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Food Hydrocolloids 24 (2010) 512–517

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Food Hydrocolloids

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Phenomenological viscoelasticity of some rice starch gels

Navdeep Singh Sodhi a,b, Tomoko Sasaki a, Zhan-Hui Lu a,1, Kaoru Kohyama a,*

a Food Physics Laboratory, Food Function Division, National Food Research Institute, National Agriculture and Food Research Organization, 2-1-12 Kannondai, Tsukuba,Ibaraki 305-8642, Japanb Department of Food Science and Technology, Guru Nanak Dev University, Amritsar – 143 005, Punjab, India

a r t i c l e i n f o

Article history:Received 16 September 2009Accepted 24 December 2009

Keywords:Rice starchComposite gelDynamic viscoelasticityRelaxation spectraContinuous Maxwell model

* Corresponding author. Tel.: þ81 29 838 8031; faxE-mail address: kaoruk@affrc.go.jp (K. Kohyama).

1 Present address: College of Food Science and NAgricultural University, P.O. Box 40, Beijing 100083, P

0268-005X/$ – see front matter � 2010 Elsevier Ltd.doi:10.1016/j.foodhyd.2009.12.009

a b s t r a c t

The applicability of a powerful but still easy to use technique, based on a phenomenological theory ofviscoelasticity, for processing and analyzing dynamic mechanical data of some rice gels was investigated.Based on this theory a continuous relaxation spectra was generated by application of Tikhonov regula-rization procedure on continuous Maxwell model. Interpretation of relaxation spectra in terms ofnumber of peaks, its peak intensity H(l) and appearance of its main distribution peak and magnitude ofequilibrium elasticity modulus (Ge) of continuous Maxwell model was found to appropriately reflectmain peculiarities of the viscoelastic behavior of rice starch gels. An increase in number of peaks in therelaxation spectra was observed for starch gels having higher amylose content indicating the creation ofmore heterogeneous structure. H(l) and Ge values also increased with increase in amylose contentdemonstrating a transition of the system to more stable state like a gel.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Mechanical properties of polymeric materials are used to char-acterize the micro-mechanisms that control their linear viscoelasticbehaviors (Povolo & Hermida, 1992). During evaluation ofmechanical properties, a broad spectrum of relaxation timesgenerating relaxation spectra has been observed for macromole-cules (Winter, 1997). This relaxation spectrum is a fundamentalquantity in the linear theory of viscoelastic materials (Honerkamp& Weese, 1993) and its shape is often correlated with specificmolecular architectures (Winter, 1997). According to Malkin (2006),the spectrum correctly reflects main characteristics of viscoelasticbehavior of real polymeric materials. Further, the molecularmobility of polymeric liquids and solids expresses itself in a relax-ation-time spectrum (Baumgaertel & Winter, 1992). Moreover, thisspectrum can also be used to study the rheological characteristics ofpolymer blends (Honerkamp & Weese, 1993). However, directmeasurement of relaxation spectra is impossible, as it can only becalculated on the basis of experimental data (Malkin, 2006) e.g.dynamic mechanical experiments are the most effective formeasuring the relaxation modes of polymeric liquids and solids(Baumgaertel & Winter, 1989).

: þ81 29 838 7996.

utritional Engineering, ChinaR China.

All rights reserved.

Stress relaxation experimentation is a fundamental dynamicmechanical analysis which gives a direct approach in the elucida-tion of molecular dynamics of relaxation process of three-dimen-sional biopolymer structure (Kontogiorgos, Jiang, & Kasapis, 2009).However, the challenge is to mathematically obtain relaxationspectra from such experimental data. The same can be achievedthrough inversion of Fredholm integral equation (Eqn. (1)) of firstkind by a numerical method (Honerkamp & Weese, 1989).

gðsÞ ¼Zb

a

Kðs; tÞf ðtÞdt (1)

