Supramolecular Organization of Heteroxylan-Dehydrogenation

Jan 23, 2008 - Telephone: 00 33 (0)2 40 67 50 68 . ... The formation of local chemical heterogeneities was demonstrated by use of two fluorescent pola...
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Biomacromolecules 2008, 9, 487–493

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Supramolecular Organization of Heteroxylan-Dehydrogenation Polymers (Synthetic Lignin) Nanoparticles Abdellatif Barakat,† Cédric Gaillard,‡ Didier Lairez,§ Luc Saulnier,‡ Brigitte Chabbert,† and Bernard Cathala*,‡ UMR614 Fractionnement des Agro-Ressources et Emballage, INRA, Université de Reims Champagne Ardennes, F-51100 Reims, France, UR1268 Biopolymères Interactions Assemblages, INRA, F-44300 Nantes, France, and Laboratoire Léon Brillouin, CEA/CNRS, CEA Saclay, 91191 Gif-sur-Yvette cedex, France Received September 4, 2007; Revised Manuscript Received November 12, 2007

The supramolecular organization of particles composed of heteroxylans (HX) and synthetic lignin (dehydrogenation polymer, DHPs) was studied by light scattering (LS), atomic force microscopy (AFM), and fluorescent probes. Results from static and quasi-elastic light scattering indicate a dense core surrounded by a soft corona. Such organization is also supported by AFM images of the particles that display Gaussian height profiles when a low tapping force is applied, whereas the shape of the profile obtained at a higher mechanical solicitation is irregular and sharp due to deformation of the particles resulting from the tip indentation. This suggests a difference in mechanical behavior between the inner and outer parts of the particles. The formation of local chemical heterogeneities was demonstrated by use of two fluorescent polarity probes (pyrene and methyl-amino-pyrene) to be induced by the core-corona organization.

Introduction In nature, lignins and hemicelluloses are two major components of woody plants such as trees, straw, and grass. They are tightly bound together in the cell wall, forming a cohesive glue between the cellulose microfibrils despite the fact that one is thought to be hydrophobic (lignin) and the other hydrophilic (hemicelluloses). This amorphous composite material provides transversal mechanical strength to the cell wall1 and participates in other crucial functions such as waterproofness or resistance against pathogens. The formation of lignin-hemicellulose complexes occurs during the lignin polymerization process. Lignin is formed by the slow polymerization of lignin monomers within the predeposited polysaccharide network.2 The structural characteristics of lignins and hemicelluloses vary according to biological parameters such as plant species or tissue type, thereby producing a wide range of chemical structures that influence the final properties of these complexes. In an attempt to understand the underlying mechanism of formation of hemicellulose-lignin composites, we recently reported the synthesis of a set of four heteroxylans (HX)-synthetic lignin (Dehydrogenation polymer, DHPs) nanoparticles combining two HX and two lignin monomer mixtures.3 The first xylan was extracted at low temperature and contains a significant amount of ferulic acid, while the second one extracted at higher temperature is devoid of ferulic acid. Xylans solutions were used as solution media for the polymerization of the gaiacyl monomer (G) and gaiacyl/syringyl monomers mixture (GS). As xylans constitute the most abundant hemicellulose family (Figure 1) and G and GS lignins are the most commonly found lignin monomers, these building blocks are of biological relevance. * Corresponding author. E-mail: [email protected]. Telephone: 00 33 (0)2 40 67 50 68. Fax: 00 33 (0)2 40 67 50 25. † UMR614 Fractionnement des Agro-Ressources et Emballage, INRA, Université de Reims Champagne Ardennes. ‡ UR1268 Biopolymères Interactions Assemblages, INRA. § Laboratoire Léon Brillouin, CEA/CNRS, CEA Saclay.

