| DOI: 10.3933/APPLRHEOL-24-24766 | WWW.APPLIEDRHEOLOGY.ORG

Comparison of Viscoelastic Properties of and Acorn by Means of Mechanical Models with an In-built Springpot

Magdalena Orczykowska, Marek Dziubi ski* ń 1Faculty of Process and Environmental Engineering, ódz University of Technology, ul. Wólczanska 213, 90-924 ódz,Ł Poland Ł *Corresponding author: [email protected] Fax: x48.42.6365663

Received: 25.9.2013, Final version: 6.12.2013

Abstract: The effect of concentration on viscoelastic properties of chestnut and acorn starch is discussed in the paper. The starch struc- ture was assessed using a rheological fractional standard linear solid model FSLSM in contrary to very simple power-law mod- el usually used in many published papers concerning determination of rheological properties of starch. Rheological parame- ters of this model were determined and their changes for different concentrations of the two tested types of starch were discussed. The values of the rheological parameter of FSLSM model give a useful of information concerning the elastic prop- erties of materials such as total elasticity of networks, network oscillations, gel stiffness, structure of cross-linking and relax- ation time of the materials. The proposed method for the interpretation of rheological measurements of the two types of starch allows for a comprehensive estimation of the analyzed biomaterial structure. The fractional rheological models can be very useful to control the biomaterial structure the needs of the final to meet envisaged product which is particularly signif- icant from the point of view of materials engineering.

Key words: fractional standard linear solid model, chestnut and acorn starch, viscoelastic behavior

1 INTRODUCTION pea (Pisum sativum) [4, 5], but also acorn (Quercus ilex L.) [6–11] and sweet chestnut ( Mill.), Polysaccharides, including starch, are the biopolymers etc. can be found in the literature [12–20]. which due to their physicochemical properties are com- An interesting source of starch is sweet chestnut monly used in many industrial applications. However, (Castanea sativa) which should not be confused with primarily, they find the widest applications in the food the common horse chestnut (Aesculus hippocastanus). processing industry. It is estimated that annually in the Sweet contain up to 70% starch, 17% sugar world about 60 million tons of starch is extracted from (saccharose), 6% and 2% . A high content of various types of cereals, tubers and root crops, at which starch in the chestnut makes it attractive for use in food. about 60% is used in food related applications (e.g. Similarly, another interesting source of starch are bread, sauces, soups, syrups, ice cream, snacks, meat acorns, i.e. apparent of trees (Quercus) com- products, baby food, drinks, and fat substitutes), while posed of a and a cupule. Oak , i.e. acorns con- the remaining 40% is applied in the production of med- tain starch and other amounting to 37% icines and in the manufacturing of packaging materi- and 7%, respectively. They also contain 8.1% protein als [1]. In food industry starch of various botanical ori- and 31.4% fat as well as about 7% . gins has been used for years, e.g. starch obtained from Due to the growing interest in both chestnut and potatoes, corn, wheat, oat, rye, rice, or tapioca, which acorns starch, the authors of the present paper have differs in the shape and size of or the content of undertaken to analyze the mechanical state of structure amylose and amylopectin. The extremely wide applic- of pure paste obtained from chestnut and acorn starch, ability is a reason for searching for the new sources of using the results obtained by Kim and Yoo and Moreira starch, hence studies on starch obtained from kiwifruit [9, 18] and to explain the effect of the concentration of (Actinidia deliciosa) [2], banana (Musa paradisiaca) [3], these two types of starch on the rheological properties

