mechanism of associations of neutral semiﬂ exible biopolymers … · 2016-07-17 · 3 mechanism...

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Full PaperMacromolecularChemistry and Physics

wileyonlinelibrary.com DOI: 10.1002/macp.201300265

Mechanism of Associations of Neutral Semifl exible Biopolymers in Water: The Xyloglucan Case Reveals Inherent Links

François Muller ,* Bruno Jean , Patrick Perrin , Laurent Heux , François Boué , Fabrice Cousin *

The mechanisms of association between neutral xyloglucan chains extracted from tamarind seeds are explored. Mesoscale structures involving a few chains are evidenced and monitored by static light scattering and low-shear viscosity experiments as a function of the xyloglucan concentration, obtained from increasing the dilution of an initial dispersion. The mechanism of association is addressed by means of multiangle dynamic light scattering. The associations exist whether the chains are in the dilute regime or in the semi-dilute regime and are characteristic of weak interactions. Their progressive loosening by dilution is evidenced and their level depends only on the xyloglucan concentration. The associations are due to a mechanism inherent to the nature of the chains.

Dr. F. MullerNaNo@ECE, ECE-Paris Ecole d’Ingénieurs, 37 Quai de Grenelle, F-75015 Paris, FranceE-mail: [email protected]; [email protected] Dr. F. Muller, Dr. F. Boué, Dr. F. CousinLaboratoire Léon Brillouin, CEA Saclay, 91191 Gif sur Yvette Cedex , France E-mail: [email protected] Dr. B. Jean, Dr. L. HeuxCERMAV, CNRS UPR 5301 , BP 53 38041 Grenoble Cedex , France Prof. P. PerrinPPMD/SIMM, CNRS-ESPCI-UPMC UMR 7615 , 10 rue Vauquelin 75231 Paris Cedex 05

of many biopolymers (made from several chemical groups polymerized along various sequences and architectures). This usually has as a consequence: the formation of meso-scale structures (aggregates, networks, concentration fl uc-tuations, etc.) that are not desirable for designing new materials. In this contribution, an alternative solubiliza-tion process and experimental approach are used for a biopolymer (which is also of interest for application pur-poses) in order to gain understanding on this general and open problem when using biopolymers extracted from natural compounds.

The polymer studied belongs to the class of xyloglucans (XG), a major class of polysaccharides belonging to the large family of hemicelluloses. They are complex polysac-charides designed by nature to act as binders between the amorphous matrix and the cellulose micro-fi brils in plant cell walls or as storage carbohydrates in seeds. XG are indeed essential as cross-linking agent in the primary cell walls of dicotyledons, playing an important role in the plant growth. [ 1,2 ] As these natural polymers can be obtained as a powder product in large quantities, they are often used in industrial applications such as food thick-ener or paper additives. They are a typical example of

1. Introduction

Neutral biopolymers are nowadays regularly used in engi-neering applications for designing innovative biomimetic materials. In many cases, the intrinsic properties of the biopolymers are not used in the materials in an optimal way as they could. Indeed, the material formulation fi rst requires the dissolution (“solubilization”) of the natural polymer compound in aqueous media. This step is often uncontrolled because of the complex molecular structure

Dedicated to the memory of Michel Delsanti

Early View Publication; these are NOT the final page numbers, use DOI for citation !!

Macromol. Chem. Phys. 2013, DOI: 10.1002/macp.201300265© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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( θ -solvent statistic), whereas tamarind seed XG have a swollen coil conformation (good solvent statistic). [ 14 ] Such differences come from the fact that water is a solvent of lower quality for xylose groups than for G backbone units and galactose side residues. Similarly, it has been shown that the degalactosylation of XG leads to a sol–gel tran-sition, evidencing the role of side chain residues in the solubilization behavior of this polymer. [ 15 ] Such molecular complexity leads indeed to different kinds of local inter-actions that coexist in solution (e.g., H-bonding or hydro-phobic interactions). These interactions may induce weak associations between residues, either from the same chain (intrachain) or from different chains (interchain) that may strongly impact the macroscopic properties.

Different procedures have been proposed to overcome the tendency to self-association, like XG carboxylation that obviously changes the molecular architecture, [ 16 ] and pressure cell-assisted solubilization that decreases the molecular weight and improves XG solubility. [ 17 ] In the latter case, the characterization of the molecular mass by GPC was impossible with the raw samples, illus-trating the crucial importance of the dissolution process. Recently, an alternative approach was proposed based on the use of solvent with a chaotropic character during the dissolution. [ 14 ] This achieved the solubilization at a mole-cular level of unfractionated XG chains and led to solu-tions that were stable over weeks.

Apart from the solubilization process, the other pre-requisite for the optimal use of XG chains in complex architectures is the characterization of the possible struc-tures that XG chains may form in water at the mesoscale as well as their mechanisms of formation. In particular, knowledge of the possible reorganizations of such struc-

tures upon dilution is very important for the design of XG-based composites in water, as it may enable to determine the best initial conditions for complex architecture design like the multilayer building that has been shown to depend strongly on the XG concentration. [ 5 ]

We previously used the chaotropic solubilization process in order to obtain fully solubilized XG chains in water and to characterize the chain behavior at local scale by small angle neutron scat-tering (SANS). [ 14 ] We evidenced that the chains behave like semifl exible worm-like chains with excluded volume sta-tistics (good solvent). However, the scat-tering features at the smallest Q -values probed in this SANS study (i.e., the largest investigated length scales), sug-gest that structures larger than isolated chains are present within the samples,

ideal candidates as building block units for the rational design of smart biomimetic materials obtained by green formulation when using water as solvent. A very prom-ising axis of development is to design advanced nano-structured composites made of XG chains and cellulose nanocrystals as recently reported in the literature. [ 3–6 ]

A diffi culty to overcome for such use of XG chains is the control of their dissolution in aqueous media. The fi rst diffi culty arises from the diversity of structures depending upon the biological origin of the XG chains, linked to their fi nal biological target. Secondly, there is a diversity of solubilization situations due to their complex molecular structure, which has been widely discussed in the literature. [ 7–9 ]

The XG chain is made of four repeating units with a cellulose-like backbone of (1,4)- β - D -Glc-linked glucose (G), decorated with other saccharide residues of increasing length according to the nomenclature referring to the side chain nature on each residue. [ 10 ] The XG structure from tamarind seeds is based on XXXG repeating units (13% molar), which can contain 0, 1, or 2 galactose residues, giving also XLXG (9%), XXLG (28%), and a majority of XLLG (50%), where G is the unsubstituted unit, X stands for α -(1,6)- D -xylose, and L for β - D -galactose-(1,2)- α - D -xylose. [ 11 ] This chemical structure is represented in Scheme 1 .

