Influence of Fines on the Surface Energy Heterogeneity of Lactose for Pulmonary Drug Delivery

Transcription

1 Influence of Fines on the Surface Energy Heterogeneity of Lactose for Pulmonary Drug Delivery Raimuno Ho, a Arian S. Muresan, b Geral A. Hebbink, c an Jerry Y. Y. Heng a,* a Surfaces an Particle Engineering Laboratory, Department of Chemical Engineering, Imperial College Lonon, South Kensington Campus, Lonon SW7 2AZ, Unite Kingom b FrieslanCampina Research, Harerwijkerstraat 416, 7418 BA Deventer, The Netherlans c FrieslanCampina DOMO, Hanzeplein 25, 817 JD, Zwolle, The Netherlans * Corresponing author: Tel: +44 () ; Fax: +44 () aress: jerry.heng@imperial.ac.uk (Jerry Y.Y. Heng) 1

2 ABSTRACT The effects of the blening of lactose fines to the overall ahesion property of coarse α-lactose monohyrate carrier particles were investigate. Five samples, three of them commercial samples from DOMO (Lactohale LH1, LH21, an LH25) whilst the other two are blens of LH21 an LH25, were stuie. Characterisation inclue particle sizing, SEM, PXRD an IGC. Dispersive surface energy γ was etermine using a finite concentration IGC metho to obtain a istribution profile. The γ istribution of lactose crystals were foun to vary from 4-48 mj/m2. The unmille coarse crystalline lactose sample (LH1) γ was lowest an showe less heterogeneity than the mille sample (LH25). Fines (LH21) were foun to have the highest γ value. The samples with loae LH21 were foun to have a higher energy than LH1. The amount of LH21 in Blen 1 was not able to ecrease surface energy heterogeneity, whereas sample Blen 2 showe aequate loaing of fines to obtain a relatively homogeneous surface. Aition of fines resulte in an increase in γ, suggesting that coarse lactose surfaces were replace by surfaces of the fines. Increasing the loaing of fines may result in a more homogeneous surface energy of lactose particles. Keywors: Carrier Particle; Lactose; Pulmonary Drug Delivery; Inverse Gas Chromatography; Surface Energy. 2

3 1. Introuction Pulmonary rug elivery is an attractive way of introucing meication for lung iseases like asthma an COPD. Besies, pulmonary elivery is increasingly use for elivery of rugs in meications that cannot be swallowe like proteins an pepties (Del Valle et al., 29). The lungs are very attractive for the uptake of meications ue to their large surface area (7 1 m 2 for an ault) an their easily permeable membrane. In orer to reach the active area of the lungs, rug particles nee to be in the aeroynamic particle size range of 1 5 µm. These small particles ten to form strong agglomerates cause by cohesive forces an these forces nee to be overcome to prouce an aerosol with particles that are able to reach the lungs. In ry power inhalers, a coarse carrier, most commonly lactose monohyrate, is blene with the micronise rug particles. Current literature reports that upon inhalation, an aerosol is prouce where the fine rug particles are etache from the coarse carrier particles. The performance of carrier-base ry power inhalation (DPI) formulation is etermine, to a significant egree, by the preparation of the formulation, as well as the esign of aerosolisation evice, the inhalation moe an the respiratory-tract anatomy an physiology of the patient (Timsina et al., 1994). One of the methos, that have been extensively researche, to optimise rug elivery of the active ingreient is the use of a ternary formulation where a small amount of fine excipient particles or fines is ae to the coarse carrier an the rug blen (Poczeck, 1998; Louey an Stewart, 22; Shur et al., 28). Despite the evience that the use of such methos show an improve fine particle ose (FPD) or fine particle fraction (FPF) of the active rug, the mechanism by which the fine particles alters the performance of the formulation has remaine elusive (Jones an Price, 26). 3

