Core−Shell Structure of Degradable, Thermosensitive Polymeric

Jan 1, 2008 - ... the micelle's aggregation number changed with the incubation time. This feature and the initially small size and dense structure in ...
0 downloads 0 Views 204KB Size
Download PDF
784

J. Phys. Chem. B 2008, 112, 784-792

Core-Shell Structure of Degradable, Thermosensitive Polymeric Micelles Studied by Small-Angle Neutron Scattering Aissa Ramzi,† Cristianne J.F. Rijcken,† Theo F.J. Veldhuis,† Dietmar Schwahn,‡ Wim E. Hennink,† and Cornelus F. van Nostrum*,† Department of Pharmaceutics, Utrecht Institute for Pharmaceutical Sciences, Faculty of Pharmaceutical Sciences, Utrecht UniVersity, The Netherlands, and Institute of Solid State Research, Research Center, Ju¨lich, D-52425 Ju¨lich, Germany ReceiVed: May 14, 2007; In Final Form: October 8, 2007

The structure of assemblies of block copolymers composed of thermosensitive, biodegradable poly(N-(2hydroxypropyl) methacrylamide-dilactate) and poly(ethylene glycol) (pHPMAmDL-b-PEG) has been studied by small-angle neutron scattering (SANS). Three amphiphilic copolymers with a fixed PEG of 5 kDa and a partially deuterated pHPMAmDL(d) block of 6700, 10400, or 21200 Da were used to form micelles in aqueous media by heating the polymeric solution from below to above the cloud point temperature (around 10 °C) of the thermosensitive block. Simultaneous and quantitative analysis of the scattering cross sections obtained at three different solvent contrasts is expedited using core-shell model, which assumed a homogeneous core of uniform scattering length density. The mean core radius increased from 13 to 18.5 nm with the molecular weight of the pHPMAmDL(d) block, while the thickness of the stabilizing PEG layer was around 8 nm for the three investigated assemblies. In addition, the volume fraction values of the stabilizing PEG chains in the shell are low and decreased from 31% to 14% with increasing the size of pHPMAmDL(d) block which shows that the shell layer of the assemblies is highly hydrated. The corresponding PEG chain grafting densities decreased from 0.22 to 0.11 nm-2 and the distance between PEG chains on the nanoparticles surface increased from 2.4 to 3.4 nm. The pHPMAmDL-b-PEG micelles showed a controlled instability due to hydrolysis of the lactic acid side groups in the thermosensitive block; that is, an increase of the degradation time leads to an increase of the size of the core which becomes less hydrophobic and consequently more hydrated. Neutron experiments supplied accurate information on how the size of the core and the micelle’s aggregation number changed with the incubation time. This feature and the initially small size and dense structure in aqueous solution make the polymeric micelles suitable as carriers for hydrophobic drugs.

Introduction Amphiphilic block copolymers have found applications in a wide variety of technological areas, including use as detergents,1 in emulsions,2 drug delivery systems,3 and dispersions.4 These copolymers can self-assemble into micelles with core-shell structures if they are dissolved in a selective solvent, that is, a thermodynamically good solvent for one of the blocks and a nonsolvent for the other. Micelles can be spherical but other topologies, including shapes such as ellipsoids and cylinders, are also possible. Polymeric micelles with poly(ethylene glycol) (PEG) chains as the outer shell have attracted growing interest in pharmaceutical applications because of their long-circulating properties after intravenous administration.5-14 Drugs can be incorporated into the core of the micelles by either covalent (e.g., doxorubicin)15,16 or noncovalent bonding such as hydrophobic17-19 or ionic interactions.14,20,21 A variety of carriers based on block copolymers of PEG with poly(lactic acid),22 polyglycolide,23 poly(-caprolactone),24 poly(lactic acid-co-glycolic acid),25,26 or poly(β-benzyl-L-aspartate)27 have been extensively investigated for drug delivery purposes,15 since the core-forming block is fully biodegradable. Also * To whom correspondence should be addressed. Telephone: +31302536970. Fax: +31-302517839. E-mail [email protected]. † Utrecht Institute for Pharmaceutical Sciences (UIPS). ‡ Institute of Solid State Research.

triblock copolymers of PEG and poly(propylene oxide) (Pluronics)28 form micellar structures in aqueous solution and have been studied for a wide variety of pharmaceutical and biomedical applications. Recently, a new class of block copolymers based on thermosensitive polymers29 has been introduced to prepare smart drug carriers.16,17 PEG-ylated block copolymers consisting of a thermosensitive block, PEG-b-p(N-isopropylacrylamide) (PEGb-pNIPAAm), form micelles above the cloud point temperature (CP) of the thermosensitive block, which is close to 32 °C in water.30-34 Destabilization of these micelles and concomitant release of encapsulated drugs can be triggered by decreasing the temperature below the CP. Introduction of comonomers with hydrolyzable side groups, for example, copolymers of Nisopropylacrylamide (NIPAAm) with the biodegradable comonomer N-(2-hydroxypropyl) methacrylamide-lactate (HPMAmlactate), has been studied as an alternative way of destabilizing the micelles by chemical hydrolysis of the lactate side chains.35-40 Soga et al.41 showed that poly(N-(2-hydroxypropyl) methacrylamide-dilactate) (poly(HPMAm-dilactate)) exhibits a lower critical solution temperature (LCST) behavior in aqueous solution. It was demonstrated that the cloud point increases with time because of hydrolysis of the lactoyl lactate side groups. Poly(HPMAm-dilactate) is a particularly interesting polymer

10.1021/jp073673d CCC: $40.75 © 2008 American Chemical Society Published on Web 01/01/2008

