LUKÁŠ RECMAN DEFORMATION BEHAVIOR OF NANO/MICRO REINFORCED PMMA

DEFORMATION BEHAVIOR OF NANO/MICRO REINFORCED PMMA

by

LUKÁŠ RECMAN

Submitted for partial fulfillment of the requirements for the Degree of Doctor of Philosophy in Macromolecular Chemistry

At

Brno University of Technology Fall 2010

CONTENT

Prohlášení _____________________________________________________________ 3 Declaration ____________________________________________________________ 3 DECLARATION ____________________________________________________________ 4 FOREWORD_______________________________________________________________ 5 ABSTRACT _______________________________________________________________ 6 ABSTRAKT_______________________________________________________________ 7 SURVEY OF THE THESIS _____________________________________________________ 8 GENERAL INTRODUCTION TO THE TOPIC________________________________________ 10 1.1 Theories of Polymer Glasses________________________________________ 10 1.2 Acrylates _______________________________________________________ 13 1.3 Microcomposites _________________________________________________ 15 1.4 Nanocomposites with spherical particles ______________________________ 17 Literature Cited ________________________________________________________ 20 EFFECT OF NANO AND MICRO PARTICLES ON THE MAGNITUDE OF COMPOSITE STIFFNESS___ 22 2.1 Introduction _____________________________________________________ 22 2.2. Materials and Methods ____________________________________________ 26 2.3 Results _________________________________________________________ 28 2.4. Discussion ______________________________________________________ 35 2.5 Conclusions _____________________________________________________ 40 Literature Cited ________________________________________________________ 42 EFFECT OF NANO AND MICRO PARTICLES ON THE YIELD AND REJUVENATED YIELD STRESS 43 3.1 Introduction _____________________________________________________ 43 3.2 Materials and Methods ____________________________________________ 46 3.3 Results _________________________________________________________ 47 3.4 Discussion ______________________________________________________ 54 3.5 Conclusion______________________________________________________ 58 Literature Cited ________________________________________________________ 60 STRAIN HARDENING PHENOMENON OF NANO AND MICRO COMPOSITES_______________ 61 4.1 Introduction _____________________________________________________ 61 4.2 Materials and Methods ____________________________________________ 65 4.3 Results _________________________________________________________ 65 4.4 Discussion ______________________________________________________ 76 4.5 Conclusions _____________________________________________________ 82 Literature Cited ________________________________________________________ 85 FINAL CONCLUSIONS______________________________________________________ 86 FARTHER INVESTIGATIONS__________________________________________________ 88 ACKNOWLEDGEMENT______________________________________________________ 89 CURRICULUM VITAE ______________________________________________________ 90

RECMAN L., Deformation Behavior of Nano/Micro Reinforced PMMA, PhD práce na Fakultě Chemické Vysokého Učení Technického v Brně, Ústav Chemie Materiálů.

Prohlášení

Prohlašuji, že jsem disertační práci vypracoval samostatně a že všechny použité zdroje jsem správně a úplně ocitoval. Disertační práce je z hlediska obsahu majetkem Fakulty Chemické Vysokého Učení Technického v Brně a může být použita ke komerčním účelům jen se souhlasem vedoucího disertační práce a děkana FCH-VUT.

Declaration

I declare that this Ph.D. thesis has been worked out independently and that all used references have been cited correctly and fully. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form, or any means, electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the supervisor of this work and the dean of Brno University of Technology – Faculty of Chemistry.

______________________________

Signature

Declaration

I would like to declare this PhD work to my family. First to my dear grandmother Květoslava Žídková whom a longer time with us has not been given. Farther goes to my mother Taťána Recmanová for her never-ending support and faith and to my father Oldřich Nádvorník for encouragement. Thank you for all the ordinary banalities.

E. Roosevelt

The future belongs to those who believe in their dreams

A. Einstein

Imagination is more important than knowledge

Foreword

The aim of this work is to provide a new look of a current state of understanding of the deformation behavior of polymer glasses. The deformation response of polymer glass is altered by adding a micro and nano particles. For microcomposites a series of micromechanical models, were derived. These models are based on several simplifications where matrix is considered a continuum with average properties. Since the introduction of nanoparticles as filler, a question of quantifying the reinforcing effect raised. At first micromechanical models, were simply applied. A significant discrepancy of measured data and theoretical predictions were obtained. These observations are sometimes interpreted with a broad term “nano effect”. It is shown that observed trends could be rationally interpreted using basic concepts of polymer physics.

While continuum mechanics is used for microcomposites and large discrepancies are observed for nanocomposites, where the nano scale effects becomes important. There suppose to be a point where the nano- and micro- scaled mechanics meet. The set of experiments is based on the assumption that a particle threshold must exist where the micromechanical models are not valid and the nano-scale effects dominate the deformation behavior of a composite. The effect of nanoparticles on the elastic modulus of composites has been studied extensively, but the effect of nanoparticles on post-yield deformation is somehow omitted.

This work set up experiments dealing with deformation behavior of polymer composites with fillers with the size ranging from nano to micrometer rang. Experiments, results and interpretation are viewed from the perspective of microcomposites and the attention is paid to the proper explanation of observed phenomena.

Abstract

The effect of particle size on the elastic modulus and the post-yield response was investigated.

It was shown that both types of mechanical response showed pronounced particle size dependence. The objective of this work was to correlate a number of experimental facts and theoretical considerations regarding the mechanism of elastic and plastic deformation of amorphous polymers in general and, of glassy PMMA particularly. Deformation behavior of PMMA filled with spherical particles was observed in elastic and plastic region. The effect of particle size dependence on the modulus, yield stress and strain hardening response was observed.

