sucked into the polymer matrix by intense mechanical agitation to form a uniform foam body. Air and emulsifier or surfactant can be added to shorten the molding cycle. It is not necessary to add a foaming agent, but it has the disadvantage that the bubbles generated by this process are easy to disappear, and it is difficult to meet the production requirements of microcellular foam.
1.2.2 Physical Foaming
Physical foaming refers to the process in which gas is directly injected into a polymer melt to create a cellular structure. There are typically three approaches utilized:
Inert gas is dissolved into a plastic melt or paste under pressure, then the pressure is released quickly, resulting in the creation of cells within the polymer matrix.
Low-boiling temperature liquids that are dissolved in the polymer melt and are then evaporated at elevated temperature to form gas bubbles in the polymer matrix;
Hollow microspheres or expandable microspheres are directly added to the polymer matrix via melt blending to form a porous foam structure.
In the process of physical foaming, the physical foaming agent undergoes only a change in state, such as from a saturated solution to liquid/gas, or a supercritical fluid (SCF) state to a gas, and the composition of the gas does not change. Physical foaming agents typically can be divided into two categories, namely, inorganic foaming agents and organic foaming agents. Inorganic foaming agents include CO2, N2, air, etc., while organic foaming agents include hydrocarbons, chlorinated hydrocarbons, fluorinated and chlorinated hydrocarbons, etc. However, due to potential environmental pollution and safety issues associated with the chemical foaming agent, such as flammability, explosiveness, and ozone depletion, most of them have been phased out or restricted for use, as people have become more aware of safety and environmental protection.
The physical foaming method using physical foaming agents has a relatively low cost, especially for CO2 and N2, which are inexpensive and nonpolluting. They are also flame retardant, making them highly valuable. However, it usually requires special molding machines and auxiliary equipment, and inert gases such as CO2 and N2 require high pressures to achieve foaming, making the process highly technically challenging and equipment demanding.
SCF foaming technology is a physical foaming method using SCF as the foaming agent. SCF refers to fluids in their supercritical state where both the temperature and pressure exceed their critical points (Figure 1.1) [6]. SCF is in the state between liquid and gas, with viscosities and diffusion coefficients close to gases and densities and solvation capabilities close to liquids. It has the advantages of both liquid and gas, such as good fluidity, large mass transfer coefficient, easy adjustment of fluid density, good diffusivity, and solubility [7]. The most commonly used SCFs are CO2, N2, water, ethane, etc. As listed in Table 1.1, the critical point of CO2 is the temperature above 31.1 °C and pressure above 7.38 MPa, which is relatively easy to reach compared with other gas/liquid [5]. In addition, attributing to the high solubility and high diffusion rate of supercritical CO2 (scCO2), physical foaming using scCO2 as the foaming agent could achieve a higher gas content, greater expansion ratio, and higher cell density. Considering the advantages of SCF foaming using scCO2 and scN2, it has been widely researched in recent years and employed in the production of various thermoplastic polymer products.
Table 1.1 Critical points of common supercritical fluids.
Source: Adapted from Cha [8].
Supercritical fluid
Critical temperature (°C)
Critical pressure (MPa)
scCO
2
31.1
7.38
ScN
2
−147.1
3.39
scH
2
O
374.2
21.83
ScC
2
H
6
32.3
4.82
Figure 1.1 Phase diagram of fluid: T, triple point; C critical point.
Source: Nalawade et al. [5]/with permission of Elsevier.
1.2.3 Chemical Foaming
The chemical foaming method relies on chemical reactions to generate gases to form cells in the polymer matrix. Gases are typically generated by the decomposition reaction via the heating of a chemical foaming agent added to a polymer matrix. At present, common chemical foaming agents mainly include sodium bicarbonate, ammonium nitrate, azo compounds, sulfonyl hydrazides, and nitroso compounds, etc. In the chemical foaming of materials like polyurethane, gas is generated by the cross-linking reaction between the isocyanate functional groups and water molecules. For chemical foaming, the temperature and gas content of the reaction is the key to determining the foaming quality, the reaction temperature at the time of gas generation should match the processing temperature of the polymer, the rate of gas generation needs to be controllable, and the gas content needs to be adequate.
