New Research Article Modelling pH-Optimized Degradation of...

Research ArticleModelling pH-Optimized Degradation ofMicrogel-Functionalized Polyesters

Lisa Buumlrgermeister1 Marcus Hermann2 Katalin Feheacuter3 Catalina Molano Lopez4

Andrij Pich4 Julian Hannen5 Felix Vogt6 and Wolfgang Schulz12

1Fraunhofer Institute for Laser Technology Steinbachstrasse 15 52074 Aachen Germany2Nonlinear Dynamics of Laser Processing RWTH Aachen University Steinbachstrasse 15 52074 Aachen Germany3Institute of Textile Technology RWTH Aachen University Otto-Blumenthal-Strasse 1 52074 Aachen Germany4Functional and Interactive Polymers DWI RWTH Aachen University Forckenbeckstrasse 50 52074 Aachen Germany5Innovation Strategy and Organization Group RWTH Aachen University Kackertstrasse 7 52072 Aachen Germany6Department of Cardiology RWTH Aachen University Pauwelstrasse 30 52074 Aachen Germany

Correspondence should be addressed to Lisa Burgermeister lisabuergermeisteriltfraunhoferde

Received 6 May 2016 Accepted 29 June 2016

Academic Editor Hendra Hermawan

Copyright copy 2016 Lisa Burgermeister et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

We establish a novel mathematical model to describe and analyze pH levels in the vicinity of poly(N-vinylcaprolactam-co-acetoacetoxyethyl methacrylate-co-N-vinylimidazole) (VCLAAEMVIm) microgel-functionalized polymers during biodegrada-tion Biodegradable polymers especially aliphatic polyesters (polylactidepolyglycolidepolycaprolactone homo- and copolymers)have a large range ofmedical applications including delivery systems scaffolds or stents for the treatment of cardiovascular diseasesMost of those applications are limited by the inherent drop of pH level during the degradation processThe combination of polymerswith VCLAAEMVIm-microgels which aims at stabilizing pH levels is innovative and requires new mathematical models forthe prediction of pH level evaluation The mathematical model consists of a diffusion-reaction PDE system for the degradationincluding reaction rate equations and diffusion of acidic degradation products into the vicinity A system of algebraic equationsis coupled to the degradation model in order to describe the buffering action of the microgel The model is validated against theexperimental pH-monitored biodegradation of microgel-functionalized polymer foils and is available for the design of microgel-functionalized polymer components

1 Introduction

Cardiovascular diseases are the number one cause of deathworldwide globally claiming 17 million lives each year andaccounting for 29of all deaths [1]Through the introductionof minimally invasive procedures like percutaneous coronaryintervention (PCI) and the use of intravascular stents thetreatment of many cardiovascular diseases such as coronaryartery disease the obstruction of a coronary artery due todevelopment of atherosclerosis has been revolutionized [23]

Nevertheless efficacy and safety of available stents arelimited in part as suitable autologous tissue engineered stentsare lacking [4]Mostly nondegradable syntheticmaterials are

substituted to repair the injured cardiovascular tissue Meantto prevail at the implantation site these foreign and thereforeinherently thrombogenic materials can be associated withseveral risks including calcification and acute or late stentthrombosis which require prevention by antiplatelet therapy[5]

In contrast tissue engineered bioresorbable stents pro-vide temporary scaffolding for the formation of autologoustissue with the capacity to regenerate and grow After thedegradation process of the stent only the restored vesselremains which might reduce the risk of late stent thrombosis

The most frequently used resorbable polymers forbiomedical implants including bioresorbable stents are thealiphatic polyesters polylactic acid (PLA) and polyglycolic

Hindawi Publishing CorporationJournal of Healthcare EngineeringVolume 2016 Article ID 8125416 8 pageshttpdxdoiorg10115520168125416

2 Journal of Healthcare Engineering

acid (PGA) and their copolymers The mechanism of poly-ester degradation has been well investigated Polymer chainsare degraded by hydrolytic scission of ester linkages in thepolymer backbone and thereby create carboxylic end groupsThese acidic carboxyl end groups diffuse into the vicinity ofthe polymer and decrease the pH level there [6ndash10]

This pH drop is one of the main drawbacks of usingaliphatic polyesters for implants as a low pHmay cause tissuereactions like inflammation [11ndash13]

Still biodegradable stents have marked potential long-term advantages [4 14] In order to overcome the disadvan-tage of acidic pH levels during degradation of biodegradablestents we investigate the fabrication of polylactic acid (PLA)fibers for cardiovascular stents with pH-optimized degrada-tion behavior using VCLAAEMVIm (8mol)-microgels asinsoluble buffers [15]

Microgels are defined as hydrogel particles with a dimen-sion from 10 nanometers up to themicrometer range Hydro-gels in general are novel components that arouse specialinterest in the biomedical field and nanotechnology [16 17]

Depending on the molecular building units and the syn-thesis procedure it is possible to synthesize colloidal hydro-gels with controlled particle size Those can be defined aspolymer networks with smart properties such as water-uptake capacity degree of swelling and responsiveness toexternal stimuli Furthermore these nanoparticles show highcolloidal stability a well-defined structure and a high sur-face area Through variation of the monomer type andorintroduction of comonomers responsiveness to temperaturepH magnetic field or light intensity can be tailored Thisproperty in combination with the swelling features makesthe utilization of microgels as biocompatible materials forpharmaceutical applications possible [16 18ndash23]

Monomers like N-isopropylacrylamide (NIPAAm) andN-vinylcaprolactam (VCL) have been used for the synthesisof thermoresponsive microgels because they can form water-soluble polymers with lower critical solution temperature(LCST) [18 20 24 25] Other interesting components suchas N-vinylimidazole (VIm) can be used to achieve pH-sensitivity due to its protonationdeprotonation process atdifferent pH levels Pich et al [26] have successfully synthe-sized VCLVIm-based microgels which show both tempera-ture and pH-responsiveness In this study the swelling couldbe controlled by the VIm content in the microgel

However cardiovascular stents require for the degrada-tion period to last over months making their experimentalresearch as well as their design and optimization rathertime-intensiveThis study aims at developing a mathematicalmodel able to predict the pH level resulting from polymerdegradation and taking into account the buffering action ofeventually incorporated microgels This mathematical modelwill be validated against the experimental pH-monitoredbiodegradation of microgel-functionalized polymer foils andwill be available for the design of microgel-functionalizedpolymer stents and other components

