Use of Viscoelastic Measurements for Investigating Interparticle

Langmuir 2002, 18, 7663-7668

7663

Use of Viscoelastic Measurements for Investigating Interparticle Interactions in Dispersions of Micellar-like Poly(lactic acid)-Poly(ethylene glycol) Nanoparticles T. Riley,† S. Stolnik,*,† M. C. Garnett,† L. Illum,† S. S. Davis,† P. Taylor,‡ and Th. F. Tadros§ School of Pharmaceutical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom, and Syngenta, Jealott’s Hill International Research Centre, Bracknell, Berkshire, RG42 6EY, United Kingdom Received March 12, 2002. In Final Form: June 25, 2002

A series of poly(lactic acid)-poly(ethylene oxide) (PLA-PEG) AB block copolymers have been synthesized and used to produce aqueous dispersions of micellar-like nanoparticles. The hydrodynamic radius of the PLA core plus the stabilizing 5 kDa PEG layer, as determined by photon correlation spectroscopy, increased with the molecular weight of the PLA block. PLA-PEG particles have possible application as drug carriers for targeted drug delivery. In addition to particle size, the layer thickness and mobility of the hydrated PEG chains will be important in determining the particle’s ability to avoid uptake by the defense system of the body, the phagocytic cells of the reticuloendothelial system. Viscoelastic measurements were used to investigate interparticle interactions in concentrated dispersions of the PLA-PEG nanoparticles. This approach has not previously been used to study how the interactions in dispersions of micellar-like assemblies depend on the copolymer geometry. When the volume fraction of the dispersions, φcore, was increased, the storage modulus, G′, became greater than the loss modulus, G′′, indicating steric interaction between the PEG chains. At higher φcore values, compression of the grafted polymer chains was observed. The critical volume fraction at which overlap of the PEG chains commences, φcorecrit (i.e., G′ ) G′′), was used in conjunction with the overall hydrodynamic radius to determine the grafted PEG chain layer thickness. Micellar-like nanoparticles assembled from a PLA-PEG copolymer with a 5 kDa PEG block and a relatively low molecular weight 3 kDa PLA chain had an appreciable steric layer thickness of 6.3 nm. Hence, interparticle interactions in the concentrated dispersion were “soft” in nature as a result of the long-range interactions, as shown by the weak scaling dependence of the storage modulus on the volume fraction. The layer became more extended as the molecular weight of the PLA block was increased from 3 to 6 kDa, and as a consequence the PEG chains became less compressible. By using this method to characterize the PEG layer, it should be possible to rationalize the in vivo performance of the PLA-PEG nanoparticles and therefore aid the design of particulate drug carriers.

1. Introduction Particulate drug carriers injected into the body are normally rapidly recognized as foreign and removed from the blood circulation by the phagocytic cells of the reticuloendothelial system (RES).1,2 The process of phagocytosis is mediated by the adsorption of certain blood components, such as proteins, onto the particle surface.3 Hence, the design of long-circulating drug carriers has focused on surface modification to modify the quality and quantity of plasma components adsorbed. In particular, particles stabilized with poly(ethylene glycol) (PEG) are known to avoid phagocytosis and achieve prolonged circulation times.1,4 A hydrophilic steric barrier may be achieved either by grafting PEG to the particle surface5 or by physical adsorption of polymeric surfactants.6 Both * Corresponding author. Tel: +44 (0)115 9515121. Fax: +44 (0)115 951 5122. † School of Pharmaceutical Sciences, University of Nottingham. ‡ Syngenta, Jealott’s Hill International Research Centre. § Retired, consultant. (1) Stolnik, S.; Illum, L.; Davis, S. S. Adv. Drug Delivery Rev. 1995, 16, 195. (2) Kreuter, J. J. Controlled Release 1991, 16, 169. (3) Moghimi, S. M.; Davis, S. S Crit. Rev. Ther. Drug Carrier Syst. 1994, 11, 31. (4) Lee, J.; Martic, P. A.; Tan, J. S. J. Colloid Interface Sci. 1989, 131, 252. (5) Dunn, S. E.; Brindley, A.; Davis, S. S.; Davies, M. C.; Illum, L. Pharm. Res. 1994, 11, 1016.

