water, solute and protein diffusion in physiologically...

Biomaterinls 17 (1996) 1203-1218

0 1996 Elsevier Science Limited Printed in Great Britain. All rights reserved

0142.9612/96/$15.00

Water, solute and protein diffusion in physiologically responsive hydrogels of poly(methacryli6 acid-g-ethylene glycol) Cristi L. Bell and Nikolaos A. Peppas Biomedical Materials and Drug Delivery Laboratories, School of Chemical Engineering, Purdue University, West Lafayette, IN 47907.1283, USA

Grafted poly(methacrylic acid-g-ethylene glycol) [P(MAA-g-EG)] copolymers were synthesized and

their pH sensitivity was investigated. P(MAA-g-EG) membranes showed pH sensitivity due to complex

formation and dissociation. Uncomplexed equilibrium swelling ratios were 40 to 90 times higher than

those of the complexed states and varied according to copolymer composition and poly(ethylene

glycol) (PEG) graft length. Mesh sizes in the two states were determined. Swelling under oscillatory

pH conditions revealed the dynamic sensitivity of P(MAA-g-EG) membranes as well as the diffusional

mechanisms causing network expansion and collapse. Network collapse (complexation) occurred

more rapidly than network expansion (decomplexation). A Boltzmann superposition model was used

to analyse this behaviour. Mechanical testing was used to evaluate the strength of P(MAA-g-EG)

membranes and to elucidate the mesh size under various conditions. Solute diffusion coefficients

were higher in uncomplexed than in complexed P(MAA-g-EG) membranes and decreased as solute

size increased. Lower diffusion coefficients were observed with membranes or hydrogels containing

longer PEG grafts, since in the uncomplexed state the PEG grafts dangled into the polymer mesh

space. Membrane permeability was responsive to changing pH conditions, and separation of solutes

was achieved. Copyright 10 1996 Elsevier Science Limited

Keywords: Drug delivery, hydrogels, complexation, hydrogel-bonding hydrogels, mesh size

Received 23 June 1995; accepted 26 September 1995

Hydrogels are hydrophilic polymer networks that are capable of imbibing large amounts of water, yet are insoluble because of the presence of physical or chemical cross-links, entanglements, or crystalline regions. Hydrogels can be used in biomedical applications such as drug delivery systems, biosensors, contact lenses, catheters, and wound dressings’. These materials have also been used extensively as separation membranes because the cross-links provide a characteristic exclusion due to the mesh size’.

Because of the presence of certain functional groups along the polymer chains, hydrogels are often sensitive to the conditions of the surrounding environment’. For example, the swelling ratio of these materials may be sensitive to the temperature, pH, or ionic strength of the swelling agent, or even to the presence of a magnetic field or ultraviolet light’. The environmentally sensitive behaviour has led to the extensive use of hydrogels in controlled drug delivery systems and in membrane separations, where they can respond to

Correspondence to Dr N.A. Peppas.

changes in the environment and, thus, regulate drug release or solute diffusion’.

In characterizing the environmentally sensitive behaviour of hydrogels of these applications, several parameters are important: the swelling ratio under changing conditions, the permeability coefficient under a variety of conditions, the diffusive characteristics of certain solutes through the mesh space of the polymer network, and the mechanical behaviour of the hydrogels. The equilibrium swelling ratio describes the amount of fluid which can be contained in the hydrogel at equilibrium. This parameter is a function of the hydrophilicity and degree of ionization of the network as well as the degree of cross-linking and the network structure”. Knowledge of the equilibrium degree of swelling allows for calculation of structural parameters such as the molecular weight between cross-links and the mesh size of the gel under a variety of conditions”,4.

The hydrogel permeability of various solutes under equilibrium and changing conditions and the diffusive characteristics of these solutes are also essential

1203 Biomaterials 1996, Vol. 17 No. 12

1204 Poly(methacrylic acid-g-ethylene glycol) hydrogels: CL Bell and N.A. Peppas

properties to be determined in characterizing hydrogels for use as membranes. These parameters describe the size of solutes which may diffuse through the network, which in turn describes the mesh space available for solute diffusion within the membranes. Finally, the mechanical behaviour of a hydrogel is relevant to its use as a membrane, as it must be able to withstand the conditions of the intended application. Mechanical testing under a variety of conditions may also be used to elucidate further the molecular weight between cross-links and the mesh size of the polymer networks.

The materials of interest in this research were poly(methacrylic acid-g-ethylene glycol) grafted copolymers, henceforth designated as P(MAA-g-EG) hydrogels. In these copolymers, interpolymer complexes can form between the PMAA main chains and the PEG grafts’. These materials are unique in that the two species involved in the interpolymer complexation are actually bound together within the same polymer. This allows for the reversible formation of complexes under appropriate conditions. This interpolymer complexation is due to hydrogen bonding between the hydrogens on the carboxylic acid groups of the PMAA and the oxygens in the PEG chains, and results behaviour5, ‘.

in pH-sensitive swelling The complexation forms only at a pH

low enough to ensure substantial protonation of the carboxylic acid groups. At low pH values, the complexes form, resulting in increased hydrophobicity in the polymer network. Thus, the network does not swell to a high degree. At higher pH values, these acid groups become ionized, and the hydrogen bonding breaks down. As a result, the network swells to a high degree because of the electrostatic repulsion produced within the network. The focus of the present paper was to synthesize these complexing graft copolymers and to characterize this pH-sensitive swelling behaviour in relation to the use of these biomaterials in controlled drug delivery and in bioseparations.

Early investigations of environmentally sensitive materials addressed the factors influencing the swelling behaviour, including the pH, ionic strength, and chemical composition solution, Kuhn et a1.7

of the surrounding noticed that the shape of

ionizable polymeric molecules, specifically polyacids and polybases, depended on the degree of ionization of the molecule chains. They observed that by ionizing the carboxyl groups of PMAA they could cause the originally coiled molecule to expand because of the electrostatic repulsion produced along the main chains. Liu et al.’ verified these conformational changes as a function of backbone ionization. Ionized (expanded) molecules could collapse upon addition of the salt because the salt was more soluble in the polyacid than in the methanol solventg. Katchalsky” also worked with PMAA cross-linked with a low percentage of divinyl benzene. This polymer network also swelled to a high degree in basic solutions and contracted or deswelled upon addition of acidic solution. Katchalsky et a1.“~‘2 presented an extensive theoretical treatment of the behaviour observed in these solutions and gels. Thus, with these early investigations, the first synthetic

examples of mechanochemical systems were produced, and the idea of synthetic materials responding to their surrounding environment was born.

In more recent years, a large amount of research has been done using materials that are sensitive to the chemical nature of their surrounding solution. For example, Ohmine and TanakaI observed that a discrete volume change occurred in ionized polyacryla- mide gels upon varying the salt concentration in acetone-water solutions. The critical salt concentration depended on the valence of the positive ions in the salt.

