25896 | Phys. Chem. Chem. Phys., 2014, 16, 25896--25905 This journal is© the Owner Societies 2014

Cite this:Phys.Chem.Chem.Phys.,

2014, 16, 25896

Phases in the temporal multiscale evolution of thedrug release mechanism in IPN-type chitosanbased hydrogels

E. S. Bacaita,*a B. C. Ciobanu,b M. Popa,b M. Agopa and J. Desbrieresc

The study proposes modeling calcein release kinetics (considered as a hydrophilic drug model) from an

interpenetrating network matrix of hydrogels, based on the combination of two polymers, of which

chitosan is the most commonly used polymer. The release process is analyzed for different increasing

time intervals, based on the evolution of the release kinetics. For each time interval, a dominant release

mechanism was identified and quantitative analyses were performed, to probe the existence of four

distinct stages during its evolution with each stage governed by a different kinetics model. An interesting

and original aspect, which is analyzed through a novel approach, is that of drug release at longer time

scales, which is often overlooked. It revealed that the system behaves as a complex one and its

evolution can be described through a nonlinear theoretical model, which offers us new insights into its

order-disorder evolution.

1. Introduction

One method commonly used to achieve the sustained releaseand control of drugs in drug release processes is the inclusionof the drug in a matrix with a three-dimensional structure (gel),which may be hydrophobic or hydrophilic, depending on thenature of the therapeutic agent. In most cases, biologicallyactive compounds are hydrophilic; therefore, the matrices usedare based on polysaccharides or their derivatives, proteins(such as collagen and gelatin) and even some synthetic poly-mers, provided that they are biocompatible and biodegradablesuch as poly(vinyl alcohol), poly(lactic acid), and poly(glycolicacid). Since the inclusion/encapsulation of the active principaltakes place in moderate conditions, the distortion/degradationof sensitive drugs during their association with the polymermatrix is avoided.

In most cases, the polymer matrix is structured/cross-linkedbefore being placed in contact with a concentrated solution ofthe drug, which is able to swell it (through solvent swellingtechnique).1 Drug loading is performed through a diffusionprocess, and the driving force that determines the flow of the

drug within the matrix is the concentration gradient betweenthe solution and the macromolecular support.2 A variant forobtaining such systems is cross-linking the linear chains in thesolution in which the drug is dissolved.

Regardless of the method used for drug loading in thehydrogel matrix, the release of drug is determined by theconcentration gradient between the matrix and the liquid inwhich the hydrogel-drug system is placed. Obviously, therelease phenomena is of diffusional nature, described byFick’s law.3

Typical release curves, which are encountered most often inspecialized studies, follow an exponential trend, which is some-times followed by a constant plateau. However, the subsequentevolution of the following process, especially over a longertimescale, exhibits an unusual behavior, which is influencedby the polymer matrix type: i.e. large variations for the CS/GELmicroparticles,4 or a decrease in the amount of the drugreleased from hydrogels,5 which is difficult to explain underthe classical approach. This raises the legitimate question: howcan we explain these evolutions? What kinetic models aregoverning these processes? What phenomena become domi-nant and are responsible for the change in the release kinetics?

The aim of this work is to establish the kinetic models thatare most suitable for describing the drug release from hydrogel-based matrices at different time scales. In particular, attentionis paid to the evolution at longer timescales, which is of theorder of days, during which the phenomena that appear andtheir time evolution may be difficult to quantify in amplitudeand dependence.

a Department of Physics, ‘‘Gheorghe Asachi’’ Technical University of Iasi,

Prof. Dr. docent Dimitrie Mangeron Rd., No. 73, Iasi 700050, Romania.

E-mail: bsimona77@yahoo.com; Tel: +40 744 667 749b Department of Natural and Synthetic Polymers, ‘‘Gheorghe Asachi’’ Technical

University of Iasi, Prof. Dr. docent Dimitrie Mangeron Rd., No. 73, Iasi 700050,

Romaniac Universite de Pau et des Pays de l’Adour, IPREM (UMR CNRS 5254),

Helioparc Pau Pyrenees, 2 Avenue P. Angot, 64053 PAU Cedex 09, France

Received 30th July 2014,Accepted 26th September 2014

DOI: 10.1039/c4cp03389b

www.rsc.org/pccp

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The present study was conducted using polymer matrixhydrogels of semi- or full-interpenetrating type with very lowporosity, which is obtained by the chemical co-cross-linking oftwo pairs of polymers: chitosan–gelatin and chitosan–poly(vinylalcohol).

