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Direct encapsulation of water-soluble drug into silica microcapsules for sustained release applications Jie-Xin Wang a , Zhi-Hui Wang a , Jian-Feng Chen a,b, * , Jimmy Yun c a Key Lab for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029, PR China b Research Center of the Ministry of Education for High Gravity Engineering and Technology, Beijing University of Chemical Technology, Beijing 100029, PR China c Nanomaterials Technology Pte. Ltd., 28 Ayer Rajah Crescent #03-03, Singapore 139959, Singapore Received 10 October 2007; received in revised form 24 January 2008; accepted 14 February 2008 Available online 10 March 2008 Abstract Direct encapsulation of water-soluble drug into silica microcapsules was facilely achieved by a sol–gel process of tetra- ethoxysilane (TEOS) in W/O emulsion with hydrochloric acid (HCl) aqueous solution containing Tween 80 and drug as well as cyclohexane solution containing Span 80. Two water-soluble drugs of gentamicin sulphate (GS) and salbutamol sulphate (SS) were chosen as model drugs. The characterization of drug encapsulated silica microcapsules by scanning electronic microscopy (SEM), FTIR, thermogravimetry (TG) and N 2 adsorption–desorption analyses indicated that drug was successfully entrapped into silica microcapsules. The as-prepared silica microcapsules were uniform spherical particles with hollow structure, good dispersion and a size of 5–10 mm, and had a specific surface area of about 306 m 2 /g. UV–vis and thermogravimetry (TG) analyses were performed to determine the amount of drug encapsulated in the microcapsules. The BJH pore size distribution (PSD) of silica microcapsules before and after removing drug was examined. In vitro release behavior of drug in simulated body fluid (SBF) revealed that such system exhibited excellent sustained release properties. # 2008 Published by Elsevier Ltd. Keywords: A. Interfaces; B. Sol–gel chemistry; C. Infrared spectroscopy; C. Thermogravimetric analysis 1. Introduction Over the past two decades, there has been rapid growth in sustained/controlled drug delivery in the field of modern medication and pharmaceuticals since sustained/controlled release can bring therapeutic and commercial value to health-care products [1]. Among a wide number of materials, micelles liposomes, and polymeric and co-polymeric nanoparticles are widely employed as drug carriers for sustained/controlled delivery. For these organic systems, however, there are some limitations such as poor thermal and chemical stability, rapid elimination by immune system, and clinical defects [2–5]. Recently, there has been increased interest in mesoporous silica materials for use as carriers in controlled drug release due to their several attractive features, such as stable uniform mesoporous structure, high www.elsevier.com/locate/matresbu Available online at www.sciencedirect.com Materials Research Bulletin 43 (2008) 3374–3381 * Corresponding author at: Key Lab for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029, PR China. Tel.: +86 10 64446466; fax: +86 10 64434784. E-mail address: [email protected] (J.-F. Chen). 0025-5408/$ – see front matter # 2008 Published by Elsevier Ltd. doi:10.1016/j.materresbull.2008.02.011

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Page 1: Direct encapsulation of water-soluble drug into silica microcapsules for sustained release applications

Available online at www.sciencedirect.com

www.elsevier.com/locate/matresbu

Materials Research Bulletin 43 (2008) 3374–3381

Direct encapsulation of water-soluble drug into silica

microcapsules for sustained release applications

Jie-Xin Wang a, Zhi-Hui Wang a, Jian-Feng Chen a,b,*, Jimmy Yun c

a Key Lab for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029, PR Chinab Research Center of the Ministry of Education for High Gravity Engineering and Technology,

Beijing University of Chemical Technology, Beijing 100029, PR Chinac Nanomaterials Technology Pte. Ltd., 28 Ayer Rajah Crescent #03-03, Singapore 139959, Singapore

Received 10 October 2007; received in revised form 24 January 2008; accepted 14 February 2008

