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Alginate gels: Rupture characteristics as a function of the conditions of gel formation
Journal of Food Engineering 91 (2009) 448–454
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Alginate gels: Rupture characteristics as a function of the conditions of gel formation B.S. Roopa, Suvendu Bhattacharya * Food Engineering Department, Central Food Technological Research Institute, KRS Road, Mysore 570 020, Karnataka, India
a r t i c l e
i n f o
Article history: Received 3 June 2008 Received in revised form 17 September 2008 Accepted 25 September 2008 Available online 4 October 2008 Keywords: Soft solids Gelation Texture Large deformation Rupture
a b s t r a c t Alginate gels were formed by varying the concentrations of sodium alginate (0–3%), calcium chloride (0– 2%), pH (2–5), and temperature (0–40 °C) employing a second order central composite rotatable design. These gels were characterised with particular reference to texture parameters (linear limit, firmness and rupture characteristics like rupture force/strain/energy). Multiple correlation coefficients between 0.840 and 0.925 (significant at p 6 0.01) indicate the suitability of the second order polynomial in terms of these four variables. The concentration of sodium alginate mostly provides a negative effect on the rupture characteristics (significant at p 6 0.05) while calcium chloride has a positive (p 6 0.01) effect on the linear limit of gels. The hierarchical cluster analysis involving the response functions shows a strong similarity between these three rupture characteristics. The principle component analysis (PCA) can segregate the conditions like ‘no gel formation’ and ‘strong gel’ zones. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Food gels consist of mainly water with the solid character being provided by a space-filling network. Food gels show viscoelastic behaviour, which is dependent on time and strain rate (Walstra, 2003). Fracture or rupture mechanics for gels have been used to study the failure behaviour of gels (Stading et al., 1995). Generally, the compression curves show two prominent regions – elastic and plastic zone. In the initial stage, the sample is deformed elastically in a linear manner followed by the non-linear plastic deformation zone that may show major and minor rupture points. The type and number of rupture points in plastic zone depend on several factors, such as, the structure of material, moisture content, extent and speed of compression. The low values of rupture strain indicate that the samples are brittle (Ravi et al., 2007). The low magnitudes of maximum force indicate that the product offers less resistance and compresses elastically up to a small strain level until showing a rupture (minor or major) on the outer boundary to create a crack which is often known as ‘surface raisers’ (Bourne, 2002). When the imposed strain is further increased, the material fails by disintegrating into several pieces. Nevertheless, most of the theories on rupture/fracture postulates that rupture initiates from small cracks or weak regions. Rupture occurs when a strain of sufficient magnitude causes structural damage on a macroscopic scale resulting in a sudden decrease in force/stress values. Though the microscopic structural elements * Corresponding author. Tel.: +91 0821 2514874/2513910; fax: +91 0821 2517233. E-mail address: [email protected] (S. Bhattacharya). 0260-8774/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2008.09.023
have failed prior to visible fracture, the sample shows rupture only when the failed network gel structure reaches some noticeable macroscopic level. Such findings are useful in the development of food gels in which fruits, vegetables, juices, pulps and slurries may be incorporated, used to have restructured gel products. In this context, it is equally important to know how these textural properties depend on the gel forming conditions. One of the most important and useful properties of alginates is its ability to form gels by reaction with calcium salts (King, 1983). The alginate with a large percentage of polyguluronate segments forms a rigid and brittle gel, which tend to undergo syneresis, or loss of bound water. Alginate gels have been reported to exhibit strain-hardening behaviour during large deformation (Zhang et al., 2005). Mechanisms of strain hardening have been reported by a number of researches (Mitchell and Blanshard, 1976; Mancini et al., 1999; Groot et al., 1996; Truong and Daubert, 2000). Texture of gels can be characterised by deformation studies at low strains as well as testing under large deforming strains. Compression studies on alginate gels have been conducted by Zhang et al. (2005) and Truong and Daubert (2000) in which, fracture stress and strain have been calculated to measure the strength of gel. In a recent study, we reported the sensory assessments and textural attributes of alginate gels by employing the two-cycle compression method (Roopa and Bhattacharya, 2008). Data on detailed rupture characteristics of alginate gels as a function of gel forming variables are scarce. Further, the relationships among the various texture parameters of alginate gels are yet to be reported. In the present study, we apply the large deformation studies to have an understanding of the rupture characteristics while low strain tests have been used to characterise the gel.
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The objective of the present study is to investigate the effect of important variables (concentrations of sodium alginate and calcium chloride, pH and temperature) on gel formation including rupture behaviour and elastic property of the formed alginate gels by employing response surface methodology (RSM).
2. Materials and methods
(linear limit), Y2 (firmness), Y3 (rupture force), Y4 (rupture strain), Y5 (rupture energy) were approximated by a second-degree polynomial Eq. (1) with linear, quadratic and interaction effects (in coded level of variables) using the method of least squares (Little and Hills, 1978)
Y ijk ¼ b0 þ
n X
b i xi þ
i¼1
n X n X
bij xi xj þ 2ijk :
ð1Þ
i¼1 j¼1 ij
2.1. Materials Sodium alginate (sodium poly mannuronate) (C6H7O6Na) and calcium chloride were obtained from Loba Chemie and Ranbaxy Fine Chemicals, Bombay, India, respectively. Covered plastic petri dishes of diameter 40 mm and height 10 mm were used to set gels. 2.2. Gel formation Alginate gels were prepared by varying the concentration of sodium alginate (0–3%), pH (2–5), temperature (0–40 °C) and concentration of calcium chloride (0–2%) according to the preselected experimental design as detailed earlier by (Roopa and Bhattacharya, 2008). Five gels were prepared each time and the whole process of gel formation was repeated twice. 2.3. Texture The cylindrical gel samples (40 mm in diameter and 10 mm in height), after taking out from moulding container, were subjected to penetration testing at three locations of each sample by using a flat-bottomed circular stainless steel of 3 mm diameter (Jena and Bhattacharya, 2003). The gels were initially drained to remove the excess solution from the surface, if any, followed by penetration up to a depth of 5 mm. The tests were conducted at a crosshead speed of 1 mm s1 employing a texture-measuring instrument (Model # TAHDi, Stable Microsystems, Surrey, UK). The software provided by the manufacturer was used to calculate the different textural parameters from individual force-deformation curves. Five samples were examined each time. Textural properties related to rupture characteristics of gels were calculated. The linear elastic zone was denoted as linear limit, which was expressed as percent strain. Firmness was calculated from the initial slope of the linear zone of the force-deformation curve (Ravi et al., 2007). The rupture energy was obtained as the area under the curve till rupture point. The rupture force is the force at which material shows a sudden drop in force, and the corresponding strain was reported to be rupture strain (MacDonald and Hamann, 1992). Rupture strain was calculated as the ratio of the distance where rupture occurs to the height of sample at the beginning of the experiment, and was expressed as per cent basis. 2.4. Experimental design and analysis of data The experimental design employed was a four variable (five levels of each variable), second order central composite rotatable design (Myers, 1971) with six replications at the centre points (0, 0, 0, 0) in coded levels of variables (2, 1, 0, 1 and 2). The four independent variables were X1 (concentration of sodium alginate), X2 (pH), X3 (temperature of gel formation) and X4 (concentration of calcium chloride). The analysis of experimental results was conducted by following the response surface method (RSM; Myers, 1971; Khuri and Cornell, 1989) in which matrix operation was the main feature to find the coefficients of the second order regression equations. The experimental design in the actual (X) and coded (x) levels of variables is shown in Table 1. The response functions (Yijk) are Y1
The number of variables is denoted by n, while i, j, and k are integers. The coefficients of the polynomials are represented by b0, bi and bij, and ijk is the random error; when i < j, bij represents the interaction effects of the variables xi and xj. The response surface graphs were obtained from the regression equations in actual level of variables, keeping the response function on the Z axis with X and Y axes representing the two independent variables while keeping the other variables (third and fourth) constant at their centre points (corresponding to 0 in coded level of variables). The detailed analysis of variance (ANOVA) was conducted in coded level of variables to know the effects of individual variables. 2.5. Optimization Optimization was conducted by employing canonical analysis (Khuri and Cornell, 1989) wherein the levels of the variables (x1, x2, x3, and x4, within the experimental range) were determined to obtain the maximum values of the response functions. Optimisation of the response functions consists of the translation of the response function (yk) from the origin to the stationary points (Myers, 1971). Then the response function was expressed in terms of the new variables, the axes of which correspond to the principal axes of the contour system. Further, the roots (k1, k2, k3, and k4) of the auxiliary equation (k2 k + 1 = 0) were calculated initially to know the nature of optimum. The response function is maximized if all the roots have negative values, and minimum if all roots are positive. If some of the roots have positive values and some negative, then it is the situation of a saddle point (Bhattacharya and Prakash, 1994). 2.6. Statistical analysis and inter-relations Correlation matrix plot among the response functions were generated along with the correlation coefficients (r). The significance of r-value was judged at a probability level of 0.01. The texture parameters, such as, rupture energy, rupture force, rupture strain, firmness and linear limit were subjected to cluster analysis employing hierarchical tree structuring to know the similarity between independent variables (Jacobsen and Gunderson, 1986). The Euclidean distance was noted by considering the average neighbour method in which the closeness was obtained in terms of percent similarity. The textural parameters (linear limit (Y1), firmness (Y2), rupture force (Y3), rupture strain (Y4), rupture energy (Y5)), derived from the force-deformation curve of alginate gels, were subjected to principal component analysis (PCA) to explore the underlying relationship between the independent variables (concentrations of sodium alginate (X1), pH (X2), temperature (X3) and calcium chloride (X4) on the dependent variables (Y1, Y2, Y3, Y4 and Y5). The analysis was performed by using the statistical software STATISTICA ‘99 (StatSoft, Tulsa, OH, USA). The loading and scores of the results were superimposed in a 2D biplot (Lawless and Heymann 1998; Jena and Bhattacharya, 2003) to obtain the PCA plots for interpretation of results.
