investigation of the structure of cellulose in licl/dmac solution and its gelation behavior by...

8
Investigation of the Structure of Cellulose in LiCl/DMAc Solution and Its Gelation Behavior by Small-Angle X-Ray Scattering Measurements Daisuke Ishii, 1 Daisuke Tatsumi,* 1 Takayoshi Matsumoto, 1 Kazuki Murata, 2 Hisao Hayashi, 2 Hiroshi Yoshitani 3 1 Division of Forest and Biomaterials Science, Graduate School of Agriculture, Kyoto University, Kitashirakawa Oiwake- cho, Sakyo-ku, Kyoto 606-8502, Japan E-mail: [email protected] 2 Faculty of Science and Technology, Ryukoku University, 1-5 Yokotani, Oe-cho, Seta, Otsu 520-2194, Japan 3 Minase Research Laboratories, Sekisui Chemical Co. Ltd., 2-1 Hyakuyama Shimamoto-cho, Mishima-gun, Osaka 618-8589, Japan Received: December 2, 2005; Revised: February 14, 2006; Accepted: February 14, 2006; DOI: 10.1002/mabi.200500231 Keywords: cellulose; gels; LiCl/DMAc; molecular properties; small-angle X-ray scattering (SAXS); solutions Introduction Lithium chloride/ N,N-dimethylacetamide (LiCl/DMAc) is one of the most efficient solvent system for cellulose. [1–3] It dissolves cellulose with high molecular weight (>10 6 ) molecularly at the ambient temperature without noticeable degradation. [4] In order to develop cellulose materials to the ones having novel functionality and superior performance, some attempts concerning this solvent have been made. For example, it has been reported that the slow coagulation of cellulose from the LiCl/DMAc solution causes the formation of characteristic supramolecular structure or the exhibition of the optical anisotropy. [5,6] However, the mechanisms of these phenomena have not been clarified yet. The clarification of such mechanisms requires the understanding of the molecular properties and the dissolved state of cellulose in LiCl/DMAc solution. The molecular properties of cellulose in LiCl/ DMAc solution have been extensively investigated by various research groups. [2,4,7–12] These studies were performed using static and/or dynamic light scattering, [2,4,7–10] rheologi- cal, [4,7–9] size-exclusion liquid chromatography, [10,11] and NMR [12] measurements. These methods give us the information on the molecular weight [2,4,7–11] and its distri- bution, [10,11] the dimension of cellulose molecular chain, [2,4,7–11] and the interaction between cellulose and solvent molecules. [12] However, the relation between the dissolved state and the structure formation mechanism of cellulose molecules has not been investigated yet. Summary: Cellulose gels were prepared from cellulose in lithium chloride/N,N-dimethylacetamide (LiCl/DMAc) sol- ution. When the cellulose concentration in the solution is above the one at which cellulose molecules overlap, cellulose gels were formed. While the gel prepared by the addition of water was turbid, the one prepared by the ion exchange was colorless, transparent, and optically aniso- tropic. In order to explain this gelation behavior of cellulose, small-angle X-ray scattering (SAXS) measurements of the cellulose solutions and the gels were performed. The SAXS profiles of the cellulose solutions and the gels suggested that the large-scale fluctuation of the molecular chain density in the solution can be the origin of the molecular aggregates formed in the gel. Furthermore, the differences in the structure of the gels at the macroscopic and the molecular level were discussed in terms of the phase separation and the molecular association. Polarized optical photograph of the cellulose gels. Macromol. Biosci. 2006, 6, 293–300 ß 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Full Paper DOI: 10.1002/mabi.200500231 293

Upload: daisuke-ishii

Post on 15-Jun-2016

213 views

Category:

Documents


1 download

TRANSCRIPT

Investigation of the Structure of Cellulose in

LiCl/DMAc Solution and Its Gelation Behavior by

Small-Angle X-Ray Scattering Measurements

Daisuke Ishii,1 Daisuke Tatsumi,*1 Takayoshi Matsumoto,1 Kazuki Murata,2 Hisao Hayashi,2 Hiroshi Yoshitani3