Computational methods to model the degradation ofbiodegradable polymers have been proposed by a quantityof research teams Siparsky et al [27] described the kineticsof hydrolysis reaction by rate equations and their analytic

solutions Han [28] used Monte Carlo methods to predictthe degradation of PLA PGA and some copolymers Healso investigated the influence of chemical buffers on thedegradation process and the pH level Wang et al [29]presented a reduced model for polymer degradation usingtwo rate equations for the concentrations of carboxylic endgroups and ester bonds in the PLA phase Pan et al [30]included a model for chemical buffers in such a reducedmodel for biodegradation Moreover rate equations for theconcentrations of different molecules sizes which the poly-mer undergoes in its degradation process were built up andanalyzed by Lazzari et al [31] The buffering action of thepoly(N-vinylimidazole) hydrogel wasmodelled and analyzedby Horta et al [32 33] To the best of the authorsrsquo knowledgeso far no publishedmodel for the biodegradation of polymersbuffered with VCLAAEMVIm-microgels exists

Investigating microgel-functionalized resorbable poly-mers with pH-regulatory potential a recent study of Feher etal [15] employs a publication-based keyword search strategyto investigate the existing knowledge base underpinning thetopic The authors find that only a marginal number ofstudies is dedicated to investigate the pH-regulative potentialof microgel containing degradable polymers This clearlydemonstrates an underinvestigated topic Given the poten-tial scope of application ranging from drug-coated pH-regulating degradable textiles to stents this paper is alignedto the apparent research gap

2 Materials and Methods

21 VCLAAEMVIm (8mol)-Microgel The synthesis ofVCLAAEMVIm (8)-microgel is well described in Feheret al [15] The description is not repeated here

22 Polymer VCLAAEMVIm (8mol)-Microgel FoilsPoly(L-lactide-co-glycolid) PLG 8523 by Purac and themicrogel are weighed separately Both samples are thenfilled up with a solvent in a way that the mass fraction ofpolymer119908Pol and microgel 119908MG amount to 015 respectivelyThe sealed samples are stirred at 250 rpm for 24 hours ina magnetic stirrer The resulting microgel and polymersolutions are mixed thoroughly to ensure a homogeneoussolution The solutions are evenly spread on a petri dish andthereby infused to a foil After 48 hours within the distractorhood the solvent is fully evaporated allowing for the foil tobe peeled from the glass

23 Degradation Experiment The degradation experimentsare carried out according to ISO 13781 [34] Each samplecontains 01 g of the produced foil and is supplemented withdistilled water (specific conductivity lt 01 120583Scm at 25∘C)at the ratio of 1 100 The samples are prepared in 20mLglass containers and sealed during degradation periods Thecontainers are only opened for pH measurement

Throughout the degradation process the samples arestored in an oven at 37∘C pH measurement is conducteddaily within the first 20 days followed by weekly readingsfor a total time period of at least 30 days To determine

Journal of Healthcare Engineering 3

the pH level the samples are withdrawn from the ovenDue to the high temperature sensitivity of the pH level thesamples are cooled down to ambient temperature (20∘C)prior to the measurement Each measurement is repeatedtwice and the three results are averaged To increase theexperimentrsquos significance each sample is prepared twiceand the average is calculated from the results To ensure ahomogeneous distribution of hydron H+ during measuringthe samples are swiveled prior to the measurement The pH-meter ldquoSevenEasytrade S20rdquo with an uncertainty of plusmn001 byMettler Toledo Gieszligen Germany is used The electrode ofthe pH-meter is calibrated beforehand using buffer solutionswith pH levels of 401 700 and 921

24 Physical Model Reduction and Mathematical ModellingIn order to analyze the pH level in a vicinity of a degradingpolyester component we predict the concentration of hydron[H+] resulting from dissociation of carboxyl groups of thedegrading polymer As the dissociation of the carboxylgroups COOH to COOminus and hydron H+ in aqueous solutiontakes place on a very short timescale we make use of theequilibrium constant 119870COOH = [COOminus][H+][COOH] forthe dissociation reaction and insert it into the balance ofmassand charge to calculate the concentration of hydron [H+]

[H+] =119870w[H+]+

119870COOH [M][H+] + 119870COOH

(1)

with the equilibrium constant for the dissociation of H2O to

OHminus and H+ 119870w = [H+

][OHminus] The brackets [X] mark theconcentration of the corresponding species X We used thefact that the concentration of oligomers [M] corresponds tothe concentration of carboxyl groups [COOH] The concen-tration of H

2O is not part of the equation as we assume it to

be constant because the water penetration into the polymeris on a very short timescale

The concentration of carboxyl groups increases with theprogressing scission of polymer chains by hydrolysis reactionand is thus time dependent Hydrolysis of polyesters proceedspartly as spontaneous reaction andpartly catalyzed by hydronH+ The reaction is called autocatalytic as the reaction prod-ucts hydroxyl alcohol and carboxylic acid end groupsmdashalsoreferred to as oligomers [28]mdashdissociate and acidize the envi-ronment and as a result accelerate the rate of hydrolysis [27]The hydrolysis reaction is explained in detail elsewhere [35]

We implement a phenomenological model for the degra-dation of biodegradable polymers initially introduced byWang et al [29] As a result we predict the evolution in timeof oligomer concentration [M]init after degradation andbefore buffering as well as the evolution in time of concen-tration of ester bonds [E] inside the calculation area by tworate equations

119889 [E]119889119905

= minus119896 [E] minus 119896cat [E] [H+] (2)

119889 [M]init119889119905

= minus

119889 [E]119889119905

(3)

with the rate coefficients 119896 and 119896cat for spontaneous and cat-alytic scission of ester bonds inside the polymer respectivelyUsing the equilibrium constant119870COOH we transform (2) to

119889 [E]119889119905

= minus119896 [E] minus 119896catradic119870COOH [E] radic[M] (4)

[M] refers to the concentration of oligomers available for theautocatalytic scission

After dissociation of oligomers the hydrons are bufferedby the VIm groups of the microgel Microgel and polymerform a two-phase system The hydrons diffuse inside themicrogel and are bound to the VIm The dissociation prod-ucts COOminus bound to the oligomers will also diffuse insidethe microgel and remain there unbound due to electrostaticforces The diffusion processes will continue until the ther-modynamic equilibrium between the two phases is reachedUsing the assumption that the buffer reaction is fast comparedto the degradation processes we use the equilibrium constantof the buffer reaction 119870P = [P][H