HX-DHPs nanoparticles were synthesized via the bioinspired Zutropverfahren process that consists of slow addition of the lignin monomer to a solution of HX and peroxidase (Figure 1).4 We demonstrated that the final supramolecular organization of the resulting nanoparticles can be controlled by the fine chemical structure of the building blocks such as substitution of the HX with ferulic acid. This suggests that the chemical variability of plant polymers can be used to design new nanoparticles. Attention has been focused on the synthesis of nanoparticles because of their great potential in biotechnological applications such as drug delivery,5,6 design of new materials,7 reinforcing, and toughening of polymeric matrices8,9 and many others. Those nanoparticles that display heterogeneous organization, such as core–shell particles for instance, have been particularly investigated because heterogeneity induces local variation in chemical or physical properties, thereby increasing the functionality of the particle. In this paper, we aim to describe the organization and properties of a particle composed of HX devoid of ferulic acid and gaiacyl DHPs (Figure 1). Particle internal structure was investigated by light scattering (LS), atomic force microscopy (AFM), and fluorescent probes. We conclude that polymers are not homogenously distributed within particles forming a dense inner core surrounded by a soft corona

Materials and Methods All the reactants except HX were obtained from Sigma-Aldrich and were used without further purification. HX Extraction and Synthesis of the HX-DHPs Complex. HX (Figure 1) was isolated from maize bran as previously described10 and extracted under severe alkaline conditions, namely 1% Ca(OH)2 at 90 °C for 2.5 h. Thus the HX fraction obtained was almost devoid of ferulic acid and corresponded to the HX90 fraction described in our previous study.3 Synthesis of the HX-DHPs complex was as recently described.3 Coniferyl alcohol was obtained from coniferaldehyde according to.11

10.1021/bm7009812 CCC: $40.75  2008 American Chemical Society Published on Web 01/23/2008

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Figure 1. Chemical structure of coniferyl alcohol, dehydrogenation polymers (DHPs), and heteroxylans (HX). Polymerizations were carried out according the Zutropfverfharen (ZT) method, which consists of continuous addition of the monomer and hydrogen peroxide (enzyme cofactor) to a solution of polysaccharides containing the oxidative enzyme (horse radish peroxidase). Monolignols are oxidized by a monoelectronic process into radicals that react to form the DHPs. During this process, HX become bound to the DHPs by noncovalent and covalent linkages to yield the HX-DHP complex.

The HX-DHPs complex was synthesized by the Zutropverfahren method4 that consists of slow addition of coniferyl alcohol (1g/L final concentration) and hydrogen peroxide (peroxidase cofactor; 2 equiv compared to coniferyl alcohol) to a 1g/L solution of HX containing 5 mg of horse radish peroxidase (type VI; 250–330 unit/mg). The addition time was 4 h and the final volume 150 mL. Static and Dynamic Light Scattering. Light scattering experiments were performed at LLB/Saclay with a homemade spectrometer using a vertically polarized Ar laser at wavelength λ0 ) 488 nm. Samples were placed in a cylindrical quartz cell of 2.5 cm diameter. Scattered intensity was measured in the horizontal plane, at a scattering angle θ ranging from 15° to 150°, with a Hamamatsu H7155 photomultiplier module. The scattered intensity per scattering volume unit of toluene taken as reference was shown to be independent of scattering angle within 1% error bars. The Rayleigh ratio of toluene at this wavelength was taken as equal to 42.7 × 10-6 cm-1. The refractive index increment of heteroxylan was (dn/dC)HX ) 0.147 cm3 g-1.12 The refractive index increment of the heteroxylan/DHP complex was calculated following ref 13 as equal to (dn/dC)HX/DHP ) 0.282 cm3 g-1. The contrast factor, K2, was thus calculated as equal to 0.442 × 10-6 for heteroxylan and to 1.72 × 10-6 cm2 g-2 mol for the HX/DHP complex. Quasi-elastic light scattering measurements were performed by computing the timedependent autocorrelation function of the scattered intensity with a Flex2K-12 multi-tau correlator from Correlator.com. Atomic Force Microscopy. Sample Preparation. Starting from initial solutions with a concentration of 1 mg/mL, HX-DHPs were diluted to 10 µg/mL concentration with distilled water. Aliquots (5 µL) of the diluted samples were immediately deposited on freshly cleaved mica surfaces and then dried under a stream of argon for 10–20 min. AFM Imaging. Atomic force microscopy (AFM) was performed at room temperature using an Autoprobe CP Park Scientific Instrument (Sunnyvale, CA). AFM imaging was carried out in tapping mode in air using beam-shaped phosphorus-doped silicium cantilevers (Veeco Probes, CA) with a quoted spring constant of 50 N/m and that were

excited at a frequency proximate to a resonant frequency of around 282 kHz. Sample surfaces were scanned with the probe at a scanning frequency of 0.5–1 Hz. The drive amplitude was chosen either to get a high value of the average tapping force (Fav) or to obtain a weaker value of Fav. These two separate conditions were systematically used throughout the AFM experiments to provide either a true imaging of the specimen (lower Fav value) or a morphological distortion along with the hardness or softness of the phase scanned by the probe (higher Fav value). The Fav value was determined according to the empirical equation.14