The detailed structure just described is very relevant in solubilization issues: a slight difference in chemical com-position may have a strong impact on the physical proper-ties of chains in aqueous solution. For example, XG chains from Detarium gum, structural composition of which is made of the same four repetition units (XLLG, XLXG, XXLG, and XXXG), but with a lower content in galactose residues L, [ 12,13 ] display a Gaussian coil conformation

Scheme 1. Chemical structure of XG chains from tamarind seeds: the chains are based on XXXG repeating units (13% molar), which can contain 0, 1, or 2 galactose residues, giving also XLXG (9%), XXLG (28%), and a majority of XLLG (50%), where G is the un-substituted unit, X stands for α -(1,6)- D -xylose, and L for β - D -galactose-(1,2)- α - D -xylose. The subscript X = 0 or 1 and the subscript Y = 0 or 1.



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obeyed for the values of R g found in Table 1 : the max-imum values of R g lead to an upper limit in Q close to 3 × 10 −3 Å −1 , with experimental values recorded between 1.5 × 10 −3 and 2.48 × 10 −3 Å −1 . The increase of R g with the

despite the perfectly swollen conformation at the local scale. The investigation of these large structures as a function of dilution is thus the main objective of the pre-sent contribution. We use static light scattering (SLS) and low-shear viscosity experiments as a function of the XG concentration obtained from dilution of the initial dis-persions. The mechanism of association is addressed by means of the multiangle dynamic light scattering (DLS) technique.

2. Results and Discussion

Before reporting and analyzing of the results at the mes-oscale, it is important to remind the reader of the charac-teristics and parameters of the XG chains at the local scale, previously obtained for similar samples: [ 14 ] the chains behave like semifl exible worm-like chains with self-avoiding conformation (Flory exponent of ν = 0.588) with a persistence length of l p = 80 Å and a cross-section of 6.3 Å. The persistence length corresponds to four times the chem-ical structure displayed in Scheme 1 . The individual chains have an average molecular mass of M W ≈ 465 000 g mol −1 with a polydispersity index of 1.44.

2.1. Evidence and Properties of Mesoscale Structures

2.1.1. SLS Measurements

The structures of XG chains from tamarind seeds have been fi rst explored at the mesoscale through SLS for the initial stock solution (7.8 g L −1 ) and its dilutions (down to 1.0 g L −1 ). We tried to probe a lower concentration (0.5 g L −1 ) but it was not possible to obtain reliable data due to a lack of scattering.

The scattering curves are shown in Figure 1 a (they are compared with the previous SANS measurements in the Supporting Information, Figure S1). It appears that the SLS results do not follow the pure form factor of worm-like chains in good solvent at low Q values. This result points out a more complex structure at large scale than single isolated chains.

To better characterize these scattering curves, we plot ln(I (Q)) versus Q 2 for each concentration (inset of Figure 1 a). They are all found to be linear in such a rep-resentation showing that one probes the Guinier regime. Therefore, following Equation 12 (see Experimental Sec-tion), the corresponding apparent radii of gyration can be deduced (Table 1 ). Indeed for polymeric objects, the Guinier regime remains valid up to QRg ≈ 3 because the transition to the Q−Df decay associated with the con-formation scaling law of the chains (linear or branched) at intermediate scale is not abrupt ( D f = 1.7 for linear chains in excluded volume for example). QR g ≈ 3 is

Figure 1. SLS data at XG concentrations of: 1.0 g L –1 (squares), 3.9 g L −1 (triangles), 5.0 g L –1 (circles), and 7.8 g L –1 (diamonds): a) I ( Q , c ) versus Q representation. The solid lines represent the best fi ts using the Guinier approximation for each concentration. In inset, ln ( I (Q)) versus Q 2 plot for the data (similar symbols) showing the linear behavior allowing the determination of the apparent radii of gyration. The solid lines correspond to the linear fi ts; b) Zimm-plot of the data (similar symbols). Points (crosses) are extrapolations to zero wave vectors. The solid lines represent the best fi ts as explained in the text.

Table 1. Results obtained from SLS data analysis on the apparent radius of gyration as a function of XG concentration.

c [g L −1 ]

Rg

[Å]

1 930 ± 200

3.9 960 ± 180

5 975 ± 200

7.8 1050 ± 160



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a positive value of 1.56 × 10 −3 : repulsion is thus observed in average between all scatterers (which comprises individual and associated chains). Finding such a positive value is in agreement with the local self-avoiding con-formation of the XG chains previously demonstrated by SANS. [ 14 ] This can be phrased as follows:

– As the probed objects are larger than individual chains, there are some attractions in the system. From its chemical structure (Scheme 1 ), it is known that XG chains can easily form aggregates via hydrogen bond-ing. [ 18 ] These links can also be due to hydrophobic inter-actions.

– However, the associated chains could repel each other at the local scale, due to the repulsion between strands of the chains they contain.

These opposite variations make the determination of A 2 diffi cult in such systems and its value should be viewed in a semi-quantitative rather than a fully quanti-tative way. Furthermore, note that the obtained value is also in good agreement with data obtained on partially hydrolyzed tamarind seeds XG. [ 17 ] We are then confi dent about the overall positive value of the second virial coef-fi cient in XG solutions in the dilute regime, which will strengthen the forthcoming DLS analysis.

The structure of the large scatterers—the associated chains—is most probably swollen, therefore excluding compact aggregates, since the apparent average molec-ular mass of the structure corresponds to only three XG chains, whereas the corresponding average radius of gyration is as large as 1000 Å, a value twice larger than R g of an isolated chain (compactness would imply a factor 2 3 between the masses). Moreover, in the case of dense aggregates, it is likely that the local conformation of chains would have deviated from the self-avoiding conformation at local scale. Although SLS results give us some information about the existence and the properties of large structures, these data do not lead to a complete and unambiguous determination of the large-scale struc-tures. Measurements of the viscosity as a function of the dilution can improve the description of the association.

2.1.2. Viscosity Measurements

Determination and analysis of the macroscopic viscosity as a function of the XG concentration is able to inform us about the presence and properties of large structures, that is, to estimate the contribution of interchain links and their reversibility (see Experimental Section for further details). We used the same set of samples as for the SLS measurements.

