Kinetics of Release from Polydisperse Core Particles Coated with Layers of Fine Soluble Particles

Transcription

1 Intrnatonal Journal of Chmal Engnrng and Applatons Vol. No. 4 August 011 Knts of Rlas from Polydsprs Cor Partls Coatd wth Layrs of Fn Solubl Partls Bors Golman Mmbr APCBEES Abstrat Th knts of rlas of atv matral was nvstgatd for th polydsprs or partls oatd wth layrs of fn solubl partls dsprsd n th mprmabl bodgradabl wax. A dtald mathmatal modl was dvlopd to smulat th rlas knts govrnd by dffuson through th vod spa of th oatng layr formd aftr th dssoluton of solubl partls. Th ffts of th sal and shap paramtrs of th Rosn-Rammlr typ of th or sz dstrbuton wr studd numrally on rlas profl. As a rsult th low rlas rat was obtand for th or sz dstrbuton of larg sal paramtr manly du to th small spf surfa ara of partls as wll as for th oatng layr of low volum fraton of solubl partls owng to th sgnfant dffusonal rsstan. Indx Trms Rlas knts Coatd partl Polydsprs or Rlas modl. I. INTRODUCTION Th rlas of atv omponnts at a ontrollabl rat s an ssntal fatur of advand formulatons of drug dosags [1] food ngrdnts [] frtlzrs and pstds [] t. Svral typs of ontrolld-rlas partls hav bn proposd nludng mbddd wthn an nrt matrx ontrolld by hmal raton and napsulatd [4]. Enapsulatd partls produd by oatng of atv matral wth polymr dssolvd n organ solvnt ar most wdly usd to ontrol th rlas rat. Howvr thr applaton wll b rstrtd n th nar futur du to nvronmntal ssus arsng out of th solvnt arnogn proprts and th rsdual polymr lft n th sol aftr th dssoluton of th atv omponnt. To ovrom th dsadvantags of suh oatd partls th dry-basd pross was dvlopd for oatng of atv or omponnts wth a layr of fn solubl [5] or prmabl [6] partls dsprsd n mprmabl bodgradabl wax. Th rqurmnts for th total rlas tm and th rlas profl vary wdly n dffrnt applaton flds. Th oatng wth multpl layrs of dffrnt thknss and volum fratons of solubl and prmabl partls has bn studd to ahv an addtonal ontrol ovr th rlas profl [7 8 9]. Th rlasd rat ould also b nflund by th sz dstrbuton of or partls as suggstd by Brhan t al. [10] for th matrx typ of drug formulatons. Th objtv of th prsnt study s to larfy th fft of th sz dstrbuton of or partls on th knts of rlas Manusrpt rvd Jun 0 011; rvsd July 011. B. Golman s wth th Shool of Chmal Engnrng Suranar Unvrsty of Thnology Nakhon Rathasma 0000 Thaland (-mal: golman@sut.a.th). of atv matral through th oatng layr of fn solubl partls dsprsd n mprmabl wax. Th mathmatal modlng s appld to quantfy th ontrbuton of th oatng layr thknss and th volum fraton of th solubl partls to th rlas rat of th atv omponnt from polydsprs or partls. II. THEORETICAL Th rlas modl was onstrutd for oatd partls assumng that th dffuson of dssolvd or matral through th oatng layr govrns th rlas rat. Whn th oatd partl s suspndd n watr n th rsrvor onntd solubl partls dsprsd n th oatng layr dssolv ratng vod spas. Watr pntrats nto ths vods formng a watr ntwork nsd th oatng layr known as pntraton paths. Th dssoluton rat of fn solubl partls s supposd to b hgh nough for watr to rah mmdatly th outr surfa of th or partl. Thraftr th dssolvd or matral dffuss to th outr surfa of th oatd