Degradable Thermosensitive Polymeric Micelles because its CP (around 10 °C) is far below body temperature. It was shown that block copolymers composed of PEG and poly(HPMAm-dilactate) form polymeric micelles under physiological conditions (37 °C) and can gradually dissolve in time because of the hydrolysis of the lactic acid side groups with concomitant release of an encapsulated drug (paclitaxel). In this work, we examined the structural properties of poly(HPMAm-dilactate)-b-PEG (pHPMAmDL-b-PEG) assemblies in aqueous solution. A series of pHPMAmDL-b-PEG assemblies with different molecular weights of the thermosensitive block were synthesized. Static and dynamic light scattering techniques have been successfully used to study these systems.42 However, these techniques only provide information about the structure of the assemblies as a whole, such as the radius of gyration and the hydrodynamic radius of the core plus the stabilizing PEG layer. The internal structural information of the coreshell nanoparticles can be accessed very effectively with the small-angle neutron scattering (SANS) technique and can be studied in great detail using contrast matching methods, via the variation of scattering contrast by selective isotopic substitution of protons for deuterium.43-48 This technique has been amply demonstrated for, for example, polymer-coated particles,49,50 a self-assembled surfactant,51,52 and various block copolymer53,54 systems, but this is the first and unique study carried out on degradable and thermosensitive polymeric micelles (pHPMAmDL-b-PEG) by means of SANS and solvent contrast variation method. In this study, pHPMAmDL(d)-b-PEG block copolymers with partially deuterated pHPMAmDL(d) blocks were synthesized and the structural parameters of the micelles were extracted by fitting a core-shell model to the scattering data, obtained at three different contrasts. Furthermore, the degradation behavior of the micellar core was studied by SANS and compared to light scattering results, where the destabilization of the whole micelle is followed in time. Experimental Methods Materials. Deuterated (d6)-methacrylic acid (98.1 atom % D) was purchased from C/D/N Isotopes (Quebec, Canada). Samples of dl-1-amino-2-propanol (99+% purified prior to use) and toluene (pro analysi) were obtained from Acros Organics (Geel, Belgium); 4-Methoxyphenol 99% was obtained from Fluka (Zwijndrecht, The Netherlands); stannous octoate (tin (II) 2-ethyl hexanoate, SnOct2, approximately 95%) was purchased from Acros (Zwijndrecht, The Netherlands). Partially deuterated HPMAm esterified with optically pure di-l-lactic acid (abbreviated as HPMAmDL(d)) was synthesized as described previously.36 Monomethyl ether of poly(ethylene glycol), MW ) 5000 g/mol (PEG5000), was supplied by NEKTAR (San Carlos, CA). 4,4-Azobis (4-cyanopentanoic acid) (ABCPA) was from Fluka, Chemie AG (Buchs, Switzerland). The PEG2-ABCPA macroinitiator with PEG5000 was prepared as described previously.35 Synthesis of Partially Deuterated 2-Hydroxypropyl Methacrylamide (HPMAm(d)). A mixture of 1.1 g of deuterated (d6)-methacrylic acid (12.05 mmol), 5 mg of p-methoxyphenol (0.04 mmol, 0.33mol%), and 1.44 g of thionyl chloride (12.10 mmol, ratio 1:1) was stirred for 2 1/4 h at 60 °C under a nitrogen atmosphere. At the end of this reaction, 5 mL of dry dichloromethane was added, and the reaction was continued for 1/2 h leading to deuterated methacryloyl chloride. 20 mL of dry dichloromethane was added to the above mixture and dropwise added to an ice-cold solution of 1.81 g of distilled dl-1-amino2-propanol (24.1 mmol, molar ratio 1:2), 2.02 g of sodium

J. Phys. Chem. B, Vol. 112, No. 3, 2008 785 bicarbonate (24.1 mmol, molar ratio 1:2) in 15 mL of dry dichloromethane. Subsequently, the mixture was stirred overnight under nitrogen atmosphere. The crude product was filtered, and the solvent was evaporated. Synthesis of Partially Deuterated HPMAm(d) Dilactate (HPMAmDL(d)). Partially deuterated HPMAmDL(d) was synthesized essentially as described by Neradovic et al.36 In brief, a mixture of 900 mg of deuterated HPMAm (6.04 mmol) and 870 mg of L-lactide (6.04 mmol, ratio 1:1) was heated to 110 °C until the lactide was molten. Subsequently, a catalytic amount of tin (II) 2-ethylhexanoate (24.6 mg, 1 mol % with respect to HPMAm) pre-dissolved in toluene (2 mL) and a radical scavenger 4-methoxyphenol (30.2 mg, 4 mol % with respect to HPMAm) were added. The resulting mixture was stirred for 1 h at 110 °C and thereafter cooled to room temperature. After dissolution of the product in 5 mL of water/ acetonitrile (50:50), the HPMAmDL(d) was fractionated with preparative chromatography essentially as described by Neradovic et al.36 Synthesis of Deuterated pHPMAmDL(d)-b-PEG Block Copolymers. Partially deuterated poly(N-(2-hydroxypropyl) methacrylamide-dilactate)-b-poly(ethylene glycol) (pHPMAmDL(d)-b-PEG) block copolymers were synthesized by radical polymerization using partially deuterated HPMAmDL(d) as monomer and PEG2-ABCPA as initiator. HPMAmDL(d) and PEG2-ABCPA were dissolved at a total concentration of 0.3 g/mL in acetonitrile. To obtain block copolymers with different pHPMAm block lengths, the ratio of monomer to macroinitiator was varied between 35/1 to 140/1 (mol/mol). The polymerization was conducted at 70 °C for 24 h in a nitrogen atmosphere. The polymers were collected by centrifugation after precipitation in diethyl ether. The polymers were purified by dissolving them in cold water, followed by filtration through a 0.22 µm filter and freeze drying. Three pHPMAmDL(d)-b-PEG block copolymers with different pHPMAmDL(d) block lengths (Mn ) 6700, 10400, and 21200 Da, determined by 1H NMR) and with a fixed PEG molecular weight (Mn ) 5 kDa) were synthesized in yields between 50 and 70%. The polydispersity (Mw/Mn) of the block copolymers vary between 1.5 and 2.5. The products were characterized by 1H NMR and gel permeation chromatography (GPC). 1H NMR spectra of the partially deuterated pHPMAm(d)-b-PEG copolymers dissolved in deuterated chloroform (CDCl3) were obtained using a Gemini 300 MHz spectrometer (Varian Associates Inc. NMR Instruments, Palo Alto, CA). The molecular weights and their distributions of the different polymers were determined by GPC. Two serial Plgel 3 µm MIXED-D + Plgel 3 µm MIXED-E columns (Polymer Laboratories) were used with a Waters system (Waters Associates Inc., Milford, MA) with a differential refractometer model 410. Poly(ethylene glycol)s of defined molecular weights were used as calibration standards. The eluent was DMF containing 10 mM LiCl; the elution rate was 0.7 mL/ min, and the temperature was 40 °C. 1H NMR (all protons are from pHPMAmDL(d) block except for the methylene protons from PEG) δ: 6.5 (b, CO-NH-CH2), 5.0 (b, NH-CH2-CH(CH3)-O and CO-CH(CH3)-O), 4.4 (b, CO-CH(CH3)-OH), 3.6 (b, PEG methylene protons, O-CH2CH2), 3.4 (b, NH-CH2-CH(CH3)), 1.6 (b, CH2-CH(CH3) and CO-CH(CH3)-O), 1.2 (b, CO-CH(CH3)-OH). The central line of CDCl3 at 7.24 ppm was used as reference line. Micelle Formation. The polymers were dissolved overnight at a concentration of 10 or 20 mg/mL in either D2O/H2O mixtures or Tris buffer in D2O/H2O mixtures (pH 8.6, 150 mM) at 0 °C. Then, each polymer solution (∼1.5 mL) was quickly