increasing the length7 and enhancing the surface density5 of the stabilizing PEG chains have been shown to reduce the uptake of particles by the RES. More recently, researchers in this field have taken advantage of the inherent core-shell structure of micelles and nanoparticles assembled from block copolymers.8,9 Poly(ethylene glycol) is typically used as the hydrophilic block, which forms a grafted steric barrier which cannot be displaced by plasma components. For drug delivery applications, it is obviously essential that the hydrophobic core of the assembly is constructed from biodegradable polymers. Drugs may incorporated by physical entrapment into a hydrophobic matrix of, for example, poly(lactic acid) (PLA) or poly(lactic-co-glycolic) acid (PLGA).9,10 Alternatively, drugs have been covalently or ionically bound to functionalized water-soluble polymers such as poly(aspartic acid), which then form the micellar core.11 (6) Stolnik, S.; Felumb, N. C.; Heald, C. R.; Garnett, M. C.; Illum, L.; Davis, S. S. Colloids Surf., A 1997, 122, 151. (7) Gref, R.; Minamitake, Y.; Peracchia, M. T.; Trubetskoy, V.; Torchilin, V.; Langer, L. Science 1994, 263, 1600. (8) Kataoka, K.; Harada, A.; Nagasaki, Y. Adv. Drug Delivery Rev. 2001, 47, 113. (9) Zhang, X.; Jackson, J. K.; Burt, H. Int. J. Pharm. 1996, 132, 195. (10) Govender, T.; Riley, T.; Ehtezazi, T.; Garnett, M. C.; Stolnik, S.; Illum, L.; Davis, S. S. Int. J. Pharm. 2000, 199, 95. (11) Yokoyama, M.; Okano, T.; Sakurai, Y.; Suwa, S.; Kataoka, K. J. Controlled Release 1996, 39, 351.

10.1021/la020248x CCC: $22.00 © 2002 American Chemical Society Published on Web 08/16/2002

7664

Langmuir, Vol. 18, No. 20, 2002

Riley et al.

We have synthesized a series of poly(lactic acid)-poly(ethylene glycol) (PLA-PEG) copolymers, to investigate the influence of copolymer geometry on the physicochemical characteristics of the particulate carrier and the subsequent impact on biological performance.10,12 Following precipitation into aqueous media from a watermiscible organic solvent, these copolymers assemble into spherical micellar-like nanoparticles. The hydrodynamic radius of the core plus the stabilizing PEG layer, Rhyd, may be determined by photon correlation spectroscopy (PCS). In this way, the overall size of nanoparticles assembled from copolymers with a 5 kDa PEG block has been shown to increase with the molecular weight of the PLA segment.12,13 However, little is known about the effect of copolymer geometry on the structure of the hydrated PEG layer. Tadros and collaborators14-16 have demonstrated how dynamic rheological measurements on concentrated dispersions can be used to obtain the thickness of grafted PEG layers, ∆. Essentially, the storage and loss moduli are measured as a function of the volume fraction of the dispersion. As the surface-to-surface distance between the particles approaches twice the grafted layer thickness, a strong interaction occurs and the system becomes predominantly more elastic than viscous. From a knowledge of the critical volume fraction at which this occurs, the thickness of the steric layer can be calculated. The rheological properties of concentrated dispersions can also be correlated with interparticle interactions.17,18 In general, the storage modulus of a dispersion scales with the core volume fraction (φcore) with an exponent, n, that is,

G′ ) kφcoren

(1)

