Biomacromolecules 2000, 1, 730-738
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New Insight into Agarose Gel Mechanical Properties Vale´ ry Normand,*,† Didier L. Lootens, Eleonora Amici, Kevin P. Plucknett, and Pierre Aymard Unilever Research Colworth, Colworth House, Sharnbrook, Bedfordshire, MK44 1LQ, U.K. Received July 12, 2000; Revised Manuscript Received August 31, 2000
The current study focuses on the effects of the molecular weight on the mechanical behavior of agarose gels. The small strain rheology and large strain deformation/failure behavior of three different molecular weight agarose gels have been examined, with the results expressed in term of molar concentration. For small deformation strains, the gelation temperature at low concentrations and the critical concentration for gel formation are strongly affected by the molecular weight. In addition, the elasticity of the network is also very sensitive to this parameter. It has been demonstrated that the experimental gelation cure curves can be superimposed on a universal gelation master curve, independent of the cure time. This would indicate selfsimilarity of the network at different scales, irrespective of concentration. A relationship between the elastic modulus and the molecular weight has been extracted from these results, where the molecular weight dependence exhibits a power law exponent of 2.42. For large deformation strains, the Poisson ratio has been estimated to be 0.5 for each of the agarose types examined, which indicates that these gels are incompressible. The strain at failure is largely dependent on the molecular weight, and is essentially independent of the biopolymer concentration. This result highlights the fact that the strain at failure is sensitive to the connectivity distances in the gel network. However, the failure stress and Young’s modulus of agarose gels show a dependence on both concentration and molecular weight. The observations regarding Young’s modulus are in good agreement with those found for small deformation strain rheology for the shear modulus. One of the primary advantages of using the lowest molecular weight agarose is that higher molar concentrations can be reached (more molecules per unit volume). However, the mechanical response of agarose gels is very sensitive to the molecular weight at fixed molar concentration, and if the present results are extrapolated to very low molecular weight, it can be suggested that below a limiting molecular weight a percolating network will not be formed, as suggested by the Cascade model (Carbohydr. Polym. 1994, 23, 247-251). This speculation is based on the influence of the “connectivity” at long distances, which influences the strain at failure (when the strain at failure is zero, the system is not connective). 1. Introduction It is important to understand the physical behavior of biopolymer food gels, as they are being continually introduced into industrial food products (i.e., ice creams, low fat spreads, dressings, etc.). It is therefore of considerable interest for the food industry to investigate the characteristics of these gelling biopolymers, to both lower production costs and improve product quality. In the present work, the gelling polysaccharide agarose has been selected as a “model” biopolymer, and the relationships that link its gel properties to number-average molecular weight have been investigated. Agarose is a linear polysaccharide extracted from marine red algae, and consists of β-1,3 linked D-galactose and R-1,4 linked 3,6-anhydro-RL-galactose residues (see Figure 1). Sometimes, traces of sulfate groups can be present on the agarose chain, and may modify the gel properties. In all the samples used here, the sulfate content is given by the supplier to be below 0.2% of the dry matter. In this study, the effect of sulfate groups will therefore be neglected, and to simplify, † Current address: Fermenich S.A., 1 Route des Jeunes, CH-1211 Geneva 8, Switzerland.
Figure 1. Fundamental unit of agarose, M ) 306 g‚mol-1.
agarose is assumed here to be chemically and electrically neutral. Agarose forms a gel when a homogeneous solution is cooled from 99 °C to a temperature below the ordering temperature (coil-helix transition), which is around 35 °C for normal agarose. The gel is formed when an infinite threedimensional network of agarose fibers, formed by helices of agarose, develops. The melting of agarose gels occurs at a comparatively higher temperature (around 85 °C). This setting-melting hysteresis behavior, observed by a variety of techniques, has been attributed to the occurrence of aggregation of helices. The melting transition is believed to be the true equilibrium process of aggregate-helix conversion, whereas the setting is a kinetically controlled nucleationbased process, in which the rate-limiting step is the helixhelix aggregation.2,3
10.1021/bm005583j CCC: $19.00 © 2000 American Chemical Society Published on Web 11/16/2000
Biomacromolecules, Vol. 1, No. 4, 2000 731
Agarose Gel Mechanical Properties
The structure and physical behavior of agarose gels have been extensively studied during the past 20 years. Watase and Nishinari4 have reported a complete investigation of the effects of molecular weight upon the rheological characteristics of agarose gels in 1983. In that work, the behavior of agarose was compared to previous investigations on alternative biopolymer gel systems, such as gelatin,5 alginates,6 and κ-carrageenan.7 The purpose of the present study is to reexamine the effects of number-average molecular weight on both the gelation properties (small deformation rheology) and large deformation mechanical properties of agarose gels4 using a different approach. In all the studies cited above, regardless of the nature of the biopolymer, a fall in elastic modulus has been demonstrated when the molecular weight is lowered at a constant weight concentration, following the relationship5
xG′ ∝ Mw c
Figure 2. Molecular weight distributions of the three different agarose species tested.