Available online 10 March 2008

Abstract

Direct encapsulation of water-soluble drug into silica microcapsules was facilely achieved by a sol–gel process of tetra-

ethoxysilane (TEOS) in W/O emulsion with hydrochloric acid (HCl) aqueous solution containing Tween 80 and drug as well as

cyclohexane solution containing Span 80. Two water-soluble drugs of gentamicin sulphate (GS) and salbutamol sulphate (SS) were

chosen as model drugs. The characterization of drug encapsulated silica microcapsules by scanning electronic microscopy (SEM),

FTIR, thermogravimetry (TG) and N2 adsorption–desorption analyses indicated that drug was successfully entrapped into silica

microcapsules. The as-prepared silica microcapsules were uniform spherical particles with hollow structure, good dispersion and a

size of 5–10 mm, and had a specific surface area of about 306 m2/g. UV–vis and thermogravimetry (TG) analyses were performed to

determine the amount of drug encapsulated in the microcapsules. The BJH pore size distribution (PSD) of silica microcapsules

before and after removing drug was examined. In vitro release behavior of drug in simulated body fluid (SBF) revealed that such

system exhibited excellent sustained release properties.

# 2008 Published by Elsevier Ltd.

Keywords: A. Interfaces; B. Sol–gel chemistry; C. Infrared spectroscopy; C. Thermogravimetric analysis

1. Introduction

Over the past two decades, there has been rapid growth in sustained/controlled drug delivery in the field of modern

medication and pharmaceuticals since sustained/controlled release can bring therapeutic and commercial value to

health-care products [1]. Among a wide number of materials, micelles liposomes, and polymeric and co-polymeric

nanoparticles are widely employed as drug carriers for sustained/controlled delivery. For these organic systems,

however, there are some limitations such as poor thermal and chemical stability, rapid elimination by immune system,

and clinical defects [2–5]. Recently, there has been increased interest in mesoporous silica materials for use as carriers

in controlled drug release due to their several attractive features, such as stable uniform mesoporous structure, high

* Corresponding author at: Key Lab for Nanomaterials, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029, PR

China. Tel.: +86 10 64446466; fax: +86 10 64434784.

E-mail address: [email protected] (J.-F. Chen).

0025-5408/$ – see front matter # 2008 Published by Elsevier Ltd.

doi:10.1016/j.materresbull.2008.02.011

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J.-X. Wang et al. / Materials Research Bulletin 43 (2008) 3374–3381 3375

surface area, tunable pore sizes, well-defined surface properties [1,6], nontoxic nature [7], and good biocompatibility

[8,9]. Several research groups have reported on the design of mesoporous silica-based carriers for sustained/controlled

drug delivery systems [10–12]. Furthermore, hollow silica spheres facilitate a high drug storage capacity and excellent

sustained release properties because of their unique hollow core structures as reservoir for active molecules [13,14].

Therefore, in very recent years, much attention has also been focused on sustained drug release from hollow silica

spheres besides mesoporous silica.

Up to now, the encapsulation of drug into mesoporous silica or hollow silica is mainly post-synthesis, that is, the

silica carrier is first synthesized, followed by storage of the drug molecules. The post-synthesis introduction of drug

molecules is commonly achieved by physical adsorption of drug molecules in mesoporous silica or hollow silica with

an immersion method [10–14]. In this case, the pore size of mesoporous silica materials usually determines the size of

the drug molecules that can be adsorbed into mesopores. Accordingly, only a few drug molecules with a small size

could be well entrapped by entering the mesoporous channels or passing through the pores into hollow spaces [15].

Drug molecules with a large dimension larger than the pore sizes are hard to be introduced into hollow spaces.

Therefore, it will be very valuable if a suitable procedure is developed for the good entrapment of drugs with different

dimensions in silica matrix.

The use of emulsions as templates to synthesize hollow silica spheres made it possible to encapsulate drugs directly.

Despite few publications, Fujiwara et al. have succeeded in direct encapsulation of biomacromolecules such BSA and

DNA into hollow silica spheres by utilizing W/O/W double emulsion for the good immobilization of enzyme [16].

Recently, we also found that some drug macromolecules could be included in silica microcapsules directly by

interfacial hydrolysis and condensation of TEOS in W/O emulsion. To the best of our knowledge, it is reported for the

first time that water phase in W/O emulsion is utilized as container for the direct encapsulation and storage of water-

soluble drugs into silica microcapsules for sustained release applications.