+

][PH+] with the con-centration of free buffer molecules [P] and occupied buffermolecules [PH+] respectively and find a system of algebraicequations describing the buffering action of themicrogelThederivation is explained in detail for poly(N-vinylimidazole)by Horta and Pierola [33]

[COOminus]gel

=

[H+]3

gel + [H+]2

gel (119870P + [P]0) minus [H+]gel sdot 119870w minus 119870P sdot 119870w

[H+]gel sdot ([H+

]gel + 119870P)

[COOminus]gel

= minus([H+] minus

119870w[H+]

) sdot

119881bath119881gel+ ([H+]init minus

119870w[H+]init)

sdot

119881init119881gel

[H+] = radic[H+]gel [COOminus]gel + 119870w

(5)

where [X]gel represents the concentration of the species Xin the microgel phase [X]init represents the concentration inthe polymer before the buffering reaction 119881initgelbath are thevolumes occupied by the polymer without the gel the volumeof the microgel and the volume of the polymer including themicrogels respectively and [P]

0is the initial concentration

of buffer molecules in the system Using (1) we calculatefrom [H+] the concentration of oligomers [M]bath after thebuffering action of the microgel and complete the ODEsystem ((2) + (3)) by a rate equation for the concentrationof oligomers [M] after buffering which allows for diffusion ofthe oligomers

119889 [M]119889119905

=

[M]bath[M]init(minus

119889 [E]119889119905

) + 1198630Δ [M] (6)

with1198630being a constant diffusivity of oligomers

The calculation area and initial and boundary condi-tions are chosen appropriate for the degradation experiment


Table 1 Parameters used for simulation

Symbol Value Unit Description Source

119870COOH 10minus387 molL

Equilibrium constant ofdissociation reaction of COOH at

37∘C[28]

119870119908

18 sdot 10minus14 (molL)2 Equilibrium constant of

dissociation reaction of H2

O at 37∘C [36]

119896 0005 1week Rate constant of spontaneous esterbond scission Fit to experiments

119896catsdot radic119870COOH 05 sdot 10

minus3

radicm3molweek Rate constant for autocatalyzedester bond scission Fit to experiments

119870P 1 sdot 10minus10 molL Equilibrium constant for buffer

reaction at 20∘C Fit to experiments

[P]0

03487 molL Initial buffer concentration Fit to experiments

119881gel119881init 942 sdot 10minus6 mdash Fraction of volumes occupied by gel

and polymer Derived from experimental procedure

119881bath119881init 1 minus 119881gel119881init mdash Fraction of volumes occupied bypolymer + gel and polymer mdash

1198630p 2 sdot 10

minus9 m2week Diffusion constant of oligomer inthe polymer [28]

1198630w 2 sdot 10

minus8 m2week Diffusion constant of oligomer inwater [37]

119889p 015 mm Thickness of polymer foil Derived from experimental procedure

119889w 196 mm Thickness of water column abovepolymer foil Derived from experimental procedure

described aboveAs a consequence of the typical extensions ofa polymer foil diffusion will be dominant in one dimensionThus we set up a 1D diffusion model and use 119909 as thecoordinate in space The calculation area consists of twocomponents the (microgel containing) polymer with thethickness 119889p and the surrounding water with the thickness119889w At time 119905 = 0 ester bonds have the initial concentration[E]0in the polymer foil (0 le 119909 le 119889p) and 0 in the water

volume (119909 gt 119889p) and the initial concentrations of oligomers[M]init and [M] are 0 everywhere

[E] (119905 = 0)|0le119909le119889p= [E]0

[E] (119905 = 0)|119909gt119889p= 0

[M] (119905 = 0) = [M]init (119905 = 0) = 0

(7)

The boundaries at 119909 = 0 and 119909 = 119889w are isolated and donot allow for diffusion of oligomers At the boundary 119909 = 119889pcontinuity of oligomers is required

119889 [M]119889119909

10038161003816100381610038161003816100381610038161003816119909=0

=

119889 [M]119889119909

10038161003816100381610038161003816100381610038161003816119909=119889w

= 0

[M] (119909 = 119889minusp) = [M] (119909 = 119889+

p)

(8)

A schematic representation of experimental set-up and thecalculation area is depicted in Figure 1

The diffusivity of oligomers1198630p and1198630w is considered to

be constant in the polymer and the water layer respectivelyIn order to simulate the swiveling of the samples in theexperimental procedure we increase the diffusion constant1198630w in (6) by a factor of 103 for a very short period on every

simulated measurement event

pH meter

Water

Polyester foil

Glass container

0

x

1D calculation area

dw

dp

Figure 1 Schematic representation of the 1D simulation area where119909 depicts the coordinate in space and 119889p and 119889w are the positions ofthe boundary of polymer foil and water layer respectively

The parameters which have been used to carry out thesimulation experiments discussed in the following chapterare listed in Table 1

3 Results and Discussion

31 Buffering Action of VCLAAEMVIm-Microgels As thebuffering model (5) was originally applied to a poly(N-vin-ylimidazole) gel [33] we investigate its appropriatenessfor the VCLAAEMVIm-microgels in a preliminary study


1 2 3 4 5 61

2

3

4

5

6

7

8

SimulationExperiment

pHba

th

pHinit

Figure 2 pH level (pHbath) of different initial concentrations ofhydrochloric acid (pHinit) after buffering with 01 g microgel

Therefore we adjust hydrochloric acid to different initialpH levels pHinit add 01 g of VCLAAEMVIm-microgeland measure the pH level of the common bath pHbath Wecalculate the resulting pH levels pHbath using (5) and the sameinitial pH levels as in the experiment The simulation resultin comparison to the experiment is plotted in Figure 2 Weconsider the unknown equilibrium constant for the bufferreaction 119870P and the amount of VIm molecules per microgelunit 120590 as fitting parameters and use the withdrawn valuesof 119870P = 1 sdot 10

minus10 molL and 120590 = 1522 sdot 1020 1g for fur-ther simulation The preliminary study shows a thresholdbehavior for the buffering effect Initial pH levels above 4(pHinit ge 4) are buffered by VCLAAEMVIm-microgel toa neutral pH level For initial pH levels below this value thebuffering action of VCLAAEMVIm-microgel in the usedconcentration is not sufficient to receive a neutral pH level

