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26 February 2024 Inhalation insight into the more pronounced shell-forming potency of trileucine in contrast to leucine. In addition to the static tensiometry parameters, the kinetics of surface adsorption holds significant importance, particularly considering that spray dry- ing is a rapid process, affording only a limited time- frame for the shell formers to envelop the surface. Dynamic surface tension measurements offer valu- able insights into the rate of surface adsorption. Fur- thermore, mathematical relationships or numerical simulations can be employed to this end, aiding in the understanding of the surface coverage kinetics [10]. In the context of spray drying for inhalable par- ticles, the analytical solution for surface adsorption on a semi-infinite medium can often be applied. is solution provides the time needed for monolayer sat- uration in most practical scenarios (Γ=Γ ∞ ) [16]: t Γ max = πΓ 2 max 4DC b 2 Here, D is the diffusion coefficient of the surface- active compound of interest in the solution, and C b is its bulk concentration. It is worth noting that the bulk concentration of all solutes within the droplets does increase during the drying process. However, owing to the generally faster rates of surface adsorp- tion in comparison to droplet drying, employing the initial feed concentration of the target excipient has been demonstrated to be sufficiently accurate for the majority of scenarios [10]. During the formulation particle [11]. In a particular study, spray-dried powders comprising hydroxypropyl methylcellu- lose (HPMC) and bovine serum albumin (BSA), which have dilatational moduli of 25-55 and 70 mN/m, respectively, exhibited wrinkled surfaces. In contrast, particles containing poloxamer, which has a dilatational modulus of 7 mN/m, showed smooth surfaces. Notably, all these compounds demonstrated high surface adsorption attributed to their surface activity [11]. At a specific temperature, each surface-active mate- rial possesses a maximum capacity for adsorption on the surface, denoted as Γ max . Gradually increasing the bulk concentration results in an increase in equilib- rium surface adsorption, accompanied by a reduction in the solution's surface tension. Upon reaching sur- face saturation, further surface adsorption becomes unattainable, yet the surface tension continues to decrease due to the ongoing rise in solute activity within the bulk phase [6]. Upon reaching a specific concentration, known as the critical micelle concentration (CMC), the sur- face tension reaches its minimum value, or equiv- alently, the surface pressure reaches its maximum value, π max . Once the CMC is reached, any addi- tional solute introduced to the bulk prompts the surface-active molecules to assemble into colloidal clusters called micelles, which do not further dimin- ish the surface tension [6]. For each surfactant, these equilibrium parameters— namely, Γ max , π max and CMC—can be determined by assessing the surface tension of the solution across various levels of bulk concentration. is can be achieved using diverse tensiometry techniques such as the Wilhelmy plate, Du Noüy ring and pendant drop methods, as illustrated schematically in Figure 3. Direct extraction of π max and CMC from such a plot is feasible, while Γ max can be deduced from the slope of the linear segment of the plot, employing the sim- plified Gibbs adsorption equation [13]: Γ= − 1 ∙ dσ nRT dlnC where n = 1 for nonionic or zwitterionic solutes and n = 2 for one-by-one ionic solutes in the absence of any additional electrolyte [14]. In this equation, R represents the universal gas constant, σ is the surface tension, and C denotes the solute's bulk concentration. In relation to shell-forming excipients, it is gener- ally understood that a compound characterized by a larger Γ max is likely to be more effective in enhancing the aerosol properties of the spray-dried powders. As an example, based on surface tension data at 25 °C [7,15], the maximum surface excess concentrations for trileucine and leucine are calculated to be 0.99 and 0.15 mg/m², respectively. ese numbers offer Figure 3 Schematic plot illustrating a typical tensiometry measurement of a solution containing a surface-active compound, highlighting the relevant parameters of interest. Surface Tension Ln (Concentration) π max -nRT Γ max CMC