Experimental investigation and mathematical modeling of ... · Experimental investigation and mathematical modeling of the mechanical response of hydrogels Aristeidis A. Papadimitriou,

Experimental investigation and mathematical modeling of the

mechanical response of hydrogels

Aristeidis A. Papadimitriou, Jérémy H. M. Liely

Department of Mechanical and Manufacturing Engineering, Aalborg UniversityFibigerstraede 16, DK-9220 Aalborg East, Denmark

Email: [email protected] , [email protected],

AbstractPoly(2-hydroxyethyl methacrylate) hydrogels were manufactured via photo-initiated polymerization at various waterto monomer concentrations for investigation upon swelling in de-ionized water and salt solution (NaCl). To analyzecharacteristic features of their behavior, both as-prepared and fully swollen hydrogels were subjected to uniaxialtensile and relaxation tests. Cyclic test with a strain-controlled program is also performed where cyclic loading isinterrupted by swelling for analysis of the self-recovery phenomenon of hydrogels. Experimental data are treated asmeans of appropriate constitutive models to ascertain the effects of composition and degree of swelling (Q) on thevisco-elastic response. The constitutive model treats a hydrogel as a two-phase continuum composed of a solid andfluid constituent subjected to swelling under arbitrary deformation with finite strains. Structure-property relations wereinvestigated which allow mechanical properties of the gel to be predicted as function of its composition.

Keywords: pHEMA hydrogels, swelling behavior, mechanical properties, self-recovery, constitutive modeling

1. IntroductionHydrogels are three-dimensional hydrophiliccrosslinked polymers which can extensively swellin a solution medium while maintaining their structure.Dated back to 1950’s, hydrogels were invented andpatented by D.Lim and O.Wichterle for their potentialbiological use as soft contact lenses [1].A variety of chemical compositions can formulatedifferent hydrogels via chemical or physical cross-linkjunctions [2] and in an array of physical forms; i.e.films, nanoparticles, rods, bars etc. [3]. With respect tothis, crosslinked 2-hydroxyethyl methacrylate (HEMA)based hydrogels have attracted a lot of attention fortheir broad range of applications and technologiesto be utilized as bio-materials and specifically, asdrug delivery systems [3], hygienic products [4],scaffolds for controlled stem cell differentiation [5, 6],pharmaceuticals [7] and tissue engineering applications[8].Hydrogels are known to be homogeneous when thecritical concentration of water in the monomer mixtureis lower or equal to 45%, whereas heterogeneous whenthe concentration is above this value [9]. Monomermixture is the solution comprised of the cross-linking agent, initiator and monomer. Heterogeneoushydrogels, also known as sponges due to their porousmorphology, constitute of a phase separation at the

onset of polymerization induced by the diluent (water).Therefore, understanding key features regardingthe physical and mechanical properties of poly-2-hydroxyethyle methacrylate (pHEMA) hydrogels isessential.During this study, homogeneous and heterogeneouspHEMA hydrogels are synthesized via photo-initiatedpolymerization in solution in the presence of a freeradical initiator and de-ionized water as diluent. Theconcentration of water to monomer mixture is alteredwhile the water concentration is kept constant. Thesolvent uptake is investigated by subjecting samplesin swelling tests in a similar manner as presentedin previous publications [10, 11]. Keeping in mindthat the concentration of cross-linking agent in thenetwork alters the swelling behavior of hydrogels, thecross-linking concentration was kept constant whilethe monomer concentration was modified in order toanalyze its effect upon swelling [12]. Swelling of thepHEMA hydrogels is performed both in de-ionizedwater and salt solution of 1M NaCl by observingalternations in weight measurements over time. Theswelling in salt solution is performed to analyse theeffect of addition of salt on the swelling properties ofpHEMA hydrogels.Assessment of the effect of swelling is implementedby uniaxial tension, relaxation and multi-cyclic tests

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mailto:[email protected] , [email protected]

where deformation is interrupted by swelling. Thegrowth of the swelling degree is expected to lead tothe decrease of stresses of hydrogels as a functionof time and subsequently, to the reduction of theresidual strain under retraction. Thus, the hypothesistested in a previous study by Drozdov et.al. (2014) isfurther investigated, in which "swelling results in thedisappearance of plastic deformation acquired undercyclic pre-loading (self-recovery)" [13]. Consideringa hydrogel subjected to uniaxial tension up to itsmaximum elongation ratio κmax and further unloadedto zero stress, residual strains arise after retraction,characterized by the elongation ratio κmin. Self-recovery in hydrogels subjected to cyclic loading, asstated by Sun et.al. (2012) and Drozdov et.al. (2014),is a process in which the swelling of hydrogel resultsin the reduction of residual strain [13, 14].The objective of this study is to investigate how thecomposition of pHEMA hydrogels affects the degree ofswelling (Q) and in return their physical and mechanicalbehavior under uniaxial loading. All experimental dataare treated as means of appropriate constitutive modelsto ascertain the effects of composition and degreeof swelling on the visco-plastic and visco-elasticresponse. Hence, prediction of the mechanical responseof HEMA hydrogels as a function of its compositioncan be achieved.The constitutive equations utilized in this study forsolvent diffusion through by treating a hydrogel asa two-phase continuum and are grounded by thefollowing assumptions : (i) the reference state of anequivalent polymer network (where stresses in chainsvanish) coincides with the as-prepared state of a gel butdiffers from that of a dry undeformed specimen, and(ii) transport of solvent through the polymer network isdescribed by the diffusion equation with the equivalentcoefficient of diffusion strongly affected by volumefraction of solid phase. Adjustable parameters in thegoverning equations are found by fitting experimentaldata acquired through tensile, relaxation and cyclictests.The exposition of the current study is as follows.Section 2 includes the manufacturing process ofHEMA gels for each composition. Governing equationsof the mathematical model utilized are developed inSection 3. The solvent uptake over a period of time ofHEMA-based hydrogels immersed in both de-ionizedwater and salt solution is presented in Section 4.1.The mechanical response of both as-prepared and fullyswollen hydrogels under tension are reported in Section

4.2, while assessment of Q upon the time-dependentresponse is found in Section 4.3. Investigation of theself-recovery phenomenon of hydrogels through cyclicloading interrupted by swelling is inscribed in Section4.4. A discussion of the results found in this studyis provided in Section 5 and concluding remarks aredrawn in Section 6.

2. Experimental2.1 MaterialsAll chemicals were purchased from Sigma Aldrich andused as received (without purification), unless other-wise specified. Six series of pHEMA hydrogels weresynthesized at various water:monomer-mixture con-centrations. 2-hydroxyethyl methacrylate (HEMA) wasused as a monomer, di(ethylene glycol) dimethacrylate(DEGDMA) as a crosslinking agent and 2,2-dimethoxy-2-phenylacetophenone (DMPA) as initiator. De-ionisedwater with a low conductivity (≈ 0, 055 µS) was usedas a solvent during polymerization.