In this paper, gentamicin sulphate (GS), which is widely used in osteomyelitis treatment in the form of implanted

controlled release formulations [17–19], was first adopted as an important model drug because of its relatively large

molecule size, water solubility and excellent antibacterial effect. Salbutamol sulphate (SS) was the other selected

water-soluble model drug with large molecule size for verifying the feasibility of this procedure. The as-prepared drug

encapsulated samples were characterized by scanning electronic microscopy (SEM), FTIR, TG, UV–vis spectroscopy,

and N2 adsorption–desorption analyses. Drug release profiles were also determined.

2. Experimental

2.1. Materials

The raw materials of GS and SS were purchased from Furong Raw Drug Company and Shenzhen Xianbang

Chemical Co. Ltd. (China), respectively, which are in accordance with BP2000. The molecular structures of two drugs

are shown in Fig. 1. Hydrochloric acid (HCl) (Beijing Chemical Factory, China), tetraethoxysilane (TEOS) (Tianjin

Fuchen Chemical Reagent Factory, China) and cyclohexane (Beijing Chemical Factory, China) were purchased from

the indicated suppliers. As biodegradable and biocompatible surfactants, Span 80 and Tween 80 (Tianjin Fuchen

Chemical Reagent Factory, China) were used in the experiment. Span 80 and Tween 80 are chemical pure, and others

are analytical pure reagents. Deionized water was used throughout the study.

Fig. 1. Molecular structures of GS (a) and SS (b).

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2.2. Preparation of silica microcapsules encapsulating drug

Silica microcapsules encapsulating drug were derived from the hydrolysis and condensation reaction of TEOS in a

W/O emulsion with the existence of acid as catalyst in the inner water phase. A typical preparation procedure with an

example of GS is described as follows: drug aqueous solution was initially obtained by dissolving 0.2 g of GS raw drug

and 0.04 g of Tween 80 into 2 ml of 2 M HCl aqueous solution. Subsequently, the above solution was added into 50 ml

of cyclohexane solution containing 2.0 g of Span 80. After vigorous agitation for 30 min, 1.865 ml of TEOS was added

into the formed W/O emulsion, and then the mixture was sealed to prevent the evaporation of solvent, stirring for 24 h

at room temperature. The solid was collected by filtration, washed with cyclohexane, and dried at 40 8C at 2 h to avoid

the structure change of drug. Finally, silica microcapsules including drug were achieved after washing with ethanol to

effectively remove the residual surfactants and drying at 40 8C overnight. For comparison, vacant silica microcapsules

were prepared with the same process except the absence of drug in the water phase. In addition, direct encapsulation of

SS into silica microcapsules was also performed in the same procedure including the same amounts and ratios of

reactants except the difference of drug molecules.

2.3. Characterization

The morphology of the as-prepared samples was observed by using a JEOL JSM-6360 SEM. Transmission infrared

spectroscopy spectra were recorded in a BRUKER Nicolet-210 spectrometer. To determine the drug loading amount in

silica microcapsules, TG was performed by a Netzsch STA449C thermal analyzer at a heating rate of 10 8C/min. N2

adsorption–desorption isotherms were obtained on a Micromeritics ASAP 2010 Analyzer, in which the samples were

outgassed first in vacuum at 423 K overnight and the measurements were then carried out at 77 K over a wide range of

relative pressures from 0.01 to 0.995. Specific surface areas and pore size distributions (PSD) were calculated using the

Brunauer–Emmett–Teller (BET) and Barrett–Joyner–Halenda (BJH) models from the adsorption branches,

respectively.

For in vitro release test, the samples were compacted into 0.1 g disks (10 mm in diameter and 1 mm in thickness)

under pressure of 3 MPa. One disk of samples was immersed into 250 ml simulated body fluid (SBF) of pH 7.4 at

37 8C under stirring at a rate of 100 rpm. 5 ml filtrates were withdrawn for analysis at different time intervals and

replaced with the same volume of pre-heated SBF. The concentration of GS was analyzed using the o-

phthaldialdehyde method [20]. The maximum absorbance of gentamicin-o-phthaldialdehyde complex was measured

on a Shimadzu UV-2501 UV–vis spectrophotometer at a wavelength of 333 nm. In addition, SS contents in release

medium were monitored at 276 nm. Each sample was analyzed in triplicate.