(1)
where the concentration c is expressed in g‚L-1. However, this relationship is rather empirical and was first proposed for application to gelatin gels. It has recently been shown, for gelatin gels, that the relationship between molecular weight and modulus is more complex and the influence of the contribution of each of the molecular weight fractions must be considered in the expression of the modulus.8 Agarose gel formation and aging mechanisms are different from those occurring in gelatin gels. Small differences in agarose gelation temperature have been observed for agarose solutions with different intrinsic viscosities. This is believed to be a linear function of the average molecular weight. In addition, differences have been noted for the agarose gel modulus, failure properties, and melting temperatures. In the current work, the effect of the molecular weight (numberaverage) on agarose gel properties (elasticity and failure behavior) is investigated from the perspective of the concentration of chains involved in the gel network, rather than simply the monomer concentration. 2. Materials and Methods Two different types of purified agarose (supplied by Sigma) have been used in the context of this study: a high viscosity agarose (Type I-A, low EEO, A-0169, H, lot 56H1046) and a low viscosity agarose obtained after enzymatic degradation, which was provided in two different lots (Type XII, A-7299, L1, lot 17H0207, and L2, lot 88H0070). The molecular weight distribution of these biopolymers have been estimated at 60 °C using size exclusion chromatography with multiangle laser light scattering (HPSEC-MALLS). The concentration of the agarose solution used for this determination was 0.03% w/w in 100 mM LiCl solution. This solution was first heated to 95 °C for 30 min before being cooled to 60 °C. The refractive index provides information on the amount of agarose being eluted, while the light scattered is proportional to the product of the concentration and the apparent mass, at a given angle (cMapp). Measurement at several angles and several concentrations (Zimm plot) allows extrapolation of Mw and the
Table 1. Weight Average Molecular Weight (Mw), Number Average Molecular Weight (Mn), and Polydispersity for the Three Batches of Agarose Investigated sample
Mw (g‚mol-1)
Mn (g‚mol-1)
Mw/Mn
56H1046 type 1-A (H) 88H0070 type XII (L2) 17H0207 type XII (L1)
162 000 132 000 116 000
93 590 73 090 63 150
1.731 1.806 1.837
radius of gyration Rg. Typical chromatograms for the three agarose variants are shown in Figure 2, and corresponding molecular weight data (weight-average molecular weight and polydispersity) for these samples are summarized in Table 1. Distributions of molar mass for the different samples clearly overlap, due to polydispersity index of about 1.8, and mean values differ no more than 50%. However, as shown later, significant differences in rheological behavior are observed and are discussed with regards to current understanding of these effects. As may be interpreted from the nomenclature, the higher the molecular weight the higher the solution viscosity, as the viscosity of a solution is directly related to the hydrodynamic volume of the molecular species present, hence to its molecular weight. The number of residues per chain is different from one batch to another, and the average length of the chain decreases as the molecular weight decreases. Gels were prepared by dissolving the powdered agarose in deionized water at 98 °C under strong stirring for 30 min, until a transparent solution was formed. As a first approximation, the relationship used to convert concentration in weight to molar concentration was as follows: 1 c [agarose] ) 103 100 - c Mn
(2)
The density of the solution is assumed to equal the density of the solvent. The resulting concentration is commonly called the molality. For the purposes of this study, the molality is very close to the molar concentration. At high agarose polymer concentrations, it was generally necessary to leave the solution to rest for several hours at 98 °C to remove air bubbles trapped by the high solution viscosity. The solutions were then poured either into the
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Normand et al.
