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Stress relaxation studies as dental materials 2. Simple restorative resins
Journal
of Dentistry,
6, No. 4, 1978,
pp. 321-326.
Printed
in Great Britain
Stress relaxation studies as dental materials 2. Simple restorative resins J. M. Paddon, BSc(Eng Met), ARSM A. D. Wilson, BSc, DSc, CChem, FRIC Laboratory of the Government Chemist, London
ABSTRACT The effect of ageing restorative resins has observed were small accommodate induced
on the stress relaxation properties and modulus of elasticity of two simple been studied. In contrast to the behaviour of dental cements, the changes up to 1000 hours. However, on further ageing the resin became less able to stresses.
INTRODUCTION The significance of stress relaxation, the loss of stress in a material subjected to a fixed strain, has been discussed by Paddon and Wilson (1976) in the first paper in this series. The present paper describes the application of the technique to two examples of restorative resins which are used directly by the dentist. One is a simple methyl methacrylate system used for direct fillings, and the other an epimine resin used for temporary crowns. The formula for the monomer is depicted in Fig. 1 (Braden et al., 1971). The mechanism of polymerization is by cationic polymerization with scission of the imine ring by R+ cations provided by the benzene sulphonate ester (C, Hs .S03 R). MATERIALS
AND METHODS
Materials Two materials were studied. Sevriton* comes in the form of polymethyl methacrylate beads (containing a p-toluene sulphinic acid salt polymerization initiator and benzoyl peroxide) which are mixed with a liquid, principally a methyl methacrylate monomer containing minor amounts of methacrylic acid and a cross-linking agent, ethylene glycol dimethyl methacrylate (Richards et al., 1977). Scutant comes as an epimine resin paste, consisting of an ethylene iminer monomer (see Fig. I) and a polyamide filler, which is mixed with a liquid cross-linking agent, benzene sulphonate ester. Specimen preparation Resins were prepared from these materials, using the appropriate proportions, at 23+ 1 “C and 50*5 per cent relative humidity. The pastes were packed into split moulds, 6 mm long x 4 mm diameter, and clamped between end plates and stored at 37°C. One hour after mixing the end plates of the moulds were removed and the ends of the cylinders were wet-ground flat and parallel using a 600-mesh carbide paper on a polishing wheel. The *Amalgamated Dental Company, London. tESPE, Seefield, Germany.
Journal of Dentistry,
322
Fig. 1. Monomer
I
0,
0
I
u/log
4
of the epimine resin.
,I 3 Log t f
2
Log f
Fig. 2. Typical log t,/*
Vol. ~/NO.
t curve showing
o*,
u,
and
(see text).
specimens were then stored in water at 37 “C until required for testing (periods varied from 2 to 10 000 hours) when their exact dimensions were measured. Test procedure
The determination of the stress relaxation rate (at 22 “C) was carried out by first loading specimens, using a constant cross-head rate, 0.1 mm/m@ to a pre-set test load, F,, of c 480 N. On reaching the set load the cross-head movement was stopped and the decay of the applied load, F, with time, t, was recorded. The machine constant, the ‘give’ of the machine, its fittings and the load cell, was determined by loading the machine, without a specimen, at a cross-head speed of O-1 mm/ min. The value found was 27 x lo-’ mm/N. RESULTS
Values from the experimental F/t curves were used to plot u(stress)/log t curves. The general form of these curves is illustrated by Fig. 2, which shows a straight line section spanning several decades of time. This straight line portion can be represented by: u = q + u* log t,
(1)
where ur is the value adopted by u when t = 1 min is substituted in equation (l), and
Paddon and Wilson: Stress relaxation
IO Fig. 3. Variation
of restorative
resins
323
loo storage time (h)
of the stress relaxation
function,
Fig. 4. Variation
E’, with
U”, with the resin age 0.
of the strain conversion
function,
the resin age 0.