Fav )

[

]

Asp 1k 1A (f )β 2Q A0(f0) 0

(1)

where k is the spring constant of the cantilever, Asp is the set point amplitude corresponding to the oscillation amplitude when the tip is in contact with the sample surface, f0 is the resonant frequency of the tip when the cantilever is freely oscillating, A0(f0) is the free amplitude corresponding to an oscillation in air at the resonant frequency, f is the working frequency used for imaging, A0(f) is the free amplitude corresponding to an oscillation in air at the working frequency, β ) A0(f)/A0(f) is the off-resonance parameter, and Q ) f0/∆f is the quality factor where ∆f is the full bandwidth at 0.707 of the maximum amplitude. Two sets of Fav were used for imaging surface morphology: Fav ) 4.1 nN and Fav ) 77.8 nN standing respectively for weak and high vibration energy conditions. The experimental parameters needed to determine Fav were measured from the response curves of the oscillating cantilever, giving the amplitudes of vibration as a function of frequency (see Table 1). Fluorescence Measurements. Pyrene or methyl amino pyrene probes were purchased from Aldrich and were not subjected to further purification. Appropriate volumes of concentrated ethanol solution (5 × 10-4 M) were added to water, methanol, or a 0.1 g/L HX-DHP

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Table 1. Experimental Parameters Measured from the Response Curve of the Cantilever during the Application of Two Different Drive Amplitudes and the Corresponding Fav Values drive amplitudea

f0 (Hz)

A0(f0) (µm)

F (Hz)

A0(f) (µm)

Asp (µm)

β

∆f (Hz)

Q

Fav (nN)

2% 20%

281710 182530

0.183 0.297

281420 278070

0.134 0.271

0.06 0.123

0.732 0.912

710 6070

396.7 46.5

4.1 77.8

a

Working value, indicated as percentage of the allowable applied voltage to the oscillating cantilever.

Figure 2. Concentration dependence of apparent molecular mass, Mapp, and radius of gyration Rapp, obtained from linear fitting of the reverse scattered intensity vs the square scattering vector. Actual molecular mass, Mw and radius of gyration, Rg, values correspond to extrapolation to Cf0.

solution dissolved in phosphate buffer to reach the final probes concentration of 5 × 10-7 M. Fluorescence emission spectra were recorded on a SPEX Fluoromax spectrophotometer (Edison, USA) equipped with a thermostatically controlled cell at 25 °C. The excitation wavelength was 335 nm. The emission spectra recorded between 350 and 700 nm showed five vibronic peaks and no eximer. The intensities of the vibronic peaks at 372 nm (intensity I1) and 382 nm (intensity I3) were measured to calculate the I1/I3 ratio.

Figure 3. Quasi-elastic light scattering data for HX-DHP complexes at concentration C ) 2 mg/cm3: dynamic structure factor, S(q,t), measured at different values of scattering vector q, vs tq2. Bottom: log–log scale; top: log-lin scale. Dashed straight line corresponds to S(q,t) ) exp(-D × tq2), with D ) 3.1 ( 0.1 nm2/µs.

Results and Discussion

gyration Rg was obtained by extrapolation to zero concentration of Rapp (Figure 2). We found:

Polymerization of lignin monomer in a polysaccharide solution leads to the formation of a colloidal suspension of composite nanometric particles. In the case of heteroxylans extracted from maize bran, this suspension is stable and thus can easily be handled and studied by appropriate techniques. Static and Quasielastic Light Scattering. Dilute solutions of HX-DHP complexes were studied by light scattering. The total scattered intensity per unit volume, I, was measured at different concentrations, C, between 0.5 and 2 mg/cm3, as a function of the scattering angle θ. In this concentration range, one has:

(

)

q2Rg I(q,C) ) M 1 + .... (1 - 2MA2C + ...) w 3 CK2

(2)

where q ) sin(θ/2)4πn/λ0 is the scattering vector, Rg the radius of gyration of the HX-DHP complexes, Mw their weightaveraged molecular mass, and MA2 their twobodies interaction term (second virial coefficient). At a given concentration, the apparent molecular mass, Mapp, and radius of gyration, Rapp, were deduced from linear fitting of 1/I(q) as a function of q2 (Zimm approximation). The actual molecular weight, Mw, and the second virial coefficient, MA2, were obtained by linear fitting of Mapp as a function of C (Figure 2). The actual radius of