© Appl. Rheol. 24 (2014) 24766 | DOI: 10.3933/ApplRheol-24-24766 | 1 | measurements [24]. Various rheological models are used to describe the rheological behavior of pastes. One of them is the standard linear solid model (SLSM). The standard linear solid model consists of a spring and a Figure 1: Fractional standard linear solid model – FSLSM. system of elements of the Maxwell model, i.e. the spring connected in series with a dashpot. Such a of biomaterials produced from them by applying a rhe- mechanical model describing the behavior of media ological fractional standard linear solid model FSLSM. representing properties of solid bodies, in which elas- The proposed method of discussion of the results of rhe- tic properties dominate over viscous ones (G’ > G”). In ological measurements makes it possible to present a this model, Newton’s viscous element, i.e., the dashpot, comprehensive evaluation of the analyzed medium can be replaced by the so called viscoelastic element structure. In the original works of Kim and Yoo [9] and that combines both elastic properties of Hook’s ele- Moreira [18] experimental data only show gel-like ment, i.e. a spring, and viscous properties of Newton’s behaviour of chestnut and acorn starch. Their major element. This element is called Scott-Blair’s element or focus was to show that very interesting additional infor- a springpot. If the dashpot is replaced by a springpot, mation could be extracted from the same experimental the standard linear solid model becomes a fractional data if by employing the FSLSM model. The values of standard linear solid model (FSLSM). The model con- FSLSM model parameters presented a wide spectrum of taining Scott-Blair’s viscoelastic element is therefore a information concerning the structure of starch pastes, fractional mechanical model describing viscoelastic viscoelastic properties of material, total elasticity of net- behavior of solids. A fractional standard linear solid works, network oscillations, gel stiffness, structure model is shown in Figure 1. cross-linking and relaxation time of the material. A sim- An advantage of the fractional rheological models ilar approach for describing the rheological data by is that they can describe dynamic behavior by means of Bahlouli and Melito [21, 22]. a single equation which contains a number of constant parameters determining the viscoelastic properties of a material being tested. In the case of application of the 2 MATERIALS AND METHODS fractional rheological model, it is very important to iden tify the parameters of this model on the basis of The curves of the storage G’ and loss G” moduli for experimental data. The process of identification is the chestnut starch, obtained during oscillation measure- so called reciprocal problem. This means that in the ments in the oscillation frequency from 2 to 70 rad/s at process of identification experimental results are first- a constant deformation of 2%, were described by Mor- ly approximated by trigonometric functions, and then eira [18] and for acorn starch in the oscillation range rheological parameters of the model are determined. from 0.62 to 62.8 rad/s at a constant deformation of 2% Dinzart and Lipi ski [25] described several frac- were described by Kim and Yoo [9] with the power-law tional rheological modelsń to determine the viscoelastic model [23] in the following form: properties of tested media. Particularly noteworthy is a fractional standard linear solid model, modulii so called fractional Zener model [26, 27]. The values of the (1) storage G’ and loss G” moduli for this model can be described using trigonometric functions leading to the following equations: (2)

The values of the power-law model parameters k’ and k” as well as n’ and n” are available in the original papers of Kim and Yoo [9] and Moreira [18] and hence are not repeated here. In view of the role of starch in food production, the (3) most important are its rheological properties, so to evaluate the structure of starch pastes or mixtures of these pastes with different additions, a number of methods are used such as steady-shear flow, oscillato- ry shear, small and large deformation shear, creep, stress relaxation and large deformation extensional (4)

© Appl. Rheol. 24 (2014) 24766 | DOI: 10.3933/ApplRheol-24-24766 | 2 | Table 1: Rheological parameters of the Zener model calculated on the basis of Moreira’s experimental data for chestnut starch pastes at 25°C. (5)

