the elastic modulus of soft denture liners

The elastic modulus of soft denture liners

Bryan Ellis Department of Ceramics Glasses and Polymers, University of Sheffield, England D. J. Lamb Department of Restorative Dentistry, University of Sheffield, England Suad Al-Nakash Department of Ceramics Glasses and Polymers, University of Sheffield, England

Under certain circumstances, e.g., when treating “denture sore mouth” or after the provision of immediate dentures, dentures may be lined with soft rubberlike materials which have Young’s moduli within the range -lo5 N m--2. Measurement of the compression modulus E , of such soft liners is described and Gent and Lindley‘s method of calculating Young’s modulus E was evaluated. It was established that the Young’s modulus may be calculated using: E, = E(1

+ 2kS2), where k = 1 for soft rubbers, and for disks S is a shape factor and = radius12 X thickness. It is also shown that Young’s modulus is a linear function of log(rate of strain) for both tension and compression measurements. When gellation has oc- curred subsequent to mixing there is an increase in Young’s modulus due to loss of ethanol. When immersed in brine the elastic modulus remains approximately constant from a day to a week or longer.

INTRODUCTION

Two main types of soft liner may be applied to dentures, the temporary and the semipermanent. The semipermanent often misnamed ”resilient liners” are based on chemically crosslinked polymers such as silicone rubbers,l or hydroxyethyl methacrylates. Such liners may be colonized by bacteria, and long term degradation of their mechanical properties may occur. For these reasons they have not found favor with all clinicians, and will not be consid- ered further.

Temporary soft liners on the other hand, with a useful life measured in days or weeks, are popular and many indications exist for their clinical use. They are particularly useful for the treatment of trauma caused by an ill fitting denture, to aid the treatment of “denture sore mouth,” and during the reab- sorption phase following the provision of immediate full dentures. Their function is to form a cushion between the relatively hard acrylic denture base and the soft supporting tissues. Because they are initially capable of viscous flow, isolated areas of high pressure are relieved and the source of trauma eliminated.

The most common material used for temporary soft liners is plasticized polyethyl methacrylate, together with ethanol.2 Most but not all of them are

Journal of Biomedical Materials Research, Vol. 14,731-742 (1980) 0 1980 John Wiley & Sons, Inc. 0021-9304/ 80 / 0014-0731$01.20

732 ELLIS, LAMB, AND AL-NAKASH

prepared immediately prior to use by mixing a fine powder, polyethyl methacrylate, with a liquid containing a plasticizer and ethanol. The role of the ethanol is to increase the rate of diffusion of the plasticizer into the polymer beads, which then swell. Polymer molecules in adjacent particles mutually interdiffuse so that a “gel” is formed. Within 15-30 min of mixing (depending on composition) an elastic material is obtained.

Immediately after mixing ethanol starts to diffuse out of the elastic gel, 2/3

diffusing out by an a process relatively rapidly, i.e., within 10 hr at 37°C. About l/3 of the ethanol diffuses out very slowly by a process, taking about 2 years to complete.2 During the time of clinical use the alcohol that remains in the elastic gel functions as an ancillary plasticizer.

It will be shown by the present work that the soft liners available to the clinician have Young’s moduli within the range 105-106 Nm-2 (106-107 dyn cm-2), that is they are very soft elastomers.

The purpose of the present paper is to discuss the measurement of Young’s modulus for such materials, to determine the effects due to immersion of the materials in water and brine (a salt solution with equivalent ionic strength to saliva) and present measured moduli for several soft liners.

EXPERIMENTAL METHODS

Preparation of test pieces

For measurement of the compression modulus of soft liners, disks with nominal dimensions of diameter 15 mm and thickness 1 mm are required. It is important to use samples of about the same thickness as would be applied to a denture because in use the properties will depend on the amount of water diffusing into, and ethanol diffusing out of, the sample. This in turn will be affected by the dimensions of the sample, particularly the thickness, 1 (the rate of loss or gain of material being proportional to 1-2). For soft liners supplied as a polymer powder and a liquid which must be mixed together, the components were weighed so reducing errors inherent in the volumetric method normally used. The proportions of polymer powder and liquid used are specified in Table I.