partl through th pntraton paths and rlass to th rsrvor. Th rlas of or matral s onsdrd to prod n two onsutv tm stags. Th sold or gradually dssolvs and shrnks n sz but s stll prsnt durng th ntal stag of rlas. Th nsd spa btwn th nnr surfa of th oatng layr and th sold or trmd as an nnr soluton s flld wth th atv omponnt dssolvd n watr. Th volum of th nnr soluton nrass wth tm untl th sold or ompltly dsappars. Th sond stag of rlas starts at ths pont. Durng ths stag th onntraton of th nnr soluton oupyng th or spa drass wth tm untl t qulbrats wth th soluton n th rsrvor. Th notaton of th rlas modl s llustratd n Fg. 1. r r n Cn Cl r out Coatng layr Innr soluton Sold or Cout Rsrvor Fg. 1. Notaton for rlas modl of typ oatd partl. A. Modlng of Rlas Knts Th rlas knts of atv or matral by dffuson 8

2 Intrnatonal Journal of Chmal Engnrng and Applatons Vol. No. 4 August 011 through th porous spa of th oatng layr formd aftr th dssoluton of dsprsd solubl partls ould b prdtd on th bass of a modl dvlopd n our prvous papr [4] for monodsprs or partls. Th modl s furthr laboratd n th prsnt study to onsdr th rlas knts of polydsprs or partls. Suppos that thr ar N t typs of oatd partls nvolvd dffrng n th or sz th oatng layr thknss and th volum fraton of th solubl partls dsprsd n th oatng layr. Th numbr of or partls n th -th sz ntrval N s N 6 M f( x ) dx = (1) T ρ πx whr f ( x ) s th wght basd dstrbuton funton of th or damtr x M T s th total amount of or partls and ρ s th dnsty of th or matral. Th onntraton of atv or matral Cl () r t n th porous spa of th oatng layr of typ partl s gvn by th mass balan ovr th sphral shll as Cl () r t Cl () r t Cl () r t ε = Dff + () t r r r whr r s th radus of th shll t s th dffuson tm D s th fftv dffusvty and ε s th vodag of th ff oatng layr. Th vodag s assumd to b qual to th volum fraton of solubl fn partl dsprsd n th oatng layr φ. Th mass transfr rsstan btwn th lqud phas n th rsrvor and th outr surfa of oatd partls s ngltd du to th ntnsv mxng n th rsrvor. Thrfor a boundary ondton for Eq. () at th outr partl surfa r out s C ( r = r t) = C ( t) () l out out To alulat th nras n th onntraton of th atv omponnt n th rsrvor wth tm th amount of th atv matral rlasd by dffuson through th outr surfa of typ partl s multpld by th numbr of partls of ths typ N and summd up for all sz ntrvals dcout C l Vout = NDff 4π rout (4) dt r V = 1 r= rout whr out s th rsrvor volum. Th boundary ondton for Eq. () at th nnr surfa of th oatng layr r n s = = (5) C C ( r r t) C ( t) l n n whr n s th onntraton of dssolvd or matral n th nnr soluton. Durng th ntal stag of th rlas whn th sold or stll xst th onntraton of th dssolvd matral n th nnr soluton rmans onstant and qual to th onntraton at th saturaton ondton C sat = (6) Cn C Aftr th dsapparan of th sold or th onntraton of th dssolvd matral n th nnr soluton drass wth laps of tm by dffuson through th nnr surfa of th oatng layr n aordan wth th followng matral balan quaton dcn Cl Vor = Dff 4π rn (7) dt r sat r r = n whr V or s th ntal sold or volum 4π rn Vor =. Introdung V or nto Eq. (7) and rarrangng t rsults n dcn Dff Cl = (8) dt rn r r= rn Th ntal ondton for Eq. (8) s = = (9) C ( t t ) C