Brannon-Peppas and Peppas14-17 have done considerable work with pH-sensitive hydrogels for use in controlled drug delivery. They investigated the swelling behaviour of poly(2-hydroxyethyl methacry- late) (PHEMA) and copolymers of HEMA with MAA, maleic anhydride, and isopropyl acrylamide. Under cyclic pH conditions from pH 10 to 2, the gels showed increased swelling in the basic solution followed by a drop in swelling when placed in acidic solution. The equilibrium swelling behaviour of these materials was described in detail with a model based on the mixing, elastic-retractive, and ionic contributions to the free energyX5. The pH sensitivity of cationic gels has also been investigated by Hariharan and Peppas”. These gels contained cationic pendant groups which resulted in pH-sensitive behaviour and collapsed under basic conditions. Thus, solutes could be released from these networks under acidic conditions.

Interpolymer complexes in hydrogels are often sensitive to the surrounding environment’“. Such molecular associations are often accompanied by a change in conformation, shape, or hydrophilicity and thus have potential use in the conversion of chemical energy into mechanical work. They could be applied in such areas as chemical engines, actuators, biosensors, separations, drug delivery, and underwater or space energy supply systems”.

Of particular interest to this work are two systems that exhibit interpolymer complexation due to hydrogen bonding: PMAA with PEG and poly(acrylic acid) (PAA) with PEG. The protons of the carboxylic acid groups form hydrogen bonds with the ether oxygens on the PEG chain. Since the acidic groups on the macromolecular chains are involved in this complexation, it is accompanied by an increase in the pH of the solution. Also, since complexation in these systems occurs between the hydrophilic acid groups of the PAA or PMAA and the oxygens on the PEG chain, the resulting interpolymer complex is more hydrophobic than the constituent polymers. An added hydrophobic group, as with PMAA causes an added increase in hydrophobicitylg.

Early studies of these complexes used viscometry in order to investigate the effect of pH on the complexation formation”. Antipina et a1.22 showed that when PEG of molecular weight 1000 was added to a dilute solution of PMAA there was no effect on the pH of the solution. In fact, up lo a PEG molecular weight of 3000 there was no pH increase observed. After a molecular weight of 3000, the pH of the solution rose gradually.

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Poly(methacrylic acid-g-ethylene glycol) hydrogels: CL. Bell and N.A. Peppas 1205

Addition of PEG samples of molecular weight of 6000,

15 000, and 40000 caused a rapid rise in pH. Osada and Sato23,24 studied the same complexation in water and ethanol-water mixtures. These observations illustrate again the effect of the hydrophobic interactions on stabilization of the complex.

Baranovsky et a1.25 studied complex formation between PMAA and monosubstituted PEG in water and found that by introducing a hydrophobic group on to the PEG, the critical chain length for complexation was lowered. Osada and Takeuchiz6 did pioneering work based on interpolymer complexation in PMAA- PEG and PAA-PEG systems. Drastic dilations and contradictions due to complexation were seen as a function of pH when a PMAA membrane was treated with PEG.

Copolymers based on the complexation of PMAA and PEG were first produced by Peppas and collabora- tors536*27. NMR spectroscopy confirmed the presence of a PMAA-matrix with PEG grafts. Swelling studies showed good pH sensitivity in that swelling was low in acidic pH where the PEG grafts interacted with the PMAA matrix to form a tight network, and swelling was high in basic pH where the complexation could not occur because of neutralization of the PMAA. Minimum swelling occurred at a 1: 1 ratio of PEG : MAA.

In this work, we report on recent studies on the equilibrium and oscillatory swelling behaviour of these grafted copolymers and on mechanical and diffusive experiments using these membranes.

MATERIALS AND METHODS

Synthesis of poly(methacrylic acid-g-ethylene glycol) hydrogels

Graft copolymers of poly(methacrylic acid) and poly(ethylene glycol) were synthesized by free radical solution polymerization. The monomers used were vacuum-distilled methacrylic acid (MAA, Aldrich Chemical Co., Milwaukee, WI, USA) and poly(ethylene glycol) monomethacrylate (PEGMA, Polysciences, Warrington, PA, USA) of molecular weight ZOO, 400, and 1000. Copolymers with feed compositions (weight ratios) of 60: 40, 50: 50, and 40:60 PMAA : PEGMA were prepared and investigated. Tetraethylene glycol dimethacrylate (TEGDMA, Polysciences) was added as a cross- linking agent in the amount of 2 wt% monomer. The reaction mixture was diluted in a 50: 50 ethanol : water mixture to inhibit autoacceleration during the polymerization reaction. A 50: 50 mixture of ammonium persulfate (Polysciences) and sodium metabisulphite (Fisher Scientific, Fair Lawn, NJ, USA) was used as redox initiators in the amount of 0.025 wt% of the total monomers. Nitrogen was bubbled through the reaction mixture for 20min to remove oxygen, which acted as a free radical scavenger.

Hydrogel disks were prepared by pouring the reaction mixture into polypropylene vials, and polymerizing for 24 h at 37°C. Upon completion, the

cylindrical-shaped polymer samples were removed, dried in air and cut into 0.5-mm thick disks. Hydrogel membranes were prepared by pouring the reaction mixture between glass plates separated by rubber gaskets and polymerizing for 24 h at 37°C. All samples were washed in distilled/deionized water for 1 wk to remove unreacted monomer, cross-linking agent, or initiator. After washing, the samples were dried in air and stored in a desiccator until use.

Swelling studies

The equilibrium swelling behaviour of the P(MAA-g- EG) hydrogels as a function of pH was studied by weighing dry samples and placing them in approximately 50ml of a solution of specific pH at 37°C. Aqueous solutions were prepared by adding sodium hydroxide, hydrochloric acid, or sodium acetate. The samples were taken out, blotted, and weighed, and the solution was changed daily until the weight of the samples changed by no more than 0.01 g over a 48 h period. The equilibrium weight swelling ratio, 9, of the samples was then calculated as

where W, is the equilibrium weight of the swollen sample and Wd is the weight of the dry sample.

The swelling response of the gels under varying pH conditions was also characterized. This was done by equilibrating samples in an acidic solution of pH = 4 at 37”C, then placing them in a solution of pH= 7 (still at 37°C) for 45 min with the samples being weighed every 5min, placing them back into acidic solutions and repeating over several cycles.

Mechanical testing

The strength of the P(MAA-g-EG) hydrogels was characterized using a tensile tester (model 4301, In&on Corp., Canton, MA, USA). Samples were equilibrated in a pH of either 4 or 7 and then cut into rectangles of 8.0mm width. The load was applied at a rate of 2 mm min-’ and the force was determined as a function of sample length. The stress-strain data were analysed using Equation 2:

Here, fi is the force applied to the polymer per unit area in the unstrained network, G is the elastic modulus of the gel, u2,s is the polymer volume fraction in the swollen network, and i is the elongation of the sample.

