The Kinetics of De-agglomeration of Magnesium Stearate Dry-Coated Salbutamol Sulphate Powders †

The objective was to investigate the effect of dry coating of salbutamol sulphate (SS) with magnesium stearate (MgSt) on the kinetics of powder de-agglomeration. The relative de-agglomeration of the MgSt coated SS powders was higher than uncoated SS at all air flow rates; the SS coated with 2 % MgSt showed the highest extent of de-agglomeration (> 5 % MgSt coated SS > 1 % MgSt coated SS). Rate of de-agglomeration was described by a cumulative de-agglomerated versus time profile. Profiles fitted a mono-exponential model and the deagglomeration rate constant (kd) was estimated. No significant differences existed between any of the uncoated and coated powders. The significance of this study relates to the improved aerosolization and de-agglomeration performance of the MgSt coated SS powders with optimum performance of 2 % MgSt coated SS. More significant is the finding that no change existed in de-agglomeration rate constants between the coated and uncoated powders, with the potential implications that their aerosol plume concentration and deposition patterns were similar.


Introduction
Dry powder inhalers (DPIs) have received increasing attention for use in respiratory drug delivery in recent years.In order to reach the lower respiratory tract, the drug particle size needs to be less than 5.0 μm (Qui et al., 1997).These small particles form agglomerates due to the balance of attachment and detachment forces favoring cohesion/adhesion.Detachment forces are mainly gravitational or centrifugal and decrease as the mass of the particle decreases.Adhesion and agglomeration occur when the attachment forces, such as electrostatic, intermolecular and capillary forces, exceed detachment forces (Visser, 1989).Agglomeration results in poor efficiency of aerosolization of dry powder inhalers.Different approaches have been investigated to increase the deagglomeration properties of the drug powders by decreasing the interaction between particles.The use of ternary components such as fine lactose (Louey and Stewart, 2002;Zeng et al., 1998), force control agents such as magnesium stearate (MgSt) and leucine (Begat et al., 2009), and modification of carrier surface (Islam et al., 2004) are a few examples of the approaches explored.A comprehensive list of these approaches can be found in a review (Xu et al., 2011).
One recent approach was to change the surface properties of powders by dry coating or mechanofusion of powders with hydrophobic materials to modify the surface energy and reduce particle interaction (Pfeffer et al., 2001).Mechanofusion is the process of mechanical dry coating in which submicron-sized guest particles directly attach onto relatively larger, micron-sized host or core particles; the process uses shear and compression to produce a thin continuous film of the guest material on the surface of the host.Mechanofusion has attracted attention because it is solvent free, relatively simple, cheap and capable of being scaled up.Previous studies have demonstrated that the de-agglomeration behavior of a range of different powders such as fine lactose and Pharmatose ® 450 M (P450, median particle size approximately 20 μm) could be increased substantially via mechanofusion with MgSt as the coating material (Zhou et al., 2010a).In another study, three drugs (e.g., salbutamol sulphate, triamcinolone acetonide and salmeterol xinafoate) showed greater extents of de-agglomeration, determined by laser diffraction particle sizing of the aerosolized plume at a single flow rate of 60 L/min after mechanofusion with 5 % (w/w) MgSt (Zhou et al., 2010b).The respiratory patterns of patients during inhalation may affect the depositions of the inhaled particles, because the flow rates in different regions of the respiratory tract are affected by the lung capacity and the frequency of breathing (Gonda, 1990;Martinez and Amidon, 2002).Thus, the extent of deagglomeration and resultant delivery of the drug is usually dependent on the air flow rate.
While the extent of de-agglomeration of coated powders has been studied to some degree, the kinetics of de-agglomeration of mechanofused powders from inhalers has not been studied.The rate of de-agglomeration describes how quickly the respirable fractions will be produced by the device and thus relate to the concentration of the powder of the plume in the airways of the lung.The aerosol concentration may influence the deposition patterns in the lung which may modify dissolution and absorption.Generally, few studies have described the kinetics of de-agglomeration.Kinetic studies have been reported on the de-agglomeration of particles of size range of 250-1000 μm (deVilliers, 1997), the detachment of drug from carriers in carrier based formulations (de Boer et al., 2004) and the de-agglomeration of particles in suspensions (Ding and Pacek, 2008).Our group has recently reported the kinetics of powder de-agglomeration where the rate of de-agglomeration of two cohesive powders salbutamol sulphate (SS) and Lactohale 300 were studied from three different inhalers (Behara et al., 2011a).The de-agglomeration rate constants (k d ) of both SS and Lactohale 300 were estimated and were related to the material, air flow rate and device.
Several studies have also addressed the influence of MgSt concentration on surface properties of a coated material (Das et al., 2011b;Zhou et al., 2011).Increasing MgSt concentrations increased surface coverage until an optimum concentration was reached (1-2 % w/w MgSt).Further coating adversely affected surface properties by changing morphology and increasing surface energy (Das et al., 2011b).
It was hypothesized that due to mechanofusion and the resultant surface modifications, the extent and rate of de-agglomeration of coated powders would be dependent on the concentration of coating material used in the mechanofusion.Therefore, a study was designed to determine the comparative extent and rate of de-agglomeration of an uncoated model drug for respiratory delivery (SS) and SS mechanofused with different concentrations of MgSt.The study was designed to mechanofuse SS with 1 %, 2 % and 5 % (w/w) MgSt.The de-agglomeration behavior was defined using relative de-agglomeration versus air flow rate profiles obtained between air flow rates of 45-120 L/ min.The percentage de-agglomeration obtained from the aerosolized plume obtained in these profiles was normalized against the actual proportion of respirable fines from the primary particle size distribution to obtain the relative de-agglomeration.A non-linear least square model was used to fit relative de-agglomeration versus air flow rate profiles.The regression parameters provided an understanding of powder cohesive structure.The use of aerosol concentration versus time profiles and the emitted dose versus time profiles allowed the construction of cumulative de-agglomeration versus time profiles from which de-agglomeration rate constants were obtained.