Immediately after mixing the soft liner was packed into an aluminum mold taking care to avoid the inclusion of air bubbles. After a time the materials

TABLE I The Proportions of Polymer Powder and Liquid

Powder/ Liquid Gelation E,, x 10-5 a

Material Ratio Time lminsl (N m-21 ~~ _____

Coe-soft 5.5 /4.1 15 1.18 Visco-gel 311.5 45 1.51 Coe-comfort 6.516.1 30 0.31 Ivoseal 1 15 0.85 Ardee Preformed sheet 0.42

a E o at 37°C after 7 days in brine.

SOFT DENTURE LINERS 733

gelled and it was then possible to remove the samples from the mold without distortion. The gelation times were determined as the minimum time from mixing to extraction of a coherent undistorted test piece from a mold at 2loC, and are given in Table I. The thickness and radius of each test piece was measured using a travelling microscope, and an average of 5 readings taken for each. To aid measurement of the radius the impression of a central pop mark was used to indicate the center of the test piece.

"Ardee" is supplied as "ready to use" sheets. Suitable disk specimens were cut from the sheet and the radius r calculated from

r2 = w l p d

where w = weight of test piece, p = density of test piece, and 1 = thickness of test piece.

The treatment of the test pieces prior to the measurement of their moduli is specified in Table 11.

Measurement of compression modulus

The uniaxial compression modulus of the test pieces was measured using a specially constructed jig (Fig. 1) which has been described el~ewhere.~ The test pieces were subjected to increasing loads from 393 to 1593 g weight, using a step loading sequence of 200 g at 1 min intervals. At the end of each minute the "position" of the upper plate of the jig could be measured to 1 pm by use of a micrometer screw gauge.

RESULTS AND DISCUSSION

The compression load-deformation curves for a typical soft liner are shown in Figure 2. Provided that the strains were small, linear load-deformation curves were always obtained. When first prepared these soft liners are softer and hence for the same loads the deformations are larger. When strains are greater than about 6% nonlinear load-deformation curves are Obtained. Under these circumstances, for reasons which are discussed below, linear graphs were

TABLE I1 Treatment of Test Pieces Prior to Measurement of Their Moduli

Material Treatment Compression

Duration Temu.

Coe-soft Conditioning 37OC Water immersion 37°C Brine 37°C Brine 37°C

Visco-gel Conditioning 37°C Brine 37°C

Coe-comfort Brine 37°C Ivoseal Brine 37OC Ardee Brine 37°C

7 days 12 days 7 days

34 days 5 days 7 days 7 days 7 days 7 days

Room temp. 37°C 37°C 37°C Room temp. 37°C 37°C 37°C 37°C


Figure 1. Compression test piece in place prior to application of load.

obtained by plotting L / ( 1 + e) vs. e (Fig. 3), where L = the applied load, e = the compressive strain = ( lo - E)/Zo, l o = the initial thickness, and E = compressed thickness. Only for a few samples, which were tested within a few hours of mixing, was it necessary to plot L / (1 + e) vs. e in order to measure the elastic modulus.

The tissue conditioners behave as soft rubbers. The glass transition temperature of polyethyl methacrylate is 65"C, but that of the tissue conditioners is very low because a large amount of plasticizer is present. A softening temperature was determined, and even when losSof ethanol by the a process was complete, the softening temperature was -35°C. Thus, these materials

1600.

1200.

Load

~ 0 . 0 4 4 Position (rn.rn.)

Figure 2. Load/deformation curves for Visco-gel conditioned at 37°C and compressed at 22°C. (0) 3 hr conditioning, maximum strain 5.1%; (0 ) 6 hr conditioning, maximum strain 3.7%; (X) 7 hr conditioning, maximum strain 4%; (A) 2 days conditioning, maximum strain 4%; (0 ) 5 days conditioning, maximum strain 3.8%.