Furthermore we analyze the amount of VCLAAEMVIm-microgel necessary for successful buffering action toa neutral pH level The result is shown in Figure 3 InitialpH levels of 375 and higher can be buffered to neutral levelby a total amount of 0005 g microgel (solid black line inFigure 3) This corresponds to a microgel mass fraction 119908MGof 005 in the polymer foils (for preparation see above) Athreshold below which very strong decay of pH level arisesis seen at pHinit = 178 for the 0005 g VCLAAEMVIm-microgel Lower VCLAAEMVIm-microgel amounts (non-solid and gray lines in Figure 3) lead to higher thresholdpH levels Thus the curves in Figure 3 are shifted to theright with decreasing VCLAAEMVIm-microgel amountThe threshold behavior is less distinct for lower microgelamounts Hence the curves in Figure 3 are also flattenedwith decreasing VCLAAEMVIm-microgel amount Nearlyno buffering action is predicted for a mass of 1 sdot 10minus6 gVCLAAEMVIm-microgel

This analysis is valid for the ideal case when considering ahomogenous VCLAAEMVIm-microgel distribution inside

1

0

2

3

4

5

6

7

pHba

th

0 1 2 3 4 5 76pHinit

5 times 10minus3 g

1 times 10minus3 g

1 times 10minus4 g

1 times 10minus5 g

1 times 10minus6 g

Figure 3 Predicted pH-value (pHbath) after buffering differentinitial pH levels (pHinit) with different constant microgel amount

the polymer where diffusion of oligomers to reach the VIm-molecules is not necessary and no barriers for exampleelectrostatic reasons occur

32 Degradation Studies The experimental results from thedegradation studies of polymer foils with VCLVCLAAEMVIm-microgelmass fractions of119908MG = 000 and119908MG = 005respectively are depicted in Figure 4 via the mean andthe standard deviation of the two measurement series (seeabove) Without microgel a drop in pH level arises asexpected leading to pH = 54 after 35 days As the pH levelis measured in the water component of the experimental set-up (119889p le 119909 le 119889w in Figure 1) the pH level in the core ofthe polymer foil (119909 = 0) will be lower This lowest pH levelis relevant to choosing the appropriate VCLAAEMVIm-microgel content

We use the experimental results of polymer foils witha microgel mass fraction of 119908MG = 000 to determine therate constants in the degradation model (2) in order tofind a good agreement between simulation and experimentalmeasurements The simulation result as average pH level inthe water component (119889p le 119909 le 119889w in Figure 1) is plotted as asolid line in Figure 4The influence of the simulated swivelingprocess can be seen clearly as steps in the pH level curveTheobtained degradation rates as all other model parameters arelisted in Table 1

The pH level in the center of the polymer foil (119909 = 0in Figure 1) is evaluated and plotted over time in Figure 5The pH level drops to 142 after 35 days using a mass fractionof 119908MG = 000 (solid line) Applying a VCLAAEMVIm-microgel buffer with a mass fraction of 119908MG = 005 to theresulting solution (pHinit = 142) will not be sufficient tobuffer the pH to a neutral level but only to a pH level ofapproximately pHbath = 2 according to Figure 3 Neverthe-less in the center of the foil after 35 days only a small decrease


0 5 10 15 20 25 30 353

35

4

45

5

55

6

65

7

75

pH

Time t (d)

= 000 simulation= 005 simulation

= 000 experiment= 005 experiment

wMGwMG

wMGwMG

Figure 4 pH level over time during degradation experiment ofpolymer foils with a VCLAAEMVIm-microgel mass fraction119908MGof 000 and 005 respectively in comparison to the simulation (forevaluation in water component see Figure 1)Themodel parametersare given in Table 1

0 5 10 15 20 25 30 35 401

2

3

4

5

6

7

pH

Time t (d)

= 000

= 005

wMGwMG

Figure 5 Simulated pH level over time for polymer foils with aVCLAAEMVIm -microgel mass fraction of 119908MG = 000 and119908MG = 005 respectivelyThe pH level was evaluated at the center ofthe polymer foil (119909 = 0 in Figure 1)Themodel parameters are givenin Table 1

in pH level (sim537) is predicted for a microgel mass fractionof 119908MG = 005 (dotted line in Figure 5) This discrepancyresults from the deceleration of the degradation processthroughVCLAAEMVIm-microgelThe deceleration can beexplained via the reduction of the autocatalyzed degradationThe normalized concentration of ester bonds in the polymercomponent over time is depicted in Figure 6 It illustrates

0 5 10 15 20 25 30 35 4001

02

03

04

05

06

07

08

09

1

Time t (d)

= 000

= 005

[E][E

] 0

wMGwMG

Figure 6 Simulated normalized ester bond concentration [E][E]0

over time for polymer foils with a VCLAAEMVIm-microgelmass fraction of 119908MG = 000 and 119908MG = 005 respectively Theconcentration was evaluated as an average of the polymer foil (0 lt119909 lt 119889p in Figure 1) The model parameters are given in Table 1

the reduction of overall degradation rate by incorporationof VCLAAEMVIm-microgel Thus a VCLAAEMVIm-microgel mass fraction of 119908MG = 005 will possibly be suf-ficient to buffer the pH to a neutral level Figure 4 confirmsthis expectation in theory and experiment The predicteddecrease of pH level in the water component is smaller thanin the center of the foil and is in good accordance with themeasurements

In order to briefly demonstrate the influence of the exper-imental procedure on the development of pH level threedifferent swiveling procedures are simulated and the resultingaverage pH levels in the water phase are plotted in Figure 7(no swiveling dashed line swiveling at discretemeasurementevents solid line and continuous swiveling dotted line)Thestrong deviation in simulated pH levels shows the importanceof standardized experimental procedures

33 Limitations of the Study The rate equation system fordegradation of polymers ((1)ndash(3) and (6)) is a very reducedmodel Any difference between scission of ester bonds atmolecule ends and that of bonds in themiddle of the polymermolecules is neglected as well as the effects of crystallinityof diffusivity varying in time and others Nevertheless avery similar model is already considered very useful for theprediction of size and shape effects on biodegradation [29]One has to perform reference experiments without incor-poration of VCLAAEMVIm-microgels to determine therate coefficients of the presented degradation model Withthese references our model can be used for investigating thepH levels in the vicinity of polymer components and foranalyzing buffering behavior The reference experiments willhave different results using different polymers and thereforehave to be performed for every material that is investigated