Mechanofusion or dry coating of the materials
The salbutamol sulphate (SS, Cambrex Profarmaco, Milan, Italy) was dry coated with magnesium stearate (MgSt, Mallinckrodt Chemicals, Phillipsburg, USA) in a Nobilta mechanofusion system (AMS-Mini, Hosokawa Micron Corporation, Osaka, Japan).SS (about 10 g) was mixed with 1 % (w/w), 2 % (w/w) and 5 % (w/w) MgSt prior to mechanofusion treatment.Each mixture was added into the process vessel (process volume 80 ml).The mechanofusion processing was performed for 10 min at processor rotation speeds of 5000 rpm.In order to prevent vessel temperatures exceeding 25 °C, cold water was circulated through the water jacket.

Dispersion of powders
The Spraytec ® laser diffraction system (Malvern Instrument, Worcestershire, UK) provided real time spray characterization of the powders.Mechanofused powders (20 ± 1 mg) were filled into No. 3 gelatine capsules (donated by Capsugel, NSW, Australia).Filled capsules were dispensed by using Rotahaler ® (GSK, Middlesex, UK).Measurements were carried out under flow rates of 45 L/min, 60 L/min, 90 L/min and 120 L/min of the inhalation cell of the Spraytec in the horizontal position.The flow rate was calibrated by an external flow meter and continuously monitored by the digital flow meter (DFM 2000, Copley Scientific Limited, Nottingham, UK) connected to a Spraytec.Rapid real time measurements were carried out, capturing 100 measurements per second over a 5 second period.Data acquisition were made using a 300 mm lens, which was suitable to measure particles in the size range of 0.1-900 μm.Measurements were performed with data collection triggered manually.All the devices, capsules, powder and capsule retentions were weighed by a five figure balance (model XS105 dual range, Mettler-toledo AG, Greifensee, Switzerland).The results were the mean of five replicates.

Primary particle size distributions
The primary particle size distributions of mechanofused SS were determined by laser diffraction (Mastersizer ® 2000, Malvern Instruments, Worcestershire, UK) using 300RF lens equipped with 150 ml dispersion unit.Approximately 100 mg samples were dispersed in 5 ml of propane-2-ol and then sonicated for 5 minutes.An imaginary refractive index of 0.01 was used in this project.The particle size analyses of the samples were performed using 2000 sweeps and analyzed with refractive indices of mechanofused SS as 1.553 and of isopropyl alcohol as 1.378.The mean particle size distribution was characterized by derived parameters Dv10, Dv50 and Dv90.The experiments were carried out on five replicates.