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Table 1 Design of experiments and response functions for alginate gels. Expt. no
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24a 25 26 27 28 29 30a
Variables (coded level)
Variables (actual level)
Response functions (textural parameters)
x1
x2
x3
x4
X1
X2
X3
X4
Linear limit (%)
Firmness (N mm1)
Rupture force (N)
Rupture strain (%)
Rupture energy (mJ)
1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 2 0 2
1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 2 0 0 2 0 0 0 0
1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 2 0 0 0 2 0 0 0 0 0
1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 2 0 0 2 0 0 0
0.75 2.25 0.75 0.75 1.50 1.50 0.75 2.25 2.25 2.25 2.25 1.50 0.75 2.25 0.75 2.25 2.25 1.50 0.75 0.75 1.50 1.50 1.50 1.50 1.50 1.50 1.50 3.00 1.50 0
2.75 4.25 4.25 4.25 3.50 3.50 2.75 4.25 4.25 2.75 2.75 3.50 4.25 2.75 2.75 4.25 2.75 3.50 4.25 2.75 3.50 3.50 2.00 3.50 3.50 5.00 3.50 3.50 3.50 3.50
10 30 10 30 20 20 10 30 10 10 10 20 10 30 30 10 30 20 30 30 0 20 20 20 40 20 20 20 20 20
1.50 0.50 1.50 1.50 1.00 1.00 0.50 1.50 1.50 1.50 0.50 1.00 0.50 0.50 0.50 0.50 1.50 1.00 0.50 1.50 1.00 1.00 1.00 0 1.00 1.00 2.00 1.00 1.00 1.00
2.62 1.26 1.50 6.41 6.11 6.11 2.95 5.5 2.11 4.22 2.05 5.38 2.01 1.99 3.28 1.80 3.42 5.38 4.42 4.72 5.52 5.25 5.25 – 4.92 6.84 3.96 2.11 5.25 –
0.16 0.09 0.22 0.12 0.22 0.22 0.13 0.15 0.14 0.14 0.17 0.12 0.25 0.15 0.11 0.12 0.22 0.12 0.14 0.14 0.16 0.20 0.27 – 0.15 0.21 0.14 0.13 0.20 –
1.57 0.21 1.22 1.21 2.29 2.29 1.52 0.25 0.48 0.89 0.42 1.15 0.89 0.34 1.24 0.11 0.44 1.15 0.89 1.59 0.60 2.21 1.95 – 0.56 2.58 2.17 0.16 2.21 –
67.11 30.17 50.42 45.72 71.56 71.56 55.27 22.41 33.36 31.78 29.44 53.38 55.00 21.65 58.34 27.01 39.50 53.38 71.56 54.87 24.27 45.91 54.11 – 35.44 76.54 51.12 2.23 45.91 –
3.10 0.80 4.00 6.00 5.10 5.10 3.70 1.83 1.70 1.50 1.72 3.20 3.00 0.50 2.20 0.40 1.19 3.20 5.10 3.10 1.79 5.10 6.90 – 1.50 5.90 6.50 1.34 5.10 –
X1, Concentration of sodium alginate; X2, pH; X3, Temperature; and X4, Concentration of calcium chloride. a Indicates that no gel was formed.
3. Results and discussion The texture of alginate gel is delicate in nature and complex in behaviour. It is difficult to express the texture of a gel by a single parameter. For example, firmness and linear limit indicate the material behaviour within elastic limit when no rupture is expected. On the other hand, rupture occurs at higher strain levels and outside the zone of elastic behaviour. Hence, rupture characteristics have also been included in the present work. Rupture force shows the requirement of force that is needed to bite. Rupture strain means at what level of compression or strain, the material fails. Furthermore, rupture energy indicates the extent of energy required to bite the sample. In summary, texture of a gel is a multi-dimensional characteristic that requires a few parameters for detailed characterisation. 3.1. Effect of variables of response functions The design of experiments and response functions for alginate gels are shown in Table 1. High multiple correlation coefficients (r) between 0.840 and 0.925 indicate the suitability of the second order polynomials to predict the response functions (Yijk) in terms of four independent variables (Table 2). The condensed analysis of variance for five response functions in coded level of variables is also shown in Table 2. The linear limit for gels is an indication of the extent of deformation of the sample can withstand without undergoing any significant damage in the structure. The magnitude of the linear limit is between 1.26% and 6.84%, and is positively correlated with the concentration of calcium chloride and temperature (Table 2). Further, the significant (p P 0.01) quadratic effect of the concentration of calcium chloride is negative meaning that at a high con-
centration of calcium chloride, there is a decrease in linear limit (Fig. 1A). In a similar manner, the quadratic effect of alginate concentration imparts a strong negative role on linear limit (Fig. 1B) such that high levels of alginates also decreases linear limit. This means that these gels formed with a high concentration alginate and/or calcium chloride lose their elastic character and exhibit a plastic deformation leading to rupture. The change in the force values due to deformation of sample during compression is exhibited by firmness. The firmness of alginate gels varies between 0.09 and 0.27 N mm1 (Table 1) and is mostly a function of the quadratic effects of calcium chloride and pH (Table 2). The interaction term of alginate and pH has a significant negative effect meaning that the effect of alginate on firmness is dependent on the level of pH (Fig. 2), and vice versa. A change in pH (acidic range) induces the inter-conversion of sodium alginate to alginic acid. Hence, at a low pH, the availability of residual calcium is high which reacts with alginate and enhances the process of gelation. Even at a low concentration of alginate like 0.75%, at a pH of 4.25, and with 1.5% of calcium chloride, the gel strength is high (Table 1). An increase in alginate concentration decreases the texture parameters. As the alginate concentration increases, the network cross-link density increases and gives rise to increasing fracture stress (Zhang et al., 2005). Another study by Sanderson and Ortega (1994) mentioned that hardness rapidly increases to a maximum (1.5–2.1 lbs force) and then gradually decreases with increasing calcium ion concentration. On the contrary, an increase in the concentration of calcium chloride usually increases the response functions. In unbuffered sodium alginate dispersion, even at a minimum level of calcium concentration, the gelation process is expected to occur, and hence, response functions will increase.