2.2 Specimens preparationHydrogels with different compositions, as observed inTable I, were prepared similarly in the following man-ner. The corresponding grams of HEMA and DEGDMAwere dissolved at constant 5.15 g of de-ionised water.Subsequently, DMPA was added into the solution andstirred with a Heidolph MR 3003 Control C magneticstirrer at 750 rpm for approximately 10 min. Finally thesolution was degassed for 10 minutes in an BandelinSonorex ultrasound bath at a frequency of 35 kHz forremoving air bubbles at room temperature.Hydrogel specimens were manufactured in three differ-ent shapes: (i) cubic specimens of ≈ 2 mm3, (ii) disksof approximately 2 mm thickness and a diameter of 27mm and (iii) flat dumbbell specimens for tensile tests(ASTM standard D-638) using a silicon mold under UVirradiation. Both disk and cubic specimens are used onlyduring experimentation of solvent uptake, in order to an-alyze the effects of the shape upon swelling properties.Polymerization process was performed for 1 hour underargon atmosphere, ensuring the polymerization of thesolution’s network with a hand held UV Lamp of 6W-Model UVGL-58 and wavelength of 365 nm.After polymerization as-prepared hydrogels werewashed with a water and ethanol mixture, thus removingany excess of un-reacted species, which appeared inthe form of a "skin" on the surface of the specimens.Each specimen was weighted on a digital scale with aprecision of ± 1 mg.

2

During fitting of observations, specimens of disk shapeare modeled as thin plates while cubic specimens asspheres. For reasons of statistical quality control, eachexperimental value noted in this study is the result ofthree repetitions, unless otherwise stated.

Table. I Sample compositions

Sample no. HEMA DEGDMA DMPA di-H2O1 50 g 1 g 0.51 g 5.15 g(mol) (0.38) (4.1×10−3) (1.99×10−3) (0.29)2 40 g 0.8 g 0.41 g 5.15 g

(0.31) (3.3×10−3) (1.56×10−3) (0.29)3 30 g 0.6 g 0.31 g 5.15 g

(0.23) (2.5×10−3) (1.17×10−3) (0.29)4 20 g 0.4 g 0.21 g 5.15 g

(0.15) (1.65×10−3) (8.19×10−4) (0.29)5 10 g 0.2 g 0.11 g 5.15 g

(0.08) (8.26×10−4) (4.29×10−4) (0.29)6 5 g 0.1 g 0.01 g 5.15 g

(0.04) (4.13×10−4) (3.90×10−5) (0.29)

2.3 SwellingThe swelling kinetics of pHEMA hydrogels wereinvestigated by immersing specimens into de-ionisedwater and 1M of NaCl solution, at room temperaturefor at least 72 hours. Before each weight measurement,the sample was wiped with paper to absorb any excessof water on its surface and then placed back into thewater bath. The degree of swelling denoted as Q wasmeasured through

Q =W(tsw)−Wdry

Wdry(g/g) (1)

where W (tsw) denotes the mass of the sample at timetsw and Wdry the mass of the dry hydrogel. Wdry ofthe specimens was calculated theoretically by

Wdry =Wap

Q0 + 1(g) (2)

where Wap is the mass of the sample after polymer-ization and Q0 denotes the degree of swelling of as-prepared samples in (g/g) (initial degree of swelling).

2.4 Mechanical testingDifferent uniaxial tests were conducted on a universaltesting machine Instron-5944 equipped with a 2 kNload cell at room temperature. Similarly to the swellingexperimentation, each specimen was wiped with paperbefore measurement and its cross-sectional area wasmeasured using an electronic caliper. The universal

testing machine was used to monitor the evolution ofthe engineering stress σ, which is defined as the ratio ofaxial force to the cross-sectional area of the undeformed(pre-loaded) specimen. Uniaxial tests performed in thisstudy include (i) tensile deformation, (ii) relaxationand (iii) cyclic deformation using a strain controlledprogram.

2.4.1 Tensile testsTensile tests are used to obtain the rubber elasticbehavior of the hydrogel. Generally, tensile testing ofhydrogel is performed on a totally immersed samplein a water-bath [15]. However, due to the highcost of including a water-bath to the Instrom-5944the specimens tensile properties were measured non-immersed. The samples were kept non-immersed forless than 10 minutes due to the substantial evaporationof water. In other study, it has been reported thatwithin 20 minutes, a rigid skin is formed on the lateralsurface of the specimens [16]. The rigid skin is to beavoided in order to guarantee the validity of the results.When hydrogel are tested, the water loss during theexperiment can significantly influence the mechanicalbehavior [15]. Tensile tests were performed at a constantstrain rate by varying the load, where the strain ratewas chosen to be ε = 4.8 × 10−3s−1 (cross headspeed of 20 mm/min). Since the load deformationcharacteristics of a specimen depends strongly on itssize, to minimize these geometrical factor, load andelongation are normalized respectively to engineeringstress σ and engineering strain ε. Thus the followingequations define σ and ε

σ =F

A0(3)

ε =Li − L0

L0=

∆l

L0(4)

where F is the load, A0 the initial cross section area, Liis the instantaneous length and L0 the initial length ofthe specimen [17].

2.4.2 Stress Relaxation testsStress relaxation is when a constant strain is appliedto a specimen and the time dependence of the stressrequired to maintain that strain is recorded, as seen inFig. 1. Molecular relaxation processes which take placeinto the polymer causes the stress to decrease with time.Relaxation modulus E(t) can be defined as

3

E(t) =σ(t)

ε0(5)

where σ(t) is the time-dependent stress and ε0 theconstant strain level [17].

ε

Time

σ

0

Fig. 1 Stress relaxation, at t=0, a constant strain is appliedand the evolution of stress is measured as the time increases[17].

Relaxation tests are performed with an initial strain rateof ε = 4.8×10−3s−1 up to ε0 = 0.3. It is recommendedto proceed relaxation in trel = 20 min (ASTM E-328)but as stated previously, due to the plausible substantialevaporation of water within 20 min, trel = 7 min wasused [13].

2.4.3 Cyclic deformation interrupted by swellingAn additional test is performed to relate the swellingproperties of pHEMA specimens to their plastic defor-mation, at which specimens are loaded up to a certainstrain, and subsequently unloaded to zero stress. Itis believed that hydrogel specimens, during the firstloading cycle, are subjected to plastic strain. Subse-quently, swelling before the final loading cycle resultsin a reduction of stresses and residual strain [13, 18].This phenomenon is commonly refereed to as selfrecovery and it has been analyzed in other studies[19, 20, 21]. The cyclic test performed is using a straincontrolled program where the sample after polymeriza-tion is loaded with a strain rate ε = 4.8 × 10−3s−1, amaximum strain of εmax = 0.3 and a zero minimumstress (σmin = 0MPa). Specimens are then immersedinto a water bath and are allowed to swell until theyreach equilibrium Qeq, and loaded again using the sameparameters.