rheometer, or the appropriate tension/compression testing molds and cooled to 10 °C using various cooling ramps. Small deformation strain mechanical properties of the agarose gel samples were measured in oscillatory mode using a Carrimed CSL 500 rheometer with double concentric cylinders set at large gap, which is adapted for the measurements of three-dimensional gel networks (gap ) 3 mm).9 The gel samples, supported on perfluoro-methyl-decaline (density ) 1.98 g‚cm-3), were protected from dehydration by a layer of mineral oil (density ) 0.7 g‚cm-3). All the measurements were performed within the linear viscoelastic deformation domain of the gel, using the strain-control option. A constant strain amplitude of 0.2% was chosen to avoid disturbing the gel network during the measurement. For all the small deformation rheological investigations, a cooling rate of 1 °C min-1 was applied (from 60 to 10 °C) in order to accurately measure the apparent gelation temperature and gelation rate. A cure period of several hours at 10 °C was also necessary when measuring the equilibrium modulus of the gel as accurately as possible. The large deformation and failure behaviors of these gels have been assessed in both tension and compression using an Instron universal testing machine (Instron 4501, High Wycombe, U.K.), equipped with an environmental chamber held at a constant 10 °C temperature. For the compression tests, hot solutions of agarose were poured into cylindrically shaped molds, with dimensions of 13 mm diameter (d) and 13 mm height (H0). Vaseline grease was used on the surface of these molds to avoid the agarose gel sticking. Prior to measurement, the samples were kept for 24 h in the fridge (5 °C) after rapid quench cooling. The tests were performed under lubricated conditions, using dodecane, to avoid shear deformation due to friction between the specimen and the Instron platens. Samples were equilibrated at 10 °C prior to testing, with a minimum of eight specimens tested for each composition to determine the typical experimental deviation. For tension specimens, the hot agarose solutions were poured between two glass plates separated by 1.4 mm thick (e) spacers and cooled quickly to 10 °C using two water baths, one set at 60 °C to allow pouring of the gel, and the other at 10 °C to gel the sample. After storage (24 h at 5 °C), samples were cut from the gel sheets using “dog-bone” shaped cutters (60 mm gauge length (L0) and 6 mm width (l)). Samples were then gripped using double-sided tape and polymeric glue and stuck to cardboard tabs, to minimize handling damage. In both cases, the stress and the strain were estimated according to the following equations, if incompressibility is assumed as it has been measured for agar.10 For the compression load/displacement curves true stress σ )
F(H0 - ∆H) π(d/2)2H0
true strain ) ln
(
)
H0 - ∆H H0
and for the tension load/displacement curves
(3)
(4)
true stress σ )
F(L0 + ∆L) leL0
true strain ) ln
(
)
L0 + ∆L L0
(5)
(6)
where F is the applied load and ∆L and ∆H, are the tension and compression displacements, respectively. According to eqs 4 and 6, and to the sample’s dimensions and shapes, the relationship between strain rates and deformation rates (imposed by the testing apparatus) are significantly different depending on whether a sample is tested in compression or in tension. To compare the results obtained with these two techniques, different deformation rates have been imposed, i.e., 100 and 50 mm min-1 for tension and compression, respectively. Under these testing conditions, tension strain rate and lateral expansion strain rate (compression tests) are comparable, if the Poisson ratio is close to 0.5 and if the strain at failure does not exceed 0.5 in tension. 3. Results and Discussion The aim of the current work was to establish the relationship between mechanical properties and molecular weight for the different types of agarose investigated (i.e., gelation temperature, gel strength, loss properties, elastic modulus, failure stress/strain, etc.). Low viscosity agarose (L1 and L2) was investigated and the results were compared to those obtained with the high viscosity sample (H). 3.1. Small Deformation Studies. Agarose rheological properties were measured at different concentrations (from 0.3 to 7.5% for the low viscosity L2 sample, and from 0.1 to 2% for the high viscosity material H). The apparent gelation temperature was defined, to a first approximation, as the temperature of the crossover of G′ and G′′.11 This is an apparent gelation temperature, since it depends on the thermal history. Also, the elastic modulus at equilibrium (long aging time) was measured and analyzed as a function of the concentration and the type of agarose. The cure curves were also analyzed. 3.1.1 Gelling Temperature of Agarose. The gelation of agarose occurs during the cooling of an agarose solution to below its temperature of ordering (conformational transition of the polymer chain ) coil to helix transition), which is close to 35 °C. Agarose helices associate into long fiberlike aggregates that eventually form a percolating network, which is the criterion for the presence of a gel. It has been suggested that, prior to network formation, a mechanism of solution demixing also occurs, which leads to formation of heterogeneities within the gel network (i.e., low concentration regions (rich in solvent) and more highly concentrated regions (rich in biopolymer)).12,13 The apparent gelling temperature is plotted in Figure 3 as a function of the biopolymer concentration. As a first approximation, at high polymer concentrations, the dependence of the measured gelling temperature upon concentration is similar for the different agarose samples investigated. However, at low concentrations, a large dif-
