Scaling law, fractal analysis and rheological characteristics of physical gels cross-linked with sodium trimetaphosphate

Accepted Manuscript Scaling law, fractal analysis and rheological characteristics of physical gels crosslinked with sodium trimetaphosphate Ali Rafe, Seyed M.A. Razavi PII:

S0268-005X(16)30309-5

DOI:

10.1016/j.foodhyd.2016.07.021

Reference:

FOOHYD 3514

To appear in:

Food Hydrocolloids

Received Date: 16 March 2016 Revised Date:

20 July 2016

Accepted Date: 21 July 2016

Please cite this article as: Rafe, A., Razavi, S.M.A., Scaling law, fractal analysis and rheological characteristics of physical gels cross-linked with sodium trimetaphosphate, Food Hydrocolloids (2016), doi: 10.1016/j.foodhyd.2016.07.021. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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trimetaphosphate

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Scaling law, fractal analysis and rheological characteristics of physical gels cross-linked with sodium

a.

Department of Food Processing, Research Institute of Food Science and Technology (RIFST), PO Box 91735-147, Mashhad, Iran

Food Hydrocolloids Research Center, Department of Food Science and Technology, Ferdowsi University of Mashhad (FUM), POBox: 91775-1163, Mashhad, Iran

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Ali Rafea∗∗, Seyed M.A. Razavib

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Corresponding author: Tel: +98 513 5425385; Fax: +98 513 5425406, Email: [email protected]

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Scattered cotton/batting structure of BSG

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BSG as a Glucomannan back-bone structure: R-OH

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+STMP at alkaline pH

Crosslinked chain of BSG

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Concentration (%)

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Elastic stress (Pa)

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G' (Pa)

Df measurement by rheological work

BSG without STMP BSG cross-linked by STMP

2% 1.5% 1% 0.5%

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0.1

Improvement of the BSG gel network by adding STMP 0.001

0.01

Strain (%)

0.1

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Scaling law, fractal analysis and rheological characteristics of

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physical gels cross-linked with sodium trimetaphosphate

4 Ali Rafea∗∗, Seyed M.A. Razavib a.

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Department of Food Processing, Research Institute of Food Science and Technology (RIFST), PO Box

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91735-147, Mashhad, Iran b.

Food Hydrocolloids Research Center, Department of Food Science and Technology, Ferdowsi University

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of Mashhad (FUM), PO Box: 91775-1163, Mashhad, Iran

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Abstract

The scaling behavior and fractal analysis of basil seed gum (BSG) cross-linked with

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sodium trimetaphosphate (STMP) have been investigated by rheological small amplitude

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oscillatory shear measurements. Storage modulus and critical strain (γo) of the gels

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exhibited power law relationships with BSG concentration. Based on the power-law

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exponent values, the fractal dimension (df) of gels was estimated using scaling models,

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revealed the weak-link regime of BSG. The df values lied well within the range of fractal

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dimension values (1.5–2.8) reported for protein gels. However, they slightly differed

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from df for diffusion-limited and reaction limited cluster-cluster aggregation processes.

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Stress sweep test was shown that STMP addition to BSG made a stronger gel than that of

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BSG lacking STMP. Mechanical spectrum of gels was also revealed that adding STMP

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can improve the elasticity of gels. BSG had a tan δ of > 0.1, indicating paste-like weak

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∗ Corresponding author: Tel: +98 513 5425385; Fax: +98 513 5425406, Email: [email protected]

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gel, while tan δ of BSG-STMP has approached to 0.1 exhibited the character of a cross-

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linked network near to “true gel”. BSG-STMP was also recognized as a thermo-

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reversible physical gel, which gelation and thermal properties did not affect by STMP.

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Therefore, the scaling behavior can be applied for hydrocolloids gels to extract structural

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information through rheological measurements. Moreover, the rheological characteristics

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of BSG-STMP showed it can be used as a proper hydrogel in food and pharmaceutical

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applications.

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Keywords: Basil seed gum, Cross linking, STMP, Fractal analysis, Rheology, Gel.

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1. Introduction

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Basil seed gum (BSG) is a natural, water-soluble polysaccharide which is extracted from

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the outer pericarp of basil seeds (Ocimum basilicum L.), can be soaked in water, swells

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into a gelatinous mass and forms a colloidal gel (Rafe & Razavi, 2012). It is a renewable

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hetero-polysaccharide that contains glucomannan, xylan and glucan (Tharanathan &

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Anjaneyalu, 1974), and can be formed a suitable hydrogel at alkaline conditions,

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particularly at pH 8.0 (Rafe & Razavi, 2013). The frequency and easily extraction of

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BSG make it as an excellent opportunity to be utilized in many functions such as

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lubricant (Zhang et al., 2016), emulsifying agent (Hosseini-Parvar et al., 2016),

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thickening or stabilizing agent (Hosseini-Parvar et al., 2010, Bahramparvar & Goff,

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2013). As BSG has a weak network structure, it is essential to improve its gelling

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strength by applying some chemical cross linkers in order to elaborate BSG hydrogels in

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food and pharmaceutical applications.