Chemical cross-linking agents such as formaldehyde andglutaraldehyde, which are commonly used in the synthesis ofhydrogels, are toxic to the human body and therefore attentionis directed to the use of ionic cross-linkers such as sodiumsulfate (Na2SO4) and sodium tripolyphosphate (TPP). However,covalent bonds induce better mechanical properties in hydro-gels, and, consequently high stability over a longer timescale.This is why the covalent cross-linker (glutaraldehyde) was notcompletely replaced for preparing the hydrogel; however, it wassubstituted with the ionic one up to the limit above which thestability of the system would be affected. Accordingly, the firstpart of the research was to find the equilibrium between thecovalent (toxic in general) and the ionic (biologically acceptable)cross-linker amounts, in order to obtain hydrogels with superiorproperties compared to the existing ones, especially from thepoint of view of biocompatibility.6,7

Next, the kinetics of calcein release (with a water-solubledrug used as a model) from these hydrogels was analyzed andcompared by fitting at different timescales to the known lawsfor drug release, in order to identify the most appropriaterelease mechanisms and to establish, through quantitativeanalysis, similarities, differences and possible correlationsbetween the evolution of different samples.

2. Experimental results2.1 Materials and methods

The materials used were high and medium molecular weightchitosan (HC/MC), type B gelatin (GEL) of bovine origin,poly(vinyl alcohol) (PVA) with a hydrolysis degree of 80%,glutaraldehyde (GA) (aqueous solution of 25%), sodium sulphate(Na2SO4), sodium tripolyphosphate (TPP), and calcein.

Preparation of the hydrogels was based on a partial covalentcross-linking with AG of polymers (amount of AG ensures cross-linking of 20% of the functional groups of the polymer mixture),followed by ionic cross-linking with Na2SO4 or TPP. In the caseof the chitosan–gelatin system, both polymers participate inthe cross-linking reactions. For the chitosan–PVA system, thesynthetic polymer participates only in the covalent cross-linking,as it is free of substituents with an ionic character.

Considering the presence of the amine groups of chitosanand gelatin as substituents and given that the cross-linkingreaction is carried out in an acidic medium, in Fig. 1, weillustrate schematically the reactions that may occur betweenthe ammonium ions formed in the acid medium, both with thecovalent and with the ionic cross-linkers (sulfate anion in thiscase), which leads ultimately to the interpenetrating networkstructure (IPN).

The procedure for obtaining the polymer films loaded withcalcein is not the subject of this paper, but it is described in

ref. 8. In order to obtain drug-loaded hydrogels, calcein wasadded to each polymer solution prior to cross-linking. Thehydrogels were processed as thin films of 0.1 mm thickness.

The drug release was monitored by fluorescence spectroscopyanalysis. The calcein release was performed at 37 � 1 1C, in thedark, to protect calcein from degradation under the possibleaction of light radiation. Moreover, the release experiments werecarried out into media approximating a normal therapeuticsituation. The studies were performed in triplicate for eachsample and the average values were used in the data analysis.

2.1.1 Chitosan–gelatin hydrogels. Hydrogels based onchitosan and gelatin (CG) were prepared by a partial covalentcross-linking with AG, followed by ionic cross-linking withNa2SO4 or TPP. The influence of the polymer mass ratio andthe ionic cross-linking agent amount were also verified. Thecodes of the synthesized matrix and their parameters arepresented below (Table 1(a)).

2.1.2 Chitosan–poly(vinyl alcohol) hydrogels. These gelswere obtained by the same method as previous cases, exceptthat, in all cases, the covalently cross-linked hydrogels wereimmersed in 4 ml 1% ionic cross-linker solutions. The codesof the synthesized matrix and the polymer mass ratios areillustrated in Table 1(b).

2.2 Experimental kinetics of calcein release from hydrogels

The experimental release kinetics are plotted in Fig. 2.It should be noted that for the CG-S hydrogels (Fig. 2a),

about 80% of the loaded drug was gradually released into the

Fig. 1 Schematic presentation of the structure of the hydrogels producedby ionic cross-linking with sodium sulfate ion or covalent one with GA toform covalent imine groups or acetal cycles and semiacetalic bondsbetween GA and polymers (green chain – PVA, dark magenta – chitosan).

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supernatant over seven days. The parameters modified accordingto Table 1 do not significantly influence the amount of calceinreleased or the release kinetics characteristics.

A similar behavior was observed for CG-T hydrogels (Fig. 2b),but in this case, there was a lower efficiency of calcein release,which was about 65%, and a slight influence of the modifiedparameters, according to Table 1(b) (molar ratio CS/GEL andTPP amount).

Hydrogels with PVA show release kinetics similar to thoseof hydrogels with gelatin, for the same ionic cross-linker, althoughthe release is faster, as the amount of calcein released reaches amaximum value compared to the previous CG hydrogels after(3 days compared to 4–5 days). Moreover, these CP hydrogels showa lower stability than CG hydrogels, as estimated by the timeinterval for which the released calcein has a constant value. In thisrespect, an influence of the ionic cross-linker is noticed: 3 h forCG-S, 4 h for CG-T, 2 h for CP-S and 3 h for CP-T.

