Polysulfone and polyvinyl pyrrolidone blend membranes with reverse phase morphology as controlled release systems: experimental and theoretical studies

Journal of Membrane Science 227 (2003) 23–37

Polysulfone and polyvinyl pyrrolidone blend membranes with reverse phase morphology as controlled release systems: experimental and theoretical studies夽 Rajarshi Bhattacharya, T.N. Phaniraj, D. Shailaja∗ Organic Coatings and Polymers Division, Indian Institute of Chemical Technology, Hyderabad 500007, India Received 20 December 2002; received in revised form 2 July 2003; accepted 25 July 2003

Abstract Blend membranes of poly(bis phenol–A-ether sulfone) (PSF) and poly(n-vinyl pyrrolidone) (PVP) in ratios (90:10 to 10:90; with increments of 10) were prepared via solution casting technique. The membranes were characterized using X-ray diffraction (XRD) and scanning electron microscopy (SEM). It was found that the blend is immiscible having the major phase of the blend homogeneously dispersed in the continuum of the minor phase indicating the presence of “reverse phase morphology” (RPM) by SEM analysis of the dissolution treated membranes. The interaction parameter χPVP/PSF was calculated and the ternary phase diagram with tentative spinodal along with the super-imposed experimental cloud points has been illustrated. The symmetric spherical geometry of the dispersed phase was explained theoretically with the help of the Flory Huggins Theory. The performance of these membranes as rate controlling membranes in controlled release applications was studied by coating them on paracetamol tablets and the effect of the ratio of PVP in the blend membrane on the rate of drug release was monitored. Models of mass transfer employing Fickian principles at constant temperature and pressure were elucidated to support the experimental findings. The predicted models were found to be in excellent agreement with the experimental release profiles. © 2003 Elsevier B.V. All rights reserved. Keywords: Barrier membranes; Controlled release; Drug permeability; Water sorption and diffusion; Reverse phase morphology

1. Introduction The process of blending has wide applications, as it is a versatile method to tailor materials for specific end uses [1,2]. Blending techniques of immiscible polymers in this regard has received erstwhile emphasis; especially the membranes consisting of high molecular weight polymers. Blends comprising of water soluble and water insoluble polymers are known 夽

IICT Communication No. 021105. Corresponding author. Tel.: +91-40-719-3991; fax: +91-40-716-0387. E-mail address: [email protected] (D. Shailaja). ∗

to give unique swelling properties to the membranes prepared, by solution casting technique or thermal gelation [3–5]. Polymer blends having ternary systems comprising of the two polymers and the solvents are explored extensively to study the influence of their phase behavior on the properties of the blend [6–8]. Research work carried out so far throws some light on the distinct morphologies observed in a persistent three-phase system [9]. Hobbs et al. observed the encapsulations among the minor components in the system, resulting in features resembling core shells. Kim et al. [10] studied the in situ kinetic behavior during asymmetric membrane formation via phase inversion technique using Raman spectroscopy. The effect of

0376-7388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2003.07.014

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viscosity and interfacial interaction parameter χ is pronounced in the process of compatibilization. Hemmati et al. [6,7] probed ternary phase systems and demonstrated the role of interfacial tension and melt viscosity on the appearance of core shell encapsulations in PP/PS/rubber system. Another concurrent investigation by the same authors demonstrated the influence of composition of the different components on the size of the dispersed phase. Polymeric membranes with symmetric geometry find avid use in the field of controlled release technology and are used with consequent success. Congruent geometry of the membranes can result in controlled release close to zero order. Polymeric drug reservoirs score over conventional drug delivery systems due to the localization of drug action to those tissues requiring treatment leading to maximum therapeutic response. Zero order release is an excellent way of enhancing the patient compliance to a particular drug and helps eliminating the problem of multiple dosage and side effects [11]. This can be attained more effectively using blend membranes having “reverse phase morphology” (RPM) especially in reservoir type controlled release systems. The drug diffusion process obeys fundamental laws of “mass transfer”. Although several researchers are working towards achieving drug delivery systems with zero order release, the method of using reverse phase morphology for the same has not been extensively utilized. The characterization and morphology of ternary blended systems, exhibiting reverse phase morphology has so far not been meticulously probed. The present work therefore is aimed at the preparation of poly(bis phenol–A-ether sulfone) (PSF)/poly(n-vinyl pyrrolidone) (PVP) blend membranes and their characteristic morphology was studied using scanning electron microscopy (SEM) and X-ray diffraction (XRD). The utility of these membranes with specific morphology as rate controlling membranes was studied by coating them over paracetamol tablets to monitor their release profiles in aqueous medium. The quantitative estimation of the drug released was done experimentally and a plausible theoretical model complementing the experimental observations has been presented. The coexistence of the two phases in the polymer blend was theoretically explained with the aid of Flory Huggins Theory. The occurrence of the characteristic reverse phase morphology of the membranes