Figure 2 displays the specifi c viscosity obtained ηsp(c) (see Equation 4 in the Experimental Section) as a func-tion of [η]c . From the raw data measured, the intrinsic viscosity [ η ], which corresponds to the limit of ηsp/c when

XG concentration c comes from the fact that the deter-mination of the radius of gyration from the Guinier plot (inset of Figure 1 a) is progressively altered by the second virial coeffi cient contribution. Hence, the most accurate determination of R g is achieved at 1 g L −1 . What is striking is that its value (930 Å) is much larger than the one that can be calculated for isolated chains assuming self-avoiding conformation with the average mass previously found by SANS and SEC technique (≈500 Å). [ 14 ]

The apparent molecular mass of the objects and inter-actions between the objects were determined from a Zimm-plot representation of the data (Figure 1 b). Herein, the scattering constant K , as defi ned by Equation 14 (see Experimental Section), has been found equal to K = 1.84 cm 2 g −2 mol. The constant B , which represents a con-stant factor chosen to give a convenient spacing between the data points (see Experimental Section), has been fi xed at a value of 0.01. The extrapolations at zero wave vector lead to an average value of the intercept at Q2 = 0 of 7.2 × 10 −7 ± 0.1 × 10 −7 mol g −1 . This corresponds to an average apparent molecular mass of M w = 1 400 000 ± 8000 g mol −1 . This value is larger than the average one found using SEC-MALLs technique, which was around M w = 465 000 g mol −1 with a concentration injected of 0.5 g L −1 (i.e., only twice lower that the lower concentra-tion studied here). [ 14 ] Note that our SLS measurements are in situ measurements (done on the solution at rest) con-trary to SEC-MALLS. Indeed, in the latter experiment, all samples were fi ltered on a 0.2 μ m pore membrane before injection in order to retain large aggregates, if any, and where the high shear applied to the solution during its fl ow through the size-exclusion column may also break loose associations. In this concentration range (1–7.8 g L −1 ), we thus found an intrinsic aggregation of chains. It is noteworthy that the apparent mass increase ( M w / M w ≈ 3) corresponds to a mean value over all concentrations. In fact, the apparent molecular mass is slightly increasing with the concentration as shown by the increase of the apparent radii of gyration (Table 1 ). It is not possible from the data to determine the exact distribution of aggrega-tion number. In particular, there probably remain isolated chains that coexist with the associated chains. However, the low value of M W / M w associated with the values of R g is a clear evidence of associations involving a small number of chains and not large ones like microgels.

It appears in Figure 2 b that the extrapolation at zero wave vector increases for concentrations ranging from 1 to 5 g L −1 but decreases at the highest concentration, cor-responding to the initial stock solution at 7.8 g L −1 . This change of sign corresponds to the fact that a simple Virial expansion limited to the second Virial coeffi cient A 2 becomes invalid at large concentration. This is coherent with the fact that the stock solution is in the semi-dilute regime. The value of A 2 can be extracted for c ≤ 5 g L −1 to



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admit a few links per chains and have a structure not far from a linear chain.

In summary, in this section, the mesoscale structures have been evidenced and monitored by SLS and low-shear viscosity experiments as a function of the XG concentra-tion obtained from dilution of an initial stock dispersion. The main results show that the aggregates are swollen (few links per chain) with a conformation near the one of a linear chain, but these associations are present within the dispersions even in the dilute regime. However, at this point the mechanism of association between the XG chains is still unknown. In order to go further in the understanding of the mechanism of association, multi-angle DLS technique represents an ideal tool to obtain complementary and new information.

2.2. Mechanism of Associations

2.2.1. DLS Measurements

We performed multiangle DLS experiments on the same set of solutions to probe the characteristic dynamics of the samples, as well as their concentration dependence.

In a polymeric system like XG solutions, the analysis of the auto-correlation functions has to be carefully made. At a given angle of detection (i.e., at a given Q value), the dynamic structure factor S ( Q,t ) appears to have multiple dynamical modes (more than one characteristic decay time) at all concentrations, as shown in the typical example at θ = 90° in Figure 3 . At a given concentration, this multiple decay time feature is clearly angle dependent (Figure 4 ). The contribution of longer decay times is much more pro-nounced upon increasing XG concentration. This indi-cates that linking or jamming is present between the XG chains of the most concentrated solutions and that under

c → 0 , was found to be equal to [ηsc

]= 0.35 L g −1 , in very

good agreement with the value derived from SEC-MALLS. [ 14 ] The specifi c viscosity ηsp(c) of a linear polymer should follow the Huggins equation [ 19 ] (see also Experimental Sec-tion). The change of power law (from 1 in the dilute regime to 2 in the untangled semi-dilute regime) should occur, in case of a linear polymer, exactly at c∗ [η] = 1 . Remark-ably in Figure 2 , a change between a slope equal to 1 and a slope equal to 2 is visible with a threshold corresponding to ηsp (c) = 2 and to c [η] = 1.2 , very close to the expected values within the experimental errors.

Such behavior of viscosity agreeing with linear chains characteristics may seem in contradiction with the aggre-gates or associations evidenced by SLS measurements. One reason could be that the associated chains probed in the static measurements are involving a few chains only and do not differ much from a linear structure. This is supported by the actual value of the effective overlap concentration c∗ using c∗ [η] = 1 (Figure 2 ), which gives 3.4 g L −1 . A c* value corresponding to individual chains, assuming the values obtained previously by SEC-MALLS [ 14 ] of = 465 000 g mol −1 and Rg ≈ 500 Å, would be equal to c * = 6.2 g L −1 . Inversely, assuming that all the chains are belonging to the aggregates yields to an effective overlap concentration c∗

Agg ≈ c∗/N4/5Agg (NAgg is the mean aggre-

gation of the chains and the conformation of the chains within the aggregates is assumed similar to the one of an individual chains). This value c∗

Agg is found in remarkable agreement with the experimental one if we take NAgg between two and three chains. Therefore, viscosity results are in perfect agreement with the SLS results, both sug-gesting that the aggregates observed in the dispersions

Figure 2. Log–log representation of the specifi c viscosity deduced from the measured macroscopic viscosity as a function of the reduced concentration c [η] . The full lines indicate the slopes. The arrow displays the position where the slope is changing from 1 to 2 as expected.

Figure 3. Log–log representation of S ( Q , t ) versus t at a given angle of detection of θ = 90° for XG solutions at: c = 1.0 g L –1 (squares), c = 3.9 g L –1 (triangles), c = 5.0 g L –1 (circles), and c = 7.8 g L –1 (diamonds).