The interpretation of the reinforcing effect of particles in nanocomposites was based on the concept of immobilization and the kinetics of the disentanglement. While for the modulus measurement a large extent of data was published, trying to interpret the observed trends, the strain-hardening region is somehow omitted. In an elastic region, the structure of the material remains the same as prepared; however, after passing the yield point, the primary structure is transformed. It was shown that incorporation of the nanoparticles yielded to the increase of strain hardening. It is assumed that the particles can serve as physical cross-links yielding to physically denser network. The effect of particles on the strain hardening response was evaluated using two alternative approaches. First, laid in use of the WLF equation. A linear correlation was found between data and the strain rate. The dependence of the shift factor on reciprocal temperature was linear for neat PMMA and became increasingly non-linear with increasing silica content. Second approach used a yield stress as a suitable parameter for scaling the strain hardening. A linear correlation was found for neat matrix, the addition of nanoparticles yielded to an increasing nonlinearity, while approaching to the Tg. Yield stress and rejuvenated yield stress were evaluated from stress strain curves. It was shown that both yield stresses were governed by the same principles. Data were assembled to create a master curve and evaluated using a simple Eyring´s theory. Parameters of the Eyring´s equation were derived. Observed trends were interpreted using current concepts of yielding theories of glasses. Temperature dependence of the yield stress in nanocomposites show a pronounced effect, suggesting on the additional mechanisms associated with the chain stiffening.

An amorphous, polymethylmethacrylate glassy matrix was chosen to avoid the effects associated with crystallization. Relaxation spectrum shows one sub-Tg transition below the glass transition temperature. The PMMA matrix was selected for its moderate brittleness and entanglement density compared with polystyrene and polycarbonate. In addition, the dissolution and handling was easy. As reinforcement, micro and nano beads were chosen to avoid a complications resulting from particle orientation during sample preparation.

Abstrakt

Práce sledovala vliv velikosti částic na deformační odezvu v elastické oblasti a oblasti za mezí kluzu pro skelný polymer plněný nano a mikro plnivem. Bylo zjištěno, že jak elastická oblast, tak oblast za mezí kluzu ukazuje silnou závislost chování na velikosti vyztužujících částic.

Cílem této práce bylo poukázat, že elastická oblast a oblast za mezí kluzu vykazuje silnou závislost na velikosti vyztužujících částic a propojit oddělené oblasti kontinuální mikro mechaniky a diskrétní nano mechaniky.

Deformační chovaní plněného PMMA bylo pozorováno v elastické a plastické oblasti.

V obou těchto oblastech byl sledován vliv velikosti částic na velikost elastického modulu, meze kluzu a deformačního zpevnění. Mechanizmus vyztužení pomocí nano částic je často interpretován s použitím imobilizační teorie. Nano částice mají silný vliv na molekulární dynamiku a kinetiku tvorby zapletenin. Ačkoli pro velikost modulu byla publikována značná množství dat, vliv velikosti částic na tuhost materiálu nebyla řádně zkoumána. Během elastické deformace je primární struktura materiálu neměnná. Za mezí kluzu toto neplatí a primární struktura je změněna. Bylo prokázáno, že obsah nano částic zvyšuje mez kluzu a vede k vyššímu deformačnímu zpevnění. Je předpokládáno, že nano částice slouží jako další fyzikální uzly, které vedou k fyzikálně více zapletenému systému. Jednoznačná interpretace deformačního zpevnění a přijatelný způsob vyhodnocení deformačního zpevnění stále chybí.

Jeden ze zde představených způsobů využívá škálování pomocí WLF rovnice. Druhým navrženým způsobem byla korelace s mezí kluzu. Obě závislosti vykazovaly lineární závislost s rostoucí směrnicí v závislosti na rostoucím obsahu plniva. Pro všechny pozorované oblasti, elastickou, mez kluzu a oblast deformačního zpevnění byla nalezena silná závislost sledovaných parametrů na velikosti částic. Na křivce napětí deformace byla definována mez kluzu. Byla stanovena rejuvenovaná mez kluzu a mez kluzu po vyžíhání. Naměřené hodnoty byly použity pro vytvoření master křivky, která byla vyhodnocena s pomocí Eyringovy teorie meze kluzu. Byly stanoveny parametry rovnice. Naměřená data byla vyhodnocena s přihlédnutím k aktuálním znalostem deformačního chování polymerních skel. Předpokládá se, že efekty řetězové imobilizace hrají podstatnou roli se snižující se velikostí částic, naproti tomu u mikro kompozitů hrají tyto efekty méně podstatnou roli.

Jako modelový materiál byla vybrána amorfní matrice se sférickým plnivem. Amorfní matrice byla vybrána z důvodu, vyhnout se aspektům souvisejícím s krystalizací.

Polymethylmethakrylát PMMA se z tohoto pohledu jevil jako ideální z důvodu své křehkosti a příjemným zacházením. Jako výztuž bylo použito sférické plnivo s rozměry v mikro a nano oblasti. Sférické plnivo bylo rovněž vybráno z důvodu jednoduchosti fyzikální interpretace, za účelem vyhnout se nepříjemnostem s orientací plniva během přípravy a měření vzorku.

Survey of the Thesis

PhD work was divided into four chapters. First chapter provides reader the theoretical basis of polymer nano and micro composites. Attention was paid to the recent theories dealing with the stiffening mechanisms of nanocomposites, the dynamic fragility and energy landscape model of polymer glasses and application of acrylate polymers. The heart of this work lies in the following tree chapters plus theoretical introduction. Each part is provided with the introduction to the topic and motivation, experimental set up, primary results followed with discussion, final statement and literature cited.

This work deals with deformation behavior of glassy nano and micro composites.

Elastic region, yield stress and rejuvenated yield stress and the strain hardening were investigated. The deformation behavior was altered by adding a nano- and micro- meter sized particles. An extensive deformation studies were performed. The tensile, compression and dynamic mechanical analysis were employed to obtain a complete stress strain curves and dynamic data for the prepared materials. The influence of testing parameters and internal structure of nano and micro composite on the macroscopic behavior was observed. The deformation behavior was related to the internal structure of the composite. Conclusions are made on the effect of particle size dependence on the macroscopically observed deformation behavior.

