Supramolecular Organization of Heteroxylan-DehydrogenationPolymers (Synthetic Lignin) Nanoparticles

Abdellatif Barakat,† Cédric Gaillard,‡ Didier Lairez,§ Luc Saulnier,‡ Brigitte Chabbert,† andBernard Cathala*,‡

UMR614 Fractionnement des Agro-Ressources et Emballage, INRA, Université de Reims ChampagneArdennes, 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 (dehydrogenationpolymer, 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. Suchorganization is also supported by AFM images of the particles that display Gaussian height profiles when a lowtapping force is applied, whereas the shape of the profile obtained at a higher mechanical solicitation is irregularand sharp due to deformation of the particles resulting from the tip indentation. This suggests a difference inmechanical behavior between the inner and outer parts of the particles. The formation of local chemicalheterogeneities was demonstrated by use of two fluorescent polarity probes (pyrene and methyl-amino-pyrene) tobe induced by the core-corona organization.

Introduction

In nature, lignins and hemicelluloses are two major compo-nents of woody plants such as trees, straw, and grass. They aretightly bound together in the cell wall, forming a cohesive gluebetween the cellulose microfibrils despite the fact that one isthought to be hydrophobic (lignin) and the other hydrophilic(hemicelluloses). This amorphous composite material providestransversal mechanical strength to the cell wall1 and participatesin other crucial functions such as waterproofness or resistanceagainst pathogens. The formation of lignin-hemicellulosecomplexes occurs during the lignin polymerization process.Lignin is formed by the slow polymerization of lignin monomerswithin the predeposited polysaccharide network.2 The structuralcharacteristics of lignins and hemicelluloses vary according tobiological parameters such as plant species or tissue type,thereby producing a wide range of chemical structures thatinfluence the final properties of these complexes.

In an attempt to understand the underlying mechanism offormation of hemicellulose-lignin composites, we recentlyreported thesynthesisofasetof fourheteroxylans (HX)-syntheticlignin (Dehydrogenation polymer, DHPs) nanoparticles com-bining two HX and two lignin monomer mixtures.3 The firstxylan was extracted at low temperature and contains a significantamount of ferulic acid, while the second one extracted at highertemperature is devoid of ferulic acid. Xylans solutions were usedas solution media for the polymerization of the gaiacyl monomer(G) and gaiacyl/syringyl monomers mixture (GS). As xylansconstitute the most abundant hemicellulose family (Figure 1)and G and GS lignins are the most commonly found ligninmonomers, these building blocks are of biological relevance.

HX-DHPs nanoparticles were synthesized via the bioinspiredZutropverfahren process that consists of slow addition of thelignin monomer to a solution of HX and peroxidase (Figure1).4 We demonstrated that the final supramolecular organizationof the resulting nanoparticles can be controlled by the finechemical structure of the building blocks such as substitutionof the HX with ferulic acid. This suggests that the chemicalvariability of plant polymers can be used to design newnanoparticles.

Attention has been focused on the synthesis of nanoparticlesbecause of their great potential in biotechnological applicationssuch as drug delivery,5,6 design of new materials,7 reinforcing,and toughening of polymeric matrices8,9 and many others. Thosenanoparticles that display heterogeneous organization, such ascore–shell particles for instance, have been particularly inves-tigated because heterogeneity induces local variation in chemicalor physical properties, thereby increasing the functionality ofthe particle. In this paper, we aim to describe the organizationand properties of a particle composed of HX devoid of ferulicacid and gaiacyl DHPs (Figure 1). Particle internal structurewas investigated by light scattering (LS), atomic force micros-copy (AFM), and fluorescent probes. We conclude that polymersare not homogenously distributed within particles forming adense inner core surrounded by a soft corona

Materials and Methods

All the reactants except HX were obtained from Sigma-Aldrich andwere used without further purification.

HX Extraction and Synthesis of the HX-DHPs Complex. HX(Figure 1) was isolated from maize bran as previously described10 andextracted 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 ferulicacid and corresponded to the HX90 fraction described in our previousstudy.3

Synthesis of the HX-DHPs complex was as recently described.3

Coniferyl alcohol was obtained from coniferaldehyde according to.11

* Corresponding author. E-mail: cathala@nantes.inra.fr. Telephone: 0033 (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.