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to the variations expected in case of polymer concentra-tion fl uctuations, [ 20,21 ] large aggregates, [ 22 ] or polymer domains, [ 23 ] as well as internal modes of long polymer chains. [ 24–26 ] This rules out the CONTIN method here (which works assuming γ = 1) within the whole correla-tion–time range. Inversely, this reinforces the accuracy of using Equation 17 for a correct analysis.

Looking now at the decay time τ 0 , we see that for all concentrations it scales with Q with an unambiguous −2 power law (Figure 5 a). For dilute systems, this Q − 2 behavior corresponds to a diffusive motion. For polymeric systems in semi-dilute regime, such Q − 2 decay can also be observed. In this case, it is no longer associated with the diffusive motion of an isolated object but comes from an elastic mode of the transient network arising from concentration fl uctuations due to osmotic compressibility: this is a collec-tive or cooperative motion. Note that, remarkably, the vari-ation of τ 0 with XG concentration is much weaker than for τ 1 . Differences are however seen when the data are plotted as τ0

)−1 versus Q 2 , as shown in Figure 5 b. The data are in

successive dilutions the larger structures disaggregate. This already suggests weak associations between chains.

The multiple mode dependence shown by the plots of Figures 3 and 4 can in practice be modeled by the sum of two terms, one corresponding to a single time, and another corresponding to a stretched exponential func-tion (see Experimental Section, Equation 17 ). As shown in Figure 4 , a very satisfactory agreement is obtained for all angles and for all concentrations with such a model. The variations of the amplitudes A 0 and A1 as a function of Q are given in Supporting Information (Figure S2). The exponent of the stretched exponential relaxation func-tion, γ , which describes the width of the relaxation time distribution, is comprised between 0.5 and 0.7 in the whole Q range.

We can then pay attention to the variation of τ1 = 1/�1

as a function of Q (Figure 5 a): for all concentrations, τ 1 approximately follows a Q −3 scaling law. At the same time, the average value of γ can be taken equal to 2/3 (as evoked in the experimental section). It is very close

Figure 4. Log–log representation of S ( Q , t ) versus t for XG solutions at: a) c = 1.0 g L –1 , b) c = 3.9 g L –1 , c) c = 5.0 g L –1 , and d) c = 7.8 g L –1 . The angles of detection are displayed in all panels: full lines represent the best fi ts found for all angles of detection using the model as described by Equation 17 (called coupling model in all panels).



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Dapp is the signature of a cooperative motion (elastic mode of a network) that will be called DCoop .

Following this line of thought, we remind that in the dilute regime, DSelf can be expressed as a linear function of polymer concentration, like for colloidal suspensions: [ 27 ]

DSelf = D̄0Self (1 + kφ ) (1)

where φ is the volume fraction of the objects, D̄0Self is the

diffusion coeffi cient of individual chains, and k a para-meter that depends on intermolecular thermodynamic interactions and hydrodynamic interactions. [ 26 ]

Hence, the diffusion coeffi cient of individual chains D̄0Self can be deduced from the intercept of the linear

slope (Figure 6 ) at infi nite dilution, yielding D̄0Self =

0.85 × 10 −11 m 2 s −1 . The corresponding hydrodynamic radius R̄0H can be derived using the Stokes–Einstein relation:

D̄0Self = kT

6πηsR̄0H

(2)

where η s is the solvent viscosity at the experimental tem-perature T , leading to R̄0H ≈ 290 Å. If one considers that iso-lated chains are recovered at infi nite dilution, one obtains R̄0H/Rg = 0.58 by taking the value of R g of 500 Å derived from SEC-MALLS, [ 14 ] close to the theoretical prediction of 0.64 for chains in good solvent. [ 28,29 ]

The parameter k of Equation 1 is related to A 2 because it takes into account intermolecular thermodynamics. Its positive sign confi rms, like for A 2 the picture of chains repelling each other on average, as observed by SLS, despite the existence of some associations between chains.

The viscosity of the dispersions can be derived from the variation of the slow motion τ 1 with the XG concentration,

a very good agreement with linear laws τ0)−1 = DappQ

2 at all Q values for all concentrations. The variation of the deduced apparent coeffi cient of diffusion Dapp is plotted as a function of the concentration c in Figure 6 .

We observe that Dapp seems to follow a linear behavior as a function of c for the lowest concentrations, up to approximately c ≤ 5 g L −1 . The obtained value at 7.8 g L −1 no longer follows such a linear behavior; the crossover between the dilute and semi-dilute regime has been passed (the effective overlap concentration c* is 3.4 g L −1 as determined in the previous section). The data are com-patible with the fact that up to a concentration of 5 g L −1 (even if this concentration is just above c *), Dapp closely behaves as the diffusive motion of individual objects, and will be called DSelf , whereas above this concentration,

Figure 5. a) Log–log representation of decay times τ 0 and τ 1 as deduced from the fi ts of the dynamic structure factors versus Q for: c = 1.0 g L –1 (squares), c = 3.9 g L –1 (triangles), c = 5.0 g L –1 (cir-cles), and c = 7.8 g L –1 (diamonds); b) Inverse short decay time τ0

)−1 versus Q 2 for the same concentrations (similar symbols). The full lines represent the best fi ts found by a linear fi t given access to the apparent coeffi cient of diffusion Dapp .

Figure 6. Apparent coeffi cient of diffusion Dapp deduced from the analysis of τ 0 versus the XG concentration. A typical linear behavior is observed at low concentration. The dashed line cor-responds to the value deduced for D0

Self .



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as demonstrated by Esquenet and Buhler in the case of charged polysaccharides in the semi-dilute regime. [ 30 ] The existence of associations between the chains immersed in a solution leads to an apparent increase of τ 1 , what-ever the origin of such associations, because the number of links or of overlaps between chains is increasing with c . This leads to the local effective viscosity (or hydrody-namic interactions) tending to equal the macroscopic viscosity of the solution. By analogy with dilute solutions of long polymers, [ 25 ] the authors showed successfully that the effective viscosity deduced from τ 1 is similar to the macroscopic viscosity measured independently. In order to test the origin of τ 1 in our case, we apply such an approach. Therefore, a viscosity can be written as by Esquenet and Buhler [ 30 ] to be:

Figure 7. Viscosity deduced from the analysis of τ 1 versus Q 3 (light scattering viscosity) assuming a value for the factor A of 0.0083 (circles) and macroscopic viscosity (crosses) as a function of the XG concentration.