4 One such hypothetical mechanism that has been propose is the passivation of strong bining sites or high energy sites by fine excipient particles (Jones an Price, 26). The fines are thought to preferentially ahere to the surface regions of the coarse carrier with the highest surface energy, therefore forcing rug particles to bin to surfaces with lower surface energy. When the formulation is kinetically activate through the respiratory-tract, the rug particles are more easily separate from the surface of the carrier, thus increasing the inhale ose in the lower airways (Fig. 1). Zeng et al. (1999) observe an increase of ~12% in FPF of the rug when fine lactose particles were blene to the coarse lactose carrier before the aition of rug to the formulation, thus proviing the fines with the first opportunity to ahere to the high energy sites. Other blening orer was foun to yiel a smaller increase in FPF compare to the control, i.e. the binary mixture of coarse carrier an rug. However, it was also note that the blening orer ha no significant impact on the formulation performance when the blening time was increase, speculatively ue to the reistribution of particles between bining sites for prolonge blening time (Zeng et al., 2). It is clear that with the current state of knowlege, the influence of fine particles to improve DPI formulation will require a more funamental unerstaning of the interparticulate interactions of the components in the mixture, in orer to clarify the mechanism by which the fines work (Jones an Price, 26). In an attempt to unerstan the change in the overall ahesion property when lactose fines are ae to the coarse carrier, this stuy seeks to etermine the surface energetic istribution of ifferent processe coarse lactose an the subsequent changes to the surface energy istributions by the blening of fine lactose particles. Such a stuy will confirm (or otherwise) the commonly an wiely accepte view that aition 4

5 of fines leas to a reuction in surface energy. This was conucte via a recently evelope methoology using inverse gas chromatography (IGC) at finite concentrations Inverse gas chromatograhy (IGC) The inverse gas chromatography technique has been wiely use in the characterisation of solis, fibres, films incluing pharmaceutical solis (Heng et al., 26). By measuring the time a probe molecule takes to elute through a packe column of sample materials, the thermoynamic properties of the soli phase can be etermine. The net retention volume, V N which is a funamental surface thermoynamic property of the soli-vapour interaction process, is given by: V N j T = F ( t R t ) (1) m where T is the column temperature in Kelvin (K), F is the carrier gas exit flow rate at 1 atm an K, t R is the retention time for asorbing probe an t is the mobile phase hol-up time (ea-time), m is the sample mass in the packe column an j is the James-Martin correction, which corrects the retention time for the pressure rop along the column be. V N can be relate to the free energy of asorption, ΔG, an the work of ahesion of vapour asorbates to the surface, W, by: A ΔG = RT lnv N + K = N A a m W A (2) where R is the universal gas constant, K is a constant, N A is the Avogaro s number, a m is the cross sectional area of the asorbate. Accoring to Owens an Went (1969), the work of ahesion between a soli an liqui is the summation of geometric mean terms of ispersive an polar surface energy components as 5

6 shown in Eq. 3: WA = 2 γ γ + 2 γ γ (3) LV p LV p Hence, the injection of a series of infinite concentration of non-polar ( γ sample column will result in a linear regression on a plot of RTlnV N versus p LV = ) probes into the 1/ 2 a ( m γ LV ), anγ can be calculate from the slope (Schultz et al., 1987) (Fig. 2). The polar component of surface energy can also be etermine by applying a polar asorbate ( γ p LV ) an as such, the V N measure is summation of a ispersive an polar component. Knowing γ LV of the polar probe allows the polar (also cite in literature as aci-base) energy of asorption, Δ G AB, to be obtaine. IGC has been use to access the performance of ry power inhalation formulations (Cline an Dalby, 22; Tong et al., 26). Tong et al. (26) investigate the relative influence of rug-rug cohesion an rug-carrier ahesion on the in vitro performance of salmeterol xinafoate (rug) with lactose (carrier) by measuring surface energies an solubility parameters of the components by IGC at infinite ilution (zero surface coverage). The inhaler performance of salmeterol xinafoate was foun to improve significantly if the rug-carrier ahesion was stronger than rug-rug cohesion. Cline an Dalby (22) similarly observe that increasing surface energy interaction between rug an carrier resulte in an improve FPF of the rug Surface free energy istribution A recently evelope metho (Thielmann et al., 27) using inverse gas chromatography at finite concentration has been shown to be able to istinguish surfaces energetics of pharmaceutical solis exhibiting markely ifferent surface properties, i.e. heterogeneity an 6