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B.S. Roopa, S. Bhattacharya / Journal of Food Engineering 91 (2009) 448–454 Table 2 Condensed analysis of variance (ANOVA) for response functions in coded level of variables. Source of variation
Constant x1 x2 x3 x4 x21 x22 x23 x24 x1x2 x1x3 x1x4 x2x3 x2x4 x3x4 R
Firmness (N mm1)
Linear limit (%)
Rupture force (N)
Rupture strain (%)
Rupture energy (mJ)
Coefficient of polynomial
F-Value
Coefficient of polynomial
F-Value
Coefficient of polynomial
F-Value
Coefficient of polynomial
F-Value
Coefficient of polynomial
F-Value
5.580 0.232 0.122 0.439 0.785 0.980 0.001 0.204 1.026 0.111 0.485 0.347 0.537 0.082 0.466 0.916***
– 0.942NS 0.369NS 4.744** 10.721*** 14.728*** 0.0001NS 1.122NS 16.171*** 0.202NS 3.857* 1.980NS 4.738** 0.111NS 3.565*
0.180 0.004 0.004 0.009 0.009 0.012 0.013 0.007 0.017 0.023 0.018 0.006 0.015 0.004 0.009 0.840***
– 0.239NS 0.384NS 1.681NS 1.153NS 1.925NS 3.739* 1.144NS 3.440* 6.528** 4.010* 0.577NS 2.980NS 0.233NS 1.073NS
1.715 0.368 0.062 0.042 0.195 0.342 0.068 0.352 0.121 0.041 0.024 0.004 0.040 0.005 0.025 0.859***
– 7.748** 0.312NS 0.143NS 2.190NS 5.920** 0.416NS 10.988*** 0.748NS 0.094NS 0.032NS 0.001NS 0.089NS 0.001NS 0.035NS
56.950 13.840 0.939 0.715 0.109 6.948 1.999 6.868 1.591 0.216 0.659 2.551 0.831 3.774 2.198 0.925***
– 32.800*** 0.214NS 0.124NS 0.002NS 7.300** 1.057NS 12.482*** 0.383NS 0.007NS 0.070NS 1.053NS 0.111NS 2.303NS 0.781NS
4.466 1.059 0.138 0.013 0.538 0.642 0.289 0.899 0.303 0.418 0.268 0.069 0.521 0.184 0.084 0.899***
– 13.321*** 0.320NS 0.003NS 3.442* 4.332* 1.536NS 14.849*** 0.968NS 1.961NS 0.806NS 0.054NS 3.054NS 0.381NS 0.079NS
X1, Concentration of sodium alginate; X2, pH; X3, Temperature; and X4, Concentration of calcium chloride; NS, Non-significant at p P 0.10. * Significant at p 6 0.10. ** Significant at p 6 0.05. *** Significant at p 6 0.01.
A 0.3 6 5 4 Linear limit 3 (%) 2 1 0 2
Firmness (N/mm)
0.2
0.1 0
0 pH 3.5 5
2
1 Calcium chloride (%)
Sodium 1.50 1 alginate (%)
-2 -1 2 1
3
2 5
0 3.5 pH B
Fig. 2. Firmness of alginate gels as a function of pH and sodium alginate.
B 6
parameters are mostly quadratic in nature but is possibly offset by the strong effects of the concentrations of alginate and calcium chloride.
Linear limit 3 (%)
3.2. Rupture characteristics
0 0
Sodium alginate (%)
2
1.5
3.5 pH 3
5
Fig. 1. Linear limit of gels as a function of independent variables.
Generally, a high level of temperature decreases the strong association between alginate and calcium ions (Sanderson and Ortega, 1994), and thereby affects the textural parameters. In the present investigation, the effect of temperature on these texture
During compression, as the imposed strain is increased, a gel shows rupture at the macromolecular level and the corresponding resistance offered by the sample is called rupture force. One or more macroscopic planes get ruptured at this stage, and show a peak in force-deformation curve. Rupture force for alginate gels is between 0.11 and 2.58 N and is mostly a function of alginate concentration (significant at p 6 0.05) and temperature (Table 2). A negative effect of temperature indicates that an increase in the gel forming temperature decreases the rupture force (Fig. 3). The strain at rupture is an index that signifies the ability of stretching or longness. For algin/calcium gels, the rupture strain ranges from 2.23% to 76.54% (Table 1). An increase in the concentration of alginate decreases the rupture strain in a curvilinear manner (Fig. 4A), which is also true for the effect of temperature. This means that an increase in alginate concentration produces a
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2.5
Rupture force (N)
1.5
0.5 2
-1
3.50
1
pH
0
0 20 Temperature (°C)
240
5
Fig. 3. Rupture force as influenced by temperature and pH.
gel that fractures easily without requiring a high strain level for rupturing. Hence, a low concentration of alginate in combination with low temperature possibly can offer a gel with chewy mouthfeel. The rupture energy, an indication of the energy required to induce rupture in gel by compression, is between 0.40 and 6.90 mJ,
A
and it decreases with an increase in alginate concentration (Fig. 5A). An increase in calcium chloride increases rupture energy (significant at p 6 0.10) while temperature decreases rupture energy in a quadratic manner (Fig. 5B). Rupture stress is generally related to the strength of a material. The area till the occurrence of rupture of the force-deformation curve can be integrated to obtain the work of rupture or energy for rupture. Walstra (2003) has mentioned about the term ‘toughness’ when a plot of stress versus strain has been employed. Rupture strain can be called ‘longness’ but is rarely used in practice. The term ‘shortness’ or ‘brittleness’ is a common term and may be defined as the reciprocal of fracture strain. If the fracture strain is high, it may be called ‘extensibility.’ In several cases, the material undergoes the phenomenon of yielding under stress. During yielding, some of the existing bonds between constituting molecules breaks while new bonds are also formed. Alginate gels are anionic polysaccharides that form eggbox junction zones in presence of divalent cation(s) (King, 1983). Damages in the network structures may occur due to large deformation. Most gels undergo an irreversible change in structure due to large deformation and part of the deformation is permanent. Most food gels possess cross links in the form of junctions and numerous entanglements. These structural aspects affect the linear region. The critical strain (Hencky’s strain) for alginate gel has been reported by Walstra (2003) to be 0.20 (corresponding engineering strain is 0.04). Level above this critical strain indicates that the modulus becomes a function of strain.
A
80
7 50 Rupture strain (%)
Rupture energy (mJ)
20
4 1
0 0
2 Sodium alginate (%)
1.5 3
2
0 3.5 pH
Sodium 1.5 alginate (%)
5
B
3.5 pH 3
5
B 60
5
Rupture strain 30 (%)
Rupture energy (mJ)
1
0
0 Temperature ( °C)
0 0
0
20 1 40
2
Calcium chloride (%)
Fig. 4. Rupture strain as a function of independent variables.
Temperature 20 (°C)
1 40
2
Calcium chloride (%)
Fig. 5. Rupture energy as a function of independent variables.
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3.3. Optimisation The optimum conditions for obtaining maximum linear limit, firmness, rupture force, rupture strain and rupture energy are shown in Table 3. The k values are negative and positive in character in each case indicating a situation of saddle points. It means that a true optimum, if present, is outside the range of the experimental range of the variables. Hence, a canonical search method was employed to obtain individual optimum (maximum) condition of these texture parameters within the range of experimental variables (Table 3). The optimum calcium chloride concentration ranges between 0.13% and 1.45% irrespective of the texture parameter selected. On the other hand, a gel with highest firmness is obtained with an alginate concentration of 0.56%, a pH of 5.0 and a low temperature of 5 °C. Further, a gel with high rupture characteristics means a gel that do not ruptures or fails easily. This type of gel can be obtained with 1.46% alginate and a pH of 2.0, and a low temperature and calcium chloride concentration of 11 °C and 0.13%, respectively. Hence, a good set gel is reflected by maximum rupture characteristics values that can be obtained with an alginate concentration of 0.7–1.4%, pH of 2.0–5.0, temperature of 11– 24 °C and concentration of calcium chloride in range of 0.1–1.4%.
Rupture energy
(0.864)
Rupture force
(0.764)
(0.822)
(0.574)
(0.556)
Rupture strain
(0.593)
Firmness Linear limit
(0.676)
(0.650)
(0.595)
(0.490)
Fig. 6. Matrix plot showing linear relationships among the texture indices. Values in brackets indicate correlation coefficients.