Figure 8. Schematic picture of the behavior of XG chains from tamarind seeds upon dilution. The structural features of the dispersions are represented for each concentra-tion regime. From top panels to down panels, the changes with time for each concentra-tion regime are displayed. In each panel: the reversible bonding links are pictured in red and a red chain is represented in order to show the movement with time.

ηAkT τ1Q3 (3)

where η is a viscosity (that we refer in the following as light scattering viscosity) and A a numerical constant that physically depends on the quality of the solvent. [ 31 ] The mean value of the viscosity normalized by the pre-factor A is obtained from plotting kT τ1Q

3 as a function of Q . The results are compared with the macroscopic vis-

cosity η (c) as a function of the XG concentration in Figure 7 . Within the experimental errors, a good agree-ment is obtained between the macroscopic and the light scattering viscosities taking a value for the factor A of 0.0083. This factor A is related to the quality of the solvent. Expected values can be obtained according to approaches based on either linear response or renor-malization group calculation. However, the exact value is complex to determine as many local parameters such as the rigidity of the chains can infl uence it, as noticed by Esquenet and Buhler. [ 30 ]

This good agreement with former analysis validates the appropriate choice of the analysis model (Experimental Section, Equation 17 . Furthermore, it confi rms that the time τ 1 is effectively due to internal dynamics of aggre-gates (i.e., to chain associations). This also indicates that the number or level of associations in the samples is only dependent of the XG concentration. The results also agree with the idea that associations are independent from the regime of the solution. This is different from what was obtained on Xanthan and Hyaluronan by Esquenet and Buhler. [ 30 ] who observed the slow Q−3 mode in semi-dilute regime only. The authors ascribed this slow mode to the deformation of the network occurring in the semi-dilute regime when fl uctuations of polymer concentration are relaxing cooperatively, yielding a local stress fl uctua-

tion that relaxes on a much longer time scale. In our case, mechanisms behind the presence of these long relaxation times appear different as they originate from associations between XG chains and have no reason to be linked with a given regime of dilution of the chains.

2.2.2. Describing the Associations

In combination with our previous study on the behavior at local scale by SANS, [ 14 ] the detailed light scattering investigations at large scale enables us to give a full description of the behavior of tamarind seed XG chains in water. Figure 8 presents a schematic picture of the XG chains as a function of dilution, as derived from the structural informa-tion obtained by SLS, viscosity, and DLS.



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The main structural and dynamical features of the large scale behavior are listed below: there are associa-tions of chains in the swollen regime (excluded volume) with a typical radius of gyration about twice that of an isolated chain, which involve a very limited number of chains (of the order of 3, on average) for the concentration range (1–7.8 g L −1 ).

– There are only a few links between chains in average because there are repulsions between the chains, since the overall A 2 is positive.

– The linked structure gives rise to a slow Q−3 mode and the total number of links strongly increases with the concentration.

– The associations are reversible : the slow mode progres-sively disappears upon dilution.

– It is likely that the associations would completely dis-appear at infi nite dilution. While it is diffi cult to per-form measurements at very low concentration due to the lack of scattering, a good support of this line of thought can be found in the fact that the value of the hydrodynamic radius R̄0H interpolated at infi nite dilu-tion from the D̄app in dilute regime (D

0

Self ) corresponds to the one of a single chain.

– The variation of D̄app as a function of c , as well as the macroscopic viscosity data, shows that the transition from dilute to semi-dilute regime occurs in the concen-tration range investigated. The transition between the two regimes does not affect the mechanism of associa-tion/dissociation of the chains.

The level of associations between chains is only dependent on the concentration. Therefore, for any given concentration, there is a probability for a chain residue to interact with another that only depends on the con-centration, whatever the regime. It is thus likely that the links breaks and re-forms like for a mass action law.

In order to answer the question of the permanence and the number of links, we can evaluate how these links may infl uence the overall size of aggregates. For that purpose, let us consider two limit cases: (case 1) we assume a very weak total number of associations with the chains associ-ating themselves only by linking their chain-ends, (case 2) we make the hypothesis of a large number of associations with the chains leading to highly branched aggregates.

In case 1, because XG chains are semifl exible chains in good solvent, the radius of gyration of one chain is given by: Rg = bN0.588 with b the persistence length and N the number of repetition units per chain. Assuming that the mean aggregation of the chains is noted N Agg as previously, the radius of gyration of one aggregate would be: Rg,Agg = b(NAggN)0.588 . Therefore, within our hypothesis, a simple relation between Rg,Agg and R g exists such as Rg,Agg /Rg = N0.588

Agg . Experimentally, we found by SLS, Rg,Agg ≈ 900 Å, and by SEC-MALLS, Rg ≈ 500 Å. This leads to Rg,Agg /Rg = 1.8 , while remarkably N0.588

Agg ≈ 1.9 for aggregates containing three chains (as expected by the

evaluation of the molecular mass of the objects and by the viscosity measurements).

In case 2, where the large average number of links per chain yields to highly branched aggregates, the relation between Rg,Agg and R g should tend to Rg,Agg /Rg = 1 , since Rg,Agg≈ Rg as obtained for star-like structure. [ 32 ]

These simple estimations of Rg,Agg /Rg better support the assumption of a few active links per chains than the for-mation of highly branched objects. This is comforted by the estimate given above of the effective c * from viscosity measurements: c * also agrees better with aggregates con-taining around three chains.

Because the viscosity deduced from the DLS slow modes fi ts very well the macroscopic viscosity at all investigated concentrations (Figure 7 ), it can be assumed that the bonding links are reversible. Indeed, without reversible links, the local viscosity deduced from DLS would have been different from the macroscopic viscosity since the samples will have been heterogeneous. Further-more, the chains in the stock solution are not entangled since the specifi c viscosity still varies as c [η]

)2 at 7.8 g L −1 (Figure 2 ). Therefore, the chains for all further dilutions are also unentangled meaning that the good solubiliza-tion of the XG chains has been achieved at every con-centration. Therefore, the in situ links that we have evi-denced are an inherent characteristic of the system.

3. Conclusion

The study on aqueous dispersions of neutral xyloglucan extracted from tamarind seed, combining viscosity, static and DLS measurements, reveals the mechanisms of asso-ciations between the chains in water. This leads to two conclusions: i) the dissolution protocol that we used is effi -cient, ii) however, there is inherent associations between the xyloglucan chains in water.