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Sodium trimetaphosphate (STMP) is a safe, non-toxic crosslinking agent suitable for

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polysaccharides matrices elaboration which approved by the Food and Drug

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Administration (FDA, 1995). It has been used as a phosphorylation agent for both protein

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and sugars as a means of enhancement to improve their functional properties (Li et al.,

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2010; Li et al., 2005). It works by linking the polymer chains with phosphates (Autissier

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et al., 2006; Lack et al., 2004), and is mainly used to prepare food-grade phosphorylated

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starches (Khondkar et al., 2009). Although, many researchers have mainly used STMP on

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starches (Woo & Seib, 2002; Sang et al., 2007; Carmona-Garcia et al., 2009; Sang et al.,

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2010), but it has also been utilized for guar gum (Gliko-Kabiret et al., 2000), carboxy

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methyl cellulose (Leone et al., 2008), konjac glucomannan (Liu et al., 2007), hyaluronan

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(Dulong et al., 2004), xanthan (Bejenariu et al., 2009) and pullulan (Lack et al., 2004;

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2007; Dulong et al., 2011). The mechanism of the reaction of STMP with some

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hydrocolloids has been described in the literatures (Lack et al., 2007; Dulong et al., 2011).

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Fractal analysis through rheological experiments has been attracted a great deal of

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interest as a simple quantitative procedure to characterize physical properties of

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macromolecules such as the elasticity of gels (Mandelbrot, 1982; Stauffer & Aharony,

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1994). A fractal is a self-similar structure which can be characterized by a noninteger

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dimension; the fractal dimension df (Mandelbrot, 1982; Viscek, 1989). It can be

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measured by small amplitude oscillatory shear (SAOS) methods using the dynamic shear

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storage modulus, G', as an indicator of the connectivity of the gel network. The fractal

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structures of gels formed by aggregation have been investigated on gold (Weitz &

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Oliveria, 1984), bovine serum albumin and β-lactoglobulin (Hagiwara et al., 1997; 1998),

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caseinate gel by glucono-δ-lactone (Bremer et al., 1990; 1993), boehmite alumina

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colloidal gels (Shih et al.,1990) and egg white protein (Ould Eleya & Gunasekaran, 2004).

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However, the dynamic rheological behavior of BSG at different conditions such as pH,

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ion strength and concentrations have been studied (Rafe & Razavi, 2012, 2013), but the

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scaling law and fractal analysis of polysaccharides such as BSG did not consider yet and

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most studies have been carried out on protein gels and fat crystal networks (Hagiwara et

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al., 1997; 1998; Ould Eleya & Gunasekaran, 2004; Tang & Marangoni, 2006). Moreover,

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the fractal dimension of BSG and BSG cross-linked with STMP as a polymer gel will be

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precious in controlling macroscopic physical properties of the gel. Therefore, the

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relationship between the structure of the aggregates and the macroscopic physical

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properties were explored. Furthermore, the influences of BSG concentration and

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temperature on the chemical crosslinking during heating, cooling and reheating of such

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gels by dynamic rheology were investigated.

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2. Materials & Methods

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2.1. Fractal models

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When colloidal gels are far from its gelation threshold, the scaling law for the elasticity

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and the limit of linearity (γo) can be considered by the fractal nature of the colloidal flocs

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(Shih et al., 1990). Depending on the strength of inter and intra-floc links, there are two

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regimes, including strong-link regime (inter-floc links have higher elasticity than those in

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the intra-floc links) and weak link regime (inter-floc links are weaker than intra-floc

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links).

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In the strong-link regime, the dependency of the elasticity and the limit of linearity of the

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gels on the particle concentration (φ) can be described as follows:

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′ ~ ()/(  )

(1)

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~ ()/(  )

(2)

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In the weak-link regime:

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′ ~/(  )

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~/( )

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where d is the Euclidean dimension, df is the fractal dimension of the flocs (df≤3), and x

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is the fractal dimension of the floc backbone (1≤ x
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(4)

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(3)

Recently, Wu & Moridelli (2001) have extended the Shih et al. model by considering an

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appropriate effective microscopic elastic constant α (where α ∈ [0, 1]) to estimate the

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fractal dimension for both inter- and intra-floc links. It indicates the relative importance

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of these two contributions and lets identifying different gelation regimes prevailing in the

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system.

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′ ~ /(  )

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~ (  )/( )

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 = ( − 2) + (2 +  )(1 − )

(5)

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(6) (7)

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2.2. Materials

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Basil seeds (Isfahan variety) were purchased from the local markets of Mashhad, Iran.

