Manipulating the percolation threshold of carbon nanotubes in
polymeric composites
Citation for published version (APA):
Hermant, M. C. (2009). Manipulating the percolation threshold of carbon nanotubes in polymeric composites. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR642602
DOI:
10.6100/IR642602
Document status and date: Published: 01/01/2009 Document Version:
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PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof.dr.ir. C.J. van Duijn, voor een
commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op woensdag 20 mei 2009 om 16.00 uur
door
Marie Claire Hermant
prof.dr. C.E. Koning
en
prof.dr.ir. L. Klumperman
Copromotor:
dr.ir. P.P.A.M. van der Schoot
A catalogue record is available from the Eindhoven University of Technology Library. ISBN: 978-90-386-1771-8
This research forms part of the research program of the Dutch Polymer Institute (DPI), DPI project number 529.
Printed by: Universiteitdrukkerij, Technische Universiteit Eindhoven Cover design by: Marie Claire Hermant and Paul Verspaget
To three amazing ladies,
1.1 Polymeric composites: From a macro- to nano-scale...2
1.2 Carbon nanotubes...4
1.3 Understanding and manipulating percolation network formation ...8
1.4 Objective and thesis outline ...11
1.5 References...12
! " ! " ! " ! " #### 2.1 Segregated networks and dynamic percolation ...16
2.2 Bimodal polymer molecular weight distributions: The role of low molecular weight material on percolation thresholds ...18
2.2.1 Characterization of PS and PMMA latexes ...19
2.2.2 CNT – polymer composite percolation thresholds...23
2.3 SDS as a plasticizer...27
2.4 Processing techniques and percolation thresholds ...29
2.4.1 Composites prepared with a high Tg latex ...30
2.4.2 Composites prepared with a low Tg latex ...33
2.5 Conclusions...35
2.6 Experimental ...37
$
3.1 Reducing non-contact resistivity...42
3.2 The role of PS/PEDOT:PSS in SWCNT polymeric composites...45
3.2.1 SWCNT exfoliations...45
3.2.2 Blends of PS and PEDOT:PSS ...49
3.2.3 SWCNT – PS/PEDOT:PSS composite conductivities...51
3.3 Co-operative behaviour of a multi-component system ...55
3.4 Substituting the conductive filler ...62
3.4.1 Analysis of SWCNT batches ...63
3.4.2 SWCNT dispersions ...64
3.4.3 Carbolex SWCNT – PS/PEDOT:PSS composite conductivities ...67
3.5 Conclusions...69 3.6 Experimental ...70 3.7 References...71 + + + + ,%,%,%,% 4.1 Semi-conducting and metallic nanoparticles...74
4.2 Quantum dots ...77
4.2.1 Preparation of QDs and QD-containing latexes...78
4.2.2 The influence of QDs on the percolation threshold of PS – SWCNT composites...82
4.3 Gold nanoparticles ...86
4.3.2 Block copolymer and AuNP synthesis...88
4.3.3 The influence of AuNPs on the percolation threshold of PS – SWCNT composites...97
4.4 Conclusions...100
4.5 Experimental ...100
4.5.1 Quantum dot synthesis and nanocomposite preparation ...100
4.5.2 Gold particle synthesis and nanocomposite preparation ...102
4.6 References...104 # # # # ---- ./ )./ )./ )./ ) '0'0'0'0 1111 2, 2, 2, 2, 5.1 Excluded volume and inverse emulsions ...108
5.2 Conventional polyHIPE systems including SWCNTs ...110
5.3 Conventional polyHIPE systems including SWCNTs and PEDOT:PSS ...119
5.4 Pickering-polyHIPE composite foams ...121
5.5 Conclusions...128 5.6 Experimental ...128 5.7 References...130 $ 3 $ 3 $ 3 $ 3 4444 %%%%%%%% 6.1 CNT – polymer composites as metal electrode replacement materials...134
6.2 SWCNT – polymer composites as semi-conducting materials ...138
6.3 Percolation network manipulation strategies: Is it feasible? ...140
5 5 5
5 ++++++++
Appendix A Analysis Instrumentation ...144
Appendix B Preparation of CNT dispersions...146
Appendix C Preparation and analysis of polymer – CNT composite films...147
Appendix D Segregated networks ...147
Appendix E Multi-component continuum connectedness percolation theory...148
Appendix F Effect of excluded volume on percolation ...149 ' ' ' ' #### 5 " ! 5 " ! 5 " ! 5 " ! #+#+#+#+ 6 6 6 6 #$#$#$#$
AFM Atomic force microscopy AuNP Gold nanoparticle
ATRP Atom transfer radical polymerization CMC Critical micelle concentration
CNT Carbon nanotube
CNF Carbon nanofiber
CTA Chain transfer agent
DRI Differential refractive index
DVB Divinylbenzene
EMI Electromagnetic interference ESD Electrostatic dissipation FET Field effect transistor
HIPE High internal phase emulsion HOMO Highest occupied molecular orbital HLB Hydrophilic-lipohilic balance
ITO Indium tin oxide
MWD Molecular weight distribution MIP Mercury intrusion porosimetry
NIR Near-infra red
NP Nanoparticle
PDI Polydispersity index
PDMAEMA Poly(2-(dimethylamino) ethyl methacrylate) PEDOT Poly(3,4-ethylenedioxythiophene)
PL Photoluminescence
PMA Poly(methyl acrylate) PMMA Poly(methyl methacrylate)
PS Polystyrene
PSS Poly(styrene sulfonate) PSD Particle size distribution
PU Polyurethane
PV Photovoltaic cell
QD Quantum dot
SEC Size exclusion chromatography SDS Sodium dodecyl sulfate
SPR Surface plasmon resonance SWCNT Single-walled carbon nanotube TEM Transmission electron microscopy TGA Thermogravimetric analysis TFT Thin film transistor
UV-Vis Ultra-violet visible light Tg Glass transition temperature
ϕp Percolation threshold
∆ Connectedness criterion Conductivity
t Critical exponent
ξ Electron tunneling distance
D Carbon nanotube diameter
" ! ! 5 4 4 4 4 ! 4 4 5 7 8
In a response to the ever increasing demands placed by society on everyday materials, material scientists have turned to the field of composite materials.1 A composite material is defined as a
multi-component system in which components, of quite a different nature, are blended such that at least one component constitutes the major continuous phase, the matrix, and the others are discrete minor components, the fillers. The ability to improve one material’s properties by simply adding an appropriate second material is well known.2 For material scientists this ability, added to the fact that
in most cases the original properties of both components remain unchanged, makes composite materials good candidates to perform various tasks simultaneously. In the last few years, the interest in polymeric composites has grown exponentially. Advances in the production and availability of nano-structured materials like layered silicates (nano-clays), silica nanoparticles, quantum dots, fullerenes, carbon black and carbon nanotubes have sparked an increase in industries’ interest in the field of polymeric nanocomposites.3 This definition refers to a composite system in which the matrix is a polymer or polymer blend, and the filler has at least one dimension below 100 nm. The transition from macro- through micro-, and finally to nano-scales for filler particles introduces increased surface area/volume ratios, as well as length/diameter ratios (also called the aspect ratio). These dimensional changes can alter certain properties of the nano-filler itself, as well as the behaviour of the filler within the matrix.