3. Results and discussion

Fig. 2 schematically illustrates the procedure for direct encapsulation of water-soluble drugs into silica

microcapsules by the hydrolysis and condensation of TEOS in the interface of W/O emulsion. In this encapsulation

procedure, the formation of silica microcapsules as carriers and the entrapment of drug could be simultaneously

achieved, which would possibly simplify the preparation of drug delivery system. According to the principle, it is

reasonable to deduce that most of water-soluble drugs with different molecular dimensions could be directly

Fig. 2. The schematic procedure for direct encapsulation of water-soluble drugs into silica microcapsules.

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J.-X. Wang et al. / Materials Research Bulletin 43 (2008) 3374–3381 3377

encapsulated in this system. Especially, this procedure is very suitable for the entrapment of drug molecules with large

dimension and other biomacromolecules.

Fig. 3 shows typical SEM images of vacant silica sample and silica microcapsules encapsulating GS and SS,

respectively. The uniform spherical particles with a size of about 5–10 mm and good dispersion were clearly observed.

There was no apparent difference between vacant silica microcapsules (Fig. 3A and B) and drug encapsulated silica

microcapsules (Fig. 3C–F). Some crushed and broken spheres could be observed in Fig. 3(B), (D), and (E), indicating

the nature of hollow silica structure. Furthermore, it was well noted that a large number of small spherical

nanoparticles were obviously found on the internal wall of hollow silica microspheres, as shown in Fig. 3E. The very

possible reason was that GS molecules dissolved in water phase of W/O emulsion separated and formed drug

nanoparticles during the drying process, justifying the feasibility of direct encapsulation of drug into inner cores of

silica microcapsules in this system.

Fig. 3. SEM images of samples (A and B) vacant silica microcapsules, (C–E) silica microcapsules encapsulating GS, and (F) silica microcapsules

encapsulating SS.

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Fig. 4. FTIR spectra of (a) raw GS, (b) silica microcapsules encapsulating GS, (c) silica microcapsules encapsulating GS before washing with

ethanol, and (d) vacant silica microcapsules after calcination.

Fig. 4 displays the FTIR spectra of raw GS, silica microcapsules encapsulating GS, silica microcapsules

encapsulating GS before washing with ethanol and calcined vacant silica microcapsules (the sample was calcined in

air at 823 K for 2 h), respectively. Comparing with curves a and d, it could be seen that there were bands at 1537, 1468,

1387 and 615 cm�1 except the typical bands for silica in curve b, mainly ascribed to the vibrations of the characteristic

groups of GS molecules. This further proved the successful encapsulation of GS into silica microcapsules. Since GS

and SS have little solubility in ethanol, the step of ethanol washing can only remove the surfactant residues. The results

were also confirmed by the disappearance of the bands at 2927, 2854 and 1716 cm�1 corresponding to the residual

surfactants and the existence of the bands for GS, as compared in curves b and c.

Thermogravimetric analysis (TGA) curves of vacant silica microcapsules, silica microcapsules encapsulating GS

and silica microcapsules encapsulating GS before washing with ethanol were depicted in Fig. 5. The occurrence of a

large weight loss before 120 8C was mainly due to the incomplete removal of the mixture of water and ethanol in

samples dried at 40 8C. By the comparison of curve a with curve b, the encapsulation amount of GS in silica

microcapsules was calculated to be about 15.7 wt%, which corresponded to the weight loss between 200 and 800 8Cby deducting the weight loss of vacant silica microcapsules in the same temperature range. Relative to curve b, curve c

Fig. 5. TG curves of (a) vacant silica microcapsules, (b) silica microcapsules encapsulating GS, and (c) silica microcapsules encapsulating GS

before washing with ethanol.

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J.-X. Wang et al. / Materials Research Bulletin 43 (2008) 3374–3381 3379

Fig. 6. N2 adsorption–desorption isotherms (inset) and the corresponding pore size distributions of silica microcapsules before (a) and after (b)

calcination.

