Acta Biomaterialia 10 (2014) 2233–2240

Contents lists available at ScienceDirect

Acta Biomaterialia

journal homepage: www.elsevier .com/locate /actabiomat

Degradation mechanisms of bioresorbable polyesters. Part 2. Effectsof initial molecular weight and residual monomer

http://dx.doi.org/10.1016/j.actbio.2014.01.0171742-7061/� 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +44 (0)116 223 1092; fax: +44 (0)116 252 2525.E-mail address: jp165@le.ac.uk (J. Pan).

Andrew Gleadall a, Jingzhe Pan a,⇑, Marc-Anton Kruft b, Minna Kellomäki c

a Department of Engineering, University of Leicester, Leicester LE1 7RH, UKb Purac Biomaterials, PO Box 21, 4200 AA Gorinchem, The Netherlandsc BioMediTech and Department of Electronics and Communications Engineering, PO Box 692, 33101 Tampere, Finland

a r t i c l e i n f o

Article history:Received 19 June 2013Received in revised form 8 January 2014Accepted 15 January 2014Available online 26 January 2014

Keywords:Biodegradable polymersRandom scissionEnd scissionInitial molecular weightResidual monomer

a b s t r a c t

This paper presents an understanding of how initial molecular weight and initial monomer fraction affectthe degradation of bioresorbable polymers in terms of the underlying hydrolysis mechanisms. A mathe-matical model was used to analyse the effects of initial molecular weight for various hydrolysis mecha-nisms including noncatalytic random scission, autocatalytic random scission, noncatalytic end scission orautocatalytic end scission. Different behaviours were identified to relate initial molecular weight to themolecular weight half-life and to the time until the onset of mass loss. The behaviours were validated byfitting the model to experimental data for molecular weight reduction and mass loss of samples with dif-ferent initial molecular weights. Several publications that consider initial molecular weight werereviewed. The effect of residual monomer on degradation was also analysed, and shown to acceleratethe reduction of molecular weight and mass loss. An inverse square root law relationship was foundbetween molecular weight half-life and initial monomer fraction for autocatalytic hydrolysis. The rela-tionship was tested by fitting the model to experimental data with various residual monomer contents.

� 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

1. Introduction

Biodegradable polymers are regularly used in the medical fieldfor applications such as sutures, fixation plates, screws and drugdelivery. The major benefit over permanent metal orthopaedic de-vices is that the polymers degrade over a period of months or yearsto become fully absorbed by the body, therefore negating the needfor repeat surgery for removal. It is important to understand thedegradation and factors that affect this process. In this study the ef-fects of initial molecular weight and residual monomers are con-sidered, neither of which are fully understood at present. Initialmolecular weight significantly affects degradation as has beenshown by several experimental publications [1–6]. If the initialmolecular weight of biodegradable polymers varies by an orderof magnitude, so too does the number of polymer chains and there-fore the number of scissions required to halve the molecularweight. In addition, the ratio of end scission to random scissionis likely to be higher for lower molecular weight samples whichhave a higher ratio of bonds at the chain ends. Mass loss may alsobe affected by initial molecular weight since more monomers willbe produced if there is a greater number of chain ends, due to a

greater rate of end scission. Experimental results in which samplesof different initial molecular weights show the same trends shouldactually be interpreted as evidence for different rates of chain scis-sion. The effect of initial molecular weight depends of the type ofhydrolysis such as noncatalytic random scission, autocatalytic ran-dom scission, noncatalytic end scission or autocatalytic end scis-sion. These hydrolysis mechanisms are discussed in detail in Part1 of this series of papers [7] using a mathematical model. The mod-el simulates bulk mass loss due to the diffusion of monomers oroligomers out of the polymer. Significant mass loss due to surfaceerosion is not typically expected for the polymers considered inthis study. In addition, substantial mass loss may occur when thepolymer begins to break apart in the very late stages of degrada-tion, by which time the model is no longer valid. A monomer isproduced by each end scission, whereas oligomers are producedwhen a random scission occurs near a chain end. One aim of thispaper is to understand the effects of initial molecular weight andrelate them to the fundamental hydrolysis mechanisms. Simula-tions are conducted using a more detailed version of a previouslydeveloped mathematical model [8–11].

A polymer may contain residual monomer that remains frompolymerization or is thermally generated from processing tech-niques such as melt extrusion. The initial monomer content in bio-degradable polymers has been shown to have an impact on the

2234 A. Gleadall et al. / Acta Biomaterialia 10 (2014) 2233–2240

degradation trends [6,12–14]. In all experiments of which theauthors are aware, the rate of degradation has been acceleratedby an increased initial monomer content. The acceleration can besubstantial. In the experiments of Paakinaho et al. [12] residualmonomers accelerated the rate of degradation of inherent viscosityand strength by approximately one order of magnitude. The exper-imental data in the literature [6,12–14] support the theory of auto-catalysis in which the degradation is catalysed by the acid chainends of residual monomers. The initial monomer is not expectedto affect degradation, which is purely noncatalytic in nature. In thisstudy, the effect of residual monomer is analysed by simulationswith the mathematical model detailed in Part 1 [7]. It should benoted that many of the experimental degradation studies prior tothe year 2000 could have high residual monomer contents due totheir processing conditions although this was rarely measuredand thus is not detailed in the publications. It is of critical impor-tance that residual monomer is measured or removed for presentand future experiments of biodegradable polymers in order fortheir degradation characteristics to be fully analysed.

Initial molecular weight and residual monomer were chosen foranalysis because they have a significant effect on degradation andare not fully understood. As a result of the lack of clear understand-ing, these factors are often not discussed in the analysis of experi-mental data. The simple trends identified in this work can be usedto estimate the effects of both factors. The mathematical model isideally suited for the analysis of initial molecular weight and initialmonomer content because both factors are directly implementedin it. Initial molecular weight is almost always stated in experi-mental publications, so the findings of this study can be used whenanalysing historical experimental data. Although residual mono-mer is not always measured, it can be estimated to some degreeif polymer processing conditions are known in detail and it hasbeen measured more often in recent years.