~sewiron --- Scuran
I00
IO rroqe
Fig, 5. The variation
time (h)
IO00
IOWYI
of the modulus of elasticity,
E, with resin age, 6.
u* (do/d log t), the stress relaxation function, is the slope of the best-fitting straight line. The time taken for or to be reduced to aq2 is shown in Fig. 2 as tu12. The decrease in stress is accompanied by a loss of elastic strain, and the strain conversion function, E*, is given by: e*= A dlogt ’ The method of calculating this function and the modulus of elasticity, E, has already been given by Paddon and Wilson (1976). The variation of u*, E* and E with the age, 8, of the resins Sevriton and Scuton are presented in Figs. 3, 4 and 5 respectively. The variation of log tu12 with 0 is shown in Fig. 6.
DISCUSSION The results of these stress relaxation experiments may be interpreted in terms of the theory of viscoelasticity. The form of the u/log t curves, with their straight line portions, suggests that the Maxwell model, which can be represented by a dashpot and spring in series, is the appropriate one for analysis. In stress relaxation experiments the specimen is instantaneously strained by a fixed amount and in terms of a Maxwell unit all this strain is
Journal of Dentistry,
324
Ok
loo
Iwo
Vol. ~/NO. 4
10000
Storage t,me (h)
Fig. 6. The variation age, e.
of log f,,b (see text) with resin
taken up by the spring. The spring exerts a force on the dashpot and with time the strain becomes transferred to the dashpot and the spring returns to its original unstressed state. Thus the model explains the decay of stress and loss of elastic strain observed in these stress relaxation experiments. The equation describing the behaviour of a simple Maxwell unit is: de = a + -.1 77 E
dt
-da
3
(2)
dt
where u is the applied stress, E is the strain, 77the viscosity of the dashpot fluid and E the modulus of elasticity. If the strain is kept constant then: dt and equation (2) reduces to:
where u. is the initial stress and r = q/E is the relaxation time. Polymers have more than one relaxation time and are to be represented by several Maxwell units in parallel. In many examples the form of the distribution of relaxation times is approximately box-shaped. In these cases the u/log t curves have a straight line portion covering the region of the distribution of relaxation times (Alfrey, 1948; Nielsen, 1962). Since this type of curve was recorded in these experiments, then it follows that the Maxwell model is the appropriate one for describing the results obtained.
Paddon
and Wilson:
Stress relaxation
of restorative
Within the straight line portion time scale is H&T), is given by:
325
of the curve the distribution
H&r) Nhere F,(t) = g is the relaxation
resins
of relaxation
times on a log
= - d ‘s
modulus.
In terms of these experiments: H (In 7)
=-
do Ed Int
The characteristics of the time dependence of the properties of Sevriton (polymethyl methacrylate, PMMA) and Scutan (epimine resin) may be attributed to three factors: the initial polymerization reactions, long term water absorption and other long term structural changes. The modulus of elasticity (E) (Fig. 5) of both polymers increases during the time of polymerization and may be enhanced by loss of monomer. Subsequently, the modulus of the epimine resin decreases while that of the PMMA resin remains stationary. This difference in behaviour may be attributed to differences in molecular structure, their response to loss of monomer and the effect of water as a plasticizer. Stress relaxation, u*, and loss of elastic strain, E*, decrease during the polymerization period for both polymers, sharply in the case of the PMMA resin, a process which subsequently becomes less marked. The curves for the variation of log toi with cement age, 0, are the most interesting. Initially, during polymerization, this parameter increases for both polymers, the increase being more marked in the case of the epimine resin. Subsequently, as water continues to be absorbed, there is a further slight increase of log tuL2 with 8, observable for both polymers, followed by a dramatic increase after about 1000 hours of immersion in water. This effect is more pronounced in the case of the epimine resin and, significantly, this material is not used for permanent restorations but only for temporary crowns. Also PMMA resins used as denture base materials are known to increase in brittleness and fail after they have been in service for a period, the effect being generally attributed to fatigue. An increase in tu/, , which implies that the rate of dissipation of induced stress is reduced, is to be associated with an increase in brittleness. The results obtained in this study contrast with those found for dental cements (Paddon and Wilson, 1976), where there was evidence for hardening reactions continuing for several months. Thus, whereas E continually increases for dental cements as they age; the dental resins, once they have fully polymerized, show no increase in E, which either remains stationary (PMMA resin) or even decreases (epimine resin). The lOOO-hour E values for the resins are about one-tenth of those found for the dental silicate and glass-ionomer cements. The stress relaxation function, u *, for dental resins only slightly decreases once polymerization is complete, compared with the sharp increases encountered with the glass-ionomer and zinc polycarboxylate cements. The lOOO-hour U” values for the resins are about the same as that of the polycarboxylate cement, but one or two orders of magnitude greater than those of the dental silicate and glass-ionomer cements.