0 5 10 15 20 25 30 35 401

2

3

4

5

6

7pH

Time t (d)

D0w

D0w

times 103

D0w + D0w times 103120575(t minus ti)

Figure 7 Simulated pH level over time for polymer foils without anyVCLAAEMVIm-microgel content The diffusivity was changedfrom a low value (119863

0w) to a higher value (1198630w sdot 103) to a low value

with several peaks 119894 (1198630w + 1198630w sdot 10

3

120575(119905 minus 119905119894

) with the Kroneckerdelta 120575)The pH level was evaluated as an average of the water phase(119889p lt 119909 lt 119889w in Figure 1)Themodel parameters are given in Table 1

The simulated model task consisting of a 1D calculationarea is a simplified task and deviations from experimentalmeasurements are expectable It is adequate for a first bench-mark of the model with experiments and appropriate formodel development as very short computation time resultsfrom the simple task

Model refinements and extensions are necessary in orderto investigate the influence ofmicrogel distribution inside thepolymer and buffering reaction kinetics For this purposenew specific experiments have to be conducted

We study the degradation behavior of polymer foils ina preclinical set-up according to ISO 13781 Any biologicalinfluences like enzymes vascularization buffering in bodyfluids or patient individual factors cannot be investigated indegradation experiments of this kind As can be seen fromsimulation results (Figure 7) conditions (eg flow of liquidmedium) during degradation experiments have an importantinfluence on the degradation results Thus the authors sug-gest building up a more complex test bench for degradationexperiments simulating blood flow amongst others beforebeginning with clinical studies

4 Conclusions

VCLAAEMVIm-microgel-functionalized fibers with pH-optimized degradation behavior are a promising approach fora wide range of medical applications In particular the treat-ment ofmany cardiovascular diseases such as coronary arterydisease will benefit from biodegradable material for stents

without the drawback of acidic pH levels as a consequenceof degradation

Within this study a mathematical model is presentedwhich can deal as an important tool to design componentswith pH-optimized degradation behavior Iterative designof suitable degradation behavior based on mathematicalmodelling is shown to exploit the potentials of the medicalapplication and will save engineering costs and time fordegradable polymer devices and can contribute to reducinganimal studies

The mathematical model consists of a reduced degra-dation model based on a rate equation system includingdiffusion of acidic degradation products into the vicinity ofthe componentThis degradation model is coupled with a setof algebraic equationsmodelling the buffering action of VCLAAEMVIm-microgel Both models (rate equations fordegradation and algebraic buffering model) are evaluatedseparately in comparison to experimental measurements ofpH level and show good agreement with them

The pH level during the degradation of polymer foilsis monitored during 35 days and serves as reference to fitthe rate constants of the mathematical degradation modelAdditionally initial pH levels are buffered with a constantamount of VCLAAEMVIm-microgel to calibrate themodelfor the buffer reaction

A VCLAAEMVIm-microgel mass fraction of 119908MG =005 is found to deliver a sufficient buffering action withinat least 35 days of degradation of polymer foils Simulation aswell as experimental studies confirmed this buffering effect

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The current research project ldquopHaserrdquo is funded by the Excel-lence Initiative of the German federal and state governments

References

[1] WHO ldquoCardiovascular diseases (CVDs) fact sheetN∘317rdquo 2016httpwwwwhointmediacentrefactsheetsfs317en

[2] R L Mueller and T A Sanborn ldquoThe history of interventionalcardiology cardiac catheterization angioplasty and relatedinterventionsrdquo American Heart Journal vol 129 no 1 pp 146ndash172 1995

[3] P W Serruys M J B Kutryk and A T L Ong ldquoCoronary-artery stentsrdquo The New England Journal of Medicine vol 354no 5 pp 483ndash495 2006

[4] M Generali P E Dijkman and S P Hoerstrup ldquoBioresorbablescaffolds for cardiovascular tissue engineeringrdquo European Med-ical Journal Interventional Cardiology vol 1 pp 91ndash99 2014

[5] P W Serruys J A Ormiston Y Onuma et al ldquoA bioabsorbableeverolimus-eluting coronary stent system (ABSORB) 2-yearoutcomes and results from multiple imaging methodsrdquo TheLancet vol 373 no 9667 pp 897ndash910 2009


[6] A Weiler H-J Helling U Kirch T K Zirbes and K ERehm ldquoForeign-body reaction and the course of osteolysis afterpolyglycolide implants for fracture fixation experimental studyin sheeprdquoThe Journal of Bone and Joint Surgery B vol 78 no 3pp 369ndash376 1996

[7] F W Cordewener M F Van Geffen C A P Joziasse et alldquoCytotoxicity of poly(96L4D-lactide) the influence of deg-radation and sterilizationrdquo Biomaterials vol 21 no 23 pp2433ndash2442 2000

[8] S W Shalaby Biomedical Polymers Designed-to-Degrade Sys-tems Hanser Publishers New York NY USA HanserGardnerPublications Toronto Canada 1994

[9] M S Taylor A U Daniels K P Andriano and J Heller ldquoSixbioabsorbable polymers in vitro acute toxicity of accumulateddegradation productsrdquo Journal of Applied Biomaterials vol 5no 2 pp 151ndash157 1994

[10] C M Agrawal and K A Athanasiou ldquoTechnique to controlpH in vicinity of biodegrading PLA-PGA implantsrdquo Journal ofBiomedical Materials Research vol 38 no 2 pp 105ndash114 1997

[11] E J Bergsma F R Rozema R R M Bos and W C de BruijnldquoForeign body reactions to resorbable poly(L-lactide) boneplates and screws used for the fixation of unstable zygomaticfracturesrdquo Journal of Oral and Maxillofacial Surgery vol 51 no6 pp 666ndash670 1993

[12] OM Bostman ldquoOsteolytic changes accompanying degradationof absorbable fracture fixation implantsrdquo Journal of Bone andJoint Surgery B vol 73 no 4 pp 679ndash682 1991

[13] O Bostman and H Pihlajamaki ldquoClinical biocompatibilityof biodegradable orthopaedic implants for internal fixation areviewrdquo Biomaterials vol 21 no 24 pp 2615ndash2621 2000

[14] A Colombo and E Karvouni ldquoBiodegradable stents lsquoFulfillingthe mission and stepping awayrsquordquo Circulation vol 102 no 4 pp371ndash373 2000