1Division of Forest and Biomaterials Science, Graduate School of Agriculture, Kyoto University,Kitashirakawa Oiwake- cho, Sakyo-ku, Kyoto 606-8502, JapanE-mail: [email protected]

2Faculty of Science and Technology, Ryukoku University, 1-5 Yokotani, Oe-cho, Seta, Otsu 520-2194, Japan3Minase Research Laboratories, Sekisui Chemical Co. Ltd., 2-1 Hyakuyama Shimamoto-cho,Mishima-gun, Osaka 618-8589, Japan

Received: December 2, 2005; Revised: February 14, 2006; Accepted: February 14, 2006; DOI: 10.1002/mabi.200500231

Keywords: cellulose; gels; LiCl/DMAc; molecular properties; small-angle X-ray scattering (SAXS); solutions

Introduction

Lithium chloride/N,N-dimethylacetamide (LiCl/DMAc) is

one of the most efficient solvent system for cellulose.[1–3] It

dissolves cellulose with high molecular weight (>106)

molecularly at the ambient temperature without noticeable

degradation.[4] In order to develop cellulose materials to the

ones having novel functionality and superior performance,

some attempts concerning this solvent have been made. For

example, it has been reported that the slow coagulation of

cellulose from the LiCl/DMAc solution causes the formation

of characteristic supramolecular structure or the exhibition of

the optical anisotropy.[5,6] However, the mechanisms of these

phenomena have not been clarified yet. The clarification of

suchmechanisms requires the understanding of themolecular

properties and the dissolved state of cellulose in LiCl/DMAc

solution. The molecular properties of cellulose in LiCl/

DMAc solutionhave beenextensively investigated byvarious

research groups.[2,4,7–12] These studies were performed using

static and/or dynamic light scattering,[2,4,7–10] rheologi-

cal,[4,7–9] size-exclusion liquid chromatography,[10,11]

and NMR[12] measurements. These methods give us the

information on the molecular weight[2,4,7–11] and its distri-

bution,[10,11] the dimension of cellulose molecular

chain,[2,4,7–11] and the interaction between cellulose and

solvent molecules.[12] However, the relation between the

dissolved state and the structure formation mechanism

of cellulose molecules has not been investigated yet.

Summary: Cellulose gels were prepared from cellulose inlithium chloride/N,N-dimethylacetamide (LiCl/DMAc) sol-ution. When the cellulose concentration in the solution isabove the one at which cellulose molecules overlap,cellulose gels were formed. While the gel prepared by theaddition of water was turbid, the one prepared by the ionexchange was colorless, transparent, and optically aniso-tropic. In order to explain this gelation behavior of cellulose,small-angle X-ray scattering (SAXS) measurements of thecellulose solutions and the gels were performed. The SAXSprofiles of the cellulose solutions and the gels suggested thatthe large-scale fluctuation of the molecular chain density inthe solution can be the origin of the molecular aggregatesformed in the gel. Furthermore, the differences in thestructure of the gels at the macroscopic and the molecularlevel were discussed in terms of the phase separation and themolecular association. Polarized optical photograph of the cellulose gels.

Macromol. Biosci. 2006, 6, 293–300 � 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Full Paper DOI: 10.1002/mabi.200500231 293

Small-angle X-ray scattering (SAXS) measurements are

expected to give the information on the structure of cellulose

in both themolecularly dispersed and aggregated states.[13] In

this paper, the structure of cellulose in LiCl/DMAc solution

and the gels prepared from the solution are investigated by

SAXSmeasurements. Furthermore, on the basis of the results

of the SAXS measurements, the relation between the

structure of cellulose in dissolved and gelled states is

discussed.

Experimental Part

Materials

Cellulose solution in LiCl/DMAc was prepared following theprocedure already described elsewhere.[4] Softwood dissol-ving pulp (Nippon Paper Co. Ltd., Mw ¼ 3.8� 105)[6] wasemployed for the preparation of the solution. The solutionswith the cellulose concentration of 1, 3, 5, and 8 wt.-% weresupplied for the SAXS measurements. On the other hand, thesolutions with the cellulose concentration of less than 1 wt.-%were used for the preparation of cellulose gels.