2.4.4 Additional experimentationAny un-reacted products that may exist in the waterbath after polymerization are investigated throughFTIR analysis with a PerkinElmer Spectrum 100 andUV-scattering on a Varian Cary 50 Bio UV-visible

spectrophotometer. FTIR and UV spectroscopy wereperformed on the water bath after 48 hours of swellingon HEMA-50, 40 and 30 in order to analyze if anyun-reacted species from the network diffused into thebath.

3. Mathematical modelingThe present constitutive model was formulated byDrozdov et.al. (2016) in a recently submitted study [22].Transport of solvent under swelling is considered asthe diffusion of water molecules through a gel, whichby applying the Flory theory of swelling constitutesanother model approach for the kinetics of water uptake.When compared to the linear theory of poroelasticity,constitutive equations provide a small amount ofparameters adjustable to experimental data. However,diffusivity of water molecules is not a constant, thusrequiring an extra equation describing the increase incoefficient of diffusion which is proportional to theconcentration of water molecules.

3.1 Mechanic relationsHydrogels, as previously mentioned, are regarded asa two-phase medium consisting of a solid (network)and a solvent (water). Although both phases during thisstudy disregard mass exchange in the medium, they areconsidered however as an inter-penetrating continua; i.e.any elementary volume contains both phases.Macrodeformation of a hydrogel coincides with that ofthe polymer network and obeys the molecular incom-pressibility condition, at which volume deformation isdriven only by the changes in water concentration. Foran elastic deformation the Cauchy-Green tensors Be andCe are connected to the macrodeformation tensors B andC by

Be = f−23 B, Ce = f−

23 C (6)

where f is the coefficient of inflation under transitionfrom dry into the as-prepared state. Since the transportof water molecules is modeled as its diffusion throughthe polymer’s network and as previously mentioned, itsdiffusivity D depends on the concentration c of watermolecules in the initial state, hence the flux vector is ofthe form

j = − Dc

kBT∇µ (7)

4

where D denotes the diffusivity, c is the concentrationof water molecules per unit volume in the initial state,kB is Boltzmann’s constant, T is absolute temperature,∇ is the gradient operator and µ denotes the chemicalpotential of water molecules. Subsequently combinationof Eq. 7 along with the molecular incompressibilitycondition and the mass conservation law for molecules,results in the equation of diffusion with respect to thedeformation gradient F for transition from the initial toactual configuration, see Eq. 8.

C = ∇0 ·(

DC

kBTF−1 · ∇0µ · F−1

)(8)

The flux vector j is the summation of two vectors, j1 andj2 which the former characterizes transport of solventdriven by the inhomogeneity in distribution, while thelatter describes permeation of solvent induced by theosmotic pressure’s gradient. This results in two limitingcases: (i) when degree of swelling is small (Q«1) theflux vector transforms into the Fick’s law, whereas ifits high (Q»1) then it is equivalent to Darcy’s law. Itfollows, that the boundary condition at the interfacebetween a gel and an aqueous solution is

lnCu

1 + Cu+

1

1 + Cu+

χ

(1 + Cu)2+

Πu

kBT= 0 (9)

where u stands for the volume occupied by a watermolecule, χ is the Flory-Huggins parameter; i.e. regardsfor interactions between water molecules and chainsegments and Π stands for the Lagrange multiplier arosefrom the molecular incompressibility condition.For an elastic network and a solvent, transport of watermolecules within the continuum theory of mixtures isdescribed by Eq. 10, in which ζ denotes coefficientof friction between water molecules and segments ofchains, vw−vn the relative velocity and φw the volumefraction of water molecules.

ζ(vw − vn) = −φw∇Π (10)

3.2 Governing equationsConstitutive equations of the model are developed bymeans of the free energy imbalance inequality andinvolve equations of continuum theory of mixtures,chemical potential of water molecules, strain energy

density (assuming an incompressible neo-Hookean ma-terial) and stress-strain relations (Cauchy stress and rate-of-strain tensors).Helmholtz free energy of a hydrogel per unit volumein the initial configuration Ψ is defined as the sum ofenergy of water molecules disregarding interactions withthe solid phase Ψ1, energy of network not interactingwith water Ψ2 and energy of mixing Ψ3. Differentiationof Helmholtz free energy with respect to time leads to

Ψ = KC + 2Ke : D (11)

During this study spherical and thin film hydrogel spec-imens were manufactured by photo-initiated polymer-ization in solution. In the following sections, governingequations are presented along with their correspondingboundary conditions for both shapes. A more compre-hensive review of the governing equations and theirderivation are enclosed in a recently submitted studyby Drozdov et.al. (2016) [22].

3.2.1 Sphere swellingAssuming a spherical gel particle occupies a domain(Ω) in a three-dimensional space (0≤ Ω ≤ 2π) andsymmetric swelling induced deformation, the governingequations in the new notation are described by

∂Q

∂t=

∂

∂x

(x

13 (1 +Q)β−2

3x

[ (1 + (1− 2χ)Q

(1 +Q)3

+gQ

(1 +Q)2

)(F

x

) 43

+gQ

(1 +Q0)23

]∂Q

∂x

− 2gQ

(1 +Q0)23

F

x

((1 +Q)

x

F− 1

)2)(12)

and

lnq

1 + q+

1

1 + q+

χ

(1 + q)2

+g

1 + q

((1 + q)2

(1 + Q0)23 (F|x=1)

43

)= 0 (13)

where Q0 denotes the degree of swelling in the as-prepared state, g is the dimensionless elastic modulus(g = Gu

kBT) and the average degree of swelling for

spherical specimens is found to be

Q =1

U0

∫ Q0

0

QdU = F |x=1 − 1 (14)

5

The corresponding boundary conditions to the abovegoverning equations include

Q|t=0 = Q0,∂Q

∂x|x=0 = 0, Q|x=1 = q

∂F

∂x= 1 +Q, F |x=0 = 0

Diffusivity of solvent molecules in a spherical hydrogelwas found to be

Dsphere0 =

R′02K

3(1 +Q0)23

(15)

where R′0 denotes the radius of the as-prepared speci-men and K is a parameter in the model which minimizesinconsistencies between experimental data and simula-tion results.

3.2.2 Thin film swellingConsidering a thin film specimen occupying the domainΦ with a thickness t much smaller than any otherdimensions of the sample (tfilm << length,width)and allowing unconstrained swelling; i.e. sample isconsidered to be immersed in a solvent and notconnected to any substrate, the governing equations aregiven by

∂Q

∂t=

1

F (1 +Q0)43

∂

∂x

((1 +Q)β−2

[1 + (1− 2χ)Q

(1 +Q)3

+ gQ

(F

(1 +Q0)23

+1

(1 +Q)2

)]∂Q

∂x

)(16)

and

lnq

1 + q+

1

1 + q+

χ

(1 + q)2

+g

1 + q

(F(1 + q)2

(1 + Q0)− 1

)= 0 (17)

The corresponding boundary conditions to the abovegoverning equations include

Q|t=0 = Q0,∂Q

∂x|x=0 = 0, Q|x=1 = q

F =

(∫ 1

0(1 +Q)−1 dx∫ 1

0(1 +Q) dx

) 23

Diffusivity of solvent molecules in a thin film iscalculated by

Dfilm0 =

H2apK

4(1 +Q0)2. (18)

where Hap denotes the thickness of as-prepared speci-mens.