326
Journal of Dentistry,
Vol. ~/NO. 4
CONCLUSIONS The age dependence of the stress relaxation properties and the modulus of elasticity of the dental PMMA and epimine resins is related to polymerization and water absorption processes. Once fully cured the resins exhibit only changes in stress relaxation, o*, and modulus of elasticity, E, a behaviour which contrasts to that of the dental cements and reflects an absence of the slow hardening reactions characteristic of dental cements. However, t,l,, the time recorded for the induced internal stress to halve, dramatically increases after the resins have aged for more than 1000 hours in water and is an indication of a marked increase in brittleness.
Acknowledgements The authors thank the Government Chemist, Dr H. Egan, for permission to contribute paper. Crown Copyright. Reproduced by permission of Her Majesty’s Stationery Office.
this
REFERENCES
Alfrey T. (1948) The Mechanical Behaviour of High Polymers. New York, Inter-Science, p. 553. Braden M., Causton B. and Clarke R. L. (1971) An ethylene imine derivative as a temporary crown and bridge material. J. Dent. Res. 5, 536-541. Nielsen L. E. (1962) The Mechanical Properties of Polymers. New York, Reinhold, Chap. 4. Paddon J. M. and Wilson A. D. (1976) Stress relaxation studies on dental materials. 1. Dental cements. J. Dent. 4, 183-189. Richards C. P., Gilhooley R. A. and Pringuer M. A. (1977) Personal communication.
of Dentistry,
6, No. 4, 1978,
pp. 321-326.
Printed
in Great Britain
Stress relaxation studies as dental materials 2. Simple restorative resins J. M. Paddon, BSc(Eng Met), ARSM A. D. Wilson, BSc, DSc, CChem, FRIC Laboratory of the Government Chemist, London
ABSTRACT The effect of ageing restorative resins has observed were small accommodate induced
on the stress relaxation properties and modulus of elasticity of two simple been studied. In contrast to the behaviour of dental cements, the changes up to 1000 hours. However, on further ageing the resin became less able to stresses.
INTRODUCTION The significance of stress relaxation, the loss of stress in a material subjected to a fixed strain, has been discussed by Paddon and Wilson (1976) in the first paper in this series. The present paper describes the application of the technique to two examples of restorative resins which are used directly by the dentist. One is a simple methyl methacrylate system used for direct fillings, and the other an epimine resin used for temporary crowns. The formula for the monomer is depicted in Fig. 1 (Braden et al., 1971). The mechanism of polymerization is by cationic polymerization with scission of the imine ring by R+ cations provided by the benzene sulphonate ester (C, Hs .S03 R). MATERIALS
AND METHODS
Materials Two materials were studied. Sevriton* comes in the form of polymethyl methacrylate beads (containing a p-toluene sulphinic acid salt polymerization initiator and benzoyl peroxide) which are mixed with a liquid, principally a methyl methacrylate monomer containing minor amounts of methacrylic acid and a cross-linking agent, ethylene glycol dimethyl methacrylate (Richards et al., 1977). Scutant comes as an epimine resin paste, consisting of an ethylene iminer monomer (see Fig. I) and a polyamide filler, which is mixed with a liquid cross-linking agent, benzene sulphonate ester. Specimen preparation Resins were prepared from these materials, using the appropriate proportions, at 23+ 1 “C and 50*5 per cent relative humidity. The pastes were packed into split moulds, 6 mm long x 4 mm diameter, and clamped between end plates and stored at 37°C. One hour after mixing the end plates of the moulds were removed and the ends of the cylinders were wet-ground flat and parallel using a 600-mesh carbide paper on a polishing wheel. The *Amalgamated Dental Company, London. tESPE, Seefield, Germany.