55.34
The inter-relations among the variables and/or response functions were obtained by employing matrix correlations (Fig. 6), hierarchical clustering (Fig. 7) and principal component analysis (PCA) (Fig. 8). The matrix plot (Fig. 6) is an indication of the linear interrelationship among these six texture indices (response functions). The highest correlation coefficient of 0.864 between rupture energy and rupture force (significant at p 6 0.01) means that an increase in rupture force increases energy values proportionately. On the other hand, linear limit and firmness show poor correlations with other response functions, and between them. The method of hierarchical clustering is one of the most popular classes of clustering techniques in food research and product development. A nested structure of clusters is characterised to understand the similarities between the response functions. The dendogram (Fig. 7) shows that the firmness is an outlier with the lowest similarity of about 55% with other indices meaning that the change in firmness hardly matches with the extent of change that occurs in other indices. Best similarity of about 85% exists be-
Similarity ( % )
3.4. Interrelationships 70.23
85.11
100.00 Rupture energy
Rupture force
Rupture Linear limit Firmness strain
Textural parameters Fig. 7. Dendogram of textural indices employing hierarchical cluster analysis.
Table 3 Optimized results for response functions. Linear limit (%)
Firmness (N mm1)
Rupture force (N)
Rupture strain (%)
Rupture energy (mJ)
0.233 0.330 0.829 1.283
0.022 0.007 0.019 0.021
0.071 0.121 0.335 0.363
2.899 1.945 7.063 7.301
0.408 0.307 0.675 0.982
Maximized optimum condition Coded level of x1 0.454 variables x2 1.617 x3 2.000 x4 0.725 Actual level of X1 1.159 X2 4.713 variables X3 40.000 X4 1.363
1.252 2.000 1.489 0.183 0.561 5.000 5.107 0.908
0.166 2.000 0.388 0.877 1.376 5.000 23.875 1.438
0.052 1.999 0.834 1.735 1.461 2.000 11.66 0.133
1.055 1.638 0.443 0.902 0.709 4.728 24.429 1.451
0.349
1.947
76.6514
7.405
Parameters
Roots of the auxiliary equation
k1 k2 k3 k4
Optimized response function
8.696
X1, Concentration of sodium alginate; X2, pH; X3, Temperature; X4, Concentration of calcium chloride.
Fig. 8. Principal component analysis (PCA) to show discrimination among the experiments, variables and textural parameters. Numbers: 1–30 indicate the experiment numbers as mentioned in Table 1. Variables – X1: Concentration of sodium alginate, X2: pH, X3: Temperature, and X4: Concentration of calcium chloride. Response functions – Y1: Linear limit, Y2: Firmness, Y3: Rupture force, Y4: Rupture strain and Y5: Rupture energy.
tween rupture force and energy, whereas rupture strain is also closely related with these two indices. It is interesting to note that all three indices related to rupture phenomenon form a cluster with a
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similarity of about 80%. If a cut-off similarity of 75% is selected to segregate all these texture indices, it appears that any of the rupture properties can be considered as the indicator parameters of gel texture. The five textural properties (linear limit (Y1), firmness (Y2), rupture force (Y3), rupture strain (Y4), rupture energy (Y5)), of the alginate gels were subjected to principal component analysis (PCA) to find their interrelationship with the four independent variables like concentration of alginate (X1), pH (X2), temperature (X3) and concentration of calcium chloride (X4). The first and second principal components (PC), accounted for about 43% and 13%, respectively, of the total variation in data (Fig. 8); they together explained the variance to about 57%. The response functions such as linear limit and firmness belong to the same quadrant, and both increase markedly with calcium chloride concentration, and to a lesser extent with alginate concentration. These two response functions are associated with similar slope on the positive side of the PC 1. The rupture characteristics like rupture force/strain/energy (Y3, Y4 and Y5), appear on the same quadrant with ten experimental points (1, 3, 4, 7, 12, 13, 18, 19, 20 and 26). These three textural parameters are significantly affected by pH (X2) and temperature (X3). Based on the results of the PC analysis of experimental design points, three major groups are possible though the existence of minor groups which can not be ruled out. The experimental points 24 and 30 located on the negative side forms the first group, i.e., ‘no gel formation’ zone. This indicates that the presence of sodium alginate (X1) as a gelling agent and calcium chloride (X4) as a cross-linking agent are mandatory to form a gel. On the contrary, the second group is the ‘strong gel’ region and is situated on the opposite side of ‘no gel’ zone (Fig. 8). The experiment numbers 5, 6, 22, 23, 27 and 29 (Table 1) are part of this region. Among the independent variables, the concentration of alginate (X1) was the most discriminate variable followed by the concentration of calcium chloride (X4) while pH (X2) and temperature (X4) has lesser effects as reflected by lesser magnitudes in the PCA plot. Therefore, the analysis employing PC shows a clear discrimination among the textural parameters obtained from the force-deformation characteristics and identified the textural parameters, which are closely associated with each other. 4. Conclusions Texture properties of alginate gels were described by using five response functions that were derived from the force-deformation curves. The response functions showed a high multiple correlation coefficients (r) between 0.840 and 0.925 (significant at p 6 0.01) indicating the suitability of second order polynomials to predict the response functions in terms of four independent variables such as concentrations of sodium alginate and calcium chloride, pH and temperature. The magnitude of the linear limit was between 1.26% and 6.84%, and was positively related with temperature and the concentration of calcium chloride. Alginate gels at a high concentration of sodium alginate lost their elastic characters and exhibited a plastic deformation leading to rupture. The firmness of alginate gels varied between 0.09 and 0.27 N mm1 and was mostly a function of the quadratic effects of calcium chloride and
pH. Rupture force for alginate gels was between 0.11 and 2.58 N and mostly depended on alginate concentration (significant at p 6 0.05) and temperature. An increase in alginate concentration produced a gel that ruptured easily without requiring high strain/energy level for rupturing. The matrix plot and dendogram showed the inter-relationships and correlation coefficients among the different textural indices. The analysis of PCA showed a clear discrimination among the textural parameters obtained from the force-deformation characteristics and identified the textural parameters, which are closely associated with each other. It was also possible to demarcate the zones like ‘no gel’ and ‘strong gel’ areas in the PCA plot. Acknowledgement The first author (Roopa B.S.) wishes to thank the Council of Scientific and Industrial Research (CSIR), New Delhi, India for providing the Senior Research Fellowship (SRF) to conduct the Ph. D. research programme.