For systems in which the polymer and filler have an affinity for each other (strong adsorption), increases in the surface area/volume ratio of the filler can result in large changes in the volume fraction of polymer that is henceforth considered to be “bound” to the filler interface.4 Many changes in physical phenomena related to the polymer chain dynamics, for example the glass transition temperature (Tg) and degrees and rates of polymer crystallization, could be drastically
altered due to this bound layer. This has been referred to as the “nano-effect”.5 Cases where Tg
shifts are observed, the effect is somewhat similar to that reported for thin polymer films.6 The most important result of an increased bound-polymer layer is the consequent changes in mechanical properties of the final composite.7
Transport properties, such as electrical and thermal conduction, of polymer composites are less sensitive to the filler surface area/volume ratio, but are highly affected by the aspect ratio of the filler.8 This can be explained by the role of the aspect ratio in the formation of filler networks called
the percolation of the filler within a matrix. Percolation describes the long range (infinite) connectivity of filler clusters.9 A simplistic scheme of the formation of such a filler percolation
%
network within a matrix is illustrated in Scheme 1.1. At low filler concentrations, the filler particles are isolated from each other by the matrix. At a certain loading, the first “connected-path” is created and the filler is said to percolate the composite. This critical loading is defined as the percolation
threshold (ϕp). If the filler is conductive, and the polymeric matrix is insulating (inert), below this
value the conductivity will be low. The formation of connected paths leads to a steep rise in the composite conductivity. At higher filler concentrations, the path with fewest connections (lowest path resistivity) is created and the conductivity levels off (a level which is often called the ultimate
conductivity or saturation point). 10
Filler loading C on du ct iv ity (lo g sc al e) ϕp Filler loading C on du ct iv ity (lo g sc al e) ϕp
Scheme 1.1: Network formation or percolation of a conductive filler within an insulating matrix. Models of the complex percolation network formation of fillers in matrixes have been under constant development.11 Beginning from statistical percolation models that describe equilibrated systems,12 more complex models based on chemical thermodynamic principles have been
proposed,13 each model having its own limitations. Most of these models use filler particles of
spherical geometry and use the definition of true volume for the filler material. Using rather the excluded volume of the filler particles, the formation of a percolated filler network of hard-core rods was predicted to occur at much lower loadings than that required for spherically shaped fillers.14 Systems based on non-equilibrated or kinetic percolation describe even lower percolation
thresholds for both rod15 and spherically shaped fillers.16 The attraction of composite systems with
such ultra-low percolation thresholds lies in the fact that composites can be prepared cheaply, with minimal alteration of the intrinsic matrix material properties, but most importantly, with high optical transparency. Highly conductive, transparent materials are sought after in various fields within organic electronics.17
Reducing the dimensions of certain inorganic semi-conductor materials and metals can also have a dramatic effect on their physical properties.18 Nano-confinement (to below 20 nm) of such materials
+
The effect of this quantization is illustrated in Scheme 1.2.19
E1 E2 E11E22E33 E111E333
E1 E2 E11E22E33 E111E333
Scheme 1.2: The idealized density of states (y axis) for one band of a semi-conductor material with decreasing dimensions (changing from 3D to “0D” from left to right). Ex represents the distinct
energy levels (possible energetic transitions).
Examples of such semi-conductor nanoparticles are quantum dots, which show characteristic optical properties directly linked to the size of the particles. The application of quantized matter in catalytic and photovoltaic systems has attracted much interest in the last years.
1.2
Carbon nanotubes
CNTs, the third allotrope of carbon, were discovered in 1991.20 Since this time their exceptional
properties, such as extremely high tensile strengths (150 – 180 GPa)21 and modulus (640 GPa –
1 TPa)22, “ballistic” thermal conduction23 and exceptional electrical conductivity,24 have been unveiled. These properties are directly attributed to their unique structure. CNTs are long cylinders of covalently bonded carbon atoms, which look somewhat like graphene sheets that have been rolled-up into seamless tubes. The tube ends may be capped by hemi-fullerenes. Single-walled carbon nanotubes (SWCNTs) comprise only one such cylinder; whilst multi-walled carbon nanotubes (MWCNTs) contain a set of coaxial cylinders, see Figure 1.1.
#
Creating a seamless cylinder from a graphene sheet can be done in three manners, each resulting in a tube that is said to have a distinct chirality or helicity (see Figure 1.2). The chirality of a specific SWCNT (which could be a single shell of a MWCNT as well) is described by the chiral or “roll-up” vector C . This vector is defined as the summation of multiples of the unit vector cells h a1and a2
given in Equation 1.1. 2 1 m a a n Ch = ⋅ + ⋅ (1.1) RULE: If value of (n – m ) is:
1. 0, then the tube is metallic (armchair), with
Eg = 0 eV.
2. a multiple of 3, then the tube is semi-metallic with Eg≅ meV (zigzag).
3. not a multiple of 3, then the tube is semiconducting with Eg = 0.5-1 eV (chiral).
Figure 1.2: Rolling up a graphene sheet to produce zigzag, armchair and chiral SWCNTs, each with different band gap energies (Eg).