Permeation studies

The solutes used in the permeation and partition studies are summarized in Table 1. Permeation studies through the gel membranes were performed using the experimental set-up shown in Figure Z. The diffusion cells were Valia-Chen cells (Crown Glass CO., Somerville, NJ, USA) consisting of donor and receptor reservoirs. The water jackets around the cells provided temperature control at 37°C. Magnetic stirrers (600rpm) in each reservoir kept the solutions in the


1206 Poly(methacrylic acid-g-ethylene glycol) hydrogels: C.L. Bell and N.A. Peppas

Table 1 Solutes used in permeability experiments

Solute Molecular Hydrodynamic Solute diffusion Reference weight radius (nm) coefficient at 25 C

Do x lo6 (cm’/s- ‘)

Vitamin B12 1335 0.85 3.79 28 Lysozyme 14100 1.60 1.04 29 Chymotrypsinogen 23 200 2.25 0.95 29 Ovalbumin 45 000 2.76 0.78 29 Bovine serum albumrn 65 000 3.61 0.59 29 FITC-Dextran 4400 4.70 1.1 30

membrane [ Recirculating Pump )

Magnetic Stirrer (connected to pump)

UV-Vis Spectrophotometer

Figure 1 Experimental set-up for permeation studies.

cells well mixed. A membrane was preswollen under the pH

conditions of the experiment (usually pH = 4 or 7) was placed between the two half cells, and the donor cell was filled with the pH solution containing 0.1 mg ml 1 of solute. The receptor cell was filled with pure solvent. Periodically, the contents of the receptor cell were removed and replaced by pure solvent. The solution removed from the receptor cell was analysed using the UV-Vis spectrophotometer mentioned above as a function of time. From this experiment, the permeability coefficient, P, of the membrane was determined using the following equation,

In this expression, c, is the concentration in the receptor cell at time t, c0 is the initial concentration in the donor cell, V is the volume of each half cell, and A is the effective area of permeation. A plot of -(V/2A) ln(l - z(c,/c~)] versus t yielded a line with slope P. The diffusion coefficient of the solute in the membrane was then calculated by

D = PI/K,, (4)

where Kd is the partition coefficient of the membrane and 1 is the membrane thickness.

In another type of permeation study, samples were equilibrated in pH 7 (uncomplexed] and mounted in the diffusion cell apparatus. The procedure was as described above except that at various time intervals, when the contents of the receptor cell were removed, they were replaced by a 0.1 mgml ’ solute solution at pH 4. After another time interval, the membrane was subjected to pH 7 conditions with the cycle repeated several times. Experiments were also done in which the membranes were equilibrated in pH 4 (complexed). The membrane was then subjected to pH 7, then to pH 4, and the cycle repeated as described.

In a final type of permeation experiment a membrane containing PEG grafts of molecular weight 200 was equilibrated at either pH 4 or pH 7, and placed in the diffusion cell apparatus. The receptor cell was filled with pure solvent and the donor cell was filled with solvent containing 0.1 mgml ’ of chymotrypsinogen and FITC dextran. The diffusion of the solutes through the membranes was then measured as described before.

Partition experiments

In order to determine the partition coefficient for P(MAA-g-EG] membranes, gels were equilibrated in a desired pH solution and then placed in 20ml of the same pH solution containing 0.1 mg ml-’ of the solute of interest. The concentration of the surrounding solution was monitored over a 3 h period using UV-Vis spectroscopy. The partition coefficient, K,], was calculated as

(51

Here, c,,, is the concentration of the solute in the membrane, c, is the concentration in the solution, ci is the initial concentration of solute in the solution, cc1 is the concentration of solute in the solution after equilibrium has been reached, and VS/sor and VI,, are the volumes of the solution and the membrane, respectively. The value of the partition coefficient was then used in the analysis of the permeability data to determine the solute diffusion coefficient.

RESULTS AND DISCUSSION

Equilibrium swelling studies

The equilibrium swelling behaviour of P(MAA-g-EC) hydrogels was investigated as a function of pH. Samples containing 40: 60, 50: 50, and 60 :40 of

Biomaterials 1996. Voi. 17 No. 12

Poly(methacrylic acid-g-ethylene glycol) hydrogels: CL Be// and N.A. Peppas 1207

PMAA:PEG were studied, and the molecular weights of the PEG grafts were 200, 400, and 1000. Figure z shows the typical swelling behaviour of these hydrogels. At low pH, when complexation occurs, the polymer network was collapsed and the swelling ratio was low. The presence of hydrogen bonding in the complexes causes added constraints in the network and makes the network less hydrophilic because the carboxylic acid groups on the PMAA main chains are occupied in the complexes. Thus, at low pH when the complexes are very stable, the P(MAA-g-EG) networks did not swell much. In fact, the swelling ratio in this region was around 1.5, and this behaviour was seen up to about pH 4.

In the region of pH 4 to about pH 8, as pH was increased the swelling ratio of the gels increased. This occurred because the complexes broke and the carboxylic acid groups on the PMAA became progressively more ionized. Electrostatic repulsion from this ionization drove the network chains apart and swelling resulted. As the pH increased, the acid groups also began to become neutralized by cations. At pH 8, the concentration of the counterions in the gels was such that the negative charges were screened and electrostatic repulsion was diminished. Because of this screening, the gels shrank somewhat between pH 8

and 12. Figure 3 shows the equilibrium swelling ratio as a

function of pH for samples containing the same ratio of PMAA to PEG but with molecular weight of the PEG grafts of 200, 400, and 1000. All samples displayed the same general swelling behaviour trends as a function of pH; the extent to which the networks swelled in the uncomplexed state increased as the molecular weight of the PEG grafts increased. As the same weight of PEG was added in the reaction mixture for all PEG molecular weights, samples containing shorter PEG grafts ended up with more grafts in the hydrogel structure than samples containing longer grafts. As a result, the samples containing longer PEG grafts were more hydrophilic because of the presence of fewer grafts and thus,

100 c I I I I I I i

5 E 80 2 s 6 60

6 6 10 12 14

PH

Figure 2 Equilibrium swelling ratio as a function of pH for a sample containing 40% PMAA and 60% PEG, with the molecular weight of the PEG grafts being 1000.

0 4

0 2 4 6 6 10 12 14

PH

Figure 3 Equilibrium swelling ratio as a function of pH for samples containing 40% PMAA and 60% PEG, with the molecular weight of the PEG grafts being: 0, 200; n , 400; A, 1000.

100

0

0 2 4 6 8 10 12 14

PH

Figure 4 Equilibrium swelling ratio as a function of pH for samples containing PEG grafts of molecular weight 1000, with the ratio of MAA:PEG being: 0, 60:40; n , 50:50; A, 40:60.

more hydrophilic MAA units. This added hydrophilicity resulted in a higher degree of swelling in the uncomplexed state for samples containing longer PEG grafts.

To confirm the dominant hydrophilicity of the PMAA chains in the copolymer, equilibrium swelling studies were performed with samples containing various ratios of MAA: PEG. Figure 4 shows the swelling ratio of samples containing PEG grafts of molecular weight 1000 where the ratio of MAA to PEG was varied at 60 :40, 50: 50, and 40 : 60. All the samples showed the same type of swelling behaviour as a function of pH. The gels were collapsed in the complexed state and expanded as pH increased and the complexes were broken. However, the extent to which the networks swelled in the uncomplexed state increased as the amount of MAA in the copolymer increased, owing to the hydrophilicity of the MAA units.


1208 Poly(methacrylic acid-g-ethylene glycol) hydrogels: CL. Be// and N.A. Peppas

Determination of network mesh size

The change of P(MAA-g-EG) swelling as a function of pH translates to a change in the mesh size of the gel. In order to determine the mesh size from the equilibrium swelling data, the Peppas-Merril13* equation was used to determine the number average molecular weight between crosslinks, fc?,.