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sodium trimetaphosphate (STMP), Sodium hydroxide and Hydrochloric acid in analytical

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grade were purchased from Alfa Aesar (Lot No, 5002, Lancashire,United Kingdom) and

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from the Merck Company (Merck KgaA, Darmstadt, Germany), respectively. 5

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114 2.3. Basil seed gum preparation

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Basil seed gum was prepared according to our previous work, which extracted at

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optimum conditions (temperature 68°C, water to seed ratio 65:1 and pH 8) (Rafe &

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Razavi, 2012). Based on the previous works, the carbohydrate to protein ratio of BSG

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was obtained 2.7 for our variety (Razavi et al., 2009). BSG suspensions at various

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concentrations (0.5, 1, 1.5 & 2% w/v), were prepared by dispersing appropriate amounts

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of BSG powder to a portion of alkaline water (pH 8.0) that contained 0.02% sodium

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azide as an anti-microbial preservative. These solutions were made in stock solutions

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then divided into smaller stocks (with and without STMP). For STMP, an aqueous

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solution of STMP (10% w/v) was added and the reaction mixture was stirred one minute

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(Woo, 1997 & Duval et al., 2000). Then, the solutions were agitated for 2 h at room

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temperature and shook by a roll mixer overnight to complete the hydration. These

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samples were kept in a refrigerator at 5 oC before the experiments.

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2.4. Dynamic oscillatory measurements

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Rheological measurements were performed with an AR2000-EX rheometer from TA

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instrument (New Castle, New Jersey, US) using parallel plate geometry (diameter 40 mm,

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gap 1 mm). The linear viscoelastic region (LVE) is determined by amplitude sweep tests

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in controlled shear stress (CSS) mode at 20 oC and 1 Hz. The viscoelastic parameters,

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such as the storage modulus (G'), the loss modulus (G'') and tan δ, were calculated using

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the manufacturer's software (US200 Physica® version 3.40 Anton Paar GmbH,

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Germany).

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In order to study thermo-reversibility of BSG, the solutions were heated on the rheometer

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in situ from 20 to 90 °C during the temperature sweep and held at this temperature for 10

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minutes, followed by a cooling down to 20 °C, to observe thermal hysteresis and gel

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forming characteristics of BSG. Then, the samples were subjected to a stress sweep at a

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constant frequency of 1 Hz. The strain values were measured and critical strain or the

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limit of linearity (γo) was determined from the G'-strain profiles of the gels. In order to

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study gel melting; the temperature was increased to 90 °C. All heating and cooling

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processes were performed at a rate of 5 °C/min. Gelling time was also determined by

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time sweep tests and associated to the first value of tanδ<1.

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2.5. Determination of fractal dimension

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The volume fraction of particles (φ) in the gels was assumed to be proportional to the

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hydrocolloid concentration (C). Fractal dimension values of BSG gels were evaluated

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using values of slopes of log G' versus log C and of log γo vs. log C and based on the

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models of Shih et al. (1990) and Wu & Morbidelli (2001).

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2.6. Statistical analysis

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All the experiments were carried out in triplicates. Rheological data, graphs and statistical

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analysis were determined by Rheoplus software (version 3.40 Anton Paar GmbH,

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Germany) and Sigmaplot (version 12.0; Jandel Scientific, Corte Madera, CA, USA),

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respectively.

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3. Results and discussion

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160 3.1. Stress sweeps

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Amplitude sweep has been used to distinguish weak and strong gels and give information

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about macromolecular structural strength. Strong gels have more critical strain than weak

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gels (Steffe, 1996). Most of soft solid foods have a linear viscoelastic regime within 0.1-

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2% strain (Heldman & Lund, 2007). Therefore, the stress sweep of BSG without STMP

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and cross-linked with STMP at different concentrations were carried out at a frequency of

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1 Hz and 25 oC. The dynamic moduli of the BSG in presence and lacking STMP as a

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function of stress are presented in Figs. 1 & 2. For all BSG concentrations, G' was more

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than G'' and both moduli remained constant and then decreased as stress increases. This

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reduction in G' showed breaking of bonds within the gel network and a transition from

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linear to non-linear behavior, which is reversible to the previous crosslinking network by

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removing the force. The BSG sample without STMP formed a relatively weak gel which

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was also reported in previous work (Rafe & Razavi, 2012). By comparison Figs. 1 & 2, it

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can be concluded that STMP addition to BSG can improve G' and G'' (except 0.5%) and

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as a result, cause to improve gel strength as well as linearity limit (Table 1). Similar

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pattern is also found for the phase angle (δ), which it was greater for STMP cross-linked

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than that of BSG lacking STMP at all concentrations, except 0.5%.

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In order to have a better understanding of gel strength, crossover point, fracture strain and

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fracture stress are calculated (Table 2). Many complex materials exhibit yield stress,

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which has been described as the biggest applied shear stress before material flow occurs

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(Walls et al., 2003). The crossover is considered to be a good indicator when the yield

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stress is exceeded, the structure ruptured and the flow behavior started (Knudsen et al.,

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2006). In our study, the crossover point of BSG without STMP was increased from 1.25-

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9.35 Pa by increasing solute content from 0.5-2% (Table 2), which is also in agreement

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reported previously, 2.99 and 9.38 Pa at 1 & 2%, respectively (Rafe & Razavi, 2012).