First part deals with composite stiffness. Modulus is determined in a sub-T_g region (glassy state) and above matrix T_g (rubbery state). Correlation of measured data with existing micromechanical models is presented. It is shown that with decreasing particle size (increasing specific surface area of the filler) the greater the discrepancy between theoretical models and measured data. It was found that moduli show pronounced particle size dependence. The largest influence was found for nanocomposites above matrix main transition temperature. The reinforcement of composites is related to the volume of the rigid filler (microcomposites) and contribution related to the molecular stiffening (nanocomposites). It was shown that composite stiffness is strongly particle size dependent.

The second part is focused on the onset of plastic deformation, the yield point. Here, pronounced particles size dependence is well established. Correlation was made between the annealed and rejuvenated yield stress. Below glass transition temperature, significant differences were found for samples tested in temperatures deeply below T_g and around T_g. These differences were pronounced in nanocomposites compared with microcomposites suggesting that chain stiffening plays a significant role in yielding mechanisms. Rejuvenated yield stress and annealed yield stress were evaluated by a simple Eyring´s approach. The constants of Eyring´s equation were derived. It was shown that nanoparticles effectively restrict the physical aging of the polymer, which is understand as a continual relaxation toward equilibrium and yields to stress delocalization and pronounced chain cooperativity in nanocomposites.

The effect of nano and micro particles on the strain hardening response was observed in third part. It has been shown that nanoparticles affect the molecular dynamics in polymer melts and elastomers including the kinetics of disentanglement. After passing the yield point,

the secondary interactions are broken and primary bonds are holding polymer glass. Guth- Gold equation was used to analyze the effect of particle content. It was shown that strain hardening response is strongly temperature dependent and additional chain stiffening is responsible for data observed around Tg. Strain hardening was scaled in two ways; first, the WLF equation is used to assemble the master curves for all silica concentrations. In second approach the correlation of strain hardening modulus (G_H) on the rejuvenated yield stress, showed a linear correlation for neat matrix with increasing non-linearity with addition of nanoparticles.

CHAPTER 1

General Introduction to the topic

General introduction into a field of glassy polymers and composites is presented here. Recent theories of polymer glasses are presented. It is shown that polymer glasses are system with qualitatively larger complexity. Current state of research on polymer glasses is preferentially focused on theories explaining the behavior of polymer glasses and vitrification. Energy landscape paradigm and fragility concepts are introduced. Among the polymer glasses, the acrylates are described in details including commercial applications. Polymer glasses filled with micro and nanoparticles are introduced. Literature review on polymer glasses filled with rigid particles is presented from basic concepts to recent advances on deformation behavior. Recent theories on reinforcement in micro and nanocomposites are introduced. The survey is limited to polymer glasses and composites with spherical particles only.

1.1 Theories of Polymer Glasses

Liquids below their glass transition temperature T_g produce a glass where the chain motion is restricted and only side chain motions are possible [1]. Near Tg the molecular motion occurs very slowly. Above the Tg, the glass is in a rubbery or liquid rubbery state and the molecular motions are rapid and governed by chain dynamics theories [2]. In rubbery region, the polymer is in equilibrium, while going down below the T_g the system is constantly evolving, hence glass is not thermodynamically equilibrated state (Figure 1.1 right). The

Figure 1.1 Left: Schematic representation of entropy as a function of temperature. The glass transition temperature (T_g) depends on the cooling rate of the glass. T_K indicates the Kauzmann temperature, where the crystal and glass are having the same entropy. Right; Energy landscape depiction, the internal energy of a system depends on the configuration of all its particles (simplified to one direction) from ref [3].

temperature of this transition depends on how quickly the liquid is cooled or heated. It has seemed natural to describe the process in terms of kinetics rather than thermodynamics.

Several theories have been derived to describe the glass and glass transition phenomena with more or less accuracy [4, 5]. However, an agreement on the comprehensive theory of glasses including even metallic, inorganic, and low molecular weight organics is still missing.

Recently, new theories were introduced, trying to look on the glass phenomenon from another side. From these theories, the energy landscape introduced by Stillinger (Figure 1.1 left) [6]

and concepts of fragility introduced by Angell [7] do the most comprehend.

Two phenomenological approaches are widely employed to interpret polymer relaxation. One is the free volume model based on “kinetic blocking”, where the increased chain mobility requires an additional amount of free volume. The free space gathering is done via diffusion of defects. Unfortunately, the free volume has a certain limitations such as is not directly measurable. However, based on this simple assumption the alpha relaxation time is defined as:











= 

Vf

b V exp τ0

τ_α

or

( )

0 1 0

ln T T

T T

C _REF

−

−

≅ −







 τ τ_α

, (1.1) where τ0 is an elementary time scale, b a number of order unity, V (Vf) the molar (free) volume, C₁ a no universal parameter, T_REF a reference temperature (typically T_g), and at T₀>0 the free volume goes to zero and the relaxation time exceeds infinity. Polymer aspects and parameters enter only empirically and indirectly.

A second class of theories is centered on the thermodynamic configuration entropy, supplemented with an entropy crisis or catastrophe at a nonzero temperature. This

“Kauzmann paradox” postulates S_C (T = T_K) → 0 [8, 9]. Adam and Gibbs proposed that this entropy determines the relaxation time as:

( )

^





 ∆

= S T

S

C C

* 0exp β µ τ

τ , (1.2) where β ^{= 1/k}BT is the inverse thermal energy, and ∆µ is the high temperature non- collective activation energy and S_C^* is the configuration entropy [10]. If S_C (T) is approximated as a linear function of temperature, the classic Vogel-Fulcher-Tamman-Hesse (VFTH) equation is obtained [11, 12]. The polymer chain dynamics is activated with a barrier proportional to the number of elementary unitsS_C^*/S_C (T) that moves simultaneously in a cooperatively rearranging fashion [13]. The entropy crisis was worked out by Gibbs et al [5]

based on the assumption that TK is a direct indication of the laboratory Tg.