n ds sat Th rlas fraton R s dfnd as Cout Rt () = C ( t = ) out (10) whr Cout ( t = ) s th onntraton of th or matral n th rsrvor soluton at nfnt tm. B. Modlng of Sz Dstrbuton of Cor Partls Th sz dstrbuton of or partls s assumd to b of th Rosn-Rammlr typ [11]. Th umulatv ovrsz dstrbuton F( x ) s n x F( x ) = xp (11) x whr x s th sal paramtr and n s th shap paramtr. Th sal paramtr s th haratrst valu of th dstrbuton and th shap paramtr ontrols th wdth of th frquny dstrbuton of szs wth th hghr valu orrspondng to th narrowr dstrbuton. Th frquny dstrbuton f ( x ) s n 1 n n x x f( x ) = xp (1) x x x III. METHODS Th nflun of th or sz dstrbuton on th rlas knts of oatd partls was analyzd wth th hlp of th dvlopd abov modl.th systm of modl quatons Eqs. 84

3 Intrnatonal Journal of Chmal Engnrng and Applatons Vol. No. 4 August 011 (1) - (1) was solvd numrally usng a mthod of lns [1].A sond-ordr ntral-dffrnng shm was utlzd to dsrtz th spa drvatvs n Eq. (). Thn th soluton of rsultng systm of ordnary dffrntal quatons was arrd out mployng Gar s mthod [1]. Th total amount of th atv or matral was kpt onstant for all smulatons. Th rfrn valu of paramtrs usd n smulaton ar as follows: th thknss of th oatng layr was assumd to b proportonal to th or sz wth th rato of th layr thknss to th or radus qual to 77 and th volum fraton of th solubl partls n th oatng layr s prsumd to b qual 0.. IV. RESULTS AND DISCUSSION Th fft of th sal paramtr of Rosn-Rammlr dstrbuton of or szs on th rlas profl s llustratd n Fgs. and. Th dstrbutons of or partl szs wr gnratd by varyng x n Eq. (11) at th fxd valu of n n = as dmonstratd n Fg. (a) by th umulatv ovrsz dstrbuton funtons and n Fg. by th frquny dstrbuton funtons. Th rlas profls dffr sgnfantly wth th sal paramtr and th rlas rat drass for or partls of th sz dstrbuton of largr x as shown n Fg.. Wth nrasng x th or sz dstrbuton shfts to th largr szs. Sn th thknss of th oatng layr s assumd to b proportonal to th or sz th largr partls ar oatd wth th thkr layr. Thus th or matral dssolvd n th nnr soluton has to dffus a long dstan nsd th thk oatng layr to rah th outsd surfa. Th larg or partls ar also of a small spf surfa ara that lmts supply of th atv omponnt from th nnr soluton to th oatng layr through th nnr surfa aordng to Eq. (8). Thrfor both th thk oatng layrs and th small spf surfa ara of larg partls ontrbut to th dras of rlas rat. To larfy ontrbutons of th layr thknss and th surfa ara to th rlas rat smulatons wr also arrd out for th or partls oatd wth layrs of th sam thknss of 100 μm. As llustratd n Fg. th rlas urv for or partls of a wd sz dstrbuton x = 000 oatd wth layrs of varabl thknss almost ond wth th urv for layrs of onstant thknss. Thrfor th dln n th spf surfa ara s manly rsponsbl for th rduton of th rlas rat of larg partls. Cumulatv dstrbuton F (x ) [%] Rosn-Rammlr dstrbuton n x Partl sz x (a) Frquny dstrbuton f (x ) [% μm -1 ] Rosn-Rammlr dstrbuton n x Partl sz x Fg.. Rosn-Rammlr dstrbutons of or partls for varous sal paramtrs: (a) umulatv ovrsz dstrbutons frquny dstrbutons. Rlasd fraton R [-] Layr Thknss Rosn-Rammlr dstrb. 