CNTs can be synthesized through three techniques: arc discharge, laser ablation and chemical vapour deposition. Each technique results in CNTs of varying lengths, chirality and quality (damaged walls and amount of impurities), which often results in large discrepancies in performance. Differences in quality between two suppliers, and even more importantly, between batches from one supplier, have often been found.25 Developing viable methods to sort metallic and
semi-conducting CNTs is under rigorous investigation due to the fact that the composite conductivity is lowered with an increasing fraction of semi-conducting CNTs.26,27
Besides the inherent inhomogeneity in as-produced CNTs, their macroscopic arrangement also complicates their use in composite production. SWCNTs bundle due to strong intrinsic van der Waals attraction (~0.5 eV/nm)28 whereas MWCNTs are often highly entangled. In order to exploit
the high aspect ratios of CNTs, it is of vital importance that they are brought into a debundled or
exfoliated state. Debundling can be achieved by introducing functionalities on the CNT surface,29
absorbing surfactants30 or polymers31 onto the surfaces and by mechanically pulling the CNTs apart
$
lead to complete debundling of the CNTs. The use of ultrasound in conjunction with aqueous surfactant solutions33 and organic solvents34 is a widely studied technique to achieve optimal CNT exfoliation. Analytical techniques such as atomic force microscopy (AFM), cryo-transmission electron microscopy (Cryo-TEM), ultra violet-visible-near infra red light (UV-Vis-NIR) absorption spectroscopy, NIR photoluminescence (PL) and Raman spectroscopy are commonly used to evaluate the degree of CNT exfoliation. Most of these techniques are time-consuming and require expensive equipment. The use of UV-Vis spectroscopy for off-line monitoring of the dispersion process of CNTs in aqueous surfactant solutions has been shown to be a reliable and easy-to-use technique.35 Bundled CNTs do not show any absorbance in the UV-Vis range (if the concentration is kept low enough to circumvent errors due to scattering),36 therefore, using the Lambert-Beer law, the degree of CNT individualization can be determined by examining the absorbance at a specific wavelength. This is illustrated in Figure 1.3 (i), where the UV-Vis absorption spectra at different time intervals are shown, and in Figure 1.3 (ii), where the final exfoliation profile is given in terms of the absorbance at a set wavelength (nm) versus the energy added via sonication.
300 600 900 0.1 0.2 0.3 0.4 0.5 0.6 0 50 100 150 200 0.1 0.2 0.3 0.4 ii U V - V is a bs or ba nc e (-) Wavelength (nm)
Increasing sonication time/energy
i U V a bs or ba nc e at 3 00 n m (-) Energy Input (kJ)
Figure 1.3: Results from UV-Vis spectroscopy analysis showing (i) the absorbance spectra and (ii) the exfoliation profile for a 0.1 wt% SWCNT exfoliation in a 0.2 wt% SDS solution.*
Introducing individualized CNTs into polymers can be done in various ways, each resulting in differing degrees of CNT dispersion within the matrix.37 The first basic methods investigated, such
,
as melt- and solution blending, resulted in poor CNT dispersion. Several new techniques attempt to improve the CNT dispersion quality through various strategies including coagulation,38 organic
templating39-42 and polymer-grafting. One straightforward technique that does not require the functionalization of the CNT surface, or the use of large amounts of organic solvents, is latex
technology.42 It is a type of organic templating method that uses latex particles (polymer particles suspended in an aqueous environment) as a means to restrict the distribution of suspended carbon nanotubes to small interstitial spaces rather than allowing a homogeneous distribution. This concept is illustrated in Scheme 1.3. A latex is added to an aqueous dispersion of individual, surfactant-stabilized CNTs resulting in a two component colloidal mixture. The continuous water phase is removed (lyophilization) and the resultant powder is processed to give the final composite.
Colloidal mixture
Lyophilization
Processing
Latex particle Water Polymer CNT
Colloidal mixture
Lyophilization
Processing
Latex particle Water Polymer CNT
Scheme 1.3: Three basic steps comprising latex technology.
This technique has been shown to work for a wide range of polymers (available in a latex form) and carbon nanotube types. Multi-component colloidal systems are complex in the respect that the phase behaviour is very sensitive to the concentration and dimensions of the components.43,44
Depletion-induced attraction forces, arising through the presence of the spherically shaped latex particles, can induce aggregation of the rod-like CNTs during the colloidal mixture stage shown on the left in Scheme 1.3.45,46 This is an important fact to take into account when the distribution of one of the components will dramatically change the performance of the final system.
Keeping in mind the sensitivity of the formation of the percolated CNT network on the dispersion of the CNTs within the polymer matrix, it is obvious that each composite production technique leads to vastly different percolation thresholds. Whilst many methods are very good at producing highly dispersed composites, this can act counteractively when it is realized that the CNTs do actually have to touch (or approach within a limit of a few nanometers) to allow for satisfactory electron conduction.
9
The formation of connected clusters, where connected clusters are those that physically touch, can be called geometrical percolation. The excluded volume argument applied to geometrical percolation theory has generated a formalism in describing the percolation of long, hard, non-penetrating rods. It was found that the percolation threshold of such rods is proportional to the inverse of the aspect ratio, ϕp∝ D/L, where D is the rod diameter and L the rod length.14 For typical
CNTs, this generates values for ϕp in the order of 0.1 wt%, which is often reflected in experiments.
Ultra-low percolation values are often described in literature especially for thermoset composites such as epoxy-based systems.47 In these cases, the formation of the network is governed by kinetics
rather than being statistically driven. Shear-induced CNT aggregation can alter the network formation greatly, and in these systems most percolation theories fail. In extreme cases, two percolation thresholds have even been observed, each one attributed to a different network formation mechanism.48 Geometrical percolation, based on an excluded volume argument, has been refined to a more accurate continuum connectedness percolation theory, which introduces the phenomenological variable ∆ or the connectedness criterion (see Scheme 1.4).49 The introduction of
such a connectedness criterion arises from the fact that electrical percolation does not require a direct connection between clusters, but rather a proximity that enables electron tunnelling.
L D L D − ∆ = 1 1 2 1 D L D p ϕ (1.2)
Scheme 1.4: Definition of the connectedness criterion and its contribution to the percolation threshold as defined for mono-disperse hard-core rods.