What exactly is the glass? When lowering the temperature, the viscosity of the liquid increases and the molecules move more and more slowly. At some temperature, the molecules are moving so slowly that they do not have a chance to rearrange at the time of the experiment. At this temperature, the time scale for the rearrangement will become infinitely long compared to the time possible for observation and the material becomes frozen. From that statement, the glass transition temperature is not a true phase-transition, but rather a temperature where the time scale of the molecular movement and time scale of observation are crossing each other [14]. Glass on a contrary with crystal cannot be considered as a thermodynamically stable. It is slowly relaxing toward a more stable state, seeking local energy minimum. This dynamic evolution can be related to the changes in the nature of the energy landscape. The energy landscape paradigm is mostly used to explain a metastable and

complex system behavior. The landscape topology controls the kinetics and the thermodynamics perspective is viewed as an average of energy minima visited at certain temperature [15]. With decreasing temperature, a point is reached where the movement to a lower minimum becomes impossible – time consuming. Bringing the temperature up a little, allows the system in a reasonable time to explore a surrounding minima and to evolve that direction. This process is called relaxation or annealing.

The concept of liquid fragility is closely related to the energy landscape paradigm.

Angell [16] was the first, who broadly extended the fragility concept in both the dynamics (viscosity for example) and thermodynamics (heat capacities). The term fragility can be simplified as sensitivity to temperature changes. The glasses that are very sensitive to the temperature changes and strongly deviate from the Arrhenius temperature dependence of the relaxation properties (Figure 1.2) are termed fragile. Strong liquids, exhibit a nearly Arrhenius dependence of dynamic properties. Fragile liquids exhibit VFTH or WLF behavior. Vogel- Fulcher-Tamman-Hesse equation is defined as:

( )

_









= −

T∞

T T η₀exp B

η , (1.3) where η₀is an infinite high temperature viscosity (or it could be an infinite high temperature time). T_∞is the so called VFTH divergence temperature and B is the material specific parameter related to the activation energy of the observed process and temperature [17 - 19].

The WLF equation is defined as:

( )

ref 2

ref 1

T C T T

T T a C

− +

−

= −

log , (1.4) where C₁, C₂ are the WLF parameters specified for each polymer at reference temperature Tref [20, 21]. Both equations are related to dynamic fragility index - m and apparent activation energy EG at Tg. The index of dynamic fragility or sometimes called the

Figure 1.2 Strong and fragile behavior in glass-forming liquids. Continuous lines represents the VFT equation by varying the parameter B. Inset graph shows the heat capacity at T_g by rationing the liquid (glass) data to the crystal values at each temperature form ref. [7]with permission of Elsevier.

steepness index - m, characterizes the rapidity of the change of measured properties (Figure 1.5). The steepness index is quantified as:

( )

Tg

T g

T d T

x m d

 =

























= log

, (1.5)

where x can be viscosity, relaxation time or other thermodynamic variable. Importantly, the dynamic fragility is effectively a T_g normalized activation energy. The thermodynamic fragility is often represented by the ratio or increment of heat capacities at the glass transition temperature, or the change of the Tg-scaled excess entropy:

( ) ( )

Tg

T g

g

T d T

T S

T d S

=

















∆

∆

, (1.6)

where ∆^S

( )

^T denotes the entropy difference between the liquid and crystalline states at temperature T. Although it was believed that there existed a positive correlation between dynamic and thermodynamic fragility, mutual correlation is controversial. Resent progress was provided by McKenna, where the glasses were divided into several groups according to the fragility index. A roughly linear correlation between dynamic fragility and glass transition temperature was found [22, 23]. In the concept of the energy landscape paradigm, the fragile liquids are glasses with numerous minima and sparser minima are found in non-fragile liquids. Polymer materials are mostly fragile liquids because having long chains mostly with certain degree of polydispersity. With increase in glass transition temperature an increase of dynamic fragility was observed.

Angell [24] published a comprehensive study on glass formation, relaxation dynamics, and fragility and energy landscape concept, so reader interested in the related topic is referred to information found here. Computational simulations are also a valuable source of information. They actually help in better understanding of observed trends and extend the current knowledge beyond the experimental possibilities [25-27].

1.2 Acrylates

The most versatile polymer glasses today are Polystyrene (PS), Polyacrylates (PAC) and Polycarbonate (PC). All the polymers glasses show no detectable crystallinity and their Young’s modulus is approximately the same. However, their post-yield deformation behavior differs significantly (Figure 1.3). While PC is a ductile and tough material the PS is very brittle at room temperature, while the PAC stays somewhere in the middle. The elastic modulus of polymer glasses tends to be very similar. It is because the secondary forces primarily govern the elastic response of polymer and for these PS, PAC and PC have approximately the same magnitude. Meijer [28] proposed that the entanglement density governs the post-yield response. Polymers that are more entangled, like PC, show pronounced strain-hardening, on the other hand low entangled PS have practically no strain-hardening and breaks in a brittle way at small tension deformations. The combination of strain softening and

strain hardening at large deformations proves to be the key issue in understanding the deformation behavior of polymer glasses. Their mutual ratio determines whether the polymer fails in a ductile or brittle way.

Acrylates are common in use now, mostly the artificial glass is known, but their usage is spread in dental restoratives, toughening agents, lacquers and nanoparticles as well. Acrylates are broad polymer group: From thermoplastic polymers to crosskicked acrylate networks (dental materials) and acrylate rubbers (toughening agents). Most of the thermoplastic polymers are made by a bulk polymerization of acrylate monomer. Linear thermoplastic polyalkyl methacrylates differ mostly by the size and the nature of the side chain, from the most common one polymethylmethacrylate PMMA to hydroxyl propylmethacrylate PHMA for example. A common trend existed, where the magnitude of the side chain length decreases the Tg of acrylate. The sub-Tg relaxation shows several peaks depending on the length and complexity of the side chain groups [30].