Surface energy
Surface energies of both uncoated and MgSt coated SS powders were determined using an Inverse Gas Chromatography (IGC, Surface Measurement Systems Ltd, and London, UK).Approximately 0.40 g of each powder was filled in presilanised glass columns (300 mm long × 3 mm internal diameter) and both the ends were closed by glass wool.The powder filled column was then fitted in IGC.Helium was passed through the column for 2 hour at 273 K to remove any impurities in the powder.Helium run at 10 sccm (standard cubic centimeter per minute) was used to carry all the probes.The dead volume was calculated from the retention time for methane while the retention times were detected by a flame ionization detector.Methane was run at a concentration of 0.1 p/p0 (where p denotes the partial pressure and p0 the vapor pressure).The detailed methodology for determination of total surface energy distribution calculation can be found in the literature (Das et al., 2011a).Non-polar surface energy (γ NP ) was determined from the retention volumes of GC grade hexane, heptane, octane, nonane and decane (Sigma-Aldrich GmbH, Steinheim, Germany) and the polar surface energy (γ P ) was determined from the retention volumes of two polar probes (i.e., dichloromethane and ethyl acetate).Combining non-polar (γ NP ) and polar surface energies (γ P ), the total surface energy (γ T ) was calculated (van Oss et al., 1988).The experiments were conducted in triplicate on the same batch.

Statistical modelling and analysis
The Spraytec data calculations were modelled using a non-linear least square regression analysis in the SigmaPlot 12.0 software (Systat Software, Inc., IL, USA).The statistical significance was carried out using one-way analysis of variance with Tuckey's post-hoc analysis at a p-value of 0.05 using SPSS (version 19.0, SPSS, Inc., IL, USA).

Characterising de-agglomeration behaviour of
powders using de-agglomeration profiles 3.1.1Changes in the particle size distribution of the aerosol plume with magnesium stearate coating The extent of de-agglomeration of the model cohesive powders, SS and MgSt dry coated SS, was determined by the laser diffraction particle sizing of the aerosol plume for two batches of the powder using the Malvern Spraytec.The powders were aerosolized from a commercial inhaler device (Rotahaler) at air flow rates between 45-120 L/min.The particle size distributions following the aerosolization at 60 L/min were selected to demonstrate the change in particle distribution in the aerosol plume that occurred with uncoated and MgSt coated SS (60 L/min was a common flow rate used in previous studies to calculate the relative de-agglomeration (Coates et al., 2005;Srichana et al., 1998;Chew and Chan, 2001)).The comparative particle size frequency distributions of uncoated and coated SS particles in the aerosol plume at 60 L/min and in the fully dispersed form are presented in Fig. 1.
The primary particle size distribution of SS was smaller than the particle size distribution of the aerosolized plume dispersed from the Rotahaler at an air flow rate of 60 L/ min (Fig. 1).The SS powders aerosolized from the Rotahaler were not fully dispersed and all uncoated and coated powders contained agglomerates following aerosolization, demonstrated by either a shoulder on the distribution or a bi-modal distribution.The 2 % (w/w) MgSt dry coated SS powder showed the greatest extent of deagglomeration following aerosolization, with the rank order being 2 % (w/w) MgSt > 5 % (w/w) MgSt > 1 % (w/w) MgSt > uncoated SS (data not shown).The relevant deagglomeration of the powders at other air flow rates showed a similar rank order of aerosolization performance and, in general, the relative de-agglomeration increased with air flow rate.The importance of observing the full particle size distributions of the aerosol plume was to observe the changes over the whole of the particle size range.In particular, the data in the full particle size distribution provide an indication of the cohesive nature of the powders, the agglomeration behavior and the change in aerosolization performance of the powder with MgSt coating.The multi-modal nature of the full particle size distribution demonstrated the resilience of agglomerates of the uncoated and coated cohesive drug to comminution.