Where K(s, t) is the kernel function that describes the system,g(s) is the measured signal, and f(t) is the unknown integral solu-tion. The aim is to estimate function f(t) that represents therelaxation spectrum of the material. However, numerical solvationof Fredholm integral equation is a classical example of an ill-posedproblem (Morozov, 1984) that requires special mathematicaltreatment (Groetsch, 1984). Therefore, regularization methodswhich allow incorporation of additional information for therequired function are employed for such problems (Kontogiorgoset al., 2009). Provencher (1982), Friedrich and Hofmann (1983),Honerkamp and Weese (1989) and Elser, Honerkamp, and Weese(1992) have given formal approach to solve ill-posed problemsbased on regularization procedure. Some other methods like least-square approximations (Baumgaertel & Winter, 1989; Laun, 1978;Tanner, 1968), Contin (Provencher, 1979) and maximum entropy

N.S. Sodhi et al. / Food Hydrocolloids 24 (2010) 512–517 513

methods (Elster & Honerkamp, 1991; Livesey, Licinio, & Delaye,1986) are also available in literature. The regularization methodshave been applied earlier for predicting relaxation and retardationspectrum of synthetic polymers (Tan, Tam, & Jenkins, 2000; Weese& Friedrich, 1994) and biopolymers (Mao, Tang, & Swanson, 2000;Ptaszek et al., 2009; Ptaszek & Grzesik, 2007).

Bhattacharya, Bhattacharya, and Narasimha (1999) summed upthat the rheological behavior of food gels can offer necessaryinformation on the selection of appropriate raw materials, estab-lishing the specifications for raw materials, and is important for thequality control of the finished product, process scale-up, productformulation and process optimization. Jena and Bhattacharya(2003) further stressed the importance of modeling rheologicalbehaviors as they can lead to wider use of the results compared toperforming empirical tests on a texture measuring equipment.

Starch is widely used in food processing and preparation notonly as a main ingredient of staple foods such as bread andnoodles but also as a thickener, gelling agent, stabilizer, and fatreplacer (Funami et al., 2008). Such extensive applications ofstarch are mainly because it can yield gels or pastes, the deter-minants of food texture, depending on concentration andtemperature conditions (Rosalina & Bhattacharya, 2002). Thestructure of gel or paste depends not only on the starch concen-tration but also on the structure of swollen starch granules, theamounts of amylose and amylopectin leached out from the gran-ules and on the heating conditions such as time, temperature andrate of heating (Genovese & Rao, 2003; Keetels, van Vliet, &Walstra, 1996a, 1996b; Rao, Okechukwu, Da Silva, & Oliveira, 1997;Ring, 1985). Rice starch, unlike other starches, is primarilycomposed of a single-size granule distribution and thus makes anexcellent model system to study the effect of composition,primarily amylose/amylopectin ratio, and physical characteristicsof the granules on the thermomechanical properties of starch gels(Biliaderis & Juliano, 1993). Therefore, our dynamic mechanicaldata of rice starch composite gels presented earlier (Lu et al.,2009) with varying amylose content was investigated phenome-nologically by developing their relaxation spectra. The presentinvestigation was carried out with an objective to attempt theapplicability of a phenomenological theory of viscoelasticity,widely used for studying synthetic polymers, for understandingthe behavior of model starch gel systems by monitoring relaxationpatterns of their macromolecules.

2. Methods

2.1. Rheology data of rice starch gels

Dynamic mechanical data of storage modulus (G0) and lossmodulus (G00) reported previously (Lu et al., 2009) were used. Themeasurements were conducted by frequency sweep tests of the ricestarch gels with a concentration of 38% (w/w), the same as used inindustrial rice noodle processing, with angular frequency (u)ranging from 0.05 to 50 rad/s at 4 �C. The investigated rice starchgels with different amylose content (1.2%, 6.8%, 14.2%, 17.0% and19.8%) were prepared by mixing Indica and waxy Japonica ricestarch in different ratios of 0:100, 30:70, 70:30, 85:15 and 100:0,respectively. Starch gel prepared from Japonica rice cultivar havingan amylose content of 17.8% was also studied.

2.2. Relaxation spectra analysis

Mechanical tests e.g. stress relaxation using constant strain instatic or oscillatory modes are commonly used in viscoelastictesting of polymers. During testing in oscillatory mode, a complexviscoelastic modulus G* consisting of a real part i.e. storage

modulus (G0) and imaginary part i.e. loss modulus (G00) is obtained(Eqn. (2)) (Ferry, 1980). The storage modulus represents the amountof energy stored by the system and loss modulus is an indicator ofenergy dissipated by the system (van Vliet, 1995).