The following items show a possible application of acrylate derives. Introduced to the clinical application a few decades ago, dental composites are usually made up of rapidly curing organic polymer resin, pure inorganic fillers and interfacial coupling agents (Figure 1.4 right). One of the widely used polymer matrices in the dental composites is derived from 2, 2- bis(p-2-hydroxy-3-methacryloxypropoxyphenyl)propane (bis-GMA). The viscous bis-GMA resin is often diluted with low-viscosity monomers such as triethylene glycol dimethacrylate (TEGDMA), methyl methacrylate (MMA), and/or ethylene glycol dimethacrylate. These resins are mostly filled with micro fibers and particles. As a coupling agent between the matrix and the reinforcement, a γ-methacryloxpropyltrimethoxysilane and other acrylate derives are typically used. Molecules have a reactive head to interact with the filler and vinyl group or other reactive groups to interact with the oligomeric matrix. Ideally, the covalent bond is formed between the filler and the matrix. For dental applications, the resins and its constituents are mixed together with an accelerator, curing agent and stirred. A polymerization is carried using an UV source [31]. A proper interphase must be form to prevent any separation between matrix and the filler. Several approaches are available for surface treatment of fillers, among them: Solvent technique, Chemical vapor deposition and plasma treatment [33]. For increasing volume stability and resistance to moisture environment a chopped and continuous fibers are mostly added. Incorporation of chopped fibers yields to

Figure 1.3 Deformation behavior of three polymer glasses: PMMA polymethylmethacrylate, PC polycarbonate, PS polystyrene. Left part in compression and in tension at the right part. From ref [29] with kind permission of Elsevier

stiffness increase if high stiffness fibers are used or to toughness increases if tough and deformable fibers are used [33, 34]. As a result, materials provide a wide range of properties yielding to tailored properties [35, 36].

Adding rubber particles into a polymer yields to decrease in modulus. Adding an inorganic filler to rubber toughened polymer compensate the decrease of modulus. Mammeri [39] showed another approach, where the inorganic structure is directly embedded into the rubbery matrix. The composite is generated by a chemical reaction of inorganic tetraethoxysilane in organic acrylic rubber (Figure 1.4 left). The silica is uniformly distributed and bonded to the matrix. These unique properties combining an increase in stiffness and impact toughness lies in the sol-gel process and the formation of the inorganic silica network.

Among other properties, the transparency so important for the polymer glasses maintains approximately, the same due to the small size and distribution of nano scale silica domains within the matrix.

1.3 Microcomposites

Micro composites represent the most used composite materials today. For micro filled composites, four factors must be controlled, component properties, composition, structure and interfacial interactions. Polymer composites evolved from simply filled systems, to the complex materials possessing additional advantages. The composites are now common in automotive, textile and consumer goods industry. The spherical filler plays a significant role in thermoplastic matrices semicrystalline or glassy, but they can be found in thermosets and elastomer too. Spherical fillers have a benefit over the non-spherical, that their properties are isotropic and exhibit no orientation effects during the manufacturing.

One of the benefits of micro composite over the neat matrix is the increased stiffness.

An attention must be paid to uniform dispersion and surface treatment of the used filler.

Current micromechanical theories assume that the effective properties of composite materials such as Young’s modulus, yield strength and elongation at break are related to the properties of their constituents, volume fraction of components, shape and spatial arrangement of filler and properties of the matrix/filler interphase. The properties of the material are considered independent of the particles. This is correct for systems with particles in micro size range.

Figure 1.4 Core shell particles, PMMA core (light) and polydimethylsiloxane shell (dark) from ref. [40] the size of the particles is 10µm. Dental restorative materials on the right

Vollenberg showed that particle size dependence plays a certain role even in microcomposites [41]. Nevertheless, his explanation lies mostly in the changes of particle filler interaction and changes at the character of the interphase rather than the extent of the interphase.

Micromechanical models are based on the assumption that the polymer matrix is a homogeneous continuum that may be characterized using its average properties. The effect of reinforcement in the size of micro range is mostly dependent on the volume fraction of the microparticles. In addition, all well established models, such as Guth-Gold [42], Kerner- Nielsen [43], show the correspondence between increasing volume fraction and increase in stiffness. Usually, nanocomposites show a steep increase in modulus for a small amount of nanoparticles ~ 0.03-0.05. The modulus increase exceeds the continuum mechanics models derived for microcomposites. For the matrix reinforced with nanoparticles, these models are no longer valid. First, the sizes of the nanoparticles around ~ 10 nm are comparable with the average random coil size (~10 nm) of most conventional polymers [44]. When the sizes are comparable, the assumption of matrix continuity is no longer valid. In addition, the contact between the matrix and the particles reaches a larger extent, due to the high specific surface area and the close interparticle distance even for low volume fractions. Thus, the main reinforcing mechanism in nanocomposites is found different from that in microparticles [45].

Demjen and Jancar [46, 47] showed the importance of surface treatment in microcomposites. The composites with adhering particles show an increase in stiffness compared with composites with weak particle matrix interaction. However, for spherical particles this increase is negligible. Parameter that is strongly affected by the quality of the interphase is the yield stress. For good adhering particles a yield stress larger than yield stress of the neat matrix was recognized, on a contrary for the particles with non-adhering surface treatment, lower values of yield stress than in matrix was measured [48, 49]. For non- adhering fillers, the particles are considered as holes in effective cross sectional area of the specimen, which might cause crack propagation even in the elastic region (Figure 1.5). For the effect on yield strength similar conclusions can be drawn. Yield strength is understood as the maximum limit of the material use. Above the yield point, the material is plastically

Figure 1.5 (A) Microcomposite filled with adhering particles, shear bands and void formation at the poles of the particle (dashed square).

deformed. For the interacting filler, increased yield strength was observed [50] while for the particles with non-adhering surface treatment a premature failure before reaching a yield point usually occurs. Interaction of the stress fields around the particles and larger value of debonding stress were determined as a primary source of increased yield strength. Particles serve as a stress concentrators, where the localized stress fields are distributed to the whole specimen and thus leading to an increase of yield stress [51, 52].