Two different methods for the coagulation of cellulose wereemployed.One is the deionization of the cellulose/LiCl/DMAcsolution with ion exchange resins. In this method, the cellulosesolutions were poured onto the pretreated ion exchange resins(Biorad, AG-501 X8) and allowed to stand. The pretreatmentof the resins were performed by the overnight sorption indistilled water or 1 M NH4Cl (aq) and by the subsequentexchange of water or NH4Cl (aq) solution to DMAc. Gelationof the system was examined by inversing the sample tube.Hereafter in this paper, the cellulose gel prepared by thismethod is referred to as ‘‘deionized gel’’ for simplicity. Theother method employed was the dropping of distilled water tothe cellulose/LiCl/DMAc solution (‘‘water-coagulated gel’’).These cellulose gels were supplied for the experiments in theas-prepared state.

SAXS Measurements

SAXS measurements were performed using Rigaku RINT2500 NANO-VIEWER at Ryukoku University. A 2.7-kW(45 kV, 60 mA) CuKa irradiation was focused and mono-chromatized (l¼ 0.1542 nm) simultaneously using OSMICConfocal MaxFlux1 multilayer mirror. Then the incidentbeam was collimated by two pinholes (0.5 and 0.3 mm f) andone guard slit. Samples were packed within laboratory-madestainless cell with 51.4 mm-thick Kapton windows and placedon an open-air holder.[14] Optical paths except around thesample holder were evacuated in order to avoid overlapping ofair scattering. The distance between the sample cell and thedetector was set to 0.89 m. The q space determined by the first-and second-orderBraggpeaks of lead stearate (d¼ 5.1 and2.55nm) ranged from 0.16 to 2.1 nm�1, corresponding to the real-space length scales from 3.0 to 40 nm. The intensity of thescattered X-ray was detected using one-dimensional position-sensitive proportional counter equipped with 2 048 channelswith the distances between channels of 35 mm (Dq¼ 0.0016

nm�1). Although the detector aperture had a height of ca. 1 cm,the effect of smearing on the scattering profile was notrecognized. Samples were irradiated for 250 000 s, accumulat-ing 500 slices of 500-s data acquisition. Fluctuation of theirradiated beam intensity during the acquisition was correctedusing the scattered intensity from HDPE measured before andafter the measurements of cellulose samples. Acquired intensitydata were corrected for the transmittance, and then thecontribution from the solvent was subtracted. As for the gelsamples, ionic strength in the liquid phase is supposed to bedifferent from that in the solution due to the ion exchange.Considering this effect, the liquid soaked out of the gels wascollected, and the scattered intensity from the liquidwasused forthe correction of scattered intensity from the gels.

Results

Aggregation Behavior of Cellulose

It is recognized that the dissolution state of cellulose in

LiCl/DMAc is affected by both the cellulose concentration

and ionic strength in the solution.[15] This in turn suggests

that the aggregation behavior of cellulose from the dis-

solved state is also affected by these factors. Therefore, we

attempted to control the aggregation behavior of cellulose

from the LiCl/DMAc solution by varying the polymer

concentration in the solution, c. When c is lower than

0.2 wt.-%, precipitation of cellulose occurred. On the other

hand, the gelation of cellulose was observed when c is

higher than 0.3 wt.-%.

The gelation behavior of cellulose was also affected by

the gelationmethods. The addition of water to the cellulose/

LiCl/DMAc solution instantly generated a cellulose gel. On

the other hand, the gelation of cellulose by the addition of

ion exchange resins proceeded quite slowly; typically it

took more than several weeks for the complete gelation.

Appearances of the gels were also different: While the

water-coagulated gel contained the slight turbidity, the

deionized gel was colorless and transparent.