Conductive filler networks that follow classical geometrical percolation theory (where filler bonding occurs) obey a universal conductivity-loading relationship just above the percolation threshold. This relationship is described by Equation 1.3.9
t p)
(ϕ ϕ
σ ∝ − (1.3)
Here and are the systems conductivity and filler loading, respectively. The universal value for the critical exponent (t) is 2 for 3D systems. Many conductive filler networks, including CNT
:
networks in polymeric composites, exhibit a non-universal value for t. This has been linked to the fact that the electrical percolation networks in these systems are not geometrical and tunneling between nearest-neighbours governs the conduction mechanism.49
From Equation 1.2 it is evident that parameters like the length of the CNT largely influence the percolation threshold calculated from theory. However, in reality any CNT sample will have a distribution of lengths, which experimentally has shown to influence the percolation threshold.15,50
Other phenomena, including the CNT tortuosity and the bending of tubes, have been shown to influence the theoretically determined percolation threshold as well.51,52 Choosing an appropriate connectedness criterion will also play an important role on the final ϕp value. In order for a
connected network to be electrically conducting, the inter-tube distance is of great importance, i.e., the value of ∆ is not arbitrary. This distance should be in the order of the electron tunneling length, ξ (∆ - D ≈ ξ).53 The electron tunnelling length could be influenced by the material that is present
within the inter-tube junction, further implying that changing the matrix material could alter the percolation threshold. Substituting the matrix material within the inter-tube junctions with a conductive material has shown to result in changes of the composite percolation threshold.54 Hence it is possible to see that manipulating variables such as L and ∆, as well as utilizing systems that are
kinetically (thermoset epoxy-based systems) rather than statistically driven, can lead to composites with lower percolation thresholds. However, increasing the CNT length leads to manifold problems with processing (CNT entanglement leads to high viscosities requiring extreme processing temperatures). Moreover, composites prepared by thermosetting techniques often have limited application due to poor material properties of conventionally-used thermoset materials. Controlling the inter-tube distance is also practically inefficient. For this reason researchers have turned to alternative strategies in the quest for lower percolation thresholds.
The processing history of CNT composites plays a significant role in determining the final transport properties. Each composite production technique induces different network formations and resultant percolation thresholds can vary widely.55 From the initial methods to produce conductive CNT –
polymer composites, more elaborate methods have been reported that attempt to manipulate or
nano-structure the formation of percolated CNT networks such that the resulting percolation
threshold is reduced. Two approaches towards nano-structuring polymeric nanocomposites include: external-in (top-down) and internal-out (bottom-up) approaches. The first approach is described by a direct patterning of nanoparticle dispersions, and the second by the mesophase assembly of nanoparticles.56 Techniques included in these two approaches are given below.
2
1. Mechanical deformation 2. Magnetic and/or electric fields
3. Electrostatic and/or hydrogen bonding 4. Multi-component interfacial segregation
a. Immiscible blends b. Pickering emulsions
1. Nanoparticle-macromolecular systems 2. Structured block copolymer nanoparticles 3. Nanoparticle-nanoparticle systems
4. Liquid crystals (lyotropic and thermotropic)
Within the field of CNT – polymer nanocomposites, direct patterning techniques have often been used to induce CNT alignment. These techniques use an external stimulus to achieve a desired conformation on a nano-scale. Post- and pre-fabrication techniques, based on patterning through mechanical deformation (1), include mechanical stretching,57 spin-casting,58 wet spinning, melt-fiber spinning59 and electrospinning.60 These techniques have been used to prepare highly
aligned CNT networks. It has however been shown that alignment can also negatively effect the percolation threshold.59,61 Theoretically it has been shown that partial alignment results in minimal resistivity.62 The use of magnetic63 and electric64,65 fields (2) has shown to influence composite conductivities and/or percolation thresholds, but these techniques are limited to certain processing techniques and composite dimensions. In order to pattern more complex composite shapes (or to prepare larger composites), techniques that are driven by thermodynamics are more suitable. When two immiscible phases, being either two polymers or liquids, are brought into contact, three regions result, the two bulk phases and an interface. The chemical discontinuities can result in a segregation of a filler within either one of these regions (4). This process is thermodynamically driven. The use of interfaces between immiscible polymeric phases (4a) for the structural organization of fillers such as clay,66-69 carbon black,70-72 carbon fibers73,74 and carbon nanotubes75-77 has been reported.
The presence of the fillers has been shown to lead to changes in blend morphology and phase-separation kinetics, and in the case of conductive fillers, changes in percolation threshold have been observed and simulated.78 Systems in which the two phases are liquids are often called Pickering emulsions (4b).
Nano-structuring through mesophase assembly is a more complex route based on the phase behaviour of hard-body particles.79 This phase behaviour can be manipulated by altering the interface of the nanoparticles (through functionalization and/or grafting),80 changing the interaction
between the nanoparticle and the matrix (using block polymers instead of homopolymers)81 (somewhat similar to segregation in immiscible blends) and introducing a second nanoparticle to induce new depletion-induced atttraction forces.82 The use of liquid crystals to create ordered CNT phases has also been explored.83 These techniques are all thermodynamically driven.
1.4
Objective and thesis outline
Methods to manipulate the percolation threshold of CNTs in polymeric composites can be divided into two different length scale categories. For the first, microscopic network formation can be manipulated by using direct patterning or mesophase assembly techniques. Second, at a nanoscale, the value of ϕp can be changed by physically decreasing the inter-tube distance and/or increasing
the electron tunnelling distance. In this thesis, various techniques to reduce the experimental percolation threshold by manipulating either the composites micro- or nano-structure are presented. The main aim was to prepare conductive CNT – polymer composites with CNT loadings as low as possible. In all but one chapter, the latex-based composite processing technique is used so as to allow for easy comparison between various manipulation strategies.
Chapter 2 examines the importance of processing conditions on the final network structure. The concept of dynamic percolation is introduced and investigated with respect to the influence of plasticizers and processing techniques on the final percolation threshold.
Chapter 3 deals with the use of a conductive polymeric component as a means to lower the inter-tube junction resistivity, i.e., to change the electron tunnelling distance.
Chapter 4 addresses the affect that a second nano-filler has on the network formation of SWCNTs. The ability of this nano-filler to act as an inter-tube junction bridge and/or its ability to induce depletion-induced interactions is assessed.