[15] K Feher T Romstadt C A Bohm et al ldquoMicrogel-function-alised fibres with pH-optimised degradation behaviourmdashapromising approach for short-term medical applicationsrdquo Bio-NanoMaterials vol 16 no 4 pp 259ndash264 2015

[16] S Saxena C E Hansen and L A Lyon ldquoMicrogel mechanicsin biomaterial designrdquo Accounts of Chemical Research vol 47no 8 pp 2426ndash2434 2014

[17] A S Hoffman ldquoHydrogels for biomedical applicationsrdquo Ad-vanced Drug Delivery Reviews vol 54 no 1 pp 3ndash12 2002

[18] V Aseyev H Tenhu and F M Winnik ldquoNon-ionic thermore-sponsive polymers in waterrdquo in Self Organized Nanostructuresof Amphiphilic Block Copolymers II A H E Muller and OBorisov Eds vol 242 ofAdvances in Polymer Science pp 29ndash89Springer Berlin Germany 2011

[19] S Nayak and L A Lyon ldquoSoft nanotechnology with soft nano-particlesrdquo Angewandte ChemiemdashInternational Edition vol 44no 47 pp 7686ndash7708 2005

[20] V Boyko A Pich Y Lu S Richter K-F Arndt and H-JP Adler ldquoThermo-sensitive poly(N-vinylcaprolactam-co-ace-toacetoxyethyl methacrylate) microgels 1mdashsynthesis and char-acterizationrdquo Polymer vol 44 no 26 pp 7821ndash7827 2003

[21] K Raemdonck J Demeester and S De Smedt ldquoAdvancednanogel engineering for drug deliveryrdquo Soft Matter vol 5 no4 pp 707ndash715 2009

[22] L A Lyon Z Meng N Singh C D Sorrell and A St JohnldquoThermoresponsive microgel-based materialsrdquo Chemical Soci-ety Reviews vol 38 no 4 pp 865ndash874 2009

[23] R Pelton ldquoTemperature-sensitive aqueous microgelsrdquo Advan-ces in Colloid and Interface Science vol 85 no 1 pp 1ndash33 2000

[24] B Tasdelen N Kayaman-Apohan O Guven and B M BaysalldquoSwelling and diffusion studies of poly(N-isopropylacrylam-ideitaconic acid) copolymeric hydrogels in water and aqueoussolutions of drugsrdquo Journal of Applied Polymer Science vol 91no 2 pp 911ndash915 2004

[25] X Zhou F Su Y Tian and D R Meldrum ldquoDually fluorescentcore-shell microgels for ratiometric imaging in live antigen-presenting cellsrdquo PLoS ONE vol 9 no 2 Article ID e881852014

[26] A Pich A Tessier V Boyko Y Lu and H-J P Adler ldquoSyn-thesis and characterization of poly(vinylcaprolactam)-basedmicrogels exhibiting temperature and pH-sensitive propertiesrdquoMacromolecules vol 39 no 22 pp 7701ndash7707 2006

[27] G L Siparsky K J Voorhees and F Miao ldquoHydrolysis of poly-lactic acid (PLA) and polycaprolactone (PCL) in aqueous ace-tonitrile solutions autocatalysisrdquo Journal of Environmental Poly-mer Degradation vol 6 no 1 pp 31ndash41 1998

[28] X Han ldquoDegradation models for polyesters and their compos-itesrdquo 2011

[29] Y Wang J Pan X Han C Sinka and L Ding ldquoA phenomeno-logical model for the degradation of biodegradable polymersrdquoBiomaterials vol 29 no 23 pp 3393ndash3401 2008

[30] J Pan X Han W Niu and R E Cameron ldquoA model for bio-degradation of composite materials made of polyesters andtricalcium phosphatesrdquo Biomaterials vol 32 no 9 pp 2248ndash2255 2011

[31] S Lazzari F Codari G Storti MMorbidelli andDMoscatellildquoModeling the pH-dependent PLA oligomer degradation kinet-icsrdquo Polymer Degradation and Stability vol 110 pp 80ndash90 2014

[32] A Horta M J Molina M R Gomez-Anton and I F PierolaldquoThe pH inside a swollen polyelectrolyte gel poly(N-vinyl-imidazole)rdquoThe Journal of Physical Chemistry B vol 112 no 33pp 10123ndash10129 2008

[33] AHorta and I F Pierola ldquoPoly(N-vinylimidazole) gels as insol-uble buffers that neutralize acid solutions without dissolvingrdquoThe Journal of Physical Chemistry B vol 113 no 13 pp 4226ndash4231 2009

[34] ISO ldquoPoly(L-lactide) resins and fabricated forms for surgicalimplantsmdashin vitro degradation testingrdquo ISO 137811997 1997

[35] N Lucas C Bienaime C Belloy M Queneudec F Silvestreand J-E Nava-Saucedo ldquoPolymer biodegradation mechanismsand estimation techniquesmdasha reviewrdquoChemosphere vol 73 no4 pp 429ndash442 2008

[36] 2016 httpwwwchemiedelexikonDissoziationskonstantehtml

[37] A C F Ribeiro V M M Lobo D G Leaist et al ldquoBinary dif-fusion coefficients for aqueous solutions of lactic acidrdquo Journalof Solution Chemistry vol 34 no 9 pp 1009ndash1016 2005

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



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Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



acid (PGA) and their copolymers The mechanism of poly-ester degradation has been well investigated Polymer chainsare degraded by hydrolytic scission of ester linkages in thepolymer backbone and thereby create carboxylic end groupsThese acidic carboxyl end groups diffuse into the vicinity ofthe polymer and decrease the pH level there [6ndash10]

This pH drop is one of the main drawbacks of usingaliphatic polyesters for implants as a low pHmay cause tissuereactions like inflammation [11ndash13]

Still biodegradable stents have marked potential long-term advantages [4 14] In order to overcome the disadvan-tage of acidic pH levels during degradation of biodegradablestents we investigate the fabrication of polylactic acid (PLA)fibers for cardiovascular stents with pH-optimized degrada-tion behavior using VCLAAEMVIm (8mol)-microgels asinsoluble buffers [15]

Microgels are defined as hydrogel particles with a dimen-sion from 10 nanometers up to themicrometer range Hydro-gels in general are novel components that arouse specialinterest in the biomedical field and nanotechnology [16 17]