The above-mentioned structural features were also

recognized by the polarized optical microscopy. Figure 1

shows the polarized optical photographs of the cellulose

gels. In the water-coagulated gel, a fibrous texture was

observed [Figure 1(a)]. No such texturewas observed in the

deionized gel. Therefore, it is likely that this fibrous

morphology makes the appearance of the water-coagulated

gel turbid. However, as shown in Figure 1(c), the bire-

fringence was also observed in the deionized gel. Further-

more, as shown by Figure 1(b) and (c), this optically

anisotropic region evolves along with the gelation. These

results show that the gelation of cellulose accompanies the

formation of the oriented structure at any spatial scale.

SAXS Profiles of Cellulose Solutions and Gels

In order to investigate the relation of the gelation behavior

and the obtained gel structure of cellulose to the structure of

294 D. Ishii, D. Tatsumi, T. Matsumoto, K. Murata, H. Hayashi, H. Yoshitani

Macromol. Biosci. 2006, 6, 293–300 www.mbs-journal.de � 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

cellulose dissolved in LiCl/DMAc, SAXS measurements

were performed.

First, we investigated the structure of cellulose in the

solution with various cellulose concentrations. Figure 2

shows the SAXS profiles of 1 wt.-% cellulose in LiCl/

DMAc solution. As shown in more detail in the later

section, the profile was analyzed by fitting two Lorenzian

[Ornstein-Zernike (OZ)] functions.

SAXS measurements were also performed for the

cellulose gels to investigate the aggregation state of

cellulose molecular chains. Figure 3 shows the SAXS

profiles (logI(q) vs. logq) of the cellulose gels prepared

from 1 wt.-% cellulose/LiCl/DMAc solution. In these

profiles, plots at q> 1.34 nm�1 are linearly approximated.

This shows that the system in these length scales has a

complex structure that is characterized by the fractal

dimension. Namely,

IðqÞ � q�Dm ; 1 � Dm � 3 formass fractals ð1Þ

and

IðqÞ � q�ð6�DsÞ; 1 � Ds < 3 for surface fractals:½16�

ð2Þ

Dm and Ds in Equation (1) and (2) represent the fractal

dimensions of the mass and the surface, respectively. The

fractal dimensions estimated from the profiles are shown in

Figure3. In the large-q region,while thedeionized gel has the

mass fractal dimension, the water-coagulated one has a

surface fractal dimension. This shows that the water-

coagulated gel has a more densely packed structure than

the deionized one. In addition to the large-q region, another

fractal regime is found in the small-q region in the profile of

water-coagulated gel. In contrast, the deionized one does not

have such a fractal dimension in the small-q region.

Therefore, it is supposed that thewater-coagulated gel forms

larger aggregation structure than the deionized one.[17]

Differences in the structure of the gels are found more

significantly in the Kratky plot (Figure 4, q2I(q) vs. q). No

significant peaks are found in the Kratky plot of the

deionized cellulose gel, as in that of the dissolved cellulose.

On the other hand, that of the water-coagulated cellulose

shows a peak at q¼ 0.285 nm�1. These profiles suggest that

the structure of cellulose in the LiCl/DMAc solution is

preserved in the deionized gel, whereas that in the water-

coagulated gel is considerably different from that in the

Figure 1. Polarized optical photographs of the cellulose gels:(a) the water-coagulated gel; (b) the deionzed gel at the startup ofthe gelation; (c) the deionized gel after 5 d passed since the startupof the gelation. The particles at the bottom of the sample tubeobserved in (b) and (c) are the ion exchange resins. Anisotropicphase evolves at the surface of the resins.

Figure 2. SAXS profile of 1 wt.-% cellulose in LiCl/DMAcsolution.

Investigation of the Structure of Cellulose in LiCl/DMAc Solution and Its Gelation Behavior . . . 295

Macromol. Biosci. 2006, 6, 293–300 www.mbs-journal.de � 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

LiCl/DMAc solution. Details on the structure of these gels

are discussed in the following section (‘‘Structure of the

Cellulose Gels’’).

