Corrigendum to “Characterization of nanoparticles made of ethyl cellulose and stabilizing lipids: Mode of manufacturing, size modulation, and study of their effect on keratinocytes” [Int. J. Pharm. 607 (2021) 121003] (International Journal of Pharmaceutics (2021) 607, (S0378517321008097), (10.1016/j.ijpharm.2021.121003))

The authors wish to make the following corrections. The corrected Section 3.6: 3.6. Influence of the addition rate of the non-solvent on the nanoparticle size As described in the previous section, the addition of active ingredients (such as CBD and CUR) or a polymer with higher molecular weight (such as EC100) results in a particle size reduction. This finding has led to a hypothesis that the process occurs by a combination of core formation and polymer deposition on existing cores. The nucleation kinetics, and particularly the nuclei (or core) formation rate is directly related to the solute supersaturation ratio C/C*, were C is concentration of the solute in a bulk solution and C* is the equilibrium solute concentration (Mahajan and Kirwan, 1994). The nucleation induction time is related to the supersaturation ratio as: [Formula presented] Therefore, at higher supersaturation ratios, the nucleation happens relatively faster. The non-solvent addition rate changes the fraction f of the solvent in the solvent-nonsolvent mixture and thus allows controlling the extent of supersaturation and the rate of new nuclei formation. Thus, in processes with fast addition rates of non-solvent that maintain high supersaturation ratios, the core formation process would have a dominating influence on the final particle size rather than the polymer deposition on the cores. When slow addition rates of the non-solvent are used, the polymer deposition process would predominate its influence on the particle size. The non-solvent addition rate controls the rate of the solvent fraction f change. The rate of the solvent fraction f change can also be dictated by determination of the initial volume of the solvent (while the non-solvent addition rate kept constant). The volume fraction of the solvent f is defined as: [Formula presented] where [Formula presented] is the volume of the solvent and x is the non-solvent addition rate expressed in ml/min. The ratio between [Formula presented] and x can be defined as [Formula presented] and [Formula presented], so Eq. (6) can be transformed to: [Formula presented] Therefore, in a lower [Formula presented] value, corresponding to a higher achievable super-saturation ratio [Formula presented], a smaller particle radius is expected and vice versa. As seen in Fig. 3, the particle size changes linearly with increase in [Formula presented], confirming that the particle size increases in higher [Formula presented] values which corresponds to a slower change of f. Fig. 3 shows the data obtained from three different sets of experiments. In two sets of experiments, the non-solvent addition rate was kept constant (x = 5.2 and 22.5 ml/min), while the volume of the solvent [Formula presented] was modified. In the third experiment, the volume of the solvent was kept constant while the non-solvent addition rate x changed. The results obtained from the experiments performed with constant x and modified [Formula presented] demonstrated two nanoparticles size-related regions. At [Formula presented] values below 4 min the nanoparticle size sharply increased with the increase in [Formula presented], whereas at [Formula presented] values >4 min, the size increased moderately. It may be postulated that in the first set of experiments, the high addition rate x dominated the creation of cores while in the second set of experiments, the low x dictated mainly the polymer deposition on the existing cores. The third set of experiments was performed by changing the non-solvent addition rate x while [Formula presented] was kept constant. The relationship between particle radius and [Formula presented] obtained from the third set, reassured the two-region pattern. Fig. 4 shows the relationship between the polymer concentration and resulting particle radii. The nanoparticles were prepared at two extremely low addition rates with [Formula presented] values corresponding to 19.2 min and 38.5 min, much above the threshold value of 4 min, which is hypothesized that corresponds to extensive nuclei formation. At such high [Formula presented] values, the obtained supersaturation ratio in the system would be low as well, contributing to polymer deposition on existing particle cores rather than to extensive formation of particle cores. Ideally, according to Eq. (1), the n value in the relationship between the particle radius R and the polymer concentration [Pol] is equal to ⅓ when the nanoparticles are obtained by polymer deposition only. Since a part of the polymer molecules is expected to form nanoparticle cores even at high [Formula presented] values, n tends to get closer to ⅓. As shown in Fig. 4, the extrapolated n value was about 0.25 at [Formula presented] = 19.2 min (x = 1.04 ml/min), whereas the extrapolated n value was about 0.30 at [Formula presented] = 38.5 min (x = 0.52 ml/min). These two values of [Formula presented] corresponded to the lowest non-solvent addition rate feasible by the laboratory equipment used. At such slow non-solvent addition rates, the formation of visible aggregates was noted, however, no aggregates were formed when the process was run at higher non-solvent addition rates. The nucleation/particle growth mechanism brought up in this paper was further supported by testing the influence of temperature on the obtained nanoparticle size. Although it was not statistically significant (p = 0.09), it was found that the particle size for process performed at controlled temperature of 0 °C was lower (170 ± 25 nm) than particle size of nanoparticles prepared at ambient temperature (205 ± 6 nm). At a lower temperature, the solubility of both active ingredient and the polymer is decreased, and supersaturation is achieved at an earlier stage hence more nuclei are formed. In numerous studies dealing with nanoparticle formulation by nanoprecipitation (or solvent displacement method), a significant process parameter is the stirring or the mixing velocity. Nevertheless, the mixing velocity parameter is solely applicable for processes in which the polymer solution is added to the non-solvent, but it is less effective factor in a non-solvent ‘dropping-in’ process as noted in the present report. The influence of several process parameters such as the type of stirrer and the stirring speed, the temperature, the solvent/non-solvent ratio, and the ethyl cellulose concentration in the alcoholic solution was explored (Plasari et al., 1997). According to these findings, the polymer concentration was most important parameter for controlling the particle size. On the other hand, it was shown that the final nanoparticle size was reduced with the increase of the stirring velocity (Allemann et al., 1992). Another group (Afonso et al., 2020) observed an inverse relationship between the solvent/non-solvent ratio and the obtained particle size. According to the model we present in this paper, there is a ‘critical’ solvent/non-solvent ratio during the process (at about 60% v/v of the non-solvent) that once reached, the polymer solubility turns to be too low for any free polymer available for further precipitation and particle growth. Corrected Fig. 3: [Figure presented] Fig. 3: Influence of the non-solvent addition rate-x and the solvent volume-V_s (V_s/x = 1/β) on the final particle size. Unloaded particles were prepared with 0.01% cetyl alcohol and 0.05% triethyl citrate, ethyl cellulose EC7 concentration was 0.05%w/w. Corrected Fig. 6: [Figure presented] Fig. 6: Micrographs of HaCaT cells incubated with nanoparticles loaded with CBD/CUR combination. Left: light microscopy of HaCaT cells treated with nanoparticles loaded with CBD and CUR magnification ×600; Right: fluorescence microscopy of the same HaCaT cells (Excitation: 469 nm wavelength, exposure time: 0.8 s).