Upps al a univ ersit ets l ogot yp
UPTEC F 21031
Examensarbete 30 hp Juni 2021
Lifetime prediction of a
polymeric propellant binder using the Arrhenius approach
A thesis about polymer degradation Johannes Bohlin
Civilingenj örspr ogrammet i t ek nisk fysik
Teknisk-naturvetenskapliga fakulteten Uppsala universitet, Utgivningsort Uppsala/Visby
Handledare: Fritjof Nilsson, Carina Eldsäter Ämnesgranskare: Håkan Engqvist Examinator: Tomas Nyberg
Upps al a univ ersit ets l ogot yp
Lifetime prediction of a polymeric propellant binder using the Arrhenius approach
Johannes Bohlin
Abstract
The thermal-oxidative degradation of a crosslinked hydroxy-terminated polybutadiene (HTPB) /cycloaliphatic diisocyanate (H12MDI) based polymer, which is commonly used as a polymeric binder in propellants, is investigated at temperatures from 95°C to 125°C with the aim of estimating the lifetime of the material in storage conditions (20°C) using the Arrhenius approach. Furthermore, the effect of antioxidants and to a lesser extent plasticizer on the degradation process was also studied. Diffusion-limited oxidation (DLO) was theoretically modelled and DLO conditions were estimated by gathering oxygen permeability and
consumption data from similar studies. It was concluded that DLO-effects might be present at the highest experiment temperature (125°C) depending on the actual properties of the material investigated. The mechanical degradation was monitored by conducting tensile tests in a DMA apparatus and photographs using a microscope was taken to examine potential DLO effects.
The degradation process of the stabilized polymer (with antioxidant) did not showcase Arrhenius behaviour, which was confirmed by the failure to construct a satisfactory master curve. This was most likely due to loss of antioxidants, resulting in autocatalytic oxidation (acceleration of the oxidation process). However, the induction period of the stabilized polymer showcased Arrhenius behaviour in the temperature region 95-125°C with an ~E_a = 90 kJ/mol.
If the activation energy E_ai s assumed to remain constant, the lifetime at ambient temperature (20°C) is predicted to be approximately 176 Years for a 2mm thick sample. However, this is probably an overestimation since curvature in the Arrhenius plot has been observed for many rubber materials in the lower temperature region. Assuming the E_a drops from ~90 kJ/mol to
~71 kJ/mol, a more conservative lifetime prediction of 58 Years was estimated.
Tek nisk-nat urvetensk apliga f ak ulteten, Upps ala universit et . Utgiv nings ort U pps al a/Vis by . H andledare: Fritjof Nilsson, Cari na El dsäter, Äm nesgranskar e: H åk an Engqvist, Ex aminat or: T om as Ny berg
Popul¨ arvetenskaplig sammanfattning
I moderna kompositkrut ¨ar den energetiska materialkomponenten bunden i ett polymert matrismaterial.
Detta g¨or krutet mer elastiskt och d¨armed reducerar risken f¨or sprickbildning i materialet. Sprickor i materialet ¨okar dess area vilket resulterar i att krutet brinner snabbare, och eftersom trycket beror p˚a brinnhastigheten kan detta leda till att raketmotorn exploderar. Ett problem med att anv¨anda poly- merer ¨ar att de ˚aldras och med tiden f˚ar gradvis f¨ors¨amrade mekaniska egenskaper. F¨or att kunna undvika stora explosionsartade olyckor, ¨ar det d¨armed av central betydelse att kunna f¨oruts¨aga hur grava ˚aldringseffekterna blir efter en viss tids f¨orvaring med k¨anda lagringsbetingelser.
I detta projekt unders¨oktes den termo-oxidativa nedbrytningen av ett tv¨arbundet hydroxylterminerat polybutadien (HTPB) / cykloalifatiskt diisocyanat (H12MDI) baserat polymer, som vanligtvis anv¨ands som ett polymert bindemedel i kompositkrut. Diffusionsbegr¨ansad oxidation (DLO), vilket ¨ar motsvarigheten f¨or ytlig korrosion f¨or polymerer, modellerades teoretiskt och DLO-villkor uppskattades genom att samla parameterv¨arden fr˚an liknande studier. Baserat p˚a detta kunde slutsatsen dras att DLO-effekter kan f¨orekomma vid ˚aldringsexperiment vid h¨oga temperaturer (∼ 125◦C) beroende p˚a de faktiska egenskaperna hos det unders¨okta materialet. Vidare utf¨ordes praktiska accelererade degraderingsex- periment vid f¨orh¨ojda temperaturer fr˚an 95◦C till 125◦C i syfte att uppskatta materialets livsl¨angd under lagringsf¨orh˚allanden (20◦C) genom att extrapolera resultatet med hj¨alp av Arrhenius-metoden (t ∼ exp(−ERTa)). Den mekaniska nedbrytningen med tiden unders¨oktes genom att kontinuerligt utf¨ora dragprov i en DMA-apparat och fotografier med ett mikroskop togs f¨or att unders¨oka potentiella DLO- effekter. Nedbrytningsprocessen f¨or prover med antioxidanter uppvisade inte beteende enligt Arrhenius ekvation, vilket bekr¨aftades av misslyckandet att konstruera en tillfredsst¨allande “Master curve”. En ty- dlig induktionsperiod observerades i degraderingsprocessen, vilket k¨annetecknas som en pl¨otslig markant f¨or¨andring i egenskaper efter en relativt l˚ang period med inga st¨orre f¨or¨andringar i egenskaper. Detta
¨
ar troligen resultatet av fullst¨andig konsumtion av antioxidanter i materialet, vilket ger upphov till autokatalytisk oxidation (acceleration av oxidationsprocessen). Induktionsperioden f¨or de stabiliserade proverna (med antioxidanter) visade emellertid beteende enligt Arrhenius ekvation i temperaturomr˚adet 95 − 125◦C med en ∼ Ea = 90 kJ/mol. Om aktiveringsenergin Ea antas f¨orbli konstant f¨orv¨antas livsl¨angden vid rumstemperatur (20◦C) vara cirka 176 ˚ar f¨or ett 2mm tjockt prov. Detta ¨ar dock troligtvis en ¨overskattning eftersom f¨or¨andring av aktiveringsenergin har observerats f¨or m˚anga gummi- material i den l¨agre temperatur regionen. Om vi antar att Easjunker fr˚an ∼ 90 kJ/mol till ∼ 71 kJ/mol, uppskattas ist¨allet en mer konservativ livstidsl¨angd p˚a 58 ˚ar.
Acknowledgements
First and foremost, I would like to thank my supervisors, Fritjof Nilsson from KTH and Carina Elds¨ater from the Swedish Defence Research agency (FOI), for continuous support throughout the work on this thesis. I am grateful for your constructive criticism and for always being interested in the project and its development.
My gratitude is extended to everyone at FOI stationed at Grindsj¨on, in particular Viktor Bladholm, for patiently helping me conduct the aging experiments, and for providing me with a great work environment despite an ongoing pandemic.