The main advantage of the chemical foaming agent is that it does not require any modification of existing plastic processing equipment, and the process of injection molding/extrusion of polymer foams using a chemical foaming agent is essentially the same as the general injection molding/extrusion process. The heating, mixing, plasticization, and most of the foaming expansion of the plastics were done in an injection molding machine/extruder. Compared to physical foaming agents, the disadvantages of chemical foaming are mainly that they are more demanding for the reaction conditions, the foaming agents usually cost more, the potential environmental pollution, and the volatile organic compound (VOC) emission.
1.3 Fundamentals of SCF Foaming
In the polymer foaming process, a homogeneous system of polymer/gas solution is obtained by blending dissolution or saturation of a two-phase system consisting of polymer and gas, and then the equilibrium state of the system is broken by changing the external conditions (usually pressure and temperature) to trigger the nucleation of the cells due to the separation of the gas phase from the polymer phase owing to the transfer of the gas from the supercritical state to the gas state. Thus, the cells are the product of this phase separation process. The formed cells can, therefore, be seen as a way to counteract changes in external conditions [9], while the first half of the foaming process can be seen as a transition from a stable (homogeneous) state to a metastable or unstable (multiphase) state.
However, it is crucial to recognize that the cells formed within this metastable state lack stability due to the high molecular mobility inherent to the polymer matrix. Consequently, a reinforcement treatment, such as cooling, applied to the polymer-dense phase surrounding the cells is imperative. This treatment serves to immobilize the advantageous structure acquired during the foaming process, ultimately leading to the attainment of a stable foaming product. The latter half of the foaming process can thus be construed as a transformation of unstable foaming products into stable ones.
From the foregoing exposition, it becomes evident that the polymer foaming process is an intricate thermodynamic and kinetic undertaking. The fundamental process can be broadly delineated into five stages, as depicted in Figure 1.2[10].
1.3.1 Preparation of Homogeneous Solution
A homogenous solution needs to be constructed as the basis for the physical foaming process. During the formation of gas polymer homogeneous systems, the solubility of the gas is one of the most important parameters deciding the content of the foaming agent that can be introduced to the system, which in turn affects the final foam density and cell size. Determining the solubility of the foaming agent in the polymer is fundamental to the overall subsequent foaming process, so understanding the interaction between gases and the polymer melt and the influencing factors on solubility is critical.
Figure 1.2 Schematic illustration of the five stages in the SCF foaming process.
Source: Zhai et al. [6]/with permission of Taylor & Francis.
Binary systems of gases/polymers are usually described using Henry’s law, and the solubility of gases in polymers can be derived from Henry’s law [11]
where C is the gas solubility, KH is Henry’s constant, and P is the gas pressure.
Thus, increasing pressure is an effective mean to enhance gas solubility, and of course, a similar effect is obtained by lowering temperature. Henry’s law combined with van’t Hoff equation can explain the relationship between temperature and gas solubility [12].
where KH is Henry’s constant, K0 is pre-exponential factor, ΔHS is the heat of the solution, R is the gas constant and T is temperature.
Henry’s equation is based on ideal dilute solution solvent conditions without considering the interaction between gas and polymer melt, especially under high-pressure conditions, where the interaction between SCF and the polymer is more complicated. When a large amount of SCF is dissolved in the polymer, the plasticizing effect would affect the surface tension and rheological properties of the system.
The Flory Huggins equation [9] is a good guideline to determine the amount of gas used in a system, and it is expressed as:
The left-hand side of Eq. (1.3) ΔFm refers to the mixing of free energy after the mixing of polymer and gas. On the right-hand side of the equation, ng and ϕg refer to the moles and volume fraction of the gas, while np and Φp refer to the moles and volume fractions of the macromolecules, χ is a parameter to describe the action of macromolecules and gases (consists of both entropic and enthalpic components, with an average value of about 0.3 for an entropic component of most polymer/gas systems, and the enthalpic component is determined by the solubility parameter [10]), K is the Boltzmann constant, and T is the thermodynamic temperature. Vg in Eq. (1.4) represents the molar volume of the gas, R is the ideal gas constant, and δ is the solubility parameter.
In practice, solubility is greatly affected by the temperature, pressure, and crystallization behavior of polymers [13]. Normally, the solubility of liquid/gas in a polymer matrix would increase with the increase of pressure, while decrease as the increase of temperature [14].