Agarose Gel Mechanical Properties
Figure 3. Evolution of the gelling temperature against the agarose concentration. High viscosity agarose (open circles), low viscosity agarose (solid squares). C* represents the critical concentration for entanglement for high viscosity agarose.13
ference appears. Nevertheless, for the two agarose types, the apparent gelling temperature increases with increasing molar concentration. The rate of increase is greater when the molecular weight is small. This dependence of the apparent gelling temperature leads to an approximate definition of a critical concentration (Cc) that is different for each agarose type. This critical concentration is believed to be the lowest limit at which a gel can be formed. At lower concentrations, the system evolves from the coil state at high temperature to ordered high molecular weight aggregates at a temperature below the ordering temperature. These aggregates are unable to associate further to produce a three-dimensional gel network. The estimated critical concentrations, found by extrapolation of the gelling temperature data to an asymptotic concentration value, are: 0.065 ( 0.005 × 10-4 mol L-1 for the high viscosity agarose (H)12 and 0.106 ( 0.005 × 10-4 mol L-1 for the low viscosity agarose (L2). These observations are difficult to interpret, as thermodynamic (coil to helix equilibrium) and kinetic (related to the choice of a given cooling rate) effects are difficult to deconvolute. The results obtained here however suggest that the ordering temperature decreases with decreasing molecular weight, probably due to the existence of a critical helix length with regards to thermal stability. As the slowest step is believed to be the helix nucleation,3 this could explain the shift in the apparent gelation temperature. 3.1.2. Equilibrium Elastic Modulus and Gelation Kinetics Master Curve. The equilibrium shear modulus is defined as the modulus, at long time scales, where further increase with time becomes negligible. At this point, it can be said that the gel network is fully “mature” and does not evolve further. It has been shown for several biopolymer systems that the evolution of the equilibrium elastic modulus follows a power law with the concentration. The exponents of these power laws are usually close to 2, and it has been suggested that it reflects to the kinetic order of the mechanism of gel formation (two chains forming a network cross-link or two helices).
Biomacromolecules, Vol. 1, No. 4, 2000 733
Figure 4. Master curve for low viscosity agarose (L2). Reference concentration 2.225 × 10-4 mol L-1 (1.6% (w/w)).
The storage modulus (G′) dependence with the concentration can be written as G′ ∝ Cn or G′ ∝
() C Cc
n
(7)
Recently, a kinetic approach has been suggested, which involves the whole cure curve and the development of an overall master curve which is independent of the concentration (and indeed C/Cc). This method has recently been reported by Meunier et al. for κ-carrageenan14 and Normand et al. for both gelatin8 and maltodextrin.15 It appears to be consistent with fractal theories of gelation, which propose that the gel structure is fundamentally constant with only the length scale and the time scale varying. To construct such a master curve, a reference cure curve (G′(t)) is selected at a polymer concentration in the middle of the concentration range investigated. All the other cure curves are then shifted both horizontally and vertically in a double logarithmic representation. The shift factors are then considered as functions of the nominal concentration (C). In the present case, the reference concentration (C0) chosen to build the master curve for the low viscosity agarose (L2) gelation kinetics was 2.225 × 10-4 mol L-1 (1.6% (w/w)). The expressions defining the master curve are log(G′(t)) ) aG + log(G′0(t)) ) n log
() ()
log(τ) ) at + log(τ0) ) m log
C + log(G′0(t)) (8) C0 C + log(t0) C0
(9)
where at and aG are the horizontal and the vertical shift factors, respectively, and τ represents the time scale. Figure 4 shows such superposition of the experimental cure curves (G′ ) f(t)) for seven different agarose concentrations. When the concentration considered is higher than the reference, the vertical shift is negative and the horizontal shift positive, and when the concentration considered is lower than the reference, the vertical shift is positive and the horizontal shift negative. The value of the exponents n and m of the power laws, introduced previously in eqs 8 and 9,
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Normand et al.
Figure 5. Determination of the exponents of the power laws necessary to build the master curve. Storage modulus translation (solid squares) and time translation (solid circles).
