Article pubs.acs.org/Langmuir
Nanostructured Lipid Carriers: Effect of Solid Phase Fraction and Distribution on the Release of Encapsulated Materials Nily Dan* Department of Chemical and Biological Engineering, Drexel University, Philadelphia, Pennsylvania 19104, United States ABSTRACT: Emulsions, solid lipid nanoparticles (SLN), and nanostructured lipid carriers (NLC) containing a mix of liquid and solid domains are of interest as encapsulation vehicles for hydrophobic compounds. Studies of the release rate from these particles yield contradictory results: Some find that increasing the fraction of solid phase increases the rate of release and others the opposite. In this paper we study the release of encapsulated materials from lipid-based nanoparticles using Monte Carlo simulations. We find that, quite surprisingly, the release rate is largely insensitive to the size of solid domains or the fraction of solid phase. However, the distribution of the domains significantly affects the rate of release: Solid domains located at the interface with the surrounding solution inhibit transport, while nanoparticles where the solid domains are concentrated in the center enhance it. The latter can lead to release rates in NLCs that are faster than in the equivalent emulsions. We conclude that controlling the release rate from NLCs requires the ability to determine the location and distribution of the solid phase, which may be achieved through choice of the surfactants stabilizing the particles, incorporation of nucleation sites, and/or the cooling rates and temperatures.
I. INTRODUCTION Lipid-based nanoparticles have been widely investigated as encapsulation vehicles for hydrophobic compounds such as drugs, food additives, or cosmetics.1,2 Emulsion lipid carriers are composed of a core of lipids that are liquid at the application temperature. These are simple to synthesize and offer high encapsulation efficiency and long shelf life but are without any mechanical stability.3,4 Solid lipid nanoparticles (SLN) are similar to emulsions but utilize lipids whose melting point is high so that they form a solid phase.5 As a result, SLNs are mechanically stable, at a cost of reduced loading efficiency (although the choice of lipid can improve loading to some degree6). Nanostructured lipid carriers (NLC) combine lowand high-temperature melting lipids.7,8 The coexistence of solid and lipid domains provides both mechanical stability and higher loading efficiency, as shown, for example, by Hu et al.,6,9 Shen et al.,10 or Chinsriwongkul et al.11 Spatial organization of the solid/liquid domains in NLCs may take several forms, as sketched in Figure 1. These include core−shell assemblies, where the solid phase forms the core or the shell. However, the spontaneous phase separation in the nanoparticles may also cause the formation of a heterogeneous structure where domains are intercalated, similar to those found in lipid bilayers.12 Indeed, experimental studies show a range of NLC structures that correspond to these idealized assemblies: Jores et al.13,14 found that the liquid phase (which contained the encapsulated compound) was ejected during the solidification process, yielding an exaggerated version of the liquid phase “shell” on the surface of a solid “core”. In contrast, Tikekar and Nitin15 find intercalated solid/liquid domains. © 2014 American Chemical Society
The nanoparticle structure greatly affects the rate of encapsulated compound release. In homogeneous particles (either emulsions or SLNs), the uniform distribution of encapsulated material requires diffusion of the compound through the entire particle. The rate of release is set, then, by the diffusion coefficient through the particle and the surface area of the nanoparticle, as combined in a characteristic time scale of a2/D where a is the particle diameter and D the diffusion coefficient.16 Since the diffusion coefficient is lower in a solid than in a liquid phase, the time scale for release in an SLN is much slower than in an equivalent emulsion drop. In NLCs, the concentration of the encapsulated compound in the liquid domains means that the spatial distribution of the phases controls release: Nanoparticles where the solid phase forms a shell will display slow release and long-term stability. In contrast, particles where the liquid phase forms the “shell”, the concentration of the compound near the solution interface will lead to rapid release. In particles with a distribution of the domains, the size of the domains is expected to play an important role in determining the rate of release. Specifically, in macroscopic systems the release rate increases monotonically with the liquid phase fraction17,18 and the size of the liquid domain “channels”.19 In nanoparticles, however, release measurements yield contradictory results: Hu et al.,6,9 Shen et al.,10 and Khalil et al.20 found that the release rate is slowest in SLNs and increases with increasing liquid phase content in NLCs, in agreement Received: July 29, 2014 Revised: September 28, 2014 Published: November 6, 2014 13809
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Figure 1. Lipid-based nanoparticles. Left: single phaseeither 100% liquid (emulsions) or 100% solid (solid lipid nanoparticles, SLNs)where the entire particle is composed of a uniform phase. Center: core/shell assemblies, where the solid phase may form either the shell or the core. Right: intercalated solid/liquid phases (nanostructured lipid carriers, NLCs).