Journal of Dentistry,
322
Fig. 1. Monomer
I
0,
0
I
u/log
4
of the epimine resin.
,I 3 Log t f
2
Log f
Fig. 2. Typical log t,/*
Vol. ~/NO.
t curve showing
o*,
u,
and
(see text).
specimens were then stored in water at 37 “C until required for testing (periods varied from 2 to 10 000 hours) when their exact dimensions were measured. Test procedure
The determination of the stress relaxation rate (at 22 “C) was carried out by first loading specimens, using a constant cross-head rate, 0.1 mm/m@ to a pre-set test load, F,, of c 480 N. On reaching the set load the cross-head movement was stopped and the decay of the applied load, F, with time, t, was recorded. The machine constant, the ‘give’ of the machine, its fittings and the load cell, was determined by loading the machine, without a specimen, at a cross-head speed of O-1 mm/ min. The value found was 27 x lo-’ mm/N. RESULTS
Values from the experimental F/t curves were used to plot u(stress)/log t curves. The general form of these curves is illustrated by Fig. 2, which shows a straight line section spanning several decades of time. This straight line portion can be represented by: u = q + u* log t,
(1)
where ur is the value adopted by u when t = 1 min is substituted in equation (l), and
Paddon and Wilson: Stress relaxation
IO Fig. 3. Variation
of restorative
resins
323
loo storage time (h)
of the stress relaxation
function,
Fig. 4. Variation
E’, with
U”, with the resin age 0.
of the strain conversion
function,
the resin age 0.
~sewiron --- Scuran
I00
IO rroqe
Fig, 5. The variation
time (h)
IO00
IOWYI
of the modulus of elasticity,
E, with resin age, 6.
u* (do/d log t), the stress relaxation function, is the slope of the best-fitting straight line. The time taken for or to be reduced to aq2 is shown in Fig. 2 as tu12. The decrease in stress is accompanied by a loss of elastic strain, and the strain conversion function, E*, is given by: e*= A dlogt ’ The method of calculating this function and the modulus of elasticity, E, has already been given by Paddon and Wilson (1976). The variation of u*, E* and E with the age, 8, of the resins Sevriton and Scuton are presented in Figs. 3, 4 and 5 respectively. The variation of log tu12 with 0 is shown in Fig. 6.
DISCUSSION The results of these stress relaxation experiments may be interpreted in terms of the theory of viscoelasticity. The form of the u/log t curves, with their straight line portions, suggests that the Maxwell model, which can be represented by a dashpot and spring in series, is the appropriate one for analysis. In stress relaxation experiments the specimen is instantaneously strained by a fixed amount and in terms of a Maxwell unit all this strain is
Journal of Dentistry,
324
Ok
loo
Iwo
Vol. ~/NO. 4
10000
Storage t,me (h)
Fig. 6. The variation age, e.
of log f,,b (see text) with resin
taken up by the spring. The spring exerts a force on the dashpot and with time the strain becomes transferred to the dashpot and the spring returns to its original unstressed state. Thus the model explains the decay of stress and loss of elastic strain observed in these stress relaxation experiments. The equation describing the behaviour of a simple Maxwell unit is: de = a + -.1 77 E
dt
-da
3
(2)
dt
where u is the applied stress, E is the strain, 77the viscosity of the dashpot fluid and E the modulus of elasticity. If the strain is kept constant then: dt and equation (2) reduces to:
where u. is the initial stress and r = q/E is the relaxation time. Polymers have more than one relaxation time and are to be represented by several Maxwell units in parallel. In many examples the form of the distribution of relaxation times is approximately box-shaped. In these cases the u/log t curves have a straight line portion covering the region of the distribution of relaxation times (Alfrey, 1948; Nielsen, 1962). Since this type of curve was recorded in these experiments, then it follows that the Maxwell model is the appropriate one for describing the results obtained.