0.5 Varabl Constant n x Tm t [s] Fg.. Efft of sal paramtr of or sz dstrbuton on th rlas profl. A spf surfa ara of a partl n th -sz rato s alulatd as π x 6 S = = (1) π x x 6 Th total spf surfa ara s 6 S = NS = NT fn( x ) dx = = 1 = 1 x (14) fn( x ) = 6NT dx x whr = 1 NT s th total numbr of partls N T N t = N = 1 and fn( x ) s th numbr basd frquny dstrbuton of or partls whh s onvrtd from th mass basd dstrbuton dfnd by Eq. (1). Th total spf surfa aras alulatd by Eq. (14) for varous sz dstrbutons ar summarzd n Tabl I. TABLE I: THE TOTAL SPECIFIC SURFACE AREA OF PARTICLES Sal paramtr of Rosn-Rammlr dstrbuton x Total spf surfa ara of partls S [m /m ]

4 Intrnatonal Journal of Chmal Engnrng and Applatons Vol. No. 4 August 011 Th fft of th shap paramtr of Rosn-Rammlr dstrbuton of or szs on th rlas profl s llustratd n Fgs. 4 and 5. Th sz dstrbutons of or partls of th sam sal paramtr x = 000 and varous valus of shap paramtr usd n th smulaton of rlas knts ar shown n Fg. 4. Inspton of Fg. 5 ndats that th rlas rat only slghtly drass wth nrasng shap paramtr. Th fft of th volum fraton of solubl partls dsprsd n th oatng layr on th knts of rlas was studd by varyng th volum fraton φ = for polydsprs or partls oatd wth mprmabl layrs of th thknss proportonal to th or damtr. Th fftv dffusvty of th oatng layr D ff was stmatd from th volum fraton of solubl partls by usng an mpral quaton [14] Dff = [ aln( bφ + ) + d] φ (15) whr a b and d ar th fttng paramtrs. Ths quaton was drvd by fttng th rsults of Mont-Carlo smulatons of th transport of atv sps by dffuson n th thr-dmnsonal porous strutur formd aftr th dssoluton of solubl partls. Th valus of th fftv dffusvty usd n th smulaton of rlas knts ar summarzd n Tabl II. Frquny dstrbuton f (x ) [% μm -1 ] Cumulatv dstrbuton F (x ) [%] Rosn-Rammlr dstrbuton n x Partl sz x Partl sz x (a) Rosn-Rammlr dstrbuton n x Fg. 4. Rosn-Rammlr dstrbutons of or partls for varous shap paramtrs: (a) umulatv ovrsz dstrbutons frquny dstrbutons. Rlasd fraton R [-] 0.5 Rosn-Rammlr dstrbuton n x Tm t [s] Fg. 5. Efft of shap paramtr of or sz dstrbuton on th rlas profl. TABLE II: EFFECTIVE DIFFUSIVITIES FOR VARIOUS VOLUME FRACTIONS OF SOLUBLE PARTICLES Volum fraton of solubl Efftv dffusvty partls φ [ ] D ff [m /s] Th rlas profls of polydsprs or partls oatd wth layrs of varous volum fratons of dsprsd solubl partls ar shown n Fgs. 6 (a) and for or sz dstrbutons of Rosn-Rammlr typ of x = 1000 and x = 000 rsptvly. Rlasd fraton R [-] Rlasd fraton R [-] 0.5 Volum fraton of solubl partls φ [ ] Tm t [s] (a) 0.5 Volum fraton of solubl partls φ [ ] Tm t [s] Fg. 6. Efft of volum fraton of solubl partls on rlas profl. Rosn-Rammlr dstrbuton of or partls wth n = and x 1000 (a) = x 000 =. Th rlas rat rdus sgnfantly whn th volum fraton drasd from φ = 0. to φ = 0.1 spally for th or partls of wd sz dstrbuton x = 000. Th dffuson of th atv matral s hndrd n th oatng layr of low volum fraton of solubl partls as th rstrtd porous spa s formd n pla of th dssolvd solubl partls du to th small ontat ara of nghbor solubl partls and th low numbr of prolaton paths. Howvr th rlas rat of partls oatd wth layrs of φ = 0. only slghtly drass n omparson wth on forφ = 0.5 as th broad porous ntwork alrady xsts n th oatng layr ofφ =