References Bhattacharya, S., Prakash, M., 1994. Extrusion cooking of blends of rice and chickpea flour: a response surface analysis. Journal of Food Engineering 21, 315–330. Bourne, M.C., 2002. Food Texture and Viscosity: Concept and Measurement, 2nd ed. Academic press, New York. pp. 171–189. Groot, R.D., Bot, A., Agterof, W.G.M., 1996. Molecular theory of the yield behavior of a polymer gel: application to gelatin. Journal of Chemical Physics 104, 9220– 9233. Jacobsen, T., Gunderson, R.W., 1986. Applied cluster analysis. In: Piggott, J.R. (Ed.), Statistical Procedures in Food Research. Elsevier Applied Sciences, London, pp. 361–409. Jena, R., Bhattacharya, S., 2003. Viscoelastic characterization of rice gel. Journal of Texture Studies 34, 349–360. Khuri, A.I., Cornell, J.A., 1989. Response Surfaces: Designs and Analyses. Marcel Dekker, New York. pp. 19–69. King, A.H., 1983. Brown seaweed extracts (Alginates). In: Glicksman, M. (Ed.), Food Hydrocolloids. CRC Press, Florida, pp. 115–183. Lawless, H.T., Heymann, H., 1998. Sensory Evaluation of Food: Principles and Practices. Chapman & Hall, New York. pp. 606–608. Little, T.M., Hills, F.J., 1978. Agricultural Experimentation: Design and Analysis. John Wiley & Sons, New York. pp. 247–266. Macdonald, G.A., Hamann, D.D., 1992. Rheology and texture properties of surmi based food. In: Lanier, T.C., Lee, C.M. (Eds.), Surmi Technology. Marcel Dekker, New York, pp. 429–500. Mancini, M., Moresi, M., Rancini, R., 1999. Uniaxial compression and stress relaxation tests on alginate gels. Journal of Texture Studies 30, 639–657. Mitchell, J.R., Blanshard, J.M.V., 1976. Rheological properties of alginate gels. Journal of Texture Studies 7, 219–234. Myers, R.H., 1971. Response Surface Methodology. Allyn and Bacon, Boston. pp. 61– 106. Ravi, R., Roopa, B.S., Bhattacharya, S., 2007. Texture evaluation by uniaxial compression of some snack foods. Journal of Texture Studies 38, 135–152. Roopa, B.S., Bhattacharya, S., 2008. Alginate gels: I. Characterization of textural attributes. Journal of Food Engineering 85, 123–131. Sanderson, G.R., Ortega, D., 1994. Alginates and gellan gum: complementary gelling agents. In: Nishinari, K., Doi, E. (Eds.), Food Hydrocolloids: Structures, Properties and Functions. Plenum Press, New York, pp. 83–89. Stading, M., Langton, M., Hermansson, A.M., 1995. Small and large deformation studies of protein gels. Journal of Rheology 39, 1445–1450. Truong, V.D., Daubert, C.R., 2000. Comparative study of large deformation methods for assessing failure characteristics of selected food gels. Journal of Texture Studies 31, 335–353. Walstra, P., 2003. Soft solids. In: Physical Chemistry of Foods. Marcel Dekker, New York, pp. 683–771. Zhang, J., Daubert, C.R., Foegeding, E.A., 2005. Fracture analysis of alginate gels. Journal of Food Science 70, E425–E431.
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Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng
Alginate gels: Rupture characteristics as a function of the conditions of gel formation B.S. Roopa, Suvendu Bhattacharya * Food Engineering Department, Central Food Technological Research Institute, KRS Road, Mysore 570 020, Karnataka, India
a r t i c l e
i n f o
Article history: Received 3 June 2008 Received in revised form 17 September 2008 Accepted 25 September 2008 Available online 4 October 2008 Keywords: Soft solids Gelation Texture Large deformation Rupture
a b s t r a c t Alginate gels were formed by varying the concentrations of sodium alginate (0–3%), calcium chloride (0– 2%), pH (2–5), and temperature (0–40 °C) employing a second order central composite rotatable design. These gels were characterised with particular reference to texture parameters (linear limit, firmness and rupture characteristics like rupture force/strain/energy). Multiple correlation coefficients between 0.840 and 0.925 (significant at p 6 0.01) indicate the suitability of the second order polynomial in terms of these four variables. The concentration of sodium alginate mostly provides a negative effect on the rupture characteristics (significant at p 6 0.05) while calcium chloride has a positive (p 6 0.01) effect on the linear limit of gels. The hierarchical cluster analysis involving the response functions shows a strong similarity between these three rupture characteristics. The principle component analysis (PCA) can segregate the conditions like ‘no gel formation’ and ‘strong gel’ zones. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Food gels consist of mainly water with the solid character being provided by a space-filling network. Food gels show viscoelastic behaviour, which is dependent on time and strain rate (Walstra, 2003). Fracture or rupture mechanics for gels have been used to study the failure behaviour of gels (Stading et al., 1995). Generally, the compression curves show two prominent regions – elastic and plastic zone. In the initial stage, the sample is deformed elastically in a linear manner followed by the non-linear plastic deformation zone that may show major and minor rupture points. The type and number of rupture points in plastic zone depend on several factors, such as, the structure of material, moisture content, extent and speed of compression. The low values of rupture strain indicate that the samples are brittle (Ravi et al., 2007). The low magnitudes of maximum force indicate that the product offers less resistance and compresses elastically up to a small strain level until showing a rupture (minor or major) on the outer boundary to create a crack which is often known as ‘surface raisers’ (Bourne, 2002). When the imposed strain is further increased, the material fails by disintegrating into several pieces. Nevertheless, most of the theories on rupture/fracture postulates that rupture initiates from small cracks or weak regions. Rupture occurs when a strain of sufficient magnitude causes structural damage on a macroscopic scale resulting in a sudden decrease in force/stress values. Though the microscopic structural elements * Corresponding author. Tel.: +91 0821 2514874/2513910; fax: +91 0821 2517233. E-mail address: [email protected] (S. Bhattacharya). 0260-8774/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2008.09.023
have failed prior to visible fracture, the sample shows rupture only when the failed network gel structure reaches some noticeable macroscopic level. Such findings are useful in the development of food gels in which fruits, vegetables, juices, pulps and slurries may be incorporated, used to have restructured gel products. In this context, it is equally important to know how these textural properties depend on the gel forming conditions. One of the most important and useful properties of alginates is its ability to form gels by reaction with calcium salts (King, 1983). The alginate with a large percentage of polyguluronate segments forms a rigid and brittle gel, which tend to undergo syneresis, or loss of bound water. Alginate gels have been reported to exhibit strain-hardening behaviour during large deformation (Zhang et al., 2005). Mechanisms of strain hardening have been reported by a number of researches (Mitchell and Blanshard, 1976; Mancini et al., 1999; Groot et al., 1996; Truong and Daubert, 2000). Texture of gels can be characterised by deformation studies at low strains as well as testing under large deforming strains. Compression studies on alginate gels have been conducted by Zhang et al. (2005) and Truong and Daubert (2000) in which, fracture stress and strain have been calculated to measure the strength of gel. In a recent study, we reported the sensory assessments and textural attributes of alginate gels by employing the two-cycle compression method (Roopa and Bhattacharya, 2008). Data on detailed rupture characteristics of alginate gels as a function of gel forming variables are scarce. Further, the relationships among the various texture parameters of alginate gels are yet to be reported. In the present study, we apply the large deformation studies to have an understanding of the rupture characteristics while low strain tests have been used to characterise the gel.
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The objective of the present study is to investigate the effect of important variables (concentrations of sodium alginate and calcium chloride, pH and temperature) on gel formation including rupture behaviour and elastic property of the formed alginate gels by employing response surface methodology (RSM).