Biomacromolecules 2008, 9, 487–493 487

10.1021/bm7009812 CCC: $40.75 2008 American Chemical SocietyPublished on Web 01/23/2008

The HX-DHPs complex was synthesized by the Zutropverfahrenmethod4 that consists of slow addition of coniferyl alcohol (1g/L finalconcentration) and hydrogen peroxide (peroxidase cofactor; 2 equivcompared to coniferyl alcohol) to a 1g/L solution of HX containing 5mg of horse radish peroxidase (type VI; 250–330 unit/mg). The additiontime was 4 h and the final volume 150 mL.

Static and Dynamic Light Scattering. Light scattering experimentswere performed at LLB/Saclay with a homemade spectrometer usinga vertically polarized Ar laser at wavelength λ0 ) 488 nm. Sampleswere placed in a cylindrical quartz cell of 2.5 cm diameter. Scatteredintensity was measured in the horizontal plane, at a scattering angle θranging from 15° to 150°, with a Hamamatsu H7155 photomultipliermodule. The scattered intensity per scattering volume unit of toluenetaken as reference was shown to be independent of scattering anglewithin 1% error bars. The Rayleigh ratio of toluene at this wavelengthwas taken as equal to 42.7 × 10-6 cm-1. The refractive index incrementof heteroxylan was (dn/dC)HX ) 0.147 cm3 g-1.12 The refractive indexincrement of the heteroxylan/DHP complex was calculated followingref 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 andto 1.72 × 10-6 cm2 g-2 mol for the HX/DHP complex. Quasi-elasticlight scattering measurements were performed by computing the time-dependent autocorrelation function of the scattered intensity with aFlex2K-12 multi-tau correlator from Correlator.com.

Atomic Force Microscopy. Sample Preparation. Starting from initialsolutions with a concentration of 1 mg/mL, HX-DHPs were dilutedto 10 µg/mL concentration with distilled water. Aliquots (5 µL) of thediluted samples were immediately deposited on freshly cleaved micasurfaces and then dried under a stream of argon for 10–20 min.

AFM Imaging. Atomic force microscopy (AFM) was performed atroom temperature using an Autoprobe CP Park Scientific Instrument(Sunnyvale, CA). AFM imaging was carried out in tapping mode inair using beam-shaped phosphorus-doped silicium cantilevers (VeecoProbes, CA) with a quoted spring constant of 50 N/m and that were

excited at a frequency proximate to a resonant frequency of around282 kHz. Sample surfaces were scanned with the probe at a scanningfrequency of 0.5–1 Hz. The drive amplitude was chosen either to geta high value of the average tapping force (Fav) or to obtain a weakervalue of Fav. These two separate conditions were systematically usedthroughout the AFM experiments to provide either a true imaging ofthe specimen (lower Fav value) or a morphological distortion alongwith the hardness or softness of the phase scanned by the probe (higherFav value).

The Fav value was determined according to the empirical equation.14

Fav )12

kQ[1-

Asp

A0(f0)]A0(f )� (1)

where k is the spring constant of the cantilever, Asp is the set pointamplitude corresponding to the oscillation amplitude when the tip isin contact with the sample surface, f0 is the resonant frequency of thetip when the cantilever is freely oscillating, A0(f0) is the free amplitudecorresponding to an oscillation in air at the resonant frequency, f isthe working frequency used for imaging, A0(f) is the free amplitudecorresponding to an oscillation in air at the working frequency, � )A0(f)/A0(f) is the off-resonance parameter, and Q ) f0/∆f is the qualityfactor where ∆f is the full bandwidth at 0.707 of the maximumamplitude.

Two sets of Fav were used for imaging surface morphology: Fav )4.1 nN and Fav ) 77.8 nN standing respectively for weak and highvibration energy conditions. The experimental parameters needed todetermine Fav were measured from the response curves of the oscillatingcantilever, giving the amplitudes of vibration as a function of frequency(see Table 1).

Fluorescence Measurements. Pyrene or methyl amino pyreneprobes were purchased from Aldrich and were not subjected to furtherpurification. Appropriate volumes of concentrated ethanol solution (5× 10-4 M) were added to water, methanol, or a 0.1 g/L HX-DHP

Figure 1. Chemical structure of coniferyl alcohol, dehydrogenation polymers (DHPs), and heteroxylans (HX). Polymerizations were carried outaccording 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 monoelectronicprocess into radicals that react to form the DHPs. During this process, HX become bound to the DHPs by noncovalent and covalent linkagesto yield the HX-DHP complex.