1.3.2 Cell Nucleation
The basic theory of cell nucleation in polymer foaming originates from the classical nucleation theory established by Gibbs in the twentieth century. Colton and Suh [15] described the nucleation process during foaming. The formation of cells is actually a phase separation process initiated by the rapid pressure change or temperature change. The cell nucleation step is driven by the thermodynamic instability of gas/polymer homogeneous systems under high-temperature and high-pressure conditions. The physical foaming method caused a sharp decrease in the gas solubility in the polymer by a rapid pressure drop to form very high supersaturations. When the unstable high-energy state gas molecules cross the free energy barrier, high-energy state molecules would aggregate with each other through the activation transition, and then stable nuclei are formed on these aggregation sites.
In the phase separation process, the nucleation of gas cells needs to overcome the phase transition energy barrier (i.e., the phase transition activation energy), the dynamic source of the phase transition being the difference between the free energy of the system’s initial state and the end state. There are typically two types of cell nucleation mechanisms according to the difference in the initial state of the nucleation system, namely, homogeneous nucleation and heterogeneous nucleation (Figure 1.3).
1.3.2.1 Homogeneous Foam Nucleation
When the system is composed of a single homogeneous phase of gas/polymer mixture, it is assumed that there are no impurities within the system that can induce nucleation. At this point, each gas molecule is a theoretical nucleation point. In a thermodynamic system composed of a polymer melt and dissolved gas, the total Gibbs free energy of the system changes according to the law of thermodynamic energy conservation ΔG consists of three parts: the change in bulk free energy, the change in chemical potential, and the change in interfacial free energy, as shown in Eq. (1.5).
Figure 1.3 Two nucleation types in a polymer–gas system (a) homogeneous nucleation, and (b) heterogeneous nucleation.
where ΔP is the pressure difference between inside and outside bubbles, μL is the chemical potential of gas molecules in polymer melts, μG is the chemical potential of gas molecules in bubbles, ng is the number of gas molecules in the gas phase, Ab is the surface area of the bubble, and γLG is the gas/liquid interfacial tension.
The first term is the work done by the volume expansion of the gas inside the cells, the second term is the difference in chemical potentials before and after nucleation, and the third term is the work required to create the liquid gas interface. Since the chemical potential difference is zero for the nucleus in chemical thermal equilibrium [15], and the cell is assumed spherical for homogeneous nucleation, Eq. (1.5) can be written as:
where r is the cell radius and σ is the surface tension of the polymer matrix.
The function curve of the free energy barrier ΔG and the radius r of the cell nucleus during homogeneous nucleation can be obtained, and the maximum value of a ΔG corresponding to the radius size of Rc can be obtained from Figure 1.4.
Since the thermodynamic system tends to maintain a low-energy state, the cell nucleus tends to collapse when the radius is smaller than Rc, while it can spontaneously grow up when the radius is larger than Rc seeking to balance Eq. (1.7) to 0.
The formula for the critical radius Rc can be derived:
Substituting Eq. (1.8) into Eq. (1.7) yields a uniform nucleation free energy barrier of:
According to the classical nucleation theory, the formula of homogeneous cell nucleation rate can be derived [15]:
Figure 1.4 Relationship between the free energy barrier and cell radius in homogenous nucleation.
Source: Colton and Suh [15]/with permission of John Wiley & Sons.
where f0 is the frequency factor of gas molecules entering the cell nucleus, expressed in 1/s, C0 is the unit volume gas concentration, k is the Boltzmann constant, and T is the absolute temperature.
From Eqs. (1.8) and (1.9), the critical radius Rc and the critical free energy barrier Whom have a strong dependence on the surface tension of the melt and the pressure difference inside and outside of the cell nucleus. Therefore, increasing the supersaturation degree, decreasing the polymer melt surface tension, and increasing the internal and external pressure difference are approaches to reduce the critical radius and the critical independent energy barrier, which would enhance the cell nucleation rate and the number of cells that can be formed. In addition, increasing the depressurization rate, the gas concentration, and the system temperature would also increase the cell nucleation rate. However, some conditions are contradicted naturally such as the gas concentration would be reduced when elevating the temperature. Hence, saturation pressure is usually recognized as the most influential factor in the cell nucleation rate.
1.3.2.2 Heterogeneous Foam Nucleation
If there is a second phase in the system, such as foreign impurities or nucleating agents, the energy barrier for cell nucleation would be lower with the coexistence of the gas–liquid–solid three phases. The composite interface can serve as a starting point for cell nucleation in heterogeneous nucleation. The critical radius Rc and free energy barriers ΔG in heterogeneous nucleation were calculated similarly to homogeneous nucleation, as shown in Eq. (1.11).
where γsg is the surface tension of the solid–gas interface, γsl is the surface tension of the solid–liquid interface, Asg is the solid–gas interface surface area, and Alg is the liquid–gas interface surface area.