4. Results4.1 Swelling in de-ionized water and salt solutionSolvent uptake of HEMA hydrogels prepared via photo-initiated polymerization in solution at various concen-trations of water:monomer-mixture was investigated.Observations of swelling in water and in 1M of NaClsolution are depicted in Fig. 2 and 3, respectively.The initial degree of swelling of all samples, as pre-viously explained is theoretically determined from Eq.2 and can be observed in Table II. It is noted thatswelling in de-ionized water was performed for bothspherical and thin plate (disc) specimens while swellingin 1M NaCl solution was performed only for thin platespecimens. Spherical samples are prepared for only onecomposition; i.e. that of HEMA-10 (see Table I).

4.1.1 Experimental swellingFig. 2 reveals that the swelling degree of each specimenat time ti; i.e. i is the ith value, is monotonicallyincreased relatively to initial swelling until equilibrium.The evolution of swelling for each thin plate specimenappears identical due to their similar shape, contrary tothe spherical samples. Equilibrium degree of swellingis reached for all thin plate samples after 24 hrs,except spheres for which is reached after 7 hrs. Highestequilibrium degree of swelling is observed for HEMA5 with Qeq= 0.85 g/g (see Fig. A.7 in Appendix A),whereas the lowest is observed for HEMA 50 withQeq= 0.48 g/g. This difference arises from the variation

Time, [hours]0 10 20 30 40 50 60 70 80

Q,[g/g]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

HEMA-10-sphere

HEMA-10

HEMA-20

HEMA-30

HEMA-40

HEMA-50

Fig. 2 Swelling degree over time for each series in water.

6

of water to monomer concentration in each series.By decreasing the concentration of monomer in thenetwork, a higher amount of solvent is able to diffusethrough the network leading to a less dense networkand thus increasing the equilibrium degree of swelling.Additionally, it is observed that the swelling behaviorof HEMA-50 is in quantitative agreement with previousstudies of Drozdov et.al. (2015) and Lee and Buchnall(2008) [10, 13].

Time, [hours]0 10 20 30 40 50 60 70 80

Q,[g/g]

0

0.1

0.2

0.3

0.4

0.5

0.6

HEMA-50

HEMA-40

HEMA-30

HEMA-20

HEMA-10

Fig. 3 Swelling degree over time for each series in saltsolution.

Observation of swelling in 1M NaCl bath illustrate areduction in Qeq between 10 to 20 % when comparedto samples in water bath as illustrated in Fig. 3. This isin good agreement with Ting and Jeng Huang (2014),at which during their study they performed an identicalexperiment on HEMA gels in which immersion in 1Mof NaCl solution resulted in a decrease of Qeq ofapproximately 20 % in comparison to Qeq in water [23].Highest degree of swelling is reported to be for HEMA-10 with Q ≈ 0.56 g/g, followed by a HEMA-20 atQ ≈ 0.43, while the remaining samples show an almostidentical swelling behavior with Q located between 0.3-0.35. All samples indicate a weight decrease duringthe first hour of measurement followed by a gradualincrease, whereas HEMA-10 decreases constantly upto 5 hrs. This seems to contradict the overshootingeffect of gels ;i.e. initial swelling up to a maximumpoint followed by a decrease until equilibrium [24, 25].However, the overshooting effect has been observed onstimuli-responsive hydrogels in an acidic medium atwhich thus far there is no universal explanation due todifferent gel systems and parameters (temperature, pH,cross-linking degree, etc). Additionally, all hydrogelshave an increase in Q above their initial degree ofswelling after approximately 3 hrs except HEMA-10which increases after 50 hrs. It is in the authors beliefthat as-prepared hydrogels contain de-ionised waterinitially in their network, at which an exchange between

de-ionised water and salt occurs when immersed in a saltsolution, thus affecting the swelling behavior.Table. II Swelling degree of specimens after polymerization.

Sample Initial swelling Weight differenceseries (g/g) (%)HEMA-50 0.09998 -0.62HEMA-40 0.12497 -0.06HEMA-30 0.16661 1.53HEMA-20 0.24988 2.37HEMA-10 0.49952 5.59HEMA-5 0.99980 7.15

An additional drying experiment was performed to ver-ify if the expected dry mass (theoretically determined)was similar to the real dry mass (experimentally de-termined). Table II indicates a small variance betweenexperimental and expected weight of hydrogel samples.During this experiment, the weight of as-prepared hy-drogels was measured before and after samples wereplaced in a vacuum oven at 50C for a week. Al-though weight differences for hydrogels at monomerconcentrations of 50, 40 and 30 did not exceed 1.5%,the difference in weight are attributed to the possibleremaining water trapped in the hydrogel network. Itis noted that the negative values represent a higherexpected weight than experimental.

4.1.2 Fitting of observationsParameters of the constitutive equations, see Eq. 16-18, including the Florry-Huggins parameter χ, dimen-sionless elastic modulus g and diffusivity D0 have beendetermined by matching experimental data to best fit themathematical model and can be seen in Table III. Fig.4-6 display experimental and simulation data, at whichswelling boundaries Qeq and Q0 were determined foreach composition in Fig. 2. As previously stated, thematerial coefficient K is chosen in order to reduce anyinconsistencies between model and experimental data.In Fig. 7 the swelling response of spherical HEMA-10samples is depicted, at which both HEMA-10-1 and 2are the raw experimental data of one sample. Fig. 6B itcan be seen that HEMA-5, when immersed into water,is subjected to shrinking from a swelling degree Q0 = 1g/g to Qeq= 0.85 g/g, nevertheless the swelling kineticsappear to be similar to disks.

4.2 Tensile tests on as-prepared and fully swollenhydrogelsThe stress-strain curves for as-prepared and fullyswollen specimens loaded up to breakage, are depictedin Fig. 8 and 9 respectively. Fig. 10 represents the fittingof experimental data for tension on swollen specimens.

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Table. III Material parameters of HEMA hydrogels.

Sample Q0 Qeq ρi g χ D0 Kseries ×10−3 ×10−6 (cm2/s) ×10−3

HEMA-50 0.10 0.48 0.9091 3.55 0.985 5.87 0.71HEMA-40 0.12 0.52 0.8889 3.37 0.956 5.61 0.71HEMA-30 0.17 0.53 0.8572 3.18 0.949 5.22 0.71HEMA-20 0.25 0.56 0.8001 3.55 0.930 4.54 0.71HEMA-10 0.50 0.67 0.6669 2.61 0.878 4.89 1.10

HEMA-5 1.00 0.85 0.4981 2.58 0.798 6.75 2.70HEMA-10-sphere-1 0.50 0.72 0.6669 2.61 0.853 4.91 6.50HEMA-10-sphere-2 0.50 0.69 0.6669 2.61 0.864 4.70 6.0

t

0 50 100 150 200 250 300 350 400 450 500

Q,[g/g]

0

0.2

0.4

0.6

0.8

1

A

0 50 100 150 200 250 300 350 400 450 5000

0.2

0.4

0.6

0.8

1

B

Fig. 4 Average degree of swelling Q versus dimensionlesstime t. Circles: experimental data of discs with thickness 2mm. Solid lines: simulation data. A: HEMA-50, D0= 5.87·10−6 cm2/s. B: HEMA-40, D0= 5.61 ·10−6 cm2/s.