Figure 6. Master curve for high viscosity agarose (H). Reference concentration 1.068 × 10-4 mol L-1 (1.0% (w/V)). All percentages are expressed in w/V.
are subsequently extracted from the representations of aG and at as functions of log(C/C0). The same approach has also been successfully applied to the high viscosity agarose cure curves. The values of the n′ and the m′ exponents are close to those found for the low viscosity agarose, with n′ ) 2.16 and m′ ) -0.17 (see Figure 6). An overall superposition of the two master curves is then also feasible according to the following steps: (1) calculation of the high viscosity agarose cure curve for the same molar concentration as the reference concentration used for the low viscosity agarose data (i.e., 2.225 × 10-4 mol L-1) G′(t) )
(
)
2.225 × 10-4 1.068 × 10-4
2.16
G′0(t)
(10)
(2) shift of this calculated high viscosity agarose curve to superimpose on the corresponding low viscosity curve at the same molar concentration, by introducing a shift factor AG log(G′H(t)) ) AG + log(G′1,2(t))
(11)
We propose that the shift parameter, AG, is a direct power law function of the number-average molecular weight, since this is the only difference between the two experiments; i.e. AG ) n′′ log
( ) Mn(H)
Mn(L2)
(12)
Mn(H)2.42
)
G′L2(t) Mn(1,2)2.42
The significance of m (the exponent linked to the horizontal shift factor, see eq 9) is not really obvious as it depends strongly on the cooling rate, therefore its value will not be discussed in the present paper. However, n (see eq 8) is related to the kinetics of formation for the gel. Values for n that have been reported previously for agar16 are very close to those found in the present work. This observation suggests the following possible mechanism of gelation k1
(13)
where the exponent n′′ ) 2.42 ( 0.3 and is in good agreement with eq 1, if the molar concentration is considered instead of the weight concentration. The same form of relationship links the time scale dependence (i.e., a horizontal shift is also needed) with an exponent equal to 0.37. The representation of the superimposition of the two curves is shown in Figure 7.
k2
2A u B u C k′1
Substituting values leads to the simple relationship G′H(t)
Figure 7. Superimposition of cure curves from high and low viscosity agarose at the same molar concentration (2.225 × 10-4 mol L-1). Open squares represent high viscosity agarose (H) and filled circles represent low viscosity agarose (L2).
k′2
where A represents one free chain in solution, B two chains linked by a helix-helix association, and C the network formed by aggregation of helices in fiberlike form. The limiting process of this mechanism can be approximated to a second-order reaction, as the experiment gives n approximately equal to 2.1. It has been shown that the exponent linking the elastic modulus (vertical shift factor) and the concentration is independent of the number-average molecular weight. Furthermore, it has been shown that universality exists for agarose, independently of its molecular weight. This indicates that the same rheological response can be reached with different chain lengths.
Biomacromolecules, Vol. 1, No. 4, 2000 735
Agarose Gel Mechanical Properties
Figure 8. Comparison of the large deformation profiles for low viscosity agarose (L1) in tension and compression, showing the effect of varying agarose concentration. Table 2. Stress and Strain at Failure for Low Viscosity Agarose (L1), Effect of the Concentrationa tension [agarose] ×104
failure
%
(mol‚L-1) (w/w) 4.06 8.33 12.84 17.59
2.50 5.00 4.50 10.0
Figure 9. Gel failure strain as a function of agarose molar concentration. Squares represent data obtained in tension, circles represent compression data. Filled symbols are low viscosity agarose (L1), and open symbols are high viscosity agarose (H).
compression failure
stress
failure
stress
(KPa)
strain
(KPa)
failure strain
77.7 ( 15 214 ( 26 302 ( 11 453 ( 20
0.143 ( 0.01 0.142 ( 0.01 0.11 ( 0.002 0.12 ( 0.01
104 ( 6 280 ( 31 488 ( 27 606 ( 53
0.36 ( 0.02 0.33 ( 0.02 0.378 ( 0.006 0.36 ( 0.01
a Averages and standard deviations were calculated from at least eight tests.
Table 3. Effect of the Concentration on Failure Stress and Strain for High Viscosity Agarose (H)a tension [agarose] ×104
%
(mol‚L-1) (w/w) 1.07 2.16 3.31
1.0 2.0 3.0
failure
compression failure
stress
failure
stress
failure
(KPa)
strain
(KPa)
strain
48 ( 8 0.208 ( 0.025 55 ( 3 0.43 ( 0.015 126 ( 13 0.209 ( 0.017 129 ( 10 0.44 ( 0.026 227 ( 22 0.213 ( 0.019 225 ( 12 0.43 ( 0.028
a Averages and standard deviations were calculated from at least 8 tests.
3.2. Large Deformation Studies. Typical “true” stress/ “true” strain deformation curves for low viscosity agarose (L1) (five different concentrations), in both tension and compression, are shown in Figure 8, according to the representation used previously for gellan gels.10 The elastic modulus has been approximated as the gradient of the stress/ strain curve near the origin (i.e., for strains