1.4 Nanocomposites with spherical particles

Nanocomposites are materials defined as composites being reinforced with particles having at least one dimension in a nano meter size range. Since the introduction of nanoparticles in the 90^th of last century, most of the effort was focused on the preparation and understanding the behavior of nanocomposites. First, concepts that were established for microcomposite were just scaled three orders of magnitude lower to describe and understand the nanocomposite behavior. As it was shown by Jancar et al [32, 53], this approach might not be the proper one. With decreasing particle size, the specific surface area increases. The large portion of polymer is in an intimate contact with the filler surface and takes a maximum advantage of interphase area. This has a strong influence of several composite properties like stiffness and yield stress. On the other hand, particles with high specific surface area tend to form aggregates easily (Figure 1.6). The formation of aggregates is governed by their tendency to obtain an optimal surface to volume ratio. Several approaches existed to circumvent the agglomeration. These concepts lie in preventing the aggregation using a surface treatment and with applying an external field (mechanic, electric, magnetic).

Nano fillers are particles with high specific surface area. With decreasing particle size, specific surface area increases. However, nano spheres tend to form agglomerates easily unless a protective colloid is used to keep them separate. It was shown that spherical nanoparticles can assemble into stripes under a loading [54]. By careful changing the parameters of this protective colloid, several hierarchical structures can be derived. By

Figure 1.6 Increasing size and decreasing specific surface area of nanoparticles - From nanocomposites on the right to a micro composite on the left. Simplified example of hierarchically organized structures found in nanocomposites.

changing the chain length of tethered chains and the grafting density of chains on the surface, platelets, rods an individual particle structures can be obtained. The outcome of this process is in a simplified view depicted on the following Figure 1.7. In the case represented on the left part of the Figure 1.7, we can find that particles with actually no grafted polymer chains minimize the contact area by phase separation (region A), while the particles grafted with dimers or tetramers yields to flattened shapes (region B). Increased length, around six molecular units, yields into strings (region C), where for chains with long enough tethered tails dispersed particles can be found (region D). Akcora and coworkers [55], showed a broad effect of self-assembled nanoparticles under a broad range of conditions into a variety of superstructures. By varying the quality of solvent, annealing time, chain length and grafting density, a various super-organized structures were found. The effect of aggregates on the deformation behavior was always considered as negative. It was believed that the deformation behavior for well separated particles yields to the largest mechanical response, for example - stiffness. Right part of the Figure 1.3 represents the scheme of possible structures yielding to various reinforcing behavior. The upper part with dispersed particles, where the chain stiffening is believed to be responsible for observed trends, while for the percolated structure (rods and platelets) the contribution of connectivity must be determined. Here, under the term of percolated structure, it is understand a higher level of organized structure (build up by particles) described with aspect ratio. The percolated structure refers to an organized inter particle connectivity, and it is far from percolated structure as defined standard for works dealing with conductivity [57]. Intuitively, it is believed that one of percolated structures on the previous Figure 1.7, as platelets and rods possess superior stiffness over the individual nanoparticles. However, the question of reinforcement efficiency for well-dispersed or percolated particles is not fully answered, yet.

There is no doubt that the incorporation of nano spherical particles with large specific surface area leads to the amplification of several molecular processes resulting in an enhanced macroscopic properties. The effect of nanoparticles on the matrix properties and the

Figure 1.7 The morphology map of polymer nanocomposites on the left. Grafting density and chain length, yields to four distinct morphologies. (A) No surface treatment – particle aggregates, (B) connected sheets for small branches (C) short springs for longer grafted chains and finally (D) isolated polymer chains with polymer brush on its surface. From ref [56]with kind permission. On the right: Possible reinforcing effects:

Chain immobilization or percolation what gives larger reinforcement?

relationship between nano-scale structural variables and the macro scale properties of polymer nanocomposites remains in its infancy.

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CHAPTER 2

Effect of nano and micro particles on the magnitude of composite Stiffness

Experimental results are reported from which it appears that stiffness of the composite is particle size dependent. Measured data were correlated with Kerner and Guth-Gold equation. For modulus below and above glass transition temperature a superior role of nano reinforcement was found. It is shown that these micromechanical models do not predict the reinforcement of nanocomposites satisfactorily. The effect of particle size and the specific surface area of the filler are not considered. It was shown that specific surface area of the nano particles play a significant role in matrix stiffening.

Hence, simple model was introduced to present a new look on nano and micro composites. The effect of particle dimensions, strain rate and temperature on the stiffness of the composite is addressed to this chapter.

2.1 Introduction

Particulate filled polymers and polymer composites are used in increasing quantities almost everywhere, theses days. The total consumption of particulate fillers only in Europe is growing geometrically [1]. The role of the interphase changes during time. In early days, the filler was added to reduce cost of the polymer (filled polymers), while the benefit of this addition was recognized lately and, nowadays, the fillers are added intentionally (polymer composites). Fillers increase stiffness, yield strength (depends on the adhesion), decrease shrinkage and improve the toughness of the composites [2]. Commonly, fillers are added to polymer to obtain a properties not possessed by the matrix. The properties of heterogeneous polymer composites are determined by three factors: component properties, composition and interfacial interactions [3]. Fillers bring about additional benefits like increased heat distortion temperature [4, 5], electrical conductivity [6, 7] and scratch resistance [8, 9]. Nevertheless, effect of component properties and interfacial area are paramount.

The elastic modulus of particulate filled material is generally determined by the properties of its constituents – matrix and filler, particle loading and aspect ratio. In the case of spherical filler, the composite stiffness depends only on the properties of its constituents and loading. Modulus of a composite has been the subject of several studies and a number of models were derived, predicting the composite modulus variation with varying accuracy.

Kerner, Mori-Tanaka and Guth-Gold models are the most respected [10 - 12]. These theories considered the matrix as an isotropic homogeneous continuum and the modulus of composite independent of filler size. Although these theories are giving a good correlation with experimental results for microcomposites, it was shown by several authors [13 -15] that there

Reproduced from:

Particle size dependence of the elastic modulus of particulate filled PMMA below and above T_g, J Jancar, L Recman, submitted to Polymer Composites

existed a certain dependence of composite modulus on particle size. With decreasing particle size, a larger modulus was observed compared with the composite modulus filled with larger particles. None of certain explanations was able to interpret the observed trends [13].