488 Biomacromolecules, Vol. 9, No. 2, 2008 Barakat et al.

solution dissolved in phosphate buffer to reach the final probesconcentration of 5 × 10-7 M. Fluorescence emission spectra wererecorded on a SPEX Fluoromax spectrophotometer (Edison, USA)equipped with a thermostatically controlled cell at 25 °C. The excitationwavelength was 335 nm. The emission spectra recorded between 350and 700 nm showed five vibronic peaks and no eximer. The intensitiesof the vibronic peaks at 372 nm (intensity I1) and 382 nm (intensityI3) were measured to calculate the I1/I3 ratio.

Results and Discussion

Polymerization of lignin monomer in a polysaccharidesolution leads to the formation of a colloidal suspension ofcomposite nanometric particles. In the case of heteroxylansextracted from maize bran, this suspension is stable and thuscan easily be handled and studied by appropriate techniques.

Static and Quasielastic Light Scattering. Dilute solutionsof HX-DHP complexes were studied by light scattering. Thetotal scattered intensity per unit volume, I, was measured atdifferent concentrations, C, between 0.5 and 2 mg/cm3, as afunction of the scattering angle θ. In this concentration range,one has:

I(q,C)

CK2)Mw(1-

q2Rg

3+ ....)(1- 2MA2C+ ...) (2)

where q ) sin(θ/2)4πn/λ0 is the scattering vector, Rg the radiusof gyration of the HX-DHP complexes, Mw their weight-averaged molecular mass, and MA2 their twobodies interactionterm (second virial coefficient). At a given concentration, theapparent 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, andthe second virial coefficient, MA2, were obtained by linear fittingof Mapp as a function of C (Figure 2). The actual radius of

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

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/(NARg

3), with NA the Avogadro’s number, is calculated fromeqs 3a and 3b to be equal to C* ) (140 ( 30) mg/cm3.

Quasi-elastic light scattering measurements were performed atdifferent scattering angles and different concentrations in dilutesolutions. Typical results for the dynamical structure factor, S(q,t),are plotted in Figure 3. S(q,t) is rescaled for values of the scatteringvector 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 asS(q,t) ) exp(-D × tq2) with D ) 3.1 ( 0.1 nm2/µs. The lattercan thus be interpreted in terms of a translational diffusioncoefficient that gives access to the hydrodynamic radius, RH )kT/(6πηD) of HX-DHP complexes, with kT the thermal energyand η the solvent viscosity. One gets:

RH ) (69( 2)nm (4)

This set of results in itself provides clear evidence that thestructure of HX-DHP complexes consists of a dense coresurrounded by a soft corona:

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

driveamplitudea f0 (Hz) A0(f0) (µm) F (Hz) A0(f) (µm) Asp (µm) � ∆f (Hz) Q Fav (nN)

2% 281710 0.183 281420 0.134 0.06 0.732 710 396.7 4.120% 182530 0.297 278070 0.271 0.123 0.912 6070 46.5 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 thereverse scattered intensity vs the square scattering vector. Actualmolecular mass, Mw and radius of gyration, Rg, values correspondto extrapolation to Cf0.

Figure 3. Quasi-elastic light scattering data for HX-DHP complexesat 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 correspondsto S(q,t) ) exp(-D × tq2), with D ) 3.1 ( 0.1 nm2/µs.

Heteroxylans-Synthetic Lignin Nanoparticles Biomacromolecules, Vol. 9, No. 2, 2008 489

1. The product MA2C* ) 15 ( 4 lies between the value of6.6 for polymers in a good solvent15 and that of 36 for hardballs.16 This is consistent with the high internal concentrationC* of the complex (due to a dense core) but smooth repulsivepotential (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 than1 for polymer chains17). This indicates friction mainly in theouter part of the complex (contrary to a polymer coil whichshows partial free draining of solvent), whereas the scatteringlength density distribution of the elementary light scatterers ishigher in the inner part.

3. The apparent diffusion coefficient D(q) ) Γ (q)/q2, withΓ(q) the exponential decay rate of the dynamic structure factor,is found to be independent of q even when qRg > 1 (see Figure4). This indicates that fluctuations in internal concentrationwithin HX-DHP complexes are negligible compared to trans-lational diffusion. For details on this point, see refs 18,19. Thisresult is again consistent with a very dense structure ofHX-DHP complexes.