Chapter 5 examines a slightly different composite-preparation technique based on an inverse emulsion. High internal phase emulsions (HIPEs) are used as organic templates for the preparation of conductive foams (polyHIPEs). A further extension of this concept, namely the use of Pickering-polyHIPEs as scaffolds, is also investigated.
Chapter 6 gives an overview of the technical applicability of the various manipulation strategies in the electronics industry.
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2.1
Segregated networks and dynamic percolation
Techniques that are based on the use of organic templates to incorporate carbon nanotubes (CNTs) into polymers generally exploit the well established concept of segregated networks.1,2 The theory
behind segregated networks is built on a system consisting of a mixture of two spherical particles with very different diameters. In such a system, reductions in the critical loading for percolation of the smaller of the particles, the filler, are theorized when compared to completely randomized networks. The basic idea of segregated networks is illustrated in Scheme 2.1.
Rp Rs Res is ta nc e [filler] Random Segregated - Matrix particles - Interstitial space - Filler particles (A) (B) Rp Rs Res is ta nc e [filler] Random Segregated - Matrix particles - Interstitial space - Filler particles (A) (B)
Scheme 2.1: Illustration of the concept of segregated networks, and their effect on the theoretically calculated percolation threshold. The dimensions Rp and Rs represent the diameters of the
filler and matrix particles, respectively.
This illustration shows how the filler particles are initially confined to the interstitial space created between the matrix particles (Scheme 2.1 (A)). When the system is processed (in the molten state), the high viscosity of the matrix reduces any possible filler diffusion, causing a restricted network structure (Scheme 2.1 (B)). For cases where Rp/Rs 0.05, as illustrated in Scheme 2.1, a 50%
reduction of the percolation threshold is predicted.* In many of the first reported applications, the
filler particles were mechanically mixed with the matrix particles and the matrix particles were subsequently sintered.3
This dry-mixing process is not favourable when dealing with high aspect ratio fillers like CNTs, due to the fact that CNTs are often aggregated and poorly separated through mechanical shear. In order to overcome this experimental hurdle, it would be best if the two constituents could first be dispersed in a liquid in which both are in-soluble, and subsequently the two dispersions could be mixed to create a two component colloidal mixture. The hydrophobicity of both CNTs and most
,
polymers, used as composite matrix material implies that water is a very good candidate as a carrier solvent for the mixing process.
The use of water-borne polymer dispersions and carbon black as a conductive filler was shown to give segregated filler networks, and, as predicted, reduced percolation thresholds.4,5 A natural progression, to applying this colloidal system to CNT – polymer composite production, followed when well exfoliated aqueous dispersions of CNTs could be achieved.6,7 The preparation of
composites utilizing polymer colloids and aqueous CNT dispersions is often referred to as latex
technology (described in Chapter 1). The transformation of the colloidal mixture to the final
composite film can be visualized in the micrographs taken using transmission electron microscopy (TEM) and scanning electron microscopy (SEM), which is shown in Figure 2.1.
Figure 2.1: Micrographs taken using (i) TEM and (ii) SEM of the process of latex technology showing the colloidal mixture and final composite, respectively.
The presence of both the CNTs and latex particles in the initial mixed colloid system is evident in Figure 2.1 (i). The viscosity of the matrix is likely to prevent much rearrangement of the CNTs in the final melt. In all these systems, it was envisaged that the initial state (CNT configuration) within the mixed colloid system would be maintained throughout all the subsequent processing steps. It has however been reported that the nature of the processing steps has a large influence on the final percolation network structure for both spherical4 and rod-like fillers.8,9 These effects have been linked to the mobility of the matrix in the inter-particle spaces,4,10 the mobility of the filler particles (network equilibration)9 and the increased interaction between adjacent tubes.8 This led to the
definition of dynamic percolation, where the network structure is not kinetically-frozen, but rather seeking an equilibrated state.
i ii
9
In this chapter various techniques to stimulate network equilibration are investigated. In Section 2.2 and 2.3, systems in which the melt viscosity is reduced by plasticising the matrix with low molecular weight polymer (2.2) and surfactants (2.3) are addressed. It was seen that lowering the matrix viscosity, stimulating network equilibration, can influence the percolation threshold to a large degree.
In Section 2.4, various processing techniques are compared with reference to the percolation network structures. Manipulating the colloidal interactions between the spherical latex particles and rod-like CNTs through the altered water removal rate was observed to change the aggregation and CNT network formation.
In this chapter, the percolation thresholds determined experimentally are fitted with the percolation relation (determined from statistical percolation theory) that predicts the dependence of the composite conductivity on the filler concentration. This is given in Equation 2.1.
p 0 (ϕ ϕ ) ,for ϕ ϕ ϕ
σ
σ = ⋅ − t − p <<
p (2.1)
Here and 0 are the composite conductivity and a fitting parameter respectively, and p are the
composite loading and percolation threshold, respectively and t is the critical exponent. The linear fitting of the experimental data was performed by plotting log( ) versus log( – p) and adjusting
the two fitting parameters p and t. The critical exponent is dependent on the dimensionality of the
system, and for a 3D system this value is given as 2, as predicted by a continuum percolation model.11
2.2
Bimodal polymer molecular weight distributions: The role of low
molecular weight material on percolation thresholds
Conventional polymers used in latex technology-based CNT – polymer nanocomposite preparation are generally of a very high molecular weight (normally produced by conventional free radical emulsion polymerization). These high molecular weight chains have very low mobility in the melt, resulting in minimal CNT diffusion.12 In order to adjust the melt viscosity, higher amounts of low molecular weight material can be introduced. This can lower the matrix Tg13 and hence, the melt
viscosity at a fixed processing temperature.14 Chain transfer agents (CTAs), like mercaptans, are
commonly used in emulsion polymerization processes to adjust or to tailor the molecular weight distribution (MWD) of the polymer products formed.15 The hydrophobic CTA is transported from
:
molecular weight control takes place. Each polymer particle is a replica of the next, i.e., the MWD profile is identical for all particles.
In this section a range of polystyrene (PS) and poly(methyl methacrylate) (PMMA) latexes were prepared with unique MWDs. These latexes were then used to prepare CNT – polymer composites by means of a latex-based route.16 Composites prepared with both single-walled carbon nanotubes
(SWCNTs) and multi-walled carbon nanotubes (MWCNTs) were investigated and the percolation thresholds for all four matrix – CNT combinations were determined. All CNT dispersions were prepared using sodium dodecyl sulfate (SDS) as surfactant.