Figure 2. Release of diffusant from homogeneous, 100% liquid lipid nanoparticles. M(t)/M0 is the fraction of diffusants remaining in the particle at time t. (A) Effect of particle size a. Red: a = 20; blue: a = 10; green: a = 5. t defined time in simulation step units. (B) Release as a function of dimensionless time Dt/a2, where D = 1.5 is the diffusion coefficient (in simulation units). Symbols are as in (A). (C) Effect of number of particles, n. Red: n = 500; green: n = 250; blue: n = 750. Box size is a = 20 for the three systems. Each curve represents a single simulation rate. However, the deviation based on three runs are smaller than 5%.
domains. We find that the domain sizefor a given solid phase volume fractiondoes not significantly affect the release rate in ordered domains (namely, when the domains are ordered in a regular pattern). In systems with identical, ordered domain size, the release rate increased with increasing fraction of liquid phase, but not significantly. The distribution of the domains in the nanoparticle, however, was found to have a significant effect on release: For example, clustering of the solid phase in the nanoparticle core enhanced the initial release rate, to a degree where it may be higher than in the equivalent emulsion system (where there is no solid phase). In contrast, the presence of solid domains at the interface with the solution inhibited release.
with the predictions from macroscopic systems. Wang et al.,21 however, found the opposite: Their SLNs displayed the most rapid release rate, while the release rate from NLCs decreased with increasing liquid lipid content. The slowest release rate was observed, quite surprisingly, in 100% liquid lipid (namely, emulsions). Tikekar and Nitin15 find similar trends. Chinsriwongkul et al.11 did not see a discernible effect on release. Teeranachaideekul et al.22 found that the initial release rate was faster than that of the 100% liquid emulsion regardless of composition. They suggested that this may be due to some expulsion of the encapsulated component, although the time period over which this occurred was longer than expected if it was the result of some compound precipitating at the solution interface.22 Over longer periods of time the trends reverse, so that the amount released decreased with increasing solid phase content. The rate of release from nanoparticles depends on the surface area: Smaller particles would release their encapsulated compounds faster than larger particles.16 Typically, though, release measurements are shown in terms of absolute time,6,9,10,15 neglecting the potential effects of differences in particle size. These could be quite significant: For example, Hu et al.6 find that the average particle size for NLCs with 30% liquid phase is approximately 1/2 that of particles with 15%. Even if the two systems had exactly the same transport characteristics, size effect alone would suggest a difference of factor 4 in the characteristic release time.16 In this paper we examine the effect of solid phase fraction, domain size, and distribution on release of an encapsulated material from NLCs using Monte Carlo simulations, assuming that the encapsulant is completely excluded from the solid
II. METHODS The simulations were conducted as follows: The nanoparticle is taken to be a 2D cubic lattice of size a with periodic boundary conditions. Sizes of a tested ranged from 5 to 50 in the simulation units. In systems composed entirely of a homogeneous, liquid phase (thereby simulating emulsions), n diffusing “molecules” are placed randomly in the particle. Values of n ranged from 500 to 1500. At each time step, all diffusants are moved randomly by one lattice site. The surrounding suspension is taken to be an infinite sink, so that diffusants that reach the boundary between the nanoparticle and solution (at either x = a or y = a) are eliminated. The number of diffusants in the system is calculated at each time step. Thus, the ratio between the initial number of diffusants and those remaining at any given time represents the mass fraction of diffusant remaining in the system. Testing the scheme on the release of diffusants from homogeneous liquid particlesemulsions (Figure 2A)we see that the profiles from different core sizes collapse to a universal curve when using a “dimensionless time” of Dt/a2, where D is the diffusion coefficient in the core medium and a is the core size. This is in agreement with the 13810
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Figure 3. Fractional release from ordered solid/liquid domains. Nanoparticle size a = 40 for all systems. Black: 100% liquid phase (hs = 0). The width of a solid domain is hs. (A) Effect of domain size. ϕ = 0.56 for all cases. Green: hs = 3; light blue: hs = 10; red: hs = 15. (B) Effect of solid phase fraction, with hs = 3 for all cases. Green: ϕ = 0.56; purple: ϕ = 0.14; pink: ϕ = 0.05. Each curve represents a single simulation rate. However, the deviation based on three runs are smaller than 5%.