7 homogeneity (Ho et al., 29a), as well as small variation in surface energy istributions resulting from small changes in crystal habits (Ho et al., 29b). In this stuy, the methoology was utilise to characterise surface energetic profiles of ifferent inhalation grae lactose, an the effects to the surface energetics when they are mixe in a two component blen were also investigate. The measurement of ispersive an polar surface energy istribution relies on a series of finite concentration IGC experiments using a series of n-alkanes an at least one polar solvent. In the current stuy, the etermination of γ an Δ G AB istribution profiles consists of three main steps which are isplaye in Fig. 3. First, the asorption isotherms for four n-alkane probes (C6- C1) an ethanol are measure using the IGC. Employing the peak maximum methoology (Thielmann et al., 27), the retention volume an equilibrium partial pressure, P, are calculate for each single injection of increasing solute concentration via Eq. 1 an 4: h P P = VLoop (4) F A T P Loop where h is the chromatogram peak height, A is the chromatogram peak area, V Loop is the injection loop volume, T Loop is the injection loop temperature an P is the saturation pressure. The asorbe amount, n, an therefore the asorption isotherm for each probe vapour can then be obtaine by integration of V N versus P. If the Brunauer-Emmett-Teller (BET) specific surface area, SSA BET, of the sample is known, the monolayer capacity, n m, for each probe vapour can be calculate from: SSA BET = a N n (5) m A m From the monolayer capacity, the corresponing surface coverage, n/n m or θ, at each injection concentration can then be measure from the amount asorbe n. Since the retention volumes of 7

8 each probe are now expresse as a function of sample surface coverage, both γ an Δ G AB can now be calculate at a particular surface coverage in the same way as escribe previously in Fig. 2 using the Schultz approach (1987). The calculations of γ an Δ G AB across a range of surface coverages, therefore, result in a istribution of ispersive an polar surface energies. Further etails of the methoology can be foun elsewhere (Thielmann et al., 27; Yla- Maihaniemi et al., 28). 8

9 2. Materials an methos 2.1. Materials Details of the five lactose samples are tabulate in Table 1. Three of them are commercial samples from DOMO (Lactohale LH1, LH21, an LH25), the other two are blens of LH21 an LH25. LH1 are coarse lactose crystals that were sieve through a 31 µm sieve, LH21 an LH25 are mille an classifie graes of lactoses, with LH21 being a fine fraction an LH25 being a coarse fraction. Blens 1 an 2 were prepare by weighing the appropriate amounts of LH21 an LH25 in a bottle an turning an rotating the close bottles for >1 minute. Blening ratios are for Blen 1: 82 g of LH25 an 18 g of LH21, an for Blen 2: 7 g of LH25 an 3 g of LH Particle size measurement Particle size istributions were measure with a Sympatec HELOS laser iffractometer (Sympatec GmbH, Clausthal-Zellerfel, Germany). All powers were isperse in air at a pressure of 1.5 bar through the etection zone of the iffractometer. The iffracte laser light was focusse with an R5 lens with a measuring range of.5/ µm Finite concentration inverse gas chromatography Lactose power ( g) samples were packe by gentle vibration into separate presilanise glass columns (3 mm 4 mm ID) with silanise glass wool packing at each en to prevent power movement. The experiments were conucte using an SMS-iGC 2 (Surface Measurement Systems, Lonon, UK) system. Prior to measurements samples were pre-treate at 9