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The crossover point of STMP cross-linked BSG was increased from 0.631 to more than

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10 Pa, as BSG increased from 0.5-2%.

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The fracture strain was determined by plotting elastic stress, the product of the elastic

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modulus and strain (G′γ), as a function of increasing strain (Eissa et al., 2004; Walls et al.,

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2003). The elastic stress versus strain for BSG without STMP and cross-linked with

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STMP is shown in Fig 3. The results showed that by increasing BSG concentration,

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fracture strain was reduced, while the fracture stress was increased. It means critical

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strain of BSG became greater by increasing concentration and the experiment can be

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performed at larger strain value. Moreover, the BSG gels with STMP have a higher

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fracture stress than its counterpart without STMP (Table 2). In overall, STMP addition

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and increasing BSG concentration would improve “gel strength”.

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3.2. Scaling behavior and fractal analysis of BSG gels

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The maximum value of G' in the linear region at 20 oC is plotted as a function of BSG

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concentration in occurrence and lack of STMP (Fig. 4). The rheological data showed that

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both samples exhibited a power-law behavior or a scaling relationship with respect to

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particle concentration that can be fitted as: G'~ Cn; where n is the power-law exponent.

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The n values were positive for both gels and for the sample containing STMP (1.52) was

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more than that of BSG does not have STMP (1.36), suggesting that STMP addition play

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an important role in the structural changes in the gel network of BSG. However, the n

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value of BSG with and without STMP were less than most of protein gels, which varied

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from 2 to 7 (Hagiwara et al., 1997, 1998; Verheul et al., 1998; Ikeda et al., 1999;

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Kavanagh et al., 2000; Ould Eleya & Gunasekaran, 2002, 2004). In comparison with

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protein gels, increasing in particle concentration of a colloidal gel made from BSG had a

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little effect on the gel elasticity. Since, the n values of BSG in presence and lack of

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STMP were less than 2.0, it reflects that our measurements are too far from the critical

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gel concentration (percolation threshold) and the overall concentration dependence of G'

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follows a simple power law model (Kavanagh et al., 2000). Consequently, the corrections

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for the frequency dependence of modulus and instrumental artifacts are not necessary and

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the scaling law theories can be used for BSG gels.

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The limit of linearity or critical strain (γo) is defined as the end point of the linear region,

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where G' deviates more than 5% from its maximum value. It is shown in Fig. 5, as a

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function of particle concentration of BSG gels at 20 oC. The maximum linear strain or

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limiting strain of BSG gels with and without STMP showed a power-law relationship

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with BSG concentration as γo~ Cm, which m is the power-law exponent. For both BSG

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gels, negative m values were obtained. The m value of BSG cross-linked with STMP

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(0.49) was more than that of BSG without STMP (0.26). While, the m value of BSG was

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less than globular protein gels. Depending on the nature of the gels and preparation

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method, the m value extends extreme range of negative and positive values from -3.4 to

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5.3. The literatures have shown that β-lactoglobulin transparent gels at pH 7 had the

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lowest m value (-3.4) and the highest m value (5.3) was obtained for bovine serum

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albumin turbid gels (Wu & Morbidelli, 2001).

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The fractal dimension (df) is an indicator of the connectivity of the gel network, which

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can uniquely describe the structure of a particular cluster (Mellema, 2000). It is in the

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range of 1 for a completely random system like an inert gas to 3 for a completely ordered

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system such as a perfect crystal. The fractal dimension of BSG in presence and lacking

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STMP was measured by scaling models of Shih et al. (1990) and Wu and Morbidelli

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(2001). The results showed that both G' and γo were grown by increasing BSG

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concentration, exhibiting that the gel system can be considered in the weak-link regime.

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It is easily calculated df and x by applying Eqs. (2) and (3) according to Shih model.

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Fractal dimension was 2.34 and 2.26, and x values were 1.3 o 1.2 for BSG in presence

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and lacking STMP, respectively. It implies that less compact 3-D clusters had formed

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(scattered cotton or batting structure) and there is more space for the solvent in the BSG

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molecules, which has been presented by SEM images in our previous work (Rafe et al.,

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2013). In fact, the molecular structure of BSG made a layer like as cotton batting in

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which there is enough space for water to entangle by functional groups of BSG. The

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particular structure may be the reason of ultralow friction and high lubricant properties of

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BSG (Zhang et al., 2016). Therefore, several layers of BSG made a pad with high water

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absorption capacity. Furthermore, by adding STMP to BSG, the df was increased which

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revealed crosslinking of STMP with functional group of BSG such as alcohol groups and

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build a structure which is desirable for swelling and hydrogel preparations such as

247

hydrogels based on pullulan crosslinked with STMP (Lack et al., 2004). The df values of

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BSG were also in good agreement with most of other protein gels, where df values

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between 1.5 and 2.8 (Bremer et al., 1990; Vreeker et al., 1992; Hagiwara et al., 1997,

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1998; Verheul et al., 1998; Ikeda et al., 1999; Marangoni et al., 2000; Ould Eleya &

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Gunasekaran, 2004).