The scaling exponent n can be obtained from log-log plots of G′ versus φcore. These plots are usually linear above the critical core volume fraction at which overlap of the stabilizing chains first occurs. The value of n depends on the compressibility of the steric layer which may be described by the ratio ∆/Rhyd. For example, if the stabilizing chains extend a considerable distance from the particle surface then interparticle interactions are termed “soft” in nature as a result of the longer range of the interaction. The storage modulus of such a system, with a high value of ∆/Rhyd, would be expected to scale weakly with the volume fraction of the dispersion, that is, low n.18 In this paper, we present results on the viscoelastic properties of concentrated dispersions of micellar-like nanoparticles, assembled from PLA-PEG block copolymers with a PEG block of 5kDa and a varying PLA segment. Measurements as a function of the volume fraction of the dispersion have been used to determine the critical volume fraction for the onset of steric interaction and thereby the grafted PEG chain thickness, ∆. In addition, the volume dependence of the elastic modulus at high volume fractions has been used to deduce (12) Riley, T.; Govender, T.; Stolnik, S.; Xiong, C. D.; Garnett, M. C.; Illum, L.; Davis, S. S. Colloids Surf., B 1999, 16, 147. (13) Riley, T.; Stolnik, S.; Heald, C. R.; Xiong, C. D.; Garnett, M. C.; Illum, L.; Davis, S. S.; Purkiss, S. C.; Barlow, R. J.; Gellert, P. R. Langmuir 2001, 17, 3168. (14) Prestidge, C.; Tadros, Th. F. J. Colloid Interface Sci. 1988, 124, 660. (15) Liang, W.; Tadros, Th. F.; Luckham, P. F. J. Colloid Interface Sci. 1992, 153, 131. (16) Hagan, S. A.; Davis, S. S.; Illum, L.; Davies, M. C.; Garnett, M. C.; Taylor, D. C.; Irving, M. P.; Tadros, Th. F. Langmuir 1995, 11, 1482. (17) Tadros, Th. F.; Liang, W.; Costello, B.; Luckham, P. F. Colloids Surf., A 1993, 79, 105. (18) Tadros, Th. F. Adv. Colloid Interface Sci. 1996, 68, 97.

information about interparticle interactions and hence the nature of the PEG layer. 2. Experimental Section 2.1. Materials. PLA-PEG block copolymers, with a PEG block of 5 kDa, were synthesized by the ring-opening polymerization of D,L-lactide using a stannous octoate catalyst.19,20 Methoxy poly(ethylene glycol) (MeOPEG, 5kDa) (Fluka, Gillingham, U.K.) was purified by partition from aqueous solution using dichloromethane, followed by precipitation into an excess of diethyl ether. D,L-Lactide (Aldrich, Gillingham, U.K.) was purified by twice recrystallizing from dried ethyl acetate. An appropriate amount of stannous octoate (Sn(II) 2-ethylhexanoate, Sigma, Poole, U.K.) was added as a solution in dried toluene to a polymerization tube containing the purified D,L-lactide and MeOPEG. The reactants were dried at 70 °C, before allowing the copolymerization to proceed at 170 °C for 5 h, under vacuum. The product was dissolved in dichloromethane, and the copolymer was isolated by precipitation into an excess of petroleum ether at 40-60 °C. The purified copolymer was dried in a vacuum oven at 70 °C for 24 h and then stored in a desiccator under vacuum. By varying the ratio of D,L-lactide to PEG 5 kDa in the reaction, it was possible to control the geometry of the resultant copolymer. 1H NMR spectroscopy (Bruker AC250, Germany) of the copolymers dissolved in CDCl3 was used to confirm their PLA to PEG weight ratios (in kDa) as 3:5, 6:5, and 15:5. The water used in all experiments was doubly distilled from an all-glass apparatus. 2.2. Preparation of Dispersions. Particulate dispersions (2% w/v) of the PLA-PEG copolymers were prepared using the precipitation/solvent evaporation method.21 A solution of the copolymer in acetone (5.8% w/v) was added dropwise to 350 mL of distilled water, while stirring with a magnetic stirrer. Following evaporation of the organic solvent, the dispersion was filtered using 1.2 µm pore size filters (Sartorius, Go¨ttingen, Germany). The filtered dispersions were concentrated to approximately 10% w/v by ultrafiltration (Amicon ultrafiltration cell, Amicon Inc., U.S.A.) using disk filters with a molecular weight cutoff of MW ) 30 kDa (PM30 Diaflo ultrafilters, Amicon Inc.). More concentrated dispersions were produced by evaporation of the 10% w/v dispersion at 40 °C, using a thermostatically controlled hot plate stirrer. This gave dispersions with concentrations ranging from approximately 20 to 28% (w/v PLA-PEG). The PLA-PEG nanoparticle concentration (w/v %) of each sample was accurately determined by freeze-drying (Edwards Modulyo freeze-drier, York, U.K.) a known mass of the dispersion. It was then possible to calculate the PLA core volume fraction, φcore, of each sample using the literature value for the bulk density of PLA (1.29 g cm-3 22). 2.3. Hydrodynamic Radius Measurement. The hydrodynamic radius of the PLA-PEG nanoparticles was determined by PCS (Malvern 4700, Malvern, U.K.) with vertically polarized light (wavelength, 488 nm) supplied by an argon-ion laser (Cyonics, San Jose, U.S.A.) operated at 20 mW. All experiments were performed using diluted dispersions at a temperature of 25.0 ( 0.1 °C. The correlation decay functions were analyzed by the cumulants method to obtain an average particle diameter and polydispersity index (defined as the variance of the lognormal distribution of particle sizes). 2.4. Rheological Measurements. Dynamic (oscillatory) measurements were performed using a Bohlin VOR rheometer (Bohlin Reologi, Lund, Sweden) interfaced with an IBM computer as described previously.14-16 This instrument operates in the frequency range 10-3-20 Hz and has interchangeable torsion bars covering a wide range of sensitivities. Measurements were made over the frequency range of 0.01-8 Hz at 25 ( 0.1 °C. A concentric cylinder measuring system (C14; sample volume, 2 mL) with a moving cup 15.4 mm in diameter and a fixed bob 14 (19) Deng, X. M.; Xiong, C. D.; Cheng, L. M.; Huang, H. H.; Xu, R. P. J. Appl. Polym. Sci. 1995, 55, 1193. (20) Churchill, J. R.; Hutchinson, F. G. European Patent Application 0 0166 596, 1983. (21) Fessi, H.; Devieseguet, J. P.; Puisieux, F.; Thies, C. French Patent 2 608 988, 1986. (22) Eling, B.; Gogolewski, S.; Pennings, A. J. Polymer 1982, 23, 1587.