786 J. Phys. Chem. B, Vol. 112, No. 3, 2008

Ramzi et al.

heated from 0 °C to 50 °C by putting them into a water bath under vigorous stirring to form micelles.55 After 1 min of incubation at 50 °C, the mixtures were slowly cooled down to room temperature. Physicochemical Properties of pHPMAmDL(d)-b-PEG Nanoparticles. The average size and size distribution of the nanoparticles were measured by dynamic light scattering (DLS) at 37 °C and at a scattering angle of 90°, using a Malvern CGS-3 multi-angle goniometer (Malvern Ltd,. Malvern, U.K.) with He-Ne JDS Uniphase laser (λ ) 632.8 nm, 22 mW output power), an optical fiber based detector, a digital LV/LSE-5003 correlator, and a temperature controller (Julabo Waterbath). Time correlation functions were analyzed using the ALV-60 × 0 Software V.3.X provided by Malvern. The solutions were filtered before measurements through a 0.22 µm filter. DLS provides the hydrodynamic radius using the Stokes-Einstein equation:

Rh ) (kBT‚q2)/(6πηΓ)

(1)

where kB is the Boltzmann constant, q is the scattering vector, (q ) (4π‚n‚sin(θ/2))/λ, where n is the refractive index of the solution, θ is the scattering angle, and λ is the wavelength of the incident laser light), η is the solvent viscosity at the measuring temperature (corrected by the software), and Γ is the decay rate. Micelle Destabilization. The colloidal stability of the micelles was monitored at elevated pH to decrease the time of the experiments (hydrolysis rate is first order with respect to hydroxyl ion concentration). The micelles of pHPMAmDL(d)b-PEG block copolymers were formed as described above in 150 mM Tris buffer (pH 8.6) in H2O/D2O mixture at a concentration of 20 mg/mL which corresponded to the SANS core scattering (see next paragraph). Then, both the size of the micelles and the intensity of the scattered light were measured by DLS at 37 °C as a function of time. Small-Angle Neutron Scattering (SANS). (a) Collection and Reduction of SANS Data. Small-angle neutron scattering experiments were performed at the spectrometer KWS1 at the Institut fu¨r Festko¨perforschung (IFF), KFA Ju¨lich, Germany. This experimental technique has been described elsewhere.43-45 The scattering vectors covered, defined as |Q| ) Q ) (4π/λ) sin(θ/2), vary between 0.002 and 0.09 Å-1 with variable neutron wavelength resolution ∆λ/λ (λ is the neutron wavelength, θ is the scattering angle, and ∆λ is the full width at half-maximum value of the neutron flux vs wavelength distribution). The neutrons are monochromatized by a mechanical selector, which was set at a wavelength resolution ∆λ/λ ) 20%. For each sample, the scattering patterns were obtained using two different spectrometer configurations: λ ) 7 Å, D ) 20 m, and C ) 20 m and λ ) 7 Å, D ) 4 m, and C ) 4 m (D is the sampledetector distance and C is the collimation length) corresponding then to two partially overlapping ranges of the scattering vectors Q: 0.002-0.018 and 0.01-0.09 Å-1, respectively. The scattering experiments were performed at 37 °C, and the data were radially averaged to reduce the statistical error. The SANS measurements duration varies between 20 min and 2 h. The scattering due to the empty cell and the solvent, as well as a calculated incoherent background caused by the protons, was subtracted. Thereafter, the neutron scattering intensity of the raw data was normalized, with the scattering of 1.5 mm of plexiglas used as a standard. The plexiglas scattering were also used to determine the detector efficiencies. The coherent scattering cross section, dΣ/dΩ(Q), was obtained in absolute units (per centimeter).

(b) Neutron Contrast Matching. In neutron scattering, a contrast matching method is used to isolate features of selectively deuterated structures.43-45 This is achieved because hydrogen and deuterium have very different neutron scattering length densities (SLDs, denoted Fi for component i) characterizing the way they interact with neutrons. In our SANS experiments, we consider the neutron contrast, (∆F),2 defined as the square of the difference in the SLDs of two components (e.g., for components A and B, (∆F)2 is equal to (FA - FB)2). The SLD of a mixture is a weighted average of the SLDs of the individual components on a volume fraction basis, allowing the SLD of an isotopically mixed system to be determined. In this work, we partially selectively deuterated the pHPMAmDL(d) block to provide neutron contrast between it and the PEG block. To observe only the scattering from the micelle core containing the pHPMAmDL(d) block, a mixture of H2O and D2O was used to tune the SLD of the dispersion medium to that of PEG blocks that form the micelle shell. This contrast condition is called the shell match. Thus, when micelles are formed in the corresponding solvent mixture, there is no contrast between the micelle shell comprising the PEG chains and the solvent. Conversely, we can use another mixture of H2O and D2O to tune the SLD of the dispersion medium to that of the pHPMAmDL(d) blocks that form the micelle’s core. We call this contrast condition core match, where only the scattering from the PEG chains that comprise the micelle shell is observed. By collecting scattering profiles in both core and shell match neutron contrasts, we can directly resolve the features of the micelle core and shell independently. In order to reduce the experimental error in the contrast matching of the core and the shell, an intermediate contrast called “interference” contrast has been measured. It corresponds to the scattering of the whole micelle. (c) Data analysis Using Core-shell Model. The core-shell model used in the analysis of the SANS data from pHPMAmDL(d)-b-PEG assemblies assumed a homogeneous core and shell with a fixed scattering length densities, Fc and Fs, respectively. The overall scattering cross section from such assemblies consists of a contrast weighted summation of the scattering from the core and shell components, together with a contribution from interference terms. This scattering intensity dΣ/dΩ(Q) is expressed as56

dΣ/dΩ(Q) ) N‚V2‚(∆F)2‚P(Q)‚S(Q) + B

(2)

where N is the number density of scattering centers, V is the volume of a scattering center, P(Q) is the form factor, S(Q) is the interparticle structure factor, and B is the incoherent background. For a dilute solution of non-interacting particles, S(Q) tends to unity and can be ignored. The intensity profile of the form factor is created by the interference effects within an individual scattering center and thus gives information about the size and the structure of the scattering centers. Analytical expressions are available for the form factors of shapes commonly encountered in small-angle scattering.57,58 For spherical particle of radius R, the form factor P(Q) takes the following analytical form:

P(Q) ) [3(sin(Q‚R) - Q‚R‚cos(Q‚R))/Q3R3]2

(3)

In the particular case where the particles in dilute solution are not interacting (S(Q) ∼ 1), eqs 2 and 3 imply that the intensity at Q ) 0 is dΣ/dΩ(0) ) N‚(4/3πR3)2‚(∆F).2 If the particle number and mass densities were conserved during the growth process, then dΣ/dΩ(0)/R6 is constant. However, in real systems,

Degradable Thermosensitive Polymeric Micelles

J. Phys. Chem. B, Vol. 112, No. 3, 2008 787

TABLE 1: Coherent Neutron Scattering Length Densities solvent mixtures/ polymers

density, δ (g/cm3)

scattering length density, F (cm-2)

17% D2O/83%H2O 28% D2O/72%H2O 39% D2O/61%H2O PEG pHPMAmDL(d)

1.02 1.03 1.04 1.13 1.35

0.628 × 1010 1.39 × 1010 2.15 × 1010 0.645 × 1010 2.15 × 1010

there is a finite distribution of particle sizes, and eq 2 has to be weighted over the entire size distribution P(R). Experimentally, it has been found that the size distribution of many colloidal systems can be adequately described by the Schultz distribution function:59

P(R) )

[

]

{

}

(Z + 1)Z+1 (Z + 1)‚R RZ ‚ ‚ exp R h R h Γ(Z + 1)

(4)

with R h as the average particle radius, Z is related to , the rootmean-square deviation of the radius, by  ) R h /x(Z + 1) (i.e., /R h is the polydispersity index), and Γ(Z) is the gamma function. The form factor for spherical core-shell assembly can be expressed as:

P(Q) ) ∆Fb2Pbb(Q) + 2∆Fb‚∆FcPbc(Q) + ∆Fc2Pcc(Q)

(5)

where ∆Fb ) Fb - Fs and ∆Fc ) Fc - Fs, with Fb, Fc, and Fs are the respective scattering length densities of the particle shell, the core, and the solvent. The terms Pbb(Q) and Pcc(Q) are the partial form factor for the shell and the core, respectively, while Pbc(Q) represents the interference term. These functions depend on the size and the shape of the particles. Table 1 shows the values of the calculated scattering length densities of the core, shell and solvents used for the contrast matching method. The SANS data sets of all assemblies at a concentration of 2% (v/v) under three different contrasts were fitted simultaneously using a core-shell model of spherical geometry. Any change in the parameters for one data set will be reflected in the two other data sets. Hence, this approach is expected to yield more accurate and representative structural parameters of the assemblies than by individual fitting of the data sets. The structural parameters characterizing the micelles were adjusted to fit the experimental data by means of a least-squares fitting program.60 Thus, the global fit yields the geometrical parameters of the micelles: the mean core radius (Rc), the polydispersity of the core radius (/Rc), the total micellar radius (Rt), the thickness of the PEG shell (Rs), and the aggregation number (Nagg). Results and Discussion In an aqueous medium composed of 39% (v/v) of D2O and 61% (v/v) of H2O, both the pHPMAmDL(d) core and the medium have equal scattering length density values (2.15 × 1010 cm-2) leading to a negligible scattering from the core, and consequently, the scattering is then predominantly from the PEG corona. Even in dilute solution, the corona can be thought of as a region of semidilute polymer solution surrounded by a pure solvent. Hence, the scattering at low momentum transfers Q will essentially look like the scattering from particles with a size given by the size of the aggregate, while at high Q the scattering will look like that from a semidilute polymer solution with its characteristic power law decay in dΣ/dΩ(Q). The characteristic exponent will be -1/ν, where ν is the Flory

Figure 1. Generalized Kratky plot of the SANS shell data for pHPMAmDL(d)(21200)-b-PEG assemblies.

exponent. At Θ conditions, the polymer is represented by a nearly ideal random walk and ν ) 1/2. For our case of a good solvent, one has ν ) 3/5 (self-avoiding random walk), and the scattering varies as Q-5/3. In Figure 1, an example of the scattering spectra of the sample pHPMAm(d)(21200)-b-PEG is shown in a generalized Kratky plot. The quantity dΣ/dΩ(Q) was multiplied by Q5/3 instead of Q2. The flatness of the curve at high Q shows that the PEG block nicely exhibits the ideal self-avoiding chain behavior in this solvent mixture. The data were fitted assuming a homogeneous SLD profile in the core as well as in the corona. This profile was used because the corona sizes are quite small and are not considerably different from those of the core. A parabola profile was tried to fit the data giving comparable results except for the lowest molecular weight of the core block (pHPMAmDL(6700)) which is close to the brush mass. Our approach was different to that of Riley et al. who used a homogeneous SLD in the core, while the corona was described by a diffuse model (additive and multiplicative diffuse-shell model).61 The best fits obtained for the three pHPMAmDL(d)-b-PEG nanoparticles dispersions, having different molecular weight of the thermosensitive block (pHPMAmDL(d)), are displayed as solid lines in Figures 2a-c, and the values of the fitted parameters are given in Table 2. The weak oscillations in the scattered patterns at high Q values were not described by the fit because of the background subtraction and the instrumental resolution which was not taken into account in the fitting. The latter does not affect considerably the characteristic parameters of the micelles and the fitting made without the instrumental resolution describes quite well the experimental data. One notices that the overall dimensions of pHPMAmDL(d)b-PEG nanoparticles (Rt) as well as the mean core radius (Rc) increase with the molecular weight of the pHPMAmDL(d) block. By comparing (pHPMAmDL(6700)-b-PEG versus pHPMAmDL(21000)-b-PEG), a 29% increase in Rt is essentially attributed to the increase of the core size (Rc) because of the increase in pHPMAmDL molecular weight. Furthermore, the three assemblies show high core polydispersites (/Rc > 0.2), which correspond to broad Schultz core-size distributions.62 The polydispersity of the nanoparticles smears some of the features in the scattering patterns. However, the average size of the shell layers was determined across the distribution of core sizes when the polydispersity is introduced in the fitting model. As can be seen from our results, the thickness of the shell (Rs) does not change significantly when increasing the molecular weight of

788 J. Phys. Chem. B, Vol. 112, No. 3, 2008

Ramzi et al.

Figure 3. Schematic representation of the internal structure of the pHPMAmDL(d)-b-PEG nanoparticles.

