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Elastomers and their molecular dynamics
Polymers are large molecules, macromolecules, composed of many repeating subunits called “monomers”. Elastomers (rubbers) are a specific type of polymer, with very weak intermolecular forces, used at temperatures well above that of their glass transition. Crosslinking of the rubbery chains are needed for the material to show its great mechanical properties. They are stretchable to high strains in a reversible way, and have a low Young’s modulus (~MPa). During this first part, an introduction to rubbers’ great elasticity and a rapid study of their dynamics in melt is proposed.
Processing and key properties of elastomers
In the rubber industry, manufacturers themselves prepare the blends on specific tools and therefore control all the processing parameters, as well as the formulation [1].
Formulation and shaping of elastomer
i. Formulation
The main component is, of course, the uncrosslinked rubber itself. It is either natural rubber, or synthetized by polymerization of oil-based monomers (ethylene, propylene, butadiene, styrene…). The polymerization technique as well as the used catalysts determine the structure and the molecular mass of the polymer. Different additives are blended, among which: fillers, plasticizers, stabilizers and vulcanizing agents. The nature and the amount of each additive is well controlled and optimized to satisfy the specifications.
Blending is performed in two steps:
– On an internal mixer to add fillers and oils. These tools operate discontinuously. During this step, temperature can rise up to 180°C due to viscous heating
– On cylinder mixers, also called “calenders”, at a much lower temperature to blend the vulcanizing agents without risking a premature crosslinking
Shaping
Once the blend is ready, it is shaped using polymer molding classical techniques: injection, extrusion or compression. In the case of tires- and helicopter fuel tanks- shaping consists in overlaying the bands of raw (unvulcanized) rubber bands, and the structure relies on each layers’ specific function and positioning. The assembly is then vulcanized in appropriate presses.
Basics of elastomers mechanical properties
Vulcanization
Vulcanization is the final step of the fabrication process. It consists in fixing the three-dimensional structure through chemically crosslinking the polymer chains. The reactions are thermally triggered. The vulcanized rubber cannot be modified afterwards and heating leads to its pyrolysis rather than its fusion. There are mainly two types of chemical agents for vulcanization: peroxides and sulfur compounds [2][3]. Sulfur bridging of polymer chains is illustrated in Figure 1.
Mechanical properties
Elastomers are a specific kind of polymer, with very weak intermolecular forces, used at temperatures well above that of their glass transition (which is lower than 0°C). Their modulus drops of several orders of magnitude (from GPa to MPa) at this specific temperature (see Figure 2) and vulcanization prevents their flow at very high temperature. In fact, once crosslinked, elastomers –similarly to other thermosets- are not re-shapable, which is the main reason for their difficult recyclability. Figure 3 shows the difference in uniaxial tensile testing between uncrosslinked and crosslinked elastomers. Although properties in the linear regime are similar, materials have very different behavior at large strains.
Figure 2 Linear mechanical properties of elastomers Figure 3 Effect of crosslinking on the large strain behavior of elastomers.
The physical origin of this mechanical behavior is introduced in the following paragraph.
Physics of rubber elasticity
To understand the physics of rubber elasticity, a brief reminder of the definition of a polymer chain and its characteristic length scales is useful. A flexible polymer is described as the assembly of n+1 bonded atoms (see Figure 4).
The end-to-end vector is the sum of all n bond vectors, and the simplest average non-zero distance is the mean-square end-to-end distance (see equation 1. 1). The latter is often used to characterize the size of linear chains. < 2>≡< 2 > 1. 1
For an ideal chain, this value is proportional to the product of the number of bonds (N) and the square of the monomer length b (or Kuhn length) such that: < 2>= ² 1. 2
In the case of an ideal linear chain, the radius of gyration Rg also scales directly with b²N.
The particular origin of their elasticity is first detailed, and its implication on unentangled and entangled polymer melts are then presented.
Thermodynamics of rubber (entropic elasticity)
The first law of thermodynamics states that for a transformation in any closed system, the change in energy is equal to that exchanged with the surrounding environment by thermal transfer (heat) and by mechanical transfer (work). The change in internal energy may therefore be written as: =−+ 1. 3
With T the temperature, S the entropy, p the pressure, V the volume, f the force for deformation and L length of deformation. TdS represents the heat added to the system, (-pdV) the work done to change the network’s volume and fdL the work done upon network deformation.