Mw ) (7.6 ( 0.4) × 106g/mol

(3a)

Rg ) (45 ( 3)nm

(3b)

1 ⁄ MA2 ) (9.2 ( 0.25)mg/cm3

(3c)

The internal concentration of HX-DHP complexes, C* ) Mw/(NAR3g), with NA the Avogadro’s number, is calculated from eqs 3a and 3b to be equal to C* ) (140 ( 30) mg/cm3. Quasi-elastic light scattering measurements were performed at different scattering angles and different concentrations in dilute solutions. Typical results for the dynamical structure factor, S(q,t), are plotted in Figure 3. S(q,t) is rescaled for values of the scattering vector q between q ) 5.9 × 10-3 and 3.2 × 10-2 nm-1, using tq2 as a reduced variable, and is found to decrease exponentially as S(q,t) ) exp(-D × tq2) with D ) 3.1 ( 0.1 nm2/µs. The latter can thus be interpreted in terms of a translational diffusion coefficient that gives access to the hydrodynamic radius, RH ) kT/(6πηD) of HX-DHP complexes, with kT the thermal energy and η the solvent viscosity. One gets:

RH ) (69 ( 2)nm

(4)

This set of results in itself provides clear evidence that the structure of HX-DHP complexes consists of a dense core surrounded by a soft corona:

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Figure 4. Apparent diffusion coefficient D(q) ) Γ(q)/q2, with Γ(q) the exponential decay rate of the dynamic structure factor, vs scattering vector q. The dashed line corresponds to the mean value D ) 3.1 ( 0.1 nm2/µs. The straight line has a slope of kT/(6πη), with η the solvent viscosity, and corresponds to that expected for fluctuations of internal concentration.

1. The product MA2C* ) 15 ( 4 lies between the value of 6.6 for polymers in a good solvent15 and that of 36 for hard balls.16 This is consistent with the high internal concentration C* of the complex (due to a dense core) but smooth repulsive potential (low MA2) attributable to a low density corona. 2. The ratio RH/Rg ) 1.53 ( 0.15 is higher than the value (5/3)-1/2 ≈ 1.29 for hard balls (note that this value is less than 1 for polymer chains17). This indicates friction mainly in the outer part of the complex (contrary to a polymer coil which shows partial free draining of solvent), whereas the scattering length density distribution of the elementary light scatterers is higher in the inner part. 3. The apparent diffusion coefficient D(q) ) Γ (q)/q2, with Γ(q) the exponential decay rate of the dynamic structure factor, is found to be independent of q even when qRg > 1 (see Figure 4). This indicates that fluctuations in internal concentration within HX-DHP complexes are negligible compared to translational diffusion. For details on this point, see refs 18,19. This result is again consistent with a very dense structure of HX-DHP complexes. Let us examine the ratio RH/Rg in more detail. On the basis of the above results, it seems reasonable to consider HX-DHP complexes as spheres made of an inner DHP-dense-core (hydrophobic component) surrounded by a HX-soft-corona (amphiphilic component). In this case, as previously demonstrated,20 the ratio of the geometrical radius of the sphere, Rtot, to the apparent radius of gyration, Rgapp, is given by:

[ ] [

Rtot 2 3 ) kDHP ∆2 + Rgapp 5 df 1 - ∆ df+2 kHX df + 2 1 - ∆ df

]

-1

with

∆)

RDHP (5) Rtot

where ki ) ωiKi/〈K〉 is the relative contrast of component i, ωi its volume fraction, Ki ∝ (dn/dC)i, 〈K〉 ) ∑iKi, and df the fractal dimension of the soft corona. In Figure 5, the ratio RDHP/Rtot is plotted as a function of Rtot/Rgapp. Assuming Rtot/Rgapp = RH/ Rg ) 1.53, (see point 2 above), and solving eq 4 with df ) 2, leads to RDHP/Rtot = 0.8 (dashed lines in Figure 5). Atomic Force Microscopy. A local scanning force technique such as atomic force microscopy (AFM) is able to produce images of the surface on a small scale of length ranging from hundreds of micrometers to a few nanometers. AFM is now widely used in many domains and has been used to study the