I would also like to acknowledge H˚akan Engqvist as the subject reader of this thesis. Fast and clear responses have been highly appreciated.
Finally, I want to thank my wonderful sister, Sarah, for always being there for me and helping me improve my academic writing throughout my time at the University. Thank you.
Contents
1 Introduction 6
1.1 Background . . . 6
1.2 Objective . . . 6
2 Theory 7 2.1 General mechanism of thermal degradation . . . 7
2.2 Dynamical mechanical analysis . . . 7
2.3 Time-temperature superposition principle . . . 8
2.4 Theoretical modelling of polymer oxidation . . . 9
3 Method/Experimental 10 3.1 Material . . . 10
3.2 Dynamical mechanical analysis . . . 10
3.3 Thermal aging in oven . . . 10
3.4 Thermal aging in DMA machine . . . 10
4 Theoretical estimation of lifetime expectancy 12 4.1 Solubility and Diffusivity . . . 12
4.2 Reaction term β . . . 12
4.3 Oxidation rate φ . . . 12
4.4 Sample thickness L . . . 13
4.5 Effect of antioxidant on degradations . . . 14
4.6 Oxidation profiles. . . 14
4.7 Coupling oxidation with mechanical degradation . . . 16
4.8 Preliminary lifetime prediction . . . 16
5 Result and Discussion 17 5.1 Color changes . . . 17
5.2 Potential diffusion-limited oxidation . . . 19
5.3 Degradation of unstabilized polymers. . . 21
5.4 Degradation of stabilized polymer. . . 22
5.5 Lifetime prediction using Arrhenius methodology . . . 25
6 Conclusion 26
7 Future work 27
1 Introduction
1.1 Background
In modern composite propellants, the energetic material component is bound in polymeric materials in order to reduce the risk of cracks in the propellant by having an elastic propellant. Formation of cracks result in a sudden increase in burning surface, which in turn can cause the rocket engine to explode since the pressure depends on the burning rate. However, as polymers age and over time gradually deteriorate, these important elastic properties may alter. Therefore, it is of great importance to be able to model and predict the effect of aging in an environment with known storage conditions.
The degradation of polymers can be induced by either heat (thermal-degradation), oxygen (thermal- oxidative degradation), light (photodegradation) or weathering (UV/Ozone degradation) [1]. Additional mechanisms sometimes also exist, for instance radiation induced degradation, biodegradation, etc. For most polymers in oxygen-containing environments, thermal-oxidation is the dominant factor in aging and oxidative degradation will either cause the polymer to harden or soften [2]. The material hardens when free radicals, produced by heat or light, combine and form new crosslinks. Conversely, softening is the result from chain scission caused by disproportionation and hydrogen abstraction. Whether or not the polymer hardens or softens depends on which process predominates, which in turn depends on the microstructure of the polymer. For elastomers, hardening is much more common [3]. Although thermal-oxidation is the dominant factor in aging, the thermal-oxidative degradation process in ambient temperatures is slow, often requiring decades of degradation before mechanical property changes can be observed [4]. Thus, conducting experiments in storage conditions is often too costly and time consuming, which is why confirming such extended lifetimes requires accelerated aging approaches.
The most common approach is to conduct the experiments at higher temperatures, accelerating the oxidation process. The degradation results are then extrapolated to the ambient temperature region normally using the Arrhenius approach [5] that is supposed to reflect the temperature dependency of the chemistry underlying the degradation process. The Arrhenius methodology assumes that a chemical process governed by a rate proportional to exp(Ea/RT) underlies the degradation (Ea is the activation energy, R the gas constant and T the absolute temperature). However, this methodology can result in inaccurate results due to various potential problems. Implicit in using the Arrhenius extrapolating approach are two potentially flawed assumptions: (1) that the underlying chemical mechanisms resulting in degradation do not change with temperature, i.e. the activation energy Ea does not change in the ex- trapolation region, and (2) that the correlation between oxidation extent and mechanical properties does not depend on temperature. Another problem is the potential presence of diffusion-limited oxidation (DLO) [6, 7]. DLO occurs when the consumption of oxygen in the cross-section of the material is faster than it can be replenished by diffusion from the surrounding air atmosphere. When this is the case, the material will oxidize heterogeneously, reducing the average degradation of the material. Furthermore, the Arrhenius activation energy is typically higher for the oxidation rate than for the oxygen diffusivity [8], in other words the oxidation rate increases faster with temperature than diffusivity. This causes DLO effects to be more pronounced at higher temperatures. Therefore, DLO effects often impact accelerated exposures significantly, but may not be present under ambient conditions, making any extrapolations attempt of limited value.
1.2 Objective
This project is a collaboration between the Swedish Defence Research Agency (FOI) and the Royal Institute of Technology (KTH), and the objective of the project is to examine the degradation process of a specific polymer used as a composite propellant. By modeling and simulating the thermo-oxidative degradation process using finite element method (FEM), as well as performing practical accelerated aging experiments, lifetime estimates are calculated. Moreover, two ways of accelerating the degradation process are explored in this thesis; (1) increasing the temperature and (2), by examining the effect of antioxidants.
2 Theory
2.1 General mechanism of thermal degradation
The general mechanism of thermal degradation is often referred to as the basic autoxidation scheme (BAS) and can be divided into three stages, called initiation, propagation and termination [2]. In the first stage, the so-called initiation, free radicals are formed via C-C and/or C-H bond cleavage induced by light or heat. These reactions can be written as:
R−H → R· + H·
R−R → R· + R·
where the symbol R is defined as a generic alkyl group. The second stage, propagation, involves a number of reactions and starts with oxygen reacting with the newly formed free radical R·. This reaction forms highly reactive peroxy radicals ROO· which soon thereafter abstract a hydrogen atom from another polymer chain, resulting in a new free radical R· and a hydroperoxide ROOH.
R· + O−O· →ROO·
ROO· + RH →R· + ROOH
The abstraction of hydrogen involves breaking C−H bonds which most often requires considerable energy.
Hence, this reaction is often the rate determining step[1]. The propagation phase continues with the decomposing of hydroperoxide ROOH via homolytic cleavage to alkoxy(RO·) and hydroxy(·OH) radicals.
These two radicals, in turn, also abstract labile hydrogen from polymers which results in even more free chain radicals. Since each radical can produce two or more new radicals, the process can accelerate which is referred as autocatalytic oxidation. Whether the process will accelerate or not depends on how reactive the termination steps are relative the propagation reactions. To slow down the process and thus also inhibiting the oxidation from accelerating, antioxidants are added. They act by decomposing hydroperoxides and/or scavenging the free radicals.
ROOH → · OH + RO·
RH + RO· →R· + ROH
· OH + RH →R· + H2O
Finally, the oxidation reaction ends with the stage called termination where either two radicals recombine or a chain radical abstracts a hydrogen from another polymer chain (hydrogen abstraction/dispropor- tionation).