5 Intrnatonal Journal of Chmal Engnrng and Applatons Vol. No. 4 August 011 V. CONCLUSIONS Th applaton of or partls of talord sz dstrbuton oatd wth layrs of fn solubl partls dsprsd n th mprmabl wax was provd to b usful for ontrollng th rlas rat of atv matral. Th dtal mathmatal modl was onstrutd to smulat th rlas knts of polydsprs or partls govrnd by dffuson through th pntraton paths nsd th oatng layr formd n pla of dssolvd solubl partls. As a rsult th low rlas rat of th atv or matral was obtand for th or sz dstrbuton of Rosn-Rammlr typ wth th larg sal paramtr manly du to th small spf surfa ara of larg sz partls. Th rlas rat was also low for th or partls oatd wth layrs of low volum fraton of solubl partls du to th hndrd dffuson n th rstrtd spa of prolaton paths. [8] R. Ito B. Golman and K. Shnohara Dsgn of mult-layr oatd partls wth sgmodal rlas pattrn Chm. Eng. Sn vol. 60 no. 0 pp [9] R. Ito B. Golman and K. Shnohara Formaton of a sgmodal rlas pattrn of or partls oatd wth layrs of solubl and prmabl partls Advand Powdr Thnology vol. 15 no. pp [10] N.S. Brhan K.H. Carson A.C. R-Fht and M.J. Andrws Efft of man damtr and polydsprsty of PLG mrosphrs on drug rlas: Exprmnt and thory Intrn. J. of Pharmauts vol. 7 no. 1- pp [11] A. Ghosh A FORTRAN program for fttng Wbull dstrbuton and gnratng sampls Computrs & Gosns vol. 5 no. 7 pp [1] W.E. Shssr and G.W. Grffths. A Compndum of Partal Dffrntal Equaton Modls: Mthod of Lns Analyss wth Matlab. Cambrdg Unvrsty Prss 009. [1] W. Gar. Numral Intal Valu Problms n Ordnary Dffrntal Equatons. Prnt-Hall [14] R. Ito B. Golman and K. Shnohara Efft of th porous strutur of a oatng layr on th rlas rat of or partl J. Chm. Eng. Japan vol. 6 no. 6 pp REFERENCES [1] X. L. Dsgn of Controlld Rlas Drug Dlvry Systms. MGraw-Hll Profssonal 005. [] N.J. Zudam V. Ndov Eds. Enapsulaton Thnologs for Atv Food Ingrdnts and Food Prossng. Sprngr 009. [] M.E.Trnkl. Slow- and Controlld-Rlas and Stablzd Frtlzrs: An Opton for Enhanng Nutrnt Us Effny n Agrultur. Intrnatonal Frtlzr Industry Assoaton 010. [4] D.L. Ws Ed. Handbook of Pharmautal Controlld Rlas Thnology CRC Prss 000. [5] R. Ito B. Golman and K. Shnohara Controlld rlas of or partl oatd wth solubl partls n mprmabl layr J. Chm. Eng. Japan vol. 5 no. 1 pp [6] R. Ito B. Golman and K. Shnohara Controlld rlas wth oatng layr of prmabl partls J. Controlld Rlas vol. 9 no. pp [7] R. Ito B. Golman and K. Shnohara Multpl-Layr Coatng of Solds wth Imprmabl Flm Dsprsng Prmabl Partls for Controlld Rlas J. Chm. Eng. Japan vol. 7 no.4 pp Dr. Bors Golman ompltd hs graduat studs n Chmal Engnrng at th D.Mndlyv Unvrsty of Chmal Thnology n Mosow Russa and n Chmal Envronmntal Engnrng at th Ktam Insttut of Thnology Ktam Japan. H obtand hs Ph.D. n Matrals Sn and Engnrng at th Hokkado Unvrsty Sapporo Japan. H has publshd mor than 65 rsarh artls n rfrrd journals and onfrn prodngs on powdr thnology and matrals ngnrng rlatd aras. Currntly h s workng as Assstant Profssor of Chmal Engnrng Suranar Unvrsty of Thnology Nakhon Rathasma Thaland. Hs rsarh ntrsts ar n th aras of produton of funtonal partls powdr flow ontrolld rlas mathmatal modlng of powdr prossng and raton prosss. 87