was explained theoretically from the point of view of viscosity, interaction parameter and surface charge on the polymers. The behavior of water soluble and water insoluble polymers in solution was considered to be analogous to that of an emulsion. 2. Materials The materials used in the preparation of blend membranes are (1) polyvinyl pyrrolidone from Aldrich and its Mw is 1,60,000. Polysulfone used was Udel 1700 from Amoco (2). Dichlromethane (DCM) solvent was purchased from SD Fine Chemicals, India. 2.1. Membrane preparation Appropriate amounts of PSF/PVP depending on the weight percent were taken and a 5% (w/v) solution of the blends and pure polymers were prepared dissolving in dichloromethane as solvent. Sufficient time was given for the polymers to dissolve (12 h) and then solutions were cast over mercury at room temperature. After 12 h the dry films were removed and kept in a vacuum oven at 45 ◦ C for another 6 h. The thickness of the dry film was found to be 110 ± 10 ␮m when measured with a dial gauge. 2.2. Solution viscosity and cloud point measurement The viscosity of the dilute pure polymer solutions in DCM was measured using Ubbelhode viscometer (Schott, Gerate, Germany) at a constant temperature of 25 ◦ C. The viscosity of the PVP was found to be 1.95 dl/g and that of PSF was 1.25 dl/g. The cloud points of the casting solutions were obtained by noting the volume fraction of the solvent evaporated at the time of turbidity appearance in the otherwise clear solutions. 2.3. Preparation of buffer solution The buffer was prepared by mixing appropriate amounts of sodium dihydrogen orthophosphate (0.2 mol/l) and disodium hydrogen phosphate (0.2 mol/l) which resulted in a solution of 7.4 pH (physiological pH). Solution ‘X’ was prepared by dissolving 6.97 g of sodium dihydrogen orthophosphate

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in 250 ml of distilled water added. Taking 7.098 g of disodium hydrogen phosphate in 250 ml distilled water made solution ‘Y’. Nineteen milliliters of ‘X’ and 81 ml of ‘Y’ were mixed and made up with 200 ml of distilled water, which resulted in a solution of pH 7.4. The pH was measured using a GLOBAL DPH 500 pH meter.

25

sured using a dial gauge. In order to obtain the above thickness, several concentrations were experimented. These tablets were dried in an oven at 40 ◦ C, and further dried under vacuum at 50 ◦ C for 48 h to remove traces of the solvent (DCM). Weight of the polymer required for coating a tablet was 15 ± 1 mg. 2.6. Calibration plot

2.4. Dissolution treatment of the membranes The buffer solution was taken in a beaker and kept in a USP20 dissolution rate tester. The tester is filled with water to a prescribed height. The temperature of the water bath was set at 37 ◦ C. Samples of 2 cm × 2 cm were taken and immersed perpendicularly in the beaker hooked to a copper wire. The paddle speed was set at 13.089975 rad/s (125 rpm) to ensure proper mixing. Samples were subjected to dissolution for 4 h, such that the water soluble PVP gets dissolved in the medium. After 4 h, the samples were taken out of the respective solutions and were submitted to SEM, to study the effect of treatment on the membrane morphology. 2.5. Polymer coating of the tablet Release studies were done using paracetamol tablets coated with polymer solution by immersion coating method. In this method, 5% (w/v) solution of the polymer blend was taken in a porcelain crucible and each tablet was dipped in the solution to give a coat of thickness 150 ± 10 ␮m, which was peeled and mea-