Interactions of PLA-PEG Nanoparticles

Langmuir, Vol. 18, No. 20, 2002 7665

Figure 1. Frequency sweep for the PLA-PEG 6:5 particulate dispersion with a PLA core volume fraction of φcore ) 0.104.

Figure 2. Frequency sweep for the PLA-PEG 6:5 particulate dispersion with a PLA core volume fraction of φcore ) 0.094.

Table 1. Hydrodynamic Radii of PLA-PEG Micellar-like Nanoparticles (from PCS Measurements) and Their Core-Shell Dimensions as Determined from Viscoelastic Measurements (See Equation 5)

Figure 1 shows a typical frequency sweep for the PLAPEG 6:5 dispersion with a PLA core volume fraction of φcore ) 0.104. At this volume fraction, the elastic modulus of the dispersion is greater than the viscous modulus (G′ > G′′) over the entire frequency range. This may be attributed to the steric interaction between the PEG chains on close approach. Furthermore, both G* and G′ are only weakly dependent on frequency. Such rheological behavior is characteristic of a viscoelastic solid, where all of the diffusional relaxation processes are slower than the oscillation time.14 At this relatively high volume fraction, the system is behaving like an “elastic gel” and it is probable that the PEG chains have undergone significant interpenetration and compression. The high values of the elastic modulus at these high volume fractions may be attributed to the small size and hence high surface area of the PLA-PEG micellar-like assemblies.23 Similar trends were observed for the PLA-PEG 3:5 dispersions. As the volume fraction of the dispersion is decreased, so the elastic modulus becomes more frequency dependent. This is illustrated in Figure 2, which shows the frequency sweep results for the PLA-PEG 6:5 dispersion with φcore ) 0.094. Indeed, below a characteristic frequency of 0.08 Hz the curves corresponding to G′ and G′′ cross over such that G′′ > G′. At low frequencies, the oscillatory deformation time is greater than the time required for the nanoparticle microstructure to rearrange, and the energy put into the system through the applied shear is dissipated through particle diffusion. This behavior is characteristic of viscoelastic liquids,24 and it is likely that at this intermediate volume fraction the PEG chains have undergone some interpenetration, without any compression. As the volume fraction of the dispersion is decreased further, the nanoparticles become well separated such that G′′ > G′ over the entire frequency range (data not shown). Figure 3 shows plots of G′ and G′′ (at 1 Hz) as a function of the PLA core volume fraction, for the PLA-PEG 3:5 and 6:5 dispersions. There is a notable curvature in the plots of the loss modulus, G′′. As the volume fraction is increased, an increase in the overall modulus of the dispersion initially results in an increase in G′′. However, an increase in the volume fraction also results an increase in the relaxation time of the dispersion. Therefore, at high