0.02 004 0 6 008 0.1

Strain

Figure 3. Coe-soft compressed 25 min after mixing. Maximum strain 10%.

are well above their glass transition temperature. Further, there are entanglement crosslinks between the polymer chains and so they may be treated as rubberlike materials, as discussed by Porter and J ~ h n s o n . ~ , ~

The stress-strain relationship for elastomeric networks6 that has found most general acceptance is the Mooney-Rivlin equation:

B = 2C1(X - A-2) + 2C2X-'(X - A-2) (1) where B is the applied stress which is the applied force divided by the cross- sectional area of the undistorted test piece, and X is the deformation ratio which is equal to the deformed length I divided by the undeformed length 10 (A = 1 / 1 0 ; for extention X > 1 and for compression X < 1). There has been much discussion of the constants C1 and C2, a subject reviewed by Mark.7

From compression measurements the values of C2 are very much smaller than C1 and it is generally accepted that C2 can be taken as essentially equal to zero for uniaxial compression. When C2 = 0 eq. (1) takes the form:

B = G(X - (2) where G = 2C1 and is the shear modulus of the elastomer.

lationship of a elastomeric network is given by eq. (2) with According to the statistical theory of rubber elasticity the stress-strain re-

G = uRT

where u is the number of network chains per unit volume, R is the gas constant, and T is the absolute temperature.

For test pieces subjected to uniaxial compression which are so well lubricated that there is no restriction to the lateral extension of the sample, eq. (2) should be an adequate representation of the stress-strain relationship and this has been confirmed by Payne8 for a range of rubber compositions. It is often difficult to ensure that the test piece is so well lubricated that the friction between the rubber and the compression plates is zero. Hence "bonding" of the test piece is more satisfactory. (In industrial practice most rubber compression pads are bonded to metal.)


When bonded test pieces are compressed they barrel and the deformation is not a simple uniaxial compression. To treat this situation various treatments have been used all of which involve a shape factor since it is obvious that the amount of barreling will depend on the height to radius ratio of a compressed disk. For bonded cylinders Payne9 found that eq. ( 2 ) could be modified by inclusion of a factor which is a function of the shape of the test piece. The relationship which he used was

u = G( X - A-2)( 1 + ~ 6 ~ ) ( 3 ) where 6 is a shape factor and K is a constant which depends on the shape of the test piece (for cylinders K = 0.413 and 6 is the ratio radius/height). We also obtained a fit by plotting stress vs. (A -

An alternative treatment of uniaxial compression measurements where the strains are not too large is based on the linearity of experimental load-deformation curves, similar to those obtained for a soft liner (Fig. 2). Gent and LindleylO have discussed the various approaches to the measurement of the compression moduIus E,, which is defined by:

(Fig. 4).

u = E,e (4)

where CJ is the stress and e is the strain as defined previously. Our data for strains less than about 6% (i,e., e X 100%) are very well represented by eq. (4) (see Fig. 2).

When strains are larger than about 6% the stress-strain curve is convex to the strain axis and Lindleyll has used the empirical equation (for e > 10%):

CJ = E,e(l + e ) (5) This proved satisfactory for the present measurements when strains were

large (Fig. 3). [Equation (5) was linearized by dividing both sides by the factor (1 + e ) , which proved to be the most suitable transform.]

The compression modulus defined by eqs. (4) or (5) can be converted to Young's modulus by defining suitable shape factors which have been evaluated by Gent and Lindley,lo who used:

E, = E(l + 2kS2) ( 6 )

Force (N.)

002 0.04 0.06 - ( A - A-' )

Figure 4. 22°C.

Coe-soft conditioned at 37°C for 21 hr and then compressed at


where S is a shape factor which is equal to one loaded area/force free area, and for circular disks S = r / 21, where r is the radius and 1 the thickness. Depending on the Young’s modulus of the rubber, k varies1* and for very soft rubbers such as soft liners, k = 1.