Depending on the molecular building units and the syn-thesis procedure it is possible to synthesize colloidal hydro-gels with controlled particle size Those can be defined aspolymer networks with smart properties such as water-uptake capacity degree of swelling and responsiveness toexternal stimuli Furthermore these nanoparticles show highcolloidal stability a well-defined structure and a high sur-face area Through variation of the monomer type andorintroduction of comonomers responsiveness to temperaturepH magnetic field or light intensity can be tailored Thisproperty in combination with the swelling features makesthe utilization of microgels as biocompatible materials forpharmaceutical applications possible [16 18ndash23]

Monomers like N-isopropylacrylamide (NIPAAm) andN-vinylcaprolactam (VCL) have been used for the synthesisof thermoresponsive microgels because they can form water-soluble polymers with lower critical solution temperature(LCST) [18 20 24 25] Other interesting components suchas N-vinylimidazole (VIm) can be used to achieve pH-sensitivity due to its protonationdeprotonation process atdifferent pH levels Pich et al [26] have successfully synthe-sized VCLVIm-based microgels which show both tempera-ture and pH-responsiveness In this study the swelling couldbe controlled by the VIm content in the microgel

However cardiovascular stents require for the degrada-tion period to last over months making their experimentalresearch as well as their design and optimization rathertime-intensiveThis study aims at developing a mathematicalmodel able to predict the pH level resulting from polymerdegradation and taking into account the buffering action ofeventually incorporated microgels This mathematical modelwill be validated against the experimental pH-monitoredbiodegradation of microgel-functionalized polymer foils andwill be available for the design of microgel-functionalizedpolymer stents and other components

Computational methods to model the degradation ofbiodegradable polymers have been proposed by a quantityof research teams Siparsky et al [27] described the kineticsof hydrolysis reaction by rate equations and their analytic

solutions Han [28] used Monte Carlo methods to predictthe degradation of PLA PGA and some copolymers Healso investigated the influence of chemical buffers on thedegradation process and the pH level Wang et al [29]presented a reduced model for polymer degradation usingtwo rate equations for the concentrations of carboxylic endgroups and ester bonds in the PLA phase Pan et al [30]included a model for chemical buffers in such a reducedmodel for biodegradation Moreover rate equations for theconcentrations of different molecules sizes which the poly-mer undergoes in its degradation process were built up andanalyzed by Lazzari et al [31] The buffering action of thepoly(N-vinylimidazole) hydrogel wasmodelled and analyzedby Horta et al [32 33] To the best of the authorsrsquo knowledgeso far no publishedmodel for the biodegradation of polymersbuffered with VCLAAEMVIm-microgels exists

Investigating microgel-functionalized resorbable poly-mers with pH-regulatory potential a recent study of Feher etal [15] employs a publication-based keyword search strategyto investigate the existing knowledge base underpinning thetopic The authors find that only a marginal number ofstudies is dedicated to investigate the pH-regulative potentialof microgel containing degradable polymers This clearlydemonstrates an underinvestigated topic Given the poten-tial scope of application ranging from drug-coated pH-regulating degradable textiles to stents this paper is alignedto the apparent research gap

2 Materials and Methods

21 VCLAAEMVIm (8mol)-Microgel The synthesis ofVCLAAEMVIm (8)-microgel is well described in Feheret al [15] The description is not repeated here

22 Polymer VCLAAEMVIm (8mol)-Microgel FoilsPoly(L-lactide-co-glycolid) PLG 8523 by Purac and themicrogel are weighed separately Both samples are thenfilled up with a solvent in a way that the mass fraction ofpolymer119908Pol and microgel 119908MG amount to 015 respectivelyThe sealed samples are stirred at 250 rpm for 24 hours ina magnetic stirrer The resulting microgel and polymersolutions are mixed thoroughly to ensure a homogeneoussolution The solutions are evenly spread on a petri dish andthereby infused to a foil After 48 hours within the distractorhood the solvent is fully evaporated allowing for the foil tobe peeled from the glass

23 Degradation Experiment The degradation experimentsare carried out according to ISO 13781 [34] Each samplecontains 01 g of the produced foil and is supplemented withdistilled water (specific conductivity lt 01 120583Scm at 25∘C)at the ratio of 1 100 The samples are prepared in 20mLglass containers and sealed during degradation periods Thecontainers are only opened for pH measurement

Throughout the degradation process the samples arestored in an oven at 37∘C pH measurement is conducteddaily within the first 20 days followed by weekly readingsfor a total time period of at least 30 days To determine




[H+] =119870w[H+]+

119870COOH [M][H+] + 119870COOH

(1)








119889 [E]119889119905


119889 [M]init119889119905

= minus

119889 [E]119889119905

(3)


119889 [E]119889119905




+


[COOminus]gel

=

[H+]3

gel + [H+]2


[H+]gel sdot ([H+

]gel + 119870P)

[COOminus]gel

= minus([H+] minus

119870w[H+]

) sdot


119870w[H+]init)

sdot

119881init119881gel


(5)




119889 [M]119889119905

=


119889 [E]119889119905

) + 1198630Δ [M] (6)








37∘C[28]

119870119908



O at 37∘C [36]



minus3




[P]0





1198630p 2 sdot 10


1198630w 2 sdot 10






[E] (119905 = 0)|0le119909le119889p= [E]0

[E] (119905 = 0)|119909gt119889p= 0

[M] (119905 = 0) = [M]init (119905 = 0) = 0

(7)


119889 [M]119889119909

10038161003816100381610038161003816100381610038161003816119909=0

=

119889 [M]119889119909

10038161003816100381610038161003816100381610038161003816119909=119889w

= 0

[M] (119909 = 119889minusp) = [M] (119909 = 119889+

p)

(8)





pH meter

Water

Polyester foil

Glass container

0

x

1D calculation area

dw

dp






1 2 3 4 5 61

2

3

4

5

6

7

8


pHba

th

pHinit






1

0

2

3

4

5

6

7

pHba

th

0 1 2 3 4 5 76pHinit

5 times 10minus3 g

1 times 10minus3 g

1 times 10minus4 g

1 times 10minus5 g

1 times 10minus6 g







0 5 10 15 20 25 30 353

35

4

45

5

55

6

65

7

75

pH

Time t (d)



wMGwMG

wMGwMG


0 5 10 15 20 25 30 35 401

2

3

4

5

6

7

pH

Time t (d)