Figure 5. Theoretical variation of Rtot/Rgapp ) RH/Rg with ∆ ) RDHPcore/Rtot. Dashed lines give RDHPcore/Rtot = 0.8 from the experimental result RDHPcore/Rtot = RH/Rg ) 1.53.

morphology of soft particles. We thus decided to investigate the morphology of isolated HX-DHPs particles after deposition on a cleaved mica surface. Images were obtained by a vibratingcantilever AFM method, an intermittent-contact or tapping mode that is generally appropriate for soft materials and particularly for biopolymers, as it reduces lateral forces on the sample.21 In the tapping method, the force applied to the sample can be tuned by changing the tapping amplitude. The closer the tapping amplitude is to the maximum amplitude value, the higher the average tapping force Fav. In some cases, variation of the Fav leads to different images that can be attributed to damage caused by the tip indentation. Thus it is recognized that height images obtained by tapping mode do not always indicate the “true” surface topography14,22 and may lead to misinterpretation. Nevertheless, in some cases, the differences observed between images with different Fav may indirectly reveal information about the mechanical behavior of the observed structure and thus offer some indication of its organization. In the present study, we applied two different Fav, the first was rather low (Fav ) 4.1 nN), whereas the second was considerably larger (77.8 nN). In the first case (Fav ) 4.1 nN, Figure 6a,c), HX-DHP particles were apparent as individual ovoid-shaped objects dispersed on the surface and reminiscent of those previously observed by transmission electron microscopy.3 The main difference was the dimension, the diameters of the objects ranging from approximately 200 to 300 nm, whereas they were significantly smaller in TEM and LS. This effect can be attributed to the flatness of the particles on the surface. This conclusion was supported by measuring the height at the top of the particle that ranged from 10 to 30 nm (Figure 6e). This is significantly lower than the diameters of the particles in solution. This demonstrates that HX-DHP particles are soft deformable objects. Nevertheless, the profiles obtained presented the regular and quasi-Gaussian patterns (Figure 6e) expected for soft and swollen materials that flatten on a surface. The second set of images (Figure 6b,d,f) was obtained by applying high Fav to the particles. The particle sizes were in the same range as observed at low Fav, but the morphologies were completely different because the particle shapes were irregular and sharply defined. The influence of the greater force applied was apparent on this soft material. The maximum height was lower than that in low Fav conditions, but the profile was no longer regular. The outer parts seem to be mashed by the AFM tip, while the central parts were apparent as bumps suggestive of more resistant material. These results are in agreement with

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Figure 6. AFM images of HX-DHPs. The (a) and (c) images were recorded at low average tapping force (Fav), whereas images (b) and (d) were obtained at high Fav. (e) and (f) are the corresponding height profiles.

images obtained with composite materials. For instance, the images of core–shell particles obtained using the contact mode at a force of 100 nN were also distorted.23 Another study reported that particles of a pressure-sensitive adhesive film appeared to be concave at low Fav when the tapping mode was used, whereas the images displayed convex shapes when a higher Fav was applied.14 All these converging elements tend to indicate that HX-DHP particles present a heterogeneous internal structure in which materials with higher mechanical resistance are located in the inner part of the particle and those of less mechanical resistance at the outer part of the structure. This cannot be attributed to a gradient of concentration of the polymer blend (HX + DHP) from the center of the particles to the outer part because the LS data indicate that the domains of the DHPs are smaller than those of HX. This supports the hypothesis of the existence of a core of DHPs or DHPs-HX surrounded by a corona of HX.

Investigation of the Local Polarity of the Particles by Fluorescent Probes. Fluorescence probe techniques have been developed for the structural study of colloidal solutions.24 Pyrene (Figure 7) has been reported to be an interesting probe because its fluorescence emission spectrum and more precisely the ratio of the intensity of the first band of emission (λ1 ) 370 nm) to the intensity of the third band of emission (λ1 ) 382 nm) varies as a function of the polarity of the surrounding micropolarity. These variations result in a polarity scale and typically the ratio I1/I3 ranges from 1.9 for a polar solvent (1.85 in water) to 0.6 in an apolar solvent such as hexane. In colloidal solutions, the variation of the I1/I3 ratio will indicate the preferential solubilization of the pyrene in a hydrophobic zone and is helpful both in monitoring the aggregation process13,25 and also in describing the local chemical environment within aggregates or particles. Many derivatives of pyrene are commercially available and offer a broad range of chemical characteristics.24 The emission

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Acknowledgment. Access to the AFM facilities of the BIBS platform (Biopolymers, Interactions, Structural Biology) of INRA-Nantes was greatly appreciated by the authors.