As-prepared specimens HEMA-50:30 display a visco-elastic response with a maximum stress located at theyielding point (≈4.5 % of strain), whereas HEMA-20illustrates a constant stress after 5% of strain, with noindications of a yielding point. Furthermore, HEMA-10and HEMA-5 display a visco-elastic response with alinear increase of stresses up to breakage.As-prepared samples of HEMA-50 and 40 differ slightly

0 50 100 150 200 250 300 350 400 450 5000

0.2

0.4

0.6

0.8

1

A

t0 50 100 150 200 250 300 350 400 450 500

Q,[g/g]

00.20.40.60.8

1

B

Fig. 5 Average degree of swelling Q versus dimensionlesstime t. Circles: experimental data of discs with thickness 2mm. Solid lines: simulation data. A: HEMA-30, D0= 5.22·10−6 cm2/s. B: HEMA-20, D0= 4.54 ·10−6 cm2/s.

0 50 100 150 200 250 300 350 400 450 5000

0.2

0.4

0.6

0.8

1

A

t0 50 100 150 200 250 300 350 400 450 500

Q,[g/g]

0.5

0.7

0.9

1.1

1.3

1.5

B

Fig. 6 Average degree of swelling Q versus dimensionlesstime t. Circles: experimental data of discs with thickness 2mm. Solid lines: simulation data. A: HEMA 10, D0= 4.89·10−6 cm2/s. B: HEMA 5, D0= 6.75 ·10−6 cm2/s.

in their stress-strain response when compared to theremaining samples. Although good reproducibility ofthe uniaxial tensile test was observed, strain at breakagedeviate profoundly for each sample. Specifically, as-prepared specimens lie in the interval between 35 and180 % of strain, whereas fully swollen specimens arelocated between 40 and 95 % of strain.

0 50 100 150 200 250 300 350 400 450 5000

0.2

0.4

0.6

0.8

1

A

t0 50 100 150 200 250 300 350 400 450 500

Q,[g/g]

0

0.2

0.4

0.6

0.8

1

B

Fig. 7 Average degree of swelling Q versus dimensionlesstime t. Circles: experimental data of spheres with differentradium R′0. Solid lines: simulation data. A: HEMA 10,R′0=1.72 mm, D0= 4.91 ·10−6 cm2/s. B: HEMA 10, R′0= 1.75mm, D0= 4.7 ·10−6 cm2/s.

8

ǫ, [%]0 5 10 15 20 25 30

σ

, [M

Pa]

0

5

10

15

20AP-50AP-40AP-30AP-20AP-10AP-5

Fig. 8 Stress σ versus strain ε for as-prepared specimens.

Stress is considerably reduced while the degree ofswelling is increasing, at which the maximum stressobserved was for HEMA-50 (≈ 16.5 MPa) and thelowest was for HEMA-5 (≈ 0.2MPa). For fully swollenand as-prepared specimens, a decrease in monomerconcentration tends to an increase of swelling degreeand subsequently to a decrease of stresses.

ǫ, [%]0 5 10 15 20 25 30

σ, [

MP

a]

0

0.05

0.1

0.15

0.2

0.25

0.3

S-50S-40S-30S-20S-10S-5

Fig. 9 Stress σ versus strain ε for fully swollen specimens.

Elastic modulus G obtained by fitting of experimentaldata, is used to calculate the coefficient G1 using theleast square method.

G1 =G

(1 +Qeq)13 (1 +Q0)

23

, σ = G1(λ− λ−2) (19)

where λ denotes elongation.

4.2.1 Effect of composition on material propertiesEvolution of diffusivity and elastic modulus for cross-linked HEMA hydrogels as a function of the monomermass fraction are displayed in Fig. 11 and 12, respec-tively. The monomer mass fraction ρi describes the massratio of the monomer mixture (HEMA, DEGDMA andDMPA) over the total amount of species in the network,

λ

0 0.2 0.4 0.6 0.8 1

σ, [

MP

a]

0

0.1

0.2

0.3

0.4

0.5

HEMA-5-S

HEMA-10-S

HEMA-20-S

HEMA-30-S

HEMA-40-S

HEMA-50-S

Fig. 10 Stress σ versus elongation ratio λ for as-prepared.Solid lines: approximation of the data using Eq. 19.

including water.Diffusivity displays a linear decrease between the firstfour hydrogel compositions (HEMA-50:20) followed bya rapid increase for the remaining series. The initialdecrease was expected due to the lowering of the initialdegree of swelling, while K and Hap are kept constant,as can be seen in Eq. 18. The highest diffusivity (D0

= 6.75 ×10−6 (cm2/s)) is reported for HEMA-5 havinga mass fraction of approximately ρi = 0.5, while thelowest is observed for HEMA-20 (D0 = 4.54 ×10−6

(cm2/s)) with a ρi = 0.8.

Elastic modulus is displayed in Fig. 12 which wasdetermined by best fitting of the elastic region of thestress-strain curve. Modulus of elasticity for as-preparedspecimens displays somewhat a relative decrease withregards to mass fraction. The difference betweenHEMA-50 and HEMA-40 series might be attributed toexperimental errors and poor reproducibility of theirtensile response with a reported maximum standarddeviation equal to 2.55.Fully swollen specimens on the other hand, exhibit alinear relation of elastic modulus with respect to the

ρi

0.40.50.60.70.80.91

D0 [c

m2 /s

]

×10-6

4.5

5

5.5

6

6.5

7

Fig. 11 Evolution of diffusivity of HEMA hydrogels withrespect to mass fraction.

9

mass fraction of monomer mixture. Specifically, a lineardecrease is observed at which the greatest modulus (G =0.39 MPa) is achieved for HEMA-50, while the lowest(G = 0.18 MPa) for HEMA-5.

ρi

0.40.50.60.70.80.91

G1 [M

Pa]

0

500

1000 As-prepared

ρi

0.40.50.60.70.80.91

G1 [M

Pa]

0

0.2

0.4Swollen

Fig. 12 Evolution of elastic modulus of HEMA hydrogelswith respect to mass fraction.

4.3 Relaxation tests on as-prepared and fully swollenhydrogelsEffects of swelling on time dependent response wasconducted by uniaxial tension on hydrogel specimensup to ε = 0.3 during a relaxation period of 7 minutes asseen in Fig. 13 and 14.As-prepared specimens displayed a stress relaxation forall except HEMA-10, while fully swollen specimensindicated no signs of relaxation. This may indicatethat an intermediate region exists at which relaxationdisappears. For this reason, an additional experimentwas performed in which samples were swollen at var-ious swelling degrees and then subjected to relaxation.Through this experiment, the swelling degree at whichthe specimens indicate no more relaxation was deter-mined to lie between 40-45 % swelling.