G*ðuÞ ¼ G0ðuÞ þ iG00ðuÞ (2)

A Maxwell element i.e. a Hookean spring and a Newtoniandashpot joined in series representing elastic and viscous nature ofthe system, respectively is most widely used to explain the stressrelaxation phenomenon (Ferry, 1980; Tschoegl, 1989). For experi-ments conducted in dynamic mode, a continuous Maxwell model(Eqn. (3)) (Ferry, 1980) can be used to predict the relaxation spectrai.e. continuous function H(l) describing distribution of relaxationtimes (l).

G*ðuÞ ¼ Ge þZþN

0

HðlÞ ðluÞ2

1þ ðluÞ2dlþ i

ZþN

0

HðlÞ lu

1þ ðluÞ2dl (3)

Where, Ge in the above equation represents the viscoelastic solidstate of an additional spring attached in series to a Maxwell modeland is called equilibrium elasticity modulus.

In the present work, methodology proposed by Weese (1992)was adopted to predict relaxation spectra. The methodology is animplementation of a solution method for Fredholm integral equa-tions of the first kind based on Tikhonov regularization (Tikhonov,Goncharsky, Stepanov, & Yagola, 1995) by minimizing the followingfunction (Eqn. (4)) while considering bHðlÞ � 0

VðaÞ ¼Xn

j¼1

1s2

j

("G0sj �

ZþN

0

HðlÞ ðluÞ2

1þ ðluÞ2dlþ Ge

!#

þ"

G00sj � ZþN

0

HðlÞ lu

1þ ðluÞ2dl

!#)2

þakDHðlÞk2 ð4Þ

Where, a, D, s and k*k are regularization parameter, differentialoperator, experimental error and Euclidean norm, respectively.

In this methodology, with an appropriate value of regularizationparameter the first term on the right side of the Eqn. (4) forces theresult to be compatible with the data and the second term leads toa smooth estimate for the spectrum H(l). This procedure offersadvantage of estimating the optimal value of the regularizationparameter by using the SC-method (SC for self consistent). This isextremely important, because it depends mainly on this parameter,whether the result obtained by a regularization method is good ornot. Honerkamp and Weese (1990) compared SC-method withother procedures which are often used for the determination of theregularization parameter. They concluded that the results obtainedwith the SC-method are much better and more reliable then theresults obtained with the other procedures.

3. Results

Continuous Maxwell model was used for predicting the relax-ation spectra from the experimentally determined G0 and G00 valuesobtained by dynamic mechanical tests for some rice starch gelswith various amylose contents. A comparison of experimentalvalues with model values is shown in inset of Fig. 1(A–F). Thefigures demonstrate the ability of the applied model to reproduceG0 and G00 values for the investigated rice starch gels. The standarddeviations (Winter, 1997) for the fitted model are given in Table 1.

The relaxation spectra thus generated from continuous Maxwellmodel using Weese (1992) methodology based on Tiknonov regu-larization are presented in Fig. 1(A–F). The investigated starch gels

0

2

4

6

8

10

12

14

0.0001 0.001 0.01 0.1 1 10 100

H

()

aP

k(

)

(s)

A

0

5

10

15

20

25

30

35

0.001 0.01 0.1 1 10 100

(s)

B

0.01

0.1

1

10

0.01 0.1 1 10 100

'G

,

"G

)a

Pk

(

1

10

100

1000

'G

,

"G

)a

Pk

('

G,

"

G)

aP

k(

'G

,

"G

)a

Pk

('

G,

"

G)

aP

k(

(rad/s)

G"

G'

0.1

1

10

100

0.01 0.1 1 10 100

'G

,

"G

)a

Pk

(

(rad/s)

G'

G"

0

20

40

60

80

100

120

140

160

180

0.001 0.01 0.1 1 10 100

C

0

50

100

150

200

250

300

350

400

0.001 0.01 0.1 1 10 100

D

G'

G"

1

10

100

1000

0.01 0.1 1 10 100(rad/s)

G'

G"

0

50

100

150

200

250

300

350

400

450

0.001 0.01 0.1 1 10 100

E

0

5

10

15

20

25

30

35

40

0.001 0.01 0.1 1 10 100

F

1

10

100

1000

0.01 0.1 1 10 100(rad/s)