Here, ?‘i?in is the number average molecular weight of the non-cross-linked polymer, u is the specific volume of the polymer, VI is the molar volume of the swelling agent, uZ.r is the polymer volume fraction after cross- linking but before swelling (the relaxed polymer volume fraction), I)~,~ is the polymer volume fraction after equilibrium swelling (swollen polymer volume fraction), and x, is the Flory polymer-solvent interaction parameter. Values of the relevant parameters are summarized in Table 2. The values of uZ,r and IJ~,~ were determined by simple swelling experiments3.

From the molecular weight between cross-links, the number of links along the polymer chain, n, was calculated as

2Mc --K (7)

where n/r, is the molecular weight of the repeating unit, The value of the root mean squared end-to-end distance of the polymer chain in the freely jointed state was calculated as

(rZ)1’2 = PJ;, (8)

Here, P (= 0.154nm) is the bond length. The root mean squared end-to-end distance of the polymer chain in the unperturbed state was then calculated as

(r;)“z = Jc,(T;Z)liZ (9)

where C, is the characteristic ratio of the polymer (see Table 2). Finally, the mesh size, i_, of the polymer network was calculated by

Table 2 Parameters for calculation of m, and <

Parameter Value Reference

Vl 18cm3mol-’ p(water) 1 g cmm-3 p(ethanol) 0.789gcm 3

p(PMAA) 1.0153gcm m3

p(PEG) 1.1135gcm~3

xi (PMAA) 0.5987

XIPW 0.55 C,(PMAA) 14.6

C,(PEG) 3.8

MO 86.0

(Ml 0.0047 mol cm 3

111 1.1 x 10-5molcm~ f 0.5

‘% 670 I mol ss’

kt 2.1 x lO”lmols-’

ki 0.0165s ’

- - - 32 32 33 33 32 32 32 -

-3 - - 32 32 32

5 = “;,;‘3(?;)‘/2 (10)

For the copolymers studied here, weighted averages of the values of the parameters for the homopolymers were used (see Table 2). The value of %?i, for linear PMAA was calculated as 19 600 from Equation 11

%i,=M, kJM1

($k&t~~l)“2 (111

Here, MO is the molecular weight of MAA unit, [M] and [I] are the concentrations of monomer and initiator, kp is the kinetic constant of propagation, kt is the kinetic constant of termination, kd is the kinetic constant of the decay of initiator, and f is the efficiency of the initiator.

Figures 5 and 6 show that the mesh sizes of the various samples were very small (between 0.3 and 0.9nm) in the collapsed or complexed states at low pH, and very high (in the range of 24-35 nm) in the

500

200

100

0

I I I I I I

0 2 4 6 6 10 12 14 PH

Figure 5 Equilibrium mesh size as a function of pH for samples containing PEG grafts of molecular weight 400, with the ratio of MAA:PEG orafts of molecular weiaht 400, with the 40:60.

ratio of MAA:PEG-being: 0, 60:40; n , 5650; A,

I I I I I I

6 8 10 12 14 PH

Figure 6 Equilibrium mesh size as a function of pH for samples containing 8 mol% PEG, with the molecular weight of the PEG grafts being: 0, 200; n , 400; A, 1000.

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Poly(methacrylic acid-g-ethylene glycol) hydrogels: CL Bell and N.A. Peppas 1209

expanded or uncomplexed states at high pH values. The % changes in the mesh sizes between the complexed and uncomplexed states for all the samples studied were between 96 and 99%. Clearly, these results illustrate the pH sensitivity of the mesh size of P(MAA-g-EG) hydrogels under equilibrium swelling conditions. These results also further confirm the potential for use of these materials as pH-sensitive membranes in controlled drug delivery and membrane separations.

Oscillatory swelling studies

Figure 7 shows the typical swelling behaviour of P(MAA-g-EG) hydrogels containing 50% MAA and grafts with PEG molecular weight of 1000 upon successive immersion in solutions of pH 10 and 2. In the initial acidic solution the gel was in a collapsed state due to complexation. When placed into a pH 10 solution, the complexes were broken and the network began to swell because of the hydrophilicity of the PMAA in the copolymer. The network swelling in a basic medium was linear as a function of time and did not approach an equilibrium value over the timescale of the experiment. When transferred to a pH 2 solution, complexes formed rapidly and the gel shrank abruptly. Good repeatability of this behaviour was exhibited over several cycles. The average rates of expansion and contraction were calculated over the cycles of the experiments (see Table 3). All samples tested exhibited an expansion rate between 0.01 and 0.033 g swollen polymer/g dry polymer per minute. In contrast, the initial rapid contraction rates of the networks when placed in acidic media were between 0.07 and 0.2g swollen polymer/g dry polymer per minute. In general, samples containing longer PEG grafts showed slightly higher rates of expansion and contraction.

The results of these experiments showed that the swelling ratio of P(MAA-g-EG) hydrogels changed quickly when the pH of the surrounding environment was changed from acidic to basic, and that this response was repeatable over several cycles. This behaviour translated to repeatable changes in mesh size over several pH cycles. The mesh sizes of the networks were calculated under oscillatory conditions and are shown in Figures 8 and 9. For all samples, the mesh size responded rapidly to pH changes. Maximum mesh sizes in the expanded states (pH 10) ranged from 1.1 to 2.7 nm, with samples containing longer PEG

H

210 * 0 50 100 150 200 250 300 350 400

Time (min)

Figure 7 Oscillatory swelling behaviour as a function of time and pH for a sample containing 50% PMAA and 50% PEG, with the molecular weight of the PEG grafts being 1000.

grafts generally showing the highest mesh sizes. Mesh sizes in the collapsed states (pH 2) were between 0.4 and O.gnm. All samples showed a 50 to 75% change in mesh size as the pH changed from acidic to basic conditions. It should be noted that the mesh sizes observed in the oscillatory studies were smaller than those observed in the equilibrium swelling results, owing to the timescale of the two types of experiments. The samples in the equilibrium swelling experiments were allowed to swell over a span of 2 wk, while the samples under oscillatory conditions only swelled in each pH for 45 min cycles.

Derivation of model and relaxation time analysis

A model was derived to describe the dynamic response of P(MAA-g-EG) hydrogels to changes in pH. The strain, E, of an isotropic sample swelling in a specific solution was defined as

e-e, ne

&=e,=e, (12)

where ! is the sample length and & is the original length. Gels subjected to various pH conditions over time exhibited the following characteristics: (i) the response (strain) to the inputs (pH changes) are additive; and (ii) the responses were independent of the specific time at which the inputs were applied.

Table 3 Average rates of expansion and contraction (g swollen polymer/g dry polymer min) of P(MAA-g-EG) hydrogels in oscillatory swelling experiments

Hydrogel composition (wt%)

Molecular weight of PEG grafts

Average rate of expansion

Average rate of contraction

Ratios of rates

40:60, MAA:PEG 200 0.018 0.100 5.6 40:60, MAA:PEG 400 0.033 0.100 3.0 5050, MAA:PEG 200 0.010 0.085 8.5 5050, MAA:PEG 400 0.015 0.100 6.7 5050, MAA:PEG 1000 0.023 0.150 6.5 60:40, MAA:PEG 200 0.023 0.080 3.5 60140, MAA:PEG 400 0.022 0.070 3.2 60:40, MAA:PEG 1000 0.030 0.200 6.7

Biomateriak 1996, Vol. 17 No. 12

1210 Poly(methacrylic acid-g-ethylene glycol) hydrogels: C.L. Be// and N.A. Peppas

40.0

z

30.0

Lo 20.0

10.0

F

1

1 0.0

0 5 0 100 150 200 250 300 350 400

time (min)

Figure 8 Oscillatory mesh size as a function of time and pH for samples containing 60% PMAA and 40% PEG, with the molecular weight of the PEG grafts being: 0, 200; n , 400; A, 1000.

