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A crosslinked system from Scleroglucan derivative: preparation and characterization
Biomaterials 22 (2001) 1899}1909
A crosslinked system from Scleroglucan derivative: preparation and characterization T. Coviello , M. Grassi, G. Rambone , F. Alhaique * Dipartimento di Studi di Chimica e Tecnologia delle Sostanze Biologicamente Attive, University of Rome **La Sapienza++, Piazzale Aldo Moro 5, 00185 Roma, Italy Dipartimento di Ingegneria Chimica, dell+Ambiente e delle Materie Prime - Universita% di Trieste, Italy Received 15 June 2000; accepted 3 November 2000
Abstract Matrices obtained by a crosslinking reaction between the polycarboxylated derivative of scleroglucan (sclerox) and 1,6-hexanedibromide have been prepared and characterized. Di!erent ratios between the alkane dihalide and sclerox yielded products with di!erent properties. Water uptake by the hydrogel with a low degree of crosslinking was remarkably a!ected by ionic strength. The determination of the crosslink density is led by simultaneously solving two Flory equilibrium equations referring to two di!erent conditions characterized by the presence or the absence of a salt in the swelling agent. Moreover, the swelling kinetics was studied by means of a recently proposed model. Finally, the permeation of two model molecules (theophylline and polystyrene sulphonatesodium salt) through the hydrogels was evaluated. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Scleroglucan; Polysaccharides; Crosslinking; Hydrogel; Sustained release
1. Introduction Scleroglucan is a general term used to designate a class of glucans produced by fungi, especially those of the genus Sclerotium. The commercial product, termed scleroglucan, is water soluble and consists of linearly linked (1P3) D-glucose residues with (1P6) D-glucose residues as side chains, one for every three consecutive glucose units. This polysaccharide is dispersed as a triple helix in water, whereas it is dissolved as a single coil in methylsulfoxide [1}3]. Because of its interesting rheological properties and its resistance to hydrolysis, scleroglucan has general industrial applications. As far as the pharmaceutical "eld is concerned, experiments performed in vitro indicate that scleroglucan is a polysaccharide suitable for sustained release formulations. In fact, it has been proposed for the formulation of monolithic swellable matrices [4}8] as well as for ophtalmic preparations [9]; furthermore, oxidized scleroglucan (sclerox) was proposed for a pH-controlled delivery from oral dosage forms [10,11]. * Corresponding author. Tel.: #39-6-49913557; fax: #39-649913888. E-mail address: [email protected] (F. Alhaique).
In a previous paper [12] we have shown a part of our studies on a new type of hydrogel obtained by a crosslinking reaction between sclerox and an alkane dihalide. One of the samples has been tested as a matrix for oral dosage forms. The release pro"les of a model drug from the tablets prepared with this new hydrogel evidenced a sustained release. The hydrogel was also prepared as a "lm that was tested as a membrane capable of regulating the di!usion of active substances. We report here further studies on such promising crosslinked hydrogel concerning its characterization, in terms of water uptake and permeation experiments. A theoretical analysis of permeation experiments allows to calculate the di!usion coe$cient of theophylline, used as a model drug. The swelling equilibrium data of hydrogels, collected at two di!erent ionic strengths, are analyzed applying a strategy, based on the Flory}Rehner theory, to estimate the crosslink density of the polymer. The swelling kinetics curves are studied applying a recently proposed theoretical approach from which it is also possible to estimate the di!usion coe$cient of the solvent molecule inside the polymeric systems. An estimation of the mesh size of the hydrogel at the highest degree of crosslinking, in terms of molecular weight cuto!, is obtained by means of permeation experiments
0142-9612/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 9 6 1 2 ( 0 0 ) 0 0 3 7 4 - 4
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T. Coviello et al. / Biomaterials 22 (2001) 1899}1909
carried out with polystyrene sulphonate-sodium salt at di!erent molecular weights.
2. Materials and methods 2.1. Materials Scleroglucan (Actigum CS 11) was provided by MeroRousselot-Satia (France). Theophylline (TPH) and NaCl were Carlo Erba products (Italy); the polystyrene sulphonate-sodium salt (PSS) of narrow molecular weight distribution (calibration kit, M /M "1.10) was pur chased from Polymer Laboratories (UK). Methylsulfoxide GR dried (DMSO), used as a medium for the crosslinking reaction, was purchased from Merck (Germany). All other products and reagents were of analytical grade; distilled water was always used. The sclerox sample was prepared from scleroglucan, using "rst periodate for the aldheydic derivative and then chlorite for the oxidation to carboxylic groups [13]. In order to obtain the sclerox samples in the tetrabutylammonium (TBA) form, the sclerox solutions were eluted through an H> exchange column (Dowex 50;8, Fluka, Switzerland) previously converted in the TBA form by treatment with tetrabutylammonium hydroxide (Fluka). The crosslinking reaction between sclerox-TBA and 1,6-hexanedibromide (Fluka) was carried out in DMSO, at 373C, in the dark, for 24 h, according to Scheme 1; the polymer concentration, c , was 1.6% (w/v). By changing the ratio r (r"(equivalents of reagent)/(equivalents of polymer)), products with di!erent properties were obtained. The results reported here, as far as the swelling properties are concerned, refer to the samples prepared with two r values: 0.5 and 1.0. In addition, a sample characterized
by r"2, is considered limitedly to PSS permeation experiment aimed to acquire information about the polymeric mesh size of the crosslinked polymer. Given r values represent the theoretical degree of crosslinking while the e!ective one should correspond to about onehalf of such r value (as argued from similar esteri"cation reactions carried out with unifunctional reagents, for which the content of ester groups was determined [14]). The hydrogels were puri"ed (24 h) in Soxhelet with acetone, dialyzed at 43C against 1.0 M NaCl, to exchange the TBA form into the Na form, and then against distilled water. The samples, freeze dried, were stored in a desiccator. The presence of the ester group in the crosslinked polymers was con"rmed by means of IR spectra (Fig. 1) recorded on "lms obtained by solvent evaporation of swelled samples using a Bruker interferometer IFS 113v with a beam splitter of KBr coated with Ge: spectra were recorded in the range 4000}400 cm\ (resolution of 1 cm\) under vacuum and with 200 aquisition scans. The characterization of the hydrogels was performed by means of solvent uptake and di!usion experiments. 2.2. Solvent uptake Solvent uptake was evaluated at 7 and 373C monitoring the increase of the weight of 100 mg samples in distilled water and in 0.9% (w/v) NaCl. 2.3. Permeation experiments Permeation experiments were carried out at 37.0#0.53C under magnetic stirring using a three-compartment di!usion cell (Scheme 2a). The central compartment, separated from the outer ones by cellophane membranes (Visking tubing, cut-o! 12,000), contained
Scheme 1. Reaction scheme to obtain the cross-linked polymers.
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48 h and then kept at room temperature to evaporate the solvent (about 48 h). 2.4. Data analysis 2.4.1. Modeling: swelling equilibrium The swelling equilibrium conditions of a chemically crosslinked polymeric gel can be obtained from the Gibbs free energy by imposing the condition of zero osmotic pressure [15}22]: !l "0, "! " (1) < < where is the osmotic pressure, and l are the chem ical potentials of the di!using species in the gel (g) and the liquid (l) phases, respectively, and V is the molar volume of the permeating molecule. According to the Flory}Rehner theory [16,21,22], the osmotic pressure can be written as Fig. 1. IR spectra of "lms obtained from scleroglucan (a), sclerox (b) and the cross-linked polysaccharide (c) (r"0.5).
the swelled crosslinked polymer. The di!usion of a model drug (TPH) from the donor compartment A to the receptor compartment B was spectrophotometrically analyzed at 272 nm (Perkin Elmer, lambda 3a, UV-VIS spectrometer) using quartz cells with pathlengths of 1 or 10 mm. After each measurement the sample solution was poured again in the receptor compartment. According to the speci"c experiment that was carried out, the central compartment contained the crosslinked polymer, the sclerox sample or only the solvent (reference). For an appropriate swelling of the hydrogel, acting as a barrier to di!usion, the system was equilibrated for at least 72 h with the solvent before each permeation experiment. The second type of cell, with two compartments (Scheme 2b), was used for the experiments with the highly crosslinked polymer (i.e. r"2.0). That was obtained in the shape of a "lm and directly inserted between the compartments. The di!usion of PSS (c "0.1% w/v) of di!erent molecular weights (i.e. 1.9;10 and 4.0;10) was carried out in NaCl 0.9% (w/v). PSS concentration was spectrophotometrically determined at 225 nm. The "lm was prepared from a small amount of sample (30 mg) that was previously swelled in distilled water at 373C for
" # # # , (2)
where is the mixing free energy term, is the
elastic contribution, connected with the deformation of the polymeric network, is the ionic contribution, due to the di!erence in ion concentration between the gel and the liquid phase, and is the electrostatic contribution deriving from the repulsive e!ects between equal charges present in the network. Even though more sophisticated approaches might be followed to express the mixing term [15,20,22}24], we adopted the Flory}Huggins expression in order to avoid more adjustable parameters which must be "xed a priori or determined through data "tting: R¹ "! [ln(1! )# # ], (3)
< where is the polymer volume fraction, R is the gas constant, T is the temperature, and is the Flory interaction parameter, related to the di!erence between the free energies of a polymer segment}segment and polymer}di!using molecule interactions. In the presence of highly swellable gels as those examined in this paper, the expression of the elastic term, according to the Flory}Huggins theory [17,22,25,26], is not appropriate. Indeed, it requests that the statistic distance between two consecutive crosslinks follows
Scheme 2. Schematic representation of the three compartment cell (a) and the two compartment cell (b).