In typical crystalline solids the energetic contribution dominates due to the increase in internal energy when crystalline lattices are distorted from their equilibrium position. In an ideal rubber network above Tg, there is no energetic contribution to elasticity, i.e. fE=0. In rubbers, the entropic contribution to the force is more important than the energetic one. This entropic elasticity explains their very particular mechanical properties in which the equilibrium states corresponds to the chains’ maximal entropy. When stressed, chains unfold to a great extent and thus decrease the system’s entropy ( ) < 0. As soon as the stress is removed, the chains , tend to come back to their initial equilibrium state. Whereas for typical crystalline solids the force decreases weakly with increasing temperature, equation 1. 8 shows that for elastomers the force increases with increasing temperature.
Rubber elasticity in a crosslinked network
The simplest model to account for this elastic deformation is the affine network model, which states that the relative deformation of each network strand is the same as the macroscopic deformation imposed on the whole network. Indeed, the overall network is stretched with the same λ coefficients (in the three space directions) as each molecular strand (see Figure 6), and the entropic change due to the network’s deformation is therefore the sum of all entropic contributions for the polymer strands.
Figure 6 Each network strand adopts the relative deformation of the macroscopic network. Picture from [4]
From 1. 4, the force required to deform a network is the rate of change of its free energy with respect to its elongational deformation. As enthalpic contributions may be ignored, the change in the materials free energy is considered to be only due to entropic changes. Due to elastomers’ incompressibility, deformation occurs at constant volume, and a relation for the evolution of stress σ with deformation is proposed:
The shear modulus G is then expressed as: = == 1. 10
With ρ the network’s density, M the average molar mass of a network strand and R the gas constant. This relation confirms that the modulus increases with temperature and shows that it increases linearly with the number density of strands.
Entangled rubber elasticity
In the above presented affine network model, the ends of each network strand are fixed in space and cannot fluctuate. In real networks of long polymers, since chains cannot cross one another, they impose topological constraints to their neighbors. These constraints are called entanglements, and Edwards proposed the tube model to account for the collective effect of all surrounding chains on a given polymer strand. The idea of such a model is to replace the network strand by an entanglement strand- which corresponds to the part of polymer in between two entanglement points- and therefore to deduce an expression for the rubbery plateau modulus of high molar mass, entangled, polymer melts:
With Me the molar mass between two entanglements such that Me=NeMo, with Ne the number of monomers (of molar mass Mo) in an entanglement strand.
Strain hardening
At high deformations, due to the chains finite extensibility, it is harder to stretch the material and a strain hardening, i.e. an increase in the measured stress at high strains, is measured. This force divergence (see Figure 9) occurs when the crosslinks strands approach their limiting extensibility. Another possible source of hardening in some network is the stress-induced crystallization.
It is now interesting to investigate the different tools available to characterize and model the mechanical behavior of elastomers.
Dynamics of viscoelastic materials
Introduction to linear viscoelasticity
Materials deform upon stressing, and the extent of this deformation may be predicted. In the hypothesis of small deformations, two extreme cases are considered. The first one is that of an elastic solid, determined by Hooke’s law. In an isotropic material, the strain σ is directly linked to the deformation Ɛ by a linear law: = ∗ Ɛ 1. 12 where E is the Young’s modulus of the material.
The other case is that of a Newtonian liquid, in which the stress is not linked to the strain, but to the strain rate Ɛ̇: = ∗ Ɛ 1. 13 with η the viscosity of the liquid.
Polymers usually do not show these limiting behaviors, but rather an intermediate one, called viscoelastic. A macroscopic picture of the mechanical behavior of viscoelastic materials is suggested in Figure 10 (left). When stressed, such materials are able to store and return some energy (called “elastic” or “stored” energy), but a certain amount of the total work done on the system is lost (“dissipated” energy).
This behavior is described phenomenologically with several models, such as Maxwell’s and Kevin-Voigt’s model, and lead to the determination of a unique relaxation time = ⁄ with G the modulus of the material. Yet polymers do not show a unique relaxation time but rather a distribution of relaxation times. The Boltzmann principle states that the response of a material to different loadings is the sum of each individual loading, and may be used to predict the relaxation times of a material. A sinusoidal stress is imposed and the polymer’s response is studied. The sinusoid’s frequencies are assumed to be directly linked to the relaxation times.