The stock solution was prepared by dissolving one paracetamol tablet (500 mg) in 250 ml of acid buffer. Solutions of appropriate dilutions were prepared and the optical densities of various concentrations were measured using a Hitachi U2000 spectrophotometer at 296 nm which is the λmax of the drug (acetaminophen) present in the paracetamol tablet. A calibration plot is shown in Fig. 1, by plotting concentration versus optical density. 2.7. Release studies Coated tablets were taken in beakers containing 250 ml buffer and kept in a shaker water bath maintained at 37 ◦ C and 13.089975 rad/s (125 rpm). The release study for each composition was done in triplicate. Periodic assays of samples after every half an hour were taken by pipetting out 5 ml of the buffer and quickly placing the tablet in a beaker with fresh solution of buffer. The samples were assayed by UV spectrophotometer set at 296 nm. The release characteristics are observed for a period of 8 h. A plot of dc/dt versus t was plotted to study the release kinetics.

1.8 y = 0.0033x

1.6

2

R = 0.9996

absorbance

1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

100

200

300

400

500

600

conc (ppm)

Fig. 1. Calibration plot of acetaminophen drug concentration vs. absorbance. Line of best fit: y = 0.0033x and R2 = 0.9996.

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2.8. Scanning electron microscopy Samples of dimension 10 mm × 10 mm were mounted on aluminum stubs using double cellophane tape and these samples were gold coated using a HUS-GB vacuum evaporator. The coated samples were viewed in a Hitachi S-520 scanning electron microscope at an acceleration voltage of 10 kV. 2.9. X-ray diffraction Samples of 3 cm × 2 cm were submitted for X-ray analysis to study the miscibility of blends. A Seimens D-5000 powder X-ray diffractometer was used with a 2.2 kW sealed copper tube as source and a graphite crystal as monochromator. 3. Results and discussions 3.1. Blend morphology The membranes of the pure polymers appear to be homogeneous smooth and transparent. Some of the blend membranes look turbid may be due to

the sensitivity of PVP to moisture and also because of the immiscible nature of the two polymers. The SEM pictures of the pure and blends are shown in Fig. 2A–H. The SEM pictures of the blends were smooth and up to 70:30 (PSF:PVP) blend. A phase separation of the PVP in the PSF matrix was visible from 60:40 (PSF:PVP) blend onwards as seen in Fig. 2D. The number of the spherical domains of the dispersed phase increased with increasing content of the PVP in the blend composition. The average size of the PVP domains was in the range of 3–5 ␮m in all the compositions. In 50:50 blend, a roughness of the continuous phase was found, showing the possibility of exchange of phases of the two polymers. However, an exchange of phases was not noticed since the number of the dispersed spherical domains increased with further increase in the PVP content up to 10:90 (PSF:PVP). The domains of 6 ␮m size are seen in the 10:90 (Fig. 2G) blend indicating not only the increase in the number but also the size of the domains. Had a phase exchange taken place, the SEM pictures from 40:60 to 10:90 would have had similar number of dispersed spherical domains to that of the 60:40 to 90:10 blends. This indicates non-occurrence of a phase exchange even though the content of the PSF was lower

Fig. 2. Scanning electron micrographs (magnification 5.00K) of pure and PSF/PVP blend membranes: (A) pure PSF; (B) (PSF/PVP) 90:10; (C) 70:30; (D) 60:40; (E) 50:50; (F) 30:70; (G) 10:90; (H) pure PVP polymer.

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Fig. 3. Scanning electron micrographs (magnification 5.00K) of blend membranes of PSF/PVP treated in buffer medium of pH 7.4 after 3 h. (A) PSF/PVP (90:10); (B) 80:20; (C) 70:30; (D) 10:90.