There is no doubt that in microcomposites, an interphase is formed and that the proper particle matrix connectivity, determines mechanical properties of polymer composites [16, 17]. However, the extent of interphase is small compared to the amount of matrix, which is not in contact with the particle. Dramatic increase of interphase is found in highly filled microcomposites like shells [18] and nanocomposites. Shells show a brick and mortar structure, where the polymer chains are in a close proximity of platelets. The close inter particle distance is also presented in nanocomposites. If we consider the interphase approach presented here, there should be a threshold particle size below, which micromechanical models can predict the matrix modulus satisfactorily. Most of the experimental data are presented in a relative merit, where composite modulus is related to the modulus of neat matrix. This approach assumes that polymer matrix is a homogeneous continuum and that mechanical properties of matrix are not significantly influenced by the incorporation of particles. In nanocomposites, the particle size is comparable with the radius of gyration of polymer coils [19]. The polymer matrix cannot be considered as a uniform continuum, but as bunch of coils with spectra of relaxation times. The relaxation time spectra are influenced significantly in the vicinity of the particles. The following Figure (2.1) shows a simplified scheme of length scales found in model composite.

Various models based on continuum mechanics are used to describe the structure and performance of interphase on a micro-scale, satisfactorily. At the micro-scale, the interphase is considered a continuum with average properties. Assumptions and models derived using this concept characterize the interphase by its thickness, modulus and shear strength. The effort to transfer the same approach and concepts to nano-scale seems not right. On the nano scale, a discrete molecular structure must be considered. The term interphase from micromechanics is loosing its meaning and has to be redefined to embrace a discrete nature of polymer coils on the nano scale. The segmental immobilization resulting in retarded chain dynamics in the vicinity of nanoparticles is thought to be more convenient on the nano scale.

Microparticle

Polymer Chain

Nanoparticle Microparticle

Polymer Chain

Nanoparticle

Figure 2.1 Simplified sketch on the length scale considered in our system. Nanoparticle has about 10 nm.

The following Figure (2.2) shows a schematic representation of “interphase” in nano and microcomposites.

Continuum mechanics is used to describe the effects of micro-scale interphase on the stress transfer in single non-spherical composite, where three distinct phases can be recognized: Reinforcing particles, bulk and interphase matrix. All the constituents can be characterized with some average properties. The stress transfer from the matrix to the filler was derived by Kelly and Tyson [20] and has been proved many times. Deformation behavior and environmental stability of micro reinforced composites is strongly depended on the quality of the interphase [21]. Tailoring of the interphase becomes crucial in this case. The uses of various types of coupling agents [22] chemically reactive with both matrix and the filler, or chemical modifications of surfaces [23] or matrix [24] are the most successful methods, providing an appropriate interfacial behavior. The extent of interphase in microcomposites is relatively small, and usually transfers the stress from matrix to the filler.

The largest portion of the reinforcement comes from the volume effect or the stress transfer to the anisometric particles like fibers or platelets. For the spherical particles, the reinforcing effect related to the volume fraction can only be considered.

The interphase behavior is crucial in understanding the reinforcing effect in polymer composites. While the interphase in the composites plays a significant role in stiffening, the extent of the interphase in micro and nanocomposites is quite different. Figure 2.1 shows a simplified scheme of the relation of polymer coil to nano and micro particle. While the size of the polymer coil is at least 1,000 times one smaller than the micro sphere, the effect of local chain conformation changes is very small. From the previous Figures 2.1 and 2.2, it is also clear, why the interphase can be considered as a continuum region. From these Figures, it is also clear, why the extent of interphase in microcomposites is so low. The proximity between the microparticles is so large that a small amount of polymer coils is in an intimate contact with the particles and forming an interphase. A large portion of polymer chains is not influenced by the particle presence and retains its bulk properties. Thus, in microcomposites, three distinct regions exist: filler, matrix and interphase and that these regions can be

Figure 2.2 schematic views on the extent of “interphase/retarded reptation zone” in micro and nanocomposites.

On the left: A simplified view on nanocomposite is shown. Due to interparticle distances and high specific surface area, large quantities of polymer coils are near nanoparticles. Three distinct regions can be easily recognized, Bulk polymer (cyan), interphase (blue) and nanoparticles (white). On the right side: A schematic view of microcomposite. The interparticle distance makes the inter penetrating of interphase impossible. A large quantity of matrix remains without any contact with particles.

Particles

Bulk

Interphase

20 nm Particles

Bulk

Interphase

20 nm Particles

Bulk

Interphase

20 nm

described by some average properties. The comparable sizes of nanoparticles and polymer chain coils [2] complicate the unambiguous development of any models to predict nanocomposites behavior. Chain conformation and changes in local dynamics must be taken into a consideration. Large contact area between matrix and filler yields to increased stiffness for low volume fraction never seen in microcomposites. This “nano effect” has its origin in the comparable sizes of polymer coil and particle and in high specific surface area of nanoparticles; these attributes have a pronounced effect even in low volume fractions.

Assuming the chain immobilization to be the primary reinforcing mechanism on nano scale, changes in conformational entropy within the polymer phase is of primary importance.

The dynamic strain softening of filled rubbers, known as a Payne effect [25] was shown in ref. [26]. The same dynamic strain softening for polymer melt was observed for PVAC melt, filled with nanoparticles [27]. Experiments performed by Sternstein and Kalfus showed that, there is no permanent interphase on the nano-scale in polymer melts. A concept of freely reptating chains in the bulk and retarded reptating chains in the vicinity of the particle was

Figure 2.3 Simplified view on nanocomposite (2.5%) mechanical response and morphology. Figure (1) dynamic shear modulus of nanocomposite as measured by dynamic mechanical analysis. Pronounced influence on modulus is recognized above T_G of the matrix (100 °C). Figure (2) Morphology of silica nanoparticles (dark spots) embedded in PMMA matrix as viewed by TEM. Red line circles the pristine matrix, the grey is affected matrix. Figure (3a) and (3b) a simplified look on the behavior of nanocomposite below and above matrix Tg.

established to interpret this phenomenon. The large specific surface area of the nano-sized inclusions is capable of immobilizing large amount of entanglements causing the steep increase in moduli. This observation confirms the purely entropic character of the reinforcement mechanism on the nano scale. All the published data support the dominant role of the chain immobilization as the main reinforcing mechanism. Due to the great extent of specific surface area of the nano fillers, almost all the polymer chains are in contact with the particle surface at very low filler loadings as shown in Figure 2.2 and 2.3.