Let us examine the ratio RH/Rg in more detail. On the basisof the above results, it seems reasonable to consider HX-DHPcomplexes as spheres made of an inner DHP-dense-core(hydrophobic component) surrounded by a HX-soft-corona(amphiphilic component). In this case, as previously demon-strated,20 the ratio of the geometrical radius of the sphere, Rtot,to the apparent radius of gyration, Rgapp, is given by:

[ Rtot

Rgapp]2

) [kDHP35

∆2 +

kHX

df

df + 21-∆ df+2

1-∆ df ]-1

with ∆)RDHP

Rtot(5)

where ki ) ωiKi/⟨K⟩ is the relative contrast of component i, ωi

its volume fraction, Ki ∝ (dn/dC)i, ⟨K⟩ ) ∑iKi, and df the fractaldimension of the soft corona. In Figure 5, the ratio RDHP/Rtot isplotted 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 techniquesuch as atomic force microscopy (AFM) is able to produceimages of the surface on a small scale of length ranging fromhundreds of micrometers to a few nanometers. AFM is nowwidely used in many domains and has been used to study the

morphology of soft particles. We thus decided to investigatethe morphology of isolated HX-DHPs particles after depositionon a cleaved mica surface. Images were obtained by a vibrating-cantilever AFM method, an intermittent-contact or tapping modethat is generally appropriate for soft materials and particularlyfor biopolymers, as it reduces lateral forces on the sample.21 Inthe tapping method, the force applied to the sample can be tunedby changing the tapping amplitude. The closer the tappingamplitude is to the maximum amplitude value, the higher theaverage tapping force Fav. In some cases, variation of the Fav

leads to different images that can be attributed to damage causedby the tip indentation. Thus it is recognized that height imagesobtained by tapping mode do not always indicate the “true”surface topography14,22 and may lead to misinterpretation.Nevertheless, in some cases, the differences observed betweenimages with different Fav may indirectly reveal informationabout the mechanical behavior of the observed structure andthus offer some indication of its organization. In the presentstudy, 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-shapedobjects dispersed on the surface and reminiscent of thosepreviously observed by transmission electron microscopy.3 Themain difference was the dimension, the diameters of the objectsranging from approximately 200 to 300 nm, whereas they weresignificantly smaller in TEM and LS. This effect can beattributed to the flatness of the particles on the surface. Thisconclusion was supported by measuring the height at the topof the particle that ranged from 10 to 30 nm (Figure 6e). Thisis significantly lower than the diameters of the particles insolution. This demonstrates that HX-DHP particles are softdeformable objects. Nevertheless, the profiles obtained presentedthe regular and quasi-Gaussian patterns (Figure 6e) expectedfor soft and swollen materials that flatten on a surface. Thesecond set of images (Figure 6b,d,f) was obtained by applyinghigh Fav to the particles. The particle sizes were in the samerange as observed at low Fav, but the morphologies werecompletely different because the particle shapes were irregularand sharply defined. The influence of the greater force appliedwas apparent on this soft material. The maximum height waslower than that in low Fav conditions, but the profile was nolonger regular. The outer parts seem to be mashed by the AFMtip, while the central parts were apparent as bumps suggestiveof more resistant material. These results are in agreement with

Figure 4. Apparent diffusion coefficient D(q) ) Γ(q)/q2, with Γ(q) theexponential decay rate of the dynamic structure factor, vs scatteringvector 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 solventviscosity, and corresponds to that expected for fluctuations of internalconcentration.

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

490 Biomacromolecules, Vol. 9, No. 2, 2008 Barakat et al.

images obtained with composite materials. For instance, theimages of core–shell particles obtained using the contact modeat a force of 100 nN were also distorted.23 Another studyreported that particles of a pressure-sensitive adhesive filmappeared to be concave at low Fav when the tapping mode wasused, whereas the images displayed convex shapes when ahigher Fav was applied.14 All these converging elements tendto indicate that HX-DHP particles present a heterogeneousinternal structure in which materials with higher mechanicalresistance are located in the inner part of the particle and thoseof less mechanical resistance at the outer part of the structure.This cannot be attributed to a gradient of concentration of thepolymer blend (HX + DHP) from the center of the particles tothe outer part because the LS data indicate that the domains ofthe DHPs are smaller than those of HX. This supports thehypothesis of the existence of a core of DHPs or DHPs-HXsurrounded by a corona of HX.

Investigation of the Local Polarity of the Particles byFluorescent Probes. Fluorescence probe techniques have beendeveloped for the structural study of colloidal solutions.24 Pyrene(Figure 7) has been reported to be an interesting probe becauseits fluorescence emission spectrum and more precisely the ratioof the intensity of the first band of emission (λ1 ) 370 nm) tothe intensity of the third band of emission (λ1 ) 382 nm) variesas a function of the polarity of the surrounding micropolarity.These variations result in a polarity scale and typically the ratioI1/I3 ranges from 1.9 for a polar solvent (1.85 in water) to 0.6in an apolar solvent such as hexane. In colloidal solutions, thevariation of the I1/I3 ratio will indicate the preferential solubi-lization of the pyrene in a hydrophobic zone and is helpful bothin monitoring the aggregation process13,25 and also in describingthe local chemical environment within aggregates or particles.Many derivatives of pyrene are commercially available and offera broad range of chemical characteristics.24 The emission

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.