Discussion

Relation Between the Macroscopic AggregationBehavior and the Molecular Properties of Cellulose

Concentration dependence of the aggregation behavior of

cellulose can bewell explained by themolecular property of

cellulose in LiCl/DMAc. It has been already shown that

the cellulose molecules in LiCl/DMAc overlap when the

cellulose concentration is above ca. 0.3 wt.-%.[4] When the

polymer coils overlap, they have the ability to associate

each other and form a gel structure. On the other hand, when

the polymer coils are dispersed without overlapping, only

the intramolecular aggregation of molecular chains occurs

and then the collapsed molecules precipitate. Therefore, it

can be said that the overlapping of the cellulose molecular

chains is necessary for the gelation of cellulose.As shown in

the following discussion, the heterogeneity in the solution

made by the overlapping of cellulose molecules is

preserved in the cellulose gels.

Structure of Cellulose in LiCl/DMAc Solutions

Information on the structure of cellulose in the dissolved

state was obtainted from the SAXS profiles in the following

way. It is generally recognized that the spatial scale of

heterogeneity in polymer solution is described by the OZ

equation:[18]

IðqÞ ¼ Ið0Þ=ð1þ q2x2Þ ð3Þ

where x is the correlation length and I(0) is the scattered

intensity at q¼ 0. From Equation (3) we have

IðqÞ�1 ¼ 1=Ið0Þ�1 þ ½x2=Ið0Þ�q2 ð4Þ

Equation (4) shows that the plot of I(q)�1 against q2

(Zimm plot) gives the value of x. Figure 5 shows the Zimm

plot of the 1 wt.-% cellulose solution. Plots in the q range

above 1 nm�1 are fitted by OZ equation. Subtraction of OZ

Figure 3. SAXS profile of cellulose gels: (a) deionized gel;(b) water-coagulated gel. Solid curves on the plots represent thefitted curves given by Equation (5) in (a) and Equation (6) in(b) (tentative value of Rg¼ 25.8 nm is assigned) in the text. Thedetails on the fitting methods are described in the Discussionsection.

Figure 4. Kratky plots of cellulose in LiCl/DMAc solution andgels.

296 D. Ishii, D. Tatsumi, T. Matsumoto, K. Murata, H. Hayashi, H. Yoshitani

Macromol. Biosci. 2006, 6, 293–300 www.mbs-journal.de � 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

component in the large-q region from I(q) gives the residual

component. The excess scattering in the small-q region

shows that the large-scale concentration fluctuation of

cellulose exists in the LiCl/DMAc solution. This compo-

nent was also fitted by another OZ equation and the large-

scale correlation length, X, was calculated.a The fitting

curves are also shown in Figure 2: The broken and the

dotted curves represent the OZ equations for x and X,respectively. The calculated values of the correlation

lengths for the cellulose/LiCl/DMAc solutions with the

various cellulose concentrations are shown in Table 1.

Figure 6 shows the double logarithmic plot ofX and xversusthe cellulose concentration, c. The relation between the

correlation lengths and c is expressed by a power law with

the power of �0.5. The scaling nature of the correlation

lengths[18] shows that the homogeneous network of

cellulose molecular chains expands in the LiCl/DMAc

solution, although the large-scale fluctuation of the chain

density exists. The length x reflects the distance between

the nearest neighboring chains in the network. The value of

the scaling exponent differs from the ones obtained for the

typical linear flexible polymers in good or y solvents (in

good solvent,�0.75 to�0.77;[18,24] in y solvent,�1[18,25])

but agrees well with the one predicted by Schaefer for

semiflexible polymer.[26] As shown elsewhere, the same

scaling relationship with a correlation length comparable to

X is found by the static light scattering measurements of

semidilute cellulose/LiCl/DMAc solutions, and the length

scale is related to the dynamic aspects, i.e., the entangle-

ment of cellulose molecules in LiCl/DMAc.[27]

Structure of the Cellulose Gels

The cellulose gels showed the differences in their structures

both at the macroscopic and the molecular levels. There-

fore, the structures at both levels are independently

discussed in the following section.