The mathematical model is fitted to experimental data contain-ing various weight fractions of initial monomer, and also to exper-imental data containing various initial molecular weights. Theexperimental data discussed in this study are for poly(lactide) orpoly(glycolide) homo- and copolymers because a large number ofexperimental publications consider these polymers in the litera-ture. The fittings serve to demonstrate the ability of the model toconsider both factors and to relate the degradation trends to theunderlying hydrolysis mechanisms. The authors are not aware ofany models for chain scission of biodegradable polymers that haveincluded initial monomer content to date. It should be noted thatthe mathematical model used here is purposely over complicated.The intention here is to use the model (i) to identify the individualhydrolysis mechanisms that are prominent in experimental stud-ies, and (ii) to understand the effect of various factors with regardsto specific hydrolysis mechanisms. Once the effects of each individ-ual factor are understood, it is then possible to simplify the modelby eliminating the unimportant factors. Currently, the model isused to understand experimental results rather than to predictthe degradation based on simple information including the poly-mer type, polymer microstructure, molecular weight distributionand degradation medium.

2. The mathematical model

The mathematical hydrolysis model is described in Part 1 [7].Eqs. (1)–(5) here are only repeated to help explain how the initialmolecular weight and residual monomer affect the model. All themodel parameters and units are given in Table 1 for reference.The rate of random scission Rrs is given by:

dRrs

dt¼ kr1Ce þ kr2Ce

Cacid

1� Xc

� �n

ð1Þ

and the rate of end scission Res is given by:

dRes

dt¼ ke1Cend þ ke2Cend

Cacid

1� Xc

� �n

; ð2Þ

which differs from Eq. (1) in that the reactant is chain ends Cend forend scission instead of amorphous ester bonds Ce for random scis-sion. Separate reaction constants are used for noncatalytic randomscission kr1, autocatalytic random scission kr2, noncatalytic end scis-sion ke1, and autocatalytic end scission ke2. The initial molecularweight affects the rate of end scission from the outset since for alower initial molecular weight there are more initial chains Nchain0

and therefore more chain ends as given by:

Cend ¼ 2Nchain ¼ 2NchainO þ 2ðRrs � ðRol=mÞÞ; ð3Þ

in which the concentration of random scissions Rrs and ester units inoligomers Rol are both zero at the start of degradation. The rate ofend scission therefore increases linearly with the number of chainsand inversely with initial molecular weight. The rate of randomscission in Eq. (1) does not increase in the same manner becauseit is not directly dependent on the number of chain ends. The ratioof end scission to random scission therefore increases. If molecularweight reduction is due to random scission and mass loss is due toend scission as suggested in Part 1 [7], mass loss may be expected tooccur earlier for a lower initial molecular weight. A greater rate ofend scission results in more monomers Cm and therefore a greaterconcentration of acid catalyst Cacid as given by:

Cacid ¼ Cm þ ðCol=mÞ: ð4Þ

This means the rate of autocatalytic hydrolysis increases, forboth random and end scission, and the ratio of autocatalytic tononcatalytic scissions increases. Another major effect of increasingthe value of Nchain0, due to lower initial molecular weight, is thatthe relative increase of Nchain due to each random scission is re-duced. In other words, increasing the terms in brackets on theright-hand side of Eq. (3) during degradation becomes less signifi-cant as Nchain0 increases. This affects the degradation of the num-ber-averaged molecular weight, calculated by:

Mn ¼ðCe þxXcÞM0

Nchain; ð5Þ

which depends primarily on the increase of Nchain. For a lower initialmolecular weight the effect of each random scission on Mn is re-duced. The balance between an increased rate of random scissionand reduced relative effect of each random scission depends onthe values of the reaction rate constants kr1, kr2, ke1 and ke2.

As the initial monomer content increases, the initial concentra-tion of acid catalyst also increases since Cm increases in Eq. (4). Thisresults in two main effects: (i) the rate of autocatalytic chain scis-sion increases, and so too therefore does the rate of Mn reductionand ratio of autocatalytic to noncatalytic hydrolysis; and (ii) therelative increase in Cacid for the same number of scissions is re-duced since Cm has a larger initial value in Eq. (4). As a result ofpoint (ii), the rate of autocatalytic random scission does not in-crease to such a great extent during degradation. Point (i) may shiftthe molecular weight—time curve, as discussed in Part 1, from non-catalytic to autocatalytic in appearance. Point 2 may have theopposite effect. The balance between these effects depends onthe reaction rate constants kr1, kr2, ke1 and ke2.

3. The effect of initial molecular weight

The effect of initial molecular weight on the degradation ofmolecular weight and mass loss is analysed for several differenttypes of hydrolysis including noncatalytic random scission, autocat-alytic random scission, noncatalytic end scission and autocatalytic

Table 1Parameters that are used in the mathematical model.

Model parameter description Symbol Units

Oligomer production rate parameter a No unitsOligomer production rate parameter b No unitsInitial concentration of ester bonds in all phases Ce0 mol m�3

Concentration of ester bonds in amorphouschains

Ce mol m�3

Concentration of catalysing carboxylic acid endgroups

Cacid mol m�3

Concentration of long chain ends Cend mol m�3

Oligomer concentration (after diffusion) Col mol m�3

Monomer concentration (after diffusion) Cm mol m�3

Diffusion coefficient (amorphous phase) D0 m2 day�1

Diffusion coefficient (pores) Dpore m2 day�1

Noncatalytic random scission reaction rateconstant

kr1 day�1

Noncatalytic end scission reaction rate constant ke1 day�1

Autocatalytic random scission reaction rateconstant

kr2 [mol�1 m3]0.5

day�1

Autocatalytic end scission reaction rateconstant

ke2 [mol�1 m3]0.5

day�1

Average degree of polymerisation of oligomers m No unitsMolar mass M0 g mol�1

Number averaged molecular weight Mn g mol�1

Dissociation power of the acid end group n No unitsOriginal concentration of chains Nchain0 mol m�3

Current concentration of chains Nchain mol m�3

End scission concentration Res mol m�3

Random scission concentration Rrs mol m�3

Total scissions concentration Rs mol m�3

Oligomer concentration (produced) Rol mol m�3

Monomer concentration (produced) Rm mol m�3

Inverse molar volume of crystalline phase x mol m�3

Degree of crystallinity Xc Volume fractionExtended degree of crystallinity Xext Volume fractionMaximum degree of crystallinity Xmax Volume fractionCrystal nucleation probability px No unitsCrystallite volume Vc m3

Avogadro’s constant gA mol�1

Table 2Model constants and initial variable values used in simulations in this study.