10 33 K an % RH for 2 hours uner flowing helium to remove any resiual moisture or solvent asorbe on the power surface. Following pre-treatment, pulse injections using a.25 ml gas loop at 33 K were performe. Purely ispersive n-alkane vapour probes (ecane, nonane, octane an heptane) an polar probe (ethanol) were injecte at.3,.5,.1,.2,.35,.55,.7,.8,.95 P/P an V N was etermine using a peak maximum analysis. Methane gas was use as a non-interacting probe giving t for the column, with concentrations of.1 P/P. Helium was use as the carrier gas at a flow rate of 1. stanar cubic centimetres per minute for all injections. The γ an Δ G AB were calculate accoring to the Schultz metho (1987) Specific surface area The BET specific surface area for all five lactose samples was obtaine base on N 2 asorption isotherm measure using a gas asorption analyzer (Tristar 3, Micromeritics, Norcross, GA). Approximately 4 g of each sample was egasse with helium flow at 5 C for at least 5 hours before BET measurement. Surface area was etermine using the BET moel in the P/P range from.5 to.3. Each sample was measure in uplicate SEM images SEM images were acquire with a tabletop microscope system TM-1 (Hitachi, Tokyo, Japan) in the charge-up reuction moe. 1

11 2.6. Polymorph ientification X-ray power iffraction spectra were obtaine for the lactose samples using a X Pert Pro iffractometer (PANalytical B.V., Almelo, The Netherlans) over the range of 7 4 2θ with a CuKα X-ray source at 4kV an 4mA. 11

12 3. Results an iscussion Particle size an BET specific surface area of LH1, LH21, LH25, Blen 1 an Blen 2 are isplaye in Table 2, whereas the SEM images are shown in Fig. 4. From Table 2, the fine lactose (LH21) has the smallest meian-average equivalent spherical iameter (18 µm) amongst the three unblene lactose samples. The unmille sample LH1 has the largest meian-average iameter, whereas the gently mille an classifie LH25 possesses a smaller meian-average iameter than LH1 ue to the size reuction proceure. The particle sizes of Blen 1 an 2 are both between the meian-average iameter of LH25 an LH21, an are also consistent with the blening ratio of LH25 to LH21. As can be seen from Fig. 4, LH1 exhibits the normal tomahawk crystal shape expecte for α-lactose monohyrate crystals (Raghavan et al., 21). On the other han, the crystal shape of the gently mille LH25, was foun to be more irregular an it seems that the ifference in crystal shapes (habit) between LH1 an LH25 coul be ue to the cleavage of weakly attache facets upon milling. The particle size of Blen 1, which was blene with 18% fine lactose, is approximately 2% bigger than Blen 2 which contains the same batch of LH25 blene with 3% fines. Post-blening operations, the fines can be seen to ahere onto particular surface regions of both Blen 1 an Blen 2. However, some portions of fine particles also seem to form into clusters or aggregates which are ahere to the coarse crystal surfaces of Blen 1 an Blen 2. The amount of fines, which is efine here as the fraction of particles below 15 µm, follow the same tren as the meian particle size: the smaller the meian size, the larger the percentage of fine particles (Table 2). The coarse LH1 an LH25 only have about 3% of fine particles, whereas the fine LH21 has over 4% of fines. The two blens can also be seen to have quantities of fines that are 12

13 there in between LH21 an LH25. The tren in BET specific surface areas, which are also isplaye in Table II, is in goo agreement with the meian-average particle size of the samples. Comparisons of γ an Δ G AB istributions for the five lactose samples are shown in Fig. 5 an Fig. 6 respectively. All unblene lactose, LH21, LH25 an LH1 show a small egree of ispersive surface energy heterogeneity within the range of surface coverage, θ, examine (Fig. 5), although very ifferent γ values. As the fines content of the unblene samples increases, the range of γ shifts to higher values. This means that the finer lactose crystals, in particular the LH21 fines, possess a greater egree of long-range van er Waals surface forces compare to the coarse lactose LH1 an LH25. β-lactose can be present in mille materials, attribute to the recrystallisation of amorphous lactose uring storage (Haque an Roos, 25). In orer to unerstan the variation in γ for these three lactose samples, polymorphic ientification was conucte by PXRD. The PXRD patterns of both coarse lactose (LH1 an LH21), the fines (LH21), incluing both blens 1 an 2, are comparable to the peaks of pure α-lactose monohyrate. As such, the higher γ measure for LH21 cannot be explaine by β-lactose content. Fig. 5 an Fig. 6 show the γ an Δ G AB istributions as a function of n/n m respectively. The γ for zero surface coverage (Fig. 5) is calculate base on infinite ilution IGC, whereby injection size of alkane probes is hel constant at P/P =.3. We obtain values: LH21 = mj/m 2, Blen 2 = mj/m 2, Blen 1 = mj/m 2, LH25 = mj/m 2 an LH1 = mj/m 2. When the fines (LH21) were blene with coarse lactose (LH25) as in Blen 1 an Blen 2, it is expecte that the surface energy of the system woul increase with increasing fines 13