Heteroxylans-Synthetic Lignin Nanoparticles Biomacromolecules, Vol. 9, No. 2, 2008 491

spectrum of methyl amino pyrene (Figure 7) also displays thepolarity dependence, but the presence of the amino group, whichhas a positive charge at the working pH, will change thehydrophobicity of the molecule. We measured the I1/I3 ratiofor pyrene and methyl amino pyrene in water, methanol, andin a suspension of HX-DHPs in phosphate buffer. For bothprobe, ratios were normalized to the water value because theabsolute value of the I1/I3 ratio for pyrene and methyl aminopyrene differ as a result of the methyl amino substitution. Thenormalized I1/I3 ratio for both molecules was lower in theHX-DHPs suspension than in water, thereby indicating the oc-currence of a hydrophobic zone. In the case of pyrene, this valuewas slightly lower than that measured in methanol, indicatingthat the inner part of the particle corresponds to an environmentsimilar to that of aliphatic alcohols. This finding is in goodagreement with the chemical structure of DHPs (Figure 1).Conversely, the value measured for methyl amino pyrene inthe HX-DHP suspension was higher than that measured inmethanol but still lower than water. This indicates that themethyl amino pyrene would be located in a somewhat hydro-phobic environment but obviously not so apolar as that in whichpyrene is solubilized. This finding suggests the existence ofclusters of different polarity within the HX-DHP particles.These polarity variations might have some influence on thereactivity, as already exemplified on the LCC formation.26

Stability of monomer radicals might be affected and influencethe ratio of the intermonomeric linkages.

In conclusion, we have evidenced by three distinct methodsthat the internal organization of the HX-DHP particle isheterogeneous. A complete diagram can be drawn in which theapolar DHPs fraction is located in the center of the particle andis surrounded by a polar HX corona. The inner part exhibitsdifferent mechanical behavior and chemical characteristics tothe external region of the particle. In future work, an in-depthinvestigation of the HX and DHPs will be carried out by neutronscattering technique on all the HX-DHP complexes we havesynthesized in order to evaluate the influence of chemicalparameters on core–shell organization.

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

Appendix

Radius Ratio for Objects with Dense Core and SoftCorona

In the case of an object made of two components, the apparentradius of gyration measured by scattering experiment 27,28 canbe expressed as:

Rgapp2 ) kaRga

2 + kbRgb2 + kakbGab

2 (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 aand b, respectively, and Gab is the distance between their centersof 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 ahomogeneous structure and a spherical shape of radius Ra. Then:

Rga2 ) (3 ⁄ 5)Ra

2 (A2)

3. Compound b forms a starlike corona around the inner core.It displays a decreasing concentration profile as a function ofthe distance r from the center of mass that can be accountedfor using the star polymer model of Daoud-Cotton.29,30

The geometrical square-radius of gyration of this corona isdefined as the ratio of the moment of inertia to the mass. It isgenerally written as:

Rgb2 )∫ 4πr2F(r)r2 dr ⁄∫ 4πr2F(r) dr (A3)

with F(r) the local concentration of compound b at distance rfrom the center of mass. The starlike corona can be viewed asa 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 Rgb2 )

∫r1 + d

f dr/∫ rdf-1 dr. Integration from Rmin ) Ra to Rmax ) Rtot

gives:

Rgb2

Rtot2)

df

df + 2× 1-∆df+2

1-∆dfwith ∆)

Ra

Rtot(A5)

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

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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.

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(4) Sarkanen K. V. In Lignins: Occurrence, Formation, Structure, andReaction; Sarkanen K. V., Ludwig G. H., Eds.; Wiley & Sons: NewYork, 1971; pp 95–155.

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Nat. Mater. 2003, 2, 577–585.(9) Crosby, A. J.; Lee, J. Y. Polym. ReV. 2007, 47, 217–229.

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

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(10) Chanliaud, E.; Saulnier, L.; Thibault, J.-F. J. Cereal Sci. 1995, 21,195–203.

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BM7009812

Heteroxylans-Synthetic Lignin Nanoparticles Biomacromolecules, Vol. 9, No. 2, 2008 493