0.0 L~~~~l~~~~I~~~~I~~‘~I~~‘~I~~~.I~.~~I’~~~’ 0 5 0 100 150 200 250 300 350 400

time (min)

Figure 9 Oscillatory mesh size as a function of time and pH for samples containing 50% PMAA and 50% PEG, with the molecular weight of the PEG grafts being, 0, 200; n , 400; A, 1000.

These characteristics allowed the application of the Boltzmann superposition principleZ4 to obtain

( 1

c(t) = I *’ L(t - T) TTl d7

.” (131

Here f:(t) is the time-dependent strain, [H’] is the concentration of hydrogen ions, 7 is a dummy variable, and L(t - z) is the mechanochemical compliance, describing a mechanical response to a chemical stimulus or conversion of chemical energy to mechanical work. The model was extended to an isotropic gel swelling in three dimensions by writing

Q(t) = v,(t) I’:( (I,, + All” -z--_

Vd (4

1; = 11 + z:(f)l,’ (14)

0

or

(151

In these equations, Q(f) is the volume degree of swelling, and V, and V,, are the polymer volumes in the swollen and dry states, respectively.

This analysis was fnrther used to describe the mesh size, <(f), of a pH-responsive gel. The mesh size was described by combining Equations 7-z o and recognizing that the polymer volume fraction, v~,~, is the reciprocal of the equilibrium volume swelling ratio, Q(f). Thus,

Substitution of the model expression for Q(f) gave

.I iIIH ’ I

I) L(f - ,),-di

I (17)

Eqrmf-ion 2 i’ was used to describe the swelling hehaviour of P(MAA-g-EG) gels over time as pH conditions changed. The results of the oscillatory swelling studies were used to evaluate the model hy assuming that parameter L was independent of time,

such that Equation 15 became

The value of L was calculated for a set interval of pH values by determining the limiting equilibrium values at the two ~1-1 units and solving Equation 28 for L. Although L was assumed to be independent of time, it was still a function of such factors as the pH of the swelling medium, the copolymer structure, and the relaxation of the polymer chains. Figure zo shows a typical model fitted to data for a gel sample containing 50% MAA and 50% PEG with a PEG molecular weight of 1000. The modei fits the data well hecause the behaviour of the gels was generally linear over the timescale of the experiments.

By analogy to similar mechanical equations for the elastic modulus. the mechanochemical compliance was also expressed as a function of the relaxation times, 0, of the polymer chains

3.01 10 I 2 I 10 I 2 1 10 ( 2 I10 / 2

I I , I I I I PH

1.0’ I 0 50 100 150 200 250 300 350 400

lme (mln)

Figure 10 Model fit of experlmental oscillatory swelling data for a sample containing 50% MAA and 50% PEG, with the molecular weight of the PEG grafts being 1000.



J’ cc

L(t) = 0

fLL(O)[l - doI; (191

The relaxation time could be determined by combining Equations 18 and 19. An approximate value of the average relaxation time of the polymer chains was determined by plotting In Q”” as a function of time14. The slope of this curve is the reciprocal of the average relaxation time, 0. This approximate calculation may be done for hydrogels which respond quickly to changes in the surrounding environment.

This type of analysis was done to the expanding and contracting results of the oscillatory swelling experiments. Each region was analysed separately for all samples in order to compare polymer relaxation during expansion and contraction. Table 4 shows that the average relaxation times were significantly greater during decomplexation (network expansion) in pH 10 than during complexation (collapse) in pH 2. In fact, the relaxation times during collapse of the gels due to complexation were between 5 and 8 times faster than those of expansion of the network due to decomplexation. The results from this analysis corresponded well with the ratios of the rates of expansion and collapse in Table 3.

Mechanical analysis

The effects of formation and dissociation of complexes on the mechanical strength of the P(MAA-g-EG) gel networks were determined using constant rate of extension tensile experiments. The shear modulus, G, of the hydrogel membranes was calculated from the stress-strain curves of the experiments and Equation 2. Figure 11 presents the shear modulus as a function of the molecular weight of the PEG grafts. Copolymers in the complexed state (in pH 4) showed higher moduli than their counterparts that had been swollen in pH 7 (uncomplexed state). The differences in moduli between complexed and uncomplexed samples were due to the amount of solvent in the hydrogel network under these two pH conditions. The modulus could be expressed as

Table 4 Average relaxation times, g, determined from oscilla-

tory swelling results

Sample composition (wt%)


Swelling

PH

?i (min)

40:60, MAA:PEG 200 10 341

40:60, MAA:PEG 200 2 52

40:60, MAA:PEG 400 10 231

40:60, MAA:PEG 400 2 50

5050, MAA:PEG 200 10 409

5050, MAA:PEG 200 2 59

50:50, MAA:PEG 400 10 409

5050. MAA:PEG 400 2 47

50:50, MAA:PEG 1000 10 264

50:50, MAA:PEG 1000 2 38

60:40, MAA:PEG 200 10 284 60:40, MAA:PEG 200 2 42 60:40, MAA:PEG 400 10 392 60:40, MAA:PEG 400 2 61 60:40, MAA:PEG 1000 10 213 60:40, MAA:PEG 1000 2 28

C 0.15

a 3 CI

2 0.1

p’ %

j 0.05 In

0 200 400 600 800 1000 1200

Molecular Weight of PEG Graft

Figure 11 Shear modulus of P(MAA-g-EG) membranes containing 8mol% PEG grafts: 0, uncomplexed, swollen in pH 7; n , complexed, swollen in pH 4.

(20)

Here, p is the network density, R is the gas constant, T is absolute temperature, M, is the average molecular weight between cross-links, M, is the primary chain molecular weight, and v~,~ is the volume fraction of polymer in the swollen network. As the molecular weight of the PEG graft increased, the modulus of the networks in both states decreased. This was a result of the fact that the samples containing longer PEG grafts swelled to a higher degree.

Equation 20 was also used to provide an additional measurement of the molecular weight between cross- links for the samples tested. The mesh size, <, was then calculated from the molecular weight between cross-links using again Equations 7-10. Figure 1.2 shows that uncomplexed samples had much higher mesh sizes than their complexed counterparts. In fact,

200 400 600 800 1000 1200

Molecular Weight of PEG Graft

Figure 12 Mesh size calculated from mechanical testing results for P(MAA-g-EG) membranes containing 8 mol% PEG grafts: 0, uncomplexed, swollen in pH 7; H, complexed, swollen in pH 4.