PLA-PEG hydrodynamic radius, Rhyd (nm) polydispersity index vol fraction where G′ ) G′′, φcorecrit PEG layer thickness, ∆ (nm) PLA core radius, Rc (nm)

3:5

6:5

15:5

11.5 0.163 0.059 6.3 5.2

15.2 0.104 0.093 7.2 8.0

19.0 0.157

mm in diameter was used. Each sample was equilibrated for 10 min in the rheometer prior to making measurements. Initially, the frequency was kept constant at 1 Hz and the strain amplitude gradually increased, up to approximately 0.2 (strain sweep), while measuring the rheological parameters. This enabled the linear viscoelastic region to be defined, where the rheological parameters are independent of the strain amplitude. Measurements were then made in the linear viscoelastic region as a function of frequency, at a fixed strain amplitude (frequency sweep). The experiments were performed at a minimum of 10 different concentrations of the PLA-PEG nanoparticles. From the stress and strain amplitudes (τ0 and γ0, respectively) and the phase angle shift, θ, it is possible to determine the following rheological parameters:

|G*| )

τ0 γ0

(2)

G′ ) |G*| cos θ

(3)

G′′ ) |G*| sin θ

(4)

where G* is the complex modulus, G′ is the storage modulus (the elastic component), and G′′ is the loss modulus (the viscous component).

3. Results and Discussion The hydrodynamic radius and polydispersity of the PLA-PEG nanoparticles, shown in Table 1, are in good agreement with previous studies where more dilute dispersions were prepared.12 As expected, the particle size of the PLA-PEG assemblies increased with the molecular weight of the PLA block.13 However, the PLA-PEG 15:5 dispersions were destabilized when attempts were made to concentrate them, with the formation of macroscopic agglomerates. Hence, this dispersion had a narrow linear viscoelastic region and could not be used in the rheological study. Such a reduced colloidal stability has previously been shown to be due to a reduction in PEG surface coverage as the molecular weight of the PLA block is increased.12

(23) Barnes, H. A.; Hutton, J. F.; Walters, K. An Introduction to Rheology; Elsevier: Amsterdam, 1989. (24) Ploehn, H. J.; Goodwin, J. W. Faraday Discuss. Chem. Soc. 1990, 90, 77.

7666

Langmuir, Vol. 18, No. 20, 2002

Riley et al.

Figure 3. Plots of G′ and G′′ versus the PLA core volume fraction, φcore, at a frequency of 1 Hz: (a) PLA-PEG 3:5 dispersion and (b) PLA-PEG 6:5 dispersion.

volume fractions less energy is dissipated as viscous flow, and hence the observed decrease in G′′. From these plots, it is possible to determine the critical volume fraction φcorecrit, at which the dispersion changes from predominantly viscous to predominantly elastic. Assuming that the crossover point where G′ ) G′′ represents the onset of interpenetration of the grafted PEG chains, then φcorecrit can be used to obtain the grafted PEG layer thickness. If the particles are arranged in a random packing fashion, then the maximum packing fraction should be approximately equal to 0.64. Hence, from a knowledge of the critical volume fraction and the hydrodynamic radius of the particles (Rhyd) as determined from PCS measurements in dilute solution, the hydrodynamic layer thickness of the grafted PEG chains (∆) can be estimated from the following equation:14-16

(

0.64 ) φcorecrit 1 +

∆ Rhyd - ∆

)

3

(5)