14 content because the fines posses both higher γ an Δ G AB. This is exactly the case for Blen 1 an Blen 2 as shown in Fig. 5 an Fig. 6. In the case of Blen 1, the introuction of fines shifte the γ profile of LH25 from approximately 42 mj/m 2 to about 43 mj/m 2, an increase of ~2.5%, at n/n m =.1, whereas the Blen 2 sample was shifte to ~44 mj/m 2 (~5% increase), resulting in a surface energy value close to that of LH21. This inicates that surfaces of the coarse lactose (LH25) were replace by surfaces of the fines (LH21), with greater propensity for Blen 2 than Blen 1, ue to the higher loaing of fine particles. It is interesting to note from the surface energy profiles that the blening of fines i not ecrease the overall surface energy of the coarse lactose, but actually increase the overall ahesion property of the blen ue to the fact that the fines possess much higher surface energy. As the high energy fines were blene with low energy coarse carrier, the fines seem to have ahere together to form clusters of fines as well as ahering to the specific regions of the coarse lactose (Fig. 4), suggesting that surfaces with high energy or bining characteristics o seem to ahere together. The blening of fines to LH25 resulting in an increase in of LH21. Δ G AB values, resulting in the blens possessing characteristics The current results provie the first evience that the surface energetics of both fine an coarse lactose is an important parameter in ternary inhalation formulation. The inclusion of higher energy fines to coarse carrier will increase the rug-carrier ahesion interactions, because surfaces are replace by those having stronger ahesion characteristics. Fines woul passivate high energy surfaces only if the fines possess smaller surface energy compare to the coarse carrier. However, the increase of rug-carrier ahesion was reporte to increase inhalation performance of rug (Cline an Dalby, 22; Tong et al., 26), an it seems that more 14

15 unerstaning is require in orer to unerstan the relative influence of rug-carrier ahesion an rug-rug cohesion of the rug in the performance of inhalation formulations. 15

16 4. Conclusions The surface properties of lactose crystals were foun to be heterogeneous an the surface energy varies from 4 mj/m 2 to 48 mj/m 2. The unmille coarse crystalline lactose sample (LH1) showe less heterogeneity than the mille sample (LH25). The loae fines (LH21) have a higher energy than the coarse lactose. The amount of fines in Blen 1 was not able to alter the surface energy heterogeneity, whereas sample Blen 2 showe aequate loaing of fines to obtain a relatively homogeneous surface. The current surface energy istribution methoology was able to istinguish the ifferences between these lactose samples. Surfaces of the coarse lactose were shown to be replace by surfaces of the fines. We conclue that the effects of fines result in an overall increase in surface energy. 16

17 Nomenclature a m A F ΔG molecular cross-sectional area of asorbates chromatogram area carrier gas exit flowrate stanar energy of asorption Δ G AB stanar polar (aci-base) asorption energy h j m n n m N A P P R SSA BET t R t T T Loop V Loop V N W A chromatogram peak height James-Martin correction factor sample mass amount asorbe monolayer coverage Avogaro s number pressure saturation pressure universal gas constant specific surface area from nitrogen asorption isotherm retention time ea time temperature injection loop temperature injection loop volume net retention volume work of ahesion γ liqui-vapour ispersive surface energy component LV p γ liqui-vapour polar surface energy component LV γ soli-vapour ispersive surface energy component p γ soli-vapour polar surface energy component θ surface coverage 17