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The model of Wu and Morbidelli (2001) lets to obtain two additional parameters, β and

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α: The parameter α indicates the relative importance of the elastic contributions of both

254

inter- and intra-floc links, and can be determined based on the values of β and x (Eq. 7).

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According to the model, the parameter α allows identifying the different gelation regimes

256

(i.e. weak-link, transition, strong-link) prevailing in the system. The x value was

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estimated two times (1 and 1.3) to calculate α value according to the model of Wu and

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Morbidelli (2001). As expected, α value was obtained 1, indicating the weak-link regime

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of BSG gels. According to the theory of Shih et al. (1990), strong-link and weak-link

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regimes have α value 0 and 1, respectively.

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In order to compare the df values of BSG with computer simulations by box counting

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method, SEM image of BSG in our previous work was applied (Rafe et al., 2013).

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Results of simulations showed that fractal aggregates made in a diffusion-limited process

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indicating a fractal dimension of 1.8. The similar findings were also found for wide range

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of colloidal particles such as latex, silica, gold and white egg protein (Aubert & Cannell,

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1986; Lin et al., 1989; Weitz & Oliveria, 1984, Ould Eleya & Gunasekaran, 2004).

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Indeed, the df of biological macromolecules such as hydrocolloids and proteins have

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higher fractal dimensions than those forecasted by simulations, which may be attributed

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to the nature of biological aggregates and its restructuring (Aubert & Cannell, 1986). As a

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result, the fractal power-law model showed good agreement between fractal dimensions

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from gel modulus and structural approaches for BSG gels.

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3.3. Frequency sweep

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In order to evaluate the mechanical specification of BSG in the presence and lack of

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STMP, the frequency sweep test was carried out at strain 0.5%, 25oC and frequency from

276

0.1 to 10 Hz. The mechanical spectrums of BSG with and without STMP at different

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concentrations are provided in Figs 6 & 7. It can be found that BSG showed a typical gel-

278

like behavior, with G' exceeding G" throughout the range of frequency, which is

279

characteristic of a gel (Labropoulos & Hsu, 1996). Furthermore, G' and G" did not

280

crossover each other in the entire of frequency spectrum, and they showed very weak

281

dependency at low frequency, but had a higher dependency at high frequency (more than

282

10 Hz, data were not shown). The results demonstrate that intermolecular interaction as

283

well as instantaneous coaceration of molecular chains of BSG was increased that

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enhanced the viscoelastic behavior and indicating of weak structural aggregates of BSG

285

without STMP.

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The dynamic viscosity (η*) showed no indication of leveling out to a constant 'Newtonian'

287

value at all frequency ranges; although log η* decreased linearly with increasing log

288

frequency from 0.1 to 10 Hz. The slope of log η* in the linear region for BSG without

289

STMP was -0.84, substantially steeper than the maximum value of -0.76 observed for

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disordered polysaccharides interacting by topological entanglement (Haque et al., 1993;

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Heldman & Lund, 2007). Although, the slope of log η* for BSG cross-linked with STMP

292

(-0.94) was more than that of BSG without cross-linker, which is also indicate gel strength

293

would improve if BSG contains STMP.

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Increasing concentration of BSG contains STMP from 0.5 to 2% brings about increase in

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G' (from, ~14 to ~200 Pa at 1 Hz), so that the G' was increased more than that of BSG

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without STMP by increasing concentration (Figs 6 & 7). It can be seen, gelation occurs

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much more rapidly, when BSG contains STMP. It seems the presence of STMP drives

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bond formation leading to an alternative network structure and having a stronger gel

299

through making cross-linked polymer. In contrast, BSG lacking STMP took considerably

300

longer to have a significant change in δ. Furthermore, the one containing STMP is

301

actually stronger, perhaps due to the ability of STMP to form bonds between proteins as

302

well as the polysaccharide. STMP forms bonds by linking the alcohol groups of two

303

different polymer chains, but needs an alkaline environment to perform (Li et al., 2010).

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The mechanism of crosslinking STMP with hydrocolloids such as starch and pullulan has

305

been described to some extent (Lack et al., 2007; Dulong et al., 2011). Briefly, STMP

306

reacts with the polymer to give grafted sodium tripolyphosphate, which then it transform

307

to cross-linked chain at alkaline conditions. Due to the glucomannan backbone structure

308

of BSG, it can be participated in the reaction with STMP like as similar hydrocolloids

309

and formed a cross-linked polymer (Woo & Seib, 1997).