TABLE 2: Characteristic Parameters of pHPMAmDL(d)-b-PEG Nanoparticles Obtained from a Simultaneous Fit of the SANS Data at Three Different Contrasts, Using Core-Shell Modela sample Mn,pHPMAmDL (Da) Rh (nm) R h c (nm) /R hc Rs (nm) Rt (nm) Sc/Nagg (nm2) St/Nagg (nm2) Nagg φp A d (nm) a

pHPMAmDL pHPMAmDL pHPMAmDL (21200)-b-PEG (10400)-b-PEG (6700)-b-PEG 21200 37.2 18.5 0.26 8.3 26.8 4.17 9.10 1017 0.14 0.21 3.4

10400 26.8 15.1 0.21 8.6 23.7 2.5 6.25 1132 0.20 0.34 2.8

6700 27.5 13.2 0.23 7.5 20.7 1.89 4.55 1165 0.31 0.52 2.4

For the description of the parameters, see text.

The average aggregation number, Nagg, of pHPMAmDL(d)b-PEG micelles was obtained using the molar volume of the core block (pHPMAmDL(d)) as follows:

δ‚ℵA 4 h c3‚ Nagg ) ‚π‚R 3 Mn

Figure 2. Scattering cross section from partially deuterated pHPMAmDL(d)(21200)-b-PEG (a), pHPMAmDL(d)(10400)-b-PEG (b), and pHPMAmDL(d)(6700)-b-PEG (c) assemblies at three different solvent contrasts. The continuous lines represent a simultaneous fit of all three data sets using core-shell model.

the core blocks and remains almost unaffected for the three investigated assemblies. The overall radius of pHPMAmDL(d)-b-PEG nanoparticles (Rt) obtained from the fit of the SANS data are somewhat lower than the hydrodynamic radius (Rh) measured using dynamic light scattering (Table 2). The difference between the two values may be due to the core-shell structure of the micelles with a thick hydrated PEG shell.63

(6)

where δ is the chain’s density (1.35 g/cm3, value estimated by the best fit of the scattered intensities), ℵA is Avogadro’s number, R h c is the average core’s radius, and Mn is the molar weight of pHPMAmDL(d). Thus, contrary to what was observed for PLA-PEG micelles,61 the aggregation number does not vary considerably for the three investigated assemblies. The calculated Nagg values were used in conjunction with the surface areas of the core (Sc ) 4‚π‚Rc2) and the total micelle (St ) 4‚π‚Rt2) to determine an estimated value of the surface available per PEG chain at the core/shell interface (Sc/Nagg) and at the periphery of the shell (St/Nagg). Figure 3 illustrates a schematic representation of the internal structure of pHPMAmDL(d)-b-PEG micelles. As can be seen from Table 2, the surface areas per PEG chain Sc/Nagg and St/Nagg increase with increasing the molecular weight of the pHPMAmDL(d) block. A study of Riley et al. on PLA(d)-PEG assemblies into micellar structures61 shows that these surface areas of PEG chains (Mw ) 5000 g/mol) at the core/shell interface are 1.9, 4.8, and 7.8 nm2 for the molecular weights of PLA core’s block 3200, 15600, and 42400 g/mol, respectively. These values are comparable to those obtained for pHPMAmDL(d)-b-PEG assemblies (Table 2). However, the surface area available to each PEG chain is

Degradable Thermosensitive Polymeric Micelles

J. Phys. Chem. B, Vol. 112, No. 3, 2008 789

considerably smaller than the surface area required for the 5 kDa chains considered in an isolated medium that is equal to πRg2 ≈ 30 nm2, where Rg ) 3.1 nm, the radius of gyration of the PEG 5 kDa chains calculated according to ref 6.4 This suggests that the PEG chains in the pHPMAmDL(d)-b-PEG assemblies are likely to interact and adopt a brush-like configuration.65,66 In contrast to De Gennes scaling theory which predicts that the layer thickness of a grafted polymer brush should exhibit an inverse dependence on the distance between grafting points,66 no big change was observed in the thickness of the PEG layer even though the grafting density is increased when the molecular weight of the core’s block is decreased. This leads to a decrease of the surface curvature at the pHPMAmDL(d)/PEG interface. The volume fractions of the PEG chains in the solvated polymer layer listed in Table 2 are determined as follows:

φp )

Nagg‚VPEG Vshell

(7)

where VPEG represents the volume of a dry PEG chain calculated from its molar volume. Thus, a molecular weight of 5 kDa leads to VPEG ) 7.35 nm3 assuming the density of PEG polymers equals to 1.13 g/cm3 (as solid).67 Vshell represents the volume of the shell layer calculated from the layer thickness determined from the fit. It is found that the PEG volume fraction in the shell layer decreases as the molecular weight of the core chains increases, in good agreement with the results reported by Riley et al. on PLA-PEG assemblies.61 For the assemblies investigated in the present work, φp varies between 14% and 31%, which is in the same order of magnitude as the values found for PLAPEG. In place of a core-shell, step-function contrast profile, one attempts to capture, in the simplest way, the role of curvature assuming that a radially symmetric core-shell structure mimics the distribution of nuclei in the self-assemblies sufficiently well. In this second approach, one assumes the PEG chains as identical rigid cylinders attached to the core surface, oriented radially outward into the solvent. The volume fraction of PEG polymers in the shell layer is then given as:68

()

r0 2 λ - 1 3 ‚ 3 φp ) ‚ Nagg‚ 4 λ -1 Rc

(8)

where r0 is the radius of the circular cross-section of the PEG polymer at the core/shell interface, Rc is the mean core radius and λ ) (1 + Rshell/Rc). The coverage area A ) π‚r02‚σ is the fraction of the sphere area occupied by the polymer, which is proportional to the grafting density.

