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Soil Science
Issue: Volume 165(10), October 2000, pp 778-792
Copyright: © 2000 Lippincott Williams & Wilkins, Inc.
Publication Type: [Technical Articles]
ISSN: 0038-075X
Accession: 00010694-200010000-00003
Keywords: Gellan gels, mechanical properties, polyacrylamide gels, soil stabilizers
[Technical Articles]
MECHANICAL PROPERTIES OF GELLAN AND POLYACRYLAMIDE GELS WITH IMPLICATIONS
FOR SOIL STABILIZATION
1
2
1
Ferruzzi, Giulio G. ; Pan, Ning ; Casey, William H.
Author Information
1
University of California, Davis, Department of Land, Air and Water Resources, Davis, CA 95616; Dr. Casey is corresponding
author.
2
University of California, Davis, Division of Textiles and Clothing & Biological and Agricultural Engineering, Davis, CA 95616
Address correspondence to Dr. William H. Casey, One Shields Ave., Davis, CA, 95616. E-mail: [email protected]
Received Jan. 10, 2000; accepted May 16, 2000.
Abstract
Organic matter can stabilize soil aggregates against disintegration upon wetting. We examined the tensile
strengths of two polymer gels that were chosen to represent features of soil organic matter. The mechanical
properties of polyacrylamide and gellan gels (gellan is a natural polysaccharide) are remarkably similar despite large
differences in molecular structure. The general shape of the stress strain curves for both gels is similar, although the
method and mechanism of gelation differs drastically between the gels. The ultimate breaking stresses for both gels
are also similar in magnitude (13 to 1100 kPa for polyacrylamide and 9 to 350 kPa for gellan), even though they differ
fundamentally in type of gel cross-links and vary drastically in their ultimate breaking strain relations. Breaking strain
tends to decrease with increased polymer and BIS concentration for polyacrylamide gels, whereas the relations
tended to be more complex for gellan gels. These measurements allow some constraints to be placed on the effects
of polymers on soil aggregate stability. For example, a 1-µm-thick layer of polyacrylamide, on a 1 mm-diameter
aggregate, can support a range of maximum internal pressures from 0.046 to 2.5 kPa.
Fertile aridic soils, such as those in the most productive agricultural areas of California, tend to slake during
irrigation events. The slaking destroys structure and reduces infiltration rates, which ultimately translates to reduced
crop yields. Good soil structure for crop growth depends on the presence of aggregates that remain stable when
wetted. Organic matter can prevent aggregate disintegration upon wetting, although the kind of organic matter, and
the way in which organic matter interacts with soil aggregates, is not completely understood. However, it is known
that organic polymers can act as a cementing or gluing agent that reinforces the aggregate architecture structurally
(Tisdall and Oades, 1982; Quirk, 1978; Russell, 1988). One can reasonably expect the stability of the aggregate to
relate to the strength of the polymers. Additionally, some polymers are more hydrophobic than the soil mineral
constituents and can increase aggregate stability by preventing, or slowing, the entry of water into the aggregate
pores (Sullivan, 1990; Coughlan et al., 1973). Understanding the interaction of the organic polymers with soil
aggregates is key to controlling erosion and hydraulic properties of soil.
The composition and structure of soil organic matter is understood poorly because it cannot be extracted from
the soil without damage. However, polysaccharides derived from plants and microbes have been isolated, and some
of these polysaccharides have demonstrated aggregate stabilizing affects (Martin, 1946; Chesters et al., 1957).
Synthetic polymers, such as linear polyacrylamides, stabilize soil aggregates by coating them with a network of
entangled polyacrylamide molecules (Fig. 1). Closer observation of the adsorbed polymer has led to the idea that
polyacrylamide molecules are adsorbed in strands of several chains (Audsley and Fursey, 1965). The elastic polymer
network that forms around an aggregate (Fig. 1) structurally reinforces it as it swells during quick wetting, such as in
the case of an irrigation event. As long as the outward force of the swelling aggregate does not exceed the inward
force of the polymer network, the aggregate is stable. This structural reinforcement should be similar to the effects
of natural soil organic matter, with the exception that the polymer acts from the outside of the aggregate only. The
stress that the adsorbed polymer network can support will be a function of network structure and composition.
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Fig. 1. Adsorbed polymer network around a soil aggregate, such that forms on immersion of an aggregate in a solution
containing polyacrylamide.
Unfortunately, it is extremely difficult to test these networks in situ. Instead, we analyze the properties of pure,
hydrated polymer networks, or gels, to represent the adsorbed polymer network counterparts. This way we can, and
do, synthesize a series of gels with varying structures and compositions and test their mechanical properties to
determine the magnitude of stabilizing forces that the networks can provide soil aggregates. One of the gels used in
this study is made from the microbial polysaccharide gellan gum (Kelcogel LT100). This unclarified, high-acyl-content
gum is used as synthesized by Sphigomonas elodea to represent natural soil microbial polysaccharides. Three of the
four sugar residues in gellan are glucose, glucuronic acid, and rhamnose which, among other sugar residues, are the
major constituents of polysaccharides produced by the soil microbes Rhizobium and Agrobacterium (Rao, 1977). The
second gel, polyacrylamide, is wholly synthetic yet similar to some soil organic matter in its ability to resist
degradation. Linear polyacrylamide has been used extensively in agriculture to control erosion and maintain
infiltration rates (Sojka et al., 1998a; Sojka and Lentz, 1996). Evidence suggests that linear polyacrylamides also
stabilize soil structure (Sojka et al., 1998a and b), most likely by adsorbing onto aggregates in the form of an elastic
polymeric network.
MATERIALS AND METHODS
Polyacrylamide Gels
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The polyacrylamide gels were prepared via free-radical polymerization using ammonium persulphate as the
initiator (Rosen, 1993). The polyacrylamide gels (compositions P1-P5) were synthesized by mixing 0.04 g ammonium
persulphate and varying amounts of acrylamide and methylene-bisacrylamide (BIS) monomers while keeping the total
monomer molarity constant at 1 M. The exact amounts of monomers used for each polyacrylamide gel composition
are summarized in Table 1. The mixture was diluted to 100 mL with deionized water, degassed under vacuum, and
polymerized in microcapillaries at 60 °C for 2.25 h. After synthesis, the gels were dried in ethanol for 24 to 48 h to
aid in the removal of the gels from the microcapillaries and then rinsed for 24 to 48 h in deionized water to remove
residual unreacted monomer.
TABLE 1 Polyacrylamide gel synthesis compositions
A second batch of polyacrylamide gels (compositions P6-P8) was synthesized by mixing 0.04 g ammonium
persulphate and varying the total monomer molarity while keeping the mole fraction of BIS at a constant value of
0.05. The mixture was then treated as mentioned above.
The polyacrylamide gels consist of polymer chains comprised of acrylamide monomers that are covalently linked
to other chains via the (BIS) molecule into a three-dimensional structure (Fig. 2A). During synthesis, microgels form
before the onset of macrogelation (Nagash and Okay, 1996). These microgels are denser than the bulk gel and richer
in cross-links (Fig. 2A). As gelation proceeds, the microgels are connected to the macrogel network through pendant
vinyls and free-radical ends (Nagash and Okay, 1996).
Fig. 2. Schematic of the gel structures in this study. (A) represents the polyacrylamide gel network (black dots
represent BIS) that forms in dilute aqueous acrylamide solutions (adapted from Nagash and Okay, 1996). (B)
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represents the gellan gel network that forms in gellan solutions in the presence of cations (adapted from Crescenzi,
1995).
Gellan Gels
The gellan gels were synthesized in the presence of dissolved calcium chloride so that the polymer chains
2+
cross-link into a three dimensional structure via Ca ionic bridges. The gellan gels (compositions G1-G4) were
prepared by heating deionized water to 95 °C, adding gellan gum (Kelcogel LT100) to the vigorously stirred solution
and allowing the gum to dissolve completely. Solid CaCl ·2H O was then added to make the calcium concentration 0.1
2
2
M. The exact amounts of gum, water, and CaCl ·2H O used for each gellan gel composition are summarized in Table
2
2
2. The solution was then degassed under vacuum conditions and transferred to microcapillaries where gelation
occurred upon cooling (Chandrasekaran et al., 1992). The gels were allowed to cure for 24 h before they were dried
in ethanol for 24 to 48 h. The gels were then extracted from the microcapillaries and rinsed for approximately 24 h in
0.1 M CaCl before mechanical properties were measured.
2
TABLE 2 Gellan gel synthesis compositions
A second batch of gellan gels (compositions G5-G8) was prepared in a similar fashion, keeping the gellan gum
constant but varying the amount of calcium chloride added, to create gellan gels with varying calcium
concentrations. The solutions were then treated as mentioned above with the exception that the gels were rinsed
with calcium chloride solutions at concentrations similar to the gel synthesis concentrations.
The gellan gels (Fig. 2B) consist of polymer chains that are linked ionically via cationic bridging during gelation.
The structure of the junction is a doubled-stranded helix that is held together by the attraction of the carboxyl
groups on the gellan polymer and a mono or divalent counter ion (Fig. 2B, detail) (Crescenzi, 1995, Chandrasekaran
and Thailambal, 1990; Chandrasekaran and Radha, 1995). In Fig. 2B, the letter a indicates the acetyl group that
occurs once every two repeating gellan units (four sugars shown) and the letter b indicates the glyceryl group that
occurs once every repeating gellan unit. The clarified, low-acyl-content gellan (Kelcogel) has been studied
extensively because of its promising performance as a food additive.
Mechanical Testing
All tests were performed on an Instron 1122 mechanical testing instrument in tensile mode with sample lengths
ranging from 2 to 7 cm in length and a constant crosshead speed of 20 mm/min at 21 °C. Accuracy and precision of
the Instron 1122 were within 1% as determined by repeated measurements of force from a standard weight. Tensile
tests were performed on fully hydrated gels. Each gel specimen was gripped at the ends by the machine's upper and
lower grips. The gel ends remained dry by keeping the ends of the gel specimens out of the respective hydrating
solution. Each specimen was inspected visually before and during each test. If failures developed at or near the
dry-end transition area, the data were discarded. The data generated by mechanical testing of the gels are force and
displacement. This information is then converted to engineering stress: Equation (1) where F is force and A is the
o
initial cross-sectional area of the specimen and strain: Equation (2) where [DELTA]L is the deformation of the sample
and L is the initial sample length. For the data to be useful, engineering stress (Eq. (1)) is converted into true stress:
o
Equation (3) where A is the cross-sectional area of the strained specimen. By making the assumptions that the
materials are isotropic and Poisson's ratio is 0.5, the total volume of the specimen remains unchanged during
deformation. The assumption that Poisson's ratio is 0.5 is made so that A can be calculated as a simple function of A ,
o
initial sample length and strained sample length. The assumption stated mathematically is: EQUATION (4) where L is
the sum of [DELTA]L and L . This allows Eq. (3) to be expressed as: EQUATION (5)
o
Equation 1
Equation 2
Equation 3
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Equation 4
Equation 5
The initial linear slope of the true stress ([sigma] ) versus strain ([varepsilon]) curve is called Young's modulus.
t
The modulus essentially describes the stress-strain behavior of a material in the initial, linear elastic region of
deformation. Rigid materials have large moduli, and more deformable materials have smaller moduli. Young's moduli
were determined for each individual specimen from its true stress-strain curve.
Stress-Strain Modeling
A simple equation was used to fit the stress-strain data: Equation (6) where K and n are fitting parameters and
[varepsilon] is true strain calculated from Eq. (2) by the following relation (Hershko and Nussinovitch, 1995):
t
EQUATION (7) Equation (6), although empirical in nature, contains variables that can be assigned physical
significance. According to Hershko and Nussinovitch (1995), the K of Eq. (6) is essentially the elastic (Young's)
modulus. Therefore, Young's Modulus calculated from the stress-strain curve and K obtained from curve fitting should
be equivalent.
Equation 6
Equation 7
RESULTS AND DISCUSSIONS
Typical stress-strain curves for the polyacrylamide gels and gellan gels tested are presented in Fig. 3. The general
shape of the stress-strain curve is similar for both the polyacrylamide gels and the gellan gels. Reproducibility in
ultimate breaking stress and strain among specimens of the same composition is reported as standard deviations in
Table 3 and as error bars in the figures.
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Fig. 3. Typical stress-strain curves for the gellan and polyacrylamide gels. (A) Stress-strain curves for the gellan gels
with various calcium concentrations (Table 2). The curve for composition G5 is obscured by the other curves, but the
ultimate breaking stress and strain are located at the arrowhead. (B) Stress-strain curves for the gellan gels with
various gum concentrations (Table 2). (C) Stress-strain curves for the polyacrylamide gels with various BIS
concentrations (Table 1). (D) Stress-strain curves for the polyacrylamide gels with various total monomer
concentrations (Table 1).
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TABLE 3 Ultimate breaking stress and strain for experimental gels
The ultimate breaking stress and strain results for the polyacrylamide and gellan gels are summarized in Table 3.
Each reported value of strain ([varepsilon]) and stress ([sigma] ) in Table 3 is the average of two to five individual
t
specimens, and the reported uncertainty is the standard deviation of the calculated average. The large uncertainty of
some measurements in Table 3 reflects real variation in behavior of similarly prepared gel specimens, not
measurement error.
An average Young's modulus is reported for each gel composition in Table 4. Again, the large uncertainty of some
measurements reflects real variation in behavior of similarly prepared gel specimens and not measurement error.
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TABLE 4 Young's Moduli and K for experimental gels
Deformation Reversibility
Most of the polyacrylamide gel's deformation is reversible within seconds of relieving strain. In contrast, the
gellan gel's deformation is not totally reversible even after 48 h of rehydrating in an appropriate solution. It was
observed that the gellan gels would begin to expel water at high strains near failure. These results indicate that the
gellan gels do not behave as incompressible materials (i.e., the Poisson's ratio is < 0.5) and that not all of the
deformation induced in the gellan gels is reversible.
The loss of water from the gellan gels during testing also indicates that the true stress is actually greater than
reported in these results. We interpret the irreversible deformation of the gellan gels as caused by the loss of water
and the unraveling of the helical junctions along with some probable main chain failures. Since the junctions can
form only at elevated temperatures not achievable during mechanical testing (>75 °C, in most cases), we consider it
unlikely that the gellan gel would recover all of its deformation if any junctions were unraveled inasmuch as the
measurements were performed at a constant 21 °C.
Stress-Strain Curves
Since all of the gels were hydrated, we expected that the gellan gels would be much weaker than the
polyacrylamide gels because the ionic cross-links associated with the gellan gels require less energy to break in an
aqueous solution (-4 to 10 kJ/mol for the bond between a divalent metal of the alkaline-earth series and a carboxyl
bond (Nancollas, 1956)) than covalent bonds (345-355 kJ/mol for a C-C bond (March, 1992)) associated with the
polyacrylamide gel. Yet the ultimate breaking stress values of both gellan and polyacrylamide gels were the same
order of magnitude. We interpret this result as a reflection of the physical structure of the gellan cationic bridge,
described in detail by other researchers (Morris et al., 1996; Chandrasekaran et al., 1995; Chandrasekaran et al.,
1992). Although the cross-links that bridge gellan main chains are ionic, the energy required to break the helical
junction is the energy required to break the main chain of the gellan, which is a covalent bond (approximately
355-380 kJ/mol for a C-O bond (March, 1992)). Therefore, the ultimate breaking stresses for the polyacrylamide and
gellan gels are on the same order of magnitude because similar bonds rupture in spite of the differences in crosslinking mechanism.
Polyacrylamide Gels
For polyacrylamide gels, ultimate breaking stress increases with total monomer concentration for a constant
2
mole fraction of BIS (Fig. 4A). There is an apparent linear correlation (R = 0.99904) for compositions P3, P6, and P7.
Composition P8 deviates from linearity as the concentration of monomer increases. This result is corroborated by
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results from Baselga et al. (1987), who found more of an exponential dependence of breaking stress on monomer
concentration for a slightly different concentration range.
Fig. 4. Ultimate properties of polyacrylamide gels. Error bars are the standard deviations as reported in Table 3. (A)
Ultimate breaking stress as a function of total monomer concentration. (B) Ultimate breaking stress as a function of
BIS concentration. (C) Ultimate breaking strain as a function of total monomer concentration. (D) Ultimate breaking
strain as a function of BIS concentration.
The correlation between ultimate breaking stress and total monomer concentration gives us insight on gel
structure and the role of inhomogeneity. Figure 2A is a representation of the polyacrylamide network at low initial
monomer concentrations (Nagash and Okay, 1996). As the monomer concentration increased, some factors became
important in dictating the final gel properties. The number of free chain ends (Fig. 2A) remained constant because
they were controlled by the amount of initiator in solution (Kulicke and Nottelmann, 1989). The number of microgels
increased with monomer concentration, and the relative distance between them decreased. More importantly, the
number of loops (Fig. 2A) that did not contribute to elasticity of the gel decreased, and the number of entanglements
(Fig. 2A) that did contribute to elasticity increased (Kulicke and Nottelmann, 1989). The overall number of network
defects in polyacrylamide gels may be least in gels synthesized with high initial monomer concentrations and low
mole fraction of BIS (Baselga et al., 1987). These factors may contribute to the observed increase in breaking stress
with respect to an increase in monomer concentration of the gels.
At the conditions of composition P8, the mole ratio of water molecules to total monomers is approximately 17:1.
At this concentration, the density of the microgels (Fig. 2A) and the density of the surrounding gel become similar.
That is, as predicted by Baselga et al. (1987), the gel becomes more homogenous. A homogeneous polymer (e.g.,
purely crystalline or completely amorphous) is transparent, but a heterogeneous polymer (e.g., differing densities
throughout the polymer) is translucent (Rosen, 1993). Thus, the clarity in polyacrylamide gels is related to the
presence of microgels in the gel structure (Bansil and Gupta, 1980) and the difference in refractive index between
the microgels and the bulk gel. From the phase diagram available in the literature (Bansil and Gupta, 1980),
polyacrylamide gels with a BIS mole fraction of 0.05 and total monomer concentrations > 0.37 M should be opaque.
The poly-acrylamide gels of compositions P3 and P7 are, in fact, opaque. Composition P6, whose composition (Table
1) is close to the phase diagram boundary, is clear. The appearance of the composition P8 gels was also clear,
indicating a more homogenous network and that an additional phase boundary for polyacrylamide may exist at high
total monomer concentrations. The increased homogeneity of composition P8 may explain the large increase in gel
strength at high total monomer concentrations observed in this study and by other researchers (Baselga et al., 1987).
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The correlation between ultimate breaking stress and BIS concentration for polyacrylamide gels with less that 0.1
mole fraction of BIS found in this study has been observed previously for a slightly different range of polyacrylamide
compositions (Baselga et al., 1987). The larger composition range used in this study has yielded information of highly
cross-linked gels indicating that a BIS mole fraction 0.1 produces the strongest gel at a given total monomer
concentration (Fig. 4B). Mole fractions of BIS less than or > 0.1 diminished the ultimate breaking stress of the gels
tested as indicated in Fig. 4B. This detail is related to the inhomogeneity of the gel and that the concentration of BIS
in the gel affects the polymerization rate and intermolecular linking (Nagash and Okay, 1996).
2
There is a good linear correlation (R = 0.99991) between ultimate breaking strain and total monomer
concentration for compositions P3, P6, and P7 (Fig. 4C). The polyacrylamide gels become more brittle with an
increase in total monomer concentration, as indicated by the decrease in ultimate breaking strain when the monomer
concentration is increased. Baselga et al. (1987) also observed a similar trend for polyacrylamide gels concentrations
of up to 2.4 M total monomer concentration.
The correlation between ultimate breaking strain and BIS concentration for polyacrylamide gels between 0.005
and 0.05 mole fraction BIS found in this study has also been observed previously (Baselga et al., 1987; Cohen et al.,
1992). The additional gels we tested above the 0.05 mole fraction BIS indicate that as more BIS is polymerized in the
gel, the more the breaking strain continues to decrease (Fig. 4D). The observed decrease in breaking strain with
respect to BIS concentration is more drastic at the lower concentrations (compositions P1, P2, and P3) than at higher
BIS concentrations (P3, P4, and P5).
The correlation between Young's Modulus and total monomer concentration (Fig. 5A) agrees with the previous
results for polyacrylamide gels (Cohen et al., 1992; Benguigui, 1995; Baselga et al., 1987). The additional gel
composition (P8) tested in this study indicates that the correlation is still valid at polyacrylamide concentrations of
up to 2.997 M total monomer. The correlation between Young's Modulus and BIS concentration (Fig. 5B) at low BIS
concentrations also agrees with previous results (Cohen et al., 1992; Benguigui, 1995; Baselga et al., 1987). The
inhomogeneity of the polyacrylamide network may account for the observed nonlinear correlation (Benguigui, 1995).
Baselga et al. (1987) and Cohen et al. (1992) observed a broad maximum in Young's Modulus between the range of the
0.02 and 0.05 mole fraction of BIS. We observed this maximum in Young's Modulus in the same region, although the
additional gel compositions (P4 and P5) tested in this study indicate a possible increase in Young's modulus at BIS
mole fractions of 0.15 concentrations (Fig. 5B). Because of the large error associated with composition P5 and
because the previous researchers did not perform tests on gels of that composition, it is difficult to relate this result
to any physical changes in the gel structure.
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Fig. 5. Young's Modulus of polyacrylamide gels as a function of total monomer concentration (A) and BIS concentration
(B). Error bars are the standard deviations as reported in Table 4.
Gellan Gels
2
For gellan gels, there is an apparent linear correlation (R = 0.97928) between ultimate breaking stress and gum
concentration (wt/wt%) for compositions G1-G4, which were gels with similar calcium concentrations but which
varied in total gum concentration (Fig. 6A). This correlation agrees with observations on a type of gellan gel with few
acyl group (Kelcogel) in a similar range of gum concentrations (Hershko and Nussinovitch, 1995; Tang et al., 1994).
Acyl groups are known to interfere with the gelation process (Chandrasekaran and Thailambal, 1990; Chandrasekaran
and Radha, 1995).
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Fig. 6. Ultimate properties of gellan gels. Error bars are the standard deviations as reported in Table 3. (A) Ultimate
breaking stress as a function of gellan gum concentration. (B) Ultimate breaking stress as a function of calcium
concentration. (C) Ultimate breaking strain as a function of gellan gum concentration. (D) Ultimate breaking strain as
a function of calcium concentration.
The relation between ultimate breaking stress and calcium concentration is more complex. Increasing calcium
concentrations from 0.001 M to 0.05 M increases the breaking stress of the gels significantly. A further increase in
calcium from 0.05 M to 0.1 M does not affect the breaking stress significantly (Fig. 6B). This correlation was also
observed by Tang et al. (1994) for a similar type of gellan gel (Kelcogel) in a smaller range of calcium concentrations.
For the compositions tested, the ultimate breaking strain and gum concentration relation is nonlinear (Fig. 6C).
There was an increase in breaking strain as the gum concentration increased from 1 to 1.5%. Additional increases in
gum concentrations of up to 2.5% did not change the observed breaking strain of the resulting gels significantly,
indicating that the breaking strain became independent of gum concentrations above 1.5%. The relation between
ultimate breaking strain and calcium concentration is similar to the relation between ultimate breaking stress and
calcium concentration. Increasing calcium concentrations from 0.001 M to 0.05 M increased the breaking strain of the
resulting gels significantly (Fig. 6D). A further increase in calcium from 0.05 M to 0.1 M decreased the breaking strain
slightly. This indicates that calcium concentrations greater than 0.05 M may prevent cationic bridging from occurring,
thus weakening the gel (Tang et al., 1994) as observed in the decrease of both breaking and stress and strain of
composition G2.
Neither the correlation between calcium concentration and ultimate breaking strain, nor the correlation
between gum concentration and ultimate breaking strain, corroborate results found by Hershko and Nussinovitch
(1995) or Tang et al. (1994). The difference in ultimate strain relations is attributable to the high acyl group content
of the gellan gum used in this study. Gellan gels with few acyl groups are known to be more brittle, and this explains
the observed differences between our strain data and that of other researchers (Sanderson, et al., 1988; Morris et
al., 1996). Previous studies with low acyl group content gellan gum indicates an increase in breaking strain as the
gellan gum concentration is increased (Hershko and Nussinovitch, 1995; Tang et al., 1994). The only difference
between the gellan gum used in our study and that of the above mentioned authors is the acyl content of the gum.
Therefore, the observed drop in breaking strain with decrease in gum concentration is directly related to the inability
of the high-acyl-group-content gellan gum used in our study to form a strong gel network at low concentrations.
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For gellan gels, there is a correlation between Young's Modulus and gellan gum concentration (Fig. 7A). The
moduli of composition G1 and G2 are statistically similar, but Young's Modulus increases with increases in gum
concentration for composition G2 through G4. However, there is no correlation between Young's Modulus and calcium
concentration (Fig. 7B).
Fig. 7. Young's Modulus of gellan gels as a function of gellan gum concentration (A) and calcium concentration (B).
Error bars are the standard deviations as reported in Table 4.
The deviation from linearity of composition G1 (Fig. 7A) may have been caused by keeping the calcium
concentration constant for these gels as the gum concentration was increased, leading to a small variance in calciumto-gum concentration ratios. Therefore, we may observe a dependence of Young's Modulus on gum concentration
along with calcium-to-gum concentration ratios since these were the only parameters that were manipulated.
Stress-Strain Modeling
The average values for K that resulted from the curve fitting of the stress-strain curves with Eq. [6] are reported
for each gel composition in Table 4. Equation [6] consistently indicated an increase in K with an increase in gum or
monomer concentration and calcium or BIS concentration, which is not the case for observed Young's Moduli of the
gels tested. For the gels in this study, K and Young's Modulus are correlated only for gels whose gum or monomer
concentration is varied (Figs. 8 and 9). Additionally, the correlation is valid only for a particular range of
concentrations. These results indicate that Eq. (6) may be used to correlate K and Young's Modulus in a series of gels
where the average chain length remains relatively constant. Once a correlation between K and Young's Modulus has
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been established for a gel series, it can be useful in predicting Young's Moduli of intermediate gel compositions.
Fig. 8. Relation between K fit to the stress-strain data from Eq. (8) and Young's Modulus for polyacrylamide gels. Error
bars are the standard deviations as reported in Table 4. Note that both the fit K value and Young's Modulus increase
greatly between compositions P7 and P8.
Equation 8
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Fig. 9. Relation between K fit to the stress-strain data from Eq. (8) and Young's Modulus for gellan gels. Error bars are
the standard deviations as reported in Table 4. Note that the fit K value decreases between compositions G1 and G2
whereas Young's Modulus is essentially similar for both compositions.
Forces on Soil Aggregates
When soils are wetted, as in an irrigation event, aggregates are quickly wetted from all sides. Any trapped air
compressed by the advancing water front can eventually disrupt the aggregate. It is inherently difficult to measure
air pressures in small fragile soil aggregates, and only one study in this regard was found in the literature.
Stroosnyder and Koorevaar (1972) measured internal air pressure of rapidly wetted loess soil aggregates of up to 8
kPa but noted that the aggregates began to fail as soon as they were immersed in water. Stroosnyder and Koorevaar's
observations indicate that not only air pressure, but also the wetting rate, play a role in aggregate disruption.
Assuming a spherical soil aggregate, membrane theory (Gere and Timoshenko, 1984) can be used to relate the
stresses in the polymer network to the internal pressure applied by the swelling soil aggregate. The stresses in a
spherical membrane are given by: Equation (8) where [sigma] is stress in the polymer layer, t is the thickness of the
polymer layer, r is the radius of the aggregate and p is the pressure on the polymer layer's inner surface (Gere and
Timoshenko, 1984). By knowing the thickness (t), aggregate radius (r), and maximum breaking stress ([sigma]) of a
particular polyacrylamide composition, the maximum inward pressure an adsorbed polymer network can apply to an
aggregate can be calculated.
Linear polyacrylamide would be the adsorbate on the aggregate because it is used in irrigation agriculture,
although it is interesting to note that the breaking stresses of gellan and polyacrylamide gels are similar. Actually,
most hydrogels (both synthetic and biological) fall within similar values of breaking stress and strain (Table 5). This
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similarity between natural and synthetic hydrogels strengthens the argument that synthetic polymers can contribute
aggregate stabilizing forces on soils similar to natural organic matter such as microbial polysaccharides. Taking into
account the ultimate breaking strain and stress of a 1-µm-thick layer of adsorbed linear polyacrylamide having the
mechanical properties of the polyacrylamide gels compositions tested on an aggregate with an initial diameter of 1
mm, we calculate a range of maximum internal pressures from 0.046 to 2.5 kPa (Table 6). The 1-µm thickness was
based on Atomic Force Microscope (AFM) imaging of polyacrylamide on vermiculite in our laboratory (unpublished
data).
TABLE 5 Ranges of ultimate breaking stresses and strains of various hydrogels
TABLE 6 Maximum pressures generated by polyacrylamide gels of various thickness on a 1-mm aggregate
Although the force of the adsorbed polyacrylamide network alone could not prevent the entrapped air from
escaping a loess aggregate at peak pressure, the network could contribute significant stabilizing pressures on the
aggregate surface. This stabilizing pressure could reinforce the aggregate when it begins to slake as soon as it is
wetted, as observed by Stroosnyder and Koorevaar (1972). In the initial moments of wetting, water enters the larger
pores most rapidly (Bolt and Koenigs, 1972). As the internal air pressure builds, the rate of wetting decreases until
the pressure inside the aggregate stops the wetting front or the aggregate ruptures. The polyacrylamide layer would
be key in providing reinforcement during this point in wetting. The entrapped air could escape through the largest
pore (Fig. 10) without disrupting or disintegrating the aggregate (Bolt and Koenigs, 1972).
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Fig. 10. Air/water relations in aggregate pores. Both, large and small pores exist on an aggregate surface (A). As the
aggregate is wetted (B), water enters larger pores faster than smaller pores. Shaded areas indicate the water-filled
part of the pore, and the arrows indicate the direction of water movement. Once a critical pressure is reached (C),
the aggregate will rupture, releasing excess air pressure. The presence of a polymer network on the surface of the
aggregate could reinforce the aggregate structure and allow excess air pressure to escape as air bubbles through the
largest pore(s) without compromising aggregate stability (D).
CONCLUSION
The mechanical properties of polyacrylamide and gellan gels are remarkably similar despite the large difference
in the molecular structure leading us to speculate that ruptures of the covalent bonds of the main chains control the
failure in both cases. The general shape of the stress strain curves for both gels are similar, even though the method
and mechanism of gelation differ drastically between the gels, and the ultimate breaking stresses for both gels are
also similar in magnitude, even though the gel cross-links are different. In terms of general trends, the two gels
differed drastically only in their ultimate breaking strain relations. Young's Modulus and K (from curve fitting with Eq.
(2)) are best correlated in cases where only the concentration of the monomer or gum of a gel is varied. Using
membrane theory, a 1-µm-thick layer on an aggregate with a 1-mm diameter, having the mechanical properties of the
polyacrylamide compositions tested, can support a range of maximum internal pressures from 0.046 to 2.5 kPa. Thus,
the adsorbed polyacrylamide network could contribute significant stabilizing pressures on the aggregate surface. The
similarities between gellan (a natural microbial polymer) gels and polyacrylamide (wholly synthetic polymer) gels,
and the pressures that an adsorbed polyacrylamide network may be able to withstand, may explain why linear
polyacrylamide polymers are currently being used successfully against erosion and soil crusting.
ACKNOWLEDGMENTS
The authors thank Dr. Michael Singer for very useful discussions and The Nutrasweet Kelco Company for providing
a sample of the gellan gum (Kelcogel LT100) used in this study. This work was funded by The Kearney Foundation of
Soil Science Grant WHCK and NSF EAR 9814152.
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[Context Link]
Key words: Gellan gels; mechanical properties; polyacrylamide gels; soil stabilizers
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Table 1
Fig. 2
Fig. 1
Equation 1
Equation 2
Table 2
Equation 3
Equation 4
Equation 5
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Equation 6
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Equation
7
Fig. 3
Table 4
Fig. 4
Table 3
Fig. 6
Fig. 5
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Equation 8
Fig. 8
Fig. 9
Table 5
Table 6
Fig. 10
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Soil Science
Issue: Volume 165(10), October 2000, pp 778-792
Copyright: © 2000 Lippincott Williams & Wilkins, Inc.
Publication Type: [Technical Articles]
ISSN: 0038-075X
Accession: 00010694-200010000-00003
Keywords: Gellan gels, mechanical properties, polyacrylamide gels, soil stabilizers
[Technical Articles]
MECHANICAL PROPERTIES OF GELLAN AND POLYACRYLAMIDE GELS WITH IMPLICATIONS
FOR SOIL STABILIZATION
1
2
1
Ferruzzi, Giulio G. ; Pan, Ning ; Casey, William H.
Author Information
1
University of California, Davis, Department of Land, Air and Water Resources, Davis, CA 95616; Dr. Casey is corresponding
author.
2
University of California, Davis, Division of Textiles and Clothing & Biological and Agricultural Engineering, Davis, CA 95616
Address correspondence to Dr. William H. Casey, One Shields Ave., Davis, CA, 95616. E-mail: [email protected]
Received Jan. 10, 2000; accepted May 16, 2000.
Abstract
Organic matter can stabilize soil aggregates against disintegration upon wetting. We examined the tensile
strengths of two polymer gels that were chosen to represent features of soil organic matter. The mechanical
properties of polyacrylamide and gellan gels (gellan is a natural polysaccharide) are remarkably similar despite large
differences in molecular structure. The general shape of the stress strain curves for both gels is similar, although the
method and mechanism of gelation differs drastically between the gels. The ultimate breaking stresses for both gels
are also similar in magnitude (13 to 1100 kPa for polyacrylamide and 9 to 350 kPa for gellan), even though they differ
fundamentally in type of gel cross-links and vary drastically in their ultimate breaking strain relations. Breaking strain
tends to decrease with increased polymer and BIS concentration for polyacrylamide gels, whereas the relations
tended to be more complex for gellan gels. These measurements allow some constraints to be placed on the effects
of polymers on soil aggregate stability. For example, a 1-µm-thick layer of polyacrylamide, on a 1 mm-diameter
aggregate, can support a range of maximum internal pressures from 0.046 to 2.5 kPa.
Fertile aridic soils, such as those in the most productive agricultural areas of California, tend to slake during
irrigation events. The slaking destroys structure and reduces infiltration rates, which ultimately translates to reduced
crop yields. Good soil structure for crop growth depends on the presence of aggregates that remain stable when
wetted. Organic matter can prevent aggregate disintegration upon wetting, although the kind of organic matter, and
the way in which organic matter interacts with soil aggregates, is not completely understood. However, it is known
that organic polymers can act as a cementing or gluing agent that reinforces the aggregate architecture structurally
(Tisdall and Oades, 1982; Quirk, 1978; Russell, 1988). One can reasonably expect the stability of the aggregate to
relate to the strength of the polymers. Additionally, some polymers are more hydrophobic than the soil mineral
constituents and can increase aggregate stability by preventing, or slowing, the entry of water into the aggregate
pores (Sullivan, 1990; Coughlan et al., 1973). Understanding the interaction of the organic polymers with soil
aggregates is key to controlling erosion and hydraulic properties of soil.
The composition and structure of soil organic matter is understood poorly because it cannot be extracted from
the soil without damage. However, polysaccharides derived from plants and microbes have been isolated, and some
of these polysaccharides have demonstrated aggregate stabilizing affects (Martin, 1946; Chesters et al., 1957).
Synthetic polymers, such as linear polyacrylamides, stabilize soil aggregates by coating them with a network of
entangled polyacrylamide molecules (Fig. 1). Closer observation of the adsorbed polymer has led to the idea that
polyacrylamide molecules are adsorbed in strands of several chains (Audsley and Fursey, 1965). The elastic polymer
network that forms around an aggregate (Fig. 1) structurally reinforces it as it swells during quick wetting, such as in
the case of an irrigation event. As long as the outward force of the swelling aggregate does not exceed the inward
force of the polymer network, the aggregate is stable. This structural reinforcement should be similar to the effects
of natural soil organic matter, with the exception that the polymer acts from the outside of the aggregate only. The
stress that the adsorbed polymer network can support will be a function of network structure and composition.
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Fig. 1. Adsorbed polymer network around a soil aggregate, such that forms on immersion of an aggregate in a solution
containing polyacrylamide.
Unfortunately, it is extremely difficult to test these networks in situ. Instead, we analyze the properties of pure,
hydrated polymer networks, or gels, to represent the adsorbed polymer network counterparts. This way we can, and
do, synthesize a series of gels with varying structures and compositions and test their mechanical properties to
determine the magnitude of stabilizing forces that the networks can provide soil aggregates. One of the gels used in
this study is made from the microbial polysaccharide gellan gum (Kelcogel LT100). This unclarified, high-acyl-content
gum is used as synthesized by Sphigomonas elodea to represent natural soil microbial polysaccharides. Three of the
four sugar residues in gellan are glucose, glucuronic acid, and rhamnose which, among other sugar residues, are the
major constituents of polysaccharides produced by the soil microbes Rhizobium and Agrobacterium (Rao, 1977). The
second gel, polyacrylamide, is wholly synthetic yet similar to some soil organic matter in its ability to resist
degradation. Linear polyacrylamide has been used extensively in agriculture to control erosion and maintain
infiltration rates (Sojka et al., 1998a; Sojka and Lentz, 1996). Evidence suggests that linear polyacrylamides also
stabilize soil structure (Sojka et al., 1998a and b), most likely by adsorbing onto aggregates in the form of an elastic
polymeric network.
MATERIALS AND METHODS
Polyacrylamide Gels
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The polyacrylamide gels were prepared via free-radical polymerization using ammonium persulphate as the
initiator (Rosen, 1993). The polyacrylamide gels (compositions P1-P5) were synthesized by mixing 0.04 g ammonium
persulphate and varying amounts of acrylamide and methylene-bisacrylamide (BIS) monomers while keeping the total
monomer molarity constant at 1 M. The exact amounts of monomers used for each polyacrylamide gel composition
are summarized in Table 1. The mixture was diluted to 100 mL with deionized water, degassed under vacuum, and
polymerized in microcapillaries at 60 °C for 2.25 h. After synthesis, the gels were dried in ethanol for 24 to 48 h to
aid in the removal of the gels from the microcapillaries and then rinsed for 24 to 48 h in deionized water to remove
residual unreacted monomer.
TABLE 1 Polyacrylamide gel synthesis compositions
A second batch of polyacrylamide gels (compositions P6-P8) was synthesized by mixing 0.04 g ammonium
persulphate and varying the total monomer molarity while keeping the mole fraction of BIS at a constant value of
0.05. The mixture was then treated as mentioned above.
The polyacrylamide gels consist of polymer chains comprised of acrylamide monomers that are covalently linked
to other chains via the (BIS) molecule into a three-dimensional structure (Fig. 2A). During synthesis, microgels form
before the onset of macrogelation (Nagash and Okay, 1996). These microgels are denser than the bulk gel and richer
in cross-links (Fig. 2A). As gelation proceeds, the microgels are connected to the macrogel network through pendant
vinyls and free-radical ends (Nagash and Okay, 1996).
Fig. 2. Schematic of the gel structures in this study. (A) represents the polyacrylamide gel network (black dots
represent BIS) that forms in dilute aqueous acrylamide solutions (adapted from Nagash and Okay, 1996). (B)
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represents the gellan gel network that forms in gellan solutions in the presence of cations (adapted from Crescenzi,
1995).
Gellan Gels
The gellan gels were synthesized in the presence of dissolved calcium chloride so that the polymer chains
2+
cross-link into a three dimensional structure via Ca ionic bridges. The gellan gels (compositions G1-G4) were
prepared by heating deionized water to 95 °C, adding gellan gum (Kelcogel LT100) to the vigorously stirred solution
and allowing the gum to dissolve completely. Solid CaCl ·2H O was then added to make the calcium concentration 0.1
2
2
M. The exact amounts of gum, water, and CaCl ·2H O used for each gellan gel composition are summarized in Table
2
2
2. The solution was then degassed under vacuum conditions and transferred to microcapillaries where gelation
occurred upon cooling (Chandrasekaran et al., 1992). The gels were allowed to cure for 24 h before they were dried
in ethanol for 24 to 48 h. The gels were then extracted from the microcapillaries and rinsed for approximately 24 h in
0.1 M CaCl before mechanical properties were measured.
2
TABLE 2 Gellan gel synthesis compositions
A second batch of gellan gels (compositions G5-G8) was prepared in a similar fashion, keeping the gellan gum
constant but varying the amount of calcium chloride added, to create gellan gels with varying calcium
concentrations. The solutions were then treated as mentioned above with the exception that the gels were rinsed
with calcium chloride solutions at concentrations similar to the gel synthesis concentrations.
The gellan gels (Fig. 2B) consist of polymer chains that are linked ionically via cationic bridging during gelation.
The structure of the junction is a doubled-stranded helix that is held together by the attraction of the carboxyl
groups on the gellan polymer and a mono or divalent counter ion (Fig. 2B, detail) (Crescenzi, 1995, Chandrasekaran
and Thailambal, 1990; Chandrasekaran and Radha, 1995). In Fig. 2B, the letter a indicates the acetyl group that
occurs once every two repeating gellan units (four sugars shown) and the letter b indicates the glyceryl group that
occurs once every repeating gellan unit. The clarified, low-acyl-content gellan (Kelcogel) has been studied
extensively because of its promising performance as a food additive.
Mechanical Testing
All tests were performed on an Instron 1122 mechanical testing instrument in tensile mode with sample lengths
ranging from 2 to 7 cm in length and a constant crosshead speed of 20 mm/min at 21 °C. Accuracy and precision of
the Instron 1122 were within 1% as determined by repeated measurements of force from a standard weight. Tensile
tests were performed on fully hydrated gels. Each gel specimen was gripped at the ends by the machine's upper and
lower grips. The gel ends remained dry by keeping the ends of the gel specimens out of the respective hydrating
solution. Each specimen was inspected visually before and during each test. If failures developed at or near the
dry-end transition area, the data were discarded. The data generated by mechanical testing of the gels are force and
displacement. This information is then converted to engineering stress: Equation (1) where F is force and A is the
o
initial cross-sectional area of the specimen and strain: Equation (2) where [DELTA]L is the deformation of the sample
and L is the initial sample length. For the data to be useful, engineering stress (Eq. (1)) is converted into true stress:
o
Equation (3) where A is the cross-sectional area of the strained specimen. By making the assumptions that the
materials are isotropic and Poisson's ratio is 0.5, the total volume of the specimen remains unchanged during
deformation. The assumption that Poisson's ratio is 0.5 is made so that A can be calculated as a simple function of A ,
o
initial sample length and strained sample length. The assumption stated mathematically is: EQUATION (4) where L is
the sum of [DELTA]L and L . This allows Eq. (3) to be expressed as: EQUATION (5)
o
Equation 1
Equation 2
Equation 3
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Equation 4
Equation 5
The initial linear slope of the true stress ([sigma] ) versus strain ([varepsilon]) curve is called Young's modulus.
t
The modulus essentially describes the stress-strain behavior of a material in the initial, linear elastic region of
deformation. Rigid materials have large moduli, and more deformable materials have smaller moduli. Young's moduli
were determined for each individual specimen from its true stress-strain curve.
Stress-Strain Modeling
A simple equation was used to fit the stress-strain data: Equation (6) where K and n are fitting parameters and
[varepsilon] is true strain calculated from Eq. (2) by the following relation (Hershko and Nussinovitch, 1995):
t
EQUATION (7) Equation (6), although empirical in nature, contains variables that can be assigned physical
significance. According to Hershko and Nussinovitch (1995), the K of Eq. (6) is essentially the elastic (Young's)
modulus. Therefore, Young's Modulus calculated from the stress-strain curve and K obtained from curve fitting should
be equivalent.
Equation 6
Equation 7
RESULTS AND DISCUSSIONS
Typical stress-strain curves for the polyacrylamide gels and gellan gels tested are presented in Fig. 3. The general
shape of the stress-strain curve is similar for both the polyacrylamide gels and the gellan gels. Reproducibility in
ultimate breaking stress and strain among specimens of the same composition is reported as standard deviations in
Table 3 and as error bars in the figures.
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Fig. 3. Typical stress-strain curves for the gellan and polyacrylamide gels. (A) Stress-strain curves for the gellan gels
with various calcium concentrations (Table 2). The curve for composition G5 is obscured by the other curves, but the
ultimate breaking stress and strain are located at the arrowhead. (B) Stress-strain curves for the gellan gels with
various gum concentrations (Table 2). (C) Stress-strain curves for the polyacrylamide gels with various BIS
concentrations (Table 1). (D) Stress-strain curves for the polyacrylamide gels with various total monomer
concentrations (Table 1).
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TABLE 3 Ultimate breaking stress and strain for experimental gels
The ultimate breaking stress and strain results for the polyacrylamide and gellan gels are summarized in Table 3.
Each reported value of strain ([varepsilon]) and stress ([sigma] ) in Table 3 is the average of two to five individual
t
specimens, and the reported uncertainty is the standard deviation of the calculated average. The large uncertainty of
some measurements in Table 3 reflects real variation in behavior of similarly prepared gel specimens, not
measurement error.
An average Young's modulus is reported for each gel composition in Table 4. Again, the large uncertainty of some
measurements reflects real variation in behavior of similarly prepared gel specimens and not measurement error.
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TABLE 4 Young's Moduli and K for experimental gels
Deformation Reversibility
Most of the polyacrylamide gel's deformation is reversible within seconds of relieving strain. In contrast, the
gellan gel's deformation is not totally reversible even after 48 h of rehydrating in an appropriate solution. It was
observed that the gellan gels would begin to expel water at high strains near failure. These results indicate that the
gellan gels do not behave as incompressible materials (i.e., the Poisson's ratio is < 0.5) and that not all of the
deformation induced in the gellan gels is reversible.
The loss of water from the gellan gels during testing also indicates that the true stress is actually greater than
reported in these results. We interpret the irreversible deformation of the gellan gels as caused by the loss of water
and the unraveling of the helical junctions along with some probable main chain failures. Since the junctions can
form only at elevated temperatures not achievable during mechanical testing (>75 °C, in most cases), we consider it
unlikely that the gellan gel would recover all of its deformation if any junctions were unraveled inasmuch as the
measurements were performed at a constant 21 °C.
Stress-Strain Curves
Since all of the gels were hydrated, we expected that the gellan gels would be much weaker than the
polyacrylamide gels because the ionic cross-links associated with the gellan gels require less energy to break in an
aqueous solution (-4 to 10 kJ/mol for the bond between a divalent metal of the alkaline-earth series and a carboxyl
bond (Nancollas, 1956)) than covalent bonds (345-355 kJ/mol for a C-C bond (March, 1992)) associated with the
polyacrylamide gel. Yet the ultimate breaking stress values of both gellan and polyacrylamide gels were the same
order of magnitude. We interpret this result as a reflection of the physical structure of the gellan cationic bridge,
described in detail by other researchers (Morris et al., 1996; Chandrasekaran et al., 1995; Chandrasekaran et al.,
1992). Although the cross-links that bridge gellan main chains are ionic, the energy required to break the helical
junction is the energy required to break the main chain of the gellan, which is a covalent bond (approximately
355-380 kJ/mol for a C-O bond (March, 1992)). Therefore, the ultimate breaking stresses for the polyacrylamide and
gellan gels are on the same order of magnitude because similar bonds rupture in spite of the differences in crosslinking mechanism.
Polyacrylamide Gels
For polyacrylamide gels, ultimate breaking stress increases with total monomer concentration for a constant
2
mole fraction of BIS (Fig. 4A). There is an apparent linear correlation (R = 0.99904) for compositions P3, P6, and P7.
Composition P8 deviates from linearity as the concentration of monomer increases. This result is corroborated by
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results from Baselga et al. (1987), who found more of an exponential dependence of breaking stress on monomer
concentration for a slightly different concentration range.
Fig. 4. Ultimate properties of polyacrylamide gels. Error bars are the standard deviations as reported in Table 3. (A)
Ultimate breaking stress as a function of total monomer concentration. (B) Ultimate breaking stress as a function of
BIS concentration. (C) Ultimate breaking strain as a function of total monomer concentration. (D) Ultimate breaking
strain as a function of BIS concentration.
The correlation between ultimate breaking stress and total monomer concentration gives us insight on gel
structure and the role of inhomogeneity. Figure 2A is a representation of the polyacrylamide network at low initial
monomer concentrations (Nagash and Okay, 1996). As the monomer concentration increased, some factors became
important in dictating the final gel properties. The number of free chain ends (Fig. 2A) remained constant because
they were controlled by the amount of initiator in solution (Kulicke and Nottelmann, 1989). The number of microgels
increased with monomer concentration, and the relative distance between them decreased. More importantly, the
number of loops (Fig. 2A) that did not contribute to elasticity of the gel decreased, and the number of entanglements
(Fig. 2A) that did contribute to elasticity increased (Kulicke and Nottelmann, 1989). The overall number of network
defects in polyacrylamide gels may be least in gels synthesized with high initial monomer concentrations and low
mole fraction of BIS (Baselga et al., 1987). These factors may contribute to the observed increase in breaking stress
with respect to an increase in monomer concentration of the gels.
At the conditions of composition P8, the mole ratio of water molecules to total monomers is approximately 17:1.
At this concentration, the density of the microgels (Fig. 2A) and the density of the surrounding gel become similar.
That is, as predicted by Baselga et al. (1987), the gel becomes more homogenous. A homogeneous polymer (e.g.,
purely crystalline or completely amorphous) is transparent, but a heterogeneous polymer (e.g., differing densities
throughout the polymer) is translucent (Rosen, 1993). Thus, the clarity in polyacrylamide gels is related to the
presence of microgels in the gel structure (Bansil and Gupta, 1980) and the difference in refractive index between
the microgels and the bulk gel. From the phase diagram available in the literature (Bansil and Gupta, 1980),
polyacrylamide gels with a BIS mole fraction of 0.05 and total monomer concentrations > 0.37 M should be opaque.
The poly-acrylamide gels of compositions P3 and P7 are, in fact, opaque. Composition P6, whose composition (Table
1) is close to the phase diagram boundary, is clear. The appearance of the composition P8 gels was also clear,
indicating a more homogenous network and that an additional phase boundary for polyacrylamide may exist at high
total monomer concentrations. The increased homogeneity of composition P8 may explain the large increase in gel
strength at high total monomer concentrations observed in this study and by other researchers (Baselga et al., 1987).
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The correlation between ultimate breaking stress and BIS concentration for polyacrylamide gels with less that 0.1
mole fraction of BIS found in this study has been observed previously for a slightly different range of polyacrylamide
compositions (Baselga et al., 1987). The larger composition range used in this study has yielded information of highly
cross-linked gels indicating that a BIS mole fraction 0.1 produces the strongest gel at a given total monomer
concentration (Fig. 4B). Mole fractions of BIS less than or > 0.1 diminished the ultimate breaking stress of the gels
tested as indicated in Fig. 4B. This detail is related to the inhomogeneity of the gel and that the concentration of BIS
in the gel affects the polymerization rate and intermolecular linking (Nagash and Okay, 1996).
2
There is a good linear correlation (R = 0.99991) between ultimate breaking strain and total monomer
concentration for compositions P3, P6, and P7 (Fig. 4C). The polyacrylamide gels become more brittle with an
increase in total monomer concentration, as indicated by the decrease in ultimate breaking strain when the monomer
concentration is increased. Baselga et al. (1987) also observed a similar trend for polyacrylamide gels concentrations
of up to 2.4 M total monomer concentration.
The correlation between ultimate breaking strain and BIS concentration for polyacrylamide gels between 0.005
and 0.05 mole fraction BIS found in this study has also been observed previously (Baselga et al., 1987; Cohen et al.,
1992). The additional gels we tested above the 0.05 mole fraction BIS indicate that as more BIS is polymerized in the
gel, the more the breaking strain continues to decrease (Fig. 4D). The observed decrease in breaking strain with
respect to BIS concentration is more drastic at the lower concentrations (compositions P1, P2, and P3) than at higher
BIS concentrations (P3, P4, and P5).
The correlation between Young's Modulus and total monomer concentration (Fig. 5A) agrees with the previous
results for polyacrylamide gels (Cohen et al., 1992; Benguigui, 1995; Baselga et al., 1987). The additional gel
composition (P8) tested in this study indicates that the correlation is still valid at polyacrylamide concentrations of
up to 2.997 M total monomer. The correlation between Young's Modulus and BIS concentration (Fig. 5B) at low BIS
concentrations also agrees with previous results (Cohen et al., 1992; Benguigui, 1995; Baselga et al., 1987). The
inhomogeneity of the polyacrylamide network may account for the observed nonlinear correlation (Benguigui, 1995).
Baselga et al. (1987) and Cohen et al. (1992) observed a broad maximum in Young's Modulus between the range of the
0.02 and 0.05 mole fraction of BIS. We observed this maximum in Young's Modulus in the same region, although the
additional gel compositions (P4 and P5) tested in this study indicate a possible increase in Young's modulus at BIS
mole fractions of 0.15 concentrations (Fig. 5B). Because of the large error associated with composition P5 and
because the previous researchers did not perform tests on gels of that composition, it is difficult to relate this result
to any physical changes in the gel structure.
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Fig. 5. Young's Modulus of polyacrylamide gels as a function of total monomer concentration (A) and BIS concentration
(B). Error bars are the standard deviations as reported in Table 4.
Gellan Gels
2
For gellan gels, there is an apparent linear correlation (R = 0.97928) between ultimate breaking stress and gum
concentration (wt/wt%) for compositions G1-G4, which were gels with similar calcium concentrations but which
varied in total gum concentration (Fig. 6A). This correlation agrees with observations on a type of gellan gel with few
acyl group (Kelcogel) in a similar range of gum concentrations (Hershko and Nussinovitch, 1995; Tang et al., 1994).
Acyl groups are known to interfere with the gelation process (Chandrasekaran and Thailambal, 1990; Chandrasekaran
and Radha, 1995).
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Fig. 6. Ultimate properties of gellan gels. Error bars are the standard deviations as reported in Table 3. (A) Ultimate
breaking stress as a function of gellan gum concentration. (B) Ultimate breaking stress as a function of calcium
concentration. (C) Ultimate breaking strain as a function of gellan gum concentration. (D) Ultimate breaking strain as
a function of calcium concentration.
The relation between ultimate breaking stress and calcium concentration is more complex. Increasing calcium
concentrations from 0.001 M to 0.05 M increases the breaking stress of the gels significantly. A further increase in
calcium from 0.05 M to 0.1 M does not affect the breaking stress significantly (Fig. 6B). This correlation was also
observed by Tang et al. (1994) for a similar type of gellan gel (Kelcogel) in a smaller range of calcium concentrations.
For the compositions tested, the ultimate breaking strain and gum concentration relation is nonlinear (Fig. 6C).
There was an increase in breaking strain as the gum concentration increased from 1 to 1.5%. Additional increases in
gum concentrations of up to 2.5% did not change the observed breaking strain of the resulting gels significantly,
indicating that the breaking strain became independent of gum concentrations above 1.5%. The relation between
ultimate breaking strain and calcium concentration is similar to the relation between ultimate breaking stress and
calcium concentration. Increasing calcium concentrations from 0.001 M to 0.05 M increased the breaking strain of the
resulting gels significantly (Fig. 6D). A further increase in calcium from 0.05 M to 0.1 M decreased the breaking strain
slightly. This indicates that calcium concentrations greater than 0.05 M may prevent cationic bridging from occurring,
thus weakening the gel (Tang et al., 1994) as observed in the decrease of both breaking and stress and strain of
composition G2.
Neither the correlation between calcium concentration and ultimate breaking strain, nor the correlation
between gum concentration and ultimate breaking strain, corroborate results found by Hershko and Nussinovitch
(1995) or Tang et al. (1994). The difference in ultimate strain relations is attributable to the high acyl group content
of the gellan gum used in this study. Gellan gels with few acyl groups are known to be more brittle, and this explains
the observed differences between our strain data and that of other researchers (Sanderson, et al., 1988; Morris et
al., 1996). Previous studies with low acyl group content gellan gum indicates an increase in breaking strain as the
gellan gum concentration is increased (Hershko and Nussinovitch, 1995; Tang et al., 1994). The only difference
between the gellan gum used in our study and that of the above mentioned authors is the acyl content of the gum.
Therefore, the observed drop in breaking strain with decrease in gum concentration is directly related to the inability
of the high-acyl-group-content gellan gum used in our study to form a strong gel network at low concentrations.
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For gellan gels, there is a correlation between Young's Modulus and gellan gum concentration (Fig. 7A). The
moduli of composition G1 and G2 are statistically similar, but Young's Modulus increases with increases in gum
concentration for composition G2 through G4. However, there is no correlation between Young's Modulus and calcium
concentration (Fig. 7B).
Fig. 7. Young's Modulus of gellan gels as a function of gellan gum concentration (A) and calcium concentration (B).
Error bars are the standard deviations as reported in Table 4.
The deviation from linearity of composition G1 (Fig. 7A) may have been caused by keeping the calcium
concentration constant for these gels as the gum concentration was increased, leading to a small variance in calciumto-gum concentration ratios. Therefore, we may observe a dependence of Young's Modulus on gum concentration
along with calcium-to-gum concentration ratios since these were the only parameters that were manipulated.
Stress-Strain Modeling
The average values for K that resulted from the curve fitting of the stress-strain curves with Eq. [6] are reported
for each gel composition in Table 4. Equation [6] consistently indicated an increase in K with an increase in gum or
monomer concentration and calcium or BIS concentration, which is not the case for observed Young's Moduli of the
gels tested. For the gels in this study, K and Young's Modulus are correlated only for gels whose gum or monomer
concentration is varied (Figs. 8 and 9). Additionally, the correlation is valid only for a particular range of
concentrations. These results indicate that Eq. (6) may be used to correlate K and Young's Modulus in a series of gels
where the average chain length remains relatively constant. Once a correlation between K and Young's Modulus has
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been established for a gel series, it can be useful in predicting Young's Moduli of intermediate gel compositions.
Fig. 8. Relation between K fit to the stress-strain data from Eq. (8) and Young's Modulus for polyacrylamide gels. Error
bars are the standard deviations as reported in Table 4. Note that both the fit K value and Young's Modulus increase
greatly between compositions P7 and P8.
Equation 8
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Fig. 9. Relation between K fit to the stress-strain data from Eq. (8) and Young's Modulus for gellan gels. Error bars are
the standard deviations as reported in Table 4. Note that the fit K value decreases between compositions G1 and G2
whereas Young's Modulus is essentially similar for both compositions.
Forces on Soil Aggregates
When soils are wetted, as in an irrigation event, aggregates are quickly wetted from all sides. Any trapped air
compressed by the advancing water front can eventually disrupt the aggregate. It is inherently difficult to measure
air pressures in small fragile soil aggregates, and only one study in this regard was found in the literature.
Stroosnyder and Koorevaar (1972) measured internal air pressure of rapidly wetted loess soil aggregates of up to 8
kPa but noted that the aggregates began to fail as soon as they were immersed in water. Stroosnyder and Koorevaar's
observations indicate that not only air pressure, but also the wetting rate, play a role in aggregate disruption.
Assuming a spherical soil aggregate, membrane theory (Gere and Timoshenko, 1984) can be used to relate the
stresses in the polymer network to the internal pressure applied by the swelling soil aggregate. The stresses in a
spherical membrane are given by: Equation (8) where [sigma] is stress in the polymer layer, t is the thickness of the
polymer layer, r is the radius of the aggregate and p is the pressure on the polymer layer's inner surface (Gere and
Timoshenko, 1984). By knowing the thickness (t), aggregate radius (r), and maximum breaking stress ([sigma]) of a
particular polyacrylamide composition, the maximum inward pressure an adsorbed polymer network can apply to an
aggregate can be calculated.
Linear polyacrylamide would be the adsorbate on the aggregate because it is used in irrigation agriculture,
although it is interesting to note that the breaking stresses of gellan and polyacrylamide gels are similar. Actually,
most hydrogels (both synthetic and biological) fall within similar values of breaking stress and strain (Table 5). This
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similarity between natural and synthetic hydrogels strengthens the argument that synthetic polymers can contribute
aggregate stabilizing forces on soils similar to natural organic matter such as microbial polysaccharides. Taking into
account the ultimate breaking strain and stress of a 1-µm-thick layer of adsorbed linear polyacrylamide having the
mechanical properties of the polyacrylamide gels compositions tested on an aggregate with an initial diameter of 1
mm, we calculate a range of maximum internal pressures from 0.046 to 2.5 kPa (Table 6). The 1-µm thickness was
based on Atomic Force Microscope (AFM) imaging of polyacrylamide on vermiculite in our laboratory (unpublished
data).
TABLE 5 Ranges of ultimate breaking stresses and strains of various hydrogels
TABLE 6 Maximum pressures generated by polyacrylamide gels of various thickness on a 1-mm aggregate
Although the force of the adsorbed polyacrylamide network alone could not prevent the entrapped air from
escaping a loess aggregate at peak pressure, the network could contribute significant stabilizing pressures on the
aggregate surface. This stabilizing pressure could reinforce the aggregate when it begins to slake as soon as it is
wetted, as observed by Stroosnyder and Koorevaar (1972). In the initial moments of wetting, water enters the larger
pores most rapidly (Bolt and Koenigs, 1972). As the internal air pressure builds, the rate of wetting decreases until
the pressure inside the aggregate stops the wetting front or the aggregate ruptures. The polyacrylamide layer would
be key in providing reinforcement during this point in wetting. The entrapped air could escape through the largest
pore (Fig. 10) without disrupting or disintegrating the aggregate (Bolt and Koenigs, 1972).
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Fig. 10. Air/water relations in aggregate pores. Both, large and small pores exist on an aggregate surface (A). As the
aggregate is wetted (B), water enters larger pores faster than smaller pores. Shaded areas indicate the water-filled
part of the pore, and the arrows indicate the direction of water movement. Once a critical pressure is reached (C),
the aggregate will rupture, releasing excess air pressure. The presence of a polymer network on the surface of the
aggregate could reinforce the aggregate structure and allow excess air pressure to escape as air bubbles through the
largest pore(s) without compromising aggregate stability (D).
CONCLUSION
The mechanical properties of polyacrylamide and gellan gels are remarkably similar despite the large difference
in the molecular structure leading us to speculate that ruptures of the covalent bonds of the main chains control the
failure in both cases. The general shape of the stress strain curves for both gels are similar, even though the method
and mechanism of gelation differ drastically between the gels, and the ultimate breaking stresses for both gels are
also similar in magnitude, even though the gel cross-links are different. In terms of general trends, the two gels
differed drastically only in their ultimate breaking strain relations. Young's Modulus and K (from curve fitting with Eq.
(2)) are best correlated in cases where only the concentration of the monomer or gum of a gel is varied. Using
membrane theory, a 1-µm-thick layer on an aggregate with a 1-mm diameter, having the mechanical properties of the
polyacrylamide compositions tested, can support a range of maximum internal pressures from 0.046 to 2.5 kPa. Thus,
the adsorbed polyacrylamide network could contribute significant stabilizing pressures on the aggregate surface. The
similarities between gellan (a natural microbial polymer) gels and polyacrylamide (wholly synthetic polymer) gels,
and the pressures that an adsorbed polyacrylamide network may be able to withstand, may explain why linear
polyacrylamide polymers are currently being used successfully against erosion and soil crusting.
ACKNOWLEDGMENTS
The authors thank Dr. Michael Singer for very useful discussions and The Nutrasweet Kelco Company for providing
a sample of the gellan gum (Kelcogel LT100) used in this study. This work was funded by The Kearney Foundation of
Soil Science Grant WHCK and NSF EAR 9814152.
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Key words: Gellan gels; mechanical properties; polyacrylamide gels; soil stabilizers
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Table 1
Fig. 2
Fig. 1
Equation 1
Equation 2
Table 2
Equation 3
Equation 4
Equation 5
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Equation 6
https://vpn.lib.ucdavis.edu/sp-3.2.4a/,DanaInfo=ovidsp.tx.ovid...
Equation
7
Fig. 3
Table 4
Fig. 4
Table 3
Fig. 6
Fig. 5
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Fig. 7
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Equation 8
Fig. 8
Fig. 9
Table 5
Table 6
Fig. 10
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