Appendix Radius Ratio for Objects with Dense Core and Soft Corona In the case of an object made of two components, the apparent radius of gyration measured by scattering experiment 27,28 can be expressed as:

R2gapp ) kaR2ga + kbR2gb + kakbG2ab

Figure 7. Ratio of the intensity ratio of band 1 over the intensity of band 3 of the pyrene and methyl amino pyrene spectra in water, methanol, and HX-DHP in phosphate buffer normalized by the ratio obtained in water.

(A1)

Here ki ) ωiKi/〈K〉 is the relative contrast of component i, with ωi its volume fraction and Ki ∝ (dn/dC)i, 〈K〉 ) ∑iKi. Rga and Rgb are the geometrical radii of gyration of compounds a and b, respectively, and Gab is the distance between their centers of mass. Let us consider the following possibilities: 1. Compounds a and b have concentric mass distributions: Gab ) 0. 2. Compound a forms the inner core of the object. It has a homogeneous structure and a spherical shape of radius Ra. Then:

R2ga ) (3 ⁄ 5)R2a spectrum of methyl amino pyrene (Figure 7) also displays the polarity dependence, but the presence of the amino group, which has a positive charge at the working pH, will change the hydrophobicity of the molecule. We measured the I1/I3 ratio for pyrene and methyl amino pyrene in water, methanol, and in a suspension of HX-DHPs in phosphate buffer. For both probe, ratios were normalized to the water value because the absolute value of the I1/I3 ratio for pyrene and methyl amino pyrene differ as a result of the methyl amino substitution. The normalized I1/I3 ratio for both molecules was lower in the HX-DHPs suspension than in water, thereby indicating the occurrence of a hydrophobic zone. In the case of pyrene, this value was slightly lower than that measured in methanol, indicating that the inner part of the particle corresponds to an environment similar to that of aliphatic alcohols. This finding is in good agreement with the chemical structure of DHPs (Figure 1). Conversely, the value measured for methyl amino pyrene in the HX-DHP suspension was higher than that measured in methanol but still lower than water. This indicates that the methyl amino pyrene would be located in a somewhat hydrophobic environment but obviously not so apolar as that in which pyrene is solubilized. This finding suggests the existence of clusters of different polarity within the HX-DHP particles. These polarity variations might have some influence on the reactivity, as already exemplified on the LCC formation.26 Stability of monomer radicals might be affected and influence the ratio of the intermonomeric linkages. In conclusion, we have evidenced by three distinct methods that the internal organization of the HX-DHP particle is heterogeneous. A complete diagram can be drawn in which the apolar DHPs fraction is located in the center of the particle and is surrounded by a polar HX corona. The inner part exhibits different mechanical behavior and chemical characteristics to the external region of the particle. In future work, an in-depth investigation of the HX and DHPs will be carried out by neutron scattering technique on all the HX-DHP complexes we have synthesized in order to evaluate the influence of chemical parameters on core–shell organization.

(A2)

3. Compound b forms a starlike corona around the inner core. It displays a decreasing concentration profile as a function of the distance r from the center of mass that can be accounted for using the star polymer model of Daoud-Cotton.29,30 The geometrical square-radius of gyration of this corona is defined as the ratio of the moment of inertia to the mass. It is generally written as:

R2gb )

∫ 4πr2F(r)r2

dr ⁄

∫ 4πr2F(r)

dr

(A3)

with F(r) the local concentration of compound b at distance r from the center of mass. The starlike corona can be viewed as a fractal of dimension df with F(r) varying as:31

F(r) ) F0(r ⁄ a)df-3

(A4)

with a the monomer size. Equation A3 then becomes R2gb ) 1 + d ∫r f dr/∫ rdf-1 dr. Integration from Rmin ) Ra to Rmax ) Rtot gives:

R2gb 2 Rtot

)

df 1 - ∆df+2 × df + 2 1 - ∆df

with

∆)

Ra Rtot

(A5)

Equations A1, A2, and A5 lead to eq 5.