The first term in Eq. (1.11) is the work done by the volume expansion of the gas inside the cell, the second term is the energy required to replace the solid–liquid interface with the solid–gas interface, and the third term is the work required to create the liquid–gas interface that constitutes the cell. The triple-phase composite interfacial energy follows the relationship described by Young’s equation (1.12).
The shape of the heterogeneous nucleating cell nucleus takes a deficient spherical shape as shown in Figure 1.3(b). The free energy barriers ΔG can be expressed as Eq. (1.13):
The volume Vg of the cell nucleus is:
The surface area of the cell nucleus Alg is:
The contact surface radius is:
By substituting the above equations into Eq. (1.13), deriving it and making it equal to 0, the critical radius of the cell nucleus of heterogeneous nucleation can be obtained as:
where θ is the wetting angle, S(θ) is the out-of-phase factor and a function of the contact angle, and σbp is the interfacial tension of polymer–gas cells.
Colton and Suh [15] found that when the wetting angle is 20°, the free energy barrier between homogeneous nucleation and heterogeneous nucleation could be on the order of 10−3. The heterogeneous nucleation rates can be derived as follows.
where f1 is the frequency factor of heterogeneous nucleation, Nhet is the heterogeneous nucleation rate, and C1 is the concentration of heterogeneous nucleation points.
Therefore, the activation energy required for heterogeneous nucleation is much lower than that required for heterogeneous nucleation, as compared in Figure 1.5.
1.3.2.3 Mixed Nucleation Theory
Cell nucleation during the foaming process may take homogeneous and heterogeneous nucleation modes, but they are not mutually exclusive. Due to the relatively low activation energy required, heterogeneous nucleation is performed first in a system contains cell nucleation agent. Whereas homogeneous nucleation would also occur since the nucleation time is short, gas diffusion in the polymer melt system is hindered by the melt viscoelastic resistance during the heterogeneous nucleation, which would form a local supersaturation. Thus, heterogeneous nucleation followed by homogeneous nucleation would take place. The two-nucleation processes are not simply additive but rather interact with each other.
Figure 1.5 Comparison of the free energy barrier between homogeneous nucleation and heterogeneous nucleation.
Source: Colton and Suh [15]/with permission of John Wiley & Sons.
On the one hand, the first occurring heterogeneous nucleation consumes part of the gas, which makes the system supersaturated, and then the subsequent homogeneous nucleation rate drops and decreases in quantity [15]; On the other hand, the internal pressure was relatively high in the cells with smaller size. When physical contact is established among these cells, the cells tend to merge, which will result in a decrease in cell density and uneven cell size. The gas concentration after heterogeneous nucleation started for time t can be expressed by:
where t is the time calculated from the occurrence of the first homogeneous nucleation, and nb is the number of gas molecules in cell nuclei.
Substituting Eq. (1.21) into Eq. (1.10) yields the rate expression for homogeneous nucleation in heterogeneous systems:
Then, the total nucleation rate of the heterogeneous system is:
In the foaming system with a large amount of nucleation agents, the homogenous nucleation is usually ignored due to the high heterogenous nucleation rate. Moreover, besides the classical nucleation theory, new nucleation theories have been established on the basis of classical nucleation theory, such as interface nucleation theory [16], free volume theory [17], shear nucleation [18], and hot spot nucleation [19].
1.3.3 Cell Growth
Right after the cell nucleation, the nucleus with a radius over the critical value would start to grow into cells. The vesicular structure is mainly formed at this stage, and the size, geometric type, density, and distribution situation of the cells all have an important influence on the performance of the foam. To study the process of cell growth, the dynamics and resistance during cell growth need to be analyzed. Due to the complexity of polymer melts and the complex transfer process of mass, momentum, and heat between cells and melt components, it is difficult to accurately describe the growth process of each cell.
Cell growth kinetics can be studied in the way of theoretical simulations and experimental observations. Ramesh [20] summarized the theoretical and experimental analysis of the bubble growth model since 1917 using the prevalent single bubble growth model [21] and the cell model [22]. The single bubble growth model (Figure 1.6) describes the process of bubble length growth behavior of a single bubble in an infinite melt, but it has limitations in practical applications.