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a Gaussian distribution, thus implying the possibility for the gel of a theoretically in"nite swelling capacity. For highly swellable gels, the polymeric chains closely approach their fully stretched conformation and behave as nonlinear elastic connectors so that a more complex distribution should be considered, namely the Langevin one [18,26]. The resulting expression of the elastic term is, then R¹ "! ( ) (
)\ I, 3
(4)
where is the crosslink density (mol/cm), is the polymer volume fraction in the reference state,
is the minimum polymer volume fraction attainable by the swollen gel (all the polymeric chains are completely stretched) and I is de"ned by
sinh() I"#
#\!coth()
, sinh()!
(5)
where is de"ned by
(6)
being L\ the inverse of the Langevin function that in its approximate form according to Warner [27], gives "L\
+ . (6)
1!
The ionic contribution to the osmotic pressure is derived from the Donnan equilibrium theory [16,22,28}30]. In the presence of a solution, the concentration of mobile ions within the gel phase is larger than in the external phase because of the charges located on the polymer chains. This di!erence gives rise to the following ionic contribution: 3
"R¹ j n ! (cH!c ) , (7) < where n is the number of ionizable groups present on the monomer, j is the ionization degree (fraction of monomers carrying the ionizable groups), < is the monomer molar volume, cH and c are the salt concentrations in the external solution and in the gel phase, respectively, and (" # ) is the sum of the positive and negative > \ valences of the dissociating salt. In the case of univalent ions present both in the solution and on the polymeric chains, "2 and Eq. (7) becomes
"!R¹ 2cH!
nj #4(cH) . <
(8)
Finally, the electrostatic term derived from the repulsive e!ects between equal charges present in the polymeric network could be calculated from the Ilavsky approach [18], but its contribution is usually negligible in comparison with the ionic term [22] thus it will not be taken into consideration. In conclusion, starting from the above assumptions, the equilibrium conditions of a polyelectrolyte gel/solution system can be derived from ln(1! )# # ! " R¹ < 1 # ( ) (
)\ I 3
nj #4(cH) "0. (9) < Accordingly, the swelled state of the system (characterized by the polymer volume fraction ) is ruled by the intrinsic features of the polymeric network, namely the crosslinks density and the intermolecular interactions between polymer segments and di!using molecules, here expressed by the Flory-Huggins interaction parameter . In the case of no salt present in the swelling medium (cH"0), Eq. (9) becomes ln(1! )# # 1 # ( ) " ! < 3 R¹ nj
;(
)\ I! "0. (10) < A pro"table strategy [31] that can be applied to calculate and is to collect the swelling equilibrium data in the presence of ( ) and in the absence of ( ) of an external salt (same temperature), and then solving, with respect to and , Eqs. (9) and (10): E(A#C) !F!D B A#C# , (11) " , "! E B
! B # 2cH!
where 1 A"ln(1! )# , B" < (
) ( ) , 3
nj
#4cH , (11) < 1 D"ln(1! )# , E" < (
) ( ) , 3 C"<
2cH!
nj
. F"!< <
(11)
T. Coviello et al. / Biomaterials 22 (2001) 1899}1909
2.4.2. Modeling: swelling kinetics Although the modeling of the swelling kinetics of a crosslinked polymeric gel has been widely matched in the past [32}34], in this work we adopt a recently developed model [35] which is able to describe the swelling kinetics of an ensemble of polydisperse spherical particles. This condition, indeed, resembles that of our gel in the dry state. Brie#y, the model supposes that the particle size distribution, in the dry state (thus corresponding to the initial powder condition), can be conveniently described by the Weibull equation, even if, in principle, whatever distribution equation could be used: < "1!e <
,
R !R
! 2
(12)
where R and R are the generic particle radius and the
minimum particle radius, respectively, and are two parameters regulating the Weibull size distribution, while V and V are the total volume occupied by the ensemble of polymeric particles and the volume occupied by those particles having a radius lower than or equal to R , respectively. Once the particle distribution is divided into N classes, each one characterized by a proper average radius R , the amount of absorbed permeating species is H achieved by numerically [38] solving the following diffusing molecule mass balances: C 1 H" [RJ ], j"1,2,2, N , H H t R R H H
(13)
where t is the time, C (R ) is the permeating species H H concentration inside the generic particle of the jth class, R is the radial variable ranging from 0 to R while H H J represents the di!using molecule #ux and it is de"ned, H according to Camera}Roda and Sarti [38], as J "J #J , j"1,2,2, N , H H H
(14)
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system. According to Camera-Roda and Sarti [39], we write D "D eE !H \! !D , (17) " eD ! \!H , (18) where C is the permeating species concentration in the completely swollen polymeric network (thermodynamic equilibrium), and D are the relaxation time and the di!using molecule di!usion coe$cient in the equilibrium conditions, respectively, while f and g are two model parameters related to the concentration dependence of the relaxation and di!usion properties. In order to ensure accuracy, the model solution has been performed adopting dt"6 s, N "8 and < "8, where < is the number of spherical shells in which the generic particle has to be subdivided in order to achieve the numerical solution.
3. Results and discussion 3.1. Swelling In Fig. 2 the relative increase of weight [(=!= )/= ] as a function of time is reported at two di!erent temperatures (7 and 373C) and at two r values (0.5 and 1.0). It is possible to observe that for both crosslinked polymers the increase of weight in water was not appreciably in#uenced by temperature variations while, as expected, it was noticeably a!ected by the degree of crosslinking. The e!ect of environmental ionic strength on solvent uptake is reported in Fig. 3. As it is possible to observe, in the case of r"0.5, the increase of weight was remarkably reduced by the presence of NaCl, while a similar e!ect was not detected for r"1.0. It is interesting to point out that the e!ect of ionic strength on water uptake behavior
where J represents the "ckian contribution to the H permeating species #ux, while the second term J acH counts for the relaxation properties of the swelling gel and it is associated with the viscoelastic nature of the polymeric network. In a spherical coordinate system, the two contributions are given by C H , j"1,2,2, N , J "!D H R H
(15)
C J H ! H , j"1,2,2, N , J "!D H R t H
(16)
where D is the permeating molecule di!usion coe$cient in the dry polymeric network, D is the di!usion coe$c ient associated with the non"ckian #ux contribution and is the relaxation time of the polymer}di!using species
Fig. 2. Distilled water uptake for r"0.5 and 1.0 in distilled water at two di!erent temperatures (7 and 373C): (䢇) r"0.5, T"73C; (*) r"0.5, T"373C; (䉬) r"1.0, T"73C; (䉫) r"1.0, T"373C.
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Fig. 3. Distilled water uptake for r"0.5 and r"1.0 in distilled water and NaCl 0.9% (w/v) at 73C. (䢇) r"0.5, water; (*) r"0.5, NaCl; (䉬) r"1.0, water; (䉫) r"1.0, NaCl.
Table 1 Equilibrium characteristics of all the tests considered
r T (3C) cH (mol/dm) (Test a) cH (mol/dm) (Test b) V (cm/mol) n j V (cm/mol)
;10
;10
;10 ;10
Test 1a}b
Test 2a}b
Test 3a}b
Test 4a}b
1.0 37 0.0
0.5 37 0.0
1.0 7 0.0
0.5 7 0.0
0.154
0.154
0.154
0.154
18.12 2 1 288.8 1.10$0.35 2.86$0.39 0.895 2.10$0.20
18.12 2 1 288.8 0.27$0.01 0.99$0.01 0.255 0.90$0.02
18.00 2 1 288.8 1.60$0.26 1.95$0.03 1.57 2.30$0.70
18.00 2 1 288.8 0.42$0.02 1.07$0.03 0.425 1.10$0.04
for the sample r"0.5 is reversible; when the hydrogel, previously equilibrated in the NaCl solution, was immersed in distilled water a further remarkable `swellinga was obtained with a corresponding release of salt. Finally, when the completely swelled polymer was again equilibrated in the NaCl solution a noticeable shrinking of the hydrogel was observed [12]. Given results indicate that the crosslinked polymer behaves as matrix stimulated, in its swelling/shrinking mechanism, by the presence of the electrolyte in solution that a!ects water activity. In order to simplify the discussion of the swelling data, examined here, the di!erent experimental conditions, speci"ed in Table 1, will be referred as tests 1a}b, 2a}b, 3a}b and 4a}b. 3.2. Swelling equilibrium The calculation of and , resorting to the simulta neous solution of equations (9) and (10), provided that
Fig. 4.