Constant Units Value

Ce0 mol m�3 17300n no units 0.5M0 g mol�1 72a no units 28b no units 2m no units 4

Variables Units Initial Values

Rol Rrs Res Rs Col mol m�3 0Rm Cm mol m�3 10�10 Ce0

Ce mol m�3 Ce0 � (Cm + xXc)

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250 300 350 400 450 500

Mn

half-

life

time

Initial Mn (kg mol-1)

Autocatalytic random and autocatalytic end scission

Autocatalytic random scission

Autocatalytic and noncatalytic random scission

Noncatalytic random scission

End scission

Fig. 1. Scenarios for Mn half-life vs. initial molecular weight for various theories ofhydrolysis: noncatalytic random (solid); autocatalytic random (long dash); acombination of autocatalytic and noncatalytic random (kr2/kr1 = 10, dash-dot);either autocatalytic or noncatalytic end (short dash); and a combination ofautocatalytic random and autocatalytic end (ke2/kr2 = 3000, dotted). Experimentaldata for poly(lactide-co-glycolide) by Raman et al. [2] (circles) and poly(lactide) byPitt et al. [3] (triangles) are included for reference.

A. Gleadall et al. / Acta Biomaterialia 10 (2014) 2233–2240 2235

end scission. Molecular weight degradation is characterised by themolecular weight half-life. It is often the case that polymer samplesshow zero mass loss for a long period at the start of degradation[15–18]. An indication of the likely duration of this delay beforemass loss onset is characterized here by the time taken for water-soluble monomers and oligomers to account for 10% of the totalpolymer weight. To simplify the results, the simulations are amor-phous unless fitting experimental data for crystallinity. Similarly,diffusion of water-soluble small chains has been previously studiedby Wang et al. [8], and so is not considered here unless fitting exper-imental data for mass loss. The model is also fitted to experimentaldata for various initial Mn, which is used here to indicate the molec-ular weight of the samples at the start of degradation, after allprocessing and sterilization. Model constants that are used for allsimulations in this study, unless otherwise stated, are given inTable 2. As in Part 1 [7], the value of initial monomer is set as zero(10�10 Ce0 or 10�8 wt.% for numerical reasons) for all simulationsunless measured experimentally. This value is not varied in thissection so that we can focus on the effect of initial molecularweight. The accuracy of fittings to experimental data is notaffected if a high concentration of initial monomer is assumed asdemonstrated in Part 1 [7]. All parameters related to crystallinityare set to zero for amorphous simulations.

3.1. Simulations to identify the effect of initial molecular weight onmolecular weight reduction

Scenarios for the effect of initial Mn on the molecular weighthalf-life for each individual hydrolysis mechanism are shown inFig. 1. Each time the initial molecular weight is halved, the Mn

half-life is halved for end scission (kr1 = kr2 = 0), doubled for

noncatalytic random scission (kr2 = ke1 = ke2 = 0), and increased by10–15% for autocatalytic random scission (kr1 = ke1 = ke2 = 0). Fornoncatalytic random scission, samples of different initial molecularweight have the same rate of chain cleavage. However, polymerswith higher initial Mn have fewer chains so the effect of each ran-dom scission on molecular weight is greater and thus there is aninverse relationship between Mn half-life and initial molecularweight. In autocatalytic random scission, this effect is offset bythe fact that for a lower initial molecular weight more oligomersare produced, since more scissions are required to reduce Mn

equally, which accelerates the rate of chain scission. For pure endscission the Mn half-life increases linearly with initial Mn.

Experimental data by Raman et al. [2] and Pitt et al. [3] are in-cluded in Fig. 1. The data points are arbitrarily normalized to suitthe existing curves. The curve for combined autocatalytic and non-catalytic random scission (ke1 = ke2 = 0) has the reaction rate ratiokr2/kr1 = 10 and the curve for combined autocatalytic random andautocatalytic end scission (kr1 = ke1 = 0) has the reaction rate ratioke2/kr2 = 3000. The same reaction rate ratios are used in the fittingsof the model to the experimental data in the next section. Theautocatalytic random scission curve may be interpreted to fit thedata of Pitt et al. [3], as opposed to a combination of random andend scission, but mass loss data does not support this theory, asdiscussed shortly. There is almost no dependence of Mn half-lifeon initial molecular weight for a combination of autocatalyticrandom and autocatalytic end scission. The effect of increasingthe rate of end scission at a lower initial Mn, and therefore therate of autocatalytic random scission, offsets the effect of more ran-dom scissions being required to reduce the normalized molecularweight.

0

10000

20000

30000

40000

50000

60000

70000

80000

0 5 10 15 20 25 30 35

Mol

ecul

ar w

eigh

t (g

mol

-1)

Time (days)

Fig. 3. Model fitting of molecular weight vs. time for a combination of noncatalyticrandom and autocatalytic random scission. Discrete points represent experimentaldata [2] for various initial molecular weights and solid lines represent the modelfitting.