2 ROO· →ROOR + O2
R· + R· →R−R RO· + RO· →ROOR
R· + RO· →ROR ROO· + HO· →ROH + O2
The recombination of two radicals results in an increase in molecular weight and crosslinking density, which hardens the material. However, termination by chain scission from hydrogen abstraction or dis- proportionate results in a decrease in molecular weight, thus softening the material. Depending on which termination step is dominant will cause the polymer to either harden or soften with time.
2.2 Dynamical mechanical analysis
Dynamic mechanical analysis (DMA) is a technique used to measure the mechanical and viscoelastic properties of various materials. By applying a sinusoidal stress via one of several different deformation modes (bending, tension, shear and compression), and measuring the corresponding strain in the material, different mechanical properties can be determined. It is often used for studying the viscoelastic behavior
of polymers, since it can measure the lag δ between the strain the stress. This can be expressed as the following:
σ = σAsin(wt + δ) (1)
= Asin(wt), (2)
where σ is the stress and is the strain. In this project DMA was used in tension mode and the tensile storage E0 (representing the elastic portion) and the loss moduli E00 (representing the viscous portion) are defined as follows:
E0 =σA
A
cos δ (3)
E00=σA
A sin δ, (4)
where σAis the amplitude of the sinusoidal stress and Ais the amplitude of sinusoidal strain (seeFig. 1 for clarity). Finally, the complex modulus E∗ is defined as:
E∗= E0+ iE00. (5)
Figure 1: Visualization of a applied sinusoidal stress σ resulting in a sinusoidal deformation with lag δ.
2.3 Time-temperature superposition principle
Time-temperature superposition principle is a concept commonly used in polymer physics. It states that the change in temperature from T to T0 is equivalent to shifting the time scale by a constant factor aT, which only depends on the two temperatures T and T0. This can be mathematically formulated as
E(t, T ) = E( t
aT, T0), (6)
where E is an arbitrary mechanical property. By assuming that the property has thermorheologically simple behaviour (same relationship between temperature and time for all curves), the principle can
be used to speed up time-consuming experiments by performing experiment at higher temperatures and shifting the data back to the reference temperature. When two or more experiment conducted at different temperatures are superposed by shifting to a reference temperature, a so-called master curve has been constructed. In the field of thermal aging the construction of a master curve is also a way of investigating whether the t-T superposition is applicable [9,10]. If the data coincides well in the master curve, it gives compelling evidence that the same chemical degradation process dominates the entire temperature range of the accelerated experiments.
2.4 Theoretical modelling of polymer oxidation
Cunliffe and Davis [6] established a DLO model based on the basic autooxidation scheme described earlier, which was further refined by Gillen et.al [8]. This model states that the steady state oxidation profile in 1D can be obtained by solving the following differential equation:
d2θ
dX2 = αθ
βθ + 1, (7)
where θ is the normalized oxygen partial pressure (assuming Henry’s law is valid) and X is the normalized position. The steady-state solution depends on two parameters, α and β given by:
α = C1L2/D and β = C2Sp0, (8)
where L is the length of the sample, D and S are the oxygen diffusion and solubility parameters in the material, C1and C2are reaction rate constants based on the BAS, and p0is the oxygen partial pressure of the surrounding atmosphere. Similarly, the time-dependent oxygen concentration in a polymeric material can be expressed using Fick’s second law with a reaction term, resulting in the following diffusion-reaction equation:
∂c
∂t = ∇(D∇c) − R, (9)
where R is the reaction term and c is the oxygen concentration. For most polymers, the reaction term R is based on the BAS scheme and can be written as:
R = C1c
1 + C2c, (10)
Although this reaction term is based on simplifying assumptions that are not necessarily correct, e.g.
certain equivalence between termination reaction rates and long kinetic chain length [11], the model is able to accurately describe the oxygen behavior of a range of polymeric materials [8, 12,13]. Inserting Eq. 10in Eq. 9and using Henry’s law (c = Sp, where S is the solubility coefficient and p is the oxygen partial pressure), we get the final expression:
∂(Sp)
∂t = ∇(D∇(Sp)) − C1Sp
1 + C2Sp, (11)
with the Dirichlet boundary condition p(x, t) = p0, x ∈ ∂Ω and initial condition p(x, 0) = 0, x ∈ Ω.
3 Method/Experimental
3.1 Material
The material investigated is based on a hydroxy-terminated polybutadiene (HTPB type R45HT)/ cy- cloaliphatic diisocyanate (H12MDI) polymer. The uncured HTPB resin was provided by industry (Cray Valley via Sartomer/EURENCO Bofors) with an OH functionality of 0.82mmol/g. Depending on the ingredients included, plasticizer and antioxidants was mixed with the prepolymer under vacuum at 40◦C in a 300 ml mixer from FEMIX Gmbh, resulting in four different mixtures (see Table 1 for specifics).
Vulkanox BKF was used as antioxidant and DOA (Dioctyl adipate) as plasticizer. Finally, H12MDI in form of Desmodur W, was mixed in and the different mixtures were poured onto 2mm and 5mm thick Teflon coated molds and cured at 40◦C for one week. However, due to inaccuracy in the manufacturing process, samples had a thickness between the continuous range 1.6 − 5mm.
Table 1: The quantity of each ingredient in every material type in parts per hundred(pph).
Type HTBP [pph] BKF [pph] DOA [pph] Desmodur W [pph] TPB [pph]
A 100 – 20 10.74 0.1
B 100 – – 10.74 0.1
C 100 1.5 20 10.74 0.1
D 100 1.5 – 10.74 0.1
3.2 Dynamical mechanical analysis
The dynamical mechanical analysis were conducted on the Dma 1 Star System machine from the manufacturer Mettler Toledo. It can be seen in Fig. 2. The samples were fastened using tension clamps and a sinusoidal stress corresponding to a displacement of 20 µm was applied to the sample at room temperature. This magnitude of displacement was observed to be in the material’s linear elastic region before and after being hardened from thermal aging, ensuring that the tensile test does not permanently deform the samples. After also conducting a frequency sweep, assuring reasonable result, the frequency of the sinusoidal stress was set to 10Hz. Furthermore, the dimension of the samples was measured using a micrometer. The mean modulus value from multiple samples (in general 3 samples) was calculated and presented.
3.3 Thermal aging in oven
Temperature-controlled, commercial, air-circulating aging ovens under atmospheric pressure (760 mmHg) were used to age samples at different temperatures. The experimental setup of the thermal aging in industry ovens is visually showcased in Fig. 3, where sheets or pre-cut samples were placed on fine meshed metal grids such that both sides had similar access to oxygen.. Samples were taken out of the oven each time mechanical tests were conducted and put back in the oven immediately after. This was possible since the mechanical test in the DMA apparatus does not permanently damage the samples.