2.2.1 Characterization of PS and PMMA latexes
Four different MWD profiles were targeted for PS latexes: (i) a monomodal distribution with a high molecular weight peak, representing a standard emulsion polymerization product (latex 1), (ii) a bimodal MWD with a large high molecular weight peak and smaller low molecular weight peak (latex 2), (iii) a bimodal MWD with comparable high and low molecular weight peaks (latex 3) and (iv) a very broad monomodal distribution with a high molecular weight peak (latex 4).
Two PMMA latexes were targeted: (i) a monomodal distribution with a high molecular weight peak, representing a standard emulsion polymerization product (latex 5), and (ii) a bimodal MWD with comparable high and low molecular weight peaks (latex 6).
Based on the results obtained by Mendoza et al.,17 the standard emulsion recipe was modified to meet the requirements (with respect to MWDs) as stated above. Details concerning these recipe modifications, as well as the experimental conditions, are given in Section 2.6.
2 0 30 60 90 120 150 180 0.0 0.2 0.4 0.6 0.8 1.0 0 15 30 45 60 75 90 Latex 1 Latex 2 Latex 3 Latex 4 ii C on ve rs io n (-) Time (min) i Latex 5 Latex 6 Time (min)
Figure 2.2: The conversion time histories of the emulsion polymerizations performed with varying CTA concentrations and different feeding strategies of (i) styrene emulsion with ( ) no CTA, ( ) 2.25 g CTA added as an instantaneous shot, ( ) 4.50 g CTA added as an instantaneous shot and ( ) 4.50 g CTA added stepwise and (ii) MMA emulsions with ( ) no CTA and ( ) 4.50 g CTA added as an
instantaneous shot.
Conventional chain transfer agents do not alter the rate of polymerization, and hence the four PS and two PMMA polymerizations display a comparable conversion-time history (within each monomer type), despite various feeding strategies applied and different amounts of CTA added. The addition of CTA as well as the feeding strategy proved to have a negligible effect on the final particle size of the latex product (see Table 2.1). This indicates that the microscopic properties of the resulting latexes are comparable (within each monomer type) and that any difference measured in the electrical and/or thermal properties of the composites is due to differences on the molecular level.
It is predicted that an important property of these latexes, in their application in the preparation of polymer – CNT composites, is the ratio between the amounts of high and low molecular weight polymer present in the particles. The integrated area of the signal generated by the differential refractive index (DRI) detector is a good approximation for the amount of polymer in the sample with the corresponding molecular weight. The ratio between the amount of high and low molecular weight polymer, defined as the peak ratio ( ), can consequently be determined by integrating the corresponding high and low MWD as obtained from size exclusion chromatography (SEC), see Equation 2.2. low high A A = β (2.2)
Here Ahigh and Alow are the integrated area under the high and low molecular weight peak,
respectively. The high molecular weight peak, present in every single MWD, is due to the conventional free radical emulsion polymerization occurring prior to the CTA addition. The low molecular weight peak or tail is formed during the later stages of the polymerization, when the CTA is present in the particles. The resulting latexes were characterized to determine their average particle sizes (dp), particle size distributions (PSDs) and MWDs, and these results are summarized
in Table 2.1. The high molecular weight distribution is referred to as the first peak, and the low molecular weight distribution (when observed) is referred to as the second peak. The polydispersity index (PDI) describes the broadness of the polymer molecular weight distribution (defined as the weight average molecular weight, Mw, divided by the number average molecular weight, Mn).
Table 2.1: Morphological and molecular properties of the prepared latexes: PSD, MWD, polydispersity index (PDI) and average particle size (dp).
PSD MWD
dp Polya 1st Peak 2nd Peak PDI
Peak Ratio ( )d
Latex
number Polymer
[10-9 m] [-] [103 g.mol-1] [103 g.mol-1] [-] Target Exp
1 100 0.02 1370 - 8.8 6.1 2b 91 0.02 >1500 22 2.8 > 1 2.5 3 94 0.02 1426 17 5.6 ~ 1 0.8 4c PS 95 0.03 1355 n/a 12.5 - 1.7 5 85.7 0.02 1450 - 5.5 5.3 6b PMMA 93.6 0.01 >1500 80 2.5 ~ 1 0.5
a This term describes the correlation between the measured PSD and the fitted Gaussian function (a value of higher than 0.1 describes a polydisperse PSD). b The molecular weight of the main peak
was outside the range of the calibration curve. c Due to the stepwise addition of the CTA to the reaction mixture, a long low molecular weight tail is obtained, rather than an individual peak .d The
peak ratio ( ) is defined by Equation 2.2 (see also Figures 2.2 and 2.3).
As mentioned before, the aim was to prepare latexes with different β values: (a) β ≈∞ (latexes 1 and 5), (b)β >1 (latex 2), (c) β ≈1 (latexes 3 and 6) and (d) a latex with a very broad MWD (latex 4). The obtained MWDs, as determined via SEC analysis, and the integrated regions are presented in Figures 2.3 (i) – (iv), 2.4 (i) and (ii), and in Table 2.1.
Figure 2.3: The MWDs of the polymer dispersions used for the preparation of PS – CNT composites: (i) latex 1, (ii) latex 2, (iii) latex 3, and (iv) latex 4. The areas used for the calculation of the peak
ratio are indicated: high molecular weight (gray) and low molecular weight (black).
Figure 2.4: The MWDs of the polymer dispersions used for the preparation of PMMA – CNT composites: (i) latex 5 and (ii) latex 6. The areas used for the calculation of the peak ratio are
indicated: high molecular weight (gray) and low molecular weight (black).
DSC was performed on the six latexes prepared in order to determine the extent to which latexes 2 to 4 and 6 have been plasticized with respect to latexes 1 and 5, respectively, by the presence of high amounts of low molecular weight material. The results given in Figure 2.5 confirm that the higher the relative amount of low molecular weight material (lower beta value), the lower the Tg.13
This implies that at a fixed processing temperature (180 oC) for the PS latexes, the viscosity of
latexes 3 and 4 will be the lowest, and that of latex 1 will be the highest, whilst for the PMMA latexes the viscosity of latex 6 will be lower than that of latex 5.14 There is a linear relationship between the latex beta values and Tg till a certain limit of β. The concentration of low molecular
%
weight material that is required to obtain a certain Tg depression appears to have an upper threshold.