in the blend that still remains as a continuum of the membrane. Such a behavior is known as reverse phase morphology, a condition of the polyblend wherein the minor component forms the continuous phase and the major component a dispersed phase [12]. In order to confirm the RPM, the SEM of the membranes treated with a buffer were taken to observe the morphological changes due to dissolution of the PVP portion of the membranes. The figures of the treated membranes are shown in Fig. 3A–D. The pores formed were of the same size of the domains which are seen in the untreated membranes. Pores were noticed even in the 90:10 and 80:20 blends although heterogeneity of the phases was not seen in the corresponding untreated membranes. This indicates that the PVP is present as dispersed phase coexisting with PSF in all compositions of the blend. The number and the size of the pores increased with increase in the content of PVP of the blend. In case of an exchange of phases in the 50:50 blend, the picture would have shown a porous behavior of the continuum along with the pore formation in the dispersed phase showing an interpenetrating bicontinuous phase. The absence of this feature accords the absence of conversion to normal phase at 50:50. However, the SEM pictures of 60:40 onwards could not be taken since the film was not intact like others on treatment in buffer solution. This could be mainly because of the occurrence of the PVP domains in more than a single layer leading to non-uniformity and agglomeration of the spheres that causes the irregular shaped PSF pieces of the membrane to fall apart. The phase morphology of the PSF/PVP blend membranes has been investigated using XRD and SEM. The XRD patterns of the pure polymers show that they are of amorphous nature as shown in Fig. 4A–G.

The PSF diffraction patterns do not show any particular diffraction peaks with high intensity, whereas the PVP shows a weak peak between 10 and 15◦ Bragg angle. All the blend compositions show a broad and diffuse peak. This indicates that PSF/PVP blends are coexisting over the entire range of composition having an ordered arrangement of the two phases, which is also seen in the SEM figures where presence of a uniform distribution of phases is noticed. As the PVP content of the blend increases it was observed that the area under the peak decreases and from Bragg angle 20◦ the peak shifts to 10◦ which is the diffraction peak of pure PVP polymer. This could be due to the agglomeration of the PVP spheres when its content in the blend increases beyond 1:1. The d spacings are found to become larger indicating the presence of some phase segregation in the blend with increasing PVP content of the blend. In spite of the phase separation, the broad intense peak in all the blends in comparison to the pure polymers indicates the presence of an ordered structure of the coexisting phases which is also supported by the SEM pictures. 3.2. Theoretical accounting for blend morphology 3.2.1. Phase separation An approximate calculation of the spinodal for the ternary system comprising of two polymers and a single solvent was done following the method of Scott [13,14]. The interaction parameter between the PVP and PSF was calculated using the Scott’s equation, χAB(cr) ≈ 16 (δP1 − δP2 )2

(1)

where δP1 is the solubility parameter of polyvinyl pyrrolidone (22.00 MPa), δP2 the solubility parameter

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of polysulfone (20.66 MPa), and χAB(cr) was found to be 0.29. Polymer solvent interaction parameter χpoly/sol was calculated for both PVP and PSF separately, using the relation: (1 + x0.5 )2 2x where ‘x’ is the volume ratio of the polymer repeat unit of the respective polymer to 1 mol of the solvent, i.e. dichloromethane [14]. χPVP/DCM was calculated to be 0.5155 and χPSF/DCM was found to be 0.5244. The points of intersection of the spinodal on the PVP/PSF axis in the ternary phase diagram can be calculated from the

χpoly/sol =

following equation [14]:
 1 φ0 + (χ02 − χ01 − χ12 )φ1 X
 1 + (χ01 − χ02 − χ12 )φ2 × Y + φ1 {1 + (χ12 − χ01 − χ02 )φ0 }
 1 + (χ01 − χ02 − χ12 )φ2 × Y + φ2 {1 + (χ12 − χ01 − χ12 )φ0 }
 1 × + (χ02 − χ01 − χ12 )φ1 = 0 X

(2)

by setting φ0 = 0 and using φ1 + φ2 = 1.

Fig. 4. X-ray diffraction of pure PVP, PSF polymers and their blends: XRD of pure polysulfone polymer; PSF/PVP (90:10) blend membrane; PSF/PVP (70:30) blend membrane; PSF/PVP (50:50) blend membrane; PSF/PVP (30:70) blend membrane; PSF/PVP (10:90) blend membrane; pure PVP membrane.

R. Bhattacharya et al. / Journal of Membrane Science 227 (2003) 23–37

29

Fig. 4. (Continued ).

φ1 and φ2 represent the volume fractions of PSF and PVP, respectively. The critical solution point is calculated from this equation of Scott [14], i.e.

χAB(cr)

1 = 2




1 1 + 1/2 1/2 X Y

2


1 1 − φs

 (3)

Substituting the value of φs obtained in the equation of the spinodal   1 1 1 1 + X−2χPSF/DCM + Y − 2χPVP/DCM φs φ1 φs φ2   1 − +χPSF/DCM +χPVP/DCM − χPSF/PVP = 0 φs



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Fig. 4. (Continued ).