2. Materials and methods
(linear limit), Y2 (firmness), Y3 (rupture force), Y4 (rupture strain), Y5 (rupture energy) were approximated by a second-degree polynomial Eq. (1) with linear, quadratic and interaction effects (in coded level of variables) using the method of least squares (Little and Hills, 1978)
Y ijk ¼ b0 þ
n X
b i xi þ
i¼1
n X n X
bij xi xj þ 2ijk :
ð1Þ
i¼1 j¼1 ij
2.1. Materials Sodium alginate (sodium poly mannuronate) (C6H7O6Na) and calcium chloride were obtained from Loba Chemie and Ranbaxy Fine Chemicals, Bombay, India, respectively. Covered plastic petri dishes of diameter 40 mm and height 10 mm were used to set gels. 2.2. Gel formation Alginate gels were prepared by varying the concentration of sodium alginate (0–3%), pH (2–5), temperature (0–40 °C) and concentration of calcium chloride (0–2%) according to the preselected experimental design as detailed earlier by (Roopa and Bhattacharya, 2008). Five gels were prepared each time and the whole process of gel formation was repeated twice. 2.3. Texture The cylindrical gel samples (40 mm in diameter and 10 mm in height), after taking out from moulding container, were subjected to penetration testing at three locations of each sample by using a flat-bottomed circular stainless steel of 3 mm diameter (Jena and Bhattacharya, 2003). The gels were initially drained to remove the excess solution from the surface, if any, followed by penetration up to a depth of 5 mm. The tests were conducted at a crosshead speed of 1 mm s1 employing a texture-measuring instrument (Model # TAHDi, Stable Microsystems, Surrey, UK). The software provided by the manufacturer was used to calculate the different textural parameters from individual force-deformation curves. Five samples were examined each time. Textural properties related to rupture characteristics of gels were calculated. The linear elastic zone was denoted as linear limit, which was expressed as percent strain. Firmness was calculated from the initial slope of the linear zone of the force-deformation curve (Ravi et al., 2007). The rupture energy was obtained as the area under the curve till rupture point. The rupture force is the force at which material shows a sudden drop in force, and the corresponding strain was reported to be rupture strain (MacDonald and Hamann, 1992). Rupture strain was calculated as the ratio of the distance where rupture occurs to the height of sample at the beginning of the experiment, and was expressed as per cent basis. 2.4. Experimental design and analysis of data The experimental design employed was a four variable (five levels of each variable), second order central composite rotatable design (Myers, 1971) with six replications at the centre points (0, 0, 0, 0) in coded levels of variables (2, 1, 0, 1 and 2). The four independent variables were X1 (concentration of sodium alginate), X2 (pH), X3 (temperature of gel formation) and X4 (concentration of calcium chloride). The analysis of experimental results was conducted by following the response surface method (RSM; Myers, 1971; Khuri and Cornell, 1989) in which matrix operation was the main feature to find the coefficients of the second order regression equations. The experimental design in the actual (X) and coded (x) levels of variables is shown in Table 1. The response functions (Yijk) are Y1
The number of variables is denoted by n, while i, j, and k are integers. The coefficients of the polynomials are represented by b0, bi and bij, and ijk is the random error; when i < j, bij represents the interaction effects of the variables xi and xj. The response surface graphs were obtained from the regression equations in actual level of variables, keeping the response function on the Z axis with X and Y axes representing the two independent variables while keeping the other variables (third and fourth) constant at their centre points (corresponding to 0 in coded level of variables). The detailed analysis of variance (ANOVA) was conducted in coded level of variables to know the effects of individual variables. 2.5. Optimization Optimization was conducted by employing canonical analysis (Khuri and Cornell, 1989) wherein the levels of the variables (x1, x2, x3, and x4, within the experimental range) were determined to obtain the maximum values of the response functions. Optimisation of the response functions consists of the translation of the response function (yk) from the origin to the stationary points (Myers, 1971). Then the response function was expressed in terms of the new variables, the axes of which correspond to the principal axes of the contour system. Further, the roots (k1, k2, k3, and k4) of the auxiliary equation (k2 k + 1 = 0) were calculated initially to know the nature of optimum. The response function is maximized if all the roots have negative values, and minimum if all roots are positive. If some of the roots have positive values and some negative, then it is the situation of a saddle point (Bhattacharya and Prakash, 1994). 2.6. Statistical analysis and inter-relations Correlation matrix plot among the response functions were generated along with the correlation coefficients (r). The significance of r-value was judged at a probability level of 0.01. The texture parameters, such as, rupture energy, rupture force, rupture strain, firmness and linear limit were subjected to cluster analysis employing hierarchical tree structuring to know the similarity between independent variables (Jacobsen and Gunderson, 1986). The Euclidean distance was noted by considering the average neighbour method in which the closeness was obtained in terms of percent similarity. The textural parameters (linear limit (Y1), firmness (Y2), rupture force (Y3), rupture strain (Y4), rupture energy (Y5)), derived from the force-deformation curve of alginate gels, were subjected to principal component analysis (PCA) to explore the underlying relationship between the independent variables (concentrations of sodium alginate (X1), pH (X2), temperature (X3) and calcium chloride (X4) on the dependent variables (Y1, Y2, Y3, Y4 and Y5). The analysis was performed by using the statistical software STATISTICA ‘99 (StatSoft, Tulsa, OH, USA). The loading and scores of the results were superimposed in a 2D biplot (Lawless and Heymann 1998; Jena and Bhattacharya, 2003) to obtain the PCA plots for interpretation of results.
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Table 1 Design of experiments and response functions for alginate gels. Expt. no
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24a 25 26 27 28 29 30a
Variables (coded level)
Variables (actual level)
Response functions (textural parameters)
x1
x2
x3
x4
X1
X2
X3
X4
Linear limit (%)
Firmness (N mm1)
Rupture force (N)
Rupture strain (%)
Rupture energy (mJ)
1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 2 0 2
1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 2 0 0 2 0 0 0 0
1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 2 0 0 0 2 0 0 0 0 0
1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 2 0 0 2 0 0 0
0.75 2.25 0.75 0.75 1.50 1.50 0.75 2.25 2.25 2.25 2.25 1.50 0.75 2.25 0.75 2.25 2.25 1.50 0.75 0.75 1.50 1.50 1.50 1.50 1.50 1.50 1.50 3.00 1.50 0
2.75 4.25 4.25 4.25 3.50 3.50 2.75 4.25 4.25 2.75 2.75 3.50 4.25 2.75 2.75 4.25 2.75 3.50 4.25 2.75 3.50 3.50 2.00 3.50 3.50 5.00 3.50 3.50 3.50 3.50
10 30 10 30 20 20 10 30 10 10 10 20 10 30 30 10 30 20 30 30 0 20 20 20 40 20 20 20 20 20
1.50 0.50 1.50 1.50 1.00 1.00 0.50 1.50 1.50 1.50 0.50 1.00 0.50 0.50 0.50 0.50 1.50 1.00 0.50 1.50 1.00 1.00 1.00 0 1.00 1.00 2.00 1.00 1.00 1.00
2.62 1.26 1.50 6.41 6.11 6.11 2.95 5.5 2.11 4.22 2.05 5.38 2.01 1.99 3.28 1.80 3.42 5.38 4.42 4.72 5.52 5.25 5.25 – 4.92 6.84 3.96 2.11 5.25 –
0.16 0.09 0.22 0.12 0.22 0.22 0.13 0.15 0.14 0.14 0.17 0.12 0.25 0.15 0.11 0.12 0.22 0.12 0.14 0.14 0.16 0.20 0.27 – 0.15 0.21 0.14 0.13 0.20 –
1.57 0.21 1.22 1.21 2.29 2.29 1.52 0.25 0.48 0.89 0.42 1.15 0.89 0.34 1.24 0.11 0.44 1.15 0.89 1.59 0.60 2.21 1.95 – 0.56 2.58 2.17 0.16 2.21 –
67.11 30.17 50.42 45.72 71.56 71.56 55.27 22.41 33.36 31.78 29.44 53.38 55.00 21.65 58.34 27.01 39.50 53.38 71.56 54.87 24.27 45.91 54.11 – 35.44 76.54 51.12 2.23 45.91 –
3.10 0.80 4.00 6.00 5.10 5.10 3.70 1.83 1.70 1.50 1.72 3.20 3.00 0.50 2.20 0.40 1.19 3.20 5.10 3.10 1.79 5.10 6.90 – 1.50 5.90 6.50 1.34 5.10 –
X1, Concentration of sodium alginate; X2, pH; X3, Temperature; and X4, Concentration of calcium chloride. a Indicates that no gel was formed.
3. Results and discussion The texture of alginate gel is delicate in nature and complex in behaviour. It is difficult to express the texture of a gel by a single parameter. For example, firmness and linear limit indicate the material behaviour within elastic limit when no rupture is expected. On the other hand, rupture occurs at higher strain levels and outside the zone of elastic behaviour. Hence, rupture characteristics have also been included in the present work. Rupture force shows the requirement of force that is needed to bite. Rupture strain means at what level of compression or strain, the material fails. Furthermore, rupture energy indicates the extent of energy required to bite the sample. In summary, texture of a gel is a multi-dimensional characteristic that requires a few parameters for detailed characterisation. 3.1. Effect of variables of response functions The design of experiments and response functions for alginate gels are shown in Table 1. High multiple correlation coefficients (r) between 0.840 and 0.925 indicate the suitability of the second order polynomials to predict the response functions (Yijk) in terms of four independent variables (Table 2). The condensed analysis of variance for five response functions in coded level of variables is also shown in Table 2. The linear limit for gels is an indication of the extent of deformation of the sample can withstand without undergoing any significant damage in the structure. The magnitude of the linear limit is between 1.26% and 6.84%, and is positively correlated with the concentration of calcium chloride and temperature (Table 2). Further, the significant (p P 0.01) quadratic effect of the concentration of calcium chloride is negative meaning that at a high con-
centration of calcium chloride, there is a decrease in linear limit (Fig. 1A). In a similar manner, the quadratic effect of alginate concentration imparts a strong negative role on linear limit (Fig. 1B) such that high levels of alginates also decreases linear limit. This means that these gels formed with a high concentration alginate and/or calcium chloride lose their elastic character and exhibit a plastic deformation leading to rupture. The change in the force values due to deformation of sample during compression is exhibited by firmness. The firmness of alginate gels varies between 0.09 and 0.27 N mm1 (Table 1) and is mostly a function of the quadratic effects of calcium chloride and pH (Table 2). The interaction term of alginate and pH has a significant negative effect meaning that the effect of alginate on firmness is dependent on the level of pH (Fig. 2), and vice versa. A change in pH (acidic range) induces the inter-conversion of sodium alginate to alginic acid. Hence, at a low pH, the availability of residual calcium is high which reacts with alginate and enhances the process of gelation. Even at a low concentration of alginate like 0.75%, at a pH of 4.25, and with 1.5% of calcium chloride, the gel strength is high (Table 1). An increase in alginate concentration decreases the texture parameters. As the alginate concentration increases, the network cross-link density increases and gives rise to increasing fracture stress (Zhang et al., 2005). Another study by Sanderson and Ortega (1994) mentioned that hardness rapidly increases to a maximum (1.5–2.1 lbs force) and then gradually decreases with increasing calcium ion concentration. On the contrary, an increase in the concentration of calcium chloride usually increases the response functions. In unbuffered sodium alginate dispersion, even at a minimum level of calcium concentration, the gelation process is expected to occur, and hence, response functions will increase.