Over a certain level, an increased concentration does not afford any observable decrease in Tg.
60 80 100 120 1 2 3 4 80 100 120 140 160 4 5 6 7 112.54 oC 122.63.oC ii 79.26 oC 86.26 oC 101.89 oC Latex 1 Latex 2 Latex 3 Latex 4 H ea t f lo w (W /g ) Temperature (oC) 109.22 oC i H ea t f lo w (W /g ) Latex 5 Latex 6 Temperature (oC)
Figure 2.5: The glass transition temperature for (i) latexes 1 to 4 and (ii) latexes 5 and 6, as determined by DSC (traces have been offset for clarity).
2.2.2 CNT – polymer composite percolation thresholds
Compression moulded CNT – polymer nanocomposite films were prepared using latexes 1 to 6 and a range of weight fractions of SDS-stabilized MWCNTs and SWCNTs. Their electrical conductivities were measured and the percolation thresholds were determined for the six latexes. The preparation of the films and the measurement method is described in Section 2.6. The results of the conductivity measurements are given in Figure 2.6 and summarized in Table 2.2. The percolation thresholds were determined by fitting the percolation law (Equation 2.1) to the experimental data.
Table 2.2: Percolation thresholds, ultimate conductivities and t values for all composites prepared.
CNT type MWCNT SWCNT
Polymer PS PMMA PS PMMA
Latex number 1 2 3 4 5 6 1 4 5 6 Ultimate conductivity, o (S/m) 20 80 50 50 20 50 20 20 100 30 Percolation threshold (wt%) 1.1 0.92 0.66 0.54 0.61 0.39 0.7 0.5 0.32 0.25 Critical exponent, t 1.99 1.5 1.95 2.29 2.4 1.8 1.9 2.02 3.4 3.1
+ 0.0 0.3 0.6 0.9 1.2 1.5 -18 -15 -12 -9 -6 -3 0 3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 -18 -15 -12 -9 -6 -3 0 3 0.0 0.4 0.8 1.2 1.6 2.0 -18 -15 -12 -9 -6 -3 0 3 0.0 0.3 0.6 0.9 1.2 1.5 1.8-18 -15 -12 -9 -6 -3 0 3 Latex 5 Latex 6 iv iii ii MWCNT loading (wt%) Latex 1 Latex 2 Latex 3 Latex 4 L og c on du ct iv ity (S /m ) MWCNT loading (wt%) i Latex 1 Latex 4 L og c on du ct iv ity (S /m ) SWCNT loading (wt%) Latex 5 Latex 6 SWCNT loading (wt%)
Figure 2.6: 4-point DC conductivity profile for composites made using latexes 1 to 6 and SDS-stabilized CNTs: (i) PS matrix with MWCNTs, (ii) PMMA matrix with MWCNTs, (iii) PS matrix
with SWCNTs and (iv) PMMA matrix with SWCNTs.
The detection limit of the equipment used is such that the conductivities in the low CNT loading range (below the percolation threshold) was simply taken as the intrinsic conductivity of PS and PMMA.
A decreasing trend of the percolation threshold value (ϕp) from latex 1 to 4 (Figure 2.6 (i) and
Table2.2) can be seen for PS – MWCNT composites (beyond experimental error, which is estimated to be approx. 10 % of the determined percolation threshold).9 All the maximum
achievable conductivities are within the same range. To ascertain any possible influence of the CTA itself on the composite conductivity, one control film was prepared by adding an amount (similar to that present in latex 4) of CTA to a normal composite formulation (using latex 1). No significant change in the composite conductivity was observed. The change in ϕp is most apparent when
#
comparing latexes 1 and 2 versus 3 and 4. The threshold value is around 1.1 wt% for latex 1, 0.92 wt% for latex 2, and 0.66 wt% for latex 3 and 0.54 wt% for latex 4. A similar downward shift in conductivity when introducing low molecular weight material was observed for PS – SWCNT composites. For this matrix, percolation thresholds were constructed for composites prepared with latexes 1 and 4. The ϕp value is decreased from 0.7 wt% to 0.5 wt% (see Figure 2.6 (iii) and Table
2.2). The results obtained for PMMA composites are similar to the PS-based composites discussed above. From Figure 2.6 (ii) (and Table 2.2) it can be seen that, with the introduction of low molecular weight material, the ϕp value changes from 0.61 to 0.39 wt% for composites prepared
with MWCNTs. For SWCNTs, Figure 2.6 (iv) (and Table 2.2), a shift from 0.32 to 0.25 wt% is observed.
An interesting point of attention is the ultimate conductivity that is achieved for the four different composite systems. There is a negligible difference in composite conductivity above the percolation thresholds when comparing both matrix materials, as well as when comparing MWCNT- and SWCNT-based nanocomposites. It has been proposed that composites with well dispersed CNTs will show ultimate conductivities that are influenced mainly by polymer tunnelling barriers.18 For this reason, the maximum achievable conductivity is linked to the matrix electrical properties. The polarizability of the matrix material within inter-tube junctions could influence the electron tunnelling efficiency across such a junction.19 The dielectric constant ( ) of PMMA is slightly higher than that of PS, viz. 3.5 as compared to 2.5. In the approximation given by Kyrylyuk et al.,19 the contribution of to changes in the electron tunnelling distance is small in comparison to possible changes due to the difference in CNT conductivity. Therefore, it seems reasonable to measure only negligible differences between PS and PMMA.
The presence of residual surfactant on the CNT surface could also play an important role on the inter-tube distance. Changes in the matrix glass transition temperatures have been observed in CNT – polymer composites, and this effect was attributed to adsorption of polymer onto the CNT interface (i.e. displacement of the SDS layer, predominantly by the low molar mass part of the MWD).20 Within this study a similar investigation into possible shifts in the Tg of the matrix
materials was performed with DSC. Up-shifts of approximately 5 oC were observed for SWCNT – PS systems, but similar shifts were not observed when MWCNTs were used. This can be attributed to a difference in surface area between MWCNTs and SWCNTs. In the latter case, a significant part of the matrix material can be immobilized. No clear trends could be observed when comparing PS and PMMA systems, which we believe is likely due to the non-comparable interactions of the two matrix materials with the CNT interfaces. The influence of such differences in interactions on
$
changes of the matrix Tg have previously been reported for other nanoparticles.21,22 It is therefore
difficult to determine the exact extent of SDS displacement within the reported systems.