We first examine the release of an encapsulated diffusant from NLCs composed of ordered, finite-sized solid domains embedded in a liquid phase (see inset in Figure 3A). In Figure 3A, we compare the release profile from NLCs with identical solid phase volume fraction, but different domain size. (Note that in the array we examine the volume fraction of the solid domain ϕ□ is not given by hs/(hs+ hL) due to the finite system size and the edge effects. We find that, as expected, the release rate from the NLCs is slower than from the 100% liquid system. Also, the release rate is similar for the different domain sizes (although some spread occurs, due to the finite size of the system). However, the effects of the solid phase are not significant initially (at short times): 10% of the encapsulated diffusants (i.e., M(t)/M0 = 0.9) are released within 20 ± 10 simulation time steps for the emulsion and the NLCs. Examining the effect of the solid phase volume fraction on release for a given domain size shows (Figure 3B) that the release profile is only weakly sensitive to the solid phase fraction. The initial rate of release (slope) is the same for all systems regardless of domain size of fraction, so that 10% release is obtained within 20 ± 10 simulation time steps for all cases. Differences evolve after a period of time, however. Achieving 75% release requires, for the emulsion case, t ≈ 1000 ± 100. The presence of domains increases this value somewhat: For ϕ = 0.05 and ϕ = 0.14, t ≈ 1200 ± 100, while for ϕ = 0.56, t = 1500 ± 200. Theoretical analysis predicts that the effective diffusion coefficient in an infinite, ordered array of domains is independent of the domain size, a weighted average of the diffusion coefficient in the two phases that depends only on the phase volume fraction ϕ□□.16−18 (Experiments, though, suggest that the rate of transport increases with increasing size of the liquid domains.19) These predictions were derived, however, for an infinite array. In nanoparticles such as the ones simulated here, edge effects may play a significant role. Indeed, the similarity between the initial rates of release in emulsions and NLCs is likely due to the fact that at short times the diffusants that transfer into the solution are those placed near the edge of the nanoparticle: In the NLCs simulated in Figure 3, solid domains are placed away from the box edges (see Figure
classic diffusion model, based on Fick’s law for diffusion out of a volume into an infinitely dilute “sink”.16 The value for the diffusion coefficient required to collapse the data for the liquid cores is 1.5 ± 0.2 in the simulation units for all cases, as expected from the definition of D (= kΔx2/Δt, where k is a constant of order unity16). It should be noted that the release profile for the fraction of diffusant as a function of time was independent of the initial number of diffusants in the range tested (250−1500), as shown in Figure 2C, although due to the small number of diffusants, noise was more pronounced at low n values. Therefore, simulations were run with n = 500 unless otherwise noted. To simulate NLCs, a number of “solid domains” are placed on the lattice. The domains may be placed in an ordered array or randomly. The volume fraction of the solid phase ϕ□□ is given by the number of solid domains times their area, divided by the area of the box. Note that, due to the finite size of the system, there are “edge effects”. We assume, for simplicity, that the diffusant is completely insoluble in the solid phase. Therefore, diffusant molecules that are initially placed in the solid domain regions are eliminated and not accounted for in the initial “mass” calculation (Figure 3). Diffusants that at any given time attempt to cross into a solid domain are reflected. As in the emulsion case, we use an “infinite sink” boundary condition where any diffusant that reaches the boundary between the particle and the surrounding solution (at x = ±a or y = ±a) is eliminated. At the end of each cycle the number of diffusants remaining in the particle is calculated, yielding M(t).
