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Chemistry and physics of crosslinked elastomeric networks
Synthesis of permanent polymeric networks
A polymeric network is a set of macromolecules that are linked together to form a three-dimensional structure. The term “permanent” means that the attachment points cannot break and reform in normal use conditions. The most basic way to do so is to link the chains with covalent bonds, in which case the final material is a thermoset.
There are basically two ways to prepare a chemically-crosslinked polymer network (see Figure 1). The first and simplest is to polymerize and crosslink the material at the same time by using a mix of mono and multi-functional monomers. The second consists in polymerizing the chains, and then couple them in a second step to get a three-dimensional network. In some specific cases, a combination of the two previous routes may also be needed.
The simultaneous route: kinetics matters
The major advantage of this strategy is its simplicity, which comes at the expense of the control of the final architecture. Since the main monomer and the bifunctional crosslinking agent are polymerized at the same time, the final structure strongly depends on the details of the polymerization reaction.
Thermosets can be made by free radical polymerization. The network formation mechanism may roughly be described by three steps [2] (see Figure 2):
• First, the initiator decomposes and reacts with mono or multifunctional monomers (crosslinkers). Since the chains are diluted in the reactive medium, most of crosslinkers react in intramolecular reactions leading to chains with loops and defects.
Figure 1: schematic representation of network formation strategies. Blue circles represent monomers. Top: simultaneous route, light blue circles represent bifunctional monomers. Bottom: sequential route, red circles are reactive comonomers that are incorporated in the polymer chains during polymerization and then reacted together to give crosslinks (green circles).
Figure 2: schematic representation of the gelation process in free radical polymerization. In the first stage, only intramolecular crosslinking occurs. In the second stage, microgels are formed. In the third stage, microgels are connected to yield the networks
• As the reaction proceeds, the polymer concentration increases and chains start overlapping. Intermolecular reactions become possible and crosslinked microgels form.
• When the polymer concentration is high, microgels start to entangle and connect with each other with their remaining pendent reactive groups. At this stage, a network is formed and keeps densifying as the reaction continues
This mechanism obviously leads to networks that are intrinsically poorly defined. Other factors may add up and impair the network ideality.
• First, the presence of two reactive groups makes the crosslinker roughly twice as reactive as a monomer, even if the functional groups are the same. The crosslinker is thus mainly incorporated in the first stages of the reaction leading to a heterogeneous distribution of crosslinker molecules in the final material.
• Second, different functional groups lead to differences in terms of kinetics of polymerization. This may be anticipated by studying the values of reactivity ratios [3] defined as follows:= / Eq. 1 where is the rate propagation constant of the reaction of monomer with monomer .
Based on the knowledge of the 4 propagation constants, several situations may occur, as shown in Table 1. In most cases however, the precise knowledge of reactivity ratios is not necessary since monomers from the same family (acrylates for example) usually exhibit reactivity ratios close to 1 [3,4].
• Third, when polymerization is performed without a large excess of solvent, transfer reactions occur and bring another level of complexity to the final macroarchitecture [5].
To sum up, the simultaneous route involves the polymerization of the network chains at the same time as their crosslinking. The resulting network necessarily contains defects for kinetic reasons and the final molecular architecture is thus heterogeneous.
The sequential route: chemistry matters
By opposition to the simultaneous route, the sequential route involves the synthesis of the polymer chains first, and then their coupling in a second separate step. This second step may have different names depending on the type of chemistry: crosslinking, curing, vulcanization, etc.
Although the simultaneous route is arguably more straightforward, the sequential route is usually applied in the rubber industry. In the case of unsaturated polymers in particular, the polymer chains contain reactive double bonds that can easily be reacted with sulfur (i.e. by vulcanization, as originally patented by Goodyear [6]) or peroxides [7].
Saturated chains like polyacrylates are more complicated to handle since usual crosslinking agents are not effective on the pristine polymer [8]. It is thus necessary to use comonomers to incorporate new reactive groups in the polymer chains in order to react them together in the second stage, using a crosslinking agent. Table 2 shows some traditional couples of comonomers and crosslinking agents that are used in the literature [8–11]. Note that the sequential route does not completely avoid kinetic issues since the way the comonomer incorporates strongly impacts the final material architecture.