G'

G"

1

10

100

1000

0.01 0.1 1 10 100(rad/s)

G'

G"

λ λ

(s) (s)λ λ

(s) (s)λ λ

λ

H(

)a

Pk

(

) λ

H(

)a

Pk

(

) λ

H

()

aP

k(

) λ

H

()

aP

k(

) λ

H

()

aP

k(

) λ

ω

0.01 0.1 1 10 100(rad/s)ω

ω

ω

ω

ω

Fig. 1. Relaxation spectra of rice starch gels with different amylose content. Graphs A–F are same samples as described in Table 1. Dynamic mechanical data (BG0exp; ,G00exp;model–values) are presented in inset.

N.S. Sodhi et al. / Food Hydrocolloids 24 (2010) 512–517514

showed several peaks in their spectra. The starch gel of waxy ricehaving amylose content of 1.2% showed three peaks in its spectrawith the first one being a multimodal peak. The composite gelswith 6.8%, 14.2% and 17.0% amylose content showed four, five andsix peaks, respectively, indicating an increase in number of peakswith increase in amylose content. However, the number of peaksdecreased to five for starch gel having amylose content of 19.8%.Rice starch gel made from Japonica cultivar having an amylosecontent of 17.8% also showed the presence of five peaks. It was alsoobserved that there was a visible increase in peak intensity H(l)values of the spectra with the increase in amylose content of thestarch gels except for starch gel from non-waxy Japonica ricecultivar. Similar increase in Ge parameter of the continuousMaxwell model with increase in amylose content was alsoobserved (Table 1).

4. Discussion

The importance of shape of relaxation spectrum can be dis-cussed in the light of interpretation given by Weese and Friedrich(1994) in their study on analyzing relaxation spectra for syntheticpolymers. They concluded that homogeneous systems producehomogeneous spectra. Similarly, Ptaszek et al. (2009) also relatedthe presence of a homogeneous spectrum to sample’s homogeneityand inferred the presence of a few separate peaks to the hetero-geneous structure of the investigated biopolymers. Winter (1997)reported that the shape of spectrum is often correlated withspecific molecular architectures. He further elaborated that thespectrum’s sensitivity to small changes in molecular connectivitymakes it a powerful tool to distinguish small differences in other-wise indistinguishable materials. Heterogeneity is known for starch

Table 1Equilibrium elasticity modulus (Ge) and standard deviation (SD) values of the fittedmodel for rice starch gels.

Sample Amylosecontenta (%)

Geb (kPa) SDc

(A) Waxy Japonica 1.2 0.097 � 0.013 0.0149(B) Waxy Japonica and Indica (70:30) 6.8 2.54 � 0.009 0.0111(C) Waxy Japonica and Indica (30:70) 14.2 75.8 � 0.19 0.0186(D) Waxy Japonica and Indica (15:85) 17.0 142.6 � 0.39 0.0295(E) Indica 19.8 181.0 � 0.46 0.0294(F) Japonica 17.8 57.9 � 0.08 0.0151

a Lu et al. (2009) using an assay kit based on Con A procedure.b Value � estimation error.c Winter (1997).

N.S. Sodhi et al. / Food Hydrocolloids 24 (2010) 512–517 515

samples (Blanshard, 1987) with starch gel being a compositematerial consisting of swollen starch granules, containing mainlyamylopectin, which are embedded in and reinforced by an inter-penetrating amylose gel matrix, or polymer gel network (Miles,Morris, Orford, & Ring, 1985a; Miles, Morris, & Ring, 1985b; Ring &Stainsby, 1982). The viscoelastic behavior of starch dispersions isdependent upon amylose-amylopectin ratio as well as starchconcentration-temperature-time protocols (Biliaderis, 1992; Lau-nay, Doublier, & Cuvelier, 1986). It is generally accepted that boththe continuous phase (amylose) and the swollen granulescontribute to the mechanical properties of the gel composite(Biliaderis & Juliano, 1993; Biliaderis & Zawistowski, 1990). Themechanical properties of starch gels are also dependent upon thevolume fraction of the particles, and the interactions betweenthe dispersed and continuous phase (Luyten & van Vliet, 1990; vanVliet, 1988). Hence, several peaks were observed in the relaxationspectra owing to the heterogeneity arising from the combinedeffect of above discussed factors and mainly due to the presence ofmore than one type of polymers with different chain lengths. Eachof these chains contributes into a global relaxation process (Ptaszek& Grzesik, 2007).

The increase in number of separate peaks with increase inamylose content (Fig. 1A–D) suggests that the spectrum of relaxa-tion processes is altered by the addition of another macromoleculein the system and thus causes an increase in heterogeneity in thespectra. Therefore, with the addition of starch from Indica ricecultivar to waxy rice starch, the number of peaks in the spectra gotincreased from three to six indicating creation of more heteroge-neous structure. However, decrease in number of peaks for starchgels with 19.8% (Fig. 1E) and 17.8% (Fig. 1F) amylose content may beattributed to the reason that they are not composite gels of twostarches from different cultivars. Rheological and thermal proper-ties investigated for above discussed samples using dynamicrheometer and differential scanning calorimetry (DSC), respec-tively, corroborated with this phenomenological theory (Lu et al.,2009). We reported two peaks for G0 and G00 for the starch sampleswith 14.2% and 17.0% amylose content in temperature sweeptesting. Similar observations of dual peaks were observed by DSCanalysis of these samples. It was hypothesized that the appearanceof these dual peaks at different temperatures can be attributed toheterogeneity of the samples arising from differences in morpho-logical and structural characteristics of starch granules (Hageni-mana, Pu, & Ding, 2005) in the composite system. The relaxationspectra predicted in the present study substantiated our postulateof getting dual peaks because of blending of two starches bygenerating more heterogeneous spectra for blended starch gels.Moreover, the addition of starch from other cultivar contributesheterogeneity because of differences in structural rigidity of starchgranules from two different sources (Singh, Singh, Kaur, Sodhi, &Gill, 2003), since granule rigidity plays an important role in the

rheological behavior of the system (Keetels et al., 1996a; Lu, Duh,Lin, & Chang, 2008; Malumba, Massaux, Deroanne, Masimango, &Bera, 2009; Steeneken, 1989). The observed higher heterogeneity inhigher amylose starch gels’ spectra may also be explained from thefact that these gels are having amylose and amylopectin, theincompatible macromolecules (Doublier & Llamas, 1993; Kali-chevsky & Ring, 1987), in greater proportions. Furthermore,German, Blumenfeld, Guenin, Yuryev, and Tolstoguzov (1992) intheir study on starch-water system carried out using pulsed-NMRtechnique indicated that aggregates (structural elements)composed of amylose macromolecules are formed during gelati-nization of starch, which subsequently causes unhomogeneousstructural characteristics in starch-gel network. The same is man-ifested in the relaxation spectra by separate peaks, owing to theirdifferences in mechanical behaviors, thus resulting in increasedheterogeneity. Whereas, the presence of fewer separate peaks inlower amylose starch gels’ spectra may be attributed to the stabi-lizing effect of amylopectin (Hermansson & Svegmark, 1996),however, the multimodal nature of these may be due to themolecular mass distribution characteristics (Ptaszek et al., 2009) ofamylopectins, which are polymodal in distribution (Hizukuri,1986).

The increase in peak intensity of H(l) of spectra with increase inamylose content of starch gels is an indication of the transition ofthe system to a more stable state like gel. Ptaszek et al. (2009) alsoreported an increase in peak intensity of the relaxation spectra ofinvestigated maize starch gels with increase in xanthum gumconcentration owing to their more stable structure. As describedearlier (Lu et al., 2009) we found a well-formed gel structure byhigher amylose starch gels (14.2–19.8%), whereas a weak gel forcomposite starch gel with 6.8% of amylose and a sticky paste likebehavior for waxy starch (1.2% amylose) was observed even afterkeeping at 4 �C for 2 h. The same may be attributed to entrappedswollen starch granules in the gel matrix of the amylose whichmight have strengthened the gel structure (Lii, Tsai, & Tseng, 1996;Ring, 1985; Ring & Stainsby, 1982). Miles et al. (1985a) reported thatthe rearrangement of amylose molecules upon cooling of suffi-ciently concentrated dispersions forms an elastic gel. Further, theappearance of main distribution peak in the relaxation spectrumtowards much shorter times for waxy starch gel as compared toother starch gels implies a fast relaxation process (Ptaszek &Grzesik, 2007), hence more fluidization in the system which wasconsequently found to be in accordance with its sticky paste likebehavior. Intramolecular interactions proposed by Tako and Hizu-kuri (2000) by van der Waals forces of attraction in rice amylo-pectin molecules validate the higher dissipating phase in waxystarch gel as these weak bonds cause flow in a material by openingand closing again later on (Figura & Teixeira, 2007).