18 References Cline, D., Dalby, R., 22. Preicting the quality of powers for inhalation from surface energy an area. Pharm. Res. 19, Del Valle, E.M.M., Galan, M.A., Carbonell, R.G., 29. Drug elivery technologies: the way forwar in the new ecae. In. Eng. Chem. Res. 48, Haque, K., Roos, Y.H., 25. Crystallization an X-ray iffraction of spray-rie an freezerie amorphous lactose. Carbohyr. Res. 34, Heng, J.Y.Y., Pearse, D.F., Wilson, D.A., Williams, D.R., 26. Characterisation of Soli State Materials Using Vapour Sorption Methos. In: Zakrzewski, A. an Zakrzewski, M. (E.), Soli State Characterisation of Pharmaceuticals, ASSA Inc., Danbury, pp Ho, R., Hiner, S.J., Watts, J.F., Dilworth, S.E., Williams, D.R., Heng, J.Y.Y., 29a. Determination of surface heterogeneity of D-mannitol by sessile rop contact angle an finite concentration inverse gas chromatography. Int. J. Pharm. (Accepte) Ho, R., Wilson, D.A., Heng, J.Y.Y., 29b. Crystal habits an the variation in surface energy heterogeneity. Cryst. Growth Des. 9, Jones, M.D., Price, R., 26. The influence of fine excipient particles on the performance of carrier-base ry power inhalation formulations. Pharm. Res. 23, Louey, M.D., Stewart, P.J., 22. Particle interactions involve in aerosol ispersion of ternary interactive mixtures. Pharm. Res. 19, Owens, D.K., Went, R.C., Estimation of the surface free energy of polymers. J. Appl. Polym. Sci. 13, Poczeck, F., Ahesion forces in interactive power mixtures of a micronise rug an carrier particles of various particle size istributions. J. Ah. Sci. Tech. 12, Raghavan, S.L., Ristic, R.I., Sheen, D.B., Sherwoo, J.N., 21. The bulk crystallisation of alpha-lactose monohyrate from aqueous solution. J. Pharm. Sci. 9, Schultz, J., Lavielle, L., Martin, C., The role of the interface in carbon fibre-epoxy composites J. Ahes. 23, Shur, J., Harris, H., Jones, M.D., Kaerger, J.S., Price, R., 28. The role of fines in the moification of the fluiisation an ispersion mechanism within ry power inhaler formulations. Pharm. Res. 25,

19 Thielmann, F., Burnett, D.J., Heng, J.Y.Y., 27. Determination of the surface energy istributions of ifferent processe lactose. Drug Dev. In. Pharm. 33, Timsina, M.P., Martin, G.P., Marriott, C., Ganerton, D., Yianneskis, M., Drug-elivery to the respiratory-tract using ry power inhalers. Int. J. Pharm. 11, Tong, H.H.Y., Shekunov, B.Y., York, P., Chow, A.H.L., 26. Preicting the aerosol performance of ry power inhalation formulations by interparticulate interaction analysis using inverse gas chromatography. J. Pharm. Sci. 95, Yla-Maihaniemi, P.P., Heng, J.Y.Y., Thielmann, F., Williams, D.R., 28. Inverse gas chromatographic metho for measuring the ispersive surface energy istribution for particulates. Langmuir 24, Zeng, X.M., Martin, G.P., Tee, S.K., Abu Ghoush, A., Marriott, C., Effects of particle size an aing sequence of fine lactose on the eposition of salbutamol sulphate from a ry power formulation. Int. J. Pharm. 182, Zeng, X.M., Panhal, K.H., Martin, G.P., 2. The influence of lactose carrier on the content homogeneity an ispersibility of beclomethasone ipropionate from ry power aerosols. Int. J. Pharm. 197,

20 Figure Legens Fig. 1. Passivation of high energy sites: Fines are first blene with coarse carrier particles before blening with the particles of the active rug. Fig. 2. Determination of γ an Δ G AB from a plot of net retention volume versus vapour surface property Fig. 3. Surface energy heterogeneity etermination. Fig. 4. SEM images of lactose crystals an blens of fine an coarse lactose. Fig. 5. Dispersive surface energy istributions (versus surface coverage) for all lactose samples use in the stuy. Fig. 6. stuy. Δ G AB (ethanol) istributions (versus surface coverage) for all lactose samples use in the 2