1212 Poly(methacrylic acid-g-ethylene glycol) hydrogels: CL. Bell and N.A. Peppas

Table 5 Mesh size, 5, in complexed and uncomplexed P(MAA- g-EG) hydrogels as calculated from swelling studies and mechanical testing

Sample composition

Swelling

pf-f

Mesh size from swelling 5 (nm)

Mesh size mechanical testing

5 (nm)

8 mol% PEG 200 4 1 .o 3.4 8 mol% PEG 200 7 32.1 17.3 8 mol% PEG 400 4 1.8 4.8 8 mol% PEG 400 7 33.9 23.0 8 mol% PEG 1000 4 0.5 5.3 8 mol% PEG 1000 7 32.9 23.8

all samples tested showed a mesh size in the uncomplexed (highly swollen) state that was between 78 and 80% larger than that of the complexed (collapsed) state. Also, as in the equilibrium swelling experiments, samples containing longer PEG grafts showed higher mesh sizes.

The mesh sizes determined from mechanical testing were slightly different from those calculated from the equilibrium swelling experiments, as shown in Table 5. The differences in the mesh sizes in the uncomplexed states were attributed to the nature of the two types of experiments. In the complexed state, the differences in the mesh sizes were attributed to the fact that the collapsed networks contained a number of physical cross-links or entanglements contributing to the mesh size. These entanglements were easily broken during tension under the conditions of the mechanical testing, whereas they remained intact under conditions of swelling. As a result, the mesh sizes in the complexed states were larger when determined by mechanical testing than when determined by equilibrium swelling studies.

Determination of diffosional mechanism

Water transport in polymer networks may be described by Equation 21, which contains contributions from Fickian diffusion and polymer relaxation:

Mt __ = k,t’!2 + k,t MC%

(21)

Here, Mt is the amount of water absorbed at time t, M, is the amount absorbed at equilibrium, and k, and k2 are constants. Ritger and Peppas”’ derived a useful semi-empirical expression which was able to describe the mechanism of diffusion for different geometries:

The diffusion exponent, n, takes on different values for various diffusion mechanisms and geometries. In purely Fickian diffusion, macromolecular relaxation does not affect penetrant transport, while Case II transport refers to the situation in which macromolecular relaxation controls penetrant diffusion. Anomalous transport occurs when both Fickian diffusion and macromolecular relaxation affect penetrant transport.

This type of analysis was applied to the experimental

results of the oscillatory swelling experiments using Equation 23, which relates the water uptake to the weight swelling ratio, q:

Mt (4 - l) kt”

MS--= (46 - 1)

In the case of the oscillatory swelling experiments the value of qoc was taken as the maximum value of q in the uncomplexed state. A computer program using SAS was utilized to determine the most accurate value of n in the expansion regions of the oscillatory swelling studies along with the 95% confidence limits of these values. These values are shown in Table 6. The important stage of the network collapse was between the first two data points in the pH 2 regions. Beyond these points, some collapse occurred but it was not as significant as that of the first 5min in acidic media. Thus, values of n for the contracting regions of the oscillatory swelling experiments were not determined. In general, the results indicate Fickian behaviour with values of n ranging from 0.3 to 0.59 with confidence limits between 0.08 and 0.15. These results are an indication that chain relaxation is not as important a phenomenon as penetrant transport in the swelling- deswelling process.

Permeability studies with equilibrium swollen membranes

P(MAA-g-EG) membranes containing 8 mol% PEG grafts of various molecular weights were swollen to equilibrium in the complexed (pH 4) and uncomplexed states (PH 7) and subjected to permeation by various solutes (Table 1). Figures 13 and ~4 present typical data of the receptor cell solute concentration as a function of time. Solutes permeated the uncomplexed membranes to a higher degree than the complexed membranes. In permeation through uncomplexed membranes, the concentration of the receptor cell generally decreased as the size of the permeating solute increased. Also, the concentration of the receptor cell was lower for diffusion in membranes containing PEG grafts of molecular weight 400 than for those containing grafts of molecular weight 200. Permeation of membranes with longer PEG grafts also showed slightly longer lag times. This is due to the fact that in the uncomplexed state the PEG grafts were free to dangle in the mesh

Table 6 Average values of diffusional exponent n from analysis of the expansion and contraction of P(MAA-g-EG) hydrogels in oscillatory swelling experiments

Sample composition (wt%)


Exponent n during expansion

Average number of points

4060, MAA:PEG 40:60, MAA:PEG 5050, MAA:PEG 5050, MAA:PEG 5050, MAA:PEG 60:40, MAA:PEG 60:40, MAA:PEG 60:40, MAA:PEG

200 0.40 & 0.11 a 400 0.50 + 0.15 9 200 0.34 f 0.10 9 400 0.36 k 0.11 9

1000 0.47 f 0.13 9 200 0.50 + 0.11 9 400 0.30 i 0.08 9

1000 0.59 +Z 0.08 9



0 200 400 600 600 1000

Time (min)

Figure 13 Receptor cell concentration of vitamin I312 permeating through P(MAA-g-EG) membranes containing 8mol% PEG grafts of molecular weight 200: 0, uncomplexed, swollen in pH 7; n , complexed, swollen in pH 4.

.

5 Z = . 9 z . . . B .

0.0 I I I

0 100 200 300 400 600

Time (min)

Figure 14 Receptor cell concentration of lysozyme permeating through P(MAA-g-EG) membranes containing 8mol% PEG grafts of molecular weight 400: 0, uncomplexed, swollen in pH 7; n , complexed, swollen in pH 4.

space of the polymer network. Longer grafts (higher molecular weights) dangled into the mesh space of the polymer to a greater extent, and thus interfered with solute diffusion through the network more than did shorter grafts. The length of the PEG grafts was calculated using a method described by Merrill et a1.36. The root mean squared end-to-end distance of the PEG grafts was calculated as

(rZ)W = aC;/2n’/2[ (24)

Here, C, is the characteristic ratio equal to 4.0 and e is the bond length (0.154nm). The number of bonds, R, was determined as before and the intramolecular extension factor, c(, was calculated as

Table 7 Root mean square end-to-end distances of PEG grafts in P(MAA-g-EG) membranes

PEG molecular weight (f”‘)* (nm)

200 1.34 400 2.24

1000 4.35

1 0 10 20 30

Solute Radius, r(A)

40 50

Figure 15 Permeability of P(MAA-g-EG) membranes containing 8 mol% PEG grafts of molecular weight 400 as a function of solute radius: 0, uncomplexed, swollen in pH 7; n , complexed, swollen in pH 4.

For PEG, C, was equal to 0.105, $, was 0.5, and 0 was 368K. Table 7 shows that the PEG grafts of molecular weight 200 extended into the mesh space of the polymer a maximum distance of 1.34nm, while those of molecular weight 400 extended a distance of 2.24 nm.

Figure 25 shows the permeability coefficient of P(MAA-g-EC) membranes determined by Equation 4 as

a function of solute radius (Table 1). The permeability of the membranes was higher in the uncomplexed state than in the complexed state, owing to the larger mesh sizes available for solute permeation, The permeability of the membranes decreased as the size of the solute increased, with the exception of the permeability of lysozyme which was higher than that of the smaller vitamin Bl2 solute. This effect was attributed to the manner in which lysozyme partitioned within the membrane, as discussed below. Bovine serum albumin did not permeate any of the membranes, while the seemingly larger (higher hydrodynamic radius) FITC dextran (molecular weight 4400) solute permeated the membranes containing PEG grafts of molecular weight 200 to a small degree. This was attributed to the fact that albumin is a spheroidal molecule while dextran has a rod-like configuration. The permeability coefficients of the membranes in the uncomplexed states were lower in membranes which contained PEG grafts of molecular weight 400 than in those containing grafts of molecular weight 200. This was the result of the longer PEG grafts interfering with solute diffusion to a higher degree, as discussed above.