All elastomers are viscoelastic and the stress-strain curve depends on the rate of deformation, which must be defined. Gent12 increased the load from zero by equal increments waiting 1 min before measuring the corresponding deformation, and a similar procedure was used in the present work. The treatment of time-dependent effects in the elastic properties of rubbers has been discussed by Ferry13 and the treatment that he applied was introduced by Chasset and Thirion14 who proposed that the elasticity and time dependence of the stress are separable so that

a(A,f) = a,(A)az(t) (7 ) where a,(X) represents the purely elastic stress and a2(f) = (1 + r ( t ) l , having a transient term r ( t ) which tends to zero at infinite time.

It is difficult to measure compression moduli over a range of strain rates but higher rates of deformation can be readily attained in tension. Measurement of the elastic modulus of soft liners over a range of strain rates in tension as well as the 1 min step loading in compression allows direct comparison both of moduli measured under a different type of deformation and the effects of rate of straining. From Figure 5 it can be seen that Young’s modulus is a linear function of log (strain rate). It is shown in the Appendix that the time-dependent function r ( t ) introduced by Chasset and Thirion14 would not give a relationship between Young’s modulus and strain rate which would fit the data given in Figure 5.

It has often been observed15 in stress relaxation measurements (A = constant) on elastomers that the stress (or reduced stress) is a linear function of log (time) over several (3-4) decades of time, that is:

I 4.4

Young’s 3’61 Modulus

2.0 -3 -2 -1 0 1

tog strain rate/(log min-‘)

Figure 5. The effect of strain rate on the Young’s modulus of Coe-soft, conditioned for 7 days, stressed at 22°C. (0) Van Noort tensile testing rig;16 ( 0 ) Instron Universal testing machine; (A) Compression jig.

7 38 ELLIS, LAMB, AND AL-NAKASH

o(t) = constant - n log t (8)

Thus using the principle of separability postulated by Chasset and Thirion14 and defining the modulus for a specific strain, an equation for the time dependence of elastic modulus may be written by analogy with eq. (8). The rate of strain 6 is given by

P = e l t

and hence log P = log e - log t . The time-dependent Young’s modulus is then obtained from eq. (8)

where a and b are constants. Thus the time-dependent elastic modulus is given by

(9)

where i is the rate of strain. The present data (Fig. 5) for both uniaxial compression and tension of a soft liner fits eq. (9) over a range of strain rates of lo4. This also shows that the method used to calculate Young’s modulus from compression measurements is in good agreement with uniaxial tension provided due allowance is made for the effect of strain rate. Previously the ac- curacy of equations such as 6 containing shape factors have not been checked by direct measurement of elastic moduli using an alternative type of applied stress. As can be seen from Figure 5, exact agreement would not have been obtained unless a correct allowance for the effects of strain rate had been applied.

The changes in Young’s modulus of “Visco-gel” when ”conditioned” in a dessicator at 37°C are shown in Figure 6. Similar changes occur with the other soft liners with the exception of Ardee which is supplied in a preformed sheet. For the soft liners prepared by mixing a polymer powder with a liquid containing a plasticizer and ethanol, there is a loss of ethanol immediately after mixing. Two processes are responsible for the loss.* About */3 of the ethanol present diffuses out by a faster a process, the remainder being lost by a slower

Figure 6. at 37°C.

Changes in Young’s modulus and weight of Coe-soft conditioned


1200.

Load

(gm.wt.)

L O O .

p process. For a test piece 1 mm thick, loss of the final 1/3 would take approximately 2 years. Also shown in Figure 6 are the weight changes associated with the loss of ethanol by the CY process. From the results it can be seen that the increase in Young's modulus is due to the diffusion of ethanol from the sample.