III. RESULTS AND DISCUSSION We examine here the effect of NLC structure on the release of encapsulated diffusant into an “infinite sink” solution. We define the release profile as the fraction of encapsulated diffusant in the nanoparticle, as a function of time. Thus, if M0 is the number (or mass) of diffusants in the nanoparticle at t = 0 and M(t) the number at any given time t, the release profile would be M(t)/M0 as a function of time t. The release rate is the slope of this profile, namely, the (fractional) amount of diffusant released per unit time (namely, the slope of M(t)/ M0). The latter changes with timeit is always highest initially, decreasing to zero when all of the diffusant crossed into the surrounding solution. For simplicity, when discussing the rate of release we will focus on the initial rate, namely, around t = 0. 13811
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Figure 4. Effect of domain placement on the release profile from NLCs. For both cases shown, a = 40, the domain size is 10 and the solid phase volume fraction φ = 0.56. (A) Initial distribution of diffusant in an NLC with domains placed away from the nanoparticle/solution interface. Solid gray: liquid domain; solid blue: solid domain. Black dots: diffusant molecules. (B) Initial distribution of diffusant in an NLC with domains placed at the nanoparticle/solution interface. Colors and symbols are as in (A). (C) The release profile. Green circles: domains away from the surface (as in part A). Blue triangles: domains placed at the interface (as in part B). Each curve represents a single simulation rate. However, the deviation based on three runs is smaller than 5%.
Figure 5. Release from NLCs with randomly placed domains. a = 40, domain size 10, and ϕ = 0.56. Solid gray: liquid domain; solid blue: solid domain. Black dots: diffusant molecules. (A) A random distribution of solid domains that resembles a core/shell array with the solid domains forming the core. (B) A random distribution of solid domains that resembles a core/shell array with much of the solid phase at the solution interface. (C) Release profiles from different random arrays. Black line: 100% liquid (emulsion). Open green squares correspond to (A) and closed green squares to (B). Diamonds (orange) are another, randomly ordered system. Each curve corresponds to a different domain placement. Runs with the same domain placement show less than 5% deviations.