1214 Poly(methacrylic acid-g-ethylene glycol) hydrogels: C.L. Bell and N.A. Peppas

Table 8 Partition coefficients of solutes in P(MAA-g-EG) membranes

Sample composition Solute Swelling pH Partition coefficient k,

8 mol% PEG 200 Vitamin B12 7 1.3 8 mol% PEG 200 Lysozyme 7 9.23 8 mol% PEG 200 Chymotrypsinogen 7 3.8 8 mol% PEG 200 Ovalbumin 7 3.8 8 mol% PEG 200 FITC-Dextran 4400 7 0.24 8 mol% PEG 400 Vitamin B12 7 1.24 8 mol% PEG 400 Lysozyme 7 9.74 8 mol% PEG 400 Chymotrypsinogen 7 5.4 8 mol% PEG 200 Vitamin 812 4 1.8 8 mol% PEG 200 Lysozyme 4 2.6 8 mol% PEG 200 Chymotrypsinogen 4 3.4 8 mol% PEG 400 Vitamin 812 4 0.96 8 mol% PEG 400 Lysozyme 4 2.68 8 mol% PEG 400 Chymotrypsinogen 4 4.17 8 mol% PEG 1000 Vitamin 812 4 0.78

Partition studies

In order to determine the diffusion coefficients of the solutes in P(MAA-g-EG) membranes, knowledge of the partition coefficient was necessary. The partition coefficient, Kd, is a parameter which relates the amount of solute incorporated into the membrane to the amount of solute in the surrounding solution, and was calculated by Equation 5.

Table 8 summarizes the partition results. The partition coefficients of lysozyme were of interest because the permeability of lysozyme was found to be higher than that of the smaller vitamin B12 solute. The partition coefficients of lysozyme in uncomplexed P(MAA-g-EG) membranes were the highest values obtained, and these partition coefficients were much lower in complexed membranes. This was attributed to the fact that lysozyme contains a large number of ionizable groups within its structureX7. In addition, lysozyme has positive charges because its isoelectric point is 11 and, thus, it strongly interacts with negatively charged PMAA. These ionizable groups probably interacted with the ionizable groups in the uncomplexed P(MAA-g-EG) hydrogels, resulting in a high partition coefficient.

3.0

2.0

1.0

0.0

0 10 20 30 40 50

Solute Radius, r (A)

Figure 16 Diffusion coefficient as a function of solute radius in P(MAA-g-EG) membranes containing 8mol% PEG grafts of molecular weight 200: 0, uncomplexed, swollen in pH 7; n , complexed, swollen in pH 4.

Determination and analysis of solute diffusion coefficients

The diffusion coefficients of the solutes were calculated from Equation 6 and the previous data. Figure 16 shows

the diffusion coefficients of the solutes as a function of solute radius for P(MMA-g-EG) membranes containing PEG grafts of molecular weights 200. In general, diffusion coefficients decreased as the size of the solute increased. The diffusion coefficients were higher in uncomplexed membranes than in complexed membranes, as expected, and the differences between the two states decreased as the size of the solutes increased. Also, the diffusivity was decreased by the presence of longer PEG grafts. Figure 17 clearly illustrates that longer PEG grafts inhibit solute diffusion more than shorter grafts. The differences between the two types of membranes decreased as solute size also increased.

comparing the effective size cut-offs of uncomplexed membranes containing grafts of molecular weight 200

and molecular weight 400. The diffusion coefficients of solutes through membranes with PEG 200 grafts dropped to near zero at a solute size of 3.6nm, while diffusion coefficients through membranes containing PEG 400 grafts dropped to near zero at a solute size of about 2.8nm. The difference in the approximate cut- off sizes of the two types of membranes was 0.8 nm. As seen in Table 7, PEG grafts of molecular weight 400 were found to be about 0.9nm longer than grafts of molecular weight 200. This result could confirm the theory that the uncomplexed PEG grafts dangled into the mesh space of the polymer network and interfered with solute diffusion.

Further analysis of the diffusion data was done using the equation of Peppas and Reinhart”a:

(26)

An interesting observation relating to the effect of Here, D,,, is the solute diffusion coefficient in the PEG graft length on solute diffusion was noted by swollen membrane, D,,, is the solute diffusion


Poly(methacrylic acid-g-ethylene glycol) hydrogels: CL. Be// and N.A. Peppas 1215

P 2.0 - E 0, u a= 8 0 z 7.0 -

2 I a

0.0 ’ ’ ’ ’

0 10 20 30

Solute Radius, r(A)

40 50

Figure 17 Effect of PEG graft length on diffusion coefficient as a function of solute radius in P(MAA-g-EG) membranes containing 8mol% PEG grafts: 0, graft molecular weight =200; n , graft molecular weight =400.

coefficient in pure water, kI and k2 are structural parameters of the polymer-water system, Q, is the degree of swelling of the membrane, r, is the radius of the diffusing solute, &i= is the molecular weight between cross-links, g, is the molecular weight of the non-cross-linked polymer (= 19,600 here) and &if is the theoretical molecular weight between cross-links, below which diffusion of a solute of size r, could not occur.

According to this theory, a plot of In (D,,/D,,) versus rz should yield a straight line. Figure ~8 shows that diffusion results through uncomplexed P(MAA-g-EG) membranes of molecular weight 200 and 400 fit the model. P(MAA-g-EG) membranes containing PEG grafts of molecular weight 200 adhered to the predictions of the Peppas-Reinhart theory better than those containing PEG grafts of molecular weight 400. Longer PEG grafts interfered with solute diffusion to a higher degree than shorter grafts, and this theory cannot account for this effect. In the uncomplexed state, PEG grafts dangling in the mesh space of the polymer effectively reduced the mesh size of the network, thus reducing the diffusion coefficients of solutes through the network. From these results, the longer PEG grafts of molecular weight 400 reduced the effective mesh space of the network and lowered the solute diffusion coefficients to such an extent that deviation from the Peppas-Reinhart theoretical predictions was seen.

Results for complexed P(MAA-g-EG) membranes could not be analysed using this theory because the Peppas-Reinhart model was developed for highly swollen membranes such as P(MAA-g-EG) membranes in the uncomplexed state. Complexed P(MAA-g-EG) membranes were not highly swollen and, thus, their behaviour deviated from that predicted by this theory. Figure 19 shows the Peppas-Reinhart model fitted by taking into account the swelling ratio of the membranes. Again, the results for uncomplexed membranes were predicted by the theory, whereas the behaviour of the complexed membranes deviated from

2.0

3 0.0 n”

‘E

c +

-2.0

-4.0

Figure 18 Peppas-Reinhart model fitted to diffusion results of P(MAA-g-EG) membranes containing 8mol% PEG grafts: 0, molecular weight of grafts = 200; n , molecular weight of grafts = 400.