Time, [s]0 50 100 150 200 250 300

σ, [

MP

a]

0

5

10

15

AP-50

AP-40

AP-30

AP-20

AP-10

Fig. 13 Relaxation for as-prepared specimens over time.

Time,[s]0 50 100 150 200 250 300

σ, [

MP

a]

0

0.05

0.1

0.15

0.2

0.25

0.3

S-50

S-40

S-30

S-20

S-10

Fig. 14 Relaxation for fully swollen specimens over time.

4.4 Cyclic loading of as-prepared and fully swollenhydrogelsRelation between the degree of swelling and the plasticdeformation was evaluated through cyclic loading usinga controlled strain program. During the first cyclicloading, as-prepared sample of HEMA-10 displayed aresidual strain of εres = 2.9 % , whereas the samespecimen in its fully swollen state exhibited a decreasein stress and a lower residual strain of εres = 1.6 % afterthe final cyclic loading as depicted in Fig. 15.

ǫ, [mm]0 5 10 15 20 25 30 35

σ, [

MP

a]

-0.05

0

0.05

0.1

0.15

0.2

0.25

HEMA-10AP

HEMA-10S

Fig. 15 Cyclic loading of HEMA-10 interrupted by swelling.

5. DiscussionDuring this study, hydrogels were manufacturedvia photo-initiated polymerization at various wa-ter:monomer mixture concentrations; i.e. water concen-tration is constant (Table I). Analysis of the effects ofvarying the monomer concentration upon swelling andmechanical properties is performed. Fitting of experi-mental data lead to the acquisition of material param-eters used for further validation of the mathematicalmodel using constitutive equations.Comparison of sample series show a dependency ofmonomer concentration to the equilibrium degree ofswelling. Specifically it is shown that a higher monomerconcentration leads to a lower equilibrium and initial

10

degree of swelling. Since the fraction of monomer isincreased for the same amount of water concentration,it is expected that the initial and equilibrium degree ofswelling will be different due to the formation of a moredense material. By definition, a less porous hydrogelleads to lower amount of water molecules to diffuseinto the network. The decrease in swelling observedfor as-prepared HEMA-5 specimens is attributed to anextensively swollen state after polymerization (Q0 = 1g/g), which is above the maximum value of the averagedegree of swelling (Q ≈ 0.85 g/g) found in this study.Consequently, the elastic free energy of the cross-linkednetwork is initially higher than that of the free energyof mixing from the polymer and solvent interaction.This leads to the expulsion of water molecules fromthe hydrogel network until an equilibrium between theelastic energy and energy of mixing is achieved.Fig. 2 displays a difference in swelling kinetics be-tween spherical and thin plate samples, at which theequilibrium degree of swelling for spheres is reached ata faster time. This is in good agreement with Li andTanaka (1990) where it was shown that the swellingkinetics are affected by the shape of the specimens[26]. Furthermore, the decrease in Q amidst each seriesimmersed in 1M of NaCl solution might be explained bythe decrease in χ parameter. Since interactions betweensegments of chains and water molecules are accountedfor through the Flory-Huggins parameter, it is believedthat the reduction of χ may be due to the addition ofsalt into the water bath, thus diminishing the swellingresponse of HEMA hydrogels and subsequently theequilibrium degree of swelling.Tensile tests reveal that the swelling degree alters thestress-strain response of hydrogels. Concentration ofmonomer strongly affects the mechanical response ofHEMA gels in their as-prepared state, which as observedcan produce different tensile behavior. Specifically, itis observed that a higher monomer concentration (andlower degree of swelling correspondingly) leads to anincrease of stresses. Hydrogels during their fully swollenstate exhibit differences in stress which are significantlylower in comparison to their as-prepared state. The smalldifference observed in tensile behavior of as-preparedsamples HEMA-50 and 40 is believed to occur due to ahigh monomer concentration; i.e. 1:10 water:monomermixture, which may lead into an incomplete reactionduring polymerization. Thus causing a small amount ofun-reacted monomer to be trapped in the network.However, investigations for un-reacted monomer in thewater bath through FTIR and UV spectroscopy did not

reveal any presence of un-reacted species. Therefore theabove assumption is deemed uncertain.Hydrogels in their fully swollen state, except HEMA-10 and 5 indicate an equilibrium degree of swelling in-between 0.48 and 0.55 g/g resulting to a relatively sim-ilar elastic modulus. The elastic moduli tends to reduceinsignificantly from HEMA-50 to 20 (from 0.39 MPa to0.36 MPa) which corresponds to the small difference inthe equilibrium degree of swelling. Experimental datafrom Fig. 9 are approximated through Eq. 19 in whichthe elastic modulus G is calculated for both as-preparedand fully swollen specimens, resulting to Fig. 10.Relaxation tests on as-prepared specimens display avisco-elastic behavior as the stress reduces over time.However the visco-elastic effect is not observed forHEMA-10 and 5 due to the apparent constant stressduring the first 4 minutes after relaxation is initiated.Fully swollen specimens after approximately 4 minutesof relaxation exhibit a slight increase in stress, whichcan be attributed to the formation of a rigid "skin" onthe its surface or due to evaporation of water from itsnetwork.Plastic deformation is evaluated by subjecting hydrogelsin cyclic loading interrupted by swelling. Fig. 15 showsthat swelling of the samples up to their equilibriumdegree of swelling reduces the initial residual straininduced from the first loading cycle. The almost twofolddecrease in residual strain is attributed to the self-recovery phenomenon which is in good agreement withDrozdov et.al. (2015) [13]. Hydrogels in their swollenstate along with HEMA-10 and 5 are treated as anelastic medium, through which is further supported bythe mechanical experiments performed (Fig. 13-15).Through the governing equations developed, three ma-terial parameters are acquired, in which for a givencomposition swelling kinetics can be simulated. Theseinclude (i) the Flory-Huggins parameter χ, (ii) thedimensionless elastic modulus g and (iii) diffusivity D0.Following the simulation, χ parameter was determinedto range from HEMA-50 to HEMA-5 from 0.985 to0.798 respectively. HEMA-10, manufactured in thisstudy, illustrates a χ = 0.878 which deviates the leastfrom the values found in previous studies and specifi-cally, χ = 0.82 [27], χ = 0.841 [28] and χ = 0.853 [29].Equivalent diffusivity parameters from HEMA-50 toHEMA-10 is ranging between D0 = 5.87 10−6 and D0 =4.89 · 10−6 cm2/s, whereas for HEMA-5 is 6.75 · 10−6.Diffusivity in a previous study was found to be D0 = 4.4· 10−6 cm2/s determined through NMR spectroscopy.Hence, it is concluded that HEMA-10 discs and both

11

of HEMA-10 spheres χ = 0.853 and χ = 0.864 alongwith D0 = 4.91· 10−6 and D0 = 4.7· 10−6 cm2/s are invery good agreement with previous studies. This impliesthat a composition of water:monomer mixture (1:2) canbe considered the most appealing regarding HEMA gelsswelling and mechanical behavior.