3A, inset), so that the region near the nanoparticle/solution interface is the same for the NLC and the emulsion. For example, in the case of solid 10 × 10 domains (blue line in Figure 3A), the fraction of diffusant in the strip near the interface is of order 0.45 the total amount. The deviation
between the 100% liquid and this array occurs when the fraction decreases below M(t)/M0 ≈ 0.6, when most of the diffusants in this strip diffused into the solution. To test this hypothesis, we compare the release profile for the array used in Figure 3 where solid domains are placed away 13812
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The experiments of Zhao et al.,23 who find that release from NLCs with identical lipid composition depends on the type of surfactant used to stabilize them, suggest that the nanoparticle interface may be used to control transport properties. Specifically, while the nucleation of solid domains cannot be induced directly, it may be guided through the properties of the surfactants stabilizing the emulsion drops that form the basis for NLCs,4,24 as found in several studies where surfactants were found to act as “templates” for the solid domain crystals. Furthermore, the effects of the interfacial layer on nucleation could be enhanced or reduced through the cooling rate and temperature. As shown, for example by Howard et al.,25 the degree of crystallinity in SLNs depends on the surfactant characteristics. Therefore, judicious choice of the surfactant stabilizing the emulsion drop could either induce solid phase nucleation at the interface or suppress it.24 Another method for controlling the distribution of solid domains in NLCs may be through the addition of impurities. In typical bulk systems, impurities induce random locations for the nucleation of solid domains. Solidification of oil contained in nano/micro scale drops is known to occur at lower temperatures (deeper supercooling) than the bulk, most likely because the small volume contains few impurities that can act as nucleation sites.24,26 In NLCs, the solubilized compound may act as such a nucleating impurity, depending on its characteristics. Alternately, other neutral compounds were be mixed to induce bulk domain nucleation. As a result, systems where solid domain nucleation was inducedvia the surfactantat the particle/solution interface would display a core/shell assembly with the solid phase forming the shell. Systems where the surfactant suppresses domain formation would form an inverted core/shell, with the solid phase concentrating in the center, or a random distribution of domains. Domain distribution may be further controlled through incorporation of additives or the cooling rate and temperature.4,24,26 It should also be noted that domain coalescence may cause redistribution of the domains over extended periods of time and would need to be considered in formulations designed for a long shelf life.
from the solution interface and the same array where the solid domains are placed at the interface with the solution. As shown in Figure 4, the release rate from nanoparticles with ordered domains of the same size and volume fraction clearly depends on the placement on those domains. The initial release rate when domains are at the interface between the NLC and the solution is much slower than for the same array where the domains do not border the solution interface: 10% of release (namely, M(t)/M0 = 0.9) is reached within 20 ± 10 time steps for the domains in the center (as in Figure 3) but requires 80 ± 10 in nanoparticles with domains at the solution/particle interface. However, after a period of time the two profiles overlap: Achieving 80% release requires order 2500 ± 250 steps in both cases. This is when the diffusants that were initially near the interface have diffused out. The remainder transport through the nanoparticle interior, where the channels between solid domains are the same regardless of the interfacial domain placement. The distribution of domains in heterogeneous systems is typically random. Indeed, Tikekar and Nitin15 find a network of interwoven solid and liquid domains throughout NLCs. We therefore compare the release from systems with the same solid domain size and fraction, but where the domains are placed randomly throughout the nanoparticle. It should be noted that in systems with a high liquid or solid fraction domains tend to overlap and “coalesce”, thereby forming channels of solid phase and/or liquid phase (see for example Figure 5A,B). Furthermore, the fraction of surface area available for transport varies widely between the two limits examined in Figure 4, depending on the number of domains that interface with the solution. As shown in Figure 5C, the effect of the domain distribution is significant. Despite the fact that both the domain size and solid phase fraction were kept the same in all systems, the variations in both the initial rate of release and in the longerterm behavior are significant. Perhaps more surprising, however, is the fact that the initial release rate from 100% liquid emulsions is slower than in that of the NLCs. The differences in release profile and rates in the randomly distributed domain case are clearly attributed to the placement of the domains: Systems where the solid domains concentrate in the center of the nanoparticle (as in Figure 5A), thereby forming some type of a solid core/liquid shell array will display a rapid release rate, with a characteristic time scale that is inversely proportional to the liquid shell size. In such cases, increasing the solid domain fraction will increase the release rate, as found, for example, by Wang et al.21 If the solid phase nucleates at the solution interface to form a relatively complete shell around a liquid core, release would be significantly inhibited and there may not be a significant effect to the solid phase fraction (as long as there is enough to form the shell). Heterogeneous nucleation of relatively uniform domains, somewhat regularly spaced in the nanoparticle, would lead to an increase in release rate with increasing solid phase fraction, as observed by Hu et al.6,9 or Shen et al.10 In particular, the trends we find here are very similar to those observed by Teeranachaideekul et al.,22 namely, that regardless of composition, NLCs have an initial release rate that is faster than that of the 100% liquid emulsion. Over longer periods of time the trends reverse and the emulsion shows faster release. The results presented here indicate that the ability to control the release of encapsulated diffusants from NLCs requires control over the distribution and size of the solid lipid domains.