Relationships between relative deagglomeration and flow rates
De-agglomeration behavior of model cohesive powders, SS and MgSt dry coated SS, was compared by constructing percent relative de-agglomeration versus air flow rate profiles (Behara et al., 2011b) of the cohesive powders in the aerosolized plume, dispersed from a commercial inhaler device (Rotahaler) at air flow rates between 45-120 L/ min.The relative de-agglomeration was the percentage ratio of the extent of de-agglomeration of particles less than 5.4 μm following aerosolization and the extent of de-agglomeration of particles less than 5.4 μm of the drug powder in its fully dispersed state (Fig. 2).
At all four flow rates, the percent relative de-agglomeration of 1 % (w/w), 2 % (w/w) and 5 % (w/w) MgSt coated SS was significantly higher than the uncoated SS (p ≤ 0.009).The 2 % (w/w) MgSt coated SS displayed a significantly increased percent relative de-agglomeration in comparison with the other MgSt coated powders at flow rates of 45 L/min, 60 L/min and 90 L/min (p = 0.001, p = 0.001 and p = 0.002 respectively).However, at the flow rate of 120 L/min, there was no significant difference between the 2 % (w/w) and the 5 % (w/w) MgSt coated powders (p = 0.137); this could be due to the fact that both of the powders approached their plateaus of percent relative de-agglomeration).
The 5 % (w/w) MgSt coated SS showed a significant increase in percent relative de-agglomeration compared to the 1 % (w/w) MgSt coated powder at all flow rates (p ≤ 0.001).The de-agglomeration percentage of the 1 % (w/w).MgSt coated powder was significantly higher than the uncoated SS at all flow rates (p ≤ 0.009), but significantly lower than both 2 % (w/w) and 5 % (w/w) MgSt coated SS at all flow rates (p ≤ 0.001, p ≤ 0.000 respectively).

Modelling the profiles of relative deagglomeration versus flow rates
The de-agglomeration data in the profiles were empirically modelled in order to characterize the powder behavior in the relative de-agglomeration versus air flow rate profile (Behara et al., 2011b).Since the shape of the deagglomeration-air flow rate profiles, including the lag phase at lower air flow rates and the plateau at higher rates, suggested sigmoidal relationship between relative de-agglomeration and air flow rates (Behara et al., 2011b), these data were fitted to 3 and 4 parameter sigmoidal equations using a non-linear least squares regression algorithm (Marquardt, 1963) using SigmaPlot 12.0 software.The fitting was performed on the mean of the five replicates.The requirements to test the goodness of fitting have been described elsewhere (Draper and Smith, 1981).The statistics used to distinguish and determine the good-ness of fit were: R 2 (correlation co-efficient), F-statistic and Norm.The relative de-agglomeration versus air flow rate profile data for the MgSt coated SS powders could be fitted to both 3 and 4 parameter sigmoidal equations.For uncoated SS, only the 3 parameter sigmoidal equation could be fitted as the fitting did not converge within the maximum number of iterations for the 4 parameter sigmoidal equations.The 3 parameter sigmoidal equation (Eqn. 1) was therefore selected as an appropriate model since it provided good fits of the data for both coated and uncoated drug powders and, therefore, difference between powder behavior could be determined.
where 'a' represented the upper asymptote (or maximum relative de-agglomeration), 'x0' was the x-value or air flow at which 50 % of the maximum relative de-agglomeration occurs, 'b' represented the width of the transition and was the difference in flow rate between which 75 % and 25 % of the relative de-agglomeration occurred.The estimated parameters of 'a', 'b', and 'x0' and some of the fitting statistics to demonstrate the goodness of fit are shown in Table 1.These estimated parameters ('a', 'b' and 'x0' (Table 1)) were used to describe the relative de-agglomeration behavior.The maximum extent of relative de-agglomeration (a) was an indication of the capacity of each powder to fully de-agglomerate within the air flow field of the specific device (Behara et al., 2011b).This parameter varied from about 50 % to 82 % depending on the presence and extent of coating of the SS powders (Table 1).The change in relative de-agglomeration (b) with air flow rate also provided another measure of the ability of the powders to aerosolize.For example, in comparing 1 % batch 2 and 2 % batch 1, while the change in relative de-agglomeration (b) with air flow rate was similar (17.9 and 17.7 respectively), both the maximum extent of relative deagglomeration (a) and the air flow rate to achieve 50 % relative de-agglomeration (x0) were different, suggesting different de-agglomeration behavior.
The flow rate to achieve 50 % relative de-agglomeration was also an important parameter indicating the ability of the powder to de-agglomerate.It provided an indication of the dispersion "energy" required to overcome the internal interactions within the powder (Behara et al., 2011b) and the 2 % (w/w) mechanofused SS required least input "energy" to disperse the powder (Table 1).