It is assumed that the PEG layer does not compress until after the PEG chains have come into contact (i.e., at the critical volume fraction). The values of φcorecrit and ∆ obtained are presented in Table 1. The low values of φcorecrit indicate that the effective radius of the micellar-like assemblies is considerably larger than the radius of the core, due to the presence of the PEG layer. The values obtained for the grafted PEG layer thicknesses were reasonable for a PEG chain of MW ) 5 kDa and are comparable to those found for PLA-PEG 2:5 adsorbed onto the surface of polystyrene latex particles, 156 nm in diameter (∆ ) 6.8 nm6). However, thicker adsorbed layers have been reported for PLA-PEG 2:5 copolymers adsorbed to the surface of similar-sized PLGA

nanoparticles (∆ ) 10.5 nm25), the surface of which is less hydrophobic. The radius of gyration, Rg, of a 5 kDa PEG chain in a good solvent can be calculated to be 3.1 nm.26 Hence, the PEG layer thickness of the PLA-PEG 3:5 micellar-like nanoparticles is comparable to 2Rg (Table 5.2), which suggests that the PEG chains adopt a random coil configuration. This is in accord with earlier work, where the coronal PEG chains of the PLA-PEG 3:5 nanoparticles were shown to have a high degree of lateral freedom as a consequence of a low micellar aggregation number.13 In contrast, the grafted PEG chains of the PLA-PEG 6:5 micellar-like nanoparticles are more extended; that is, ∆ > 2Rg. This may be attributed to an increase in the micellar aggregation number and a reduction in the surface curvature as the molecular weight of the PLA block is increased.13 Similar trends of an increasing layer thickness with decreasing curvature have been observed for poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) copolymers adsorbed to the surface of polystyrene latex particles, using both dynamic light scattering27 and rheological28 techniques. Obtaining an estimate of the PEG layer thickness also enables the radius of the PLA core, Rc, to be determined. As expected, Rc increases as the molecular weight of the PLA block is increased from 3 to 6 kDa (Table 1). The elastic modulus, G′ (at 1 Hz), of the PLA-PEG 3:5 and 6:5 dispersions is plotted as a function of φcore on a log-log scale in Figure 4. In both cases, the elastic modulus initially increases rapidly (regime A) before leveling out in a plateau at higher volume fractions (regime B). As the volume fraction is increased, the grafted PEG chains on neighboring particles begin to interact repulsively on account of the loss of configurational entropy and/or increases in the enthalpy of mixing (dehydration) of the PEG chains. It is likely that in regime A of the plots, some distortion of the PEG chains is occurring. At the onset of regime B, the interparticle distance is probably significantly less than twice the layer thickness of the grafted PEG chains (2∆). In which case, the leveling of the log G′ versus log φcore relation at relatively high volume fractions may be due to a compression of the PEG chains as they strongly interpenetrate. Faers and Luckham29 have reported that dispersions of polystyrene latex particles stabilized by adsorbed PEO-PPO-PEO copolymers can exhibit similar viscoelastic behavior. The elastic modulus of polymer-coated particles, approximately 70 nm in diameter, was observed to rise sharply and then plateau at volume fractions of φ > 0.3. This change in gradient was also attributed to the compression of the stabilizing PEG chains. In contrast, the rheological behavior of larger particles approximately 430 nm in diameter, stabilized with the same copolymer, showed little deviation in comparison to that of the uncoated particles. The stabilizing PEG chains on these larger particles were said to be more “brushlike”, and hence the particles behaved as hard spheres. Therefore, as a consequence of the highly compressible PEG chains, interparticle interactions in concentrated dispersions of micellar-like PLA-PEG nanoparticles can be considered soft in nature. (25) Stolnik, S.; Dunn, S. E.; Davies, M. C.; Coombes, A. G. A.; Taylor, D. C.; Irving, M. P.; Purkiss, S. C.; Tadros, Th. F.; Davis, S. S.; Illum, L. Pharm. Res. 1994, 11, 1800. (26) Devanand, K.; Selser, J. C. Macromolecules 1991, 24, 5943. (27) Li, J. T.; Caldwell, K. D.; Rapoport, N. Langmuir 1994, 10, 4475. (28) Greenwood, R.; Luckham, P. F.; Gregory, T. Colloids Surf., A 1995, 98, 117. (29) Faers, M. A.; Luckham, P. F. Colloids Surf., A 1994, 86, 317.

Interactions of PLA-PEG Nanoparticles

Langmuir, Vol. 18, No. 20, 2002 7667

Figure 5. Plot of the elastic modulus, G′, versus the half corecore interparticle separation, h, for PLA-PEG 3:5 and 6:5 dispersions.