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B.S. Roopa, S. Bhattacharya / Journal of Food Engineering 91 (2009) 448–454 Table 2 Condensed analysis of variance (ANOVA) for response functions in coded level of variables. Source of variation
Constant x1 x2 x3 x4 x21 x22 x23 x24 x1x2 x1x3 x1x4 x2x3 x2x4 x3x4 R
Firmness (N mm1)
Linear limit (%)
Rupture force (N)
Rupture strain (%)
Rupture energy (mJ)
Coefficient of polynomial
F-Value
Coefficient of polynomial
F-Value
Coefficient of polynomial
F-Value
Coefficient of polynomial
F-Value
Coefficient of polynomial
F-Value
5.580 0.232 0.122 0.439 0.785 0.980 0.001 0.204 1.026 0.111 0.485 0.347 0.537 0.082 0.466 0.916***
– 0.942NS 0.369NS 4.744** 10.721*** 14.728*** 0.0001NS 1.122NS 16.171*** 0.202NS 3.857* 1.980NS 4.738** 0.111NS 3.565*
0.180 0.004 0.004 0.009 0.009 0.012 0.013 0.007 0.017 0.023 0.018 0.006 0.015 0.004 0.009 0.840***
– 0.239NS 0.384NS 1.681NS 1.153NS 1.925NS 3.739* 1.144NS 3.440* 6.528** 4.010* 0.577NS 2.980NS 0.233NS 1.073NS
1.715 0.368 0.062 0.042 0.195 0.342 0.068 0.352 0.121 0.041 0.024 0.004 0.040 0.005 0.025 0.859***
– 7.748** 0.312NS 0.143NS 2.190NS 5.920** 0.416NS 10.988*** 0.748NS 0.094NS 0.032NS 0.001NS 0.089NS 0.001NS 0.035NS
56.950 13.840 0.939 0.715 0.109 6.948 1.999 6.868 1.591 0.216 0.659 2.551 0.831 3.774 2.198 0.925***
– 32.800*** 0.214NS 0.124NS 0.002NS 7.300** 1.057NS 12.482*** 0.383NS 0.007NS 0.070NS 1.053NS 0.111NS 2.303NS 0.781NS
4.466 1.059 0.138 0.013 0.538 0.642 0.289 0.899 0.303 0.418 0.268 0.069 0.521 0.184 0.084 0.899***
– 13.321*** 0.320NS 0.003NS 3.442* 4.332* 1.536NS 14.849*** 0.968NS 1.961NS 0.806NS 0.054NS 3.054NS 0.381NS 0.079NS
X1, Concentration of sodium alginate; X2, pH; X3, Temperature; and X4, Concentration of calcium chloride; NS, Non-significant at p P 0.10. * Significant at p 6 0.10. ** Significant at p 6 0.05. *** Significant at p 6 0.01.
A 0.3 6 5 4 Linear limit 3 (%) 2 1 0 2
Firmness (N/mm)
0.2
0.1 0
0 pH 3.5 5
2
1 Calcium chloride (%)
Sodium 1.50 1 alginate (%)
-2 -1 2 1
3
2 5
0 3.5 pH B
Fig. 2. Firmness of alginate gels as a function of pH and sodium alginate.
B 6
parameters are mostly quadratic in nature but is possibly offset by the strong effects of the concentrations of alginate and calcium chloride.
Linear limit 3 (%)
3.2. Rupture characteristics
0 0
Sodium alginate (%)
2
1.5
3.5 pH 3
5
Fig. 1. Linear limit of gels as a function of independent variables.
Generally, a high level of temperature decreases the strong association between alginate and calcium ions (Sanderson and Ortega, 1994), and thereby affects the textural parameters. In the present investigation, the effect of temperature on these texture
During compression, as the imposed strain is increased, a gel shows rupture at the macromolecular level and the corresponding resistance offered by the sample is called rupture force. One or more macroscopic planes get ruptured at this stage, and show a peak in force-deformation curve. Rupture force for alginate gels is between 0.11 and 2.58 N and is mostly a function of alginate concentration (significant at p 6 0.05) and temperature (Table 2). A negative effect of temperature indicates that an increase in the gel forming temperature decreases the rupture force (Fig. 3). The strain at rupture is an index that signifies the ability of stretching or longness. For algin/calcium gels, the rupture strain ranges from 2.23% to 76.54% (Table 1). An increase in the concentration of alginate decreases the rupture strain in a curvilinear manner (Fig. 4A), which is also true for the effect of temperature. This means that an increase in alginate concentration produces a
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2.5
Rupture force (N)
1.5
0.5 2
-1
3.50
1
pH
0
0 20 Temperature (°C)
240
5
Fig. 3. Rupture force as influenced by temperature and pH.
gel that fractures easily without requiring a high strain level for rupturing. Hence, a low concentration of alginate in combination with low temperature possibly can offer a gel with chewy mouthfeel. The rupture energy, an indication of the energy required to induce rupture in gel by compression, is between 0.40 and 6.90 mJ,
A
and it decreases with an increase in alginate concentration (Fig. 5A). An increase in calcium chloride increases rupture energy (significant at p 6 0.10) while temperature decreases rupture energy in a quadratic manner (Fig. 5B). Rupture stress is generally related to the strength of a material. The area till the occurrence of rupture of the force-deformation curve can be integrated to obtain the work of rupture or energy for rupture. Walstra (2003) has mentioned about the term ‘toughness’ when a plot of stress versus strain has been employed. Rupture strain can be called ‘longness’ but is rarely used in practice. The term ‘shortness’ or ‘brittleness’ is a common term and may be defined as the reciprocal of fracture strain. If the fracture strain is high, it may be called ‘extensibility.’ In several cases, the material undergoes the phenomenon of yielding under stress. During yielding, some of the existing bonds between constituting molecules breaks while new bonds are also formed. Alginate gels are anionic polysaccharides that form eggbox junction zones in presence of divalent cation(s) (King, 1983). Damages in the network structures may occur due to large deformation. Most gels undergo an irreversible change in structure due to large deformation and part of the deformation is permanent. Most food gels possess cross links in the form of junctions and numerous entanglements. These structural aspects affect the linear region. The critical strain (Hencky’s strain) for alginate gel has been reported by Walstra (2003) to be 0.20 (corresponding engineering strain is 0.04). Level above this critical strain indicates that the modulus becomes a function of strain.
A
80
7 50 Rupture strain (%)
Rupture energy (mJ)
20
4 1
0 0
2 Sodium alginate (%)
1.5 3
2
0 3.5 pH
Sodium 1.5 alginate (%)
5
B
3.5 pH 3
5
B 60
5
Rupture strain 30 (%)
Rupture energy (mJ)
1
0
0 Temperature ( °C)
0 0
0
20 1 40
2
Calcium chloride (%)
Fig. 4. Rupture strain as a function of independent variables.