= 000

= 005

wMGwMG



0 5 10 15 20 25 30 35 4001

02

03

04

05

06

07

08

09

1

Time t (d)

= 000

= 005

[E][E

] 0

wMGwMG







0 5 10 15 20 25 30 35 401

2

3

4

5

6

7pH

Time t (d)

D0w

D0w

times 103





3

120575(119905 minus 119905119894





4 Conclusions







Competing Interests


Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












[H+] =119870w[H+]+

119870COOH [M][H+] + 119870COOH

(1)








119889 [E]119889119905


119889 [M]init119889119905

= minus

119889 [E]119889119905

(3)


119889 [E]119889119905




+


[COOminus]gel

=

[H+]3

gel + [H+]2


[H+]gel sdot ([H+

]gel + 119870P)

[COOminus]gel

= minus([H+] minus

119870w[H+]

) sdot


119870w[H+]init)

sdot

119881init119881gel


(5)




119889 [M]119889119905

=


119889 [E]119889119905

) + 1198630Δ [M] (6)








37∘C[28]

119870119908



O at 37∘C [36]



minus3




[P]0





1198630p 2 sdot 10


1198630w 2 sdot 10






[E] (119905 = 0)|0le119909le119889p= [E]0

[E] (119905 = 0)|119909gt119889p= 0

[M] (119905 = 0) = [M]init (119905 = 0) = 0

(7)


119889 [M]119889119909

10038161003816100381610038161003816100381610038161003816119909=0

=

119889 [M]119889119909

10038161003816100381610038161003816100381610038161003816119909=119889w

= 0

[M] (119909 = 119889minusp) = [M] (119909 = 119889+

p)

(8)





pH meter

Water

Polyester foil

Glass container

0

x

1D calculation area

dw

dp






1 2 3 4 5 61

2

3

4

5

6

7

8


pHba

th

pHinit






1

0

2

3

4

5

6

7

pHba

th

0 1 2 3 4 5 76pHinit

5 times 10minus3 g

1 times 10minus3 g

1 times 10minus4 g

1 times 10minus5 g

1 times 10minus6 g







0 5 10 15 20 25 30 353

35

4

45

5

55

6

65

7

75

pH

Time t (d)



wMGwMG

wMGwMG


0 5 10 15 20 25 30 35 401

2

3

4

5

6

7

pH

Time t (d)

= 000

= 005

wMGwMG



0 5 10 15 20 25 30 35 4001

02

03

04

05

06

07

08

09

1

Time t (d)

= 000

= 005

[E][E

] 0

wMGwMG







0 5 10 15 20 25 30 35 401

2

3

4

5

6

7pH

Time t (d)

D0w

D0w

times 103





3

120575(119905 minus 119905119894





4 Conclusions







Competing Interests


Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














37∘C[28]

119870119908



O at 37∘C [36]



minus3




[P]0





1198630p 2 sdot 10


1198630w 2 sdot 10






[E] (119905 = 0)|0le119909le119889p= [E]0

[E] (119905 = 0)|119909gt119889p= 0

[M] (119905 = 0) = [M]init (119905 = 0) = 0

(7)


119889 [M]119889119909

10038161003816100381610038161003816100381610038161003816119909=0

=

119889 [M]119889119909

10038161003816100381610038161003816100381610038161003816119909=119889w

= 0

[M] (119909 = 119889minusp) = [M] (119909 = 119889+

p)

(8)





pH meter

Water

Polyester foil

Glass container

0

x

1D calculation area

dw

dp






1 2 3 4 5 61

2

3

4

5

6

7

8


pHba

th

pHinit






1

0

2

3

4

5

6

7

pHba

th

0 1 2 3 4 5 76pHinit

5 times 10minus3 g

1 times 10minus3 g

1 times 10minus4 g

1 times 10minus5 g

1 times 10minus6 g







0 5 10 15 20 25 30 353

35

4

45

5

55

6

65

7

75

pH

Time t (d)



wMGwMG

wMGwMG


0 5 10 15 20 25 30 35 401

2

3

4

5

6

7

pH

Time t (d)

= 000

= 005

wMGwMG



0 5 10 15 20 25 30 35 4001

02

03

04

05

06

07

08

09

1

Time t (d)

= 000

= 005

[E][E

] 0

wMGwMG







0 5 10 15 20 25 30 35 401

2

3

4

5

6

7pH

Time t (d)

D0w

D0w

times 103





3

120575(119905 minus 119905119894





4 Conclusions







Competing Interests


Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1 2 3 4 5 61

2

3

4

5

6

7

8


pHba

th

pHinit






1

0

2

3

4

5

6

7

pHba

th

0 1 2 3 4 5 76pHinit

5 times 10minus3 g

1 times 10minus3 g

1 times 10minus4 g

1 times 10minus5 g

1 times 10minus6 g







0 5 10 15 20 25 30 353

35

4

45

5

55

6

65

7

75

pH

Time t (d)



wMGwMG

wMGwMG


0 5 10 15 20 25 30 35 401

2

3

4

5

6

7

pH

Time t (d)

= 000

= 005

wMGwMG



0 5 10 15 20 25 30 35 4001

02

03

04

05

06

07

08

09

1

Time t (d)

= 000

= 005

[E][E

] 0

wMGwMG







0 5 10 15 20 25 30 35 401

2

3

4

5

6

7pH

Time t (d)

D0w

D0w

times 103





3

120575(119905 minus 119905119894





4 Conclusions







Competing Interests


Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15 20 25 30 353

35

4

45

5

55

6

65

7

75

pH

Time t (d)



wMGwMG

wMGwMG


0 5 10 15 20 25 30 35 401

2

3

4

5

6

7

pH

Time t (d)

= 000

= 005

wMGwMG



0 5 10 15 20 25 30 35 4001

02

03

04

05

06

07

08

09

1

Time t (d)

= 000

= 005

[E][E

] 0

wMGwMG







0 5 10 15 20 25 30 35 401

2

3

4

5

6

7pH

Time t (d)

D0w

D0w

times 103





3

120575(119905 minus 119905119894





4 Conclusions







Competing Interests


Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15 20 25 30 35 401

2

3

4

5

6

7pH

Time t (d)

D0w

D0w

times 103





3

120575(119905 minus 119905119894





4 Conclusions







Competing Interests


Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









New Research Article Modelling pH-Optimized Degradation of...

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