IV. CONCLUSIONS In this paper we use Monte Carlo simulations to test the release from lipid nanoparticles into an infinite sink solution. Systems examined include emulsions (100% liquid phase) and NLCs with varying solid phase content. We find that in ordered arrays the size of the domains does not affect the release, and the solid phase fraction has only a weak effect. In contrast, the distribution of domains in the nanoparticle significantly affects transport: When the domains are localized near the solution interface, release is inhibited due to the reduction in surface area available. Domains concentrated in the center enhance the release ratewhich may even be higher than in the equivalent 100% liquid emulsion particle. We conclude therefore that controlling the release rate from lipid nanoparticles requires the ability to control the distribution of domains, which may be achieved through control of the nanoparticle interface, cooling rate, and/or the inclusion of nuclei-inducing impurities.
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AUTHOR INFORMATION
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[email protected]; Ph 1 (215) 895 6624; Fax 1 (215) 895 5837. 13813
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Notes
(18) Alonso, S. B. M.; Kapral, R. Effective medium approach for heterogeneous reaction-diffusion media. J. Chem. Phys. 2009, 131, No. 214102. (19) Negrini, R.; Mezzenga, R. Diffusion, molecular separation, and drug delivery from lipid mesophases with tunable water channels. Langmuir 2012, 28, 16455−16462. (20) Khalil, R. M.; Abd-Elbary, A.; Kassem, M. A.; Ghorab, M. M.; Basha, M. Costructured lipid carriers (NLCs) versus solid lipid nanoparticles (SLNs) for topical delivery of meloxicam. Pharm. Dev. Technol. 2014, 19, 304−314. (21) Wang, J.-J.; Liu, K.-S.; Sung, K. C.; Tsai, C.-Y.; Fang, J.-Y. Lipid nanoparticles with different oil/fatty ester ratios as carriers of buprenorphine and its prodrugs for injection. Eur. J. Pharm. Sci. 2009, 38, 138−146. (22) Teeranachaideekula, V.; Souto, E. B.; Junyapraserta, V. B.; Müller, R. H. Cetyl palmitate-based NLC for topical delivery of Coenzyme Q10 − Development, physicochemical characterization and in vitro release studies. Eur. J. Pharm. Biopharm. 2007, 67, 141−148. (23) Zhao, S.; Yang, X.; Garamus, V. M.; Handge, U. A.; Berengere, L.; Zhao, L.; Salamon, G.; Willumeit, R.; Zou, A. H; Fan, S. J. Mixture of nonionic/ionic surfactants for the formulation of nanostructured lipid carriers: Effects on physical properties. Langmuir 2014, 30, 6920−6928. (24) Douaire, M.; di Bari, V.; Norton, J. E.; Sullo, A.; Lillford, P.; Norton, I. T. Fat crystallisation at oil-water interfaces. Adv. Colloid Interface Sci. 2014, 203, 1−10. (25) Howard, M.; Lu, X.; Rinehart, J. J.; Jay, M.; Dziubla, T. D. Physicochemical characterization of nanotemplate engineered solid lipid nanoparticles. Langmuir 2011, 27, 1964−1971. (26) Smith, K. W.; Bhaggan, K.; Talbot, G.; van Malssen, K. F. Crystallization of fats: Influence of minor components and additives. J. Am. Oil Chem. Soc. 2011, 88 (8), 1085−1101.
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS I thank Rohan Tikekar for useful discussions. Financial support was provided by the Pennsylvania Department of HealthCommonwealth Universal Research Enhancement Program (CURE).