Cumulative fine particles mass
The cumulative fine particle masses were determined by the method outlined in Behara et al., 2011a.Firstly, using the data inherent in the particle sizing of the aerosol plume, a measure of the extent of de-agglomeration (i.e. the percentage of particles less than 5.4 μm) at specific times of aerosolization for uncoated and coated SS at four air flow rates was determined.These data show the timecourse of the aerosolization events for the uncoated and coated SS powders.The data were truncated to the time when the aerosol concentration of one of the replicates (among five replicates) approached the base-line value.The time of aerosolization varied, and the data were collected for no more than about 4 seconds.
Secondly, the calculated emitted masses at specific times (EM t ) were obtained from the product of the fractional concentration at a specific times by the total emitted mass.The EM t then was multiplied by the fractional volume less than 5.4 μm at specific times to calculate the fractional fine particle mass (FPM t ), i.e. the mass of particles less than 5.4 μm at a specific time available for respiratory deposition.The cumulative fine particle mass (CFPM t ) was determined and the CFPM t versus time profiles for the uncoated SS and the coated SS aerosolized from Rotahaler, at 45, 60, 90 and 120 L/min were presented in Fig. 3.
For both uncoated and MgSt coated SS, the time to reach maximum cumulative fine particle mass was reduced with increased flow rates.A clear difference in the extent of cumulative fine particle mass was observed between low and high air flow rates for both uncoated and coated SS powders.This behavior was expected due to increased aerosolization energy with increased air flow rate (Chew et al., 2002;Coates et al., 2005).The rate con-stant for de-agglomeration was determined from the cumulative plots by modelling and parameter estimation as described in section 3.2.2.

Estimation of de-agglomeration rate constants
The shape of the cumulative fine particle mass versus time profiles suggested that a sigmoid or mono-exponential rise to maximum (MERM) model may be appropriate and the data were fitted to both equations.Both these models have parameters that relate to the rate of deagglomeration which were the focus of the current investigation.Individual data replicates were fitted in order to obtain mean and standard deviations for the selection of the model and to find the actual variability in the rate of de-agglomeration.The coefficient of determination and Norm for both the sigmoidal and MERM models for the data in the cumulative fine particle mass versus time plots for uncoated and MgSt coated SS at the flow rate of 60 L/ min are presented in Table 2; these statistical parameters favored the MERM as the most appropriate model compared with the sigmoid.The fitting statistics shown at 60 L/min were typical of the statistics at other air flow rates.While the data were best fitted to the MERM model, the goodness of fit may be further improved by fitting the data to higher order exponential fits.Hence, the fitting process was extended to bi-exponential rise to maximum 4 parameter (BERM) equation.However, some of the replicates did not converge with BERM.Therefore, calculated cumulative fine particle mass data were mod- elled using a MERM model and the de-agglomeration rate constants (k d ) were estimated (Eqn.2).
where 'CFPM t ' is calculated cumulative fine particle mass, 'CFPM max ' is the maximum calculated cumulative fine particle mass predicted by the model, 'k d ' is deagglomeration constant in relation to particles less than 5.4 μm and 't' is the time.

3.2.3
Influence of air flow rate on de-agglomeration rate constant for uncoated and magnesium stearate coated salbutamol sulphate powders The rate constants of de-agglomeration, k d , from modelling the data using Eqn.2, plotted against the flow rates for the uncoated and MgSt coated SS powders (Fig. 4) provided an understanding of the influence of MgSt coating and air flow rate on the kinetics of de-agglomeration.Some important observations were:

Difference in k d between materials
The k d versus air flow rate profiles for the uncoated and MgSt coated SS powders were not significantly different between uncoated and coated SS powders nor among any coated SS powders (0.985 ≤ p ≤ 1.000 at the flow rate of 45 L/min; 0.559 ≤ p ≤ 0.997 at 60 L/min; 0.011 ≤ p ≤ 0.935 at 90 L/min; 0.876 ≤ p ≤ 1.000 at 120 L/min).Therefore, there was no evidence that MgSt coated SS powders increased the rate of de-agglomeration or that there was any direct relationship between the percentage of MgSt used in coating and the de-agglomeration rate constant.While the estimated k d versus air flow rate plots in Fig. 4 showed a positive trend, there was no difference between the k d values at the different air flow rates for the uncoated SS powder (0.116 ≤ p ≤ 0.999).However, there were differences in some k d for the MgSt coated SS powders.More specifically, for 1 % (w/w) MgSt coated SS, the k d at 45 L/ min was significantly lower than the k d value at 120 L/min (p ≤ 0.001); for 2 % (w/w) MgSt coated SS, the k d values of the 45 L/min and 60 L/min were significantly lower than the k d values at 90 L/min and 120 L/min (p ≤ 0.001 and p ≤ 0.001, respectively) and for 5 % (w/w) MgSt coated SS, the k d values at 45 L/min and 60 L/min were lower than the k d values at 90 L/min and 120 L/min (p ≤ 0.001 and p ≤ 0.001, respectively).