310

The tan δ values were determined as it evolves with frequency. It was found that both

311

gels of BSG had a tan δ of > 0.1 which is indicating paste-like weak gels such as WPI

312

and corn starch, while firm true gels had tan δ< 0.1 (Shim et al., 2001). Although, tan δ of

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BSG cross-linked with STMP has less than that of BSG exhibited the character of a

314

cross-linked network near to that of a “true gel”. By taking a deeper look at the value of

315

tan δ, it can be seen that tan δ of BSG cross-linked achieve to 0.2 at 2 and 1.5%, while tan

316

δ of BSG at 2% approach to about 0.3.

317

According to the polymer dynamics theory, the frequency dependency of G' values show

318

a strong power-law relation and the dependency of G' and G" with frequency can be

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described as G'~ ωp and G"~ ωq, respectively (Ferry, 1980), in which ω is oscillatory

320

frequency (Hz), p and q are indices of power law's storage and loss moduli, respectively.

321

The results showed that the frequency dependency of G' and G'' was decreased when

322

BSG concentration increased, as indicated by a decreasing value of the power law index

323

p and q (Table 3). The p value of BSG without STMP was close to the value reported for

324

κ-carrageenan and our previous work (Rodd et al., 2000; Rafe & Razavi, 2013). However,

325

the storage and loss indices (p, q) of BSG cross-linked with STMP were less than BSG

326

(~0.1 in comparison with 0.22) and they were positive, which were less than that of

327

reported for a Maxwellian fluid (G'~ω2 and G"~ ω). They did not find any statistical

328

significant difference between p and q values at different concentrations, indicating no

329

effect of concentration on the slopes’ values (p<0.05). Besides, by STMP addition to

330

BSG, frequency spectrum tends to a very low slope which is approved gel strength

331

improvement. Moreover, the power law indices were nearly similar at all concentrations

332

except 0.5%. It seems this behavior is related to liquid property of BSG at this

333

concentration.

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3.4. Temperature sweep

336

Temperature sweep test of BSG cross-linked with STMP at all concentrations was carried

337

out at 0.5% strain, 1 Hz frequency. The effect of temperature with time on G' of BSG at

338

all concentrations is shown in the Fig. 8. As it can be found, G' of BSG samples were

339

hardened with a mild slope during heating from 20 to 90 oC, and this behavior was

340

continued by keeping at 90 oC for 10 min. In addition, this increasing trend depends on

341

the concentration of BSG-STMP, and the storage modulus did not approach to the

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apparent plateau values. However, as it is shown in Fig. 8, G' was softened at the initial

343

of cooling, but hardened gradually and reach to the plateau on reheating section.

344

Increasing in G' value of the gel during the cooling period was also observed for BSG

345

samples without STMP, revealing a strengthening of the gel (Rafe & Razavi, 2012).

346

Similar increase in G' of gels by decreasing temperature has previously been found for

347

various systems, which is generally attributed to strengthening of attractive forces such as

348

van der Waals interactions and hydrogen bonding between hydrocolloid particles within

349

the gel network (Aguilera, 1995; Ould Eleya & Turgeon, 2000).

350

The gelation process was found reversible, and there was no significant difference

351

between G' in the rheological measurements between the reheating and cooling curves for

352

all concentrations of BSG-STMP (Fig. 8). It indicates the lack of thermal hysteresis, since

353

BSG gel formation was only occurred during cooling period. Such behavior in formation

354

and melting of k-carrageenan gel in the presence of gelling cations has also been reported

355

(Hermansson et al., 1991; Kohyama et al., 1996; Rochas & Rinaudo, 1980). Our results

356

have shown that cross-linked BSG is a thermo-reversible like as BSG without STMP and

357

against low-methoxy pectin and xanthan/caraob blend which have shown thermo-

358

irreversible property (Yoon & Gunasekaran, 2007, Rafe & Razavi, 2012). The thermo-

359

reversible gels show a thermal hysteresis between gelation and melting due to the

360

different energy requirements for association and disassociation of junction zones

361

(Nishinari et al., 1995).

362

The gel point (Tgel) is generally known as the point in time or temperature when at least

363

one aggregate extends from one side of a container to the opposite side and it happens

364

when G' becomes greater than the noise level (5-10 Pa). In practice, the G' of BSG was

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drastically increased by cooling to around 65 oC and the phase angle was also less than 1,

366

revealed that this temperature is the gelling temperature of BSG. Since, both temperature

367

and polymer concentrations are key factors on Tgel, gel formation should be accomplished

368

at isothermal heating (Kavangah et al., 2000). Whereas, the gelation of BSG was mainly

369

occurred by cooling and it was found 65 oC for the BSG gels (Rafe and Razavi, 2012).

370

Therefore, instead of obtaining gel times, “gel temperatures” were found that made the

371

kinetics very difficult to resolve. Consequently, the gelation kinetics should be measured

372

at isothermal conditions (65 oC after heating) to show Tgel as well as the critical gel

373

concentration (C0) of BSG in the future works.