2236 A. Gleadall et al. / Acta Biomaterialia 10 (2014) 2233–2240

3.2. Simulations to identify the effect of initial molecular weight onmass loss

Fig. 2 shows scenarios for the effect of initial molecular weighton the time taken for 10% of the total polymer weight to be watersoluble for various hydrolysis mechanisms. For end scission (kr1 =kr2 = 0), the rate of production of monomers is linearly related tothe number of chain ends so the time taken for monomers to ac-count for 10% of the polymer increases linearly with initial molec-ular weight. For random scission, however (ke1 = ke2 = 0), initialmolecular weight has a negligible effect because the number ofrandom scissions required to reduce Mn from a typical high initialvalue (i.e. 3 � 105 g mol�1) to a typical low initial value (i.e.3 � 104 g mol�1) is small compared to the number of scissions re-quired to convert 10% of the polymer to oligomers. The trendsare not affected by whether hydrolysis is noncatalytic or autocata-lytic for either random or end scission. A curve for combined auto-catalytic random and autocatalytic end scission (kr1 = ke1 = 0) isshown for the reaction rate ratio ke2/kr2 = 3000, which is the sameas that used in the fitting of the model to the experimental data ofPitt et al. [3] in the next section. It could be argued that the exper-imental data points may fit to the end scission curve if they arenormalized to an alternative value. However, the Mn half-life datafrom the same experiments, shown in Fig. 1, do not resemble thecurve for end scission in that figure.

3.3. Fitting the model to experimental data

Having identified the underlying mechanism, the model is usedto fit the experimental data of Raman et al. [2] and Pitt et al. [3],which both consider the effect of initial molecular weight. The reac-tion rate ratios that are used in the fittings are also used for simula-tions in Figs. 1 and 2. Raman et al. [2] conducted degradationexperiments on amorphous 50 lm poly(DL-lactide-co-glycolide)microspheres of various initial molecular weights in phosphate-buf-fered saline (PBS), pH 7.4 at 37 �C. The initial molecular weights were67000, 49000, 34000 and 21000 g mol�1 for which the values ofNchain0 in the model are 16.8, 22.9, 33.0 and 53.4 mol m�3 respec-tively. The model setup is the same as the previous section andTable 2 except M0 = 65 g mol�1, which is the average molar massof polylactic and polyglycolic acid. Fig. 3 shows that the model is ableto fit the experimental data for a combination of noncatalytic andautocatalytic random scission as indicated by Fig. 1. The reactionrates are kr1 = 3 � 10�5 day�1, kr2 = 3 � 10�4 [mol�1 m3]0.5 day�1

and ke1 = ke2 = 0. The same model parameters are used for all data

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350 400 450 500

Nor

mal

ised

tim

e fo

r 10%

sol

uble

frac

tion

Initial Mn (kg mol-1)

Autocatalytic randomand autocatyalytic end scission

Random scission

End scission

Fig. 2. Scenarios for the time until 10% of the polymer is water-soluble vs. initialmolecular weight is shown for various theories of hydrolysis: random scission (longdash), end scission (short dash), and an autocatalytic combination of both with areaction rate ratio of ke2/kr2 = 3000 (dotted). Experimental data for poly(lactide) byPitt et al. [3] (triangles) are included for reference.

sets except for Nchain0, which represents initial Mn. This demon-strates the ability of the model to consider the effect of initialMn. The fitting must use a combination of autocatalytic and noncat-alytic random scission but cannot be improved by including endscission. For noncatalytic random scission alone (kr2 = ke1 = ke2 = 0),Mn degrades too quickly for the samples with high initial Mn, andfor autocatalytic random scission alone (kr1 = ke1 = ke2 = 0), Mn

degrades too slowly for the samples with high initial Mn.Poly(DL-lactide) films �0.1 mm thick were degraded in vivo by

Pitt et al. [3]. The values of initial number-averaged molecularweight were approximately 42000, 107000 and 164000 g mol�1

for which the values of Nchain0 in the model are 29.3, 11.6 and7.57 mol m�3 respectively. All other parameters are the same forall three data sets. A fitting of the mathematical model for a com-bination of autocatalytic end scission and autocatalytic randomscission is shown in Fig. 4. The model setup is given in Table 2. Sim-ulations are amorphous throughout, and hence all crystallinityterms are set to zero. Diffusion is included in order to model massloss and the diffusion coefficients are D0 = 10�11 m2 week�1 andDpore = 10�7 m2 week�1. Initial porosity is set to zero. The polymerfilm is represented by 200 finite-difference nodes. Reaction ratesare kr2 = 1.25 � 10�5 week�1, ke2 = 3.75 � 10�2 [mol�1 m3]0.5

week�1, and kr1 = ke1 = 0. The experimental samples have very sim-ilar Mn half-lives but mass loss occurs earlier for samples with low-er initial Mn. The model is able to simulate these degradationbehaviours by using a combination of end scission and randomscission as can be identified by simple analysis of Figs. 1 and 2.Mass loss data for the model is not shown for high percentages be-cause the model is not designed for high mass loss—if this occurs,parts of the polymer may break away and the water-soluble chainsmay be able to diffuse through cracks in the polymer as opposed tothrough the polymer material.

The analyses on Mn half-life and time to mass loss onset inFigs. 1 and 2 do not consider the shape of the molecular weight–time curves. As discussed in Part 1 [7], the shape depends stronglyon the type of hydrolysis. The fittings here must use the correctcombination of hydrolysis mechanisms to model (i) the differencesbetween degradation of samples with different initial molecularweights, and (ii) the shape of the molecular weight–time curves.The shapes of the molecular weight–time curves in Figs. 3 and 4bear a good resemblance to the experimental data. The fittingsfor both sets of data are shown with normalized molecular weightin Fig. 5. This figure emphasizes the trend seen in Fig. 1 that in theexperiments of Pitt et al. [3] (Fig. 5b) all samples degrade at a sim-ilar rate for normalized Mn, regardless of initial molecular weight,whereas in the experiments of Raman et al. [2] (Fig. 5a) there is

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

0 10 20 30 40 50 60 70

Mol

ecul

ar w

eigh

t (g

mol

-1)

Tme (weeks)

(a)

-10

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

Mas

s lo

ss (%

)

Time (weeks)

LOWER INITIAL Mn

(b)

Fig. 4. Model fitting of (a) molecular weight and (b) mass loss vs. time for acombination of autocatalytic random and autocatalytic end scission. Lines representthe model fitting and discrete points represent experimental data [3] for variousinitial Mn: 42000 (triangle, solid line), 107000 (diamond, dashed line) and164000 g mol�1 (circle, dotted line).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40

Nor

mal

ised

Mn

Time (weeks)

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25 30 35

Nor

mal

ised

Mn

Time (days)

LOWER INITIAL Mn

(a)

(b)

Fig. 5. Alternative presentation with normalized Mn for (a) the fitting shown inFig. 3 and (b) the fitting shown in Fig. 4. The shapes of discrete symbols and linetypes are the same as used previously.