Here it has been shown, as in previous studies,9,20 that the percolation threshold and maximum conductivity depend on the rheological characteristics of the matrix material. The possibility for CNT rearrangement towards a new equilibrium conformation can reduce the mean inter-tube junction distance ( ) and concomitantly result in an increase in the resulting conductivity and a decrease in tunnelling barriers (lower t values).23 The driving-force of these conformation changes will be a density (concentration) gradient (thermodynamic driving force) on a nano-scale. An unchanged ultimate conductivity however indicates that the inter-particle tunnelling boundaries are similar in all cases. If this is the case, the lowering in percolation threshold will simply be due to the creation of contacts at lower loadings (due to partial aggregation of the CNTs). These two scenarios are illustrated schematically in Scheme 2.2.
– D Narrow MWD No. of contacts increases C on du ct iv ity CNT loading (wt%) decreases Broad MWD – D – D Narrow MWD No. of contacts increases C on du ct iv ity CNT loading (wt%) decreases Broad MWD
Scheme 2.2: Theoretical shifts of the percolation threshold due to changes in the inter-tube distance ( ), or in the number of junctions of CNTs in two polymeric latexes with different MWDs. The absence of strong evidence that SDS displacement has taken place (with the introduction of low molecular weight material) indicates that it is very likely that the inter-particle distance will be similar in all CNT – polymer composites investigated in this work. This substantiates the lack of a distinct increase in the ultimate conductivity. One other important factor is the relaxation time (equilibration time) of the system as a function of the carbon nanotube loading. For composites with CNT loadings above the percolation threshold, a high degree of CNT entanglement is expected. This will increase the overall viscosity of the system. Changes in the melt viscosity might not induce a large change in the inter-particle distance above the percolation threshold due to a longer timescale for network equilibration. This argument was also reported in a recent paper on the influence of processing conditions on MWCNT – polymer composite conductivity.9
,
Ultimately the quality of the carbon nanotube will play the most influential role on the conductive nature of the final composite. A substantial increase in ultimate conductivity (beyond the percolation threshold) with a decrease in melt-viscosity was reported for systems in which the inherent SWCNT conductivity was much lower than those used in the composites presented here.20 The higher inherent conductivity of the CNTs used in the present study could explain the absence of a large increase in ultimate conductivity with decreased melt viscosity. Differences in ultimate conductivities have been shown to vary widely across different CNT batches, thus making comparisons between different systems inaccurate.24
Results presented here on the influence of the matrix viscosity on the percolation threshold, collected using one batch of SWCNT and one batch of MWCNTs, are not only in agreement with the report on the decrease in percolation threshold with an increase in the processing temperature, as shown in earlier work from our group,9† but also agree with results reported for carbon black filled polymers.10 The influence that the matrix viscosity has on the formation of equilibrated CNT network structures cannot be overlooked. It has been shown that a reduced matrix viscosity achieved by higher processing temperatures or introducing low molar mass material leads to similar reductions in the percolation threshold.
2.3
SDS as a plasticizer
In the previous section it was shown that plasticization of the matrix in a composite formulation can lead to changes in the dynamic percolation behaviour. The surfactant used in the preparation of the CNT dispersion, as well as for the polymer latexes, namely SDS, is in itself a plasticizer. It is therefore highly likely that excess SDS in a composite formulation can result in changes in the final percolation threshold. On the other hand, if there is excess SDS in the CNT dispersion, there could even be an altered CNT orientation due to depletion-induced aggregation, stimulated by the presence of SDS micelles.25 In this section, the role of SDS as a plasticizer is investigated. A PS latex was prepared and dialyzed to ensure that there was no residual SDS in the water phase. This latex was then used to prepare composites via a latex-based technique using SWCNTs.16
The addition of 7 wt% SDS was found to plasticize the PS latex (with a Tg of 101 oC) to a large
degree. The Tg was found to be below 60 oC. The contribution of the SDS to the conductivity of
matrix material should not be neglected, since the charged groups can contribute to ionic
9
conduction and the hygroscopic nature of the surfactant will absorb some water. For this reason, one film was prepared with SDS and PS only. This film was found to have a non-negligible conductivity of 10-6 S.m-1. The percolation threshold of the PS with SWCNTs in the absence of additional SDS was also determined as a control (in these samples the wt% of SDS is always twice that of the SWCNTs). This threshold, as well as that determined for systems including 7 wt% additional SDS, is given in Figure 2.7.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -16 -14 -12 -10 -8 -6 -4 -2 0 SDS plasticized Control L og C on du ct iv ity (S /m ) SWCNT loading (wt%)
Figure 2.7: Percolation thresholds and error bars for the control composites and those prepared with 7 wt% additional SDS. The horizontal line represents the conductivity
of a PS film without SWCNTs but containing 7 wt% SDS.
These results imply that additional SDS can cause a reduction in the percolation threshold of SWCNTs in PS. At low loadings of SWCNTs, the conductivity is low and is most likely due to a combination of ionic conduction due to the SDS and electron-based conductivity of the SWCNTs. The shift in threshold is similar to that seen for systems in which the matrix plasticization was achieved by incorporating low molecular weight polymer matrix material, as discussed in Section 2.2. One interesting observation is that the ultimate conductivity of this system is similar to the systems investigated in Section 2.2.‡
There has been much speculation about the role of SDS at the interface of the CNTs, especially in conjunction with the electron transport across inter-tube junctions. For the SDS-plasticized system, SDS displacement from the CNT surface is less likely to occur because of the lack of mobile low
‡ Please note that in Figure 2.6, the conductivities were determined by 4-point measurements, whilst in Figure 2.7, the conductivities were determined by 2-point measurements. This results in a conductivity-offset, which in our experience is roughly a factor 10 when above the percolation threshold. When similar techniques are used, the offset disappears.