3.4 Thermal aging in DMA machine
Samples were prepared and placed in the DMA machine and the temperature was elevated, accelerating the aging process. A sinusoidal stress corresponding to a displacement of 20 µm was applied approxi- mately every 30 minutes and the response was measured, thus recording the mechanical deterioration with time. This allows for significantly more measuring points compared to the oven aging method where only one or two measurements per day is reasonable. In addition, this aging method does not require a person manually taking samples back and forth from the oven each time the mechanical property is to be measured. Instead it automates and simplifies the experiment process by being aged directly in the DMA machine. However, the tension clamps which fastens the sample, cuts off access to oxygen to parts of the sample, thus interfering with the aging results. A way of possible combating this problem would be by conducting 3-point bending instead of the regular tensile test.
Figure 2: Picture of the DMA apparatus from the manufacturer Mettler Toledo used for tensile measurements.
Figure 3: Experimental setup of the thermal aging in industry oven with samples placed on fine meshed metal grids.
4 Theoretical estimation of lifetime expectancy
Whilst planning the experiments, a rough estimation of the material’s lifetime expectancy at different temperatures was required. The oxidation model described in an earlier chapter was used to estimate the time interval necessary to be able to observe significant mechanical change in the material. The model requires the following parameters:
• Solubility S [cm3(ST P )/(cm3· bar)]
• Diffusivity D [m2/s]
• Reaction term β
• Oxidation rate φ [mol/(g · s)]
• Sample thickness L [m]
Since the experiments required to measure these parameter values are too time-consuming to conduct, parameter values were instead taken from literature and research performed on similar materials.
4.1 Solubility and Diffusivity
The materials transport properties (solubility S, diffusivity D and permeation P = S ·D) can be measured in mainly two different ways, by permeation [14] or sorption-desorption [15]. However, since the specific diffusivity and solubility values for our material is unknown, values for polybutadiene and polyurethane, which we hypothesized could have similar material characteristics, were used instead. The quantities temperature dependence is assumed to follow the Arrhenius equation:
S(T ) = S0e(−∆Hs/RT ) (12)
D(T ) = D0e(−ED/RT ), (13)
where ∆Hs is the molar heat of sorption and ED is the activation energy of diffusion. The solubility and diffusivity values and their corresponding activation energies were taken from the polymer handbook
”Properties of polymers” [16] for polybutadiene and polyurethane. It should be noted that extensive oxidation can cause changes in transport properties, as been observed in permeability measurements at high temperatures [9]. In this project the DLO model focuses on equilibrium conditions, in which the material properties do not change with increasing degradation extent, meaning the parameters are spatially and time-independent. However, recently an article was published where the DLO model ac- commodates for time-dependent variables that either depend on local oxidation extent or is explicitly time-dependent (spatially invariant) [17].
4.2 Reaction term β
The value of β has been observed to be on the order of 1 for many rubber materials [13]. However, Gillen et al. [9] analyzed a crosslinked HTPB/isophorone diisocyanate (IPDI) based polyurethane rubber and found β = 10 from pressure dependent oxygen consumption measurements. This is a common method used to determine the value of β. Hence, both cases (β = 1 and β = 10) was considered for our unknown material.
4.3 Oxidation rate φ
Gillen et al. also measured the oxidation rate φ of the HTPB/IPDI rubber with 1% antioxidants at different temperatures using gas chromatography. This method is sensitivity sufficient, able to measure φ values down to 1 · 10−13mol/g/s or even lower, which is necessary for very low temperature conditions.
Data from this experiment is shown in Fig. 4and the temperature dependent oxidation rate showcase non-Arrhenius behavior (change in activation energy Ea over the temperature range). At the higher temperatures Ea is approximately 120kJ/mol and at lower temperatures ∼ 70kJ/mol. Similar drops
in Ea at lower temperatures has been observed in many studies and indicates possible change in the underlying chemistry. Further evidence that supports this claim can be obtained by measuring the CO2, the main product gas, using the gas chromatography approach. Wise et al. [11] studied the degradation of nitrile rubber and found that CO2 represents 7% of oxygen consumption at 96◦C and dropping to only ∼ 1.5% at 23◦C, which is a strong indicator that the underlying process has changed.
Figure 4: Oxygen uptake rate based on measurements done on HTPB from Gillen et. al [16].
4.4 Sample thickness L
The sample thickness is one major factor determining the oxidation profile of the sample. Since DLO can cause highly heterogeneous materials, which can be problematic for extrapolation attempts to lower temperature regions, it is important to try to avoid DLO effects. This can be achieved by requiring the sample to be thinner than the critical sample thickness (L90%). The critical sample thickness L90% is the value where the integrated oxidation throughout the sample is 90% of the integrated surface value.
Thus, values below L90%ensures insignificant DLO-effects(90% of homogeneous oxidation). The critical sample thickness is commonly estimated as:
L90%=
sαcp0Pox
(β + 1)φ (14)
where αc is a factor related to sample geometry, Poxis the permeability (P = S · D) and p0is the partial pressure of oxygen at the sample surfaces. When β = 1 it follows that αc/(β + 1) ' 2 and β = 10 corresponds to αc/(β + 1) ' 8(see figure 10 in Gillen and Clogh [8]). The critical sample thickness for polybutadiene and polyurethane has been calculated and plotted inFig. 5 for both β = 1 and β = 10.
Polyurethane has a lower permeability, which results in a lower L90%. However, the value of β has a more significant effect on the resulting L90% value. Since our material is unknown the conservative approach for estimating the maximum thickness allowed would be to assume polyurethane properties and set β = 1. This would require the maximum sample thickness to be 1mm to ensure insignificant DLO-effects at 125◦C. However, the lowest thickness we could produce was approximately 1.7mm thick samples. This could still be enough depending on the actual properties of our material, as polybutadiene and polyurethane with β = 10 showcases inFig. 5(L90%> 1.7).
Figure 5: Critical sample thickness L90% versus temperature for different material properties.
4.5 Effect of antioxidant on degradations
Antioxidants are used to slow down the oxidation process of polymers by interrupting the degradation cycle. The overall process and the underlying kinetics are exceedingly complex and varies between polymers and antioxidants [18]. However, depending on their general mechanism of action, antioxidants are either referred as being primary or secondary antioxidant [19]. Primary antioxidants (also referred as radical scavengers) are hydrogen donors that removes peroxy radicals (ROO·), to a lesser extent also hydroxyl radicals (HO·), alkoxy radicals (RO·) and alkyl radicals (R·). Secondary antioxidants (hydroperoxide scavengers) decomposes hydroperoxides to non-radical products. The protection against oxidation is characterized by a induction period [20] where polymer degradation is inhibited whilst antioxidants are consumed. Once the antioxidants level in the material reaches a critical value, significant increase in degradation rate is to be expected. A sample containing no antioxidant was observed to oxidize approximately 3 orders of magnitude faster than the stabilized material with antioxidants [9]. This information was used to model the degradation when the polymer is unstabilized (without antioxidants).
4.6 Oxidation profiles
By using the gathered parameter values mentioned above, theoretical oxidation profiles can now be cal- culated by solving the differential Eq. 11. The differential equation was solved using the finite element method (FEM) and implemented in the computer software Comsol. Figure 6a and Fig. 6b showcases oxidation profiles in 1D for different sample thicknesses at 125◦C for β = 10 and β = 1 respectively.
We can observe that when L = 2mm and β = 10 the integrated oxidation throughout the sample will amount to more than 90% of the integrated surface value, but when L = 2mm and β = 1 it will not.
This is in agreement with the critical thickness L90% result shown in Fig. 5. Moreover, β also has an effect on the shape of the oxidation profile. This can be explained by looking at the differential Eq. 7, which contains β and gives the steady state solution. It follows that β = 0 will corresponds to a first order oxidation, β = 5 a moderate hyperbolic oxidation rate pressure dependence, and β = 1000 a near zeroeth order.
(a) β = 10 (b) β = 1
Figure 6: Oxidation profiles in 1D for different sample thicknesses L[mm] and β values at 125◦C .
The oxidation profiles were also calculated in 3D and are shown in Fig. 7 and Fig. 8 where the oxi- dized cross-section of the samples is visualized. The colour grading represents the relative oxidation and the center of the 5mm thick sample has only oxidized approximately 10% relative to the surface which has free access to oxygen-containing air. In contrast, the center of the 2mm thick sample has oxidized approximately 90% of the surface oxidation, which means that the sample has degraded rather homogeneously.
Figure 7: Cross-section of 5mm thick sample in 3D oxidizing at 125◦C and β = 10. Color scale is in relative oxidation.
Figure 8: Cross-section of 2mm thick sample in 3D, oxidizing at 125◦C and β = 10. Color scale is in relative oxidation.
4.7 Coupling oxidation with mechanical degradation
Finally, to be able to predict the lifetime of elastomers, the extent of oxidation needs to be coupled with mechanical degradation. Over the years, many lifetime studies on different elastomers have been conducted. Although every polymeric material differ, a general guideline for the service lifetime of elastomer is that mechanical failure corresponds to cumulative oxygen uptake of 15 ± 10 ccST P O2/g polymer [21]. This value is not universal, for example J. Wise et al. examined nitrile rubber and found that mechanical failure corresponded approximately to 45 ccSTP O2/g polymer [22], which falls above this range. Conversely, lifetimes of high-density polyethylene were discovered to be closer to 2 ± 1 ccSTP O2/g polymer [23].
4.8 Preliminary lifetime prediction
The stabilized samples (with antioxidants) lifetime is estimated at different aging temperatures based on the model and the gathered data from earlier works. Table2showcases the estimated lifetime for our material (β = 10, L = 2mm) at different temperatures and the model predicts that the material will be deficient after 365-1881 days at 65◦C. Based on this data practical experiments were only conducted at the temperatures 95, 110 and 125◦C, due to limited time and limited accessibility to industrial ovens.
Temperature [°C] Time 65 365 - 1881 [days]
80 60 - 301 [days]
95 277 - 1388 [h]
110 61 - 305 [h]
125 15 - 79 [h]
Table 2: Prelimninary lifetime estimations for our material with antioxidant at different storage temper- atures
The unstabilized polymer (without antioxidants) is expected to degrade significantly faster, aging exper- iments are therefore also attempted at lower temperatures.
5 Result and Discussion
5.1 Color changes
The main objective of the first aging experiment was to examine whether the samples without antioxi- dants would mechanically harden from a relative short time interval as our preliminary study predicted.
Thus, approximately 2mm-and 5mm sheets from the four material types were aged at the temperatures 95◦C, 110◦C and 125◦C for 67hours. Photographs of the sheets, before and after being aged in ovens, can be seen in Fig. 9. From these photographs we can observe noticeable colour differences between temperatures, but also between the material types. Whilst looking at the sheets, an intuitive prediction would be that the grade of colour possible correlates with the extent of mechanical degradation. How- ever, the sample types C and D, which contain antioxidants, were found to be mechanically unaged (no change in modulus), while material types A and B (without antioxidants) had hardened. In fact, the sheets from type A and B were hardened and brittle to the extent that samples could not be cut with the tools available without braking and forming cracks. Hence, any measurements of the hardened samples were discarded and hereafter samples were cut before the aging process, thus averting this problem.
The distinct dark colour, which type C and D acquired after being aged in ovens, can possible be explained by chemical kinetics. As mentioned, both C and D contain the antioxidant BKF, which is an antioxidant of the bisphenol type, and the chemical reactions involving this antioxidant type typically result in the end-product quinone methides. This end-product is known to impart unwanted colour [24], thus explaining the observed phenomenon.
Material A Material B Material C Material D
(a) Unaged (b) Unaged (c) Unaged (d) Unaged
(e) 95◦C (f) 95◦C (g) 95◦C (h) 95◦C
(i) 110◦C (j) 110◦C (k) 110◦C (l) 110◦C
(m) 125◦C (n) 125◦C (o) 125◦C (p) 125◦C
Figure 9: Photographs of the different material types aged 67 hours at different temperatures. Material types containing antioxidants: C and D. Material types containing plasticizer: A and C. Material type B does not contain antioxidants or plasticizer.
5.2 Potential diffusion-limited oxidation
Visually, some of the samples without antioxidants also displayed signs of heterogeneous oxidation, es- pecially the samples aged at 125◦C. This observation was further investigated and documented using a microscope. The resulting close-up images can be seen in Fig. 10and Fig. 11in which we can observe that the samples aged at 125◦C seem to have a very defined coating layer. Moreover, the thickness of the coating is approximately 0.76 − 0.8mm and does not seem to vary significantly with sample thickness, which is in agreement with DLO theory. The samples aged at 110◦C also appear to have a coating. It is measured to be approximate 1mm thick, however the coating is not as distinct and sharp as the coating of samples aged at 125◦C. Lastly, the samples aged at 95◦C did not visually show any clear signs of heterogeneous oxidation. This result is also in agreement with DLO theory, since the oxidation rate is expected to be lower at lower temperatures, which will result in a more homogeneous oxidation profile.
(a) 125◦C 2mm (b) 125◦C 5mm
Figure 10: Cross-sections of samples from material A (plasticizer without antioxidant), aged 67 hours at 125◦C.
(a) 110◦C 5mm (b) 95◦C 5mm
Figure 11: Cross-sections of samples from material A (plasticizer without antioxidant), aged 67 hours at at 95◦C and 110◦C
The mechanical tests conducted after 67 hours of aging on the unstabilized samples (without antioxidants) are showcased inFig. 12, where the complex modulus is plotted versus sample thickness. An interesting observation is the significant impact sample thickness seem to have on tensile modulus. The measured tensile modulus is a bulk material property that depends on the force integrated over the materials cross-section. If the interior regions experience lower degrees of degradation the tensile modulus will be lower. Similarly, if the sample was hardened homogeneously, we would expect all samples to be equally hardened independent of sample thickness. The result therefore indicates that DLO effects have been present during the degradation process. A model based on the close-up of the 125◦C samples (see Fig. 10aandFig. 10b) where the coating layer was observed to be 0.75mm thick was fitted to the data.
By assuming that the interior region is unaged (Mi = 1.5MPa ), knowing the area of the interior Ai
and the coating area Ac based on the observed thickness of the coating, the modulus of the sample is modelled as
MT ot= McAc+ MiAi AT ot
, (15)
where AT ot= Ai+ Acand Mcis the modulus of the hardened parts of the sample. The model parameter Mc was fitted to the measured samples aged at 125◦C for 67hours and is showcased inFig. 12together with samples aged at 110◦C and 95◦C. However, the model fits poorly to the data and there are two possible explanations why this is the case. The first obvious explanation is that the actual oxidation over the sample is more complex than the model based onFig. 10a. This argument is supported by the fact that the samples at the different aging temperatures are not discernible in terms of mechanical modulus (seeFig. 12b), although the photographs suggested that the samples aged at 125◦C had oxidized more heterogeneously than samples aged at 95◦C. Changes in aspect ratio, the ratio of the sample length, width and height, is another possible explanation why the model fits poorly to the data. Since the length and height remained constant, changing the width (thickness) implicitly causes the aspect ratio to change. In turn, this effect the stress generated by the clamping mechanism which can cause errors in modulus measurements [25]. While measuring the unaged samples a 20 − 35% difference in modulus was observed between 2mm samples and 5mm samples. If the samples in the 3-5mm range in Fig. 12 are increased with this amount the model will fit significantly better to the data.
In addition to not being able to discern any clear trend between aging temperatures whilst looking at Fig. 12b, no obvious distinction between material type A and B (with or without plasticizer) could be observed (see Fig. 12a). Due to limited project time, aging experiments and mechanical testing were hereinafter focused on the material type A and C (Plasticizer without or with antioxidants).
(a) Data labelled in specific material type. Material A has plasticizer, material B does not have plasticizer.
(b) Data labelled in the aging temperatures 95◦C, 110◦C and 125◦C.
Figure 12: Complex modulus versus sample thickness aged 67 hours at different temperatures for samples without antioxidants.
5.3 Degradation of unstabilized polymers
Unstabilized samples (without antioxidants) were also aged and monitored directly in DMA apparatus and the aging experiments are showcased inFig. 13 where the complex modulus is plotted versus aging time. The samples seem to undergo an induction period where little change is observed before abruptly degrading at significantly higher rate. Aging at lower temperatures results in a longer induction pe- riod and the induction period for unstabilized materials can be surprisingly long, e.g., years at ambient temperature [26]. However, the samples seem to degrade at similar rates once the induction period ends, except at 65◦C where the degradation rate is lower. This is an interesting observation, and the degradation curves and the similar degradation gradients post-induction period is possible the result of autocatalytic oxidation. Autocatalytic oxidation occurs when radicals can produce more free radicals faster than radicals are terminated by recombination, hydrogen abstraction and disproportionate, caus- ing the oxidation to accelerate. The concentration of hydroperoxide (radical type) is very low at the beginning of the oxidation process and the induction period is usually related to the time required for the hydroperoxide concentration to reach a steady state. The autocatalytic decomposing of hydroper- oxide in the propagation stage is usually very fast compared to the heat induced initiation reactions [2].
This possible explains why once the rapid degradation commences, the samples degrade in similar rates independent of temperature.
The mechanical degradation shown in Fig. 13 also gives another explanation of why it was difficult to distinguish the samples with different aging temperatures inFig. 12b. There is relative little difference in terms of mechanical modulus between 95◦C, 110◦C and 125◦C, and it is possible that the measurement error from the tensile test is larger than the difference in mechanical property at a specific time.
Figure 13: Mechanical degradation at different temperatures for approximately 1.9mm thick unstabilized samples aged in the DMA apparatus.
Lastly, one thing to note is that in the DMA aging experiment the mechanical tests are conducted at their respective aging temperature, unlike when samples are aged in ovens and mechanically tested at room temperature. The temperature at which the experiment is conducted at effects the mechanical properties of the material, for example a tensile modulus of 15Mpa at +100◦C corresponded to around 50Mpa at room temperature. It is a source of error that should be considered, especially if the experi-
ment temperatures lie near the glass transition temperature Tg (a region where the polymer transitions between a hard and relatively brittle state, and a viscous or rubbery state). Fortunately, cured HTPB has a glass transition temperature of approximately −70◦C [27], which means the difference in experi- ment temperature may be insignificant.
5.4 Degradation of stabilized polymer
The result from the oven aging experiment conducted on the stabilized polymer (with antioxidants) is showcased inFig. 14, where the mean of the approximately 2mm thick samples modulus is plotted versus time, and inFig. 15, where also the mechanical aging of the approximately 4mm thick samples is added.
Similar to the unstabilized samples (without antioxidants), after observing little change in modulus for a considerable time period, the stabilized samples suddenly begin to harden rapidly. The sudden change in degradation rate is probably a consequence from the antioxidants in the sample reaching a critical low concentration level, which allows for the oxidation to accelerate. This is reasonable considering that the oxidation rate is expected to be higher at higher temperatures, causing critical antioxidant level to be reached earlier at higher temperatures. Another interesting observation is that the degradation rate seem to slow down after being degraded to a certain extent. This could possible be the result of the sample starting to become completely oxidized, meaning that the sample has no more molecules that can react with oxygen. However, this explanation would be more reasonable if the degradation rate continued to reduce in a logarithmic manner, which it does not. Instead, after slowing down, the degradation rate is almost constant for a considerable time period. Whether this degradation trend will continue and for how long is unclear.
Figure 14: Mechanical aging at different temperatures for stabilized samples (with antioxidants) with thickness 1.7-1.9mm.
As expected, the antioxidants have prolonged the induction period significantly. The induction time (length of the induction period) is approximately 100 hours at 125◦C and almost 800 hours at 95◦ for the 2mm samples, which is approximately two orders of magnitude longer than the respective induction times for the samples without antioxidants. InFig. 15we can also observe that the approximately 4mm
thick samples has a longer induction period than the 2mm samples. In addition, the 4mm samples is approximately a factor 2 softer in terms of modulus than the 2mm samples. These two observations indi- cates that DLO effects are present, which the preliminary DLO calculations declared plausible, seeFig. 5.
It is possible that if the rapid degradation is the result of autocatalytic oxidation, that continuously mea- suring the mechanical change is interfering with the degradation process. Mechanical measurements are conducted by taking samples from the oven, conducting DMA tests at room temperature, and thereafter returning the samples to the oven. The advantage with this method is that the error caused by sample variance is minimized and it requires less material compared to mechanical tests where the sample is destroyed in the process. However, it is not inconceivable that the accelerated degradation caused by autocatalytic oxidation might be interrupted by being cooled down to room temperature. This would mean that the degradation process might be slowed down by constantly being tested at room tempera- ture, resulting in inaccurate results. Although Russell and Pascale studied the early stages of isotactic polypropylene oxidation [28] and found that the effects of prior exposure to oxidative conditions were cumulative to a considerable extent, which resulted in shorter induction times. Taking this into account, the error caused by the measurement technique might be negligible considering that the induction time for fresh samples is observed to be only around 10-20 hours for the temperature range 95 − 125◦C (see Fig. 13).