R. Bhattacharya et al. / Journal of Membrane Science 227 (2003) 23–37

31

1.0

DICHLOROMETHANE 1.00 0.930

0.8

0.805 0.690 one 0.575 phase zone

0.6

critical solution point

0.460

0.4

0.345

0.2

0.230 0.115

0.0 0.0 0.1 Polysulfone

immiscible zone

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1.0 Polyvinylpyrolidone

Fig. 5. Cloud point curve with approximate spinodal (→); calculated spinodal (䊏); cloud points (—) experimental cloud point fit with polynomial regression y = −0.23243 + 2.6219x − 2.50195x2 . For explanation of construction see Appendix A.

The points of intersection of the spinodal on the PVP/PSF axis were obtained as depicted in Fig. 5 where a tentative spinodal curve is obtained by fitting these three points in a smooth curve. Simultaneously, an experimental spinodal is also superimposed in the same figure, which was obtained by taking the experimental cloud points of the PSF/PVP solutions in Table 1. The spinodal behavior confirms the immiscibility of the two phases of the blend in most of the compositions. The dilute solutions are clear and as they get Table 1 Critical volume fractions of DCM corresponding to the cloud points PVP (%, v/v)

PSF (%, v/v)

Critical volume fraction of DCM (v/v)

10 20 30 40 50 60 70 80 90

90 80 70 60 50 40 30 20 10

0.14 0.2 0.3 0.36 0.43 0.52 0.43 0.46 0.4

We find a close match of the theoretical curve with that of experimental.

concentrated while formation of films on casting turn turbid due to the immiscibility of the two polymers. The blend films are therefore opaque in comparison to the pure ones but are smooth may be due to the uniformly distributed phases that coexist together making the blend a compatible one. The phase rule enunciates that in the emulsion the dispersed phase can be conveniently increased upto a volume fraction of 70% without phase inversion [15]. The blend membranes have shown a reverse phase morphology as seen in the SEM pictures with the major phase dispersed in the minor phase of the blend. 3.3. Theoretical explanation for the characteristic spherical shape of the dispersed phase The appearance of the characteristic spherical morphology of the PVP phase dispersed homogeneously in the continuum of the PSF matrix has been explained by taking an analogy of the emulsion wherein PVP domains are dispersed in the PSF/DCM solution. This is by virtue of greater surface tension and higher viscosity of PVP in comparison to PSF. The PVP molecules adhere to one another by a process comparable to flocculation in liquid medium. This process

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can be treated as the diffusion of a spherical particle of PVP in the PSF and DCM medium that has a finite viscosity (η). The rate of reduction of particles due to flocculation can be written as [16] 1 1 − = βr t N N

(4)

where N is the number of particles initially, N the number of particles in the end of flocculation, and βr is the rate constant of flocculation. PVP is normally used as a colloidal stabilizer in most of the polymer reactions, mainly due to the presence of the lone pair of electrons on N and O of the PVP molecules contributes to the surface charge on the molecules. The surface charge of PVP plays an important role in rendering the stability for PVP spherical domains in the blend solution with significant repulsion and therefore not allowing them to flocculate. The repulsion energy between any two particles having surface charge [16] can be given as   64NkTΥ 2 φr = exp(−dκ) (5) κ where d is the distance of separation, N the number of particles in the system, κ the Debye–Huckel approximation parameter, k the Boltzmann constant, T the absolute temperature, Υ = [exp(zeψ/2kT) − 1]/[exp(zeψ/2kT) + 1], z the valence number of PVP, e the electronic charge = 1.6 × 10−19 C, and ψ is the potential at the point of closest approach of another globule; the distance measured from the center of the globule under consideration(taken to be a constant of approximately 25 mV). The final expression for the potential energy of repulsion can be calculated by numeric integration [16]. It is given by   64ΠRNkTΥ 2 φr = exp(−sκ) (6) κ2 Hence, maximum repulsion occurs at rmin = s, when φr = φm : The stability of emulsions is further accounted for by a term stabilization ratio which is given by    ∞ φr −2 r dr exp (7) W = 2R kT 2R