dependence of the and parameters in the case of tests 1a and b conditions.
the experimental and values are known, requires the estimation of the
value. Although its experi mental determination is not an easy task, we shall demonstrate that an exact knowledge of its value may not strictly be necessary and only an approximate evaluation is needed. For this purpose, let us focus our attention on the swelling equilibrium characterizing tests 1a and b. The solution of the system, constituted by Eqs. (9) and (10), is performed considering di!erent
values and assuming V "18.12 cm/mol, n"2 and j"1 (each monomer carries two univalent ions), calculating the monomer molar volume (V "288.8 cm/mol) by means of the solubility parameters [40] and knowing that
"(1.1$0.35) 10\ and "(2.86$0.4) 10\ (see also Table 1). As Fig. 4 clearly reveals, the unknowns and simultaneously assume a physically consistent value only when 0.82;10\(
(0.97;10\. Moreover, while strongly depends on
, is vir tually independent and could be evaluated, for instance, by choosing the mean
value characterizing the above-mentioned interval. Accordingly, on condition to renounce to get the value, can be calculated choosing
"0.895;10\. The solution of the system of equa tions (9) and (10) repeated for the other experimental conditions, leads to similar conclusions, namely the virtual independence of on
in the interval where both and assume physically consistent values. Con sequently, the mean
values can be selected (see Table 1); it is worthwhile to notice that these
values accomplish a reasonable topological condition requiring that higher r values correspond to higher
values at both temperatures (37 and 73C) (see Table 1). Moreover, given an r value, higher is the temperature, lower is
. On this basis, the calculation is performed for each experimental condition examined and the results are reported in Table 1. Notably, at each temperature, the calculated value coming from the test characterized by a higher r value is, approximately, two times the value coming from the test characterized by a lower r value.
T. Coviello et al. / Biomaterials 22 (2001) 1899}1909
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Moreover, tests 1a}b and 3a}b give similar values as it happens for tests 2a}b and 4a}b. 3.3. Swelling kinetics A pro"table tool suitable for the swelling kinetics description is the recently proposed model brie#y described in the modeling section [35]. The numerical nature of its solution and the lack of knowledge of some model parameters (such as the particle size distribution of the dry system) make very di$cult a reliable estimation of the standard error of the "tting parameters. Thus, our attention is mainly focused on the global experimental data interpretation by means of the model rather than a detailed determination of the "tting parameters. In this light, the data "tting result is a set of experimentally compatible values of the "tting parameters. As an inspection of Figs. 2 and 3 reveals, when the crosslinking ratio r is equal to one (tests 1a}b and 3a}b), the swelling equilibrium is rapidly attained and the swelling kinetics is too fast to be recorded by the techniques used in this paper. On the contrary, when r "0.5 (tests 2a}b and 4a}b) the swelling kinetics develops in a wider time period and the gel attains the equilibrium condition in approximately 25 h. Knowing that the dry polymeric mass considered is 100 mg (corresponding to a volume of approximately 0.066 cm) the model is "tted [41] on tests 2a}b and 4a}b experimental data. Fig. 5 shows, as an example, the reasonably good agreement between the model best "tting (solid line) and the experimental data (open circles) for test 2a conditions. In this case, for a better matching of the model variables, the swelling kinetics is expressed in terms of volume of solvent absorbed instead of relative weight increase (=!= )/ = . A similar concordance can be revealed also for all the other experimental conditions (tests 2b and 4a}b), this indicating that the most important phenomena ruling the solvent uptake are properly taken into account by the model. The "tting results are shown in Table 2 where, for a better matching with the model parameters, the swelling equilibrium is reported in terms of permeating species concentration C instead of the relative weight increase. It is of paramount importance to underline the fact that, according to what previously pointed out about the aim of the kinetics data "tting, Table 2 results need to be interpreted on an order of magnitude basis. Accordingly, we can say that all the examined experimental tests request the same particle size distribution (according to what was discussed before, this distribution has only a purely indicative meaning) in accordance with the fact that the starting dry system is the same in each test. Moreover, regardless of temperature, the relaxation properties of the samples appear to be equal (same value of the relaxation time ) and the swollen gels show a liquid-like mechanical behavior (low ) [42]. Obvi
Fig. 5. Comparison between the model best "tting (solid line) and the experimental data (open circles) referring to test 2a conditions (r"0.5; T"373C; water as swelling agent).
Table 2 Kinetic properties of the considered tests
r T (3C) Permeating species (s) g (cm/g) f (cm/g) D (cm/s) D (cm/s) C (g/cm) V (cm) R (cm)
R (cm)
(cm)
(cm)
Test 2a
Test 4a
Test 2b
Test 4b
0.5 37 Water
0.5 7 Water
0.2 8 10 1.0;10\ 1;10\ 0.9906 0.066 0.075 0.001 0.065 2
0.2 8 10 4.0;10\ 1;10\ 0.9953 0.066 0.075 0.001 0.065 2
0.5 7 NaCl solution 0.2 8 10 8;10\ 1;10\ 0.9890 0.066 0.075 0.001 0.065 2
0.5 37 NaCl solution 0.2 8 10 8;10\ 1;10\ 0.9834 0.066 0.075 0.001 0.065 2
ously, although the temperature independence is not reasonable, the "tting tells us that in the studied temperature range the order of magnitude is the same. Analogously, the values of the di!usion coe$cient in the swollen gel (D ), being of the same order of magnitude for all the studied cases, are almost equal. Similarly, D , representing the di!usion coe$cient in the dry matrix, does not depend on the particular experimental conditions examined and it is surely lower than D . Thus, the main result of this "tting is that the studied kinetics is mainly ruled by the molecule di!usive properties wherever, the viscoelastic gel properties are less important as the polymeric chains relaxation is faster with respect to molecule di!usion (low values). As a consequence, we are in the presence of "ckian swelling kinetics performed by a powdered system. 3.4. Diwusion experiments The di!usion of TPH through sclerox (r"0) and the r"0.5 crosslinked polymer was studied by means of the
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Fig. 6. Release pro"les (M /M );100 of theophylline (10\ M) in distilled water for the cross-linked polymer ((䢇); r"0.5), for the sclerox (*) and the reference at 373C (䊐) (c "1.6% w/v).
three compartment di!usion cell. As it can be observed from Fig. 6, in water the di!usion through the hydrogel and the sclerox was remarkably lower than that obtained when only the solvent was present in the central compartment. The e!ect, after one day, is more evident in the case of r"0.5; thus it can be asserted that the presence of the three-dimensional network, is capable of a!ecting the permeation rate through the polymeric barrier, in spite of the quite small dimensions of the di!using molecule with respect to the mesh size of the network, as it will be discussed later. As shown before [12] the di!usion of TPH is also a!ected by the ionic strength of the medium as the polymeric matrix bears charged groups and a double e!ect for this kind of hydrogels can be detected. By adding the salt, the screening e!ect of the COO\ groups of the sclerox is promoted thus reducing the interaction between the charged chains and the drug but, at the same time, also the mesh size of the polymeric network is contracted; the permeation of a drug can be considered to be a!ected by two factors acting in opposite directions and the overall e!ect is the result of which one of those contribution is more important, (i.e. the steric hindrance of the drug or its possible interactions with the matrix). Experiments performed with the two compartment system cell using the high crosslinked polymer (r"2.0) and the visking tubing showed a lower di!usion rate of TPH through the cellophane membrane suggesting that the mesh size of the crosslinked polymer is wider than that of the visking tubing (cut-o!"12,000). Such statement can be supported by "lm permeation experiments carried out using PSS of di!erent molecular weights as di!using species. As reported in Fig. 7, PSS of M 1.9;10, i.e. above the cut-o! of the visking tubing, was still capable, though at low extent, to di!use through the crosslinked "lm, while the 4.0;10 M PSS could not at all permeate the "lm.
Fig. 7. Di!usion pro"les, at 373C, obtained for PSS of two molecular weights ((䢇) M "2.0;10; (*) M "4.0;10), in NaCl 0.9% (w/v), through the "lm of the crosslinked polymer r"2 (c "0.1% w/v).