These experimental observations can be explained by assumingthat the release efficiency is determined, mainly, by the cross-linking density of the hydrogel matrix and also by considering thefollowing characteristics of the materials that are used:

– PVA does not participate in ionic cross-linking, whichdetermines its lower cross-linking density in CP hydrogels, asreflected in faster drug release and higher efficiency in theircase, compared to CG hydrogels;

– TPP is a stronger ionic cross-linker than Na2SO4, leading toa more dense hydrogel matrix, and, furthermore, to the longerstability and lower efficiency of CG-T and CP-T hydrogels,compared to CG-S and CP-S hydrogels.

CP and CG hydrogels have very similar evolutions becauseeven if PVA does not participate in ionic cross-linking, thedegree of cross-linking with gelatin is low because of itssmall number of amino groups; therefore, the main elementresponsible for the cross-linking density is still chitosan.

All the release kinetics, regardless of the polymers and cross-linker types, show similar system evolutions, and they pass

through the same phases, but with differences in the timethresholds at which the phase transitions take place as well asthe time interval of each phase. The phase transitions areobserved in the release kinetics as inflections of the curvesshape, suggesting modifications in the release mechanism.Continuing the experiments up to longer time scales, fourtimes greater than the time corresponding to the maximumrelease, a decrease in the amount of released calcein isobserved.

Table 1 Parameters used for chitosan–gelatin (a) and chitosan–poly(vinylalcohol) (b) hydrogels

Sample CS/GEL (w/w) Na2SO4 (g) TPP (g)

CG-S1 1.9 0.0605 —CG-S2 9 0.064 —CG-S3 4.5 0.079 —CG-S4 4.5 0.0595 —CG-T1 1.9 — 0.078CG-T2 9 — 0.083CG-T3 4.5 — 0.1024CG-T4 4.5 — 0.0771

Sample CS/PAV (w/w)

CP-T1 9CP-T2 5.7CP-T3 4CP-T4 3CP-S1 9CP-S2 5.7CP-S3 4CP-S4 3

Fig. 2 The release kinetics of calcein from hydrogels based on: chitosanand gelatin cross-linked with sodium sulphate (a) and TPP (b), and chitosanand PVA cross-linked with sodium sulfate (c) and TPP (d).

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3. Mathematical modelling

Drug release from a polymer matrix is a complex process, invol-ving many interacting entities, leading to multiple phenomena,most of them superimposing each other in time and space. Foridentifying the release mechanism, several approximations areneeded in order to simplify the system mathematics.

In our case, for a hydrogel type polymer matrix immersed inan aqueous medium, we identify the following phases in thetemporal evolution of drug release:

(1) In the first few moments after immersion in the releaseenvironment, the hydrogel surface wets and the burst-effect takesplace, due to the release of the molecules from the matrix frontier,induced by a very high concentration gradient. This initial releaseis very fast and there is not enough time for water to penetrate intothe matrix; therefore, (i) the diffusivity is constant, (ii) there is aperfect sink at the interface and (iii) no swelling and erosion of thematrix takes place. In these approximations, Fick’s diffusion law inthe condition of a fixed boundary, can be applied and leads, for‘early’ times and thin films, to an equation similar to that ofHiguchi (tl/2 time dependence of the drug release efficiency):

Mt

M1¼ 4

Dt

pL2

� �1=2

(1)

where Mt is defined as the amount of drug released at time t, MN

the amount of drug released as time approaches infinity, D thediffusion coefficient and L the thickness of the film.9

In summary, a simplified Higuchi model can be expressedas follows:

Mt

M1¼ kHt

0:5 (2)

where kH is the Higuchi diffusion constant.10

(2) Subsequently, the hydrogels retain water and begin tohydrate from the periphery towards the centre, and forms a viscousswollen mass. Two diffusion fronts appear: one at the interfacebetween the dry and hydrated (swollen) polymer and the second atthe interface between the swollen polymer and the release environ-ment. The diffusion coefficients are different in the two newlyappeared areas (the swollen and non-swollen polymer) becausewater penetration determines the increasing network mesh, whichincreases the dimensions of the system and increases the macro-molecular mobilities, and consequently leads to higher diffusioncoefficients, which influence the release characteristics.