21 Table 1 Details of the lactose samples use in the current investigation. Sample Coe Description Lactohale LH1 LH1 Unmille, crystalline Lactohale LH21 LH21 Mille Lactohale LH25 LH25 Crystalline, gently mille with fines remove Lactohale LH25 with Blen 1 LH25 an LH21 in 82:18 ratio Lactohale LH21 Lactohale LH25 with Lactohale LH21 Blen 2 LH25 an LH21 in 7:3 ratio Table 2 Particle size an BET specific surface area of the lactose samples. Sample Particle Size (base on an equivalent sphere) BET Specific Surface Area (m 2 /g) 1 (µm) 5 (µm) 9 (µm) % <15 µm LH ±.16 LH ±.36 LH ±.16 Blen ±.2 Blen ±.23 21

22 Fig. 1. Passivation of high energy sites: Fines are first blene with coarse carrier particles before blening with the particles of the active rug. Fines An Coarse Carrier Particles Blening Fine excipient particle High energy sites Blening With Drug Particles Drug particles Fine excipient particle 22

23 Fig. 2. Determination of γ an Δ G AB from a plot of net retention volume versus vapour surface property via the Schultz approach. RTlnV N Polar probe ΔG AB n-ecane n-nonane n-octane Slope = 2 N A (γ ) 1/2 n-heptane a m (γ ) 1/2 LV 23

24 Fig. 3. Surface energy heterogeneity etermination. 1. Monolayer Coverage Determination VN = 25 j T F (t R t ) m n = VN P Isotherm Plot of LH21col Amount Asorbe (mmol/g) Amount (mmol) VR (mmol/g/torr) C1.3 C9.1.2 Calculate C1 Calculate C9 Calculate C8 Calculate C Retention Time (min) C8 C Partial Pressure (torr) Partial Pressure (torr) h P VLoop F A TLoop P Nonane Heptane 4.6 C N C9 4 C /2 am (γlv ).3 Surface Coverage (-) 1/2 4.4 C7 C Slope = 2NA(γ ) C8 C RTlnVN Octane Dispersive Surface Energy Dispersive Surface Free Energy (mj/m ) (mj/m2) Retention Volume V (ml/g) (ml/g) 4.8 Applie at various surface coverage Decane 8.35 LH1 12 C1.3 p/po Pressure (torr) Pressure (torr) 2. Dispersive Surface Energy Profile 1 n nm Ret.-time [min] P= θ=.1 2 SSABET = am N A nm C1 Isotherm.4.6 (mmol/(g torr)) FID-response [pa] FID Response (pa) VR (mmol/g/torr) Retention Volume C1 Chromatograms Surface Coverage (-) Surface Coverage n/nm 3. Polar (Aci-base)Ethanol Energy of Asorption Profile Applie at various surface coverage Retention Volume V (ml/g)(ml/g) (ml/g) RTlnVN 2 C1 ΔGAB (ethanol) C9 1 C8 ethanol C am (γlv)1/ Coverage.5.6 (-).7 Surface N 1.5 Polar Asorption Energy Specific Energy of Desorption (kj/mol) (kj/mol) n/nm SurfaceSurface Coverage (-) Coverage.8.9.1

25 Fig. 4. SEM images of lactose crystals an blens of fine an coarse lactose. 25

26 Fig. 5. Dispersive surface energy istributions (versus surface coverage) for all lactose samples use in the stuy. Dispersive Surface Free Energy (mj/m 2 ) LH21 LH21 (Tren) Blen 2 Blen 2 (Tren) 46. Blen 1 Blen 1 (Tren) LH25 LH25 (Tren) 45. LH1 LH1 (Tren) Surface Coverage (-) 26

27 Fig. 6. stuy. Δ G AB (ethanol) istributions (versus surface coverage) for all lactose samples use in the Polar (Aci-base) Asorption Energy (kj/mol) LH21 Blen 2 Blen 1 LH25 LH1 LH21 (Tren) Blen 2 (Tren) Blen 1 (Tren) LH25 (Tren) LH1 (Tren) Surface Coverage (-) 27