3.4. Approximate calculation of W We generate a Taylor series expansion of φr , rmin = s:     ∂φ (r − s)2 ∂2 φ + φr ≈ φm +(r − s) + ··· ∂r m 2 ∂r 2 m Taking these terms only and considering the fact that at maxima ∂φ/∂r = 0. On substituting it in Eq. (7), we get:   ∞ φm W = 2R exp exp kT 2R 
  (r − s)2 (∂2 φ/∂r 2 )m −2 × (8) r dr 2 kT Now we consider the fact that W falls off rapidly to zero on either side of the maxima, then the exponential term within the integral contributes most significantly of all (as a potential weight function) to converge the integral to zero. Hence, the term r−2 is approximated −2 as rmin . Denoting the expression {(∂2 φ/∂r 2 )m /kT)/2} as a and replacing the variable (r − s) by t and thereby changing the lower limit from 2R to 2R − s, we get the final form as,    ∞ 2R φm W= exp exp(at2 ) dt 2 kT rmin 2R–S Since the dimensions of the spherical domains are in the order of some microns, we approximate the term 2R − s to be almost 0, with a little error. The integral now becomes familiar to the known gamma function where n = 0:

 ∞ 1 Π n 2 x exp(ax ) dx = , when n = 0 2 a 0 In Eq. (7), in order to get the area under the energy curve on both sides of the maxima we multiply with 2. Eq. (8) now takes the final form as     2R φm Π W= exp (9) 2 kT a rmin The rate constant for slower flocculation βs is hence given as βs =

βr √ 2 (2R/rmin )exp(φm /kT) Π/a

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It is evident from this final expression that there is a retardation in the rate of flocculation and as the number of particles increase (φm ) also increases and βs decreases further. Thus, it can be theoretically inferred that as the amount of PVP increases the number of spherical domains also increase as observed from the SEM pictures. If other factors are assumed to remain constant, Eq. (6) shows that φm varies linearly with the no. of particles in the system and becomes double as the concentration is doubled if the constants are taken to be unity. This explains the increase in the formation of spherical PVP portions as the PVP content increases as seen in SEM pictures causing the occurrence of RPM and also the stability of the dispersed PVP phase in the blends. 3.5. Controlled release performance The application of the blend membranes in controlled drug delivery as rate controlling membranes was studied by coating the polymer solutions on to a model drug (paracetamol). Effect of composition variation on the drug release was studied to find the optimum performing coating composition that can give release close to zero order. The aim of the coating is to reduce the intake of more number of doses providing the biologically effective concentration in therapeutic level. The change in concentration for a particular interval of time (dc/dt) versus time (h) was plotted for (PSF/PVP) 90:10, 80:20, 70:30, 60:40 and 50:50 compositions. The release profiles are shown in Fig. 6. It can be seen from the above figure that all compositions of blends show an initial burst effect, which can be attributed to the greater concentration differential present at the start of the process. After this initial burst effect, which takes place in

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the first half an hour the drug concentration level in the medium drops and becomes steady for rest of the period. The drug releases in a controlled fashion for about 8 h and the drug released increases with the increase in PVP content of the blend. Thus, the 50:50 sample showed maximum release due to increased number and size of the pores in comparison to the 90:10 sample which showed the minimum. An exponential decrease of the drug released is seen with increase in the content of the PSF of the blend.

3.6. Theoretical explanation of the drug release The drug is presumed to dissolve slowly into the permeating aqueous phase and to diffuse out through swollen PVP and later through the pores formed due to its dissolution [17]. The release of the drug in to the aqueous medium involves two steps: • Step 1: Swelling process of PVP (a) Sorption of water in to the polymer membrane causing dissolution of the drug into the sorbed medium. (b) Diffusion of the drug in to the water present in the swollen PVP portions of the blend membrane until equilibrium is attained. • Step 2: Release of the drug from the tablet into the medium that comes in contact with it after pore formation in the coated membrane. 3.6.1. Step 1 A schematic representation of the swelling process is given in Fig. 7. It elucidates the simultaneous processes that take place as described above. 3.6.1.1. Process 1. The release of the drug into water explicitly fits in to the Fick’s second law of diffusion, i.e.   ∂c ∂ ∂c = D ∂t ∂x ∂x

Fig. 6. Effect of blend composition on the release of acetaminophen in pH 7.4 buffer at 37 ◦ C (ratios indicate PSF/PVP).