In the approximations that (i) the diffusivity is constant intime, (ii) there is a perfect sink at those two fronts, (iii) noerosion of the matrix takes place, (iv) the swelling rates areconstant in all directions and (v) there is no transition from theglassy to the rubbery state of the polymer, Fick’s law with amoving boundary leads to a general solution in the form:

Mt

M1¼ kKPt

n (3)

which is similar to that of Korsmeyer and Peppas, where t is therelease time, Mt is the amount of drug delivered at time t, MN isthe total amount of drug delivered, kKP is a kinetic constant,

which is a measure of the release rate, and n the diffusionalexponent that gives an indication of the mechanism of the drugrelease; moreover, it takes various values depending on thegeometry of the release device. Thus, in our case of a thin filmhydrogel, values up to 0.5 indicate a Fickian diffusion, 0.5–1.0indicate an anomalous (non-Fickian) transport (i.e. mixed diffu-sion and chain relaxation mechanisms) and 1.0 indicates a CaseII transport (zero order). Values of n greater than 1 reflect theso-called super Case II-transport.11 The smaller n values, i.e.,below 0.5, are associated with drug diffusion through a partiallyswollen matrix and through a water filled network mesh.12

(3) After the swelling is complete, the system reaches anequilibrium state, characterized by a constant value of releaseddrug and no concentration gradient between the hydrogelmatrix and release environment.

In this phase, a more general equation can be applied, onethat combines the contribution of Fickian (pure diffusivityphenomenon) and non-Fickian release (due to the relaxationof the polymer sections between the network nodes, called the‘‘relaxational’’ term), namely, the Peppas–Sahlin equation,expressed as the sum of two different powers of time:

Mt

M1¼ kDt

m þ kRt2m (4)

where the first term of the right-hand side is the Fickian contribu-tion (kD is the diffusional constant) and the second term is the CaseII relaxation contribution (kR is the relaxation constant), and m isthe purely Fickian diffusion exponent for a device of any geome-trical shape, which can be determined from the plot of the aspectratio (diameter/thickness) against the diffusional exponent n.13

The kD and kR values are used to calculate the contributionpercentage of the Fickian diffusion (FD) and relaxation (R),respectively with the following equations:

FD ¼1

1þ kR

kDtm; (5a)

R

FD¼ kR

kDtm (5b)

The Peppas–Sahlin equation actually represents a short timeapproximation of the Weibull exponential equation,14 which isa statistical distribution function of wide applicability that isused inclusively in drug release studies:

Mt

M1¼ 1� eat

b

(6)

where a and b are constants. The value of b is an indicator ofthe mechanism of drug transport through the hydrogel: b r0.75 indicates Fickian diffusion, while a combined mechanism(Fickian diffusion and Case II transport) is associated with bvalues in the range of 0.75 o b o 1; moreover, for values of bhigher than 1, the drug transport follows a complex releasemechanism. This equation is criticized by many researchersdue to the lack of a kinetics basis for its use and the non-physical nature of its parameters.

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(4) The fourth phase can be observed if the release is conductedon longer timescales (almost four times greater than the timerequired to reach the maximum drug release) when the drug and/or polymer starts to degrade. Because the complete and detaileddescription of all the sub-phenomena at longer timescales leads tovery complex models and needs the knowledge of a large number ofvariables and parameters (which are not easily determinable), somesimplifications in modelling are needed, according to the variouslevels of details required and the different timescales involved. Thetheoretical studies carried out on the drug release from degradablepolymers needed many assumptions such as affine deformations,no physical drug–hydrogel part interactions, which could signifi-cantly vary with time and position, or with the chemical reactionsbetween the drug and hydrogel parts and/or water.

In order to reduce the number of approximations, onepossible approach is a fractal one, justified by the fact that bothnatural and synthetic polymers are considered objects withfractal dimensions and their structure and behaviour can bedescribed by means of fractal geometry.15 Moreover, the abovepresented laws, valid under certain approximations, are powertype laws, specific for the fractal system evolution.16 In thisapproach, we consider the system complexity to be replacedwith fractality and, therefore, the drug release process is con-sidered to take place on curves (fractal curves), and physicalquantities can then be expressed through fractal functions(functions that are dependent both on coordinate field andresolution scales, i.e. continuous, but non-differentiable).

In this context, the entire system (drug-loaded hydrogels inthe release environment) can be considered as a medium thattotally lacks interaction among the component particles and itsevolution can be theoretically analyzed in the framework ofScale Relativity Theory (SRT),17 leading, in an arbitrary constantfractal dimension, to the operator:4

@

@¼ @

@tþ VriDðdtÞ 2=DFð Þ1Dþ

ffiffiffi2p

3D3=2ðdtÞ 3=DFð Þ1r3 (7)

where V is the complex speed field (V = V � iU), V is thestandard classical speed, independent of scale resolution (dt),whereas the imaginary part, U, is a new quantity arising fromnon-differentiability and resolution-dependence. Furthermore,D is a structure coefficient, characteristic of the fractal-non-fractal transition, DF is the fractal dimension of the drugparticle trajectory, a measure of the system nonlinearity, andD is the Laplace operator, a measure of the system dissipation.4

Applying the fractal operator (7) to the amount of releaseddrug Mt and accepting the principle of scale covariance in theform (qMt/qt) = 0, we obtain the generalized fractal diffusionequation in the explicit form:

@Mt

@t¼ @Mt

@tþ ðV � rÞMt � iDðdtÞ 2=DFð Þ�1DMt

þffiffiffi2p

3D3=2ðdtÞ 3=DFð Þ�1r3Mt ¼ 0

(8)

The eqn (8) can be analyzed in two approximations ofmotion (dissipative and dispersive).

The dissipative approximation of motion (equivalent with ashort time approximation of motion, where convective anddissipative process become dominant), results in an equationsimilar to Weibull’s eqn (6).18

In the dispersive approximation (equivalent with long timeapproximation when convective and dispersive processesbecome dominant), the efficiency of drug release is dependenton a time function e(t) and system nonlinearity (throughparameter s), in the form of a Korteweg de Vries type equation,whose explicit solution, for the unidimensional case and for aconvenient choice of integration constants, has the form:

Mt

M1ðeðtÞ; sÞ ¼ 2a

EðsÞKðsÞ1þ 2a cn2

ffiffiffiap

seðtÞ; s (9)

where cn is Jacobi’s elliptic function of s modulus, a is theamplitude, and K(s) and E(s) are the complete elliptic integrals.

4. Results and discussion4.1 Drug release over short timescales

4.1.1 Burst effect phase – Higuchi equation. In order toidentify the time threshold up to which the burst effect takesplace, the release kinetics were observed in the early times ofthe release, as seen in Fig. 3.

Fig. 3 Early time release – Burst effect phase.

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We identified the inflection points corresponding to thetime threshold at approximately 130 min. for all samples,where differences in the amount of drug release could beobserved, especially between hydrogels cross-linked with TPPand those with Na2SO4, due to the different cross-linkingdensity of the hydrogel matrix.

In order to determine the system parameters for the firstphase of release (Higuchi constant – kH, diffusion coefficientD), the release data up to Higuchi threshold are fitted with thecorresponding Higuchi model equation. The values obtained(Table 2(a) and (b)) shows, as expected, that the diffusioncoefficients calculated are higher for hydrogels cross-linkedwith Na2SO4, because the diffusion is favoured by their largernetwork mesh, which allows a higher average free path of thedrug molecules in the hydrogel superficial layer. Comparingthe values of the Higuchi constant, an indicator of release rate,it can be observed that it has the lowest value for CG-T3 (for CGhydrogels) and CP-T1 (for CP hydrogels), i.e., samples with adenser matrix, which is determined by the highest amount ofTPP used (CG-T3) and by the highest amount of chitosan used,which is the main participant in cross-linking.

For all samples, the correlation coefficients are higherthan 0.99.

4.1.2 Swelling phase – Korsmeyer–Peppas equation. TheKorsmeyer–Peppas threshold (tKP) is considered to be themoment at which the system reaches the equilibrium statewith an approximately constant calcein concentration (nogradient concentration between the hydrogel and the releaseenvironment). These moments are visualized in the releasekinetics at the beginning of constant concentration plateau(Fig. 4), and their values can be seen in Table 3(a) and (b)(average values for each sample group). tKP can be equivalent

with complete swelling time and, as expected, the hydrogelsfollow similar swelling behaviors as to when immersed inwater, and thus CG hydrogels, with higher cross-linkingdensity, swell slower than others and reach the equilibriumstate last.

Table 2 (a) Higuchi parameters for CG hydrogels. (b) Higuchi parametersfor CP hydrogels

Sample CS/GEL (w/w) Na2SO4 (g) kH D (cm2 s�1) � 1011

(a)CG-S1 1.9 0.060 0.72 1.71CG-S2 9 0.064 0.86 2.44CG-S3 4.5 0.079 0.60 1.19CG-S4 4.5 0.060 0.98 3.16

Sample CS/GEL (w/w) TPP (g) kH D (cm2 s�1) � 1011

CG-T1 1.9 0.078 0.66 1.43CG-T2 9 0.083 0.64 1.36CG-T3 4.5 0.102 0.54 0.96CG-T4 4.5 0.077 0.72 1.72

Sample CS/PAV (w/w) kH D (cm2 s�1) � 1011

(b)CP-S1 9 0.68 1.50CP-S2 5.7 0.77 1.94CP-S3 4 0.87 2.47CP-S4 3 0.96 3.01

CP-T1 9 0.42 0.60CP-T2 5.7 0.50 0.83CP-T3 4 0.62 1.26CP-T4 3 0.72 1

Fig. 4 Korsmeyer–Peppas threshold (tKP) and equilibrium plateau (sur-rounded areas).

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Moreover, the Korsmeyer–Peppas parameters obtained byfitting are presented in Table 3(a) and (b).

Referring to the n values, simple Fickian diffusion mechan-isms (n = 0.5), do not occur for any of our samples; the n valueslie below 0.5, demonstrating that the mechanism of drug releaseis the complex Fickian diffusion, consisting of drug diffusionthrough the swollen hydrogel and/or water filled pores.

In addition to giving insights into the release mechanism,the Korsmeyer–Peppas equation offers information on therelease rate, through kKP; thus, it follows the same evolutionas in the burst effect phase, in which for CG-S hydrogels, theslower release is manifested for CG-T3, with the most densenetwork due to higher amount of TPP, and the faster rate forCG-S4, where the ionic cross-linker is weaker and in smalleramounts. In the CP-T hydrogels case, in which the amount ofionic cross-linker was the same for all samples, the fasterrelease is exhibited for the one cross-linked with TPP and thehighest chitosan–gelatin molar ratio (CP-T1), and the slowestone is for the one cross-linked with Na2SO4 and the lowestchitosan–PVA molar ratio (CP-S4).

For all the samples, the correlation coefficients are higherthan 0.99.

4.1.3 Equilibrium phase. The equilibrium phases are that ofconstant concentration, and their length (surrounded areas fromFig. 4) proved to be dependent of the sample type, or more precisely,on the bond strength, which are stronger for CG-T hydrogels andweaker for CP-S hydrogels. Based on the observations of the releasekinetics in the equilibrium area, we can establish a hierarchy of thestability degree, as detailed in Table 4. Moreover, a time thresholdfor this phase can be estimated.

In addition to the predicted evolution of CG-T and CP-Shydrogels, one observation can be made for CG-S and CP-T

hydrogels: they are comparable in stability, acting as if thepolymer properties (gelatin–PVA) are compensated by those ofthe ionic cross-linker (TPP–Na2SO4).

The equilibrium phase will be analyzed through two equations:Peppas–Sahlin and Weibull, both known to describe the ‘‘entire’’release kinetics, as considered up to the constant plateau.

4.1.3.1 Peppas–Sahlin equation. The Peppas–Sahlin para-meters resulting from fitting the experimental data to thisequation are presented in Table 5(a) and (b). The value of mfor our films was 0.4, as determined from the plot of the aspectratio (diameter/thickness) against the diffusional exponent n.19

Negative values of kR were obtained, a fact that indicates aninsignificant effect of relaxation compared to the Fickiandiffusion of drug release, continuing the Fickian release fromswelling phase. Moreover, it is possible to express the prepon-derance of the Fickian mechanism compared to the relaxationone, as the values of kD are larger than kR, and less dependenton the relaxation of the polymer chains, although it is necessaryfor both phenomena to take place.20

From these parameters, the contribution of the Fickiandiffusion to the overall release (eqn (5a)) was calculated. Theresults for the representative samples of each group (CG-S4,CG-T3, CP-S4, CP-T1) versus time are plotted in Fig. 5.

Table 3 (a) Korsmeyer–Peppas parameters for CG hydrogels. (b) Korsmeyer–Peppas parameters for CP hydrogels

Sample CS/GEL (w/w) Na2SO4 (g) tKP (days) kKP n

(a)CG-S1 1.9 0.060 3 0.50 0.32CG-S2 9 0.064 0.53 0.29CG-S3 4.5 0.079 0.47 0.37CG-S4 4.5 0.060 0.56 0.26

Sample CS/GEL (w/w) TPP (g) tKP (days) kKP n

CG-T1 1.9 0.078 4 0.40 0.30CG-T2 9 0.083 0.37 0.30CG-T3 4.5 0.102 0.33 0.33CG-T4 4.5 0.077 0.43 0.29

Sample CS/PAV (w/w) tKP (days) kKP n

(b)CP-S1 9 2 0.55 0.40CP-S2 5.7 0.60 0.38CP-S3 4 0.63 0.36CP-S4 3 0.65 0.33

CP-T1 9 3 0.40 0.44CP-T2 5.7 0.46 0.38CP-T3 4 0.50 0.35CP-T4 3 0.53 0.33

Table 4 Equilibrium phase timing

SampleStartingmoment (days)

Time of equilibriumphase (days)

Equilibriumthreshold (days)

CG-T 4 5 9CP-T 3 3 6CG-S 3 3 6CP-S 2 2 4

Table 5 (a) Peppas–Sahlin parameters for CG hydrogels. (b) Peppas–Sahlin parameters for CP hydrogels

Sample CS/GEL (w/w) Na2SO4 (g) kD kR

(a)CG-S1 1.9 0.060 0.67 �0.15CG-S2 9 0.064 0.74 �0.18CG-S3 4.5 0.079 0.59 �0.10CG-S4 4.5 0.060 0.80 �0.21

Sample CS/GEL (w/w) TPP (g) kD kR

CG-T1 1.9 0.078 0.53 �0.11CG-T2 9 0.083 0.49 �0.10CG-T3 4.5 0.102 0.42 �0.08CG-T4 4.5 0.077 0.58 �0.13

Sample CS/PAV (w/w) kD kR

(b)CP-S1 9 0.68 �0.15CP-S2 5.7 0.76 �0.18CP-S3 4 0.84 �0.22CP-S4 3 0.92 �0.26

CP-T1 9 0.49 �0.08CP-T2 5.7 0.60 �0.13CP-T3 4 0.68 �0.17CP-T4 3 0.75 �0.20

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It is obvious that Fickian diffusion is more dominant forhydrogels cross-linked with Na2SO4, for which the diffusion isfaster due to the polymer network with high porosity.

For all samples, the correlation coefficients are higherthan 0.99.

4.1.3.2 Weibull equation. The same analysis was performedalso for the Weibull equation, and we obtained for parameterb values smaller than 0.75, indicating also a Fickian diffusion,which is consistent with the conclusion from the analysis basedon Peppas–Sahlin equation.

Since both equations, Peppas–Sahlin and Weibull, led to thesame conclusion, and as the correlation factors are very close(0.99 for Peppas–Sahlin equation and 0.98 for Weibull equa-tion), it raises questions about which equation is recom-mended for the further analysis. We consider that theselection must be taken based on what information is neededto be obtained: Weibull offers simple information about therelease mechanisms, whereas Peppas–Sahlin can quantify thediffusion and relaxation contribution to the overall release.

4.2 Drug release over large timescales

In this case, the experimental results show that the amount ofdrug in the release environment is reduced. This reduction canbe attributed to the interactions between calcein and thehydrogel fragments resulting from the degradation of thebonds to each other; hence, the amount of free calcein mea-sured decreases as the degradation is more advanced, and alsothe number of detached fragments that bind calcein increases.

According to eqn (9), in this situation, the efficiency of drugrelease is dependent on a time function e(t) and the systemnonlinearity, through parameter s (although it is worth point-ing out that nonlinearity can be interpreted as a disorder in thesystem evolution). This dependence is illustrated in Fig. 6.

For each sample, the normal plane section that best fits theentire release kinetics was identified, and thus the systemnonlinearity and complexity could be estimated. The inter-section between the normal section and the (e(t), s) plane of

the tridimensional plot represents a straight line, whose equationcan be written as follows:

s = s0 + ae(t) (10)

where s0 represents the initial system nonlinearity and a is the lineslope, with the physical meaning being the rate of evolution tounstable and disordered states, with the high degree of nonlinearity.As a consequence of the similarity of the release kinetics for thesamples within a group, the associated parameters were very close;therefore, in the following, we only consider the representativesamples CG-S4, CG-T3, CP-S4, and CP-T1. For these samples, theintersection line parameters are given in Table 6.

First observation is made referring to the s0 values, whichare very small, indicating thus stable, organized systems, in theinitial state of the release. The a values confirm the stabilityhierarchy from Table 4, with the most stable samples (CG-T)exhibiting the slowest evolution to unstable states.

The corresponding section planes and intersection lineswith the 3D plot (Fig. 6), which best fits the experimental data,as illustrated in Fig. 7.

Fig. 7b better reflects that, at a certain moment in the systemsevolution (a given e(t)), the nonlinearity degrees in these samplesincreases in the order CG-T3, CP-T1, CG-S4, to CP-S4, which is areverse order to that of stability (Table 4), as expected.

The intersection contours and the experimental releaseprofiles fit with correlation factors higher than 0.9 (Fig. 8).

The above results reconfirm the validity of the fractalapproach for the analysis of drug release over large timescales,offering insights on a systems evolution to unstable, disorderedstates.

Fig. 5 The contribution of Fickian diffusion to the overall release.

Fig. 6 3D dependence of the drug release efficiency on a time function(e(t)) and system nonlinearity (s).

Table 6 The parameters of the intersection line between the sectionplane and 3D plot

Sample CG-T3 CP-T1 CG-S4 CP-S4

s0 0.002 0.001 0.001 0.003a 0.29 0.31 0.33 0.36

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25904 | Phys. Chem. Chem. Phys., 2014, 16, 25896--25905 This journal is© the Owner Societies 2014

5. Conclusions

1. Interpenetrated networks based on chitosan, double cross-linked, are capable of releasing hydrophilic drugs through amulti-scale mechanism, characterized by four distinct phases,each characterized by a different kinetics model.

2. The first phase, i.e., the burst effect, can be best describedby the Higuchi equation. The corresponding threshold is notsignificantly influenced by the polymers or the cross-linkertype, is conditioned mainly by the concentration gradient.