In Figure 2.3, the effect of reinforcement below and above matrix Tg is shown. Glassy state is characterized with long relaxation time, which means highly restricted or “frozen”

mobility of main chain. When passing a T_g the chain mobility is relieved. The polymer is in a rubbery state characterized with short relaxation times and all chain conformations are accessible [28]. For the temperatures far below Tg the effect of segmental immobilization is not pronounced, where the polymer glass is in a deeply super cooled state (Figure 2.3 3a). The pronounced changes are induced when approaching the T_g from below, where the segmental mobility is increased. Its importance rises above the T_g where the free chain mobility occurs (Figure 2.3 3b). Nanoparticles serve as traps for chain segments, yielding to increase the relaxation time of chain trapped chain segments. This effect is responsible for observed increase in moduli above T_g. The reinforcement of amorphous polymers originates from the volume fraction of reinforcement and from the molecular stiffening. First mechanism prevails for microparticles with low volume fraction (<0.4), the second one for nanoparticles. Nano particles yield to superior elastic properties for almost all possible polymer matrices.

Our study is concerned with the composite stiffness reinforced with filler having different particle sizes. Composite stiffness in a sub-T_g region and above T_g region was observed. PMMA with two different molecular weights and particles having a diameter from 10 microns to 20 nanometers were used. Correlation of experimental results with existing micromechanical models was presented. Data were plotted against the volume fraction and specific surface area of the filler. With decreasing particle size, the modulus of the composite increases. Finally, a simple model was derived to show a new way to look on nano and micro composites [24].

2.2. Materials and Methods

Materials

The high molecular weight PMMA (150 kg.mol^-1 5Mc, Plexiglas Rohm Industries, Germany and Sigma Aldrich 300 kg.mol^-1 10Mc) was used as a matrix. Silton Jc-50 in the range of 5_µm (Mizusawa Industries, Japan) and Silica in range of 10 _µm and 20 nm of primary particles (Sigma Aldrich) were used as the reinforcement. Detailed information is listed in Table 1 and 2. Parameters in Table 1 were obtained from SEM, TEM and Confocal Laser Scanning Microscopy. Size distribution was measured using a Zetasizer 3000HS (Malvern Instruments Ltd). BET absorption isotherm was measured on Chembet 3000 (Quantachrom) to obtain a specific surface area needed for farther calculations.

The master batches were prepared as follows. A certain amount of filler was dispersed in a solvent (Acetone + Toluene 1:1 vol. fractions). Required amount of filler was added and stirred while sonicating for 1 hour. Meanwhile a certain amount of matrix was dissolved and added to the mixture. Master batch was then stirred and sonicated for a next 1 hour. Prepared

mixture was poured on the aluminum sheets at room temperature and dried for 4 hours at 80

°C to evaporate the solvent. Thin composite sheets were milled and dried at 140 °C for 1 hour. Prepared master batch was compression molded at 180 °C for 4 minutes into plates of thickness of 0.5 mm. Plates were cooled to room temperature immediately. The volume fraction of filler used in experiments varies from 0 to 0.1 for nanocomposite and 0.05 and 0.3.

For measurement in tension a dog-bone specimens were cut off from the sheets.

Specimens for dynamic mechanical analysis were cut off using a rectangular shaped cutter.

Compression specimens were prepared from blocks, which were prepared by stacking sheets upon each other and compressed at the same thermal conditions as previously, but for 8 minutes. From these block a compression specimens were prepared using a mill and slugger- cutter drill with internal diameter 6 mm.

Figure 2.4 SEM images of micro filler and TEM of Nano Silica

Table 1 Applied Fillers

Particle Diameter Specific Surface Area

Microscope Zeta Sizer BET

Average Size

Standard deviation

Average Size

Standard deviation

Average Size

Standard deviation Particle Material

µm/nm⁺ _µm/nm⁺ m².g^-1

SILTON

Sodium Calcium Alumino Silicate

4.24 0.87 5.62 2.85 3.8 0.1

GLASS

BEADS SiO₂ 8.77 7.20 9.21 4.35 0,3 -

FUMED

SILICA⁺ SiO₂ 20⁺ 10 19.5⁺ 2.4 272.9 1.4

Table 2 Applied Matrices

Mz Mw Mn ν *Mc

Matrix

g.mol^-1 g.mol^-1 g.mol^-1 - g.mol^-1 31 530 PMMA 168 061 115 959 67 781 1,71

24 100

PMMA 300 000

Literature values from 24 100 [29], 31 530 [30]

Methods

First series of specimens were tested using a Universal Tensile Testing Machine (Zwick 1940) in a tensile mode. Environmental chamber was used and samples were tested at 80 °C at strain rates 10^-4, 10^-3, 10^-2 s^-1 (0.1%, 1%, and 10% of overall deformation). Compression measurements were performed using the Instron 5800 at logarithmic strain rates ranging from 10^-4 to 10⁰ s^-1, at temperature range from 20 °C to 80 °C. Dynamic mechanical analysis was performed on ARG2 rheometer (TA instruments) using torsion clamps. Temperature sweeps from 40 °C to 160 °C were performed at constant frequency 1 Hz and 0.01% amplitude. For all measurements, an average value of three measurements was taken and a standard deviation was calculated. The size of the symbol in Figures represents the standard deviation. The morphology was visualized using a Confocal Laser Scanning Microscopy, SEM, TEM and Optical microscopy.

2.3 Results

Composite Stiffness below Tg

The experimentally obtained data were plotted against volume fraction of the filler in the following Figures, while changing the temperature and strain rate of the experiment. In these plots a predictions according to the modified Kerner equation [31] are presented as continuous curves. The modified Kerner equation is expressed as: