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Lifetime Prediction of Biodegradable Polymers

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Lifetime Prediction of Biodegradable Polymers Accepted Manuscript Title: Lifetime prediction of biodegradable polymers Authors: Bronwyn Laycock, Melissa Nikolic,´ John M. Colwell, Emilie Gauthier, Peter Halley, Steven Bottle, Graeme George PII: S0079-6700(17)30054-0 DOI: http://dx.doi.org/doi:10.1016/j.progpolymsci.2017.02.004 Reference: JPPS 1017 To appear in: Progress in Polymer Science Received date: 19-7-2016 Revised date: 20-2-2017 Accepted date: 20-2-2017 Please cite this article as: Laycock Bronwyn, Nikolic´ Melissa, Colwell John M, Gauthier Emilie, Halley Peter, Bottle Steven, George Graeme.Lifetime prediction of biodegradable polymers.Progress in Polymer Science http://dx.doi.org/10.1016/j.progpolymsci.2017.02.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Lifetime prediction of biodegradable polymers Bronwyn Laycock a*, Melissa Nikolić b, John M. Colwell b, Emilie Gauthier a, Peter Halley a, Steven Bottle b, Graeme George b a Cooperative Research Centre for Polymers, School of Chemical Engineering, The University of Queensland, St Lucia, QLD 4072, Australia. b Cooperative Research Centre for Polymers, School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology (QUT), GPO Box 2434, Brisbane, QLD 4001, Australia Corresponding author: [email protected] Abstract The determination of the safe working life of polymer materials is important for their successful use in engineering, medicine and consumer-goods applications. An understanding of the physical and chemical changes to the structure of widely-used polymers such as the polyolefins, when exposed to aggressive environments, has provided a framework for controlling their ultimate service lifetime by either stabilizing the polymer or chemically accelerating the degradation reactions. The recent focus on biodegradable polymers as replacements for more bio-inert materials such as the polyolefins in areas as diverse as packaging and as scaffolds for tissue engineering has highlighted the need for a review of the approaches to being able to predict the lifetime of these materials. In many studies the focus has not been on the embrittlement and fracture of the material (as it would be for a polyolefin) but rather the products of degradation, their toxicity and ultimate fate when in the environment, which may be the human body. These differences are primarily due to time-scale. Different approaches to the problem have arisen in biomedicine, such as the kinetic control of drug delivery by the bio-erosion of polymers, but the similarities in mechanism provide real prospects for the prediction of the safe service lifetime of a biodegradable polymer as a structural material. Common mechanistic themes that emerge include the diffusion-controlled process of water sorption and conditions for surface versus bulk degradation, the role of hydrolysis versus oxidative degradation in controlling the rate of polymer chain scission and strength loss and the specificity of enzyme-mediated reactions. Keywords: biodegradable polymers, lifetime, biodegradation, hydrolysis, erosion. 1 Nomenclature α Diffusion porosity constant c1 A constant of integration that accounts for β A constant introduced to regulate the the hydrolysis rate and crystallinity contribution of autocatalysis c2 Ratio of the initial concentrations of acids γ Axial stretch (γ = 1 + ε) (where ε is the and ester bonds; c2 = [COOH]0/[E]0 nominal strain) C∞ The amount of starch degraded at the end δ2 Cohesive energy density of the polymer point of the enzymatic hydrolysis reaction 2 cm Mole concentration of hydrolysed δ1 Disperse forces 2 monomers δ2 Polar forces 2 col Molar concentration of ester bonds in the δ3 Hydrogen bonding forces ε Nominal strain oligomers (mol/L) b εt Erosion number Cm Diffusion of monomers accounting for ϑ Fraction of the substrate surface occupied dissociation of acid end group by the ES complex Ct The starch degraded (expressed as mass θ A rate constant that accounts for the per unit volume) at incubation time t differences in the reactivity of polymer D Diffusion coefficient functional groups D0 Intrinsic diffusion coefficient Λ Thiele modulus D∞ Diffusivity of water into an intact, dry Λ Hydrolysis rate constant specific to a polymer polymer Deff Effective diffusion coefficient of water λ' Pseudo first order rate constant inside a polymer '’ λ Revised rate constant dh Damage parameter (equivalent to [1-σ/σ0]) λ Ei Rate constant for hydrolysis of each Dia0 Initial diameter of a cylinder corresponding type of ester bond (Ei) Dmedium Diffusion coefficient of the monomers µgp Polymer weight loss in µg produced following hydrolysis in the µgz Mass of enzyme present in µg hydrolysis medium v0 Rate of a reaction medium Nondimensional form of Dmedium ρ Polymer density W Water density