()

(9)

1 λ3 - 1 A) ‚ ‚φ 3 λ-1 p

(10)

r0 1 A ) ‚Nagg‚ 4 Rc

2

Using eqs 8 and 9, one obtains:

One notices that the coverage area A varies between 20% and 50% for the three measured assemblies. Soppimath et al.69 reported that the optimum surface density of PEG chains on nanoparticles plays an important role in steric interaction. They have shown that the distance d between PEG chains on the nanoparticles surface is critical to avoid the

Figure 4. Change in micellar size and scattering intensity by DLS of 20 mg/mL micellar solution of pHPMAmDL(d)(21200)-b-PEG block copolymers at 37 °C in Tris buffer pH 8.6 in D2O/H2O mixture (17%D2O/83%H2O).

adsorption of plasma proteins on their surface. They confirmed that a decrease in this distance on polystyrene nanoparticle’s surface from 6.2 to 5.1 nm drastically decreases the adsorption of apolipoproteins up to 90%, and a further decrease in this distance did not show significant effects on this adsorption.69 For pHPMAmDL(d)-b-PEG spherical assemblies, the distance d was calculated via ((4‚St)/(Nagg‚π))1/2, where St ) 4‚π‚Rt2 is the surface area of the total micelle. As can be seen from Table 2, the distance d varies between 2.4 and 3.4, which will likely prevent any attractive interaction with serum proteins when the micelles are applied as drug delivery systems in vivo. Destabilization of the Micelles. Micelles prepared from pHPMAmDL(d)(21200)-b-PEG copolymers were incubated at 37 °C in a Tris buffer of pH 8.6 (150 mM) in D2O/H2O mixture (17% D2O/83% H2O) while following their size and the intensity of the scattered light in time by DLS. As shown in Figure 4, the micelles were stable over the first 10 h of incubation. After that period, the size of the micelles and the scattered intensity started to increase until 20 h because of the increase of the hydrophilicity of the micellar core as a result of hydrolysis of the lactate side chains and subsequent swelling of the micelle’s core. The micelles started to dissociate after 20 h of incubation, as indicated by the disappearance of scattering, and finally a clear solution was obtained around 36 h. It is obvious that the lactic acid side groups were hydrolyzed to such an extent that the cloud point (CP) of the thermosensitive block passed 37 °C. Previously, Soga et al. showed that the same micelles (but hydrogenated) started to swell at physiological pH at 60 h of incubation and that their dissolution occurs after approximately one week at the same conditions.42 Thus, the results presented here are in agreement with the expected pH dependent (base catalyzed) degradation rate investigated by Neradovic et al.36 The destabilization and the evolution of the micelle’s core size as a function of the incubation time were also followed by small-angle neutron scattering. Figure 5 shows the scattering patterns, in logarithmic representation, from the core of pHPMAmDL(d)(21200)-b-PEG nanoparticle dispersions at 37 °C in Tris buffer pH 8.6 in D2O/H2O mixture (17% D2O/83% H2O). The data displays a plateau at low Q over the first 10 h of incubation indicating that the nanoparticles have still a size detectable by SANS. After 24 h of incubation, the scattered intensity increased, and the plateau is shifted toward the lower Q’s. The apparent size of the micelle’s core significantly increased above the instrument resolution because of the hydrophilization and the swelling of the micelles. In the intermediate Q range (0.003-0.006 Å-1), the slope of the scattering profile is close to -4, indicative of the presence of a sharp surface of the core (Porod scattering).70 After that period,

790 J. Phys. Chem. B, Vol. 112, No. 3, 2008

Ramzi et al.

Figure 5. Scattering cross section from partially deuterated pHPMAmDL(d)(21200)-b-PEG assemblies at the core contrast in Tris buffer pH 8.6 in D2O/H2O mixture (17% D2O/83% H2O) versus the incubation time at 37 °C. The solid line indicates the asymptotic Q-4 Porod scattering contribution.

the micelles started to dissociate as can be seen from the significant decreases of the scattered intensity. The scattering profiles of the nanoparticles core at different incubation times were fitted using the unified Guinier-exponential/ power-law equation described by Beaucage,71 which describes simultaneously the Guinier approach and the power law in the intermediate Q range. This equation represents an approximate form that describes a complex morphology over a wide range of Q in terms of structural levels, which are described in scattering by Guinier’s law72 and a structurally limited power law. It is important to notice that no fractal dimensions were observed in the scattering patterns because of the limited Q range in the intermediate regime. The unified equation describing the core’s form factor is given by

(

I(Q) ) G‚exp -

) ()

Q2‚Rg2 1 + B‚ * 3 Q

P

(11)

Figure 6. Fit of the core scattering data from freshly prepared solution (0 h incubation) of pHPMAmDL(d)(21200)-b-PEG block copolymers in Tris buffer pH 8.6 at 37 °C, using Beaucage analysis.

TABLE 3: Size of the Core and Aggregation Number of the Micelles versus the Incubation Time, while the pHPMAmDL(d)(21200)-b-PEG Micelles Are Destabilized, Obtained from the Fit of the SANS Data, Using Beaucage Analysis time (h)

Rg (nm)

Nagg

0 9 24

24.7 ( 0.1 30.1 ( 0.3 Data cannot be fitted: continuous increase of the signal at low Q 87.1 ( 14.1 26.7a ( 5.4 34.7a ( 17.1 34.2a ( 15.7

2500 1828

31 37 44 52

a True Rg values are much lower than these tabulated values. It was not possible to determine Rg accurately because of the absence of a plateau in the scattered intensities and the weak signal at low Q.

tion number is calculated from the fitted forward scattering I(0) as follows:

where

Nagg ) Q* )

Q k‚Q‚Rg

[ ( )] erf

3

(12)

x6

where G is the Guinier prefactor defined by the specifics of the particle composition and the concentration of particles. For dilute solutions, G ) Np‚Vp2‚(∆F),2 where Np is the number of particles in the scattering volume, Vp is the volume of a particle, and ∆F is the scattering length density difference between the particle and the solvent. B is a prefactor specific to the type of powerlaw scattering and defined according to the regime in which the exponent P falls. For Porod’s law, P ) 4 and B ) 2π‚Np‚ (∆F)2Sp, where Sp is the particulate surface area. The constant k used to define Q* is an empirical constant assumed to be equal to 1. As seen in Figure 6, the core scattering signal of a freshly prepared solution in Tris buffer pH 8.6 at 37 °C is well fitted using Beaucage analysis.71 Thus, one can obtain the core size of the micelles versus the incubation time, except at 24 h of incubation, where the core size is much bigger than the higher limit detectable by the SANS instrument. The average aggrega-

61 4 3 3

ℵA‚δ‚I(0) φ‚(∆F)2‚Mn

(13)

where ℵA is Avogadro’s number, δ is the density of the core’s block (1.35 g/cm3), I(0) is the forward scattering, φ is the volume fraction of pHPMAmDL(d) block in solution, ∆F is the scattering length density difference between the core chains and the solvent, and Mn is the chains molecular weight. The values of Rg and Nagg are reported in Table 3. The core size increases with the incubation time to reach a maximum in the interval of time between 10 and 30 h because of the swelling of the core, followed by a decrease caused by the micelles dissociation. In addition, the aggregation number decreases significantly within the first 30 h and becomes close to unity after this time because of the gradual decrease of the core hydrophobicity which favors the gradual loss of polymer molecules from the micelles. Conclusions In this study, a series of thermosensitive and biodegradable block copolymer nanoparticles were examined using SANS under varying neutron contrast media. The mean core radius increased with the molecular weight of the pHPMAmDL(d) block, while the thickness of the highly hydrated PEG shell