Variability of k d values
The k d values showed considerable variability in Fig. 4. The variability could be associated with the laser diffraction particle sizing of the aerosol plume, the uniformity of the cohesive powder samples in their capacity to aerosolize and the variability associated with aerosolization capability of the inhaler device.The cause of the variability in k d is unknown; however, the authors would assess the variability associated with laser diffraction methodology to be small.In addition, the aerosolizability variability associated with the cohesive powders (not mixtures) was likely to be related to particle size, packing fraction and surface energy properties.The particle size differences between samples of the powders were small; however, depending on the effectiveness of the intensive dry coating, the packing fraction and surface energy may change from sample to sample.It is noteworthy that the uncoated powder possessed variability which was at least as great as the coated samples.The more likely cause of variability was the aerosolizability reproducibility of the Rotahaler with variability possibly associated with its design including its large chamber and random movement of the capsule within the device.

Discussion
The relative de-agglomeration versus flow rate profiles were generated to describe and compare the aerosolization properties.MgSt dry coated SS demonstrated better de-agglomeration behavior than the uncoated SS.The 2 % (w/w) MgSt coated SS demonstrated best performance followed by the 5 % (w/w) MgSt coated SS and the 1 % (w/w) MgSt coated SS.The modelling of these profiles using the three parameter exponential equation allowed the estimation of these parameters which described the aerosolization behavior of the uncoated and coated powders.The ideal powder for respiratory delivery would possess a high maximum percentage of de-agglomeration (a), low change in de-agglomeration with flow rate values (b) and a low flow rate to achieve 50 % de-agglomeration (x0) (Behara et al., 2011b).In such a case, the aerosolised dose of drug would only need the minimum effort to reach a high percentage of de-agglomeration.The relationship between the estimated modelling parameters and the uncoated and coated powders is summarised in Fig. 5.
The modelling showed that the 2 % (w/w) MgSt coated SS exhibited the greatest extent of de-agglomeration with a relative de-agglomeration of about 80 %.Thus, 80 % of the available particles were de-agglomerated to particles less than 5.4 μm.The estimated parameter 'x0' showed a minimum value of about 48 L/min when the SS powders were coated with 2 % (w/w) MgSt.The estimated parameter 'b' was low for all powders and did not change sig- nificantly for the coated powders.The coating of MgSt onto the SS powders, therefore, changes the aerosolization behavior and the modelling demonstrates that the 2 % (w/w) MgSt coated SS produced the greater de-agglomeration properties.The study also shows that there were good correlations in performance between the two batches of the coated material indicating the reliability and reproducibility of the dry coating process.The parameters derived from modelling these profiles provided valuable information in understanding powder de-agglomeration behavior.
The reasons for the difference in aerosolization behavior between the uncoated and differently coated SS powders were not fully understood.The presence of the MgSt surface coating altered the surface energy of the powders.Fig. 6 shows the total surface energy changes of the uncoated and coated powders; these data demonstrated that the 2 % (w/w) MgSt coated SS exhibited the lowest total surface energy.Thus, the interaction between particles would have been reduced based on the powder adhesion models (Kendall and Stainton, 2001) and aerosolization of the powders would be expected to increase.However, de-agglomeration also can be related directly to packing fraction and indirectly to particle size distributions through their relationship with tensile strength (Kendall and Stainton, 2001;Das et al., 2012).In this study, the particle size distributions of all powders were not significantly different.Conversely, the packing fraction distributions demonstrated increased consolidation with coating and this would suggest a decreased aerosolization performance for the coated powders.Thus, the improved performance of the 2 % MgSt coated SS must be related to some balance between the surface energy and packing fraction effects to ensure better de-agglomeration and aerosolization.
The results obtained in this study were consistent with other studies which show that coating of particulate surface resulted in improved performance.The 1 % (w/w) MgSt coated SS presented with the lowest relative deagglomeration among the coated powders; this could be due to incomplete surface coverage of the MgSt.The 5 % (w/w) MgSt coated SS may likely have an excess amount of MgSt which could lead to uneven multilayer coating or excess MgSt particles mixing with the coated SS in the powder bed.In this study, the use of 2 % (w/w) MgSt provided the ideal concentration for improved de-agglomeration.
The CFPM t versus time profiles showed exponential increases in de-agglomeration with time which were consistent with the extent of coating and air flow rates.The modelling of the CFPM t versus time using a non-linear regression modelling estimated first order de-agglomeration rate constants, k d .The k d versus air flow rate profiles described the relative rates of de-agglomeration of the uncoated and coated powders.Generally, as the air flow rates increased, an increasing k d was observed for all powders.However, the air flow rate did not affect the rate constant of de-agglomeration of the uncoated powder.There was no significant difference in k d values observed between uncoated and MgSt coated SS.There was also no obvious relationship between the amount of coating used in the mechanofusion process and k d value.
The lack of relationship between the de-agglomeration rate constant and the extent of MgSt coat on the SS powder points to the fact that the device is more important in controlling the rate of de-agglomeration of powders than the powder characteristics.The large variability associated with the rate constants may relate to the use of the specific device (Rotahaler) in dispersing the SS powders.The mechanism by which the Rotahaler aerosolizes powders involves less controlled and more chaotic movement