Figure 4. Plots of the elastic modulus, G′, versus the PLA core volume fraction, φcore, (at a frequency of 1 Hz) on a log-log scale: (a) PLA-PEG 3:5 dispersion and (b) PLA-PEG 6:5 dispersion. Table 2. Correlation between Compressibility of the PEG Layer and ∆/Rc, as Quantified by a Power Law Fit to the Elastic Part of the log G′-log Ocore Plots (See Equation 1) PLA-PEG ∆/Rc power law exponent, n (regime A) power law exponent, n (regime B)

3:5

6:5

1.2 37.2 3.8

0.9 54.6 3.7

A scaling law can be fitted to both linear parts of the log G′ versus log φcore plots (see eq 1). For the regions of the plots where G′ changes sharply with φcore (regime A), this gives values of n ) 37.2 and n ) 54.6 for the PLAPEG 3:5 and 6:5 nanoparticles, respectively. This implies that the compressibility of the PEG layer decreases as the size of the PLA core is increased. This is in accord with the reduction in the ratio of the grafted layer thickness to the core radius, that is, ∆/Rc, as indicated in Table 2. Similar tends have previously been observed for polystyrene latex particles sterically stabilized by grafted PEG 2 kDa chains, where the value of the scaling exponent n again correlated with ∆/Rc.18 Smaller particles behaved as soft-sphere systems, whereas the larger particles approached hard-sphere systems. The scaling exponents for the regions where the plots of G′ as a function φcore level to a plateau (regime B) are independent of ∆/Rc, as shown in Table 2. At these high volume fractions, the PEG chains will be highly compressed and hence the rheological properties of the dispersions do not reflect the structure of the PEG layer. Using the core radii presented in Table 1, it is possible to calculate the half core-core interparticle separation,

Figure 6. Plot of the elastic modulus, G′, versus h/∆ for PLAPEG 3:5 and 6:5 dispersions, where h is the half interparticle separation and ∆ is the PEG layer thickness.

h, at each core volume fraction as follows:

[( )

h ) Rc

0.64 φc

1/3

-1

]

(6)

Figure 5 shows the variation of the elastic modulus at 1 Hz with h for both the PLA-PEG 3:5 and 6:5 dispersions. In both cases, the elastic modulus increases sharply as h approaches the PEG layer thickness (∆). As shown in Figure 6, if the h values are divided by the PEG layer thickness for each system the two curves become almost completely superimposed. This is especially true at low interparticle distances, where the compressed PEG chains of both dispersions would be expected to give similar rheological behavior. The principal differences between the two curves are found at higher values of h/∆, where the PEG layers are only just beginning to interpenetrate and the chain density is different for the two core sizes. 4. Conclusions Dynamic rheological measurements have been used to investigate interparticle interactions in concentrated dispersions of micellar-like PLA-PEG nanoparticles. Increasing the volume fraction of the dispersions, φcore, resulted in a rapid transition from a viscous fluid to an elastic gel. At higher values of φcore, compression of the stabilizing polymer chains was observed. By determining the critical volume fraction at which the particles start to

7668

Langmuir, Vol. 18, No. 20, 2002

interact elastically, it was possible to obtain an estimate of the hydrodynamic layer thickness of the grafted PEG chain. The grafted 5 kDa PEG layer was found to have an appreciable thickness, as compared to the particle radius, giving rise to soft interparticle interactions. The layer became more extended as the molecular weight of the PLA block was increased from 3 to 6 kDa. As a consequence, the PEG chains became less compressible. Small-angle neutron scattering experiments are currently being performed to elucidate the structure of the PEG layer. It is expected that a better understanding of the characteristics of the stabilizing PEG layer should help rationalize the in vivo performance of the PLA-PEG

Riley et al.

nanoparticles and aid in the future design of particulate drug carriers. Acknowledgment. This work was funded by a DTI Link Penta Nanotechnology Initiative project, “Biological Applications of Particle Engineering” (GR/J57889), together with a BBSRC postgraduate studentship. The authors are also grateful for helpful discussions with Dr. Paul Gellert, Dr. Raymond Barlow, and Dr. Stuart Purkiss at AstraZeneca Pharmaceuticals, Alderly Park, Macclesfield, U.K. LA020248X