References and Notes (1) Salmen, L. C. R. Acad. Sci. Biol. 2004, 327, 873–880. (2) Terashima, N.; Fukushima, K.; He, L.-F.; Takabe, K. In Forage Cell Wall Structure and Digestibility; Jung, H. G., Buxton, D. R., Hatfield, R. D., Ralph, J., Eds.; American Society of Agronomy: Madison, WI, 1993; pp 247–270. (3) Barakat, A.; Putaux, J. L.; Saulnier, L.; Chabbert, B.; Cathala, B. Biomacromolecules. 2007, 8, 1236–1245. (4) Sarkanen K. V. In Lignins: Occurrence, Formation, Structure, and Reaction; Sarkanen K. V., Ludwig G. H., Eds.; Wiley & Sons: New York, 1971; pp 95–155. (5) Yang, Y. Y.; Wang, Y.; Powell, R.; Chan, P. Clin. Exp. Pharmacol. Physiol. 2006, 33, 557–562. (6) Dang, J. M.; Leong, K. W. AdV. Drug DeliVery ReV. 2006, 58, 487– 499. (7) Caruso, F. AdV. Mater. 2001, 13, 11. (8) Sarikaya, M.; Tamerler, C.; Jen, A. K. Y.; Schulten, K.; Baneyx, F. Nat. Mater. 2003, 2, 577–585. (9) Crosby, A. J.; Lee, J. Y. Polym. ReV. 2007, 47, 217–229.

Heteroxylans-Synthetic Lignin Nanoparticles (10) Chanliaud, E.; Saulnier, L.; Thibault, J.-F. J. Cereal Sci. 1995, 21, 195–203. (11) Ludley, F. H.; Ralph, J. J. Agric. Food Chem. 1996, 44, 2942–2943. (12) Chanliaud, E.; Roger, P.; Saulnier, L.; Thibault, J. F. Carbohydr. Polym. 1996, 31, 41–46. (13) Lairez, D.; Cathala, B.; Monties, B.; Bedos-Belval, F.; Duran, D.; Gorrichon, L. Biomacromolecules 2005, 6, 763–774. (14) Lei, C. H.; Ouzineb, K.; Dupont, O.; Keddie, J. L. J. Colloid Interface Sci. 2007, 307, 56–63. (15) Raspaud, E. Macromolecules 1995, 28, 927–933. (16) Hansen, J. P.; McDonald, I. Theory of Simple Liquids; Academic Press: London, 1976. (17) Oono, Y.; Kohmoto, M. J. Chem. Phys. 1983, 78, 520–528. (18) Raspaud, E.; Lairez, D.; Adam, M.; Carton, J. P. Macromolecules 1994, 27, 2956–2964. (19) Adam, M.; Lairez, D.; Raspaud, E.; Farago, B. Phys. ReV. Lett. 1996, 77, 3673–3676. (20) Adam, M.; Carton, J. P.; Corona Vallet, S.; Lairez, D. J. Phys. (Paris) 1996, 6, 1781–1795.

Biomacromolecules, Vol. 9, No. 2, 2008 493 (21) Hansma, H. G. L. I.; Pietrasanta, I. D.; Auerbach, C; Sorenson, R; Golan, J. P. A. H. J. Biomater. Sci., Polymer Ed. 2000, 11, 675– 685. (22) Kopp-Marsaudon, S.; Leclere, P.; Dubourg, F.; Lazzaroni, R.; Aime, J. P. Langmuir 2000, 16, 8432–8437. (23) Sommer, F.; Duc, T. M.; Pirri, R.; Meunier, G.; Quet, C. Langmuir 1995, 11, 440–448. (24) Winnik, F.; Regismond, S. T. Colloids Surf., A 1996, 118, 1–39. (25) Barakat, A.; Chabbert, B.; Cathala, B. Phytochemistry 2007, 68, 2118– 2125. (26) Barakat, A.; Winter, H.; Rondeau-Mouro, C.; Saake, B.; Chabbert, B.; Cathala, B. Planta 2007, 267–281. (27) Leng, M.; Benoit, H. J. Polym. Sci. 1962, 57, 263–273. (28) Cotton, J. P.; Benoit, H. J. Phys. (Paris) 1975, 36, 905–910. (29) Daoud, M.; Cotton, J. P. J. Phys. (Paris) 1982, 531–538. (30) Halperin, A. Macromolecules 1987, 20, 2943–2946. (31) Adam, M.; Lairez, D. Fractals 1993, 1, 149–169.

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