Indeed, the existence of swollen aggregates that con-tain a few chains and persist upon dilution (even in the dilute regime) is demonstrated. The level of association depends only upon the the XG concentration and is char-acterized by living associations. There are a small number of associations within the dilute solutions that likely fully disappear only in infi nitely dilute solutions, in accord-ance with the positive value of the second Virial coeffi -cient. The association process cannot be eliminated upon changing the solubilization procedure.

The inherent associations of the chains are of central importance for engineering purposes, to design novel XG-based composites or to optimize the use of XG chains in complex architectures. It can perturb or even hamper the interaction with other partners like cellulose micro fi brils for instance. As their number decays upon dilution, a practical consequence, when mixing XG dispersions with



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a binding component of XG chains (as cellulose nanocrys-tals, for example), is the use of as dilute as possible XG solutions (having the lowest level of aggregation) in order to favor the interaction between XG chains and host com-ponents rather than between the XG chains themselves.

We hope that our current approach, coupling dilution of the stock solution with a combination of viscosity meas-urements and SLS and multiangle DLS experiments, will stimulate investigations on other types of complex neu-tral polysaccharides chains coming from different biolog-ical species like galactomanans (whose solution behavior is also shown to be very complex). This methodology, which has been applied in pioneering works on charged polysaccharides hyaluronan and xanthan by Esquenet and Buhler, [ 30 ] allows to unravel the specifi c and unex-pected behavior of the neutral XG with the experimental evidence of inherent associations. Behind the obvious importance of understanding the complex behavior of XG chains for material design, the biological relevance of such a complex behavior has still to be elucidated.

4. Experimental Section

4.1. Materials and Solubilization Process

XG chains from tamarind seeds (XG) were obtained from Dai-nippon Pharmaceutical Co., Ltd. (Osaka, Japan), grade 3S. The dis-solution protocol was the same as used by Muller et al. [ 14 ] A mass of 6 g of the product was heated at 100 °C for 3 h in a 1000 mL round-bottom fl ask containing 0.01 M NaOH (with a few milli-grams of NaN 3 to prevent microbial spoilage) under constant agitation to achieve a good dispersion of the powder. The fl ask is then allowed to cool to room temperature and its content is centrifuged for 30 min at 20 000 g (here g = 9.8 m s −2 ). The super-natant was then dialyzed against deionized water until the con-ductivity reaches a value below 5 μ S cm −1 . Chloroform drops are added to the cell dialysis and kept during all the dialysis process to prevent microbial spoilage during the removing of all salts including NaN 3 . From our observations, microbial spoilage of XG in such solution is very quick. Hence, this point requires a careful attention. The dry mass of the fi nal solution has been deter-mined and found typically between below 1 wt%, depending on the dialysis conditions. The solution is fi nally stored in a fl ask with again a few milligrams of sodium azide.

In order to provide consistent information, we used the same XG initial solution as used in Ref. [ 14 ] . This initial stock solution had a concentration of 7.8 g L −1 (0.78 wt%). Direct dilution of this stock suspension with pure water was used to produce samples with nominal concentrations of 5.0 g L −1 (0.50 wt%), 3.9 g L −1 (0.39 wt%), and 1.0 g L −1 (0.1 wt%). All samples were fl uid-like from the rheological point of view, as checked by the viscosity measurements presented in the manuscript.

The initial stock solution is similar to the one investigated in our previous work. [ 14 ] We assume that the chains behave like semifl exible worm-like chains with self-avoiding conformation (Flory exponent of ν = 0.588, persistence length of l p = 80 Å and

a cross-section of 6.3 Å) and have an average molecular mass of M w ≈ 465 000 g mol −1 with a polydispersity index of 1.44. From these values, the overlap concentration c* , which corresponds to the concentration where the XG chains start to overlap each other without entanglements, can be found to equal to c * = 6.2 g L −1 in water. This means that the initial concentration studied (see above) is in the untangled semi-dilute regime, whereas the others should be in the dilute regime.

4.2. Methods

4.2.1. Viscosity Measurements

The experiments have been carried out on a Contraves low shear 30. The apparatus allows measuring the viscosity of samples having η ≤ 210−1 Pa s, by applying low shear rates in the optimal range of 0.02 ≤ γ̇ ≤ 100 s −1 . The experimental shear rate range was chosen to ensure measurements in the Newtonian plateau at all concentrations. The data were collected using a Couette geom-etry at room temperature of 20 °C. A value of ηs = 0.956 10−3 Pa s was measured for the solvent viscosity (water).

4.2.2. Viscosity Analysis

The polymer contribution to viscosity is given by the specifi c viscosity:

ηsp(c) ≡ η (c) − ηs

ηs (4)

where η s is the viscosity of the solvent and η (c) the measured viscosity at a given concentration. For uncharged polymers in good solvent (such as XG), in dilute solution, the concentration dependence to the viscosity is under-stood and described by the Huggins equation. [ 19 ] Hence, Equation 4 can be written as to be:

ηsp (c) = [η] c + kH [η] c)

+ · · · (5)

with [ η ] the intrinsic viscosity, which corresponds to the limit of

ηsp/ c when c → 0, and k H the Huggins coeffi cient. The change of slope of ηsp (c) as a function of [η]c from 1 in

the dilute regime to 2 in the untangled semi-dilute regime Equa-tion 5 corresponds to the threshold between both regimes at the overlap concentration c* . Krause et al. [ 33 ] showed that for linear polymer chains one should obtain ηsp (c∗) ∼= 1 and c∗[η] ∼= 1 . Therefore, by measuring the viscosity, the effective overlap con-centration can be obtained. A deviation from ηsp (c∗) ∼= 1 and

c∗[η] ∼= 1 , and also the change of slopes from 1 and 2, would indicate deviation from linear chains. Hence, this will show the association of the chains.

4.2.3. SLS and DLS

The experiments have been carried out on an ALV/CGS-3 com-pact goniometer system equipped with an ALV/LSE-5003 light scattering electronics and multiple τ digital correlator and a JDS Uniphase helium-neon laser with an output power of 100 mW, which supplies vertically polarized light with a wavelength of 6328 Å. The data were collected by monitoring the scattered light



11


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intensity at 25 °C. The temperature was controlled with an accuracy of 0.1 °C using a Julabo F25 refrigerated bath circulator. The scat-tering angles investigated were comprised between 70° and 140° by steps of 10°. This gave an accessible Q range from 1.51 × 10 −3 to 2.48 10 −3 Å −1 . Here, Q is the scattering wave vector defi ned by:

Q =4πηs

λsin

θ

2 (6)

where η s is the refractive index of the solvent, θ the scattering angle, and λ the wavelength of light.