Degradable Thermosensitive Polymeric Micelles was almost unaffected for the three investigated assemblies. On increasing the molecular weight of pHPMAmDL(d) block, the surface area per PEG chain increased and consequently the distance between PEG chains on the nanoparticles surface increased from 2.4 to 3.4 nm, which will likely be small enough to prevent adsorption of serum proteins. The hydrolysis of the lactic acid side groups in the thermosensitive block provides a controlled instability of the micelles that is characterized by a swelling of the micellar core and gradual dissolution of the polymer molecules. Neutron experiments supply accurate information how the hydrophobicity of the core and its stability are changed with the incubation time. Thus, we succeeded to follow the variation of both the size of the core and the micelle’s aggregation number as a function of time. This feature, the initially small size and dense structure in aqueous solution, makes the micelles suitable as delivery carriers for hydrophobic drugs. Acknowledgment. This project is financially supported by NWO-CW/STW (Grant 790.36.110). The SANS experiments has been supported by the European Commission under the Sixth Framework Program through the Key Action: Strengthening the European Research Area, Research Infrastructures. Contract No. RII3-CT-2003-505925. We are grateful to Richard Heenan from Rutherford Appleton Laboratory (U.K.) for many helpful discussions about the FISH program and data fitting. References and Notes (1) Jo¨nsson, B.; Lindman, B.; Holmberg, B.; Kronberg, B. Surfactants and Polymers in Aqueous Solution; Wiley & Sons, Ltd.: Chichester, 1998. (2) Piirma, I. Polymeric Surfactants; Marcel Dekker: New York, 1992; Chapter 4. (3) Kataoka, K.; Harada, A.; Nagasaki, Y. AdV. Drug DeliVery ReV. 2001, 47, 113-131. (4) Alexandridis, P.; Lindman, B. Amphiphilic Block Copolymers: SelfAssembly and Application; Elsevier: Amsterdam, 2000; Chapters 13-17. (5) Dunn, S. E.; Brindley, A.; Davis, S. S.; Davies, M. C.; Illum, L. Pharm. Res. 1994, 11, 1016-1022. (6) Storm, G.; Belliot, S. O.; Daemen, T.; Lasic, D. D. AdV. Drug DeliVery ReV. 1995, 17, 31-48. (7) Brigger, I.; Dubernet, C.; Couvreur, P. AdV. Drug DeliVery ReV. 2002, 54, 631-651. (8) Allen, T. M.; Cullis, P. R. Science 2004, 303, 1818-1822. (9) Kataoka, K.; Kwon, G. S.; Yokoyama, M.; Okano, T.; Sakurai, Y. J. Control. Rel. 1993, 29, 119-132. (10) Kwon, G. S.; Yokoyama, M.; Okano, T.; Sakurai, Y.; Kataoka, K. Pharm. Res. 1993, 10, 970-974. (11) Kwon, G. S.; Suwa, S.; Yokoyama, M.; Okano, T.; Sakurai, Y.; Kataoka, K. J. Control. Rel. 1994, 29, 17-23. (12) Kataoka, K.; Harada, A.; Nagasaki, Y. AdV. Drug DeliVery ReV. 2001, 47, 113-131. (13) Stolnik, S.; Illum, L.; Davis, S. S. AdV. Drug DeliVery ReV. 1995, 16, 195-214. (14) Kwon, G. S. Crit. ReV. Ther. Drug Carrier Syst. 1998, 15, 481512. (15) Hruby, M.; Konak, C.; Ulbrich, K. J. Appl. Polym. 2005, 95, 201211. (16) Bae, Y.; Fukushima, S.; Harada, K. Angew. Chem., Int. Ed. 2003, 42, 4640-4643. (17) Taillefer, J.; Jones, M. C.; Brasseur, N.; van Lier, J. E.; Leroux, J. C. J. Pharm. Sci. 2000, 89, 52-62. (18) Soga, O.; Nostrum, C. F.; Fens, M.; Rijcken, C. J. F.; Schiffelers, R. M.; Storm, G.; Hennink, W. E. J. Controlled Release 2005, 103, 341353. (19) Taboada, P.; Velasquez, G.; Barbosa, S.; Castelleto, V.; Nixon, S. K.; Yang, Z.; Heatley, F.; Hamley, I. W.; Ashford, M.; Mosquera, V.; Attwood, D.; Booth, C. Langmuir 2005, 21, 5263-5271. (20) Yokoyama, M.; Okano, T.; Sakurai, Y.; Suwa, S.; Kataoka, K. J. Controlled Release 1996, 39, 351-356. (21) Zhang, X.; Jackson, J. K.; Burt, H. Int. J. Pharm. 1996, 132, 195206. (22) Liggins, R. T.; Burt, H. M. AdV. Drug DeliVery ReV. 2002, 54, 191-202. (23) Ikada, Y.; Tsuji, H. Macromol. Rapid Commun. 2000, 21, 117132