Fig. 7. In vitro release profiles of GS (a) and SS (b) encapsulated in silica microcapsules.

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J.-X. Wang et al. / Materials Research Bulletin 43 (2008) 3374–33813380

Fig. 8. The release percentage vs. square root time profiles for GS (a) and SS (b) encapsulated in silica microcapsules.

showed a more weight loss of about 4.4 wt% owing to the removal of the surfactant residues by ethanol washing,

which was consistent with the change of the corresponding bands in Fig. 4.

N2 adsorption–desorption isotherms and the corresponding BJH PSD of silica microcapsules before and after

calcination were shown in Fig. 6. After calcination, the PSD of sample was mainly centered at 3.7 nm, slightly larger

than that (3.4 nm) of the uncalcined sample probably due to the decomposition and removal of a small amount of drug

entrapped in the channels. Correspondingly, the BET surface area of silica microcapsules slightly decreased from

306.2 to 291.0 m2/g. Furthermore, the small change of pore volume and almost the same hysteresis loop could be

clearly observed in Fig. 6. In contrast to the significant change of pore size and pore volume resulted from the main

loading of drug in the pores [10,14,15,21], it is worth noting that there is only such a small change in PSD, BET and

pore volume of samples before and after calcination. Therefore, it could be reasonably deduced that most of drug

molecules had been indeed encapsulated in the inside of silica microcapsules in this way, while only a small fraction of

GS was probably encapsulated in the pores on silica shells.

Fig. 7 displays the cumulative drug release from GS and SS encapsulated silica microcapsules. Both systems

exhibited excellent sustained release properties, clearly demonstrating the good feasibility of direct encapsulation of

drug into silica microcapsules for sustained release applications by adopting W/O emulsion. As an example of GS

system, there was a rapid release of GS, which reached near 58% within the initial 2 h, as shown in Fig. 8a, benefiting

the fast increase of the drug concentration to the effective level. In the following long release period, the GS release

rate decreased greatly and there was a slow increase of GS release from 58% to near 75% within 60 h, maintaining the

drug concentration for meeting the requirement of a long-term treating effect. In the case of GS-loaded hollow silica

spheres obtained by immersion method [15], more than 50% of GS was delivered in 5 min, and the release amount

reached about 90% after 2 h. The main reason was that a majority of GS molecules were adsorbed on the outer surface

of hollow mesoporous silica spheres, and only a minority of GS stored in the channels. By the above-mentioned

comparison, it could be concluded that this procedure for direct encapsulation of GS into the inside of silica

microcapsules using W/O emulsion would be very promising and effective for the loading and sustained release of

water-soluble drug with large molecular dimension.

The kinetics of the release of drug from porous carrier materials was frequently described by using the Higuchi

model [22,23]. According to this model, the release of a drug from an insoluble, porous carrier matrix could be

described as a square root of a time-dependent process based on Fickian diffusion. The use of this model should be

beneficial for the system under study as the model is valid for releases of relatively small molecules that are uniformly

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J.-X. Wang et al. / Materials Research Bulletin 43 (2008) 3374–3381 3381

distributed throughout the matrix. However, from the release percentage versus square root time profiles presented in

Fig. 8, it could be clearly seen that silica microcapsules encapsulated GS and SS revealed a two-step release, which

was different from a good linear relationship. This deviation from overall linearity is probably related to the effective

encapsulation of drug molecules into the voids of silica microcapsules. Thus, drug molecules encapsulated in the inner

cores of silica microcapsules could diffuse out only through the pores in the shells. Further, the diffusion rate gradually

decreased with the decline of diffusion driving force induced by the reduction of the drug molecules inside the inner

confined space. The related release mechanism needs to be further investigated in future.