In the past it has been usual to study the behavior of soft liners after immersion in water at 37°C. However, Ellis and co-workers17 (1977) have shown that when a soft liner is immersed in an artificial saliva, there is a net weight loss compared with a weight grain when immersed in water for long periods. Further they have shown2 that the behavior of Coe-soft (a popular soft liner) is essentially the same whether immersed in artificial saliva or in a salt solution of equivalent ionic strength to saliva. Thus, in this work the compression modulus of the soft liners was measured after immersion for 7 days in a salt solution at 37°C. The load-position graphs are given in Figure 7 and the Young's moduli in Table I. The moduli were calculated using eqs. (4) and (6). It can be seen from these results that the range of elastic moduli of soft liners is 0.3-1.5 X lo5 N m-2.

There are a number of factors which will affect the "softness" of these materials, a major one being the type and amount of plasticizer. With the exception of Ardee it is possible for this to be varied simply by altering the powder/liquid ratio. Obviously for control of the properties of these materials, it is essential to dispense them accurately. Hence the use of weighing instead of the normal volumetric proportioning of the components. The necessity for accurate dispensing and the possibility of "adjusting" the properties of soft liners is not always appreciated by clinicians. In this way the powder/liquid ratio as used in this work for "Visco-gel" is higher than that specified by the manufacturers, because Bradenl8 suggested that by using a higher powder/ liquid ratio a more satisfactory material may be produced, that is one which gels more quickly and has a higher elastic modulus.

From our results the softest material is "Coe-comfort," a result which agrees with that of Wilson19 who measured the compression modulus of several soft

P P i i

I ~ 0 0 4 -

Position (m.m.1

Figure 7. sion in brine at 37°C. gel.

Load/deformation curves for some soft liners after 7 days immer- (X ) Coe-comfort; (0) Ardee; (0 ) Ivoseal; ( A ) Visco-


liners after water immersion at 37°C. Although our results confirm that ”Coe-comfort” is softest after 7 days, we found that after 30 days Ardee was softer. Immersion in brine, however, would simulate more closely conditions encountered during clinical use. After immersion in such a solution for 7 days at 37”C, the Young’s modulus is much lower (X0.4) than the modulus of sheets at room temperature prior to immersion. This reduction in elastic modulus is due to both the increase in temperature and water sorption, the water functioning as an additional plasticizer.

CONCLUSIONS

An ill fitting denture may cause trauma to its supporting tissues under the influence of the constant low magnitude pressures exerted at rest. In an at- tempt to simulate this all our compression results were obtained at a low compressive strain rate.

Using the method developed in the present work it is possible to measure the compression modulus of soft liners as used in dentistry. By using eqs. (4) or (5) for the compression stress-strain curve and eq. (6) which contains a shape factor, the compression modulus can be converted into Young’s modulus. The moduli of popular and clinically satisfactory soft liners are shown to be in the range 0.3-1.5 X lo5 N m-2. It should be noted that these moduli are specific to the rate of strain employed. Further results in tension at varying rates of strain established a linear relationship between Young’s modulus and log (strain rate).

It has been pointed out by Braden20 in his review that soft liners may harden when in use under the influence of the oral environment. From our studies in nitro there is no evidence that the changes in hardness of a tissue conditioner in the period 1 day to 7 days are clinically important. From our in uzno studies3 considerable variation existed between subjects. Similarly although weight changes reveal that variations in the ionic strength of the surrounding medium can cause changes in the diffusion proce~ses,~ such minor compositional changes had no significant effect on the Young’s modulus.

We would like to thank N. Cross and M Gregory for constructing the compression jig and Dr. R. Van Noort for the assistance with the tension measurements.