A. Gleadall et al. / Acta Biomaterialia 10 (2014) 2233–2240 2237

a reduced rate of Mn degradation for samples with lower initialmolecular weight. In the fittings to both sets of experimental data,the model finds a significantly increased rate of random chain scis-sion in the samples of lower initial molecular weight. This is due togreater production of oligomers or monomers and is necessary inorder to prevent the molecular weight of the high initial molecularweight samples reducing too quickly compared to the low initialmolecular weight samples. For a combination of autocatalyticand noncatalytic hydrolysis, the samples of lower initial molecularweight therefore have a greater ratio of autocatalytic to noncata-lytic hydrolysis, which can be seen in the slight shift of curves inFig. 5a from a noncatalytic shape to an autocatalytic shape, as de-tailed in Part 1 [7].

3.4. Review of other publications for the effect of initial molecularweight

The two sets of experimental data that have already been dis-cussed [2,3] demonstrated different effects of initial Mn. Other pub-lications that also consider initial molecular weight are discussedhere. Migliaresi et al. [1] studied the degradation of 3 mm rods ofamorphous poly(L-lactide) with initial weight-averaged molecularweights of 27000 and 177000 g mol�1 in Ringer solution at 37 �C.The molecular weight half-lives were approximately 100 days forboth samples, and thus Fig. 1 suggests a combination of autocata-lytic random scission and autocatalytic end scission may give a goodfitting of the model to experimental data. Huttunen [6] comparedthe degradation of 4 mm rods of poly(L-lactide-co-D-lactide)96L:4D and poly(L-lactide-co-DL-lactide) 80L:20DL in PBS, pH 7.4at 37 �C, with initial inherent viscosities varying from 1.45 to

4.98 dl g�1. The experimental data is only given for the early stagesof degradation but the inherent viscosity half-lives are similar for allsamples, or perhaps slightly shorter for the samples with lower ini-tial inherent viscosities. By comparison to Fig. 1, it can be seen that agood fitting may be achieved by a combination of autocatalytic ran-dom scission and autocatalytic end scission. Witschi and Doelker[19] conducted experiments on 3–5 lm microspheres of poly(lac-tide-co-glycolide) 50:50 in PBS, pH 7.4 at 37 �C. The samples identi-fied as RG-502 SD/WOW and RG-504 SD/WOW have the samecopolymer ratio but different initial number-averaged molecularweights of �6750 and �13000 g mol�1 respectively. The lowermolecular weight samples have similar or slightly longer Mn half-lives, which suggests autocatalytic random scission is likely accord-ing to Fig. 1. Grizzi et al. [20,21] conducted degradation experimentsof 2 mm thick poly(DL-lactide-co-L-lactide) plates in PBS, pH 7.4 at37 �C. The polymers had initial weight-averaged molecular weightsof�43000 and�65000 g mol�1. The time to the onset of mass loss is5–9 weeks for the 43000 g mol�1 sample and �7 weeks for the65000 g mol�1 experiment. Given that the onset of mass loss occursat similar times for both samples, Fig. 2 suggests that random scis-sion without end scission is likely. Molecular weight data for the65000 g mol�1 sample is too infrequent for comparison to Fig. 1.Pistner et al. [4] carried out degradation experiments of 2 mm thickamorphous poly(L-lactide) rods in vivo with initial number-aver-aged molecular weights of 132000 and 197000 g mol�1. There isan approximately inverse relationship between Mn half-life and ini-tial molecular weight, which suggests noncatalytic random scissionis dominant according to Fig. 1. Both samples begin to demonstratemass loss at 42.5 weeks which suggests random scission is respon-sible for mass loss according to Fig. 2. Hyon et al. [14] conductedexperiments for the degradation of 0.5 mm strips of poly(DL-lactide)with initial weight average molecular weights of 7000, 12000 and

0.001

0.01

0.1

1

1E-07 1E-06 1E-05 1E-04 1E-03 1E-02 1E-01

Nor

mal

ised

Mn

half-

life

Initial monomer weight fraction

A

BC

DEF

Fig. 6. Time to halve molecular weight vs. initial monomer weight fraction forautocatalytic hydrolysis varying from random scission (A) to end scission (F). Theend:random scission rate ratios (ke2/kr2) for combined simulations are 10 (B), 100(C), 300 (D) and 1000 (E). Discrete points are experimental data [12].

2238 A. Gleadall et al. / Acta Biomaterialia 10 (2014) 2233–2240

43000 g mol�1. The samples were manufactured via differenttechniques and were expected to have varying concentrations ofresidual monomer which significantly affects degradation. Cautionmust therefore be taken when analysing the effect of initial molec-ular weight. The increased rate of degradation for lower molecularweight samples was attributed to an increased initial concentrationof residual monomers. The effect of residual monomer is discussedin the next section of this paper, the findings of which agree withthat theory. In the experiments, samples with lower initial Mn dem-onstrated shorter Mn half-lives and more accelerated mass loss.These trends are expected for a combination of autocatalytic ran-dom scission and autocatalytic end scission according to Figs. 1and 2. It may be the case that both initial molecular weight andresidual monomer affected the results in a similar manner.