In the SLS experiments, the excess of scattering intensity was measured with respect to the solvent. The absolute scattering intensities were deduced by using a toluene sample reference for which the Rayleigh ratio is well known (i.e., IT

RR = 1.3657 × 10−5 cm −1 at 6328 Å). The scattered intensities in cm −1 (absolute scale) are then expressed by:

I (Q) = ITRR

RS (θ ) − RW (θ )RT (θ )

sinθ

(7)

where R S ( θ ), R W ( θ ), and R T ( θ ) are respectively the excess of scat-tering intensity (scattered intensity normalized by the incoming intensity) of the sample S , of the water W , and of the standard toluene sample T . The term sin θ is a correction term that takes into account the variation of the scattering volume at the dif-ferent angles.

In the DLS experiments, the normalized intensity autocorrela-tion function g 2 ( Q , t ) of the scattered light has been measured:

g2 (Q, t ) =I∗ (Q, 0) I (Q, t )

I (Q, 0) 2

(8)

This latter function is used to calculate the corresponding nor-malized time correlation function of the scattered electric fi eld or, equivalently, the autocorrelation function of the concentra-tion fl uctuations:

g1 (Q, t ) =δc∗ (Q, 0) δc (Q, t )

δc (Q, 0) 2

(9)

The latter g 1 ( Q , t ) can be identifi ed with the dynamic structure factor S ( Q , t ) which, for a Gaussian signal, is related to the inten-sity autocorrelation function g 2 ( Q , t ) by the Siegert relation:

g2(Q, t ) = B + A∣∣g1 (Q, t )

∣∣2

(10)

where A is the coherence factor of the experiments and B the measured baseline. In practice g 1 ( Q , t ) is obtained after baseline subtraction and normalization such as:

g1 (Q, t ) = S (Q, t ) =√g2 (Q, t ) − 1

C (11)

where C is the normalization parameter depending on the exper-imental geometry and obtained by the value of the intercept at t = 0 of g 2 ( Q,t ).

4.2.4. SLS Analysis

In dilute regime of scatterers (e.g., single polymer chains but also potentially associations of a few polymers), the apparent radius

of gyration is deduced from the scattered intensity using the Guinier approximation:

I(Q, c) ∝ I(0, c)e− Q2R2g / 3

(12)

where R g is the radius of gyration of the objects and c their con-centration. Typically, for linear macromolecular chains in good solvent, this is valid up to QR g ≤ 3. At higher values of Q , the scat-tered intensity should deviate from Equation 12 and exhibits a scaling law such as Q− 1/ν where ν is the Flory exponent. We previ-ously demonstrated that XG chains from tamarind seeds behave as chains in good solvent in aqueous media ( ν = 0.588). [ 14 ] It is worth noting that such an analysis is independent of the units in which both I ( Q , c ) and c are expressed.

In this Guinier regime, for more concentrated samples, a Virial expression for the osmotic pressure can be used in order to deduce the molecular mass for polymer chains, Mw, called the Zimm approximation as:

Kc

I (Q, c)=

1

MW

1 +Q2R2

g

3+ 2A2c

(13)

where A 2 is the second Virial coeffi cient describing the polymer–polymer interactions, and K the scattering constant written here following Equation 7 as:

K = 4πn2W

dn

dc

2 1

NAλ4

nT

nW

2

(14)

with n T and n W the refractive index of toluene and water, respec-tively, N A the Avogadro number, and dn/ dc the refractive index increment of the sample. For XG chains, the value adopted is equal to 0.142 as given in literature. [ 17 ] In practice, the parameters of Equation 14 are simultaneously extrapolated at both zero angle and zero concentration using a graphical representation called Zimm-plot. Such representation is achieved by plotting Kc/ I(Q, c) as a function of Q2 + BC with B a constant factor chosen to give a convenient spacing between the data points on the graph. The value of 1/Mw is obtained from the intercept of the Q 2 = 0 curve, and A 2 from the slope. The inter-cept of the c = 0 curve gives again 1/Mw, and the initial slope is proportional to R g .

4.2.5. DLS Analysis

In a solution of monodisperse polymeric chains in dilute regime, S ( Q,t ) decays exponentially. [ 34 ] However, either the polydisper-sity or the possibility to have more than one diffusive mode in the system can lead to a broad distribution of exponentials in S ( Q,t ). [ 35,36 ] In that case, it can be described as:

S(Q, t ) =∫

A τ i

)e(− t/τi)dτ i

(15)

where A ( τ i ) denotes the relative contribution of a given mode with the characteristic decay time τ i to the total correlation func-tion. The different contributions A ( τ i ) are usually determined by a Laplace inversion technique known as the CONTIN method. [ 37 ] Proceeding further in this approach, each decay rate �i = 1

/τi

)

is often related to a diffusion coeffi cient D i as:



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[8] D. R. Picout , S. B. Ross-Murphy , K. Jumel , S. E. Harding , Bio-macromolecules 2002 , 3 , 761 .

[9] J. P. Vincken , A. Dekeizer , G. Beldman , A. G. J. Voragen , Plant Physiol. 1995 , 108 , 1579 .

[10] S. C. Fry , W. S. York , P. Albersheim , A. Darvill , T. Hayashi , J. P. Joseleau , Y. Kato , E. P. Lorences , G. A. Maclachlan , M. Mcneil , A. J. Mort , J. S. G. Reid , H. U. Seitz , R. R. Selvendran , A. G. J. Voragen , A. R. White , Physiol. Plant. 1993 , 89 , 1 .

[11] A. Faik , C. Chileshe , J. Sterling , G. Maclachlan , Plant Physiol. 1997 , 114 , 245 .

[12] J. S. G Reid , M. E. Edwards , Food Polysaccharides and their Applications , Marcel Dekker , New York 1995 , p 155 .

[13] Q. Wang , P. R. Ellis , S. B. Ross-Murphy , J. S. G Reid , Carbohydr. Res. 1996 , 284 , 229 .

[14] F. Muller , S. Manet , B. Jean , G. Chambat , F. Boué , L. Heux , F. Cousin , Biomacromolecules 2011 , 2 , 3330 .

[15] A. a K. Brun-Graeppi Andriola Silva , C. Richard , M. Bessodes , D. Scherman , T. Narita , G. Ducouret , O-W. Merten , Carbohydr. Polym. 2010 , 80 ( 2 ), 555 .