0 where Ge is the equilibrium modulus, GN the plateau modulus, τ0 the relaxation time, and α is the fractional exponent. The Zener model (Equations 3 to 5) has five 0 rheological parameters, Ge, GN , τ0, α and k. These para- meters represent the following properties of tested materials [28, 29]: I Equilibrium modulus Ge: Modulus of elasticity in the Table 2: Rheological parameters of the Zener model calculated steady state flow condition represents the total on the basis of Kim and Yoo’s experimental data for acorn elasticity of the network and its reciprocal is sus- starch pastes at 25°C. ceptibility in the state of equilibrium Je. High values of modulus Geindicate an increase of elastic proper- As a result, eight rheological parameters are obtained ties of the material. which are used in a comprehensive analysis of viscoelas- I 0 Plateau modulus GN : The viscoelastic plateau mod- tic properties of the tested materials. The Zener fractional ulus is identified with the structure of cross-linking standard linear solid model holds if the following condi- 0 power. The higher the value of this modulus the tions are satisfied: Ge ≥ 0, GN ≥ 0, τ0 ≥ 0, and 0 ≤α≤1. higher the structure cross-linking. The reciprocal of this modulus is susceptibility of the structure at 0 cross-linking JN . 3 RESULTS AND DISCUSSION I Relaxation time τ0: The characteristic relaxation time defines the time after which stress relaxation Moreira [18] has determined rheological properties of will occur. Short relaxation times indicate strong chestnut starch paste for four different concentrations elastic properties of the material. of this starch, namely 4, 5, 6, and 7% at different tem- I Paramter α: The parameter indicates a characteris- peratures ranging from 25 to 70°C. The experiments tic behavior of elastic bodies if its value is equal to carried out by Moreira led to the conclusion that at the zero; when it is equal to one the behavior is charac- 6% chestnut starch concentration in the paste its vis- teristic of viscous liquids. coelastic properties increase and at a further chestnut I Paramter k: The parameter k is the damping factor starch concentration growth they do not change. of network oscillations. The higher is value, the more Chestnut starch paste at 70° C at the concentrations of the oscillations are damped by the formed network 6 and 7% shows strong viscoelastic properties which of a given biopolymer. result probably from a high amylose content in the con- The knowledge of these parameters allows us to get tinuous phase. Moreira [18] used a simple power-law additional information on the tested material proper- model (Equations 1 and 2) [23], which did not allow him ties, namely to learn the value of dispersion modulus f, to assess comprehensively the mechanical state of the cross-linking density ω0, and gel stiffness S. Relations tested chestnut starch paste structure. Kim and Yoo [9] which make it possible to determine the values of three made an attempt to determine the rheological proper- new parameters on the basis of the five parameters ties of acorn starch pastes for four different concentra- already existing in the Zener fractional model are tions of this starch, i.e. 4, 5, 6, and 7%, but contrary to described by the following equations [28–30] for the dis- Moreira’s study [18], at only one temperature 25°C. The persion modulus f, the ross-linking density ω0, and the experiments carried out by Kim and Yoo allowed them gel stiffness S: to find that an increase of acorn starch concentration in the starch paste caused an increase of elastic behav- ior of this medium. Having the experimental data concerning rheo- (6) logical properties of chestnut starch pastes presented by Moreira [18] and acorn starch pastes shown by Kim and Yoo [9], we described them by the Zener fraction- (7) al rheological model and present the obtained para- meters in Tables 1 and 2. The Zener model was applied (8) to acorn starch in the range of oscillation frequencies comparable to the range for chestnut starch, i.e. from

© Appl. Rheol. 24 (2014) 24766 | DOI: 10.3933/ApplRheol-24-24766 | 3 | 2 to 62.8 rad/s. Figure 2 show experimental relations between storage G’ and loss G” moduli as a function of ω and curves describing these values which result from the Zener model (Equation 3 to 5). Diagrams shown in Figure 2 illustrate very good agreement of the experimental data obtained by Mor- eira [18] and Kim and Yoo [9] with the curves described in this paper by the Zener fractional standard linear sol- id model. The mean error in the description of experi- mental data for chestnut and acorn starch pastes were ± 3.5 and ±6.5%, respectively. Analysis of the values of rheological parameters in the Zener fractional rheo- logical model (Tables 1 to 2) gives us much more infor- mation about the rheological behaviour of both starch- es than we are able to obtain from simple power-law model (Equation 1 and 2) and allows us to state that in all analyzed cases the medium with a structure typical of viscoelastic quasi-solid bodies is formed. This is con- firmed by the rather high values of the viscoelastic 0 plateau modulus GN both for chestnut and acorn starch. The rheological parameters obtained from the Zener model show that acorn starch has much stronger elastic properties which increase with the concentra- tion. Additionally, high power of structure cross-linking 0 GN indicates a possibility of slow down of the physical ageing of this biomaterial in time. Chestnut starch has also strong elastic properties, however much weaker than the acorn starch. In the range of dynamic studies of both types of starch, changes in the overall elasticity of the network Ge for chestnut starch are relatively small (Table 1). In a case of acorn starch, modulus Ge for 4% concentration of this starch is 3.5 times higher than for the chestnut starch and 11 times higher at 7% concentration (Table2). These differences show that the highest elasticity of the network was characteristic of acorn starch. Up to the 5% concentration both , i.e. chestnut and acorn starch pastes, represent a different type of structure. This follows from the fact that the values of cross-link- ing density represented by parameter ω0 do not occur within the same decade of oscillation frequency (Ta - bles 1 and 2, Figures 2a and 2b). Only in the range of con- centrations from 6 to 7% the oscillation frequencies are within the same decade which can indicate a similar type of structure of both media (Tables 1 and 2, Figures 2c and 2d). In general, it can be stated that the density of cross-linking 0 is higher for the acorn starch than for the chestnutω starch, the case is opposite only at the 4% concentration. The fractional exponent α for 4% and 5% chestnut Figure 2: Frequency dependence of G’ and G” for chestnut and starch concentrations remains on a constant level, like acorn starch, concentration 4 % to 7 % at 25° C in the range of angular frequency 2 to 62.8 rad/s. The curves throughout the in the case of 6% and 7% concentrations, however, in experimental data are calculated using the fractional standard this concentration range it is by 0.1 lower which indi- linear solid model (FSLSM – Zener model). cates that more elastic properties of this starch are