Furthermore, the equilibrium elasticity modulus (Ge) parameterof continuous Maxwell model gave additional informationregarding the nature of starch gels. In the present study, a Ge valueof 0.097 kPa was observed for waxy Japonica starch gel, whichincreased to 2.54, 75.8, 142.6, and 181 kPa for 6.8, 14.2, 17.0 and19.8% amylose content starch gels, respectively. Ferry (1980) andMohsenin (1970) inferred that the value of Ge is finite for visco-elastic solids and zero for viscoelastic liquids. Tang, Tung, and Zeng(1998) termed equilibrium modulus as an intrinsic property ofinvestigated gellan gels studied under stress relaxation testing andfound it to be positively correlated with their gel strengths. Nus-sinovitch, Peleg, and Normand (1989) also suggested relationbetween equilibrium stress and strength for agar and alginate gels.So, increase in Ge values with the increase in amylose content ofstarch gels indicates an increase in the elastic component of thesystem and hence a more stable system. In other words, a decreasein Ge value is an indication of increase in dissipating phase in the

N.S. Sodhi et al. / Food Hydrocolloids 24 (2010) 512–517516

system leading to an increase in fluidization of the system underconsideration and hence formation of a weak gel or sticky paste likebehavior. The same was evident from the visual examination of thestarch gels (Lu et al., 2009) as discussed above.

By comparing the relaxation spectra of rice starch gels madefrom Japonica cultivar having an amylose content of 17.8% to Indicacultivar (19.8%) and a composite gel having similar amylose content(17.0%) some significant distinctions were also observed. The firstbeing the more heterogeneity in the composite gel’s spectrum,represented with higher number of peaks, owing to blending of twostarches from different cultivars. The other prominent differencesin the spectra being in the values of peak intensity H(l) with theJaponica starch gel showing a much less intensity along witha much lower Ge value of continuous Maxwell model (Table 1).These differences are indicative of a higher viscous component(Ferry, 1980; Mohsenin, 1970; Ptaszek et al., 2009) in starch gelfrom Japonica cultivar indicating of a weaker gel formation, hencesuggesting its unsuitability for making rice noodles in practicalproduction. Additionally, it may be pointed out that the presence ofmuch higher ratio of longer chain contents in amylopectin of Indicarice starch as compared to Japonica starch (Lu et al., 2009) may beattributed to cause differences in these gels’ viscoelastic behaviorsand the same is manifested in their relaxation spectra. In the end, itis worth mentioning here, although the frequency sweep curveswere observed to be of similar pattern for investigated starch gels,yet the relaxation spectra generated could noticeably quantify thedistinctions among these, in terms of number of peaks, peakintensity H(l) and Ge values, indicating their perspective suitabilityfor specific industrial applications.

5. Conclusion

The applicability of a phenomenological theory of viscoelas-ticity, which is widely used for synthetic polymers to studymolecular models of their polymeric structure, for understandingthe molecular interactions in starch based systems was investi-gated in the present study. The study demonstrated the ability ofthe applied methodology in explaining viscoelastic behaviorsof starch gels by comparing their relaxation spectra in terms ofnumber of peaks, the peak intensity H(l) and appearance of itsmain distribution peak. The technique can be a valuable tool inelucidating the microstructural properties of starch based systemsalthough knowledge of using regularization technique or similarother methods for predicting relaxation spectra is a prerequisite.However, further studies need to be conducted to broaden ourunderstanding regarding its applicability in the biopolymerssystems. Consequently, the technique can be used for tailoringbiopolymers for specific applications in today’s highly competitivefood processing industry.

Acknowledgments

This research is supported by Grant-in-Aid for JSPS fellows(P08621).

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