3. The second phrase is dominated by the swelling of thepolymer matrix, and the most appropriate model for this is thatof Korsmeyer and Peppas. Its temporal length is proportionalwith the cross-linking density of the polymer matrix, whichimplicitly depends on the polymer or cross-linker type.

4. The analysis of the Korsmeyer–Peppas parameters showsthat the mechanism of drug release is the complex Fickiandiffusion, consisting of drug diffusion through the swollenhydrogel and/or water filled pores and that the release ratealso depends on the polymer or cross-linker type.

5. The equilibrium phase is the third one and is characterizedby a constant concentration, and its time length is dependent onthe sample type, or more precisely, on the cross-linking density.The equilibrium phase can be analyzed through two equations:Peppas–Sahlin and Weibull. The quantitative analysis of these

equations parameters shows the preponderance of the Fickianmechanism compared to the polymer matrix relaxation.

6 Since both equations, Peppas–Sahlin and Weibull, lead to thesame conclusion, the decision on which equation can be used infurther analysis must be taken based on what information is neededto be obtained: Weibull’s equation offers simple information on therelease mechanisms, whereas Peppas–Sahlin equation can quantifythe diffusion and relaxation contribution to the overall release.

7. In situations where the drug release is monitored overlonger timescales, the results show unusual evolution (in our

Fig. 7 The section planes (a) and intersection lines (b) for CG-S4, CG-T3,CP-S4, and CP-T1.

Fig. 8 The intersection contours and experimental release profiles forsamples CG-S4 (a), CG-T3 (b), CP-S4 (c), and CP-T1 (d).

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case, the amount of drug released reduces). The phenomenathat determine this (drug and polymer matrix degradation, andthe physical and chemical interactions between them) aredifficult to estimate; hence, the nonlinear mathematicalapproach is appropriate. This shows that the efficiency of drugrelease is dependent on time and on the system nonlinearity.Moreover, the nonlinearity of all the samples in the initial statehad small values, indicating thus stable, organized systems;furthermore, the rate of evolution to unstable and disorderedstates, with a high degree of nonlinearity, was influenced bythe polymer matrix stability; thus, the most stable samplesexhibited the slowest evolution to disorder.

References

1 N. A. Peppas, P. Bures, W. Leobandung and H. Ichikawa,Eur. J. Pharm. Biopharm., 2000, 50, 27.

2 G. Tataru, M. Popa and J. Desbrieres, J. Bioact. Compat.Polym., 2000, 24, 525.

3 J. Siepmann, R. Siegel and M. Rathbone, Fundamentals ansApplications of Controlled Release Drug Delivery, Springer,2012.

4 E. S. Bacaita and C. Bejinariu, et al., J. Appl. Math., 2012,2012, 653720.

5 C. Vasile and G. E. Zaikov, Environmentally Degradable MaterialsBased on Multicomponent Polymeric Systems, Brill, 2009.

6 C. A. Peptu, G. Buhus, M. Popa, A. Perichaud and D. Costin,J. Bioact. Compat. Polym., 2010, 25, 98.

7 N. Jatariu, M. Popa, S. Curteanu and C. A. Peptu, J. Biomed.Mater. Res., Part A, 2011, 98A, 342.

8 B. C. Ciobanu and A. C. Cadinoiu, et al., Cellul. Chem.Technol., 2014, 48, 485.

9 L. L. Lao and N. A. Peppas, et al., Int. J. Pharm., 2011, 418, 28.10 T. Higuchi, J. Pharm. Sci., 1963, 52, 1145.11 R. W. Korsmeyer, R. Gurny, E. Doelker, P. Buri and

N. A. Peppas, Int. J. Pharm., 1983, 15, 25.12 E. B. Souto, Eur. J. Med. Chem., 2013, 60, 249.13 N. A. Peppas and J. J. Sahlin, Int. J. Pharm., 1989, 57, 169.14 V. Papadopoulou and K. Kosmidis, et al., Int. J. Pharm.,

2006, 309, 44.15 G. V. Kozlov and G. E. Zaikov, Fractals and Local Order in

Polymeric Materials, Nova Science Publishers Inc, New York,2001.

16 V. U. Novikov and G. V. Kozlov, Russ. Chem. Rev., 2000, 69, 323.17 L. Nottale, Scale Relativity and Fractal Space-Time – A New

Approach to Unifying Relativity and Quantum Mechanics,Imperial College Press, London, 2011.

18 S. Bacaita and C. Uritu, et al., Smart Mater. Res., 2012,2012, 264609.

19 N. A. Peppas and J. J. Sahlin, Int. J. Pharm., 1989, 57, 169.20 P. R. Oliveira, L. S. Bernardi and O. L. Strusi, et al., Int.

J. Pharm., 2011, 405, 90–96.

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