© Appl. Rheol. 24 (2014) 24766 | DOI: 10.3933/ApplRheol-24-24766 | 4 | 0 GN indicates a possibility of slow down of the physical ageing of this biomaterial in time. Chestnut starch has also strong elastic properties, however much weaker than the acorn starch. Moreover, it is probable that it 0 can be unstable in time as the values of GN of this starch are significantly lower than for the acorn starch. Nev- ertheless, chestnut starch at relatively smaller overall elasticity and cross-linking power than in the acorn starch, is characterized by a high value of network oscil- lation factor k which can be the evidence of its stabili- ty and resistance to mechanical action. To better illustrate differences in the structure of pastes obtained from chestnut and acorn starch in the comparable range of oscillation frequencies from 2 to 62.8 rad/s, the curves of storage G’ and loss G” modules are presented additionally in the form of the so called 0 reduced curves in the system of coordinates G’/GN = 0 f(ω/ω0) and G”/GN = f(ω/ω0) as shown in Figures 3a and 3b. The reduced curves confirm finally that: I Chestnut and acorn starch pastes at the concentra- tions of 6 and 7% have with respect to both viscous and elastic properties similar structure although with different mechanical features. Very good su - Figure 3: Reduced curves for chestnut and acorn starch pastes per position of the reduced curves for both concen- at 25°C in the comparable range of oscillation frequencies from 2 to 62.8 rad/s. trations is confirmed additionally by cross-linking density ω0 within the decade of oscillation fre- quency 104 s-1. revealed only at higher concentrations (Table 1). In the I At lower chestnut and acorn starch concentrations, case of acorn starch, the fractional exponent α decreas- structures created during paste formation are dif- es systematically with concentration of starch (Table 2). ferent, although there is some similarity of elastic Hence, it can be concluded that with an increase of the properties between 4% acorn and 5% chestnut concentration of acorn starch its elastic properties starches. appear stronger than in the case of chestnut starch. Gel I The chestnut starch paste has the same structure stiffness S for acorn starch increases with the growth for concentrations of 6 and 7%, however cross-link- of starch concentration systematically (Table 2). For ing density ω0 shows that similar structures are chestnut starch, we can also observe an increase of gel formed by pastes at three concentrations (4, 6, and stiffness with an increase of starch concentration in the 7%), while the values of ω0 are within the same paste but this growth is much less spectacular (Table 1). decade of oscillation frequencies (104 s-1). The Thus, acorn starch pastes are characterized by higher reduced curves do not confirm this observation, gel stiffness. The damping factor of network oscilla- which is shown additionally by differences in the 0 tions k for acorn starch (Table 2) is relatively low as com- parameters of the Zener model (Ge, GN , f, and k). pared to chestnut starch (Table 1). The difference in the I In the case of acorn starch paste very similar, al - values of k is three times higher for chestnut starch, though not identical type of structures, both in view except for the 5% concentration which is related to the of viscous and elastic properties, have be observed analogous relation for the dispersion modulus f repre- for concentrations of 6 and 7%. This is also con- senting polydispersivity of the system. As a result, at firmed by the rheological parameters of the Zener higher polydispersivity of the medium, i.e. chestnut model as cross-linking density ω0, fractional expo- starch, much stiffer gels are formed with bigger possi- nent α, dispersion modulus f, and damping factor of bility of damping oscillations than in the case of acorn network oscillations k. starch. In summary, extensive analysis of the mechanical state The rheological parameters obtained from the of the structure of pure pastes obtained from chestnut Zener model show that acorn starch has much stronger and acorn starches presented in this work explains the elastic properties which increase with the concentra- effect of the concentration of starches in a solution on tion. Additionally, high power of structure cross-linking their rheological properties with the use of the Zener

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© Appl. Rheol. 24 (2014) 24766 | DOI: 10.3933/ApplRheol-24-24766 | 7 |