3.5. Numerical analysis of diwusion experiments at r"0 and 0.5 A detailed analysis of the TPH permeation through the sclerox and the crosslinked sclerox gels characterized by r "0.5 and 0 would in principle require to consider the e!ect of the drug-polymer interaction as Singh pointed out [36]. In this case the drug di!usion does not follow Fick's law. Nevertheless, due to the small membrane volume (1 cm) with respect to the sum of the receiver and donor volumes (29 cm), the e!ect of the polymer drug interaction is small in comparison with that of the network mesh size ruled by the r ratio [37]. Indeed, as the e!ect of the drug}polymer interaction in the membrane volume is to decrease the drug net #ux feeding the receiver compartment, the smaller the membrane volume, the lower the drug}polymer interaction e!ect on the permeation curve. Accordingly, with the aim of estimating the e!ect of the crosslink ratio r and on condition to renounce to an exact determination of the THP di!usion coe$cient, a traditional "ckian-based model can be adopted. For this purpose we refer to a previously described model [12] based on the numerical solution [37] of Fick's second law under the proper boundary and initial conditions. The model is particularly fruitful as it accounts for the nonlinear drug pro"le concentration inside the gel during the permeation experiment, this being typical for thick membranes [43]. Furthermore, as it neither requires the sink condition in the receiver compartment nor the constant drug concentration in the donor compartment, it assumes a wide generality and it becomes a reliable tool to determine membranes permeability. Thus, the model is "tted on the experimental permeation data (r"0.5 and 0) in order to calculate the TPH
T. Coviello et al. / Biomaterials 22 (2001) 1899}1909
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permeability P, de"ned as D K P" , h
(19)
where h is the gel thickness, D and k are the TPH di!usion and partition coe$cient, respectively. Brie#y, the model implies the numerical solution [37] of the one-dimensional Fick's second law on the gel and on the two cellophane layers sandwiching the gel:
C C , " D X X t
(20)
C C , " D t X X
(21)
C C " , D t X X
(22)
where t is the time, X is the abscissa, D , D , D and C , C , C are, respectively, the drug di!usion coe$c ient and concentration in the "rst cellophane layer, in the gel and in the second cellophane layer. Eqs (20)}(22) must be solved with the following boundary conditions: dC C "D S < dt A X C D X C D X
"D 6F
,
(23)
6
C X
,
(24)
6F
C "D , X 6F >F 6F >F
dC C "!D S < dt X
,
(25)
(26)
6F >F
C C C "K , "K , "K C C C
(27)
and the following initial conditions: C "C ,
C "C "C "C "0,
(28)
where < (14.5 cm) and < (14.5 cm) represent the do nor and receiver volume, respectively, C and C are, respectively, the donor and receiver drug concentration at time t, S (1.77 cm) is the permeation surface, h (0.005 cm) and h (0.565 cm) are, respectively, the thick ness of the cellophane membranes and the thickness of the gel, while K and K are, respectively, the drug partition coe$cient of the cellophane layers and of the gel with respect to the solution of the donor and the receiver compartment. Eq. (23) imposes that the drug amount leaving the donor compartment is equal to the
Fig. 8. Model "tting (solid lines) on the theophylline permeation data (open circles) through r"0.5 sandwiched by two cellophane layers (three compartments case; water).
Table 3 Determined D and P values
Reference r"0 r"0.5
D;10 (cm/s)
P;10 (cm/s)
69 7.0 4.75
39 12.4 8.40
TPH di!usion coe$cient, D, and membrane permeability, P, in water, assuming the partition coe$cient K is equal to one and knowing that the thickness of the sample h is 0.565 cm.
drug #ux entering the "rst cellophane layer. Eq. (24) imposes that the drug #ux leaving the "rst cellophane layer is equal to that entering the gel (X"h ), while Eq. (25) sets the equality of the drug #ux leaving the gel and entering the second cellophane layer (X"h #h ). Eq. (26) ensures that the drug entering the receiver compartment is equal to the drug #ux leaving the second cellophane layer. Eq. (27) sets to zero the drug concentration in the receiver, in the gel, in the "rst and second cellophane layers while it sets to C (198.17 g/cm) the drug concentration in the donor compartment at the beginning of the permeation. As an example, Fig. 8 shows rather a good agreement between the model best "tting (solid line) and the experimental data (open circles) relative to r"0.5. Thus, we are con"dent of the reliability of the determined P values (see Table 3). It is clear that the presence of the crosslinks led to a decrease of TPH di!usion coe$cient as it determines a lower mesh size of the polymeric network that enhances the hindering e!ect of the polymer chains on the di!using TPH molecules.
4. Conclusion Reported results on the behavior of the crosslinked sclerox indicate that these new derivatives show a very high degree of swelling in water that, in the case of r"0.5, can be reduced if salt is added to the surrounding
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medium. The study of the swelling equilibrium in di!erent ionic strength gives an estimation for the crosslinking density at di!erent r values. An uncommon strategy approach to analyze the swelling kinetics has been applied obtaining a very good agreement with the experimental data. In particular, the di!usion coe$cient of the solvent as permeating molecule in the swollen gel (D ) and in the dry matrix (D ) have been evaluated. It came out that the value of D is not a!ected by the presence of NaCl while D depends on the presence of the salt. From the permeation of PSS at di!erent molecular weight through the polymer at the highest degree of crosslinking (r"2) it is possible to have a rough estimation of the mesh size, in terms of molecular weight cut-o!, of the polysaccharidic "lm. The characterization of these new systems is very important as they can be proposed as swellable matrices for sustained release of biologically active compounds and the possibility to shed light upon their structure can help to improve the performances of the hydrogels.
Acknowledgements This work was carried out with the "nancial support of C.N.R. and MURST.
References [1] Norisuye T, Yanaki T, Fujita H. Triple helix of a Schizophyllum commune polysaccahride in aqueous solution. J Polym Sci Polym Phys Ed 1980;18:547}58. [2] Yanaki T, Norisuye T, Fujita H. Triple helix of Schizophyllum commune polysaccahride in dilute solution. 3. Hydrodynamic properties in water. Macromolecules 1980;13:1462}6. [3] Sato T, Norisuye T, Fujita H. Triple helix of Schizophyllum commune polysaccahride in dilute solution. 5. Light scattering and refractometry in mixtures of water and dimethyl sulfoxide. Macromolecules 1983;16:185}9. [4] Touitou E, Alhaique F, Riccieri FM, Riccioni G, Santucci E. Scleroglucan sustained release oral preparations. Part I. In vitro experiments. Drug Des Delivery 1989;5:141}8. [5] Alhaique F, Carafa M, Riccieri FM, Santucci E, Touitou E. Studies on the release behaviour of a polysaccharide matrix. Pharmazie 1993;48:432}5. [6] Rizk S, Duru C, Gaudy D, Jacob M, Ferrari F, Bertoni M, Caramella C. Physicochemical characterization and tableting properties of Scleroglucan. Int J Pharm 1994;112:125}31. [7] Alhaique F, Beltrami E, Riccieri FM, Santucci E, Touitou E. Scleroglucan sustained release oral preparations. Part II. E!ects of additives. Drug Des Delivery 1990;5:249}57. [8] Alhaique F, Carafa M, Coviello T, Murtas E, Riccieri FM, Santucci E. Release from a polysaccharide matrix: e!ect of the molecular weight of the drug. Acta Technol Legis Med 1993; 4:21}30. [9] Romanelli L, Alhaique F, Riccieri FM, Santucci E, Valeri P. Investigation of the features of Scleroglucan, a polysaccharide of fungin origin, as a vehicle for ocular topical administration. Pharmacol Res 1993;27(Suppl 1):127}8.
[10] Alhaique F, Riccieri FM, Santucci E, Crescenzi V, Gamini A. A possible pH-controlled drug delivery system based on a derivative of the polysaccharide Scleroglucan. J Pharm Pharmacol 1985;37:310}3. [11] Alhaique F, Riccieri FM, Santucci E, Carafa M. Environmental e!ects on the delivery of drugs from a pH-sensitive matrix. Acta Technol Legis Med 1990;1:1}9. [12] Coviello T, Grassi M, Rambone G, Santucci E, Carafa M, Murtas E, Riccieri FM, Alhaique F. Novel hydrogel system from a scleroglucan: synthesis and characterization. J Control Rel 1999; 60:367}78. [13] Crescenzi V, Gamini A, Paradossi G. Solution properties of a new polyelectrolyte derived from the polysaccharide Scleroglucan. Carbohydr Polym 1983;3:273}86. [14] Crescenzi V, Dentini M, Segatori M, Tiblandi C, Callegaro L, Benedetti L. Synthesis and preliminary characterization of new esters of the bacterial polysaccharide gellan. Carbohydr Res 1992;231:73}81. [15] Sassi AP, Blanch HW, Prausnitz JM. Macromolecular separation and identi"cation. In: Soane DS, editor. Polymer applications for biotechnology. Engewood Cli!s, NJ: Prentice-Hall, 1991 (Chapter 8). [16] Flory PJ. Principles of polymer chemistry. Ithaca, NY: Cornell University Press, 1953. [17] Erman B, Flory PJ. Critical phenomena and transitions in swollen polymers networks, in linear macromolecules. Macromolecules 1986;19:2342}53. [18] Hasa M, Ilavsky M, Dusek K. Deformational, swelling, and potentiometric behaviour of ionized poly(methacrilic acid). J Polym Sci 1975;13:253}62. [19] Kachalsky A, Lifson S. The electrostatic free energy of polyelectrolyte solutions. I. Randomly kinked macromolecules. J Polym Sci 1953;11(5):409}23. [20] Hooper HH, Blank HW, Prausnitz JM. Absorbent polymer technology. Amsterdam: Elsevier Science Publishers B.V., 1990. [21] Prange MM, Hooper HH, Prausnitz JM. Thermodynamics of aqueous systems containing hydrophilic polymers or gel. AIChE J 1989;35(5):803}13. [22] Hooper HH, Baker JP, Blanch HW, Prausnitz JM. Swelling equilibria for positively ionized polyacrylamide. Macromolecules 1990;23:1096}104. [23] Lele AK, Badiger MV, Hirve MM, Mashelkar RA. Thermodynamics of hydrogen-bonded polymer gel}solvent systems. Chem Eng Sci 1995;50(22):3535}45. [24] Colombo I, Grassi M, Fermeglia M, Lapasin R, Pricl S. Modeling phase transitions and sorption-desorption kinetics in thermosensitive gels for controlled drug delivery systems. Fluid Phase Equilib 1996;116:148}61. [25] Aven MR, Coen C. Properties of poly(dimethylsoxane) chains and gels in toluene and in toluene/methanol mixtures. Makromol Chem 1988;189:881}98. [26] Oppermann W. Swelling behavior and elastic properties of ionic hydrogels. In: Harland RS, K. Prud'homme RK, editors. Polyelectrolyte gels, properties, preparation, and applications. Washington: American Chemical Society, 1992. p. 160}70. [27] Bird RB, Armstrong RC, Hassager O. Dynamics of polymeric liquids, Fluid mechanics, vol. 1. New York, Santa Barbara, London, Sydney, Toronto: Wiley, 1990. p. 72}5. [28] Ricka J, Tanaka T. Swelling of ionic gels: quantitative performance of the Donnan theory. Macromolecules 1984;17: 2916}21. [29] Brannon-Peppas L, Peppas NA. Equilibrium swelling behavior of pH-sensitive hydrogels. Chem Engng Sci 1991;46(3):715}22. [30] Baker JP, Hong LH, Blanc HW, Prausnitz JM. E!ect of initial total monomer concentration on the swelling behavior of cationic acrylamide-based hydrogels. Macromolecules 1994; 27:1446}54.