Figure 1.6 The single bubble growth model in the foaming process.
Source: Han and Yoo [21]/with permission of John Wiley & Sons.
Cell models are roughly divided into two categories: one is a closed cell model without a blowing agent and gas loss, and the other is an extrusion foaming modified cell model with a blowing agent and gas loss, which is suitable for different application scenarios – the former is suitable for injection molding, and the latter is more suitable for extrusion molding. Based on the bubble growth kinetics of the cell model, the following equation describing the isothermal growth of cells is obtained. To analyze the cell growth process, a set of control equations needs to be solved simultaneously: the continuity of the polymer–gas solution around the cell interface, the momentum equilibrium and gas diffusion equations, the constitutive equations describing the viscoelastic properties of the polymer–gas solution, and the mass conservation equation of the gas molecules [22, 23].
where C is the gas concentration, D is the diffusion rate, Pg is the internal pressure of cells, K, n is the viscoelastic characteristic parameter obtained from the power law equation , P∞ is the pressure at the outer boundary of polymer cells, Vr is the radial velocity component , is the shear rate, and γpb is the surface energy of the polymer–cell interface. Equation (1.24) is a continuity equation that assumes that the polymer is a non-Newtonian fluid, which can be described by the power law equation. Equation (1.25) is the gas diffusion process equation, mainly resulting from the gas concentration gradient around the gas cell. Equation (1.26) describes the gas consumption equation, mainly with the process of cell expansion at the gas melt interface. By modeling the cell growth process using numerical or finite element methods, it is possible to understand the effect of different parameters in the cell growth process and give guidance on the actual production of polymer foams.
Figure 1.7In situ visualization investigating the evolution of nucleated cells.
Source: Zhai et al. [24]/with permission of John Wiley & Sons.
The experimental observational study is another avenue to investigate the growth of gas cells. Using visualization techniques, it is possible to directly observe the evolution of the cellular morphology during foaming so as to verify the theoretical model and study the actual foaming process. Park et al. have made significant contributions in this field. They [24] used an in situ visualization technique to study the cell growth kinetics during PEO foaming, and the actual process of cell growth is shown in the following Figure 1.7. They also developed a visualization system for observing the plastic foaming process under extensional stress [25] and shear stress [26].
1.3.4 Cell Coalescence and Rupture
Cell coalescence is extremely easy to occur during the cell growth phase, when the cells grow into contact, the expansion tends to move toward the “weak” side, which is usually the larger cell, so coalescence and rupture usually occur successively. From the viewpoint of cell growth dynamics, cell rupture is due to the joint force between contacting cells to promote the growth of cells under the combined effect of internal and external pressure differences, surface tension, and normal stress. Thermodynamically, the surface area after cell merging is smaller, and the total free energy of the system is lower, so connecting cells tend to merge. The merging of cells can lead to uneven distribution of cells, reduced density, and poor mechanical properties of the foam. However, when the cell rupture behavior is accurately controlled, it is possible to increase the cell opening rate and alter the microstructure of the cells. Thus, the bull rupture mechanism deserves an in-depth analysis.
Figure 1.8 Cell merging of adjacent cells due to the cell wall rupture.
1.3.4.1 The Mechanism of Cell Rupture
During cell growth, the cell wall would be subject to a stretching force along the direction of cell growth, as illustrated in Figure 1.8. The cell wall would rupture if the stretching force is much greater than the surface tension of the melt [27]. During the foaming process, the cell size is not very uniform due to the curvature radius difference between the small and large cells and the merge of cells. The larger the size difference between adjacent cells, the greater the gas pressure difference inside them, and the more likely the small cells to merge into the large cells [28].
Cell coalescence reduces the number of cells and increases the cell size. Even if a large number of cell nuclei are formed during the nucleation stage, the cell coalescence during the cell growth process often causes a reduction in cell density. Therefore, to obtain foamed materials with high cell density and small size, it is necessary to strictly control the cell coalescence during cell growth. Cell coalescence can be suppressed by improving the melt strength of the matrix polymer and controlling process conditions. The melt strength of the polymer can be enhanced by introducing branching molecular chains, cross-linking, and blending with other polymers with higher melt strength. In terms of process control, within the temperature range at which the polymer can be foamed lowering the foaming temperature of the polymer, and increasing the cooling rate can all play a role in preventing cell coalescence [28, 29].
