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Viscoelasticity of Cheese Y. S. Chang, J. S. Guo, Y. P. Lee, and L. H. Sperllng Department of Chemical Engineering, Materials Research Center $32, Lehigh University, Bethlehem, PA 18015 Two types of simple bulk materials exist. T h e first is the ideal elastic solid. which obevs Hook's law of elasticitv. T h e perfert liquid ct~nst~tutesthe-sea~nd type,whichohcy~Newron's low ut \,iscositv. Although manv low-molerular-weight compounds appear-to obey one or the other of these relations, careful measurements always reveal some influence of both. In cases involving high-molecular-weight compounds such as polymers, many important examples exist where both elasticitv and viscositv comnonents of behavior are present ro the same order of magnitude. Such l~cho\,ioris called visroelasticity, and it is convenient to talk about the viscoelastir behavior of such a polymer (1-3). This paper outlines a simple experiment for studying the viscoelastic hehnvior of a well-known mawrial, rheese. Cheese is compoied primarily of proteins, which are polymeric in nature. Of course, the basic monomers are the various amino ac~ds.Prucessed cheese. such as will he employed below, is cheese plasticized or softened by the addition of water. The viscoelastic characteristics of the various rheeses are of significant scientifir and commercial interest (4-8).
MAlWELL ELEMENT
KELVIN ELEMENT
Theory
Viscoelasticity is often modeled through the use of springs and dashpots, see Figure 1 (1-3). A spring follows Hook's law, extending instantly on being stressed, and retracting entirely on being released. A dashpot follows Newton's law, exhibiting perfect viscosity. A dashpot deforms steadily under stress but has no recovery. A metal spring is a good example of a spring, and water is a good example of a Newtanian liquid. The modulus of a spring, E, is given by the ratio of stress, a, to strain, r . The viscosity, 7 , of a dashpot is inversely proportional to the change of strain, r , with time, t. Viscoelastic materials are often modeled by using comhinations of springs and dashpots, as illustrated in Figure 1. Two simple combinations are the spring and dashpot in series, the Maxwell element; and in parallel, the Kelvin element. A simple combination of both the Maxwell and the Kelvin elements produces the four-element model, which is the simplest comhinatim of springs and dashpots that exhibit all of the maiur aspects of \,isroelasticity. When a stress is applied as shown by the arrow, first thi spring extends according to El. Then the central, Kelvin element undergo limited deformation according to Ez and q p . Simultaneously, the dashpot governed by 73 elongates continuously. The motion of the combination is called creep. In the experiment to he described below, cheese is made to undergo creep in the compression mode. rather than bv elong&ion. B; following the creep as a function of time, thk various constants can be evaluated as described below, and much information is obtained. Cheese is composed of protein with the general structure
FOUR ELEMENT
Figure 1. Basic arrangements of springs and dashpots to make viscwlastic models.
Time: About 2 h Level: Physical Chemistry or Introductory Polymer Science Principles Illustrated: 1) The viscoelasticity of processed cheese, particularly in creep. 2) Application of the four-elementmodel to the viscoelastic hehavior of cheese. Equipment and Supplies: 1 rectangular Plexiglas or wooden box, see Figure 2 1 one-pound block processed cheese (Velveetam or similar), at roomtemperatore 1clock (stopwatch is fine) 1meter stick 1small, flat plate (insert between cheese and weight) 1flat, hard surface (most desks are suitable) Weights of about 1 kg (rectangular weights of the same crosssectional area as the cheese are fine) The cheese is placed inside the box, and the original height of the cheese is recorded. Then, the plate and weight is place on the top of the cheese. Its new height is recorded immediately and each succeeding 5 min thereafter. This experiment measures creep in compression. Replace the weight and deformed cheese with another weight and new cheese, and repeat. Results
Segments containing 10-50 amino acids or mers are capable of lone-ranee. coordinated molecular motions when above their $ass &&ition temperature (the present case). These coordinated molecular motions are the cause of the observed viscoelastic behavior.
T h e initial dimensions of the one-pound block of cheese were 4 cm X 6 cm X 15 cm. Weights of 500 and 700 g were employed. The resulting creep curves are illustrated in Figure 3. An immediate elastic compression is noted, a measure of the modulus El. This is followed by a curved line of strain Volume 63 Number 12 December 1988
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Figure 4. Resolution of the experimental data according to the fourelement model. Curve 1 represents flow according to .n Curve 2 illustrates the behavior of Me middleelement, which isreally a Kelvin element. The strain at zero time up to the interception of curve 1 represents the instantaneous deformation according to the spring E,.
Characterlstlcs of Velveeta Cheese at Room Temperature According to the Four-Element Model Applied Weight
Figure 2. Holder of cheese during creep experiment. Since the cheese is soft, a slightly tilling arrangement allows the cheese to lean without significantly detracting from the basic experiment.
500 g
700 g
straight line portion a t long times, separated as curve 1, yields q3. Then, by subtraction, curve 2 was obtained. By simple curve fittings E2, 12, and 7 2 can be determined. The retardation time for Velveeta cheese was found to be about 7-9 min (see table). The value of E l , near 5 X 105 dyneslcm2, places it in the fourth region of viscoelasticity (1-3), ruhbery flow. Five regions are defined with increasing temperature: the glassy region, the glass transition region (9), the rubber elasticity region (101, the rubbery flow region, and the viscous flow region. Figure 3. Experimental creep curves for Velveeta cheese under two loads.
versus time, and a straight line portion lasting a t least two hours, see Figure 3. For the four-element model, the strain, 6, under constant stress, a, can he written:
Conclusions
A well-known ~rocessedcheese. Velveeta. was characteriled for it* \,isco&stic behavior, and found to be firted hy t h e four-element tnodel.Thir ex~erirnentreauiresabour two hours, but the important parts can he easily demonstrated in a 50-minute class. Literature Cited 11) Rodriguez. F. "Principles of Polymer Systems", 2nd ed.; McGraw-Hill: New York, ,qRv
(21 Rillmoyer, F. W. Jr.. "Textbwk of Polymer Seienee", 3rd ed.: Wiley-lntersienee:
The first term on the right of equation represents an elastic term, the second term expresses the Kelvin element, and the third term the viscous effect. The retardation time, Q, is equal to q~lE2,and provides a quantitative measure of the time required for the Kelvin element to complete its deformation. The data were analyzed in Figure 4 according to the fourelement model. First, at zero time, the strain yields El.The
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Journal of Chemical Education
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(3) Sperling. I.. H."Intrcduction toPhysicalPalyme~Seienee":Wilcy-lnteneienee: New
York. 1986
Academic: New York. 1979.
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(8) Nolan. F..J.. USDA, Philadelphia, PA.. private communication. April, 1985. (91 Snerlins. L. H.J. Chrm. Educ. 1982.59.942.