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Conclusion

376

The scaling laws, fractal analysis, mechanical and thermo-rheological properties of basil

378

seed gum gels in presence or lack of STMP were investigated. BSG cross-linked with

379

STMP is an attractive system and revealed specific characteristics. Stress sweep tests

380

showed that BSG-STMP had more strength, yield stress and fracture stress than that of

381

BSG. As BSG concentration increased, fracture strain was decreased, but fracture stress

382

and crossover points were increased. Both G' and γo of hydrocolloid gels followed a

383

power-law dependency with BSG concentration. Fractal dimension of aggregates in BSG

384

gels were estimated based on the power-law exponent values using scaling models of

385

Shih et al. (1990) and Wu and Morbidelli (2001). As BSG concentration increased, both

386

G' and γo increased, revealing that the weak-link regime. Both scaling models showed

387

identical df values and the model of Wu and Morbidelli confirmed the weak-link regime

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of BSG. The df values of BSG lied well within the range of fractal dimension of protein

389

gels (1.5-2.8). However, it was slightly differed from df for diffusion-limited and reaction

390

limited cluster-cluster aggregation processes, which made it difficult to justify an

391

assumption regarding the nature of the aggregation process of the BSG systems.

392

Frequency sweep was confirmed weak-gel property of BSG and revealed that G' and G"

393

had very low frequency dependency. Although, by adding STMP to BSG, frequency

394

spectrum tends to a very low slope which is approved gel strength improvement. Both

395

gels of BSG had a tanδ of > 0.1, indicating paste-like weak gels, while tan δ of BSG

396

cross-linked with STMP has less than that of BSG exhibited the character of a cross-

397

linked network near to “true gel”. BSG was recognized as a thermo-reversible gel for

398

both samples and adding STMP did not have any effects on the gelation and its thermal

399

properties. Fractal analysis provides valuable structural knowledge on hydrocolloid gels

400

could be determined from simple rheological measurements. Finally, our findings

401

revealed that STMP can be cross-linked with functional group of BSG such as alcohol

402

groups and build a structure which is desirable for swelling and hydrogel preparations.

403

405

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1

Tables

2 3

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4 5 6

BSG status

Concentration (%)

G' (Pa)

G" (Pa)

δ

0.5

2.65±1.42a

1.38±0.50a

30.24±6.50b

19.31±1.13b

6.52±0.30a

18.80±0.52a

48.65±7.50b

16.54±3.11a 20.80±0.68a

103.42±13.67b

33.56±3.33a 19.42±1.63a

1 BSG without STMP 1.5 2

1.09±0.10b

0.82±0.03a

40.25±0.37a

1

21.08±1.14a

6.67±0.24a

20.26±1.52a

1.5

67.48±8.32a

18.23±2.22a 16.94±0.11b

2

123.82±30.11a

33.02±7.64a 15.73±0.34b

EP

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0.5

cross-linked by STMP

SC

Table 1. The effect of STMP addition on the LVE region parameters*

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*The results are means of three replicates. The statistical significant difference between BSG without STMP and

9

cross-linked by STMP is shown in alphabetical order.

10 11 12 13 14 15 16

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17 18 19

21 22

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20

Table 2. Cross over point, fracture stress and strain of BSG with and without STMP at different

24

concentrations * Concentration (%) 0.5 BSG without

1

STMP

1.5

cross-linked by

(%)

(Pa)

1.26±0.01a

0.22±0.01a

0.54±0.11a

2.86±0.02a

0.31±0.01a

2.81±0.20a

7.10±0.02b

0.29±0.02a

5.63±0.22b

9.35±0.15

0.13±0.01b

6.83±0.32b

0.5

0.63±0.01b

0.21±0.01a

0.20±0.08b

1

2.95±0.01a

0.32±0.02a

2.82±0.23a

1.5

7.94±0.02a

0.25±0.02a

6.40±0.24a

2

More than 10

0.16±0.02a

9.44±0.47a

EP

STMP

Fracture Stress

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2

Fracture Strain

Cross over point

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BSG status

SC

23

* The results are means of three replicates. The statistical significant difference between BSG without STMP and

26

cross-linked by STMP is shown in alphabetical order.

27 28 29 30 31

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32 33

35 36

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34

Table 3. The effect of STMP addition on BSG and the frequency dependency of G' and G"

38

described by a power law model * Concentration (%)

G' index (p)

R2

G" index (q)

R2

0.5

0.42±0.01a

0.99

0.41±0.01a

0.99

0.21±0.01a

0.99

0.23±0.01a

0.99

0.22±0.02a

0.99

0.22±0.02a

0.99

0.21±0.01a

0.99

0.23±0.01a

0.99

0.42±0.01a

0.99

0.32±0.01b

0.99

1

0.08±0.02b

0.99

0.11±0.02b

0.99

1.5

0.10±0.01b

0.99

0.10±0.01b

0.99

2

0.11±0.01b

0.99

0.10±0.01b

0.99

1 BSG without STMP 1.5 2

EP

cross-linked by STMP

TE D

0.5

M AN U

BSG status

SC

37

* The statistical significant difference between BSG without STMP and cross-linked by STMP is shown in

40

alphabetical order.

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1

Figures caption

2 Fig 1. Changes of G' (filled symbols) and G'' (open symbols) in stress sweep of BSG

4

without STMP at different concentrations (ƒ=1Hz and temperature 25°C)

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Fig. 2. Changes of G' (filled symbols) and G'' (open symbols) in stress sweep of cross-

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linked BSG with STMP at different concentrations (ƒ=1Hz and temperature 25°C)

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Fig. 3. Effect of increasing strain amplitude on Elastic stress G'γ, BSG without STMP

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(filled symbols) and BSG crosslinked by STMP (open symbols)

9

Fig. 4. Double-logarithmic plots of G′ values of BSG gels as a function of concentration

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3

(f = 1 Hz, strain 0.5%)

11

Fig. 5. Double-logarithmic plots of γ0 of BSG aggregates as function of concentration (f =

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1 Hz, temperature 25 oC)

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Fig. 6. Dynamic frequency spectrum of G' (filled symbols) and G'' (open symbols) of

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intact BSG at different concentrations (ƒ=1Hz and temperature 25°C).

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Fig. 7. Dynamic frequency spectrum of G' (filled symbols) and G'' (open symbols) of

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BSG crosslinked with STMP at different concentrations (ƒ=1Hz and temperature 20°C)

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Fig. 8. Network development of BSG cross-linked with STMP at different concentrations

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during controlled heating, cooling and reheating

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EP

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21 22 23

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24 25 26

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G',G" (Pa)

100

10

1

10

Stress (Pa)

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Fig 1. Changes of G' (filled symbols) and G'' (open symbols) in stress sweep of BSG

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AC C

EP

0.1 0.1

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2% 1.5% 1% 0.5%

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without STMP at different concentrations (ƒ=1Hz and temperature 25°C)

33 34 35 2

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SC

1000

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G',G"(Pa)

100

10

0.01 0.1

1

10

Stress(Pa)

EP

40

TE D

1

0.1

2% 1.5% 1% 0.5%

Fig 2. Changes of G' (filled symbols) and G'' (open symbols) in stress sweep of cross-

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linked BSG with STMP at different concentrations (ƒ=1Hz and temperature 25°C)

43 44

AC C

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45 46 47

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2% 1.5% 1% 0.5%

1

0.1

0.001

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Elastic stress (Pa)

10

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0.01

0.1

1

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(filled symbols) and BSG crosslinked by STMP (open symbols)

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AC C

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EP

52 53

Strain (%) Fig. 3. Effect of increasing strain amplitude on Elastic stress G′γ, BSG without STMP

58 59 60 4

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100

1

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TE D

G' (Pa)

BSG without STMP BSG cross-linked by STMP

66 67 68 69

Concentration (%)

Fig. 4. Double-logarithmic plots of G′ values of BSG gels as a function of concentration

AC C

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EP

1

(f = 1 Hz, strain 0.5%).

70 71 72 5

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1

79 80 81

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1

Particle volume fraction (%)

Fig. 5. Double-logarithmic plots of γ0 of BSG aggregates as function of concentration (f =

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TE D

0.1

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Limit of linearlity (%)

BSG without STMP BSG cross-linked by STMP

1 Hz, temperature 25 oC).

82 83 84

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85 86 87

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2% 1.5% 1% 0.5%

1

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Frequency (Hz)

AC C

0.1 0.1

89 90

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1

TE D

10

EP

G',G" (Pa)

100

91

Fig 6. Dynamic frequency spectrum of G' (filled symbols) and G'' (open symbols) of

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BSG without STMP at different concentrations (ƒ=1Hz and temperature 25°C).

93 94 95 96

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2% 1.5% 1% 0.5% 1

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Frequency (Hz)

AC C

0.01 0.1

TE D

1

0.1

101 102

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EP

G',G' (Pa)

100

103

Fig 7. Dynamic frequency spectrum of G' (filled symbols) and G'' (open symbols) of

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BSG crosslinked with STMP at different concentrations (ƒ=1Hz & temperature 25°C)

105 106 107 108

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0

116

10

o

60 50 40

20

30 20 30

40

50

Time, s

Fig. 8. Network development of crosslinked BSG at different concentrations during

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70

TE D

10

1

113 114

80

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Storage Modulus, Pa

1% 0.5%

controlled heating, cooling and reheating

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90

Temperature, C

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ACCEPTED MANUSCRIPT Research highlights


Scaling laws and fractal analysis of basil seed gum gels were investigated.
Elasticity and γo of gels followed the power law dependency with BSG concentration.

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The structural-mechanical properties of BSG cross-linked with STMP were improved.
Fractal analysis provides valuable structural knowledge of BSG gels through rheology.

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BSG-STMP showed more G', γo, df, and lower tan δ than that of native BSG.