6. Conclusion2-hydroxyethyl(methacrylate) based hydrogels weremanufactured at various water to monomer concen-trations via photo-initiated polymerization, in solution.Swelling and mechanical properties were investigatedand compared for each composition. Initial and equilib-rium degree of swelling were found to increase while themonomer concentration decreases, explained by the for-mation of a more porous network. Swelling of hydrogelsimmersed in salt solution indicated a lower equilibriumdegree of swelling revealing an inverse response to theovershooting effect.Uniaxial tensile tests illustrated a dependance of me-chanical properties upon swelling and specificallystresses are reduced as the monomer concentration islowered. A region has been found at which hydrogelslose their stress-relaxation determined to be approxi-mately 40-45 % of swelling. Hypothesis of self-recoveryinduced by swelling is not rejected since a decreasein residual plastic strain was observed through uniaxialcyclic loading.A mathematical model developed for transport of sol-vent using constitutive equations with finite deforma-tions for swelling of hydrogels is utilized. Material pa-rameters, such as dimensionless elastic modulus, Flory-Huggins solubility parameter and equivalent diffusivitywere determined by fitting of experimental data to themodel. Good agreement between experimental and sim-ulation data has been found, which further supports thevalidity of the governing equations developed. HEMA-10 composition is believed to be the most preferableamongst all others, since it illustrates a satisfying set ofmaterial parameters which are in good agreement withprevious studies.

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biological use,” Nature, vol. 185, no. 4706,pp. 117–118, 1960.

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[8] L. Zhang, K. Li, W. Xiao, L. Zheng, Y. Xiao,H. Fan, and X. Zhang, “Preparation ofcollagen-chondroitin sulfate-hyaluronic acidhybrid hydrogel scaffolds and cell compatibilityin vitro,” Carbohydrate Polymers, vol. 84, no. 1,pp. 118–125, 2011.

[9] X. Lou and C. van Coppenhagen, “Mechanicalcharacteristics of poly(2-hydroxyethylmethacrylate) hydrogels crosslinked with variousdysfunctional compounds,” PolymerInternational, vol. 50, pp. 319–325, 2001.

[10] J. Lee and D. Buchnall, “Swelling behavior andnetwork structure of hydrogels synthesized usingcontrolled uv-initiated free radicalpolymerization,” J. Polym. Sci. B:PolymerPhysics, vol. 46, pp. 1450–1462, 2008.

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Structures, vol. 52, pp. 220–234, 2015.[14] J.-Y. Sun, X. Zhao, W. R. Illeperuma,

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[15] K. S.Anseth, C. N.Bowman, andL. Brannon-Peppas, “Mechanical properties ofhydrogels and their experimental determination,”Biomaterials, vol. 17, no. 17, pp. 1647–1657,1996.

[16] J. Kurnia, E. Birgersson, and A. Mujumdar, “Aphenomenological model for hydrogel with rigidskin formation,” Int. J. Appl. Mechanics, vol. 04,no. 01, p. 1250007, 2012.

[17] W.D.Callister and D.G.Rethwisch, Materialsscience and engineering, an introduction. Wiley,9 ed., 2013.

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[19] M. A. Haque, T. Kurokawa, G. Kamita, and J. P.Gong, “Lamellar bilayers as reversible sacrificialbonds to toughen hydrogel: hysteresis,self-recovery, fatigue resistance and crackblunting,” Macromolecules, vol. 44,pp. 8916–8924, 2011.

[20] T. Nakajima, T. Kurokawa, S. Ahmed,W. li Wud, and J. P. Gong, “Characterization ofinternal fracture process of double networkhydrogels under uniaxial elongation,” Soft Matter,vol. 9, pp. 1955–1966, 2012.

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[22] A. Drozdov, A. Papadimitriou, J. Liely, andC. Sanporean, “Kinetics of swelling of hdrogels.”submitted, 2016.

[23] K.-T. Huang and C.-J. Huang, “Novelzwitterionic nanocomposite hydrogel as effectivechronic wound healing dressings,” IFMBEProceedings, 1st Global Conference onBiomedical Engineering and 9th Asian-PacificConference on Medical and BiologicalEngineering, vol. 47, no. 1, pp. 35–38, 2014.

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[26] L. Yong and T. Toyoichi, “Kinetics of swellingand shrinking of gels,” The Journal of ChemicalPhysics, vol. 92, no. 2, pp. 1365–1371, 1990.

[27] F. Fornasiero, F. Krull, C. J. Radke, and J. M.Prausnitz, “Diffusivity of water through ahema-based soft contact lens,” Fluid PhaseEquilibria, vol. 228-229, pp. 269–273, 2005.

[28] A. Chauhan and C. J. Radke, “Permeability anddiffusivity for water transport through hydrogelmembranes,” Journal of Membrane Science,vol. 2, no. 214, pp. 199–209, 2003.

[29] M.Ilavsky, K.Dusek, J.Vacik, and J.Kopeek,“Deformational swelling and potentiometricbehavior of ionized gels of 2-hydroxyethylmethacrylate-methacrylic acid copolymers,”Journal of Applied Polymer Science, vol. 23,no. 7, pp. 2073–2082, 1979.

13

Part IExperimental Reports

14

Appendix ASwelling in deionised water

A.1 PurposeThis experiment was performed to analyze the swelling properties of pHEMA gels in de-ionised water at differentwater:monomer concentrations. It’s purpose is to determine how the degree of swelling is affected by the concentrationof HEMA.

A.2 Sources of errorThe samples are picked from water using polymer tongs in which high pressure on the sample should be avoided. Incase of too high pressure applied the water might be pushed out of the hydrogel network. The weight measurementswere performed on a digital scale with a precision of ± 1 mg.

A.3 UncertaintiesThe conductivity of the de-water may have been altered when comes into contact with air, thus reducing the pH of thewater. However this uncertainty is reduced by the renewal of water every 24 hours. Although each sample is wipedwith paper in order to remove any excess of water on the surface, water may remain on the surface after wiping. Theskin that was observed after polymerization of samples, was removed using a water:ethanol mixture and some mayremain on the surface, affecting the swelling process.

A.4 ObservationsUV polymerization was performed on one side of the samples, and it was observed that their surface appeared slightlydifferent. The sample’s surface that was in contact with the silicon mold resulted in the formation of a white skin.

A.5 Analysis and resultsA.5.1 Swelling in waterFig. A.1-A.7 display the swelling data obtained for each hydrogel specimen.

A.5.2 Swelling in 1M NaClFig. A.8-A.12 displayed the data obtained for each specimens while swelling in 1M NaCl.

15

Time, [hours]0 10 20 30 40 50 60 70 80

Q,[g/g]

0

0.1

0.2

0.3

0.4

0.5

0.6 HEMA-50

Fig. A.1 Average degree of swelling Q versus time t. Solid line: calculated mean, Circles: experimental data.