2.0 -

0 50 100 150 200 250 300

I,’ I (Q-1)

Figure 19 Peppas-Reinhart model fitted to diffusion results (membrane swelling ratio incorporated) of uncomplexed P(MAA-g-EG) membranes containing 8mol% PEG grafts of molecular weight 200.

the theory because of the low swelling ratios found in the complexed state.

Permeation of solutes under dynamic pH conditions

Another type of permeation study involved the diffusion of solutes through P(MAA-g-EG) membranes under changing pH conditions using some of the smaller solutes that showed good membrane permeation in the equilibrium diffusion experiments. These studies were performed on membranes containing PEG grafts of molecular weight 200 since these membranes showed the largest permeability coefficients in the equilibrium diffusion experiments.

Figures 20 and 21 show the amount of lysozyme that permeated through P(MAA-g-EG) membranes under changing pH conditions. In Figure 21, the membrane was initially in the uncomplexed state at a pH of 7 and lysozyme permeated the membrane at a rate of



0.30

0.15

0.0

4 1 7 I 4 1 7 PH I II I I] I I II

I I I

I I I

I I I

I I I

I I I

I I I (3)

membrane _ cracked _

0 50 100 150 200 250 300 350 400

Time (min)

Figure 20 Amount of vitamin 81.2 permeated through P(MAA-g-EG) membranes containing 8 mol% PEG grafts of molecular weight 200 as a function of time and pH. Membrane initially swollen in pH 4. Rates (mgmin-‘): (1) 4.5 x 10-5, (2) 6.6 x 10-4, (3) 4.5 x 10-5.

7 4 7 7 0.30 1 141 PH

g

II I I I II )I I

I I I I

0.0

I I I

I I I I

I I I I I I I I

I I I(4) 1 (5) .

II I II II II I

0 100 200 300 400 500 600 700

Time (min)

Figure 21 Amount of lysozyme permeated through P(MAA- g-EG) membranes containing 8 mol% PEG grafts of molecular weight 200 as a function of time and pH. Membrane initially swollen in pH 7. Rates (mgmin-‘): (1) 4.3 x 10m4, (2) 2.0 x 10--4, (3) 0.0, (4) 2.1 x 10-4, (5) 0.0.

4.3 x 10m4 mgmin-‘. When the pH was changed to 4, the rate of permeation dropped to 2.0 x 10e4 mg min-’ because the network collapsed. When the pH was returned to 7, the permeation rate was close to zero. This was attributed to the size of the lysozyme solute and the type of permeation cells used. In pH 4, the membrane in the diffusion cells shrank and the permeation of lysozyme was small. Upon decomplexation in pH 7, the polymer chains did not rearrange enough within the confined space of the diffusion cells to allow passage of the lysozyme solute. When decomplexation occurred, the PEG grafts were dangling in the mesh space of the network, and the network did not expand enough during the experiment to allow free space available for the diffusion of the lysozyme.

Figure 22 shows the same type of results for a

P(MAA-g-EG) membrane which was initially in the complexed state (pH =4). In the collapsed state, lysozyme permeated the membrane at a low rate of 1.2 x 10e4 mgmin-‘. When conditions were changed to pH 7, the permeation rate of lysozyme fell to zero, as seen in the other lysozyme experiment (Figure 2~). Again, this was attributed to the inability of the chains to rearrange enough upon decomplexation in the diffusion cells to accommodate the lysozyme molecules, as described above. This behaviour repeated itself over two more pH changes, as seen in Figure 22. Results similar to those obtained with lysozyme were obtained with the larger chymotrypsinogen.

Separation studies

The final type of permeation studies performed involved the diffusion of two solutes simultaneously through P(MAA-g-EG) membranes. These studies were done on membranes containing PEG grafts of molecular weight 200 that were swollen in either pH 4 or pH 7 solutions.

Figures 23 and 24 show the separation of chymotrypsinogen and FITC dextran in uncomplexed and complexed membranes. In the uncomplexed state (Figure 23), both solutes permeated the membrane, although the amount of chymotrypsinogen permeated was about 10 times higher than that of the FITC dextran because chymotrypsinogen is a much smaller molecule than FITC dextran.

Figure 24 shows that in a complexed membrane, permeation of dextran was completely stopped while chymotrypsinogen was still able to diffuse through the polymer network. The amount of chymotrypsinogen permeating through the complexed membrane was about 2.5 times lower than that permeating through the uncomplexed membrane. The results of these studies indicated that separation could be achieved using pH- sensitive P(MAA-g-EG) membranes.

4 7 4 7 0.30

PH

8 II I I I I I I

E I I I

0 100 200 300 400 500 600

Time (min)

Figure 22 Amount of lysozyme permeated through P(MAA- g-EG) membranes containing 8 mol% PEG grafts of molecular weight 200 as a function of time an! pH. Membran: initially swollen in BH 4. Rates (mg min- ): (1) 1.2 x lo- ; (2) 0.0, (3) 2.4 x lo- , (4) 0.0.

Biornakrials 1996, Vol. 17 No. 12

Poly(methacrylic acid-g-ethylene glycol) hydrogels: CL. Be// and N.A. Peppas 1217

0.0050 z

g = 0.0040 - 0 a

0' 0 b 0 h 0.0030 - u" 0 d l

l

= 0.0020 - 6 % l

P t 0.0010 -0 B 0"

0.0000 u .' . ' n ' n ' z I

0 50 100 150 200 250 300 350 400

Time (min)

Figure 23 Concentration of solutes in receptor cell as a function of time for uncomplexed (pH =7) P(MAA-g-EG) membranes containing 8mol% PEG grafts of molecular weight 200: 0, chymotrypsinogen; n , FITC Dextran 4400.

0.0000

0 50 100 150 200 250 300 350 400 lime (min)

Figure 24 Concentration of solutes in receptor cell as a function of time for complexed (pH=4), P(MAA-g-EG) membranes containing 8mol% PEG grafts of molecular weight 200: 0, chymotrypsinogen; n , FITC Dextran 4400.

CONCLUSIONS

We focussed on the synthesis of complexing graft copolymers of PMAA and PEG and the characterization of the pH sensitivity of these materials in relation to their use as membranes for controlled drug delivery and separations. In characterizing the environmentally sensitive behaviour of P(MAA-g-EG) hydrogels for these applications, several parameters were important. These parameters included the equilibrium swelling behaviour and network mesh size under various conditions, the swelling behaviour and mesh size under changing conditions, the diffusional mechanisms of water transport during swelling, the permeability of the membranes under a variety of conditions, the diffusive characteristics of certain solutes through the mesh space of the polymer network, and the mechanical behaviour of the hydrogels.

The P(MAA-g-EG) hydrogels showed pH-sensitive swelling behaviour due to the formation and dissociation of complexes. This interpolymer complexation

was due to hydrogen bonding between the hydrogens on the carboxylic acid groups of the PMAA and the oxygens on the PEG chains, and resulted in pH- sensitive swelling behaviour. The complexation formed only at a pH low enough to ensure substantial protonation of the carboxylic acid groups. At low pH vlaues, the complexes formed, resulting in increased hydrophobicity in the polymer network. Thus, the networks did not swell to a high degree. However, at higher pH values, thee acid groups became ionized, and the hydrogen bonding broke down. As a result, at high pH, the networks swelled to a high degree because of the electrostatic repulsion produced within the network.

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