[16] P. Lang , K. Kajiwara , W. Burchard , Macromolecules 1993 , 26 , 3992 .

[17] D. R. Picout , S. B. Ross-Murphy , N. Errington , S. E. Harding , Biomacromolecules 2003 , 4 , 799 .

[18] P. Lang , W. Burchard , Makromol. Chem. 1993 , 194 , 3157 . [19] H. Morawetz , Macromolecules in Solution , 2nd ed. , Wiley,

New York 1975 . [20] E. Buhler , J. P. Munch , S. J. Candau , J. Phys. II 1995 , 5 , 765 . [21] T. Csiba , G. Jannink , D. Durand , R. Papoular , L. Auvray ,

F. Boué , J. P. Cotton , R. Borsali , J. Phys. II 1991 , 1 , 381 . [22] a) J. J. Tanahatoe , M. E. Kuil , J. Phys. Chem. B 1997 , 101 , 9233 ;

b) J. J. Tanahatoe , M. E. Kuil , J. Phys. Chem. B 1997 , 101 , 10839 .

[23] B. D. Ermi , E. J. Amis , Macromolecules 1998 , 31 , 7378 . [24] M. Adam , M. Delsanti , J. Phys. Lett. 1977 , 38 , L - 271 . [25] E. Dubois-Violette , P. G. de Gennes , Physics 1967 , 3 , 181 . [26] E. Raspaud , D. Lairez , M. Adam , J. P. Carton , Macromolecules

1994 , 27 , 2956 . [27] See for instance, P. N. Pusey , in Colloidal Suspensions, Les

Houches Session L1: Liquids, Freezing, and the Glass Transi-tion , (Eds: J. P. Hansen , D. Levesque , J. Zinn-Justin ), North Holland , Amsterdam, The Netherlands 1991 , Ch. 10, 763 .

[28] A. Niu , D.-J. Liaw , H.-C. Sang , C. Wu , Macromolecules 2000 , 33 , 3492 .

[29] T. Nie , Y. Zhao , Z. Xie , C. Wu , Macromolecules 2003 , 36 , 8825 .

[30] C. Esquenet , E. Buhler , Macromolecules 2002 , 35 , 3708 . [31] A. Z. Akcasu , M. Benmouna , C. C. Han , Polymer 1980 , 21 , 866 . [32] F. Muller , P. Guenoun , M. Delsanti , B. Demé , L. Auvray ,

J. Yang , J. W. Mays , Eur. Phys. J. E 2004 , 15 , 465 . [33] W. E. Krause , E. G. Bellomo , R. H. Colby , Biomacromolecules

2001 , 2 , 65 . [34] B. J. Berne , R. Pecora , Dynamic Light Scattering with Applica-

tion to Chemistry, Biology, and Physics , Wiley Interscience , New York 1976 .

[35] B. Chu , Laser Light Scattering. Basic Principles and Practice , 2nd ed., Academic Press , Boston, MA, USA 1991 .

[36] W. Brown , T. Nicolai , in Dynamic Light Scattering , (Ed: W. Brown ), Clarendon Press, Oxford, UK 1993, Ch. 6 , p 166 .

[37] a) S. W. Provencher , J. Hendrix , L. De Maeyer , N. Paulussen , J. Chem. Phys. 1978 , 69 , 4273 ; b) S. W. Provencher , Comp. Phys. Commun. 1982 , 27 , 229 ; c) S. W. Provencher , Comp. Phys. Commun. 1982 , 27 , 213 .

�i =1

τi= DiQ

2

(16)

However, the characteristic decay times exhibited by a poly-meric chain do not necessarily obey the Q −2 dependence of Equation 16 . The latter assertion is found in particular in the semi-dilute regime where the polymer chains can display repta-tion, be associated together in networks showing branched struc-ture dynamics, or in associations that induce a heterogeneous dynamics. When the macromolecules are made of different statistical chemical groups that may interact with each other, for example, by hydrophobic association in aqueous solvent or H-bonding, intrachain relaxation modes can appear even in dilute regime.

In such cases, S ( Q,t ) is often described as the sum of two modes, an exponential term and a stretched exponential term, so that:

S(Q, t ) = A0e−�0t + A1e

−(�1t)γ (17)

where A 0 and A 1 are the amplitudes of the relaxation modes with A 0 + A 1 = 1, Γ 0 and Γ 1 are the inverse characteristic times of decays, and γ is the stretching exponent that describes the width of the distribution of relaxation times. If γ = 1, we return to 16 . For other values of γ , a particularly well known case is γ = 2/3, together with τ1 ∝ Q−3 , encountered for either polymer concentration fl uctuations, [ 20,21 ] or large associations, [ 22 ] or polymer domains, [ 23 ] as well as internal modes of long polymer chains. [ 24–26 ]

Acknowledgements : This work is funded by the French National Project ANR-08-NANO-P235–36. We thank Guylaine Ducouret (SIMM/PPMD, CNRS-ESPCI-UPMC, Paris, France) for helping us with the use of the low shear 30 viscometer.

Received: March 21, 2013 ; Revised: June 10, 2013; Published online: ; DOI: 10.1002/macp.201300265

Keywords: associations ; biopolymers ; dynamics ; structure ; viscosity

[1] S. C. Fry , The Growing Plant Cell Wall. Chemical and Meta-bolic Analysis , Longman Scientifi c & Technical Editor , Harlow, UK 1988 .

[2] N. C. Carpita , D. M. Gibeaut , Plant J. 1993 , 3 , 1 . [3] H. T. Winter , C. Cerclier , N. Delorme , H. Bizot , B. Quemener ,

B. Cathala , Biomacromolecules 2010 , 11 , 3144 . [4] B. Jean , L. Heux , F. Dubreuil , G. Chambat , F. Cousin , Langmuir

2009 , 3920 . [5] C. Cerclier , F. Cousin , H. Bizot , C. Moreau , B. Cathala , Lang-

muir 2010 , 26 , 17248 . [6] C. Cerclier , A. Lack-Guyomard , C. Moreau , F. Cousin , N. Beury ,

E. Bonnin , B. Jean , B. Cathala , Adv. Mater. 2011 , 23 , 3791 . [7] M. J. Gidley , P. J. Lillford , D. W. Rowlands , P. Lang , M. Dentini ,

V. Crescenzi , M. Edwards , C. Fanutti , J. S. G. Reid , Carbohydr. Res. 1991 , 214 , 299 .



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