Paddon
and Wilson:
Stress relaxation
of restorative
Within the straight line portion time scale is H&T), is given by:
325
of the curve the distribution
H&r) Nhere F,(t) = g is the relaxation
resins
of relaxation
times on a log
= - d ‘s
modulus.
In terms of these experiments: H (In 7)
=-
do Ed Int
The characteristics of the time dependence of the properties of Sevriton (polymethyl methacrylate, PMMA) and Scutan (epimine resin) may be attributed to three factors: the initial polymerization reactions, long term water absorption and other long term structural changes. The modulus of elasticity (E) (Fig. 5) of both polymers increases during the time of polymerization and may be enhanced by loss of monomer. Subsequently, the modulus of the epimine resin decreases while that of the PMMA resin remains stationary. This difference in behaviour may be attributed to differences in molecular structure, their response to loss of monomer and the effect of water as a plasticizer. Stress relaxation, u*, and loss of elastic strain, E*, decrease during the polymerization period for both polymers, sharply in the case of the PMMA resin, a process which subsequently becomes less marked. The curves for the variation of log toi with cement age, 0, are the most interesting. Initially, during polymerization, this parameter increases for both polymers, the increase being more marked in the case of the epimine resin. Subsequently, as water continues to be absorbed, there is a further slight increase of log tuL2 with 8, observable for both polymers, followed by a dramatic increase after about 1000 hours of immersion in water. This effect is more pronounced in the case of the epimine resin and, significantly, this material is not used for permanent restorations but only for temporary crowns. Also PMMA resins used as denture base materials are known to increase in brittleness and fail after they have been in service for a period, the effect being generally attributed to fatigue. An increase in tu/, , which implies that the rate of dissipation of induced stress is reduced, is to be associated with an increase in brittleness. The results obtained in this study contrast with those found for dental cements (Paddon and Wilson, 1976), where there was evidence for hardening reactions continuing for several months. Thus, whereas E continually increases for dental cements as they age; the dental resins, once they have fully polymerized, show no increase in E, which either remains stationary (PMMA resin) or even decreases (epimine resin). The lOOO-hour E values for the resins are about one-tenth of those found for the dental silicate and glass-ionomer cements. The stress relaxation function, u *, for dental resins only slightly decreases once polymerization is complete, compared with the sharp increases encountered with the glass-ionomer and zinc polycarboxylate cements. The lOOO-hour U” values for the resins are about the same as that of the polycarboxylate cement, but one or two orders of magnitude greater than those of the dental silicate and glass-ionomer cements.
326
Journal of Dentistry,
Vol. ~/NO. 4
CONCLUSIONS The age dependence of the stress relaxation properties and the modulus of elasticity of the dental PMMA and epimine resins is related to polymerization and water absorption processes. Once fully cured the resins exhibit only changes in stress relaxation, o*, and modulus of elasticity, E, a behaviour which contrasts to that of the dental cements and reflects an absence of the slow hardening reactions characteristic of dental cements. However, t,l,, the time recorded for the induced internal stress to halve, dramatically increases after the resins have aged for more than 1000 hours in water and is an indication of a marked increase in brittleness.
Acknowledgements The authors thank the Government Chemist, Dr H. Egan, for permission to contribute paper. Crown Copyright. Reproduced by permission of Her Majesty’s Stationery Office.
this
REFERENCES
Alfrey T. (1948) The Mechanical Behaviour of High Polymers. New York, Inter-Science, p. 553. Braden M., Causton B. and Clarke R. L. (1971) An ethylene imine derivative as a temporary crown and bridge material. J. Dent. Res. 5, 536-541. Nielsen L. E. (1962) The Mechanical Properties of Polymers. New York, Reinhold, Chap. 4. Paddon J. M. and Wilson A. D. (1976) Stress relaxation studies on dental materials. 1. Dental cements. J. Dent. 4, 183-189. Richards C. P., Gilhooley R. A. and Pringuer M. A. (1977) Personal communication.