Time, [hours]0 10 20 30 40 50 60 70 80

Q,[g/g]

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55 HEMA-40


16

Time, [hours]0 10 20 30 40 50 60 70 80

Q,[g/g]

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6 HEMA-30


Time, [hours]0 10 20 30 40 50 60 70 80

Q,[g/g]

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6 HEMA-20


17

Time, [hours]0 10 20 30 40 50 60 70 80

Q,[g/g]

0.5

0.55

0.6

0.65

0.7 HEMA-10


Time, [hours]0 10 20 30 40 50 60 70 80

Q,[g/g]

0.45

0.5

0.55

0.6

0.65

0.7

0.75 HEMA-10-sphere


18

Time, [hours]0 10 20 30 40 50 60 70 80

Q,[g/g]

0.8

0.85

0.9

0.95

1 HEMA-5


Time, [hours]0 10 20 30 40 50 60 70 80

Q,[g/g]

0.05

0.1

0.15

0.2

0.25

0.3

0.35 HEMA-50-NaCl


19

Time, [hours]0 10 20 30 40 50 60 70 80

Q,[g/g]

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4 HEMA-40-NaCl


Time, [hours]0 10 20 30 40 50 60 70 80

Q,[g/g]

0.1

0.15

0.2

0.25

0.3

0.35

0.4 HEMA-30-NaCl


20

Time, [hours]0 10 20 30 40 50 60 70 80

Q,[g/g]

0.2

0.25

0.3

0.35

0.4

0.45 HEMA-20-NaCl


Time, [hours]0 10 20 30 40 50 60 70 80

Q,[g/g]

0.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

0.56

0.58 HEMA-10-NaCl


21

Appendix BUniaxial tension on pHEMA

B.1 PurposeUniaxial tests were performed to determine the mechanical properties of pHEMA hydrogels.

B.2 Sources of errorsThe load cell used for the measurement had a maximum load of 2 kN. However, the load applied on the sample wasin the order of 1-2 % of the maximum load thus creating noise during experimentation.

B.3 UncertaintiesWhen secured, the manual force applied by clamping samples may differ between each specimen. The cross sectionaldimensions were defined from the mean of 3 different measurements. A digital caliper was used to measure bothwidth and thickness at three different positions of the sample. Additionally, dimensional measurements of the fullyswollen specimens may vary due to their rubber-like state; i.e. dimensions may appear smaller if too much force isapplied from the caliper to the sample.

B.4 ObservationsSome specimens were observed to break on the head of the specimens, which may discredit the strain at breakmeasurements. A rigid skin was observed on the hydrogels surface, when samples are kept out of water more than10 minutes during uniaxial test.

B.5 Analysis and resultsB.5.1 Error bars for tensile test on as-prepared samplesFig. B.13-B.18 display the statistical analysis done on as-prepared specimens using error bars.

B.5.2 Raw data of fully swollen specimensFig. B.19 and B.20 display the data obtained for 3 repetitions on each specimens.

B.5.3 Relaxation variance on swollen specimens.Fig. B.23 and B.24 display the relaxation tests on 2 swollen specimens for each composition.

22

Strain ǫ, [%]0 5 10 15 20 25 30

Str

ess σ

, [M

Pa]

0

5

10

15

20 HEMA-50

Fig. B.13 Stress σ versus strain ε along with error bars on as-prepared HEMA-50. Standard deviation of 2.55.

Strain ǫ, [%]0 5 10 15 20 25 30

Str

ess σ

, [M

Pa]

0

2

4

6

8

10

12

14

16

18 HEMA-40


23

Strain ǫ, [%]0 5 10 15 20 25 30

Str

ess σ

, [M

Pa]

0

2

4

6

8

10

12 HEMA-30


Strain ǫ, [%]0 5 10 15 20 25 30

Str

ess σ

, [M

Pa]

0

0.5

1

1.5

2

2.5 HEMA-20


24

Strain ǫ, [%]0 5 10 15 20 25 30

Str

ess σ

, [M

Pa]

0

0.05

0.1

0.15

0.2

0.25

0.3 HEMA-10


Strain ǫ, [%]0 5 10 15 20 25 30

Str

ess σ

, [M

Pa]

0

0.01

0.02

0.03

0.04

0.05 HEMA-5


25

Strain ǫ, [%]0 10 20 30 40 50 60 70

Str

ess σ

, [M

Pa]

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6HEMA S 50

Strain ǫ, [%]0 10 20 30 40 50 60 70

Str

ess σ

, [M

Pa]

-0.2

0

0.2

0.4

0.6HEMA S 40

Strain ǫ, [%]0 10 20 30 40 50 60 70

Str

ess σ

, [M

Pa]

-0.1

0

0.1

0.2

0.3

0.4

0.5HEMA S 30

Fig. B.19 Stress σ versus strain ε on fully swollen specimens.

Strain ǫ, [%]0 10 20 30 40 50 60 70 80 90 100

Str

ess σ

, [M

Pa]

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6HEMA S 20

Strain ǫ, [%]0 10 20 30 40 50 60 70 80 90 100

Str

ess σ

, [M

Pa]

-0.1

0

0.1

0.2

0.3

0.4

0.5HEMA S 10

Strain ǫ, [%]0 10 20 30 40 50 60 70

Str

ess σ

, [M

Pa]

-0.1

0

0.1

0.2

0.3

0.4HEMA S 5

Fig. B.20 Stress σ versus strain ε on fully swollen specimens.

26

Time, [s]0 200 400 600

σ, [

MP

a]

0

10

20 HEMA AP 50

Time, [s]0 200 400 600

σ, [

MP

a]

0

10

20 HEMA AP 40

Time, [s]0 200 400 600

σ, [

MP

a]

0

10

20 HEMA AP 30

Fig. B.21 Stress σ versus time on as-prepared specimens.

Time, [s]0 100 200 300 400 500

σ, [

MP

a]

0

1

2 HEMA AP 20

Time, [s]0 100 200 300 400 500

σ, [

MP

a]

0

0.2

0.4 HEMA AP 10

Fig. B.22 Stress σ versus time on as-prepared specimens.

27

Time, [s]0 200 400 600

σ, [

MP

a]

0

0.2

0.4 HEMA S 50

Time, [s]0 200 400 600

σ, [

MP

a]

0

0.2

0.4 HEMA S 40

Time, [s]0 200 400 600

σ, [

MP

a]

0

0.2

0.4 HEMA S 30

Fig. B.23 Stress σ versus time on swollen specimens.

Time, [s]0 100 200 300 400 500

σ, [

MP

a]

0

0.2

0.4 HEMA S 20

Time, [s]0 100 200 300 400 500

σ, [

MP

a]

-0.1

0

0.1

0.2 HEMA S 10

Fig. B.24 Stress σ versus time on swollen specimens.

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Experimental investigation and mathematical modeling of ... · Experimental investigation and mathematical modeling of the mechanical response of hydrogels Aristeidis A. Papadimitriou,

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