Temperature 20 (°C)
1 40
2
Calcium chloride (%)
Fig. 5. Rupture energy as a function of independent variables.
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3.3. Optimisation The optimum conditions for obtaining maximum linear limit, firmness, rupture force, rupture strain and rupture energy are shown in Table 3. The k values are negative and positive in character in each case indicating a situation of saddle points. It means that a true optimum, if present, is outside the range of the experimental range of the variables. Hence, a canonical search method was employed to obtain individual optimum (maximum) condition of these texture parameters within the range of experimental variables (Table 3). The optimum calcium chloride concentration ranges between 0.13% and 1.45% irrespective of the texture parameter selected. On the other hand, a gel with highest firmness is obtained with an alginate concentration of 0.56%, a pH of 5.0 and a low temperature of 5 °C. Further, a gel with high rupture characteristics means a gel that do not ruptures or fails easily. This type of gel can be obtained with 1.46% alginate and a pH of 2.0, and a low temperature and calcium chloride concentration of 11 °C and 0.13%, respectively. Hence, a good set gel is reflected by maximum rupture characteristics values that can be obtained with an alginate concentration of 0.7–1.4%, pH of 2.0–5.0, temperature of 11– 24 °C and concentration of calcium chloride in range of 0.1–1.4%.
Rupture energy
(0.864)
Rupture force
(0.764)
(0.822)
(0.574)
(0.556)
Rupture strain
(0.593)
Firmness Linear limit
(0.676)
(0.650)
(0.595)
(0.490)
Fig. 6. Matrix plot showing linear relationships among the texture indices. Values in brackets indicate correlation coefficients.
55.34
The inter-relations among the variables and/or response functions were obtained by employing matrix correlations (Fig. 6), hierarchical clustering (Fig. 7) and principal component analysis (PCA) (Fig. 8). The matrix plot (Fig. 6) is an indication of the linear interrelationship among these six texture indices (response functions). The highest correlation coefficient of 0.864 between rupture energy and rupture force (significant at p 6 0.01) means that an increase in rupture force increases energy values proportionately. On the other hand, linear limit and firmness show poor correlations with other response functions, and between them. The method of hierarchical clustering is one of the most popular classes of clustering techniques in food research and product development. A nested structure of clusters is characterised to understand the similarities between the response functions. The dendogram (Fig. 7) shows that the firmness is an outlier with the lowest similarity of about 55% with other indices meaning that the change in firmness hardly matches with the extent of change that occurs in other indices. Best similarity of about 85% exists be-
Similarity ( % )
3.4. Interrelationships 70.23
85.11
100.00 Rupture energy
Rupture force
Rupture Linear limit Firmness strain
Textural parameters Fig. 7. Dendogram of textural indices employing hierarchical cluster analysis.
Table 3 Optimized results for response functions. Linear limit (%)
Firmness (N mm1)
Rupture force (N)
Rupture strain (%)
Rupture energy (mJ)
0.233 0.330 0.829 1.283
0.022 0.007 0.019 0.021
0.071 0.121 0.335 0.363
2.899 1.945 7.063 7.301
0.408 0.307 0.675 0.982
Maximized optimum condition Coded level of x1 0.454 variables x2 1.617 x3 2.000 x4 0.725 Actual level of X1 1.159 X2 4.713 variables X3 40.000 X4 1.363
1.252 2.000 1.489 0.183 0.561 5.000 5.107 0.908
0.166 2.000 0.388 0.877 1.376 5.000 23.875 1.438
0.052 1.999 0.834 1.735 1.461 2.000 11.66 0.133
1.055 1.638 0.443 0.902 0.709 4.728 24.429 1.451
0.349
1.947
76.6514
7.405
Parameters
Roots of the auxiliary equation
k1 k2 k3 k4
Optimized response function
8.696
X1, Concentration of sodium alginate; X2, pH; X3, Temperature; X4, Concentration of calcium chloride.
Fig. 8. Principal component analysis (PCA) to show discrimination among the experiments, variables and textural parameters. Numbers: 1–30 indicate the experiment numbers as mentioned in Table 1. Variables – X1: Concentration of sodium alginate, X2: pH, X3: Temperature, and X4: Concentration of calcium chloride. Response functions – Y1: Linear limit, Y2: Firmness, Y3: Rupture force, Y4: Rupture strain and Y5: Rupture energy.
tween rupture force and energy, whereas rupture strain is also closely related with these two indices. It is interesting to note that all three indices related to rupture phenomenon form a cluster with a
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similarity of about 80%. If a cut-off similarity of 75% is selected to segregate all these texture indices, it appears that any of the rupture properties can be considered as the indicator parameters of gel texture. The five textural properties (linear limit (Y1), firmness (Y2), rupture force (Y3), rupture strain (Y4), rupture energy (Y5)), of the alginate gels were subjected to principal component analysis (PCA) to find their interrelationship with the four independent variables like concentration of alginate (X1), pH (X2), temperature (X3) and concentration of calcium chloride (X4). The first and second principal components (PC), accounted for about 43% and 13%, respectively, of the total variation in data (Fig. 8); they together explained the variance to about 57%. The response functions such as linear limit and firmness belong to the same quadrant, and both increase markedly with calcium chloride concentration, and to a lesser extent with alginate concentration. These two response functions are associated with similar slope on the positive side of the PC 1. The rupture characteristics like rupture force/strain/energy (Y3, Y4 and Y5), appear on the same quadrant with ten experimental points (1, 3, 4, 7, 12, 13, 18, 19, 20 and 26). These three textural parameters are significantly affected by pH (X2) and temperature (X3). Based on the results of the PC analysis of experimental design points, three major groups are possible though the existence of minor groups which can not be ruled out. The experimental points 24 and 30 located on the negative side forms the first group, i.e., ‘no gel formation’ zone. This indicates that the presence of sodium alginate (X1) as a gelling agent and calcium chloride (X4) as a cross-linking agent are mandatory to form a gel. On the contrary, the second group is the ‘strong gel’ region and is situated on the opposite side of ‘no gel’ zone (Fig. 8). The experiment numbers 5, 6, 22, 23, 27 and 29 (Table 1) are part of this region. Among the independent variables, the concentration of alginate (X1) was the most discriminate variable followed by the concentration of calcium chloride (X4) while pH (X2) and temperature (X4) has lesser effects as reflected by lesser magnitudes in the PCA plot. Therefore, the analysis employing PC shows a clear discrimination among the textural parameters obtained from the force-deformation characteristics and identified the textural parameters, which are closely associated with each other. 4. Conclusions Texture properties of alginate gels were described by using five response functions that were derived from the force-deformation curves. The response functions showed a high multiple correlation coefficients (r) between 0.840 and 0.925 (significant at p 6 0.01) indicating the suitability of second order polynomials to predict the response functions in terms of four independent variables such as concentrations of sodium alginate and calcium chloride, pH and temperature. The magnitude of the linear limit was between 1.26% and 6.84%, and was positively related with temperature and the concentration of calcium chloride. Alginate gels at a high concentration of sodium alginate lost their elastic characters and exhibited a plastic deformation leading to rupture. The firmness of alginate gels varied between 0.09 and 0.27 N mm1 and was mostly a function of the quadratic effects of calcium chloride and
pH. Rupture force for alginate gels was between 0.11 and 2.58 N and mostly depended on alginate concentration (significant at p 6 0.05) and temperature. An increase in alginate concentration produced a gel that ruptured easily without requiring high strain/energy level for rupturing. The matrix plot and dendogram showed the inter-relationships and correlation coefficients among the different textural indices. The analysis of PCA showed a clear discrimination among the textural parameters obtained from the force-deformation characteristics and identified the textural parameters, which are closely associated with each other. It was also possible to demarcate the zones like ‘no gel’ and ‘strong gel’ areas in the PCA plot. Acknowledgement The first author (Roopa B.S.) wishes to thank the Council of Scientific and Industrial Research (CSIR), New Delhi, India for providing the Senior Research Fellowship (SRF) to conduct the Ph. D. research programme.
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