More original strategies may be used to crosslink saturated polymer chains. For instance, the thiol-ene reaction is frequently encountered in the field of polymer chemistry [12,13]. This reaction enables the direct connection of double bonds that may be incorporated in the polymer backbone, using comonomer like allyl methacrylate [14,15]. Another interesting strategy consists in tethering a photoinitating group to the polymer backbone [16]. These units may then be activated by UV light and lead to crosslink points, either by hydrogen abstraction or direct coupling to another unit.
The sequential route therefore gives a lot of control to the polymer scientist provided the right chemical system can be found. The success of this approach relies on the choice of the adequate chemical reaction, comonomer, initiator and formulation. Better control usually means more complexity in the synthesis.
The mixed route using dual-curing systems
In some cases it becomes interesting to first prepare a crosslinked network, and then crosslink it further in a second separate step. This synthetic strategy may be called a “dual-curing system”, i.e. a chemical system that enables one to cure the material twice in two separate steps.
Typical dual-cure mechanisms rely on reactions that are different in nature. The first reaction may for instance be cationic polymerization and the second one radical, or vice versa. First examples in the literature make use of the difference in reactivity of vinyl and acrylate carbon-carbon double bonds [17,18]. In the late 20th century, Decker and Decker studied a mixture composed of vinyl ethers and acrylates with radical and cationic photoinitiators [19]. They demonstrated a dual-cure behavior by first activating the radical initiator and then the cationic one using two different UV wavelengths.
The idea of using two different reactions was also exploited using epoxies for the cationic reaction, using either a radical and a cationic initiator [20], or only a cationic initiator since the latter also generates free radicals when there are hydrogen donor molecules nearby [21–23]. In the field of adhesives, Kim’s group published a series of papers about epoxy-acrylate dual-curable pressure-sensitive adhesives [24,25]. Figure 3 gives a schematic representation of their system: acrylate functions are reacted in a first step, and epoxy functions are then reacted either together or with a carboxylic counterpart in a second cationic step.
Interestingly, the series of papers from Kim’s group began with a dual-cure mechanisms relying on largely different chemistries (see Figure 4) [26]. In a first step, a copolymer comprising benzophenone (a photoinitiating unit) and alcohol pendent groups was synthesized and isolated. The copolymer was then coated with a multifunctional isocyanate and UV-cured to crosslink the benzophenone groups. In a third step, the material was heated up to 60°C for 6 hours to react the isocyanate with alcohol groups. In this paper, the authors demonstrated that the two steps are well-separated but also reported a large decrease in the extent of reacted benzophenone groups with thickness.
Figure 3: simplified picture of the mechanism used by Kim et al. for the synthesis of dual-curable adhesives. Red dots represent epoxy functions and green dots represent acrylate functions. Initiator and curing agent are not represented. Also, the initial composition includes a triacrylate which react in the first step to bring additional crosslinks in the system.
More recent studies about dual-cure systems involving radical and cationic reactions are based on “click” chemistry [27], in link for instance with applications in shape-memory materials [28,29]. The aza-Michael addition between acrylates and amines may also be used. The main advantage of this reaction is that it proceeds at room temperature in oxygenated conditions without the use of any catalyst [30].
From these examples from the literature (summarized in Table 3), two general rules of thumb may be identified for efficient dual-curing systems. First, the two steps should rely on very efficient chemical reactions. For this, click chemistry is a great help and extensively used in the recent literature. Second, the two stages should be as well separated as possible, ideally using orthogonal chemistries in order to avoid any interference between the two reactions.
All these synthetic strategies make a toolbox the chemist can use to prepare covalently crosslinked networks. Knowing the details of the preparation process is a key to precisely understand the final material properties. The next section will now focus on mechanical properties and how to relate them to the details of the molecular architecture.
From chain physics to network properties
Polymeric materials are used in a large variety of applications because of their original mechanical properties. These properties stem from the basic physics of polymer chains, and several models have been developed throughout the years to understand the behavior of polymeric networks. These topics are extensively covered in a reference textbook from Colby and Rubinstein that is used throughout this part of the chapter [42].