Let us consider a deformation Ɛ(t) = Ɛo cos(ωt), and a resulting stress σ(t) = σocos(ωt + δ), with a pulsation ω and a phase difference δ. The elastic response of a solid does not cause any phase shift (δ=0), whereas in the case of a Newtonian liquid a phase delay is probed δ=π/2. For viscoelastic materials, an intermediate behavior exists such that 0 ≤ δ ≤ ᴨ/2, and the resulting stress has a component in phase with the deformation (elastic behavior), and one in phase quadrature (viscous behavior). The overall stress is therefore sinusoidal but out-of-phase regarding the original deformation. The complex shear modulus is defined as ∗ = ′ + ′′, with G’(ω) the elastic modulus – characterizing the stored (and restored) energy during each cycle- , and G’’(ω) the loss modulus characterizing the dissipated energy.
Due to the viscoelastic behavior of polymers, these moduli are strongly time and frequency-dependent, and the effect on the macroscopic properties of these materials is illustrated in Figure 10 (right). The study of the time-dependent relaxation processes is presented in the next paragraph for unentangled and entangled systems.
Unentangled polymer dynamics (M<Me)
When the polymer melt’s molar mass M is lower than its mass between entanglements Me (M<Me), the system is considered as unentangled, and its dynamics are described by the Rouse model. The Rouse time τR is defined as the longest relaxation time of the chain, and scales as = ²⁄ 1. 16 with Rg the radius of gyration of the chain, D the diffusion coefficient, Nζ is the total friction in the chain and kT thermal energy.
Where τ0 is the microscopic relaxation time of a Kuhn segment (~10-10s), and b the Kuhn length.
For times shorter than the Rouse relaxation time, for τ0 < t < τR, some parts of the chains are able
to relax on their own. The unrelaxed segments contribute to the modulus with an energy kT and lead to a scaling of the modulus with frequency ω
Entangled polymer dynamics (M>2Me)
From the tube model introduced in 1.2.3, De Gennes [5] and Doi & Edwards [6] proposed a description of the relaxation of entangled chains in the restricted tube: the reptation process. The idea of such a representation is that for a polymer chain to relax from its initial state, it has to find a way out of the tube.
At short times, the polymer chain does not feel the effect of the tube, and the segments between two entanglements (called “entanglement strand”) of Ne monomers relax following the Rouse dynamic of unentangled chains with the relaxation time τe, such that from equation 1. 18:
At long times, reptation, which is the diffusion of the whole chain over the length L of the tube, takes place, with a characteristic time called the reptation time τREP. In Figure 11, the red polymer chain has to disentangle from other chains which act as temporary obstacles. τREP is the longest relaxation time and is sometimes referred to as τD (terminal relaxation time): = 2 ∝ 3 1. 24 with N the polymerization index and D the diffusion coefficient. In fact, whereas theoretically τREP scales as M3, experiments measured a dependence as M3.4 [4].
At intermediate times, if entanglements are considered as fixed in time, a rubbery plateau for which G’ remains constant is probed, and the expression of Ge was given earlier (see equation 1. 11).
Rheology of entangled polymer melts
All these characteristic timescales can be experimentally determined using linear rheology. For some polymers, a general equivalence has been observed between the response to stress at low temperature and to that at high frequency (or short times). Similarly, an equivalence between the response at high temperature and that a low frequency (long times) is observed. This Time-temperature principle is true only in systems where the relaxation processes all vary with the same temperature-dependency. If so, it is possible to probe the mechanical response of a material at different temperatures and to draw a unique frequency-dependent master curve at a given temperature. This concept will be further detailed in the next chapter. Figure 12 plots, at 25°C, the storage and loss modulus G’ and G’’ as a function of reduced frequency and shows all the above-mentioned relaxation times of 1,4-polybutadiene [7].
