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[Technical Articles]

Soil ScienceIssue: Volume 165(10), October 2000, pp 778-792Copyright: 2000 Lippincott Williams & Wilkins, Inc.Publication Type: [Technical Articles]ISSN: 0038-075XAccession: 00010694-200010000-00003Keywords: Gellan gels, mechanical properties, polyacrylamide gels, soil stabilizers

MECHANICAL PROPERTIES OF GELLAN AND POLYACRYLAMIDE GELS WITH IMPLICATIONSFOR SOIL STABILIZATIONFerruzzi, Giulio G.1; Pan, Ning2; Casey, William H.1

Author Information1University of California, Davis, Department of Land, Air and Water Resources, Davis, CA 95616; Dr. Casey is corresponding

author.2University of California, Davis, Division of Textiles and Clothing & Biological and Agricultural Engineering, Davis, CA 95616Address correspondence to Dr. William H. Casey, One Shields Ave., Davis, CA, 95616. E-mail: [email protected] Jan. 10, 2000; accepted May 16, 2000.

Abstract

Organic matter can stabilize soil aggregates against disintegration upon wetting. We examined the tensilestrengths of two polymer gels that were chosen to represent features of soil organic matter. The mechanicalproperties of polyacrylamide and gellan gels (gellan is a natural polysaccharide) are remarkably similar despite largedifferences in molecular structure. The general shape of the stress strain curves for both gels is similar, although themethod and mechanism of gelation differs drastically between the gels. The ultimate breaking stresses for both gelsare also similar in magnitude (13 to 1100 kPa for polyacrylamide and 9 to 350 kPa for gellan), even though they differfundamentally in type of gel cross-links and vary drastically in their ultimate breaking strain relations. Breaking straintends to decrease with increased polymer and BIS concentration for polyacrylamide gels, whereas the relationstended to be more complex for gellan gels. These measurements allow some constraints to be placed on the effectsof polymers on soil aggregate stability. For example, a 1-m-thick layer of polyacrylamide, on a 1 mm-diameteraggregate, 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 duringirrigation events. The slaking destroys structure and reduces infiltration rates, which ultimately translates to reducedcrop yields. Good soil structure for crop growth depends on the presence of aggregates that remain stable whenwetted. Organic matter can prevent aggregate disintegration upon wetting, although the kind of organic matter, andthe way in which organic matter interacts with soil aggregates, is not completely understood. However, it is knownthat 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 torelate to the strength of the polymers. Additionally, some polymers are more hydrophobic than the soil mineralconstituents and can increase aggregate stability by preventing, or slowing, the entry of water into the aggregatepores (Sullivan, 1990; Coughlan et al., 1973). Understanding the interaction of the organic polymers with soilaggregates 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 fromthe soil without damage. However, polysaccharides derived from plants and microbes have been isolated, and someof 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 ofentangled polyacrylamide molecules (Fig. 1). Closer observation of the adsorbed polymer has led to the idea thatpolyacrylamide molecules are adsorbed in strands of several chains (Audsley and Fursey, 1965). The elastic polymernetwork that forms around an aggregate (Fig. 1) structurally reinforces it as it swells during quick wetting, such as inthe case of an irrigation event. As long as the outward force of the swelling aggregate does not exceed the inwardforce of the polymer network, the aggregate is stable. This structural reinforcement should be similar to the effectsof natural soil organic matter, with the exception that the polymer acts from the outside of the aggregate only. Thestress that the adsorbed polymer network can support will be a function of network structure and composition.

Ovid: MECHANICAL PROPERTIES OF GELLAN AND PO... https://vpn.lib.ucdavis.edu/sp-3.2.4a/,DanaInfo=ovidsp.tx.ovid...

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Fig. 1. Adsorbed polymer network around a soil aggregate, such that forms on immersion of an aggregate in a solutioncontaining 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, anddo, synthesize a series of gels with varying structures and compositions and test their mechanical properties todetermine the magnitude of stabilizing forces that the networks can provide soil aggregates. One of the gels used inthis study is made from the microbial polysaccharide gellan gum (Kelcogel LT100). This unclarified, high-acyl-contentgum is used as synthesized by Sphigomonas elodea to represent natural soil microbial polysaccharides. Three of thefour sugar residues in gellan are glucose, glucuronic acid, and rhamnose which, among other sugar residues, are themajor constituents of polysaccharides produced by the soil microbes Rhizobium and Agrobacterium (Rao, 1977). Thesecond gel, polyacrylamide, is wholly synthetic yet similar to some soil organic matter in its ability to resistdegradation. Linear polyacrylamide has been used extensively in agriculture to control erosion and maintaininfiltration rates (Sojka et al., 1998a; Sojka and Lentz, 1996). Evidence suggests that linear polyacrylamides alsostabilize soil structure (Sojka et al., 1998a and b), most likely by adsorbing onto aggregates in the form of an elasticpolymeric network.

MATERIALS AND METHODS

Polyacrylamide Gels


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The polyacrylamide gels were prepared via free-radical polymerization using ammonium persulphate as theinitiator (Rosen, 1993). The polyacrylamide gels (compositions P1-P5) were synthesized by mixing 0.04 g ammoniumpersulphate and varying amounts of acrylamide and methylene-bisacrylamide (BIS) monomers while keeping the totalmonomer molarity constant at 1 M. The exact amounts of monomers used for each polyacrylamide gel compositionare summarized in Table 1. The mixture was diluted to 100 mL with deionized water, degassed under vacuum, andpolymerized in microcapillaries at 60 C for 2.25 h. After synthesis, the gels were dried in ethanol for 24 to 48 h toaid in the removal of the gels from the microcapillaries and then rinsed for 24 to 48 h in deionized water to removeresidual unreacted monomer.

TABLE 1 Polyacrylamide gel synthesis compositions

A second batch of polyacrylamide gels (compositions P6-P8) was synthesized by mixing 0.04 g ammoniumpersulphate and varying the total monomer molarity while keeping the mole fraction of BIS at a constant value of0.05. The mixture was then treated as mentioned above.

The polyacrylamide gels consist of polymer chains comprised of acrylamide monomers that are covalently linkedto other chains via the (BIS) molecule into a three-dimensional structure (Fig. 2A). During synthesis, microgels formbefore the onset of macrogelation (Nagash and Okay, 1996). These microgels are denser than the bulk gel and richerin cross-links (Fig. 2A). As gelation proceeds, the microgels are connected to the macrogel network through pendantvinyls 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 dotsrepresent 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

cross-link into a three dimensional structure via Ca2+ ionic bridges. The gellan gels (compositions G1-G4) wereprepared by heating deionized water to 95 C, adding gellan gum (Kelcogel LT100) to the vigorously stirred solutionand allowing the gum to dissolve completely. Solid CaCl

22H

2O was then added to make the calcium concentration 0.1

M. The exact amounts of gum, water, and CaCl22H

2O used for each gellan gel composition are summarized in Table

2. The solution was then degassed under vacuum conditions and transferred to microcapillaries where gelationoccurred upon cooling (Chandrasekaran et al., 1992). The gels were allowed to cure for 24 h before they were driedin ethanol for 24 to 48 h. The gels were then extracted from the microcapillaries and rinsed for approximately 24 h in0.1 M CaCl

2 before mechanical properties were measured.

TABLE 2 Gellan gel synthesis compositions

A second batch of gellan gels (compositions G5-G8) was prepared in a similar fashion, keeping the gellan gumconstant but varying the amount of calcium chloride added, to create gellan gels with varying calciumconcentrations. The solutions were then treated as mentioned above with the exception that the gels were rinsedwith 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 carboxylgroups on the gellan polymer and a mono or divalent counter ion (Fig. 2B, detail) (Crescenzi, 1995, Chandrasekaranand Thailambal, 1990; Chandrasekaran and Radha, 1995). In Fig. 2B, the letter a indicates the acetyl group thatoccurs once every two repeating gellan units (four sugars shown) and the letter b indicates the glyceryl group thatoccurs once every repeating gellan unit. The clarified, low-acyl-content gellan (Kelcogel) has been studiedextensively 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 lengthsranging from 2 to 7 cm in length and a constant crosshead speed of 20 mm/min at 21 C. Accuracy and precision ofthe Instron 1122 were within 1% as determined by repeated measurements of force from a standard weight. Tensiletests were performed on fully hydrated gels. Each gel specimen was gripped at the ends by the machine's upper andlower grips. The gel ends remained dry by keeping the ends of the gel specimens out of the respective hydratingsolution. Each specimen was inspected visually before and during each test. If failures developed at or near thedry-end transition area, the data were discarded. The data generated by mechanical testing of the gels are force anddisplacement. This information is then converted to engineering stress: Equation (1) where F is force and A

o is the

initial cross-sectional area of the specimen and strain: Equation (2) where [DELTA]L is the deformation of the sampleand L

o is the initial sample length. For the data to be useful, engineering stress (Eq. (1)) is converted into true stress:

Equation (3) where A is the cross-sectional area of the strained specimen. By making the assumptions that thematerials are isotropic and Poisson's ratio is 0.5, the total volume of the specimen remains unchanged duringdeformation. 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 isthe sum of [DELTA]L and L

o. This allows Eq. (3) to be expressed as: EQUATION (5)

Equation 1

Equation 2

Equation 3


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Equation 4

Equation 5

The initial linear slope of the true stress ([sigma]t) versus strain ([varepsilon]) curve is called Young's modulus.

The modulus essentially describes the stress-strain behavior of a material in the initial, linear elastic region ofdeformation. Rigid materials have large moduli, and more deformable materials have smaller moduli. Young's moduliwere 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]

t is true strain calculated from Eq. (2) by the following relation (Hershko and Nussinovitch, 1995):

EQUATION (7) Equation (6), although empirical in nature, contains variables that can be assigned physicalsignificance. 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 shouldbe 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 generalshape of the stress-strain curve is similar for both the polyacrylamide gels and the gellan gels. Reproducibility inultimate breaking stress and strain among specimens of the same composition is reported as standard deviations inTable 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 gelswith various calcium concentrations (Table 2). The curve for composition G5 is obscured by the other curves, but theultimate breaking stress and strain are located at the arrowhead. (B) Stress-strain curves for the gellan gels withvarious gum concentrations (Table 2). (C) Stress-strain curves for the polyacrylamide gels with various BISconcentrations (Table 1). (D) Stress-strain curves for the polyacrylamide gels with various total monomerconcentrations (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]

t) in Table 3 is the average of two to five individual

specimens, and the reported uncertainty is the standard deviation of the calculated average. The large uncertainty ofsome measurements in Table 3 reflects real variation in behavior of similarly prepared gel specimens, notmeasurement error.

An average Young's modulus is reported for each gel composition in Table 4. Again, the large uncertainty of somemeasurements 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, thegellan gel's deformation is not totally reversible even after 48 h of rehydrating in an appropriate solution. It wasobserved that the gellan gels would begin to expel water at high strains near failure. These results indicate that thegellan gels do not behave as incompressible materials (i.e., the Poisson's ratio is < 0.5) and that not all of thedeformation 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 thanreported in these results. We interpret the irreversible deformation of the gellan gels as caused by the loss of waterand the unraveling of the helical junctions along with some probable main chain failures. Since the junctions canform only at elevated temperatures not achievable during mechanical testing (>75 C, in most cases), we consider itunlikely that the gellan gel would recover all of its deformation if any junctions were unraveled inasmuch as themeasurements 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 thepolyacrylamide gels because the ionic cross-links associated with the gellan gels require less energy to break in anaqueous solution (-4 to 10 kJ/mol for the bond between a divalent metal of the alkaline-earth series and a carboxylbond (Nancollas, 1956)) than covalent bonds (345-355 kJ/mol for a C-C bond (March, 1992)) associated with thepolyacrylamide gel. Yet the ultimate breaking stress values of both gellan and polyacrylamide gels were the sameorder 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 helicaljunction is the energy required to break the main chain of the gellan, which is a covalent bond (approximately355-380 kJ/mol for a C-O bond (March, 1992)). Therefore, the ultimate breaking stresses for the polyacrylamide andgellan gels are on the same order of magnitude because similar bonds rupture in spite of the differences in cross-linking mechanism.

Polyacrylamide Gels

For polyacrylamide gels, ultimate breaking stress increases with total monomer concentration for a constant

mole fraction of BIS (Fig. 4A). There is an apparent linear correlation (R2 = 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 monomerconcentration 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 ofBIS concentration. (C) Ultimate breaking strain as a function of total monomer concentration. (D) Ultimate breakingstrain as a function of BIS concentration.

The correlation between ultimate breaking stress and total monomer concentration gives us insight on gelstructure and the role of inhomogeneity. Figure 2A is a representation of the polyacrylamide network at low initialmonomer concentrations (Nagash and Okay, 1996). As the monomer concentration increased, some factors becameimportant in dictating the final gel properties. The number of free chain ends (Fig. 2A) remained constant becausethey were controlled by the amount of initiator in solution (Kulicke and Nottelmann, 1989). The number of microgelsincreased with monomer concentration, and the relative distance between them decreased. More importantly, thenumber 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 networkdefects in polyacrylamide gels may be least in gels synthesized with high initial monomer concentrations and lowmole fraction of BIS (Baselga et al., 1987). These factors may contribute to the observed increase in breaking stresswith 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 densitiesthroughout the polymer) is translucent (Rosen, 1993). Thus, the clarity in polyacrylamide gels is related to thepresence of microgels in the gel structure (Bansil and Gupta, 1980) and the difference in refractive index betweenthe 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 (Table1) 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 hightotal monomer concentrations. The increased homogeneity of composition P8 may explain the large increase in gelstrength 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 0.1mole fraction of BIS found in this study has been observed previously for a slightly different range of polyacrylamidecompositions (Baselga et al., 1987). The larger composition range used in this study has yielded information of highlycross-linked gels indicating that a BIS mole fraction 0.1 produces the strongest gel at a given total monomerconcentration (Fig. 4B). Mole fractions of BIS less than or > 0.1 diminished the ultimate breaking stress of the gelstested as indicated in Fig. 4B. This detail is related to the inhomogeneity of the gel and that the concentration of BISin the gel affects the polymerization rate and intermolecular linking (Nagash and Okay, 1996).

There is a good linear correlation (R2 = 0.99991) between ultimate breaking strain and total monomerconcentration for compositions P3, P6, and P7 (Fig. 4C). The polyacrylamide gels become more brittle with anincrease in total monomer concentration, as indicated by the decrease in ultimate breaking strain when the monomerconcentration is increased. Baselga et al. (1987) also observed a similar trend for polyacrylamide gels concentrationsof up to 2.4 M total monomer concentration.

The correlation between ultimate breaking strain and BIS concentration for polyacrylamide gels between 0.005and 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 thegel, the more the breaking strain continues to decrease (Fig. 4D). The observed decrease in breaking strain withrespect to BIS concentration is more drastic at the lower concentrations (compositions P1, P2, and P3) than at higherBIS concentrations (P3, P4, and P5).

The correlation between Young's Modulus and total monomer concentration (Fig. 5A) agrees with the previousresults for polyacrylamide gels (Cohen et al., 1992; Benguigui, 1995; Baselga et al., 1987). The additional gelcomposition (P8) tested in this study indicates that the correlation is still valid at polyacrylamide concentrations ofup to 2.997 M total monomer. The correlation between Young's Modulus and BIS concentration (Fig. 5B) at low BISconcentrations also agrees with previous results (Cohen et al., 1992; Benguigui, 1995; Baselga et al., 1987). Theinhomogeneity 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 the0.02 and 0.05 mole fraction of BIS. We observed this maximum in Young's Modulus in the same region, although theadditional gel compositions (P4 and P5) tested in this study indicate a possible increase in Young's modulus at BISmole fractions of 0.15 concentrations (Fig. 5B). Because of the large error associated with composition P5 andbecause the previous researchers did not perform tests on gels of that composition, it is difficult to relate this resultto 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

For gellan gels, there is an apparent linear correlation (R2 = 0.97928) between ultimate breaking stress and gumconcentration (wt/wt%) for compositions G1-G4, which were gels with similar calcium concentrations but whichvaried in total gum concentration (Fig. 6A). This correlation agrees with observations on a type of gellan gel with fewacyl 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; Chandrasekaranand 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) Ultimatebreaking stress as a function of gellan gum concentration. (B) Ultimate breaking stress as a function of calciumconcentration. (C) Ultimate breaking strain as a function of gellan gum concentration. (D) Ultimate breaking strain asa function of calcium concentration.

The relation between ultimate breaking stress and calcium concentration is more complex. Increasing calciumconcentrations from 0.001 M to 0.05 M increases the breaking stress of the gels significantly. A further increase incalcium from 0.05 M to 0.1 M does not affect the breaking stress significantly (Fig. 6B). This correlation was alsoobserved 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 ingum 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 betweenultimate breaking strain and calcium concentration is similar to the relation between ultimate breaking stress andcalcium concentration. Increasing calcium concentrations from 0.001 M to 0.05 M increased the breaking strain of theresulting gels significantly (Fig. 6D). A further increase in calcium from 0.05 M to 0.1 M decreased the breaking strainslightly. 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 ofcomposition G2.

Neither the correlation between calcium concentration and ultimate breaking strain, nor the correlationbetween 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 contentof the gellan gum used in this study. Gellan gels with few acyl groups are known to be more brittle, and this explainsthe observed differences between our strain data and that of other researchers (Sanderson, et al., 1988; Morris etal., 1996). Previous studies with low acyl group content gellan gum indicates an increase in breaking strain as thegellan gum concentration is increased (Hershko and Nussinovitch, 1995; Tang et al., 1994). The only differencebetween 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 inabilityof 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). Themoduli of composition G1 and G2 are statistically similar, but Young's Modulus increases with increases in gumconcentration for composition G2 through G4. However, there is no correlation between Young's Modulus and calciumconcentration (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 calciumconcentration constant for these gels as the gum concentration was increased, leading to a small variance in calcium-to-gum concentration ratios. Therefore, we may observe a dependence of Young's Modulus on gum concentrationalong 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 reportedfor each gel composition in Table 4. Equation [6] consistently indicated an increase in K with an increase in gum ormonomer concentration and calcium or BIS concentration, which is not the case for observed Young's Moduli of thegels tested. For the gels in this study, K and Young's Modulus are correlated only for gels whose gum or monomerconcentration is varied (Figs. 8 and 9). Additionally, the correlation is valid only for a particular range ofconcentrations. These results indicate that Eq. (6) may be used to correlate K and Young's Modulus in a series of gelswhere 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. Errorbars are the standard deviations as reported in Table 4. Note that both the fit K value and Young's Modulus increasegreatly 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 arethe standard deviations as reported in Table 4. Note that the fit K value decreases between compositions G1 and G2whereas 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 aircompressed by the advancing water front can eventually disrupt the aggregate. It is inherently difficult to measureair 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 8kPa but noted that the aggregates began to fail as soon as they were immersed in water. Stroosnyder and Koorevaar'sobservations 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 thestresses in the polymer network to the internal pressure applied by the swelling soil aggregate. The stresses in aspherical membrane are given by: Equation (8) where [sigma] is stress in the polymer layer, t is the thickness of thepolymer layer, r is the radius of the aggregate and p is the pressure on the polymer layer's inner surface (Gere andTimoshenko, 1984). By knowing the thickness (t), aggregate radius (r), and maximum breaking stress ([sigma]) of aparticular polyacrylamide composition, the maximum inward pressure an adsorbed polymer network can apply to anaggregate 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 contributeaggregate stabilizing forces on soils similar to natural organic matter such as microbial polysaccharides. Taking intoaccount the ultimate breaking strain and stress of a 1-m-thick layer of adsorbed linear polyacrylamide having themechanical properties of the polyacrylamide gels compositions tested on an aggregate with an initial diameter of 1mm, we calculate a range of maximum internal pressures from 0.046 to 2.5 kPa (Table 6). The 1-m thickness wasbased on Atomic Force Microscope (AFM) imaging of polyacrylamide on vermiculite in our laboratory (unpublisheddata).

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 fromescaping a loess aggregate at peak pressure, the network could contribute significant stabilizing pressures on theaggregate surface. This stabilizing pressure could reinforce the aggregate when it begins to slake as soon as it iswetted, as observed by Stroosnyder and Koorevaar (1972). In the initial moments of wetting, water enters the largerpores most rapidly (Bolt and Koenigs, 1972). As the internal air pressure builds, the rate of wetting decreases untilthe pressure inside the aggregate stops the wetting front or the aggregate ruptures. The polyacrylamide layer wouldbe key in providing reinforcement during this point in wetting. The entrapped air could escape through the largestpore (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 theaggregate is wetted (B), water enters larger pores faster than smaller pores. Shaded areas indicate the water-filledpart 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 theaggregate could reinforce the aggregate structure and allow excess air pressure to escape as air bubbles through thelargest pore(s) without compromising aggregate stability (D).

CONCLUSION

The mechanical properties of polyacrylamide and gellan gels are remarkably similar despite the large differencein the molecular structure leading us to speculate that ruptures of the covalent bonds of the main chains control thefailure in both cases. The general shape of the stress strain curves for both gels are similar, even though the methodand mechanism of gelation differ drastically between the gels, and the ultimate breaking stresses for both gels arealso similar in magnitude, even though the gel cross-links are different. In terms of general trends, the two gelsdiffered 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. Usingmembrane theory, a 1-m-thick layer on an aggregate with a 1-mm diameter, having the mechanical properties of thepolyacrylamide 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. Thesimilarities 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 linearpolyacrylamide 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 providinga sample of the gellan gum (Kelcogel LT100) used in this study. This work was funded by The Kearney Foundation ofSoil Science Grant WHCK and NSF EAR 9814152.

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Key words: Gellan gels; mechanical properties; polyacrylamide gels; soil stabilizers

IMAGE GALLERY

Fig. 1

Table 1

Fig. 2

Table 2

Equation 1 Equation 2

Equation 3 Equation 4

Equation 5


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Equation 6 Equation

7

Fig. 3

Table 3

Table 4 Fig. 4

Fig. 5

Fig. 6

Fig. 7


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Fig. 8

Equation 8

Fig. 9

Table 5

Table 6

Fig. 10

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