Dn Effective diffusion coefficient of an n-long σ Polymer strength polymer chain through the polymer matrix σ0 Nominal stress ÐM Molar mass dispersity where ÐM = Mw/Mn -2 σx Tensile stress (N m ) DP Average degree of polymerization σ∞ Polymer strength at a theoretical infinite DP0 Initial degree of polymerization Mn E Young’s modulus (in MPa) φA Concentration of ester bonds in the E0 Initial Young’s modulus (in MPa) amorphous fraction (mol/L) [E] Concentration of ester groups (in mol/L) ω Inverse molar volume of the crystalline [E]0 Initial concentration of ester groups (in phase mol/L) 3 -1 ϕ Coefficient (m mol ) Ea Activation energy A A pre-exponential factor for the hydrolysis ED Activation energy for the diffusion reaction rate coefficient reaction Area Substrate surface area Eh Polymer-dependent activation energy for BSR Tensile breaking strength retention; BSR = the hydrolysis reaction (0 – )/0 2 E(tn) Velocity of degradation (which is N0 Initial number of polymer chains equivalent to d[E]/dt) NA Avogadro’s number f Fractional dissolution of a polymer at time Nchains Total number of polymer chains t Ntotal Sum of polymer units in a group of chains fPn Fraction of polymer chains with degree of n Total number of chains in a group of polymerization n chains [H2O] Concentration of water (in mol/L) ne Number of esters in a monomer unit k Rate constant PA Accelerated probability density function k1 Non-catalytic reaction rate constant PC The contributions to the accelerated k2 Autocatalytic reaction rate constant probability density function due to K Adsorption equilibrium constant (from the autocatalysis Freundlich equation) PF The contributions to the accelerated K0 Arrhenius frequency factor probability density function due to Kf Rate of bond rupture events fundamental hydrolysis kb Boltzmann’s constant PBAT Poly(butylene adipate-co-terephthalate) KEQ Thermodynamic equilibrium constant for PBS Poly(butylene succinate) the polymer chain hydrolysis PCL Poly(ε-caprolactone) KCOOH Dissociation constant for the acid end PDLA Poly(D-lactic acid) groups PGA Poly(glycolic acid) kp Depolymerization rate for the polymer PHA Polyhydroxyalkanoate chain hydrolysis PHB Poly(3-hydroxybutyrate) L Thickness of the specimen PHBV poly(3-hydroxybutyrate-co-3- Lcrit Critical thickness of the specimen hydroxyvalerate) Lcrit0 Initial critical thickness of the specimen PLA Poly(lactic acid) m Molar mass of a repeat unit (in g/mol) PLGA poly(D,L-lactide-co-glycolide) Mchain Molar concentration of polymer chains PLLA Poly(L-lactic acid) (mol/L) Pn An n-long polymer chain Mchain0 Initial molar concentration of polymer [Pn] Molar concentration of an n-long polymer chains (mol/L) chain (in mol/L) Me Critical molecular weight for chain R Radius of a cylinder or sphere or the half- entanglement (in kg/mol) thickness of a slab Mn Number average molecular weight (in R Gas constant kg/mol) RH Relative humidity Mn0 Initial number average molecular weight Rind Molecular weight reaction index (in kg/mol) Rn Molar rate of formation by the collection Mnt The value of Mn after environmental of degradation chemical reactions exposure for time, t (in kg/mol) Rs Molar number of scissions per unit volume Mt Water absorption at time t (mol/L) Mth Molecular weight threshold Rscissions Ratio of random scissions to end scissions Mw Weight average molecular weight S Number of scissions per number average M∞ Water absorption at time ∞ chain Masst Mass of polymer at time t sc Critical number of chain scissions at the Mass∞ Mass of polymer at infinite time end of polymer lifetime MW Molecular weight (either Mn or Mw) [S] Substrate concentration N Number of polymer chains per unit [S]0 Initial substrate concentration volume SEC Size Exclusion Chromatography 2 t Time T Temperature tAV Average lifetime of the pixel rings in a Monte Carlo simulation tdiff Time for water to diffuse through a polymer matrix tfail Time to fail us Strength decrease rate of a material V(t) Volume fraction of polymer matrix at time t Wc Critical thickness (variation, analogous to but defined differently from Lcrit) Wm Total amount of water consumed in the hydrolysis region when mass loss starts Ws Solubility of water in the polymer W∞ Mass of water absorption at infinite time Wt Mass of water absorption at time t x Average number of repeating units of the oligomers (set at 4). <x> A mean distance Xc Degree of crystallinity XEi Molar fraction of each corresponding type of ester bond (Ei) xi Monomer concentration at a given location z A random integer between 0 and 99 [Z] Concentration of the unbound enzyme [Z]0 Initial enzyme concentration [ZS] Concentration of an enzyme-substrate complex 3 1. Introduction Plastics are ubiquitous in our modern culture, having excellent and tailorable material properties, with controllable flexibility and strength and the ability to be moulded into shape.
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