J. Phys. Chem. B, Vol. 112, No. 3, 2008 791 (24) Savic, R.; Luo, L.; Eisenberg, A.; Maysinger, D. Science 2003, 300, 615-618. (25) Zentner, G. M.; Rathi, R.; Shih, C.; McRea, J. C.; Seo, M. H.; Oh, H. S.; Ree, B. G.; Mestecky, J.; Moldoveanu, Z.; Morgan, M.; Weitman, S. J. Controlled Release 2001, 72, 203-215. (26) Jeong, B.; Lee, K. M.; Gutowska, A.; An, Y. H. Biomacromolecules 2002, 3, 865-868. (27) Kwon, G. S.; Naito, M.; Yokoyama, M.; Okano, T.; Sakurai, Y.; Kataoka, K. Pharm. Res. 1995, 12, 192-195. (28) Kabanov, A. V.; Batrakova, E. V.; Alakhov, V. Y. J. Controlled Release 2002, 82, 189-212. (29) Thermosensitive polymers are defined as polymers whose solubility changes upon changing the temperature. For example, polymers with a lower critical solution temperature (LCST) are soluble in water below their critical temperature (cloud point, CP), but above this temperature, dehydration of the polymer chains occurs, resulting in collapse and precipitation (phase separation) of the polymer. (30) Topp, M. D. C.; Dijkstra, P. J.; Talsma, H.; Feijen, J. Macromolecules 1997, 30, 8518-8520. (31) Schild, H. G. Prog. Polym. Sci. 1992, 17, 163-249. (32) Pelton, R. AdV. Colloid Interface Sci. 2000, 85, 1-33. (33) Fujishige, S.; Kubota, K.; Ando, I. J. Phys. Chem. 1989, 93, 33113313. (34) Maeda, Y.; Taniguchi, N.; Ikeda, I. Macromol. Rapid Commun. 2001, 22, 1390-1393. (35) Neradovic, D.; van Nostrum, C. F.; Hennink, W. E. Macromolecules 2001, 34, 7589-7591. (36) Neradovic, D.; van Steenbergen, M. J.; Vansteelant, L.; Meijer, Y. J.; van Nostrum, C. F.; Hennink, W. E. Macromolecules 2003, 36, 74917498. (37) Yoshida, T.; Aoyagi, T.; Kokufuta, E.; Okanno, T. J. Polym. Sci., Part A: Polym. Chem. 2003, 41, 779. (38) Sun, L. F.; Zhuo, R. X.; Liu, Z. L. Macromol. Biosci. 2003, 3, 726. (39) Zhang, X.; Wu, D.; Chu, C. C. Biomaterials 2004, 25, 4719-4730. (40) Neradovic, D.; Hinrichs, W. L. J.; Kettenes-van den Bosch, J. J.; Hennink, W. E. Macromol. Rapid Commun. 1999, 20, 577-581 (41) Soga, O.; van Nostrum, C. F.; Hennink, W. E. Biomacromolecules 2004, 5, 818-821. (42) Soga, O.; van Nostrum, C. F.; Ramzi, A.; Visser, T.; Soulimani, F.; Frederik, P. M.; Bomans, P. H. H.; Hennink, W. E. Langmuir 2004, 20, 9388-9395 (43) Higgins, J. S.; Benoit, H. Polymers and Neutrons Scattering; Clarendon Press: Oxford, U.K., 1994. (44) Cotton J. P. In Neutron, x-ray and light scattering; Lindner, P., Zemb, T., Eds.; Elsevier: Amsterdam, The Netherlands, 1991; p 19. (45) Schurtenberger, P. In Neutrons, X-rays and Light: Scattering Methods Applied to Soft Condensed Matter; Lindner, P., Zemb, T., Eds.; North-Holland: Amsterdam, The Netherlands, 2002. (46) King, S. M.; Griffiths, P. C.; Cosgrove, T. In Applications of Neutrons in Soft Condensed Matter; Gabrys, B. J., Ed.; Gordon and Breach: New York, 1998. (47) Washington, C.; King, S. M.; Heenan, R. J. Phys. Chem. 1996, 100, 7603-7609. (48) Cosgrove, T.; Ryan, K. Langmuir 1990, 6, 136-142. (49) Dingenouts, N.; Seelenmeyer, S.; Deike, I.; Rosenfeldt, S.; Ballauff, M.; Lindner, P.; Narayanan, T. Phys. Chem. Chem. Phys. 2001, 3, 11691174. (50) Hone, J. H. E.; Cosgrove, T.; Saphiannikova, M.; Obey, T. M.; Marshall, J. C.; Crowley, T. L. Langmuir 2002, 18, 855-864. (51) Bagger-Jo¨rgensen, H.; Olsson, U.; Mortensen, K. Langmuir 1997, 13, 1413-1421. (52) Bumajdad, A.; Eastoe, J.; Heenan, R. K.; Lu, J. R.; Steytler, D. C.; Egelhaaf, S. J. Chem. Soc., Faraday Trans. 1998, 94, 2143-2145. (53) Mortensen, K. J. Phys.: Condens. Matter 1996, 8, A103. (54) Willner, L.; Poppe, A.; Allgaier, J.; Monkenbusch, M.; Lindner, P.; Richter, D. Europhys. Lett. 2000, 51, 628-634. (55) Neradovic, D.; Soga, O.; van Nostrum, C. F.; Hennink, W. E. Biomaterials 2004, 25, 2409-2418. (56) King, S. M. In Modern Techniques for Polymer Characterization; Dawkins, J. V., Ed.; John Wiley & Sons Ltd: New York, 1999; pp 171232. (57) Pedersen, J. S.; Svaneborg, C. Curr. Opin. Colloid Interface Sci. 2002, 7, 158-166. (58) Castelletto, V.; Hamley, I. W. Curr. Opin. Colloid Interface Sci. 2002, 7, 167-172. (59) Kotlarchyk, M.; Chen, S.-H. J. Chem. Phys. 1983, 79, 2461 (60) Heenan, R. K. FISH Data Analysis Program; Rutherford Appleton Laboratory Report RAL-89-129, 1989. (61) Riley, T.; Heald, C. R.; Stolnik, S.; Garnett, M. C.; Illum, L.; Davis, S. S.; King, S. M.; Heenan, R. K.; Purkiss, S. C.; Barlow, R. J.; Gellert, P. R.; Washington, C. Langmuir 2003, 19, 8428-8435.

792 J. Phys. Chem. B, Vol. 112, No. 3, 2008 (62) Eastoe, J.; Dong, J. F.; Hetherington, K. J.; Steytler, D.; Heenan, R. K. J. Chem. Soc., Faraday Trans. 1996, 92, 65-72. (63) Palaniswamy, R.; Dai, S.; Tam, Michael K. C.; Gan, L. H. Molecular Engineering of Biological and Chemical Systems (MEBCS), http://hdl.handle.net/1721.1/3938, 2004. (64) Devanand, K.; Selser, J. C. Macromolecules 1991, 24, 5943-5947. (65) Leermakers, F. A. M.; Wijmans, C. M.; Fleer, G. J. Macromolecules 1995, 28, 3434-3443. (66) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces; Chapman & Hall: U.K., 1993.

Ramzi et al. (67) Washington, C.; King, S. M. Langmuir 1997, 13, 4545-4550. (68) Zackrisson, M.; Stradner, A.; Schurtenberger, P.; Bergenholtz, J. Langmuir 2005, 21, 10835-10845. (69) Soppimath, K. S.; Aminabhavi, T. M.; Kulkarni, A. R.; Rudzinski, W. E. J. Controlled Release 2001, 70, 1-20 (70) Kratky O.; Porod G. Rec. TraV. Chim. Pays-Bas 1949, 68, 11061122. (71) Beaucage, G. J. Appl. Cryst. 1996, 29, 134-146. (72) Guinier, A.; Fournet, G. Small-Angle Scattering of X-Rays; John Wiley and Sons: London, 1955.