T. Coviello et al. / Biomaterials 22 (2001) 1899}1909 [31] Mantovani F, Grassi M, Colombo I, Lapasin R. A combination of vapor sorption and laser light scattering methods for the determination of the Flory parameter and the crosslink density of a polymeric microgel. Fluid Phase Equilib 2000;167(1):63}81. [32] Lustig SR, Caruthers JM, Peppas NA. Continuum thermodynamics and transport theory for polymer}#uid mixtures. Chem Eng Sci 1992;47(2):3037}57. [33] Cohen DS. Theoretical models for di!usion in glassy polymers. J Polym Sci, Part B: Polym Phys 1984;22:1001}9. [34] Adib F, Neogi P. Sorption with oscillations in solid polymers. AIChE J 1987;33(1):164}6. [35] Grassi M, Colombo I, Lapasin R. Drug release from an ensemble of swellable crosslinked polymer particles. J Control Rel 2000; 68(1):97}113. [36] Singh M, Lumpkin J A, Rosenblatt J. Mathematical modeling of drug release from hydrogel matrices via a di!usion coupled with desorption mechanism. J Control Rel 1994;32:17}25. [37] Grassi M, Lapasin R, Carli F. Modeling of drug permeation through a drug interacting swollen membrane. Proceedings of the
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International Symposium Control Release of Bioactive Materials (Paris, 7}13 July). Deer"eld, IL, USA: The Controlled Release Society 2000;27:748}9. Patankar SV. Numerical heat transfer and #uid #ow. New York: Hemisphere Publishing, 1990. Camera-Roda G, Sarti GC. Mass transport with relaxation in polymers. AIChE J 1990;36(6):851}60. Breitkreutz J. Prediction of intestinal drug absorption properties by three-dimensional solubility parameters. Pharmaceut Res 1998;15(9):1370}5. Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical recipes in FORTRAN, the art of scienti"c computing, 2nd ed. Cambridge: Cambridge University Press, 1992. Lapasin R, Pricl S. Reology of industrial polysaccharides: theory and application. London: Chapman & Hall, 1995. Grassi M, Colombo I. Mathematical modelling of drug permeation through a swollen membrane. J Control Rel 1999;59: 343}59.
A crosslinked system from Scleroglucan derivative: preparation and characterization T. Coviello , M. Grassi, G. Rambone , F. Alhaique * Dipartimento di Studi di Chimica e Tecnologia delle Sostanze Biologicamente Attive, University of Rome **La Sapienza++, Piazzale Aldo Moro 5, 00185 Roma, Italy Dipartimento di Ingegneria Chimica, dell+Ambiente e delle Materie Prime - Universita% di Trieste, Italy Received 15 June 2000; accepted 3 November 2000
Abstract Matrices obtained by a crosslinking reaction between the polycarboxylated derivative of scleroglucan (sclerox) and 1,6-hexanedibromide have been prepared and characterized. Di!erent ratios between the alkane dihalide and sclerox yielded products with di!erent properties. Water uptake by the hydrogel with a low degree of crosslinking was remarkably a!ected by ionic strength. The determination of the crosslink density is led by simultaneously solving two Flory equilibrium equations referring to two di!erent conditions characterized by the presence or the absence of a salt in the swelling agent. Moreover, the swelling kinetics was studied by means of a recently proposed model. Finally, the permeation of two model molecules (theophylline and polystyrene sulphonatesodium salt) through the hydrogels was evaluated. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Scleroglucan; Polysaccharides; Crosslinking; Hydrogel; Sustained release
1. Introduction Scleroglucan is a general term used to designate a class of glucans produced by fungi, especially those of the genus Sclerotium. The commercial product, termed scleroglucan, is water soluble and consists of linearly linked (1P3) D-glucose residues with (1P6) D-glucose residues as side chains, one for every three consecutive glucose units. This polysaccharide is dispersed as a triple helix in water, whereas it is dissolved as a single coil in methylsulfoxide [1}3]. Because of its interesting rheological properties and its resistance to hydrolysis, scleroglucan has general industrial applications. As far as the pharmaceutical "eld is concerned, experiments performed in vitro indicate that scleroglucan is a polysaccharide suitable for sustained release formulations. In fact, it has been proposed for the formulation of monolithic swellable matrices [4}8] as well as for ophtalmic preparations [9]; furthermore, oxidized scleroglucan (sclerox) was proposed for a pH-controlled delivery from oral dosage forms [10,11]. * Corresponding author. Tel.: #39-6-49913557; fax: #39-649913888. E-mail address: [email protected] (F. Alhaique).
In a previous paper [12] we have shown a part of our studies on a new type of hydrogel obtained by a crosslinking reaction between sclerox and an alkane dihalide. One of the samples has been tested as a matrix for oral dosage forms. The release pro"les of a model drug from the tablets prepared with this new hydrogel evidenced a sustained release. The hydrogel was also prepared as a "lm that was tested as a membrane capable of regulating the di!usion of active substances. We report here further studies on such promising crosslinked hydrogel concerning its characterization, in terms of water uptake and permeation experiments. A theoretical analysis of permeation experiments allows to calculate the di!usion coe$cient of theophylline, used as a model drug. The swelling equilibrium data of hydrogels, collected at two di!erent ionic strengths, are analyzed applying a strategy, based on the Flory}Rehner theory, to estimate the crosslink density of the polymer. The swelling kinetics curves are studied applying a recently proposed theoretical approach from which it is also possible to estimate the di!usion coe$cient of the solvent molecule inside the polymeric systems. An estimation of the mesh size of the hydrogel at the highest degree of crosslinking, in terms of molecular weight cuto!, is obtained by means of permeation experiments
0142-9612/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 9 6 1 2 ( 0 0 ) 0 0 3 7 4 - 4
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T. Coviello et al. / Biomaterials 22 (2001) 1899}1909
carried out with polystyrene sulphonate-sodium salt at di!erent molecular weights.