Table 1. Correlation lengths of cellulose in LiCl/DMAcsolutions with the different cellulose concentration.

c X x

102g � g�1 nm nm

1 11.9 1.523 7.37 0.9875 5.51 0.7568 5.66 0.627

a In order to estimate the scale of the homogeneity that gives theexcess scattering, various types of functions have beenemployed.[19] The application of the squared Lorenzian, i.e.,the Deby-Bueche function,[20] has often been performed for thesemidilute solutions.[21–23] However, it seems less plausible tothink that the phase boundary assumed in the Debye-Buechemodel exists in the cellulose/LiCl/DMAc solution. In therheological measurements previously performed for the semi-dilute cellulose/LiCl/DMAc solutions,[4,7] no viscoelasticbehavior that would be attributed to the phase separation hasbeen observed. Therefore, it seems appropriate to apply theLorenzian function to the excess scattering component.

Figure 5. Zimm plot of 1 wt.-% cellulose in LiCl/DMAcsolution. Solid line shows an OZ equation given by Equation (4)in the text.

Figure 6. Dependence of the correlation length of cellulose inLiCl/DMAc solution on cellulose concentration.

Investigation of the Structure of Cellulose in LiCl/DMAc Solution and Its Gelation Behavior . . . 297

Macromol. Biosci. 2006, 6, 293–300 www.mbs-journal.de � 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

We first discuss the differences in the structure at the

macroscopic level. Turbidity of the water-coagulated

cellulose gel suggests that the submicron-order hetero-

geneity exists in it. In contrast, it was expected that there

exists no submicron-order heterogeneity in the deionized

gel because of its colorless and transparent nature. How-

ever, as the deionized gel shows optical birefringence under

the crossed polarizer, suggesting the existence of an ordered

structure in the length scale below 300 nm. Although the

details on the formation mechanism of the submicron-order

structure in the water-coagulated gel are unknown at

present, it is speculated that the phase separation is induced

by the addition of water to the LiCl/DMAc solution.

Takeshita et al. pointed out that the competition of the phase

separation and the association of the molecular chains

(crystallite formation) is the key factor that affects the

submicron-order heterogeneity in poly(vinyl alcohol)

gel.[28] In their study, when the phase separation precedes

the crystallite formation, turbid gel is formed. On the other

hand, when the crystallite formation precedes the phase

separation, transparent gel is obtained. This explanation

seems to be valid for our results. Namely, in the case of the

formation of the deionized gel, it is supposed that the

molecular association precedes the phase separation. On

the other hand, in the case of the water-coagulated gel, the

phase separation may precede the molecular association.

The densely packed structure of the molecular aggregate in

the water-coagulated gel may be due to the condensation of

cellulose that is expected to occur in the process of the phase

separation.

We then focus on the structure at themolecular level. The

SAXS profiles, in particular the Kratky plots (Figure 4),

showed that the structures of the deionized and the water-

coagulated gels are considerably different. Therefore, the

characterization of the structure of these gels is made in

different ways.

As for the deionized gel, it was suggested from the

Kratky plot that the structure of cellulose in the deionize gel

is rather similar to that in the dissolved state. Considering

this, it is supposed that the structure of the deionized

cellulose gel consisted of the homogeneous network of the

cellulose molecular chains connected at the junction zones.

This kind of model has been applied for the analysis of the

gel structure of syndiotactic polystyrene swollen by

chloroform.[29] In the mentioned study, the characteristic

length scales were calculated using the following equation

originally derived for the structural analysis of the star-

shaped polymer:[30]

IðqÞ ¼ Ið0Þ exp � 1

3q2R2

g

� �

þ KGðDm � 1Þ sin½ðDm � 1Þ tan�1ðqxÞ�qxð1þ q2x2ÞðDm�1Þ=2

ð5Þ

Here, G(x) is the Gamma function of the variable x and K is

the constant. The radius Rg represents the radius of gyration

of the star-shaped polymer cluster that has the junction zone

as the core and the independent chains radiating from the

core. The correlation length x, reflects the average inter-

chain distance in the cluster. The fractal dimension, Dm,

reflects the aggregation state of cellulose molecules in the

cluster. Using Equation (5) and the value of Dm estimated

fromFigure 3(a)with Equation (1), the characteristic length

scaleswere calculated. The fitted curve for the calculation is

also shown in Figure 3(a). The result is shown in Table 2. It

is found that the value of Rg is almost the same as that of Xin the dissolved state as shown in Table 1. This suggests that

the structure of the deionized cellulose gel originates

from the large-scale fluctuation of the cellulose chain

density in the solution. Therefore, it is supposed that the

association of cellulose chains in the solution occurs at the

region where the chain density is high.