In this part, the physics of isolated polymer chains is first reviewed. From this basis, the mechanical properties of polymeric networks are modelled. Most basic models are useful since they contain all the physics of the problem, but they can also be refined to take more aspects of polymer mechanics into account.
Physics of isolated polymer chains
A polymer chain is described as an assembly of C-C bonds of length C-C, as depicted in Figure 5. The most obvious characteristic length that comes in mind is the contour length of the chain: = C-C C-C Eq. 2
This length represents the maximum size of the chain if all monomers were perfectly aligned. In practice, the maximum size of a chain is smaller than because the valence angle between consecutive monomers is fixed by quantum mechanics rules. Introducing the tetrahedral angle (see Figure 6), the maximum size of a chain is given by Rmax = cos C-C C-C Eq. 3
For instance, in many usual polymers (polystyrene, polyacrylates, polyethylene to name only a few), the backbone of the chain is made of carbon-carbon bonds with hybridization states sp3. In these conditions, the valence angle is 109.5° and max = 0.82 .
Figure 6: schematic representation of the maximum size of a polymer chain with fixed valence angle. is the tetrahedral angle.
A fundamental characteristic length of a polymer chain is the average end-to-end distance, which represents the average size of the chain at rest. In short, a polymer chain may be described as a random walk, possibly with constraints between adjacent monomers. In the case of ideal chains made of independently-linked segments (which is a very common assumption in the study of polymeric materials), it is given by 0 = ee = ∞ C-C C-C Eq. 4 where ee is the end-to-end vector (see Figure 5) and ∞ is the structure factor of the chain, a coefficient greater than 1 that quantifies how extended is the chain compared to a perfectly random walk.
In between 0 and max, a polymer chain may be partially extended by applying a force (as in Figure 5). Contrary to crystalline materials like ceramics or metals, deforming a polymer chain does not require to break any bond. Instead, the chain unfolds and changes conformations, which implies a much lower energetic cost. This explains why polymeric materials are so easy to deform compared to crystalline materials. For ideal chains and low deformations, the relationship between the end-to-end vector and the force applied to the chain is given by = ee Eq. 5
where is the force applied, is the Boltzmann’s constant and is the absolute temperature. This linear equation is the molecular equivalent of Hooke’s law: a polymer chain behaves like a spring with increasing stiffness when either the temperature increases or the number of monomer decreases.
Assembly of chains and network elasticity
The physics of an assembly of chains ensues from the physics of isolated chains. In order to scale up from the chain to the network, the key question to address is how the chains are connected together. The links may be well defined as when chains are crosslinked, or more subtle as when molecular friction is considered.
Viscosity and molecular friction
In the absence of solvent, polymer chains may exert friction forces onto each other. The magnitude of the friction forces depends on the temperature and on the speed at which the chains deform. This dependence leads to the concept of glass transition temperature , which is basically the temperature below which polymer chains do not have enough thermal energy to move and overcome the friction forces. An easy way to visualize the viscoelastic nature of an assembly of polymer chains is to deform it periodically and measure the resulting force or vice versa. The resulting modulus ∗ may be decomposed in a real part ′ called the storage modulus and an imaginary part called the loss modulus. The ratio between the two is called the loss tangent and represents the fraction of energy dissipated in the material at a given time and frequency. Figure 7 shows the viscoelastic spectrum of a typical polymer network, which may be roughly decomposed in three regions.
– Below , the network behaves like a rigid glass and cannot be deformed easily. The modulus is high (about 1 GPa) and the structure is frozen.
– In the other extreme case, well above , friction forces are so low that they may be neglected. The material is rubbery, fully elastic, and the material behaves like a fluid at long times unless the chains are somehow attached together. The modulus is much lower (about 1 MPa).
– In between these two extreme cases, the chains may move but their motion is partially constrained. As a result, a significant part of the elastic energy that is brought to the material is dissipated.