2. Materials and methods 2.1. Materials Scleroglucan (Actigum CS 11) was provided by MeroRousselot-Satia (France). Theophylline (TPH) and NaCl were Carlo Erba products (Italy); the polystyrene sulphonate-sodium salt (PSS) of narrow molecular weight distribution (calibration kit, M /M "1.10) was pur chased from Polymer Laboratories (UK). Methylsulfoxide GR dried (DMSO), used as a medium for the crosslinking reaction, was purchased from Merck (Germany). All other products and reagents were of analytical grade; distilled water was always used. The sclerox sample was prepared from scleroglucan, using "rst periodate for the aldheydic derivative and then chlorite for the oxidation to carboxylic groups [13]. In order to obtain the sclerox samples in the tetrabutylammonium (TBA) form, the sclerox solutions were eluted through an H> exchange column (Dowex 50;8, Fluka, Switzerland) previously converted in the TBA form by treatment with tetrabutylammonium hydroxide (Fluka). The crosslinking reaction between sclerox-TBA and 1,6-hexanedibromide (Fluka) was carried out in DMSO, at 373C, in the dark, for 24 h, according to Scheme 1; the polymer concentration, c , was 1.6% (w/v). By changing the ratio r (r"(equivalents of reagent)/(equivalents of polymer)), products with di!erent properties were obtained. The results reported here, as far as the swelling properties are concerned, refer to the samples prepared with two r values: 0.5 and 1.0. In addition, a sample characterized
by r"2, is considered limitedly to PSS permeation experiment aimed to acquire information about the polymeric mesh size of the crosslinked polymer. Given r values represent the theoretical degree of crosslinking while the e!ective one should correspond to about onehalf of such r value (as argued from similar esteri"cation reactions carried out with unifunctional reagents, for which the content of ester groups was determined [14]). The hydrogels were puri"ed (24 h) in Soxhelet with acetone, dialyzed at 43C against 1.0 M NaCl, to exchange the TBA form into the Na form, and then against distilled water. The samples, freeze dried, were stored in a desiccator. The presence of the ester group in the crosslinked polymers was con"rmed by means of IR spectra (Fig. 1) recorded on "lms obtained by solvent evaporation of swelled samples using a Bruker interferometer IFS 113v with a beam splitter of KBr coated with Ge: spectra were recorded in the range 4000}400 cm\ (resolution of 1 cm\) under vacuum and with 200 aquisition scans. The characterization of the hydrogels was performed by means of solvent uptake and di!usion experiments. 2.2. Solvent uptake Solvent uptake was evaluated at 7 and 373C monitoring the increase of the weight of 100 mg samples in distilled water and in 0.9% (w/v) NaCl. 2.3. Permeation experiments Permeation experiments were carried out at 37.0#0.53C under magnetic stirring using a three-compartment di!usion cell (Scheme 2a). The central compartment, separated from the outer ones by cellophane membranes (Visking tubing, cut-o! 12,000), contained
Scheme 1. Reaction scheme to obtain the cross-linked polymers.
T. Coviello et al. / Biomaterials 22 (2001) 1899}1909
1901
48 h and then kept at room temperature to evaporate the solvent (about 48 h). 2.4. Data analysis 2.4.1. Modeling: swelling equilibrium The swelling equilibrium conditions of a chemically crosslinked polymeric gel can be obtained from the Gibbs free energy by imposing the condition of zero osmotic pressure [15}22]: !l "0, "! " (1) < < where is the osmotic pressure, and l are the chem ical potentials of the di!using species in the gel (g) and the liquid (l) phases, respectively, and V is the molar volume of the permeating molecule. According to the Flory}Rehner theory [16,21,22], the osmotic pressure can be written as Fig. 1. IR spectra of "lms obtained from scleroglucan (a), sclerox (b) and the cross-linked polysaccharide (c) (r"0.5).
the swelled crosslinked polymer. The di!usion of a model drug (TPH) from the donor compartment A to the receptor compartment B was spectrophotometrically analyzed at 272 nm (Perkin Elmer, lambda 3a, UV-VIS spectrometer) using quartz cells with pathlengths of 1 or 10 mm. After each measurement the sample solution was poured again in the receptor compartment. According to the speci"c experiment that was carried out, the central compartment contained the crosslinked polymer, the sclerox sample or only the solvent (reference). For an appropriate swelling of the hydrogel, acting as a barrier to di!usion, the system was equilibrated for at least 72 h with the solvent before each permeation experiment. The second type of cell, with two compartments (Scheme 2b), was used for the experiments with the highly crosslinked polymer (i.e. r"2.0). That was obtained in the shape of a "lm and directly inserted between the compartments. The di!usion of PSS (c "0.1% w/v) of di!erent molecular weights (i.e. 1.9;10 and 4.0;10) was carried out in NaCl 0.9% (w/v). PSS concentration was spectrophotometrically determined at 225 nm. The "lm was prepared from a small amount of sample (30 mg) that was previously swelled in distilled water at 373C for
" # # # , (2)
where is the mixing free energy term, is the
elastic contribution, connected with the deformation of the polymeric network, is the ionic contribution, due to the di!erence in ion concentration between the gel and the liquid phase, and is the electrostatic contribution deriving from the repulsive e!ects between equal charges present in the network. Even though more sophisticated approaches might be followed to express the mixing term [15,20,22}24], we adopted the Flory}Huggins expression in order to avoid more adjustable parameters which must be "xed a priori or determined through data "tting: R¹ "! [ln(1! )# # ], (3)
< where is the polymer volume fraction, R is the gas constant, T is the temperature, and is the Flory interaction parameter, related to the di!erence between the free energies of a polymer segment}segment and polymer}di!using molecule interactions. In the presence of highly swellable gels as those examined in this paper, the expression of the elastic term, according to the Flory}Huggins theory [17,22,25,26], is not appropriate. Indeed, it requests that the statistic distance between two consecutive crosslinks follows
Scheme 2. Schematic representation of the three compartment cell (a) and the two compartment cell (b).
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a Gaussian distribution, thus implying the possibility for the gel of a theoretically in"nite swelling capacity. For highly swellable gels, the polymeric chains closely approach their fully stretched conformation and behave as nonlinear elastic connectors so that a more complex distribution should be considered, namely the Langevin one [18,26]. The resulting expression of the elastic term is, then R¹ "! ( ) (
)\ I, 3
(4)
where is the crosslink density (mol/cm), is the polymer volume fraction in the reference state,
is the minimum polymer volume fraction attainable by the swollen gel (all the polymeric chains are completely stretched) and I is de"ned by
sinh() I"#
#\!coth()
, sinh()!
(5)
where is de"ned by
(6)
being L\ the inverse of the Langevin function that in its approximate form according to Warner [27], gives "L\
+ . (6)
1!
The ionic contribution to the osmotic pressure is derived from the Donnan equilibrium theory [16,22,28}30]. In the presence of a solution, the concentration of mobile ions within the gel phase is larger than in the external phase because of the charges located on the polymer chains. This di!erence gives rise to the following ionic contribution: 3
"R¹ j n ! (cH!c ) , (7) < where n is the number of ionizable groups present on the monomer, j is the ionization degree (fraction of monomers carrying the ionizable groups), < is the monomer molar volume, cH and c are the salt concentrations in the external solution and in the gel phase, respectively, and (" # ) is the sum of the positive and negative > \ valences of the dissociating salt. In the case of univalent ions present both in the solution and on the polymeric chains, "2 and Eq. (7) becomes
"!R¹ 2cH!
nj #4(cH) . <
(8)
Finally, the electrostatic term derived from the repulsive e!ects between equal charges present in the polymeric network could be calculated from the Ilavsky approach [18], but its contribution is usually negligible in comparison with the ionic term [22] thus it will not be taken into consideration. In conclusion, starting from the above assumptions, the equilibrium conditions of a polyelectrolyte gel/solution system can be derived from ln(1! )# # ! " R¹ < 1 # ( ) (
)\ I 3
nj #4(cH) "0. (9) < Accordingly, the swelled state of the system (characterized by the polymer volume fraction ) is ruled by the intrinsic features of the polymeric network, namely the crosslinks density and the intermolecular interactions between polymer segments and di!using molecules, here expressed by the Flory-Huggins interaction parameter . In the case of no salt present in the swelling medium (cH"0), Eq. (9) becomes ln(1! )# # 1 # ( ) " ! < 3 R¹ nj
;(
)\ I! "0. (10) < A pro"table strategy [31] that can be applied to calculate and is to collect the swelling equilibrium data in the presence of ( ) and in the absence of ( ) of an external salt (same temperature), and then solving, with respect to and , Eqs. (9) and (10): E(A#C) !F!D B A#C# , (11) " , "! E B
! B # 2cH!
where 1 A"ln(1! )# , B" < (
) ( ) , 3
nj
#4cH , (11) < 1 D"ln(1! )# , E" < (
) ( ) , 3 C"<
2cH!
nj
. F"!< <
(11)
T. Coviello et al. / Biomaterials 22 (2001) 1899}1909
2.4.2. Modeling: swelling kinetics Although the modeling of the swelling kinetics of a crosslinked polymeric gel has been widely matched in the past [32}34], in this work we adopt a recently developed model [35] which is able to describe the swelling kinetics of an ensemble of polydisperse spherical particles. This condition, indeed, resembles that of our gel in the dry state. Brie#y, the model supposes that the particle size distribution, in the dry state (thus corresponding to the initial powder condition), can be conveniently described by the Weibull equation, even if, in principle, whatever distribution equation could be used: < "1!e <
,
R !R
! 2
(12)
where R and R are the generic particle radius and the
minimum particle radius, respectively, and are two parameters regulating the Weibull size distribution, while V and V are the total volume occupied by the ensemble of polymeric particles and the volume occupied by those particles having a radius lower than or equal to R , respectively. Once the particle distribution is divided into N classes, each one characterized by a proper average radius R , the amount of absorbed permeating species is H achieved by numerically [38] solving the following diffusing molecule mass balances: C 1 H" [RJ ], j"1,2,2, N , H H t R R H H
(13)
where t is the time, C (R ) is the permeating species H H concentration inside the generic particle of the jth class, R is the radial variable ranging from 0 to R while H H J represents the di!using molecule #ux and it is de"ned, H according to Camera}Roda and Sarti [38], as J "J #J , j"1,2,2, N , H H H
(14)
1903
system. According to Camera-Roda and Sarti [39], we write D "D eE !H \! !D , (17) " eD ! \!H , (18) where C is the permeating species concentration in the completely swollen polymeric network (thermodynamic equilibrium), and D are the relaxation time and the di!using molecule di!usion coe$cient in the equilibrium conditions, respectively, while f and g are two model parameters related to the concentration dependence of the relaxation and di!usion properties. In order to ensure accuracy, the model solution has been performed adopting dt"6 s, N "8 and < "8, where < is the number of spherical shells in which the generic particle has to be subdivided in order to achieve the numerical solution.
3. Results and discussion 3.1. Swelling In Fig. 2 the relative increase of weight [(=!= )/= ] as a function of time is reported at two di!erent temperatures (7 and 373C) and at two r values (0.5 and 1.0). It is possible to observe that for both crosslinked polymers the increase of weight in water was not appreciably in#uenced by temperature variations while, as expected, it was noticeably a!ected by the degree of crosslinking. The e!ect of environmental ionic strength on solvent uptake is reported in Fig. 3. As it is possible to observe, in the case of r"0.5, the increase of weight was remarkably reduced by the presence of NaCl, while a similar e!ect was not detected for r"1.0. It is interesting to point out that the e!ect of ionic strength on water uptake behavior
where J represents the "ckian contribution to the H permeating species #ux, while the second term J acH counts for the relaxation properties of the swelling gel and it is associated with the viscoelastic nature of the polymeric network. In a spherical coordinate system, the two contributions are given by C H , j"1,2,2, N , J "!D H R H
(15)
C J H ! H , j"1,2,2, N , J "!D H R t H
(16)
where D is the permeating molecule di!usion coe$cient in the dry polymeric network, D is the di!usion coe$c ient associated with the non"ckian #ux contribution and is the relaxation time of the polymer}di!using species
Fig. 2. Distilled water uptake for r"0.5 and 1.0 in distilled water at two di!erent temperatures (7 and 373C): (䢇) r"0.5, T"73C; (*) r"0.5, T"373C; (䉬) r"1.0, T"73C; (䉫) r"1.0, T"373C.
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T. Coviello et al. / Biomaterials 22 (2001) 1899}1909
Fig. 3. Distilled water uptake for r"0.5 and r"1.0 in distilled water and NaCl 0.9% (w/v) at 73C. (䢇) r"0.5, water; (*) r"0.5, NaCl; (䉬) r"1.0, water; (䉫) r"1.0, NaCl.
Table 1 Equilibrium characteristics of all the tests considered
r T (3C) cH (mol/dm) (Test a) cH (mol/dm) (Test b) V (cm/mol) n j V (cm/mol)
;10
;10
;10 ;10
Test 1a}b
Test 2a}b
Test 3a}b
Test 4a}b
1.0 37 0.0
0.5 37 0.0
1.0 7 0.0
0.5 7 0.0
0.154
0.154
0.154
0.154
18.12 2 1 288.8 1.10$0.35 2.86$0.39 0.895 2.10$0.20
18.12 2 1 288.8 0.27$0.01 0.99$0.01 0.255 0.90$0.02
18.00 2 1 288.8 1.60$0.26 1.95$0.03 1.57 2.30$0.70
18.00 2 1 288.8 0.42$0.02 1.07$0.03 0.425 1.10$0.04
for the sample r"0.5 is reversible; when the hydrogel, previously equilibrated in the NaCl solution, was immersed in distilled water a further remarkable `swellinga was obtained with a corresponding release of salt. Finally, when the completely swelled polymer was again equilibrated in the NaCl solution a noticeable shrinking of the hydrogel was observed [12]. Given results indicate that the crosslinked polymer behaves as matrix stimulated, in its swelling/shrinking mechanism, by the presence of the electrolyte in solution that a!ects water activity. In order to simplify the discussion of the swelling data, examined here, the di!erent experimental conditions, speci"ed in Table 1, will be referred as tests 1a}b, 2a}b, 3a}b and 4a}b. 3.2. Swelling equilibrium The calculation of and , resorting to the simulta neous solution of equations (9) and (10), provided that
Fig. 4.
dependence of the and parameters in the case of tests 1a and b conditions.
the experimental and values are known, requires the estimation of the
value. Although its experi mental determination is not an easy task, we shall demonstrate that an exact knowledge of its value may not strictly be necessary and only an approximate evaluation is needed. For this purpose, let us focus our attention on the swelling equilibrium characterizing tests 1a and b. The solution of the system, constituted by Eqs. (9) and (10), is performed considering di!erent
values and assuming V "18.12 cm/mol, n"2 and j"1 (each monomer carries two univalent ions), calculating the monomer molar volume (V "288.8 cm/mol) by means of the solubility parameters [40] and knowing that
"(1.1$0.35) 10\ and "(2.86$0.4) 10\ (see also Table 1). As Fig. 4 clearly reveals, the unknowns and simultaneously assume a physically consistent value only when 0.82;10\(
(0.97;10\. Moreover, while strongly depends on
, is vir tually independent and could be evaluated, for instance, by choosing the mean
value characterizing the above-mentioned interval. Accordingly, on condition to renounce to get the value, can be calculated choosing
"0.895;10\. The solution of the system of equa tions (9) and (10) repeated for the other experimental conditions, leads to similar conclusions, namely the virtual independence of on
in the interval where both and assume physically consistent values. Con sequently, the mean
values can be selected (see Table 1); it is worthwhile to notice that these
values accomplish a reasonable topological condition requiring that higher r values correspond to higher
values at both temperatures (37 and 73C) (see Table 1). Moreover, given an r value, higher is the temperature, lower is
. On this basis, the calculation is performed for each experimental condition examined and the results are reported in Table 1. Notably, at each temperature, the calculated value coming from the test characterized by a higher r value is, approximately, two times the value coming from the test characterized by a lower r value.
T. Coviello et al. / Biomaterials 22 (2001) 1899}1909
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Moreover, tests 1a}b and 3a}b give similar values as it happens for tests 2a}b and 4a}b. 3.3. Swelling kinetics A pro"table tool suitable for the swelling kinetics description is the recently proposed model brie#y described in the modeling section [35]. The numerical nature of its solution and the lack of knowledge of some model parameters (such as the particle size distribution of the dry system) make very di$cult a reliable estimation of the standard error of the "tting parameters. Thus, our attention is mainly focused on the global experimental data interpretation by means of the model rather than a detailed determination of the "tting parameters. In this light, the data "tting result is a set of experimentally compatible values of the "tting parameters. As an inspection of Figs. 2 and 3 reveals, when the crosslinking ratio r is equal to one (tests 1a}b and 3a}b), the swelling equilibrium is rapidly attained and the swelling kinetics is too fast to be recorded by the techniques used in this paper. On the contrary, when r "0.5 (tests 2a}b and 4a}b) the swelling kinetics develops in a wider time period and the gel attains the equilibrium condition in approximately 25 h. Knowing that the dry polymeric mass considered is 100 mg (corresponding to a volume of approximately 0.066 cm) the model is "tted [41] on tests 2a}b and 4a}b experimental data. Fig. 5 shows, as an example, the reasonably good agreement between the model best "tting (solid line) and the experimental data (open circles) for test 2a conditions. In this case, for a better matching of the model variables, the swelling kinetics is expressed in terms of volume of solvent absorbed instead of relative weight increase (=!= )/ = . A similar concordance can be revealed also for all the other experimental conditions (tests 2b and 4a}b), this indicating that the most important phenomena ruling the solvent uptake are properly taken into account by the model. The "tting results are shown in Table 2 where, for a better matching with the model parameters, the swelling equilibrium is reported in terms of permeating species concentration C instead of the relative weight increase. It is of paramount importance to underline the fact that, according to what previously pointed out about the aim of the kinetics data "tting, Table 2 results need to be interpreted on an order of magnitude basis. Accordingly, we can say that all the examined experimental tests request the same particle size distribution (according to what was discussed before, this distribution has only a purely indicative meaning) in accordance with the fact that the starting dry system is the same in each test. Moreover, regardless of temperature, the relaxation properties of the samples appear to be equal (same value of the relaxation time ) and the swollen gels show a liquid-like mechanical behavior (low ) [42]. Obvi
Fig. 5. Comparison between the model best "tting (solid line) and the experimental data (open circles) referring to test 2a conditions (r"0.5; T"373C; water as swelling agent).
Table 2 Kinetic properties of the considered tests
r T (3C) Permeating species (s) g (cm/g) f (cm/g) D (cm/s) D (cm/s) C (g/cm) V (cm) R (cm)
R (cm)
(cm)
(cm)
Test 2a
Test 4a
Test 2b
Test 4b
0.5 37 Water
0.5 7 Water
0.2 8 10 1.0;10\ 1;10\ 0.9906 0.066 0.075 0.001 0.065 2
0.2 8 10 4.0;10\ 1;10\ 0.9953 0.066 0.075 0.001 0.065 2
0.5 7 NaCl solution 0.2 8 10 8;10\ 1;10\ 0.9890 0.066 0.075 0.001 0.065 2
0.5 37 NaCl solution 0.2 8 10 8;10\ 1;10\ 0.9834 0.066 0.075 0.001 0.065 2
ously, although the temperature independence is not reasonable, the "tting tells us that in the studied temperature range the order of magnitude is the same. Analogously, the values of the di!usion coe$cient in the swollen gel (D ), being of the same order of magnitude for all the studied cases, are almost equal. Similarly, D , representing the di!usion coe$cient in the dry matrix, does not depend on the particular experimental conditions examined and it is surely lower than D . Thus, the main result of this "tting is that the studied kinetics is mainly ruled by the molecule di!usive properties wherever, the viscoelastic gel properties are less important as the polymeric chains relaxation is faster with respect to molecule di!usion (low values). As a consequence, we are in the presence of "ckian swelling kinetics performed by a powdered system. 3.4. Diwusion experiments The di!usion of TPH through sclerox (r"0) and the r"0.5 crosslinked polymer was studied by means of the
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T. Coviello et al. / Biomaterials 22 (2001) 1899}1909
Fig. 6. Release pro"les (M /M );100 of theophylline (10\ M) in distilled water for the cross-linked polymer ((䢇); r"0.5), for the sclerox (*) and the reference at 373C (䊐) (c "1.6% w/v).
three compartment di!usion cell. As it can be observed from Fig. 6, in water the di!usion through the hydrogel and the sclerox was remarkably lower than that obtained when only the solvent was present in the central compartment. The e!ect, after one day, is more evident in the case of r"0.5; thus it can be asserted that the presence of the three-dimensional network, is capable of a!ecting the permeation rate through the polymeric barrier, in spite of the quite small dimensions of the di!using molecule with respect to the mesh size of the network, as it will be discussed later. As shown before [12] the di!usion of TPH is also a!ected by the ionic strength of the medium as the polymeric matrix bears charged groups and a double e!ect for this kind of hydrogels can be detected. By adding the salt, the screening e!ect of the COO\ groups of the sclerox is promoted thus reducing the interaction between the charged chains and the drug but, at the same time, also the mesh size of the polymeric network is contracted; the permeation of a drug can be considered to be a!ected by two factors acting in opposite directions and the overall e!ect is the result of which one of those contribution is more important, (i.e. the steric hindrance of the drug or its possible interactions with the matrix). Experiments performed with the two compartment system cell using the high crosslinked polymer (r"2.0) and the visking tubing showed a lower di!usion rate of TPH through the cellophane membrane suggesting that the mesh size of the crosslinked polymer is wider than that of the visking tubing (cut-o!"12,000). Such statement can be supported by "lm permeation experiments carried out using PSS of di!erent molecular weights as di!using species. As reported in Fig. 7, PSS of M 1.9;10, i.e. above the cut-o! of the visking tubing, was still capable, though at low extent, to di!use through the crosslinked "lm, while the 4.0;10 M PSS could not at all permeate the "lm.
Fig. 7. Di!usion pro"les, at 373C, obtained for PSS of two molecular weights ((䢇) M "2.0;10; (*) M "4.0;10), in NaCl 0.9% (w/v), through the "lm of the crosslinked polymer r"2 (c "0.1% w/v).
3.5. Numerical analysis of diwusion experiments at r"0 and 0.5 A detailed analysis of the TPH permeation through the sclerox and the crosslinked sclerox gels characterized by r "0.5 and 0 would in principle require to consider the e!ect of the drug-polymer interaction as Singh pointed out [36]. In this case the drug di!usion does not follow Fick's law. Nevertheless, due to the small membrane volume (1 cm) with respect to the sum of the receiver and donor volumes (29 cm), the e!ect of the polymer drug interaction is small in comparison with that of the network mesh size ruled by the r ratio [37]. Indeed, as the e!ect of the drug}polymer interaction in the membrane volume is to decrease the drug net #ux feeding the receiver compartment, the smaller the membrane volume, the lower the drug}polymer interaction e!ect on the permeation curve. Accordingly, with the aim of estimating the e!ect of the crosslink ratio r and on condition to renounce to an exact determination of the THP di!usion coe$cient, a traditional "ckian-based model can be adopted. For this purpose we refer to a previously described model [12] based on the numerical solution [37] of Fick's second law under the proper boundary and initial conditions. The model is particularly fruitful as it accounts for the nonlinear drug pro"le concentration inside the gel during the permeation experiment, this being typical for thick membranes [43]. Furthermore, as it neither requires the sink condition in the receiver compartment nor the constant drug concentration in the donor compartment, it assumes a wide generality and it becomes a reliable tool to determine membranes permeability. Thus, the model is "tted on the experimental permeation data (r"0.5 and 0) in order to calculate the TPH
T. Coviello et al. / Biomaterials 22 (2001) 1899}1909
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permeability P, de"ned as D K P" , h
(19)
where h is the gel thickness, D and k are the TPH di!usion and partition coe$cient, respectively. Brie#y, the model implies the numerical solution [37] of the one-dimensional Fick's second law on the gel and on the two cellophane layers sandwiching the gel:
C C , " D X X t
(20)
C C , " D t X X
(21)
C C " , D t X X
(22)
where t is the time, X is the abscissa, D , D , D and C , C , C are, respectively, the drug di!usion coe$c ient and concentration in the "rst cellophane layer, in the gel and in the second cellophane layer. Eqs (20)}(22) must be solved with the following boundary conditions: dC C "D S < dt A X C D X C D X
"D 6F
,
(23)
6
C X
,
(24)
6F
C "D , X 6F >F 6F >F
dC C "!D S < dt X
,
(25)
(26)
6F >F
C C C "K , "K , "K C C C
(27)
and the following initial conditions: C "C ,
C "C "C "C "0,
(28)
where < (14.5 cm) and < (14.5 cm) represent the do nor and receiver volume, respectively, C and C are, respectively, the donor and receiver drug concentration at time t, S (1.77 cm) is the permeation surface, h (0.005 cm) and h (0.565 cm) are, respectively, the thick ness of the cellophane membranes and the thickness of the gel, while K and K are, respectively, the drug partition coe$cient of the cellophane layers and of the gel with respect to the solution of the donor and the receiver compartment. Eq. (23) imposes that the drug amount leaving the donor compartment is equal to the
Fig. 8. Model "tting (solid lines) on the theophylline permeation data (open circles) through r"0.5 sandwiched by two cellophane layers (three compartments case; water).
Table 3 Determined D and P values
Reference r"0 r"0.5
D;10 (cm/s)
P;10 (cm/s)
69 7.0 4.75
39 12.4 8.40
TPH di!usion coe$cient, D, and membrane permeability, P, in water, assuming the partition coe$cient K is equal to one and knowing that the thickness of the sample h is 0.565 cm.
drug #ux entering the "rst cellophane layer. Eq. (24) imposes that the drug #ux leaving the "rst cellophane layer is equal to that entering the gel (X"h ), while Eq. (25) sets the equality of the drug #ux leaving the gel and entering the second cellophane layer (X"h #h ). Eq. (26) ensures that the drug entering the receiver compartment is equal to the drug #ux leaving the second cellophane layer. Eq. (27) sets to zero the drug concentration in the receiver, in the gel, in the "rst and second cellophane layers while it sets to C (198.17 g/cm) the drug concentration in the donor compartment at the beginning of the permeation. As an example, Fig. 8 shows rather a good agreement between the model best "tting (solid line) and the experimental data (open circles) relative to r"0.5. Thus, we are con"dent of the reliability of the determined P values (see Table 3). It is clear that the presence of the crosslinks led to a decrease of TPH di!usion coe$cient as it determines a lower mesh size of the polymeric network that enhances the hindering e!ect of the polymer chains on the di!using TPH molecules.
4. Conclusion Reported results on the behavior of the crosslinked sclerox indicate that these new derivatives show a very high degree of swelling in water that, in the case of r"0.5, can be reduced if salt is added to the surrounding
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medium. The study of the swelling equilibrium in di!erent ionic strength gives an estimation for the crosslinking density at di!erent r values. An uncommon strategy approach to analyze the swelling kinetics has been applied obtaining a very good agreement with the experimental data. In particular, the di!usion coe$cient of the solvent as permeating molecule in the swollen gel (D ) and in the dry matrix (D ) have been evaluated. It came out that the value of D is not a!ected by the presence of NaCl while D depends on the presence of the salt. From the permeation of PSS at di!erent molecular weight through the polymer at the highest degree of crosslinking (r"2) it is possible to have a rough estimation of the mesh size, in terms of molecular weight cut-o!, of the polysaccharidic "lm. The characterization of these new systems is very important as they can be proposed as swellable matrices for sustained release of biologically active compounds and the possibility to shed light upon their structure can help to improve the performances of the hydrogels.
Acknowledgements This work was carried out with the "nancial support of C.N.R. and MURST.
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