Next, the structure of the water-coagulated gel is

investigated. As the surface fractal dimension was calcu-

lated from the SAXS profiles, it is supposed that the

cellulose molecular chains in the water-coagulated gel is

packed more densely than in the deionized one. The peak

observed in the Kratky plot reflects the size of the

‘‘particle’’ formed by the aggregation of the cellulose

molecular chains. Surface and mass fractal dimensions, Ds

andDm, estimated from the large- and small-q regions in the

double logarithmic plot reflects the surface roughness and

the aggregation state of the particles mentioned above,

respectively. In order to describe the above-mentioned

structural model, the approach proposed by Beaucage was

Table 2. Characteristic length scales and fractal dimensions of cellulose gels.

Deionized Water-coagulated

Rg x Dm Rg Rs Dm Ds

nm nm nm nm

11.9 2.87 >15 (Beaucage)38.5 (p(r))

2.16 3.51 (Kratky)5 (p(r))

1.81 2.79

298 D. Ishii, D. Tatsumi, T. Matsumoto, K. Murata, H. Hayashi, H. Yoshitani

Macromol. Biosci. 2006, 6, 293–300 www.mbs-journal.de � 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

employed.[31] In his approach, the scattering function of

the mass fractal aggregate of rough surface particles is

expressed by

IðqÞ ¼ G exp �R2g

3q2

!þ B exp �R2

sub

3q2

� �1

q�

� �P

þ Gs exp �R2s

3q2

� �þ Bs

1

q�s

� �Ps

ð6Þ

where P and Ps are equal to Dm and 6-Ds, respectively. The

length Rg and Rs represent the radius of gyration of overall

aggregate and the particle comprising the aggregate,

respectively. The radius Rsub defines the upper cutoff

of the mass fractal regime and is generally equal to Rs. The

G,B,Gs, andBs are the constants. The quantity q* is defined

by

q� ¼ q=½erfðqkRg=61=2Þ�3 ð7Þ

where erf(x) is the error function of the variable x. The value

assigned to k, the empirical constant introduced by

Beaucage, was 1.06.[31] In the actual calculation, the

reciprocal of the value of q at the peak in theKratky plot was

assigned toRs [1/(0.285 nm�1)¼ 3.51 nm]. The dimensions

Dm andDs were calculated from the slopes in the small- and

large-q regions in Figure 3(b), respectively.[17] Using these

values, Rg was estimated as an adjustable parameter. The

good fit was obtained when the Rg was more than 15 nm, as

shown in Figure 3(b) by a solid curve. However, the

determination of the exact value of Rg was not attained, due

to the limitation of q range available. Therefore, in order to

evaluate the size of aggregate more precisely, distance

distribution function, p(r), was estimated by the equation

pðrÞ ¼ 1

2p2

ð10

qrIðqÞ sinðqrÞdq ð8Þ

Figure 7 shows the plot of p(r) against the length scale, r.

Peaks are observed at r¼ 5 nm (r1) and r¼ 38.5 nm (r2).

These correlation lengths are related to the size of the

particle comprising the aggregate and that of the overall

aggregate. The length r1 seems to correspond toRs, because

their values are almost the same. The value of r2 is three

times as large as X in the solution and Rg in the deionized

gel, but they are in the same order of magnitude. Therefore,

it can be said that r2 reflects the size of the overall

aggregate in thewater-coagulated gel. This suggests that the

structure of the water-coagulated gel also originates in

the large-scale fluctuation of the cellulose chain density in

the LiCl/DMAc solution.

Acknowledgements: This work was supported by a Grant-in-Aid for Scientific Research (B) No. 16380118 from Japan Societyfor the Promotion of Science.