4. Conclusions

In summary, a simple and effective one-step route was developed for direct encapsulation of water-soluble drug into

silica microcapsules by adopting drug with large molecular dimension, such as GS and SS, as model drugs in W/O

emulsion system. The drug-entrapped silica microcapsules had a uniform spherical hollow structure with a diameter of

5–10 mm and good dispersion. The characterization of SEM, FTIR, TG, and N2 adsorption–desorption analyses

demonstrated that drug molecules had been successfully encapsulated into the voids of silica microcapsules. In vitro

release studies of GS and SS revealed well-sustained release patterns. Obviously, this approach achieved the genuine

use of hollow space as drug storage. Similarly, it is inferred that this procedure can also be easily extended to O/W

emulsion for direct encapsulation of water-insoluble drug. Therefore, this technique would have the potential to be

applied in the direct encapsulation of drugs, biomacromolecules, fragrances and nanoparticles.

Acknowledgement

This work was financially supported by NSF of China (No. 50642042).

References

[1] S.W. Song, K. Hidajat, Langmuir 21 (2005) 9568.

[2] M. Changez, K. Burugapalli, V. Koul, V. Choudhary, Biomaterials 24 (2003) 527.

[3] M.S. Romero-Cano, B. Vincent, J. Control. Release 82 (2002) 127.

[4] N. Nishiyama, K. Kataoka, Pharmacol. Ther. 112 (2006) 630.

[5] C. Barbe, J. Bartlett, L. Kong, K. Finnie, H.Q. Lin, M. Larkin, S. Caleja, A. Bush, G. Calleja, Adv. Mater. 16 (2004) 1959.

[6] B. Munoz, A. Ramila, J. Perez-Pariente, I. Dıaz, M. Vallet-Regı, Chem. Mater. 15 (2003) 500.

[7] C. Tourne-Peteilh, D.A. Lerner, C. Charnay, L. Nicole, S. Begu, J.M. Devoisselle, Chem. Phys. Chem. 4 (2003) 281.

[8] C.Y. Lai, B.G. Trewyn, D.M. Jeftinija, K. Jeftinija, S. Xu, S. Jeftinija, V.S.Y. Lin, J. Am. Chem. Soc. 125 (2003) 4451.

[9] D.R. Radu, C.Y. Lai, K. Jeftinija, E.W. Rowe, S. Jeftinija, V.S.Y. Lin, J. Am. Chem. Soc. 126 (2004) 13216.

[10] M. Vallet-Regı, A. Ramila, R.P. Del Real, J. Perez-Pariente, Chem. Mater. 13 (2001) 308.

[11] J. Andersson, J. Rosenholm, S. Areva, M. Linden, Chem. Mater. 16 (2004) 4160.

[12] W. Zeng, X.F. Qian, Y.B. Zhang, J. Yin, Z.K. Zhu, Mater. Res. Bull. 40 (2005) 766.

[13] Y.F. Zhu, J.L. Shi, W.H. Shen, X.P. Dong, J.W. Feng, M.L. Ruan, Y.S. Li, Angew. Chem. Int. Ed. 44 (2005) 5083.

[14] J.F. Chen, H.M. Ding, J.X. Wang, L. Shao, Biomaterials 25 (2004) 723.

[15] Y.F. Zhu, J.L. Shi, Y.S. Li, H.R. Chen, W.H. Shen, X.P. Dong, J. Mater. Res. 20 (2005) 54.

[16] M. Fujiwara, K. Shiokawa, K. Hayashi, K. Morigaki, Y. Nakahara, J. Biomed. Mater. Res. 81A (2007) 103.

[17] S. Torrado, P. Frutos, G. Frutos, Int. J. Pharm. 217 (2001) 57.

[18] D. Stephens, L. Li, D. Robinson, S. Chen, H.C. Chang, R.M. Liu, Y. Tian, E.J. Ginsburg, X. Gao, T. Stultz, J. Control. Release 63 (2000) 305.

[19] M. Sivakumar, K.P. Rao, Biomaterials 23 (2002) 3175.

[20] S.S. Sampath, D.H. Robinson, J. Pharm. Sci. 79 (1990) 428.

[21] L.X. Wen, Z.Z. Li, H.K. Zou, A.Q. Liu, J.F. Chen, Pest Manage. Sci. 61 (2005) 583.

[22] T. Higuchi, J. Pharm. Sci. 50 (1961) 874.

[23] T. Higuchi, J. Pharm. Sci. 52 (1963) 1145.