(10a)

where D is the diffusion coefficient henceforth in all the systems in our calculations is taken as constant. Obtaining a power series solution for Eq. (10a) we get:

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R. Bhattacharya et al. / Journal of Membrane Science 227 (2003) 23–37

Fig. 7. Pictorial representation of the swelling process.

C =

4C  1 Πx sin(2m + 1) exp Π (2m + 1) h   −D (2m + 1)2 Π 2 t × h2

(10b)

where C is the concentration of the drug in the polymeric phase (=εC ), C the solubility of the drug in PVP, ε the porosity of the polymeric membrane, D the diffusivity of the drug in the PVP portion of the blend membrane (=P/S), P the permeability, S is the solubility of the drug in the PVP. 3.6.1.2. Process 2. Assume that the polymer dissolves faster than the drug. The flux of dissolution of polyvinyl pyrrolidone can be taken as split in to two factors: (a) flow of dissolved PVP into external sink or medium; (b) flow of solvent into the polymer membrane. Polymer flux: J¯ p = −Dp

∂C ∂x

(11a)

Solvent flux: J¯ s = −Ds

∂C ∂x

∂C (11c) ∂x ∂C Jsv = −vs Dv (s, p) (11d) ∂x Dv p, s: diffusivity of PVP into medium; Dv s, p: diffusivity of medium into PVP. Since simple dissolution takes place with no volume change:

Jpv = −vp Dv (p, s)

(11b)

where Dp and Ds are the intrinsic diffusivities of PVP and water, respectively. Total volume transfer is given by J × v, where v is the respective specific volumes of the polymer and solvent.

Jpv = Jsv vp cp : volume fraction of the polymer; cp : concentration of the polymer; vp : specific volume of the polymer. Similarly, volume fraction of the solvent = vs cs Since there are only two components we can say that v s cs + v p c p = 1 Differentiating partially with respect to x we get: ∂cp ∂cs vs + vp =0 (12) ∂x ∂x φp and φs are the respective volume fractions of the polymer and water. In the swollen state the polymer has restricted chain segmental mobility [17] where negligible diffusion is possible, Therefore, D ≈ 0; Hence, we have: D = Ds (1 − φs )

(13)

During the process of dissolution of the PVP portion of the polymeric membrane, M is taken as the

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reference or origin and movement of the solvent front is measured from here in terms of a rate of penetration given by ds/dt = ◦ s Assuming Jsv ≈ ◦ s it can be shown that ds ∂c = −Dvs dt ∂x

(14)

¯ 'C [17], On integration and replacing ◦ sl by −vs D and considering that the concentration of the solvent at the border plane between the polymer and the swollen layer to be negligible at the onset of dissolution, we have ¯ D ◦ s= (15) l where l is the thickness of the swollen surface of PVP ¯ is the mutual diffusion coefficient. and D During dissolution, the aqueous solution is stirred at a constant rpm and therefore l is constant. Hence, it can be concluded that ◦ s is a constant, i.e. ◦

s=K

¯ l. where K = D/ On integration of Eq. (14) from 0 to t from the origin we obtain, S = Kt It can be seen from Fig. 8 that h = d − s. Substituting for s by Kt and inserting h in Eq. (10b) we get   Qt 1 8  exp =1− 2 Q∞ Π (2m + 1)2
 −D(2m + 1)2 Π 2 t × (15a) [d − Kt]2