Conclusion
The dry coating of salbutamol sulphate powders using magnesium stearate was seen to modify the kinetics of deagglomeration by improving the extent of de-agglomeration but not the rate of de-agglomeration.In this study, the optimum coating was achieved using 2 % magnesium stearate during the mechanical dry coating process; in this case, using the Rotahaler device the extent of deagglomeration was about 80 %.The rate constant for deagglomeration ranged between about 0.8 and 1.4 s -1 for all powders depending on the air flow rate.For example, at 60 L/min, the rate constant was about 0.9 s -1 with the half-life of de-agglomeration being about 1.3 s.The extent of de-agglomeration was dependent on the formulation, but the rate of de-agglomeration was independent of the formulation.
A knowledge of the rate of de-agglomeration is important, because the rate of de-agglomeration will be related to the plume concentration which may influence the deposition pattern of the drug in the lungs and may, therefore, influence the dissolution and bioavailability of the drug.

Fig. 1
Fig. 1 Particle size distributions of the aerosol plume of uncoated (B), 2 % w/w magnesium stearate (MgSt) coated salbutamol sulphate (SS) batch 1 (C) and batch 2 (D) determined using the Malvern Spraytec ® when dispersed from a Rotahaler ® at 60 L/min and their primary particle size distributions determined by laser diffraction (Malvern Mastersizer ® 2000) in liquid medium.The variability of uncoated SS de-agglomeration in Spraytec determination has been shown with error bar in (A).(n = 5, data represent mean ± standard deviation).

Fig. 4
Fig.4The de-agglomeration rate constant (k d ) of the uncoated and 1, 2 and 5 % (w/w) magnesium stearate (MgSt) coated salbutamol sulphate for cumulative fine particle mass as a function of flow rate profiles (n = 5; mean ± Standard Deviation) aerosolized by Rotahaler ® .

Fig. 5 Fig. 6
Fig. 5 The relationship between estimated modelling parameters (a = maximum relative de-agglomeration, b = difference in flow rate between 75 % and 25 % of the relative de-agglomeration and x0 = air flow to achieve 50 % of the maximum relative de-agglomeration) with the uncoated (0 % Magnesium stearate, MgSt) and coated (1, 2 and 5 % MgSt) salbutamol sulphate (SS) powders (n = 2) sigmoidal equation or maximum relative de-agglomeration b width of the transition and the difference in flow rate between which 75 % and 25 % of the relative de-agglomeration occurred.CFPM max maximum calculated cumulative fine particle mass predicted by the model (mg) CFPM t cumulative fine particle mass (mg) EM t calculated emitted masses at specific times (mg) FPM t fractional fine particle mass, i.e. the mass of particles less than 5.4 μm at a specific time for respiratory deposition (mg) or air flow at which 50 % of the maximum relative de-agglomeration occurs (L/min) γ NP non-polar surface energy (mJ/m 2 ) γ P polar surface energy (mJ/m 2 ) γ T total surface energy (mJ/m 2 )

Table 1
Non-linear least squares estimated parameters of the 3-parameter fitting of the relative de-