The presence of viscoelasticity therefore strongly impacts the way the material behaves. The description of the behavior of a material in the transition region is not an easy task. The description of structure-relationship properties in the rubbery region however is much easier, which makes elastomers well above their good model materials for academic studies. It is important however to keep in mind that most industrial elastomers are actually viscoelastic, since it is a very efficient way to tune their properties and in particular their resistance to fracture, as explained later.
Table of contents :
General introduction
Chapter 1: From chemistry and physics to the design of new double network elastomers
1. Introduction
2. Chemistry and physics of crosslinked elastomeric networks
2.1. Synthesis of permanent polymeric networks
2.2. From chain physics to network properties
3. Fracture of soft materials and how to reinforce them
3.1. Description of fracture in soft materials, a matter of dissipation
3.2. General guidelines for improving the fracture resistance of soft materials
4. The multiple network strategy: from the original concept to new properties
4.1. Double network hydrogels
4.2. From hydrogels to elastomers
4.3. The challenge of describing the reinforcing mechanism theoretically
4.4. Toward new properties for multiple network elastomers
5. Bringing anisotropy to double network elastomers
5.1. Example of anisotropic polymeric systems
5.2. Oriented chains in rubbers, a key element for some applications
5.3. Battle plan, or how to make double networks anisotropic
6. Conclusions
7. References
Chapter 2: Design and preliminary study of two effective dual-curing systems
1. Introduction
1.1. Overview of the requirements specifications
1.2. Presentation of the thermal system
1.3. Presentation of the UV system
1.4. Outline
2. Generalities about chemistry and material preparation
2.1. Chemicals and formulation
2.2. Materials synthesis
2.3. Characterization methods
3. Study of the thermal system
3.1. A kinetic study of the system
3.2. Variation of the initial formulation
3.3. Partial conclusion and identification of a working point formulation
4. Study of the UV system
4.1. Effect of crosslinker content
4.2. Effect of initiator content
4.3. Effect of allyl acrylate content
4.4. The issue of sample-to-sample variability
5. Conclusions
6. References
Chapter 3: Application of the dual-cure systems to the preparation of prestretched filler networks
1. Introduction
2. Preparation process
2.1. Initial network formulations
2.2. Prestretching and second curing
2.3. Problems encountered during the thermal second curing
3. Preparation of prestretched samples and measurement of prestretching
3.1. Presentation of the results
3.2. Comparison to Flory’s model
3.3. Additional mechanical characterization for the thermal system
4. Prospective: what to expect in a double network structure?
4.1. Description of the approach
4.2. Derivation of the model
5. Conclusions
6. References
Chapter 4: Incorporation of prestretched filler networks into double network structures
1. Introduction
2. Preparation process and additional characterization tools
2.1. Filler networks
2.2. Preparation of double networks
2.3. Step-cyclic tests
2.4. Fracture tests
3. Study of two examples of prestretched DN
3.1. Relative changes in dimensions
3.2. Mechanical characterization
3.3. Toward a more detailed characterization?
3.4. Partial conclusion
4. Systematic study of the UV system
4.1. Identification of typical trends and odd ones
4.2. Study of unprestretched double network samples
4.3. Study of prestretched DN using envelope curves
4.4. Exploitation of the entire cyclic test
4.5. Suggested physical picture
5. Influence of damage on mechanical properties for the UV system
5.1. Study of viscoelastic properties
5.2. Study of fracture properties
6. Conclusions
7. References
Chapter 5: Toward glassy filler networks
1. Introduction and context
2. Materials preparation and characterization
2.1. Overall presentation of the preparation strategy
2.2. Materials preparation
2.3. Dynamic Mechanical Analysis
2.4. Tensile tests
3. Results regarding the materials preparation
3.1. Overall overview of the synthesis
3.2. Quantitative parameters associated to synthesis
4. DMA characterizations
4.1. Effect of the nature of the crosslinker
4.2. Effect of crosslinker content / UV synthesis / BDMA crosslinker
4.3. Effect of initiation type
5. Tensile characterizations
5.1. UV-polymerized DN with 0.75mol% BDMA
5.2. UV-polymerized DN with 1.5 mol% BDA
6. Conclusions
7. References
General conclusions and prospects