[1] A. Turbak, Tappi J. 1984, 67, 94.[2] C. L. McCormick, P. A. Callais, B. H. Hutchinson, Jr.,

Macromolecules 1985, 18, 2394.[3] T. Heinze, T. Liebert, Prog. Polym. Sci. 2001, 26, 1689.[4] T. Matsumoto, D. Tatsumi, N. Tamai, T. Takaki, Cellulose

2002, 8, 275.[5] E. Togawa, T. Kondo, J. Polym. Sci., Part B: Polym. Phys.

1999, 37, 451.[6] A. M. Ritcey, D. G. Gray, Biopolymers 1988, 27, 1363.[7] N. Tamai, H.Aono,D. Tatsumi, T.Matsumoto, J. Soc. Rheol.

Jpn. 2003, 31, 119.[8] N. Tamai, D. Tatsumi, T. Matsumoto, Biomacromolecules

2004, 5, 422.[9] H. Aono, N. Tamai, D. Tatsumi, T. Matsumoto, Nihon

Reoroji Gakkaishi 2004, 32, 169.[10] T. Roder, B. Morgenstern, N. Schelosky, O. Glatter, Polymer

2001, 42, 6765.[11] T. Schult, T. Hjerde, O. I. Optun, P. J. Kleppe, S. Moe,

Cellulose 2002, 9, 149.[12] A. El-Kafrawy, J. Appl. Polym. Sci. 1982, 27, 2435.[13] L. Schulz, B. Seger, W. Burchard, Macromol. Chem. Phys.

2000, 201, 2008.[14] H. Koyama, T. Yoshizaki, Y. Einaga, H. Hayashi, H.

Yamakawa,Macromolecules 1991, 24, 932.[15] G. Conio, P. Corazza, E. Bianchi, A. Tealdi, A. Ciferri, J.

Polym. Sci., Polym. Lett. Ed. 1984, 22, 273.[16] P. W. Schmidt, ‘‘The Fractal Approach in Heterogeneous

Chemistry’’, D. Avnir, Ed., J.Wiley&Sons, NewYork 1989,p. 67.

[17] D. Ishii, D. Tatsumi, T. Matsumoto, Biomacromolecules2003, 4, 1238.

[18] P.-G. de Gennes, ‘‘Scaling Concepts in Polymer Physics’’,Cornell University Press, Ithaca, NY, and London 1979.

Figure 7. Distance distribution function of thewater-coagulatedcellulose gel.

Investigation of the Structure of Cellulose in LiCl/DMAc Solution and Its Gelation Behavior . . . 299

Macromol. Biosci. 2006, 6, 293–300 www.mbs-journal.de � 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

[19] M. Shibayama, Macromol. Chem. Phys. 1998, 199, 1.[20] P. Debye, A. M. Bueche, J. Appl. Phys. 1949, 20, 518.[21] J. T. Koberstein, C. Picot, H. Benoit, Polymer 1985, 26, 673.[22] O. Kube, E. Wendt, J. Springer, Polymer 1987, 28, 1635.[23] I. Pezron, M. Djabourov, J. Leblond, Polymer 1991, 32,

3201.[24] F. Hamada, S. Kinugasa, H. Hayashi, A. Nakajima,

Macromolecules 1985, 18, 2290.[25] S. Kinugasa, H. Hayashi, F. Hamada, A. Nakajima,

Macromolecules 1986, 19, 2832.

[26] D. W. Schaefer, Polymer 1984, 25, 387.[27] H. Aono, D. Tatsumi, T. Matsumoto, J. Polym. Sci., Part B:

Polym. Phys. (submitted).[28] H. Takeshita, T. Kanaya, K. Nishida, K. Kaji, Macromole-

cules 1999, 32, 7815.[29] M. Kobayashi, T. Yoshioka, M. Imai, Y. Itoh, Macromole-

cules 1995, 28, 7376.[30] W. D. Dozier, J. S. Huang, L. J. Fetters, Macromolecules

1991, 24, 2810.[31] G. Beaucage, J. Appl. Crystallogr. 1996, 29, 134.

300 D. Ishii, D. Tatsumi, T. Matsumoto, K. Murata, H. Hayashi, H. Yoshitani

Macromol. Biosci. 2006, 6, 293–300 www.mbs-journal.de � 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim