Food Hydrocolloids VoU, no .2 pp . 125- 13-l. IYY-l

Polyacrylamide gels as elastic models for food gels

E.Allen Foegeding, C.Gonzalez l, D.D.Hamann and Suz anne Case/

Department of Food Science, No rth Carolina State University , P.O. Box 7624,Raleigh , N C 27695-7624, USA, I Department of Enginyeria Quimica , Universitatde Barcelona, Spain and 2National Starch and Chemical Co ., Bridgewater , NJ ,USA

Abstract. The physical propert ies of polyacrylamide gels ( 10% w/v ) wer e evaluated by dynam icoscilla tory testing. stress relaxat ion and tor sional fracture analysis. Gels had a linea r relat ionshipbetw een shear stress and strain when deformed to fracture ; thus sma ll strai n (storage modulus. G' )and large stra in (fracture modulu s. Gf) moduli were equi valent. Non-fracture and fracture testsshowed that gels maintained an entro py (rubber) elastic response over all test ing te mpera tures (10­80°C) . Shear stress at fractu re was independent of temperature, wher eas shear strain at fracturedecreased as temperature increased. Thi s was associated with increased thermal motion strainsdecre asing the amount of mech anically induc ed strain required for fracture . Our results have shownthat polyacrylamide gels are a suitable elastic model for understanding the molecular mechanisms offood texture .

Introduction

Gelation of biopolymers is importa nt in the manufacture of man y foods (e.g.frankfurters , cheese , de sserts) , and the function ality of food proteins andpol ysaccharides (1 ,2) . The sensory evaluation of food texture involves the forceand deformation required to cau se fracture and the viscous flow response of thefood when masticated. A basic understanding of food texture can be gained bydetermining the molecul ar mechanisms responsible for fracture , flow andrh eological properties.

If a food material can be assume d to be homogeneous and isotropic thenfundamental rheological and fracture properties can be determined , rather thanrelying on empirical observations (3). These assumptions appear to be valid formany food gels. Montejano et al . (4) determined fracture properties and sensorytexture profiles for gels made from comminuted fish, beef, pork and turkey, andegg white. Their results showed that certain sensory texture profile analysisnotes are significantly correlated (P < 0.01) with fracture properties of trueshear stress (force per unit area) and true shear strain (deformation per lengthunit) . Sensory notes of springiness, firmness, cohesiveness , denseness, coarse­ness and graininess had correlation coefficients of :::::0.80 with fracture properties.

The correlations among fracture and sensory properties implies that a basicunderstanding of food texture can be obtained by investigating the chemical andph ysical mechanisms responsible for fracture stress and strain levels . Theextensive understanding of the rubber elastic state (5) has made it a model forcomparison when conducting investigations on the physical properties ofbiopolymer gels (2) . The stress-strain relationship for a rubber-like (entropy)elastic material at an infinitesimal strain is given by Ferry (6) as

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E.A.Foegeding et al.

shear stress/shear strain = G" = gvRT (1)

where g is a constant which is close to 1 for rubber-like elasticity, G; is theequilibrium shear modulus and v is the moles of network strands per cubiccentimeter (6). If one assumes that v is a constant once food gels are formed,then an increase in temperature (T) should cause an increase in G; if theyconform to entropy elastic behavior. Food gels, however, generally show theopposite behavior. An increase in temperature causes a decrease in moduli(elastic modulus, storage modulus) of whey protein (2,7,8,9), egg protein (7,10)and pectin (11,12) gels. The reason for this behavior is that most food gels arestabilized by a combination of bonds and other interactions, in contrast to astrictly covalently bonded system, typical of most entropy elastic materials. Thepresence of low energy bonds makes the assumption of a constant v invalid if theenergy level of the gel is changed (13). The gel energy level can be altered bydeformation or added heat. Niwa et at. (14) demonstrated that the entropyelastic character of fish muscle gels is revealed after the influence of low energybonds is reduced by stress relaxation. This conclusion was based on theassumption that low energy bonds break when subjected to a high deformationenergy. The decrease in stress observed in a stress relaxation experiment istherefore due to rupture of low energy bonds.

In contrast to rheological properties based on small strain linear viscoelasticconditions, the relationship between stress and strain can show major deviationsfrom linearity at fracture-causing deformations. The pattern of deviation fromlinearity will vary among materials. Rubber, an elastic material, has a verycomplex stress-strain relationship at large deformations (1). The pattern forrubber is different than that seen for fracture of ~-lactoglobulin gels. The stress­strain curves of viscoelastic ~-lactoglobulin gels can be linear or hyperbolic,depending on gel pH (15).

In order to relate fundamental physical properties from rheological andfracture analysis to food texture, a model elastic gel should be characterized atsmall and fracture causing strains. Polyacrylamide gels are formed by a smallamount of matrix material stabilizing a large amount of solvent. This makesthem more similar to food gels than elastic solids such as rubber. The potentialvalue of establishing the fundamental rheology and fracture characteristics ofpolyacrylamide gels is that the chemistry is well known and the rheology/fractureresults for food gels can be compared with properties of polyacrylamide gels asevidence for, or against, entropy elastic character. Most food gels are stabilizedby a combination of interactions (covalent bonds, hydrogen bonds, electrostaticinteractions and the hydrophobic effect), and it may be possible to interpret therelative role these have in stabilizing food gels by comparison with polyacryl­amide gels.

Using test temperature as a means to adjust gel energy level can reveal effectsdue to ingredients or processing variables. Howe (16) used this approach withminced fish gels to show that 'setting' (a pre-heating incubation) changes thetemperature sensitivity of fracture properties. A knowledge concerning thefracture properties and temperature sensitivity of a model elastic gel is required

126

Acrylamide gelation

to und erstand the elastic component of viscoela stic food gels. The objective ofthis investigation was to det erm ine if polyacrylamid e gels conform to rubberelastic theory when tested at small and fracture-causing stra ins.

Materials and methods

Polyacrylamide gels

Gels were made by crosslinking copolymer ization of acrylamide with N,N' ­methylene-bis-acrylamide in aqueous solution. The ammo nium persulfateltetramethyl ethylenediamine (TEMED) redox system was used to initiatepolymerization at room tem per ature or 30°C. Gels were prepared at a constantmonomer concentration of 10% w/v and a constant amount of crosslinker. Th erat io of monomer to crosslinker was 100:1 (acryl amide :methylene-bis-acryl­amide ) . Polymerization was started by adding 0.1 % w/ v ammonium persulfateand 0.05% v/v TEMED to acrylamide/methylene-bis-acrylamide solutions. Allchemicals were of electrophoresis purity and supplied by Bio-Rad (Melville,NY ).

[3- L actoglobulin gels

[3-Lactoglobulin was isolated from whey protein isolate (Le Sueur Isolates, LeSueur, MN ) by the method of Eb eler et al. (17). Th erm ally induced gels weremade by heating solutions containin g 10% (w /v ) [3-lactoglobulin , 50 or 150rnmol/drrr' NaCI , pH 7.0 , at 80°C for 30 min according to the method ofFoegeding et al . (9).

Torsional fra cture test

The fracture properties of gels were det ermined using a Torsion Gelometer (GelConsult ant s , Raleigh , NC) . [3-Lacto globulin gels were ana lysed at roomtemperature as described by Fo egeding et af. (9) . Capsta n-shaped polyacryl­amide ge ls were prepared by polymerizing in a capsta n-shaped mold . Solutionswere gelled at room temperature for 50 min, removed from the mold and rinsedwith deionized water , then cut into 6 capstan-shaped samples (Fig. 1; 2.87 cm inlength and 1.0 cm in minim al diameter) and held at 5 ± 2°C until they weretested the following day «15 h holding at 5 ± 2°C).

For torsional fracture, gels were fixed onto notched styrene disposable diskswith cyanoacrylate glue and twisted to fracture at 2.5 r.p .m . (a shear strain rateof 0.126 S-I ) by the method of Kim et af. (18) . The glue does not affect thefracture properties (19). True shear stress and true shear strain at fracture werecalcul ated from the respective torque and angular displacement, using thefollowing equations of Diehl et al. (20).

as = 1580 [T,.]

"I" = 0.150 [t] - 0.0079 [Tv]

(2)

(3)

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E.A.Foegeding et al.

z

a

·_·z

Fig. t. Ca pstan shape of specimen used for torsional fracture testing. Dimensions of specimens inthis study were: Zil = 6.36 mrn , r,. = 9. 53 rnrn , a = 14.53 rnrn, length = 2H.7 rnm. minimum r = 10and 19 mm diameter end sections.

? ., I/~

'Vs = In[I + 'V;- + 'VII(I + 'V~-) -] (4)

Where 0'" is shear stress at fracture (Pa), T,. is the torque digital reading (percentof scale) , 'VII is the uncorrected shear strain at fracture (dimensionless), t is time(s) , and 'Vs is shear strain at fracture (dimensionless). Numerical constants in theequation are based on instrumental factors and testing conditions (20). Standardconditions were a rotation rate of 2.5 r.p.m. (0.262 rad/s) , full scale torque of0.0288 N 'rn and an instrument spring constant of 1.39 radians at full scaletorque ; with specimen dimension s (Fig. 1) of : Z" = 6.36 mm, rc = 9.53 mrn ,a = 14.53 mm , length = 28.7 mm and 19 mm diameter end sections.

Samples were equilibrated to 5, 20, 35, 50, 65 or 80°C by lowering thegelometer twisting fixture , with the mounted specimen, into a water bath at theappropriate temperature and holding for 3-5 min prior to twisting (16). Eachtreatment (temperature) was replicated twice and a minimum of six sampleswere tested for each replication.

Small strain rheometry

The sol-to-gel transformation of polyacrylamide solutions was monitored using aBohlin VOR rheometer (Bohlin Reologi AB , Lund, Sweden) , with a concentriccylinder (C 25) sample fixture and 103.33 g ern torque bar. Rheologicalproperties were determined using the oscillatory mode with a strain amplitude of0.0206 and a frequency of 0.05 Hz. The storage modulus (G' , a measure of theelastic rigidity in a solution or gel) and phase angle where measured at 1 minintervals. Purely viscous fluids have a phase angle of 90° and ela stic solids show a

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Acrylamide gelation

8 90

8 906 ...-.60 ~

<a 6 .!!!Q. 60 Cl::.. e

4 4 <tCJ CI)

30 III

2 30co..cQ.

2

100 200 300 400

0El"ElOGOOG a",....&1l IlIIO" &I>II'DalLI> Oil.. ......

00 1000 2000 3000 4000 5000 6000

Time (s)

Fig. 2. Polyacrylamide gelation as indicated by changes in storage modulus (G', circles) and phaseangle (squares). Bars show the standard deviation of three replications. The insert shows changes onan expanded time scale.

phase angle of 0°. The solutions were gelled isothermally at 30 ± O.l°C for 90min. After gelation, the holding temperature was changed to the desiredtemperature for stress relaxation testing. Samples were held for 20 min at testingtemperature to allow for thermal equilibration prior to starting the stressrelaxation test.

Stress relaxation tests were run at 10, 20, 30, 40 and 50°C. A shear strain of0.0377 was imposed on the sample and maintained for 4 h. The strain rise timewas 1 s. A minimum of triplicate runs were obtained for each temperature.

Results

Transformation of polyacrylamide solutions to gels was quite rapid. The phaseangle decreased to ~Oo within 1 min; however, the storage modulus (G ') did notreach equilibrium until 31 min (Fig. 2). This indicated that the elastic elements(i.e. G ') continued to develop after the acrylamide solution had been convertedto an elastic gel (i.e. indicated by a phase angle of 0°). Standard deviationsshown in Figure 2 indicated that the processes of gel formation and rheologicaltesting were quite repeatable. Stress relaxation experiments showed that therewas no decrease in stress while maintaining a strain of 0.0377 for 4 h. The gelsmaintained this pure elastic response over all testing temperatures (1O-50°C).

The acrylamide gels had a linear relationship between shear stress and strainwhen deformed to fracture (Fig. 3). Similar stress-strain curves were observedat all temperatures tested (5-80°C). A linear relationship was also seen in themore rigid ~-lactoglobulin gel (150 mrnol/drrr' NaCl treatment); however, themore deformable ~-lactoglobulin gel (50 mrnol/drrr' NaCI treatment) had ahyperbolic relationship between stress and strain.

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E.A.Foegeding et al.

30

Iill.~

VI 20VI

~iiiiaQI 10J::Ul

Shear Strain

Fig. 3. Stress-strain response of polyacrylamide (squares) and 13-lactoglobulin (circles) gels duringfracture testing at 20°C. Thermally induced 13-lactoglobulin gels were formed by heating solution,that contained 10% (w/v) protein. 50 (open) or 150 mmol/drn' (filled) "IaCI. pH 7.0. at k(fC for 30nun,

9

Ii 6ll.~

t;7

0(,

6 0

50 20 40 60 80

Temperature (ac)

Fig. 4. The effect of gel temperature on storage modulus (G'. circles) and fracture modulus iG],squares). Linear regression of the data showed that: G' = 6.1 + 0.0263 roC). ,2 = O.9k6; and thatGf = 6. I + 0.0254 (0C). ,2 = O.k94.

Since stress relaxation experiments showed that the acrylamide gels had idealelastic behavior (i.e. showed no relaxation), the fracture modulus tG], stress atfracture/strain at fracture) should be equivalent to the storage modulus (C'). Acomparison of the two values (Fig. 4) confirms that they are equivalent. Linearregression of the data indicated that there was more variation in G] values thanthe C' values. This was expected due to increased variability associated withfracture. The average temperature response of moduli among the data was thatC' or Cf increases by 25.9 Pare.

130

Acrylamide gelation

16

IV 14a..~

IIIIII

12e...en...IIIGI 10s:en

80 30 60 90

Temperature (OC)

Fig. S. The effect of gel temper ature on shea r stress at fracture. Average shear stress at fracture wasD . I ± 0.38 kPa.

2.4-r------------------,

c 2.0.~...en...IIIGI.c 1.6en

9030 60

Temperature (OC)

1.2 +---.----r---.---....---.----io

Fig. 6. Th e effect of gel tem per ature on shear strain at fracture . Linear regression of the data showe dtha t: Shear strain = 2.08 - 0.00561 (0C). r" = 0.963.

Shear stress at fracture remained constant with temperature (Fig. 5), and theaverage value was 13.1 ± 0.38 kPa. Shear strain at fracture decreased astemperature was increased (Fig. 6). Linear regression of the data indicated thatstra in decreased by 0.0056 units for each °C increase betw een 5 and 80°C.

Discussion

Th e polyacrylam ide gels used in this study had a phase angle of _0° and did notshow any stress relaxa tion after 4 h of consta nt stra in (Fig. 2) . This is indicativeof ideal elastic behavior und er the conditions of this study and supports pre vious

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E.A .Foel:eding et al.

find ings o n the elasticity of polyac rylamide gels (2 1). This means the values ofG ' and Gf can be tre ated as equilibrium values, G".

The amount of monom er and cross linke r can be used to calculate theth eoretical chemical net work den sity, Vel" which represents 100% pol ymeriz­ation and evenly spaced crosslinking (21). The molecul ar weight of elasticityeffective network chain s was ca lculated to be 3554 (based on 10% w/vacry lamide monomer and 100: I monomer to cro sslink er rati o) , which was usedto calcul ate a Ve il of 2.8 1 X 10- 5 moles/ern", and a theoret ical G" value at 20°C of68 .5 kP a . The calculated G" is much higher th an th e observe d values for G'(6 .67 kP a) and Gf (6 .84 kP a). Oppermann et al. (2 1) also observed thatmeasured G ' values were much lower than the oretical values. Th ey found thatthe effect of crosslink er on G ' was -7% of the theoretical value . Gels formedby crosslinking copolymerizat ion ofte n ha ve moduli mu ch low er than theoreticalpredictions due to imper fecti o ns and elastically ineffective rings (21). The valuesof G' (n = 5) and Gf(n = 6) , at various temperatures (1O-80°C), were used inequation 1 to calculate th e co nce ntration and apparent molecular weight ofe lastica lly effective network cha ins. The chains were es tima ted to have amolecular weight of 36500 ± 950 and a concentration o f 2.74 ± 0.07 mmol/drrr'.

The relationship bet ween stress and strain vari es with the de gree ofdeformation . At small deformati on s, with no irr eversible dam age to the gelnetwork , there is usually a ra nge which shows a line ar relati on ship betweenstress and stra in (1) . The stress-stra in relationship at large deformation s ca nshow major de viati ons from linearit y. The patt ern of deviati on from linearitywill vary among materials. Rubber ha s a very complex stress -stra in rel ationship( 1). The stress-strain curves were linear for polyacrylamide and the lessdeformabl e [3-lactoglobulin ge l (150 mrnol/drrr' NaCI treatment) . However , the[3-lactoglobulin gel with the grea te r strain at fracture had a hyperbolicrelationship between str ess and stra in. Both [3-lactoglobulin ge ls were visco­e lastic ; therefore , the differen ces in stress - strain respon se were not simplyrelat ed to a general mate rial pr operty. The stress-stra in curves of viscoelastic [3­lactoglobulin gels have been sho wn to be linear or hyperbolic , depending on thegel pH (15) . In a previous study on whey protein isol at e gels , we showed th atstra in at fracture was corr elat ed with the relaxation time of viscous elements(22) . This suggests that the hyperbolic stress- strain rel ati on ship of the 50 mmol/drrr' NaCl-containing [3-lactoglobulin gel (Fig. 3) may be related to relaxations ofviscous elements during fracture testing. In general, the stress - strain curves of[3-lactoglobulin gels are more similar to those for polyacryl amide gels thanrubber.

The stress and strain values determined by torsional fracture reflect the energyand deformation required to cau se fracture at a given shear rat e . If a viscoelasticmate rial is being tested th is mean s th at ene rgy ma y be dissipated as he at ratherth an converted into the energy required to fracture the gel matrix. In an ide alelastic material there is no viscou s flow and the energy is used to fracture the gelmatrix . Torsional fracture values for acrylamide gels at 20°C we re 13.2 kPa and1.94 for stress and strain respectively. By comparison , [3-lactoglobulin gels

132

Acrylamide gelation

(Fig. 3) and whey protein gels (23,24) at similar concentrations (10% w/vprotein) have stress values ranging from 0.6 to 41 kPa and strain values of 0.90 to2.5. The fracture properties of polyacrylamide gels are therefore within therange seen in whey protein gels.

The fracture of viscoelastic materials has been modeled based on theassumptions that fracture involves the force required to rupture a gel networkstrand and the ability to transfer the breaking energy from one filament to thenext (25). Both factors should be important to fracture of viscoelastic proteingels, whereas fracture of elastic acrylamide gels should only require the force tofracture the network. The stress at fracture did not vary with temperature,suggesting that the force required to rupture a covalently bonded gel matrix istemperature invariant. Shear stress at fracture of viscoelastic food gels normallychanges with temperature (16). Figure 4 shows that the polyacrylamide gel shearmodulus increased with temperature as we would expect for an entropy elasticmaterial (5). The shear modulus versus temperature relation is the same forsmall strain or fracture conditions. The fact that Gf depends on fracture strainbut not fracture stress is consistent with entropy elasticity. As temperatureincreases, the entropy increases due to increased random chain motion. Thisincreased motion strains the chains so that less mechanically induced strain isrequired to reach the fracture strain level. Total strain is the sum of thermallyand mechanically induced strain. It is interesting that if the regression line fordata in Figure 6 is extrapolated to absolute zero, a strain value of ~3 isdetermined. The value at absolute zero should estimate the total strain of thepolyacrylamide gels. This is a realistic value and is close to the value obtained forkonjac (a food gum) gels which exhibited an entropy elastic fracture responsesimilar to polyacrylamide (26). The linear extrapolation provides additionalinformation about temperature-associated changes in strain based on entropyelasticity, and is not intended to represent the actual strain response between 0°and 278°K. If these assumptions are valid, we can conclude that at 15°C, abouttwo thirds of the total polyacrylamide fracture strain was imposed mechanically.

Equation 1 predicts that at absolute zero G; will be zero. Considering the G'and Gf data in Figure 4 separately, and extrapolating the regression equations toabsolute zero, the intercepts are found to be -1.1 and -0.8 kPa respectively,remarkably close to zero considering the extrapolation. In contrast konjac gel(considered to have junction zones rather than point crosslinks) produces dataqualitatively similar to that shown in Figures 4-6 but the absolute zero interceptis far from zero, being about half the 5°C value (26).

The primary goal of our rheological investigation was to use the results fromacrylamide gels as standards in reference to food gels. Konjac mann an formsgels which show entropy elastic behavior. They increase in rigidity withincreasing temperature under small strain oscillatory testing (12). However,transient experiments (stress relaxation) show a relaxation in konjac gels (26).The rheological properties of Konjac mannan gels can be represented as threeMaxwell units in parallel. Temperature sensitivity was shown to be in the slow(> 10 h) relaxation time, with the fast (~1 min) and intermediate (~1 h)relaxations being temperature independent (26). The slow relaxation time

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E.A.Foegeding et al.

increases with temperature. Since this was not the case with the covalentlybonded acrylamide gels, the elastic behavior of konjac gels appears to be due tonon-covalent interactions with extremely slow relaxations.

Our results have shown that polyacrylamide gels are elastic and have a linearstress-strain relationship at small and fracture-causing strains. This makes thema suitable entropy elastic reference material when investigating the texturalproperties of foods.

Acknowledgements

This is paper no. FS93-55 of the Journal Series of the North CarolinaAgricultural Research Service, Raleigh, NC 27695-7643. The use of trade namesdoes not imply endorsement by the North Carolina Agricultural ResearchService of products named, nor criticisms of similar ones not mentioned.

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