In the above analysis, the hydrolysis mechanisms suggested bycomparison of experimental data to Figs. 1 and agree with thosesuggested in Part 1 [7]. This supports the trends identified in Figs. 1and 2 along with ability of the model to consider the effect of initialmolecular weight. It also supports the findings in Part 1 [7] thatrandom scission is responsible for the reduction of molecularweight and that autocatalytic hydrolysis may be more prevalentin degradation experiments than noncatalytic hydrolysis. One setof experiments that do not fit the expected trends predicted bythe model are those of Park [5], which consider 10 lm micro-spheres of poly(DL-lactide). The degradation rate of a high molecu-lar weight sample was negligible compared to that of a lowmolecular weight sample. However, the values of initial number-average molecular weight (900–1300 g mol�1) are orders ofmagnitude lower than typical experimental poly(lactide) whichresulted in one sample being beneath the glass transitiontemperature. The samples also contained high quantities of lowmolecular weight chains, which may have significantly affectedhydrolysis in a similar manner to that discussed in the next sectionfor residual monomers.

4. The effect of residual monomers

Residual monomer significantly affects degradation if autocata-lytic hydrolysis is assumed to occur [12,14]. Noncatalytic hydroly-sis will by definition be unaffected. The model is used here topredict the effect of initial monomer content on the molecularweight half-life for autocatalytic hydrolysis. The model is also fit-ted to experimental data to demonstrate the ability of the modelto consider residual monomer.

The effect of initial monomer content on the Mn half-life isshown in Fig. 6 for autocatalytic random scission, autocatalyticend scission, and a combination of both with reaction rate ratioske2/kr2 = 10, 102, 3 � 102 and 103. The model setup is the same asthat given in Table 2 except the initial monomer fraction variesfrom Cm = Rm = 10�1 Ce0 to 10�7 Ce0. The noncatalytic reaction ratesare set to zero (kr1 = ke1 = 0) and Nchain0 = 42.4 mol m�3. The simu-lation is assumed to be amorphous throughout with no diffusionso all model parameters related to crystallinity and diffusion areset to zero. If molecular weight reduces due to random scission(as is the case in curves A–E in Fig. 6), there is an inverse squareroot law relationship between Mn half-life and initial monomerfraction above a critical monomer content which depends on theratio of end scission to random scission. This relationship can bederived analytically from the mathematical model. Experimentaldata for the inherent viscosity half-life of poly(lactide-co-glycolide)with various initial monomer contents [12] is included in the figureand can be seen to follow the predicted trend for autocatalytic ran-dom scission and autocatalytic end scission until the initial mono-mer content is increased above 2%. The reaction rate ratio for thedotted line is the same as that used in the fitting of the model tothe experimental data for molecular weight, crystallinity and mass

loss later in this section (ke2/kr2=3 � 102). It can be seen to fitthrough the experimental data points well. The model appears tobe suitable for initial monomer contents up to 2% in Fig. 6, a valueto which the initial monomer content due to typical processingtechniques can and should fall well below in order to ensure thatproducts display reliable and repeatable in vivo behaviour. Accord-ing to the literature, the release of monomers from biodegradablepolymers causes a decrease in pH in the tissue adjacent to theproduct, which has been suggested to have adverse effects in clin-ical applications [22–26]. Therefore it is advisable to minimize theinitial monomer content to enhance biocompatibility. The cause ofthe two samples with highest initial monomer contents havinglower than predicted Mn half-lives cannot be explained by themodel. It may be due to factors that are beyond the scope for themodel such as changes in the polymer structure or the develop-ment of monomer-filled pores, as found in a previous study [14].The mathematical model assumes that monomers are evenly dis-tributed amongst the amorphous phase. It can be given as a guide-line that the processing should not create monomer quantities ashigh as 2–4% in medical products. This should be prevented fortwo important reasons: to ensure predictable degradation and toavoid the release of unsafe amounts of monomer at the start ofthe degradation process in vivo. Researchers have in the past oftennot clearly specified in their articles whether the specimens anddevices have been made of as-polymerized poly(lactide)s andpoly(glycolide)s or whether they have used purified, medical-gradepolymers. Combining the finding (i) that the high-monomer sam-ples deviate from the predicted trend of the model, and the knowl-edge (ii) that non-purified, commercially available semicrystallinepolymers such as poly(L-lactide) and fully amorphous polymerssuch as poly(DL-lactide-co-glycolide) have residual monomer con-tents of 1–2% and 1.5–3%, respectively, we recommend that onlyhighly purified raw materials should be used in medical devicesand tissue engineering scaffolds. Also, care should be taken whenmelt-processing the polymers so as not to create monomer. Initialmonomer content in the specimens and products should be mea-sured to enable correct analysis or prediction of the in vitro orin vivo behaviour.

To test the ability of the mathematical model to incorporateinitial monomer fraction, it is fitted to the experimental data ofPaakinaho et al. [12] for inherent viscosity, crystallinity and massloss. In the experiments, 1.6 mm poly(L-lactide-co-glycolide)85L:15G rods containing different fractions of initial monomerwere degraded in 37 �C Sörensen buffer solution. The initial mono-mer contents were 0.03%, 0.05%, 0.1% and 0.2%, for which initialcrystallinity Xc = 0.029, 0.067, 0.035 and 0.033 and Nchain0 = 42.4,46.9, 52.4 and 46.9, respectively. These values are derived from

Table 3Parameters used by the model in the data fitting.

Parameter Units Value Parameter Units Value

Ce0 mol m�3 1.73 � 104 M0 g mol�1 72D0 m2 day�1 2 � 10�9 x mol m�3 1.73 � 104

Dpore m2 day�1 2 � 10�5 Xmax – 0.45kr2 [mol�1 m3]0.5

day�13.4 � 10�6 px – 2 � 10�4

ke2 [mol�1 m3]0.5

day�1300*kr1 Vc m3 4.19 � 10�4

ke1, kr1 day�1 0 gA mol�1 6.02 � 1023

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

Cry

stal

linity

and

mas

s lo

ss fr

actio

n

Nor

mal

ised

I.V.

or M

n

Time (weeks)

Inherent viscosity

Crystallinity

Mass loss

Model

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

Cry

stal

linity

and

mas

s lo

ss fr

actio

n

Nor

mal

ised

I.V.

or M

n

Time (weeks)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

Cry

stal

linity

and

mas

s lo

ss fr

actio

n

Nor

mal

ised

I.V.

or M

n

Time (weeks)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

Cry

stal

linity

and

mas

s lo

ss fr

actio

n

Nor

mal

ised

I.V.

or M

n

Time (weeks)

Fig. 7. Model fitting to the experimental data [12] with an assumption of acombination of autocatalytic random scission and autocatalytic end scission. Initialmonomer contents are (a) 0.03%, (b) 0.05%, (c) 0.1% and (d) 0.2%.