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REFERENCES
(1) Selvamuthukumar, S.; Velmurugan, R. Nanostructured lipid carriers: A potential drug carrier for cancer chemotherapy. Lipids Health Disease 2012, 11, No. 159. (2) Pardeike, J.; Hommoss, A.; Muller, R. H. Lipid nanoparticles (SLN, NLC) in cosmetic and pharmaceutical dermal products. Int. J. Pharm. (Amsterdam, Neth.) 2009, 366 (1−2), 170−184. (3) Battaglia, L.; Gallarate, M. Lipid nanoparticles: state of the art, new preparation methods and challenges in drug delivery. Expert Opin. Drug Delivery 2012, 9, 497−508. (4) McClements, D. J. Advances in fabrication of emulsions with enhanced functionality using structural design principles. Curr. Opin. Colloid Interface Sci. 2012, 17, 235−245. (5) Muller, R. H.; Radtke, M.; Wissing, S. A. Solid lipid nanoparticles (SLN) and nanostructured lipid carriers (NLC) in cosmetic and dermatological preparations. Adv. Drug Delivery Rev. 2002, 54, S131− S155. (6) Hu, F.; Jiang, S.; Du, Y.; Yuan, H.; Ye, Y.; Zeng, S. Preparation and characteristics of monostearin nanostructured lipid carriers. Int. J. Pharm. (Amsterdam, Neth.) 2006, 314, 83−89. (7) Attama, A. SLN, NLC, LDC: state of the art in drug and active delivery. Recent Patents on Drug Delivery & Formulation 2011, 5, 178− 187. (8) Muller, R. H.; Radtke, M.; Wissing, S. A. Nanostructured lipid matrices for improved microencapsulation of drugs. Int. J. Pharm. (Amsterdam, Neth.) 2002, 242 (1−2), 121−128. (9) Hu, F.; Jiang, S.; Du, Y.; Yuan, H.; Ye, Y.; Zeng, S. Preparation and characterization of stearic acid nanostructured lipid carriers by solvent diffusion method in an aqueous system. Colloids Surf., B 2005, 45, 167−173. (10) Shen, J.; Sun, M.; Ping, Q.; Ying, Z.; Liu, W. Incorporation of liquid lipid in lipid nanoparticles for ocular drug delivery enhancement. Nanotechnology 2010, 21, 025101. (11) Chinsriwongkul, A.; Chareanputtakhun, P.; Ngawhirunpat, T.; Rojanarata, T.; Sila-on, W.; Ruktanonchai, U.; Opanasopit, P. Nanostructured lipid carriers (NLC) for parenteral delivery of an anticancer drug. AAPS PharmSciTech 2011, 13, 150−158. (12) Korlach, J. S. P.; Webb, W. W.; Feigenson, G. W. Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy. Proc. Natl. Acad. Sci. U. S. A. 1999, 96, 8461−8466. (13) Jores, K.; Mehnert, W.; Drechsler, M.; Bunjes, H.; Johann, C.; Mäder, K. Investigations on the structure of solid lipid nanoparticles (SLN) and oil-loaded solid lipid nanoparticles by photon correlation spectroscopy, field-flow fractionation and transmission electron microscopy. J. Controlled Release 2004, 95, 217−227. (14) Jores, K.; Haberland, A.; Wartewig, S.; Mäder, K.; Mehnert, W. Solid lipid nanoparticles (SLN) and oil-loaded SLN studied by spectrofluorometry and Raman spectroscopy. Pharm. Res. 2005, 22, 1887−1897. (15) Tikekar, R. V.; Nitin, N. Distribution of encapsulated materials in colloidal particles and its impact on oxidative stability of encapsulated materials. Langmuir 2012, 28 (25), 9233−9243. (16) Crank, J. Mathematics of Diffusion; Oxford Science Publications: Oxford, UK, 1975. (17) Kalnin, J. R.; Kotomin, E. Effective diffusion coefficient in heterogeneous media. J. Chem. Phys. 2012, 137, No. 166101. 13814
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