35

[d − Kt]2 when expanded binomially can be approximated as d − 2Kt with slight error. Replacing 2K by K , inserting it in Eq. (15) and differentiating we get    
 1 8  dQt 1 = exp Q∞ dt Π2 (2m + 1)2
 −D(2m + 1)2 Π 2 t × d − K t
 −D(2m + 1)2 Π 2 d × (16) [d − K t]2 Now with increasing ‘t’ it can be clearly seen that the term −D(2m + 1)2 Π 2 t/[d − K t] decreases, therefore the exponential function decreases progressively. Utilizing this function as a weight function coupled to the polynomial −D(2m + 1)2 Π 2 d/[d − K t]2 . It can be concluded that the whole expression for the rate, decreases with increasing time because of the fact that exponential functions converge or diverge more rapidly than algebraic functions. Thus the rate curve exhibits a steep fall as observed in the experimental release curves in the initial half an hour showing a burst of the drug with high optical density. 3.6.2. Step 2 In this part, we can consider that the release mechanism to be analogous to the release of the drug from a slab into water, which is schematically shown in Fig. 8. The solvent in the pore creates a Nernst diffusion layer thus giving rise to a steady concentration gradient. The rate of transport across a plane of unit cross-sectional area can be written as   dQ Ds = (17) (Cs − C s) dt l C s: drug concentration in the matrix at x = 0; Ds : diffusivity of the drug in the tablet matrix. Rate of transport of the drug molecules across the Nernst diffusion layer can also be represented as dQ Da = (C a − C∞ ) dt h

Fig. 8. Pictorial representation of drug diffusion after pore formation.

(18)

where C a is the concentration of drug in the water at x = 0, C∞ the concentration of drug in the water at x = h, Da the diffusivity of the drug in water, K =

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Cs/Ca, where K is the partition coefficient of tablet matrix and water. Equating Eq. (17) and (18) and solving for the unknown C s yields:    dQ Ds Cs Ds h + Da lC∞ = Cs − (19) dt l (Da l/K) + Ds h Release of the drug can also be written as dQ = C dl − 21 Cs dl

(20)

Average value of Cs is taken because, the concentration gradient is a straight line as Fig. 9, C is the total concentration of the drug in the tablet matrix. Taking the time differential and performing the required integrations [17] it can be shown that,

1/2     −Ds hC Ds hKC 2 Q= + + 2Ds Cs Ct Da Da (21) and dQ CDs Cs = dt [(Ds hCK/Da )2 + 2CDs Cst]1/2

(22)

Considering the fact that it takes almost an hour for the drug to completely dissolve in the medium it can be understood that ‘l’ is negligible initially, i.e. for the first 10–15 min of the release. Considering that l ≈ 0, which is negligible while C is large, the term [Ds hCCs/Da Ca ] becomes greater and the rate of release can be therefore approximated as dQ Ca Da = (23) dt h Hence, it can be seen that the mechanism proposed for the release of drug by this mathematical model readily accounts for a steady and constant release of drug through the PVP pores. This finding is in excellent agreement with our observed experimental results for the initial burst effect immediately after the appearance of the pores on the membrane. However, we can see that with elapsing time the term 2CDs Cst becomes significant and cannot be neglected as taken earlier and after some time the constant rate √ can be found to decline, varying with the inverse of t. This behavior of the release pattern can also be seen from the trend in the experimental graph.

4. Conclusions The PVP–PSF blend membranes in various ratios were prepared to study their morphological characteristics and application as controlled release systems. The blends were found to be immiscible due to the hydrophobic and hydrophilic nature of the polymers. However, the membranes were compatible over entire range of compositions showing a very organized arrangement of both the phases with PVP dispersed uniformly in the continuum of the PSF even when it was the major component. Thus showing the reverse phase morphological behavior of the membranes that was confirmed by SEM and XRD studies on both treated and untreated membranes. The controlled release performance of these membranes as rate controlling membranes has proved their utility by showing a constant release after the initial burst effect. A decrease in the release was found with decreasing content of PVP in the polyblend because of the lower number and size of the pores formed. The diffusion process was explained theoretically using Fick’s laws and the exponential decrease in the release with time was accounted for that was found to be in good agreement with the experimental findings. These hydrophobic and hydrophilic blend membranes can be safely used in controlled release applications mainly because of the symmetric geometry with which they are arranged in the membrane. Appendix A The Y axis of the rectangular co-ordinates has been taken as a base to construct the triangular phase diagram using the software ORIGIN. The side of the equilateral triangle has been taken as a projection of the Y axis, since in the present case, φPVP + φPSF + φDCM = 1 (where the φ’s are the respective volume fractions (v/v) and therefore no units are shown. Hence, φPVP = 1 − (φPSF + φDCM ) To construct the cloud point curve and spinodal only two independent variables are needed, while the third one gets automatically fixed. So, with appropriate transformations, an oblique pair of coordinates was generated.

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