A. Gleadall et al. / Acta Biomaterialia 10 (2014) 2233–2240 2239

experimental measurements. The values of Nchain0 represent initialmolecular weights of 2.94, 2.66, 2.38 and 2.66 � 104 g mol�1. Thesevalues are estimated through a linear relationship to the initialinherent viscosity of Mn = 27900 IV – 6890 in which the units ofMn and IV are g mol�1 and dl g�1. It is the linear best fit for 22 datapoints of poly(L/D lactide) 96/4 with IV < 4 dl g�1 [13,27]. The val-ues of all other model parameters do not vary between the datasets and are given in Tables 2 and 3 except Cm = Rm = Ce0 � 0.003,0.005, 0.01 and 0.02 mol m�3 to reflect residual monomer; a valueof n = 0.67 gives the best fitting. The initial values of porosity andextended crystallinity are zero. There are 200 finite-differencenodes to represent the rod diameter. Diffusion is included in themodel in order to model mass loss due to small water-solublechains leaving the polymer. The model is only being fitted to thefour samples in which the monomer was produced during process-ing and for which mass loss was measured. In the other three sam-ples, the monomer was added manually and may have a slightlydifferent effect on degradation if, for example, monomer-filledpores develop as previously seen [14]. In the fitting, the reductionof normalized molecular weight (mathematical model) is com-pared to normalized inherent viscosity (experimental data) sincemolecular weight was not measured. The model is able to fit thedata as can be seen in the fitting in Fig. 7. That the same set of mod-el parameters is used for all samples demonstrates the ability ofthe model to simulate the effect of initial monomer at least up to0.2%. In the fitting, the noncatalytic reaction rates can be set tozero, which suggests that chain cleavage due to noncatalytichydrolysis is negligible compared to that of autocatalytic hydroly-sis. This is to be expected since the initial monomers greatly in-crease the rate of autocatalytic scission, as can be seen in Fig. 6by the effect of initial monomer on the molecular weight half-life.The fittings of Mn to inherent viscosity are shown together in Fig. 8.The experimental data for the 2–4% initial monomer samples, towhich the model is not fitted, are also included for reference. Asthe initial monomer weight fraction increases, the catalysing car-boxylic chain ends that are produced during hydrolysis make upa smaller fraction of the total concentration of catalyst. As a result,the catalyst, and therefore the rate of chain scission, does not in-crease to such an extent during degradation and the molecularweight–time curves shift from autocatalytic (degradation rateaccelerating) towards noncatalytic in appearance, as shown inFig. 1 in Part 1 [7]. Although the molecular weight–time curvesshift towards noncatalytic in appearance, the results still supporta theory of autocatalytic hydrolysis because the monomers cata-lyse the hydrolysis. It is simply the case that the negligible increasein catalyst during degradation results in a similar trend to noncat-alytic hydrolysis. One remarkable interpretation of this could bethat many experimental publications which appear to demonstratenoncatalytic hydrolysis may have actually undergone autocatalytichydrolysis but contained high residual monomer. Paakinaho et al.[12] even found the concentration of monomer catalyst to decreaseduring degradation. This is why the rate of Mn reduction for the 4%sample decelerates to an even greater extent than the curve fornoncatalytic random scission in Fig. 1 in Part 1 [7]. In the experi-

ments of Paakinaho et al. [12], the monomer diffused out of the4% sample at a much greater rate than the 2% which can be ex-plained by Fick’s law for diffusion in which the rate of diffusionis dependent on the concentration gradient. Therefore it is plausi-ble that the monomer does not diffuse out rapidly in samples withlow residual monomer contents such as those of Paakinaho in therange of 0.03–0.2%. It should be noted that if the residual monomer

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

Nor

mal

ised

I.V.

or M

n

Time (weeks)

MORE INITIAL MONOMER

LESS INITIAL MONOMER

Fig. 8. Alternative presentation for the fitting shown in Fig. 7. Additional exper-imental data by Paakinaho et al. [12] is included for three samples with higherinitial monomer contents. Initial monomer weight percentages are 0.03% (blackdiamond), 0.05% (black square), 0.1% (black triangle), 0.2% (black circle), 2% (greysquare), 3% (grey triangle) and 4% (grey circle).

2240 A. Gleadall et al. / Acta Biomaterialia 10 (2014) 2233–2240

catalyst is assumed to diffuse out of the polymer in the first fewweeks, there may still be long-term effects because the chain scis-sions in the first few weeks lead to more chain ends and therefore agreater rate of end scission throughout the duration ofdegradation.

5. Conclusions

The mathematical model developed in Part 1 [7] was used toanalyse the effect of initial molecular weight. Various hydrolysismechanisms were considered, including noncatalytic random scis-sion, autocatalytic random scission, noncatalytic end scission andautocatalytic end scission. It was found that an increase in initialmolecular weight resulted in a decreased molecular weight half-life in the case of random scission. The decrease was greater fornoncatalytic hydrolysis than autocatalytic hydrolysis. In contrast,for end scission, increasing initial molecular weight resulted inan increased molecular weight half-life. The time taken for signif-icant mass loss increased as initial molecular weight increased ifmass loss was attributed to end scission. However, mass loss dueto random scission was unaffected by initial molecular weight.The model was able to fit experimental data for molecular weightreduction and mass loss for samples with different initial molecu-lar weights [2,3]. For the most common combination of hydrolysismechanisms identified in Part 1 [7], autocatalytic random scissionand autocatalytic end scission, the initial molecular weight did nottypically affect the molecular weight half-life, although the rate ofchain cleavage was affected.