Figure 15: Mechanical aging of stabilized samples at different aging temperatures and sample thicknesses (2mm and 4mm).
By assuming that the time-temperature superposition principle applies, i.e., that the degradation curves at different temperatures are related by a multiplicative factor called shift factor, a so-called master curve was constructed based on the data gathered from the aging experiment on the stabilized polymer (seeFig. 14). The best superposition is showcased in Fig. 16and was obtained by shifting 110◦C data with a time-factor of 3.05 and the data at 125◦C with a factor of 8.92. The data does not superimpose that well, which implies that there is more than one chemical degradation pathway that effects the entire temperature range of the accelerated experiments. This is in agreement with the result shown in Fig. 14, where we could observe that the degradation process has two modes, the induction period and the post-induction period. These two degradation segments does not seem to have the same temperature
dependence and therefore increasing the temperature does not equally accelerates all of the reactions underlying the oxidation.
Figure 16: Master curve constructed from shifting the data points shown in Fig. 14 with a constant factor aT.
5.5 Lifetime prediction using Arrhenius methodology
Although the constructed master curve showed that the degradation process as a whole does not showcase Arrhenius-behaviour, the induction time seem to follow Arrhenius-behaviour for both 2mm and 4mm thick samples. This is demonstrated inFig. 17where the induction time is plotted on an Arrhenius-plot and the result yield linear Arrhenius behaviour with an Ea ∼ 90kJ/mol independent of sample thickness.
By extrapolating the result to ambient temperatures (20◦ C), the induction period is estimated to be 176 years long for 2mm thick samples and 239 years long for 4mm thick samples. However, there exist very little confidence in this extrapolation due to the extended extrapolation regime relative to the aging temperature range examined. Small changes in the activation energy Ea will have a substantial effect on the predicted lifetime of the material. For example, Kenneth et al. kept unexposed chloroprene cable jacketing samples in the lab and tensile tested after 19 and 23.6 year exposures at approximately 24◦C [29]. A clear drop in Arrhenius Ea from ∼ 89kJ/mol to ∼ 71kJ/mol was observed in the lower temperature region (24-70◦C) and this relatively small change in slope caused the originally lifetime prediction of 96 years at 24◦C (based on extrapolation of the 89 kJ/mol Ea) to drop by 73% to 36 years. Similar changes to lower activation energy have been observed in other aging studies [9,30, 31], and curvature to lower Ea values as the temperature is reduced is not unexpected since a degradation pathway involving a combination of a high Ea process in parallel with a low Ea process will start to favour the low Ea process as the temperature decrease.
Figure 17: Arrhenius plot of the induction time at the different aging temperatures for the approximately 2mm and 4mm thick samples with antioxidants.
In addition to being sensitive to potential changes in Ea, the predicted lifetime is highly sensitive to the specific aging temperature. At 25◦C the induction period is estimated to be 95 years long for 2mm thick samples, which is a considerable drop in induction time compared to the mentioned induction period of 176 years at 20◦C. Reducing the storage temperature by small amounts can therefore have significant impact on the lifetime of the material. If we take the conservative approach and assume that our material will showcase a similar drop in Ea (from ∼ 90 kJ/mol to ∼ 71 kJ/mol at 70◦C), the predicted lifetime for the 2mm samples drops from 176 years to 58 years at 20◦C, which is a 67% reduction in predicted lifetime. This expected curvature is illustrated inFig. 18and the predicted lifetime of 4mm samples can be observed to drop from 239 to 73 years.
Figure 18: Arrhenius plot of the induction time at the different aging temperatures for the 2mm and 4mm thick samples with antioxidants, assuming the activation energy Ea drops from 90 kJ/mol to 71 kJ/mol at 70◦C.
6 Conclusion
In an attempt to predict the storage lifetime using the Arrhenius approach, the thermal-oxidative ag- ing of the HTPB/H12MDI based polymer was studied at temperatures up to 125◦C. The degradation process of the stabilized polymer (with antioxidant) did not showcase Arrhenius behaviour, which was confirmed by the failure to construct a satisfactory master curve. After undergoing an induction pe- riod, the degradation rate increased rapidly, which is probably related to the antioxidants concentration reaching a critical low level. The degradation rate post-induction period is very similar independent on temperature, which is the reason for the inability to construct a master curve in which the data coincides well. However, the induction period of the stabilized polymer (with antioxidant) showcased Arrhenius behaviour in the temperature region 95 − 125◦C with an ∼ Ea = 90 kJ/mol. If the activation energy Ea is assumed to remain constant, the lifetime at ambient temperature (20◦C) is predicted to be approximately 176 years for a 2mm thick sample. However, this is probably an overestimation since curvature in the Arrhenius plot has been observed for many rubber materials in the lower temperature region. Assuming the Ea drops from ∼ 90 kJ/mol to ∼ 71 kJ/mol, a more conservative prediction of 58 years was estimated. Due to the extended extrapolation regime relative to the aging temperature range examined, the lifetime predictions have a large margin of error. In order to to increase confidence in the lifetime estimates, further studies at lower temperatures are necessary.
Furthermore, the effect of antioxidants and to an lesser extent plasticizer on the degradation process was also investigated. Plasticizer did not have an significant effect on the overall degradation process but samples without antioxidants seem to undergo autocatalytic oxidation where the induction period of the samples is observed to be approximately two order of magnitude shorter than the induction period for samples with antioxidants. The antioxidant seem to postpone the degradation process significantly by slowing down the oxidation process, which in turn, stops the process from accelerating. In addition, the unstabilized samples (without antioxidants) showcased clear signs of DLO-effects visually, but also in terms of mechanical modulus. This was partly expected, since the oxidation rate has been observed in other studies to be significantly higher for samples without antioxidants.
7 Future work
As mentioned, the lifetime prediction using the Arrhenius approach is of limited value since the extrapo- lating region is large relative the examined temperature range. Conducting similar aging experiments at lower temperatures is one way of increasing the accuracy of the prediction, however this becomes exceed- ingly more difficult as the expected duration of the experiment gets exponentially longer as temperature decrease. At the time of writing an aging experiment at 80◦C is being conducted and is expected to be finished in the spring 2022. Another way of increasing confidence in the prediction is to analyse and measure a property which is strongly correlated with the mechanical degradation process, and can be measured within a reasonable time frame also at lower temperatures. Oxygen consumption is a excellent example of a property that fulfils these requirements and oxygen uptake experiments is widely used in the field of aging studies. Since measurements of the oxygen consumption can be conducted in the lower-temperature region, potential curvature in the Arrhenius plot can be discovered.
Another important factor on the degradation process is the presence of antioxidants. Sudden significant degradation was observed in the stabilized material, which was probably caused by the loss of antioxi- dants. In this study the stabilized material contained approximately ∼ 1.1% of the antioxidants BKF and it would be interesting to further study how the concentration of antioxidants effects the degradation process. For example, how would increasing the concentration of antioxidants with a factor two effect the lifetime of the material?