APPENDIX

To find a suitable time-dependent function r ( t ) for eq. (7), Chasset and ThirionI4 plotted the applied force (or stress) vs. log(/) and from the slope of this determined d F / d log t which they regarded as equal to d a z / d log t . They claim that a plot of log (- d F / d log f ) vs. log t is often linear over about 4 decades of time, hence

log - ___ = c - rn log t ( d ;o: t) with c and m being constants. Integration of eq. (Al) yields

SOFT DENTURE LINERS 74 1

where to is a time constant and F1 is a limiting stress at infinite time. The term in brackets in eq. (A2) is the time-dependent function 6211 + r ( t ) ] given in eq. (7). From eqs. (7) and (A2) an expression for a time-dependent elastic modulus can be obtained

This equation may be linearized by rearrangement and taking logarithms

So, for this equation to represent the present data, Figure 5, it would be necessary for log { G ( t ) - G,) = constant - m log t

G ( f ) N log { G ( t ) - G,]

(A4)

(A5)

which is impossible. At present it would appear that it is not possible to adopt a universal procedure for the

treatment of the time-dependent part of the stress, az(1 + r ( t ) ) . Thus if the measurements of stress relaxation by GentI5 and others, which fit eq. (8), are accurate, then the treatment of Chasset and ThirionI4 is obviously invalid, since such a fit would require log ( - d F / d log t ) = c and rn = 0 in eq. (Al).

References

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2.

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4.

5.

6.

7.

8.

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10.

11.

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14.

R. W. Phillips, Science of Dental Materials, 7th ed., Saunders, Philadelphia, 1973, p. 212. B. Ellis, S. Al-Nakash, D. J. Lamb and M. P. McDonald, ”A study of the composition and diffusion characteristics of a soft liner,” J . Dent., 7,133-140 (1979). B. Ellis, D. J. Lamb, and S. Al-Nakash, “Variations in the elastic modulus of a soft lining material,” B r . Dent. J., to appear. R. S. Porter and J. F. Johnson, ”The Entanglement Concept in Polymer Science,” Chern. Rev., 66, 1-27 (1966). R. S. Porter, W. J . McKnight, and J. F. Johnson, “Viscous and elastic beha- viour attributed to polymer entanglements,” Rubber Chern. Tech., 40,l-22 (1968). L. R. G. Treloar, The Physics of Rubber Elasticity, 3rd ed., Clarendon, Oxford, 1975, p. 213. J. E. Mark, ”The Constants 2C1 and 2C2 in Phenomenological Elasticity Theory and their dependence on Experimental Variables,” Rubber Chem. Tech., 48,495-512 (1975). A. R. Payne, ”Effect of Shape on the Static and Dynamic Stress-Strain Relationships of Bonded Rubber in Compression,” Nature, 177,1174-1 175 (1956). A. R. Payne, Rubber in Engineering Conference, London, September, 1956, The Natural Rubber Development Board, London, 1957, pp. 48-50. A. N. Gent and P. B. Lindley, ”The Compression of Bonded Rubber Blocks,” Proc. Inst. Mech Eng., 173,111-122 (1959). P. B. Lindley, “Load-Compression Relationships of Rubber Units,” J . Struin Anal., 1,190-195 (1966). A. N. Gent., ”Load-Deflection Relations and Surface Strain Distributions for Flat Rubber Pads,” Rubber in Engineering Conference, London, Sep- tember 1956, The Natural Rubber Development Board, London, 1957, pp.

J . D. Ferry, “Viscoelastic Properties of Polymers,” 2nd ed., Wiley, New York, 1970, pp. 149,437. R. Chasset and P. Thirion, ”Viscoelastic Relaxation of Rubber Vulcanisates between the Glass Transition and Equilibrium,” in Physics of Non-Crystdine Solids, J . A. Prins, Ed., North Holland, New York 1956, pp. 345-359.

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B. Ellis, D. J. Lamb, and S. Al-Nakash, ”Water sorption by a soft liner,” J . Dent. Res., 56,1526 (1977). M. Braden, private communication, 1977. H. J. Wilson, H. R. Tomlin, and J. Osborne, “The assessment of temporary soft materials used in prosthetics,” Br. Dent. J., 126,303-306 (1969). M. Braden, ”Polymer Prosthetic Materials,” in Scientific Aspects of Dental Materials, J. A. Von Fraunhofer, Ed., Butterworths, London, 1975, Chap. 15, pp. 425-458. See particularly p. 454.

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20.

Received January 4,1980 Accepted May 2,1980

the elastic modulus of soft denture liners

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