The effect of residual monomer on the degradation was alsoanalysed. For autocatalytic hydrolysis, an inverse square root lawwas found to relate molecular weight half-life to residual mono-mer content. This trend was also identified in experimental data[12] for degradation of samples with different residual monomercontents defined by measurements. The model was able to fit thisexperimental data by only varying the initial monomer content be-tween fittings. It was found that experimental results for sampleswith high concentrations of residual monomer may demonstratetrends similar to those expected for noncatalytic hydrolysis.

Acknowledgements

A.G. acknowledges an EPSRC PhD studentship. The authorswould also like to acknowledge Kaarlo Paakinaho from Tampere

University of Technology for supplying experimental data from aprevious study [12].

References

[1] Migliaresi C, Fambri L, Cohn D. A study on the in vitro degradation ofpoly(lactic acid). J Biomater Sci Polym Ed 1994;5:591–606.

[2] Raman C, Berkland C, Kim K, Pack DW. Modeling small-molecule release fromPLG microspheres: effects of polymer degradation and nonuniform drugdistribution. J Controlled Release 2005;103:149–58.

[3] Pitt GG, Gratzl MM, Kimmel GL, Surles J, Sohindler A. Aliphatic polyesters II.The degradation of poly (DL-lactide), poly (e-caprolactone), and theircopolymers in vivo. Biomaterials 1981;2:215–20.

[4] Pistner H, Bendi DR, Mühling J, Reuther JF. Poly (L-lactide): a long-termdegradation study in vivo: Part III. Analytical characterization. Biomaterials1993;14:291–8.

[5] Park TG. Degradation of poly(D, L-lactic acid) microspheres: effect of molecularweight. J Controlled Release 1994;30:161–73.

[6] Huttunen M. Analysis of the factors affecting the inherent viscosity of orientedpolylactides during hydrolytic degradation. J. Mater. Sci. – Mater. Med.2013:1–14.

[7] Gleadall A, Pan J, Kruft M-A, Kellomäki M. Degradation mechanisms ofbioresorbable polyesters. Part 1. Effects of random scission, end scission andautocatalysis. Acta Biomater 2014;10:2223–32.

[8] Wang Y, Pan J, Han X, Sinka C, Ding L. A phenomenological model for thedegradation of biodegradable polymers. Biomaterials 2008;29:3393–401.

[9] Han X, Pan J. A model for simultaneous crystallisation and biodegradation ofbiodegradable polymers. Biomaterials 2009;30:423–30.

[10] Han X, Pan J, Buchanan F, Weir N, Farrar D. Analysis of degradation data ofpoly(L-lactide-co-L, D-lactide) and poly(L-lactide) obtained at elevated andphysiological temperatures using mathematical models. Acta Biomater2010;6:3882–9.

[11] Gleadall A, Pan J, Atkinson H. A simplified theory of crystallisation induced bypolymer chain scissions for biodegradable polyesters. Polym Degrad Stab2012;97:1616–20.

[12] Paakinaho K, Heino H, Väisänen J, Törmälä P, Kellomäki M. Effects of lactidemonomer on the hydrolytic degradation of poly(lactide-co-glycolide) 85L/15G.J Mech Behav Biomed Mater 2011;4:1283–90.

[13] Ellä V, Nikkola L, Kellomäki M. Process-induced monomer on a medical-gradepolymer and its effect on short-term hydrolytic degradation. J Appl Polym Sci2011;119:2996–3003.

[14] Hyon SH, Jamshidi K, Ikada Y. Effects of residual monomer on the degradationof DL-lactide polymer. Polym Int 1998;46:196–202.

[15] Tsuji H, Mizuno A, Ikada Y. Properties and morphology of poly(L-lactide). III.Effects of initial crystallinity on long-term in vitro hydrolysis of high molecularweight poly(L-lactide) film in phosphate-buffered solution. J Appl Polym Sci2000;77:1452–64.

[16] Weir N, Buchanan F, Orr J, Farrar D, Dickson G. Degradation of poly-L-lactide.Part 2: increased temperature accelerated degradation. Proc Inst Mech Eng,Part H: J Eng Med 2004;218:321–30.

[17] Tsuji H. In vitro hydrolysis of blends from enantiomeric poly(lactide)s. Part 1.Well-stereo-complexed blend and non-blended films. Polymer 2000;41:3621–30.

[18] Tsuji H. In vitro hydrolysis of blends from enantiomeric poly(lactide)s. Part 4:well-homo-crystallized blend and nonblended films. Biomaterials 2003;24:537–47.

[19] Witschi C, Doelker E. Influence of the microencapsulation method and peptideloading on poly(lactic acid) and poly(lactic-co-glycolic acid) degradationduring in vitro testing. J Controlled Release 1998;51:327–41.

[20] Li SM, Garreau H, Vert M. Structure-property relationships in the case of thedegradation of massive aliphatic poly-(a-hydroxy acids) in aqueous media. JMater Sci Mater Med 1990;1:123–30.

[21] Grizzi I, Garreau H, Li S, Vert M. Hydrolytic degradation of devices based onpoly(dl-lactic acid) size-dependence. Biomaterials 1995;16:305–11.

[22] Ambrose CG, Clanton TO. Bioabsorbable implants: review of clinicalexperience in orthopedic surgery. Ann Biomed Eng 2004;32:171–7.

[23] Pietrzak WS, Sarver DR, Verstynen ML. Bioabsorbable polymer science for thepracticing surgeon. J Craniofac Surg 1997;8:87–91.

[24] Peltoniemi H. Biocompatibility and fixation properties of absorbableminiplates and screws in growing calvarium. An experimental study insheep [thesis]. Finland: University of Helsinki; 2000.

[25] Böstman O, Pihlajamäki H. Clinical biocompatibility of biodegradableorthopaedic implants for internal fixation: a review. Biomaterials 2000;21:2615–21.

[26] Suganuma J, Alexander H. Biological response of intramedullary bone to poly-L-lactic acid. J Appl Biomater 1993;4:13–27.

[27] Paakinaho K, Ellä V, Syrjälä S, Kellomäki M. Melt spinning of poly(L/D)lactide96/4: Effects of molecular weight and melt processing on hydrolyticdegradation. Polym Degrad Stab 2009;94:438–42.