References
[1] Crow Polymer. Thermal-oxidative degradation of polymers. https://polymerdatabase.com/
polymer%20chemistry/Thermal%20Degradation.html. Accessed: 2021-04-22.
[2] Crow Polymer. Auto-accelerated oxidation of plastics. http://polymerdatabase.com/polymer%
20chemistry/Autooxidation.html. Accessed: 2021-04-22.
[3] Crow Polymer. Thermal-oxidative degradation of rubber. http://polymerdatabase.
com/polymer%20chemistry/Thermal%20Degradation%20Elastomers.html?fbclid=
IwAR1r13aFQOPkGUeKyGtm5I-37JwsHRC0huBxRApzokG2De89cWEgSi6Bzv4. Accessed: 2021-04- 09.
[4] Natural ageing of rubber - changes in physical properties over 40 years. Aircraft Engineering and Aerospace Technology, 73(2), Jan 2001.
[5] Anja K¨ommling, Matthias Jaunich, Milan Goral, and Dietmar Wolff. Insights for lifetime predictions of o-ring seals from five-year long-term aging tests. Polymer Degradation and Stability, 179:109278, Sep 2020.
[6] A.V. Cunliffe and A. Davis. Photo-oxidation of thick polymer samples—part ii: The influence of oxygen diffusion on the natural and artificial weathering of polyolefins. Polymer Degradation and Stability, 4(1):17–37, 1982.
[7] Adam Quintana and Mathew C. Celina. Overview of dlo modeling and approaches to predict heterogeneous oxidative polymer degradation. Polymer Degradation and Stability, 149:173–191, 2018.
[8] Kenneth T Gillen and Roger L Clough. Rigorous experimental confirmation of a theoretical model for diffusion-limited oxidation. Polymer, 33(20):4358–4365, 1992.
[9] R A Assink, M Celina, K T Gillen, A C Graham, and L M Minier. Thermal degradation studies of a polyurethane propellant binder. 6 1999.
[10] K.T. Gillen, R. Bernstein, R.L. Clough, and M. Celina. Lifetime predictions for semi-crystalline cable insulation materials: I. mechanical properties and oxygen consumption measurements on epr materials. Polymer Degradation and Stability, 91(9):2146–2156, 2006.
[11] Kenneth T. Gillen, Jonathan Wise, and Roger L. Clough. General solution for the basic autoxidation scheme. Polymer Degradation and Stability, 47(1):149–161, 1995.
[12] M. Celina and K. T. Gillen. Oxygen permeability measurements on elastomers at temperatures up to 225°c. Macromolecules, 38(7):2754–2763, Apr 2005.
[13] J. Wise, K.T. Gillen, and R.L. Clough. Quantitative model for the time development of diffusion- limited oxidation profiles. Polymer, 38(8):1929–1944, 1997.
[14] B. Flaconneche, J. Martin, and M. H. Klopffer. Transport properties of gases in polymers: Experi- mental methods. Oil & Gas Science and Technology, 56(3):245–259, May 2001.
[15] R.M. Felder and G.S. Huvard. 17. permeation, diffusion, and sorption of gases and vapors. In R.A.
Fava, editor, Polymers, volume 16 of Methods in Experimental Physics, pages 315–377. Academic Press, 1980.
[16] D.W. Van Krevelen and K. Te Nijenhuis. Chapter 18 - properties determining mass transfer in polymeric systems. In D.W. Van Krevelen and K. Te Nijenhuis, editors, Properties of Polymers (Fourth Edition), pages 655–702. Elsevier, Amsterdam, fourth edition edition, 2009.
[17] Erik Linde, Fritjof Nilsson, Matija Barrett, Mikael S. Hedenqvist, and Mathew C. Celina. Time- and feedback-dependent dlo phenomena in oxidative polymer aging. Polymer Degradation and Stability, 189:109598, 2021.
[18] Ganna Gryn’ova, Jennifer L. Hodgson, and Michelle L. Coote. Revising the mechanism of polymer autooxidation. Org. Biomol. Chem., 9:480–490, 2011.
[19] J´an Mal´ık and Christoph Kr¨ohnke. Polymer stabilization: present status and possible future trends.
Comptes Rendus Chimie, 9(11):1330–1337, 2006. Modification, d´egradation et stabilisation des polym`eres.
[20] Walter Focke and Isbe van der Westhuizen. Oxidation induction time and oxidation onset tem- perature of polyethylene in air: Testing gimzewski’s postulate. Journal of Thermal Analysis and Calorimetry - J THERM ANAL CALORIM, 99:285–293, 06 2010.
[21] J. Reid Shelton, Fred J. Wherley, and William L. Cox. Effect of Temperature on Rate of Oxidation of Rubber. Nature of Resultant Deterioration. Rubber Chemistry and Technology, 27(1):120–133, 03 1954.
[22] J. Wise, K.T. Gillen, and R.L. Clough. An ultrasensitive technique for testing the arrhenius extrapo- lation assumption for thermally aged elastomers. Polymer Degradation and Stability, 49(3):403–418, 1995.
[23] H. J. Oswald and E. Turi. The deterioration of polypropylene by oxidative degradation. Polymer Engineering & Science, 5(3):152–158, 1965.
[24] Pospisil J., Wolf Habicher, Janneth Cayambe, S. Nespurek, J. Kuthan, G.-O Piringer, and H. Zweifel.
Discoloration of polymers by phenolic antioxidants. Polymer Degradation and Stability, 77(3):531–
538, 2002.
[25] Kevin P. Menard and Noah Menard. Dynamic Mechanical Analysis, pages 1–25. American Cancer Society, 2017.
[26] Peter P. Klemchuk and Paul-Li Horng. Perspectives on the stabilization of hydrocarbon polymers against thermo-oxidative degradation. Polymer Degradation and Stability, 7(3):131–151, 1984.
[27] A. Siegmann, D. Cohen, and M. Narkis. Polyurethane elastomers containing polybutadiene and aliphatic diols: Structure-property relationships. Polymer Engineering & Science, 27(15):1187–
1194, 1987.
[28] C. A. Russell and J. V. Pascale. The early stages of isotactic polypropylene oxidation. Journal of Applied Polymer Science, 7(3):959–969, 1963.
[29] Kenneth T. Gillen, Robert Bernstein, and Dora K. Derzon. Evidence of non-arrhenius behaviour from laboratory aging and 24-year field aging of polychloroprene rubber materials. Polymer Degra- dation and Stability, 87(1):57–67, 2005.
[30] Mathew C. Celina. Review of polymer oxidation and its relationship with materials performance and lifetime prediction. Polymer Degradation and Stability, 98(12):2419–2429, 2013.
[31] Jie Liu, Xiangbo Li, Likun Xu, and Tao He. Service lifetime estimation of epdm rubber based on accelerated aging tests. Journal of Materials Engineering and Performance, 26(4):1735–1740, Apr 2017.