Table of contents :
GENERAL INTRODUCTION
CHAPTER 1 – From molecular dynamics to strong self-adhesion properties
1 Elastomers and their molecular dynamics
1.1 Processing and key properties of elastomers
1.2 Physics of rubber elasticity
1.3 Dynamics of viscoelastic materials
2 Introduction to the adhesion of soft materials
2.1 Adhesive performance of soft materials
2.2 Macroscopic characterization of adhesion
2.3 Comments
3 Formation of a strong interface
3.1 Molecular theories
3.2 Formation of intimate contact
3.3 Polymer interfaces between polymer melts
4 Energy dissipation as key to boost adhesion strength
4.1 Introduction to debonding in soft materials
4.2 Predicting debonding mechanisms from linear rheology
4.3 Non-linear fibrillation
4.4 End of the story: final detachment
5 Effect of molar mass on adhesion
6 Nitrile Butadiene Rubber (NBR)
6.1 Introduction to poly(acrylonitrile-co-butadiene)
6.2 Adhesion and self-adhesion properties of NBR
7 Conclusion
8 References
CHAPTER 2 – Characterization of nitrile rubber
1. Material characterizations
1.1 Average molecular weight
1.2 Acrylonitrile content
2. Characterization of mechanical properties
2.1 Linear rheology
2.1 Uniaxial tensile tests
3. Characterization of adhesion properties
3.1 Choice of the characterization method
3.2 Probe-tack tests
3.3 Samples’ preparation
3.4 Self-adhesion properties
4. Conclusions and discussion
4.1 Discussion
4.2 Conclusions
5. References
CHAPTER 3 – NBR as supramolecular rubber
1. Supramolecular behavior of NBR
1.1. Ageing of the materials at room temperature
1.2. Dissolution of NBR in a solvent to accelerate ageing process
1.3. Conclusions
2. Study of structure formation in NBR
2.1. Literature
2.2. X-Ray Scattering
2.3. Atomic Force Microscopy
2.4. Transmission Electron Microscopy
2.5. 1H NMR study
2.6. Conclusions and discussion
3. “Self”-adhesion properties
3.1. Literature on block copolymers
3.2. Influence of NBR structure on its self-adhesion properties
3.3. Self-adhesion properties of freshly extruded NBR
4. Conclusions
5. References
CHAPTER 4 – Influence of tackifiers on the self-adhesion of nitrile rubber
1. Literature on the blending of tackifiers
1.1. General picture
1.2. Influence of the nature and the amount of tackifier
1.3. Additives in phase-separated materials
1.4. Conclusion and discussion
2. Introduction
2.1. Materials
2.2. Sample preparation
2.3. Objectives
3. Blending of 3% tackifier in NBR
3.1. Self-adhesion properties
3.2. Bulk properties and structure
3.3. Conclusion and discussion
4. Blending of a high tackifier content in NBR
4.1. Self-adhesion properties
4.2. Properties of the high concentration blends
5. Conclusion
6. References
CHAPTER 5 – Surface effects on the self-adhesion of nitrile rubber
1. Introduction to solvent welding
1.1. Literature
1.2. Methods
2. Influence of solvent welding on the adhesion and adhesion of NBR
2.1. Adhesion of welded NBR on glass
2.2. Self-adhesion of welded NBR
3. Influence of the solvent
3.1. Presentation of the different solvents
3.2. Influence of solvent’s quality for the polymer
3.3. Importance of solvents’ vapor pressure
3.4. Site-specific swelling for welding
3.5. Influence of the dipole moment
3.6. Conclusions
4. Effect of microstructure on solvent-welded NBR
4.1. Introduction
4.2. Influence of microstructure of self-adhesion of NBR
4.3. Conclusion
5. Influence of drying conditions
5.1. Effect on the self-adhesion properties
5.2. Investigations
5.3. Discussion
6. Conclusions
7. References
CHAPTER 6 – First insights into PVC-blended nitrile rubbers (NBR/PVC)
1. Literature: Blending of PVC in NBR
1.1. Introduction to NBR/PVC
1.2. Composition-dependent properties
1.3. Nanoscale heterogeneity
2. Samples preparation and characterization
2.1. Blends preparation
2.2. Mechanical properties of NBR/PVC blends
2.3. Structural organization
3. Self-adhesion properties of NBR/PVC
3.1. Samples’ preparation
3.2. Influence of contact time on the self-adhesion properties of NBR/PVC blends
3.3. Solvent welding to enhance self-adhesion properties
3.4. Conclusions and discussion
4. Addition of tackifiers to NBR/PVC
4.1. Self-adhesion properties of NBR/PVC with tackifiers
4.2. Mechanical properties of NBR/PVC with tackifiers
4.3. Discussion
5. General conclusions and discussion
6. References
CONCLUSIONS AND PERSPECTIVES
ANNEXES
