long period of time whereas flow implies a greater deformation produced more rapidly with a smaller applied stress.

Stress relaxation involves the application of a constant strain. Under such conditions the stress decreases as a function of time for Maxwell-type viscoelastic materials. Although stress relaxation experiments can be used to classify materials, creep tests have more practical significance for dental materials. Such tests are relatively simple to carry out. A constant load is applied to a test specimen in either compression or tension. The strain or creep is measured as a function of time. Dynamic creep tests are also carried out in which the load is applied at regular intervals and the change in the value of strain measured as a function of the number of loading cycles.

Values of creep obtained by such techniques are particularly important for dental amalgam. It is thought that creep is a precursor to fracture at the edge of the filling and hence failure for such materials.

Stress relaxation is a measure of decreasing stress at constant strain. It is not of direct relevance for most dental applications.

2.3 Rheological properties

Rheology is the study of the flow or deformation of materials. The term can be applied to both solids and liquids and in the case of solids or elastomers involves the use of elasticity and viscoelasticity theory mentioned in Section 2.2. A study of the rheological properties of liquids and pastes normally involves the measurement of viscosity and the determination of the way in which this varies with factors such as rate of shear and time.

By definition viscosity (η) is given by the equation

η = Shear stress (σ ) Shear rate(Ε )

The phenomena of shear stress and shear rate can be visualized by considering the extrusion of a fluid material from a syringe (Fig. 2.15). When the material is extruded at a constant rate the shear stress is related to the pressure required to depress the barrel of the syringe, whereas the shear rate is a function of the flow rate. Thus, a material of low viscosity requires only a low pressure to

produce a high flow rate, whereas a more viscous material may require a high pressure to produce a relatively small rate of flow.

Further characterization of the rheological properties of materials is obtained by reference to the equation

Shear stress = K (Shear rate)n

where K and n are constants. The constant n is referred to as the flow index. For the simplest case, where n = 1, the shear stress is directly proportional to shear rate and the viscosity of the material is constant and independent of shear rate. Materials which behave in this way are referred to as Newtonian fluids.

When the flow index value is less than unity an increase in shear rate produces a less than proportionate increase in shear stress. Thus the viscosity is effectively decreased with increasing shear rate (shear thinning). Such materials are referred to as being pseudoplastic. When the flow index value is greater than unity an increase in shear rate produces a more proportionate increase in shear stress, thus effectively increasing viscosity (shear thickening). Such materials are said to be dilatant.

Figure 2.15 illustrates the result which may be obtained for Newtonian, pseudoplastic and dilatant materials when viscosity is measured as a function of shear rate. For dental materials, Newtonian and pseudoplastic behaviour are commonly encountered, whereas dilatancy is rare. The rheological properties are important for many differ-

ent materials since they often control the ease of use.

Some materials exhibit so-called Bingham characteristics. Here, a finite stress, referred to as the yield stress of the substance, is required in order to cause the material to flow. Once the yield stress is exceeded the material may behave as a Newtonian, pseudoplastic or dilatant fluid. In Fig. 2.16 curve A represents the behaviour of a normal Newtonian fluid, curve B the behaviour of a normal pseudoplastic fluid, curve C the behaviour of a material with a yield stress (value E) followed by Newtonian behaviour and curve D the behaviour of a material with a yield stress followed by pseudoplastic behaviour.

Viscosity values of materials are temperaturedependent, an increase in temperature generally causing a significant reduction in viscosity.

Time-dependence of viscosity (working times and setting times): Many materials used in dentistry involve the mixing of two components, thus initiating a chemical reaction which causes the material to change from a fluid to a rigid solid or elastomer. The initial viscosity of the mixed material often governs its ease of handling. The rate at which the viscosity increases as a function of time is of equal importance. Manipulation becomes impossible when viscosity has increased beyond a certain point. The time taken to reach that point is the working time of the material.

Figure 2.17 shows a typical plot of viscosity against time for a material setting by a chemical

reaction (curve A). The material may become unmanageable when it reaches a viscosity value of V1, thus the material has a working time of T1. Curve B is the plot of a material for which the viscosity does not begin to increase until the time T2 and the viscosity has not reached V1 until the time T3. Thus the working time for this material is considerably longer than that for material A. The shape of curve B suggests that the chemical reaction involved in setting has an induction period, probably produced by chemical retarders which manufacturers sometimes use to extend working times.

The other important time used to define setting characteristics is the setting time. This is related to the time taken for the material to reach its final set state or to develop properties which are considered adequate for that application. Methods used for measuring setting characteristics vary from one type of material to another. Many types of rheometer, both simple and complex, are capable of monitoring changes in viscosity as a function of time. Unfortunately, few instruments are able to monitor both the subtle changes occurring during the early stages of setting whilst the material is still relatively fluid and the changes occurring later when the material is highly viscous and rigid. Hence, two separate instruments are sometimes required to fully characterise setting. One convenient and commonly used method is resistance to penetration. Thus a material may be considered set when it is able to resist penetration

Fig. 2.17 Viscosity increasing with time for two materials during setting. Material B has an induction period during which the viscosity is unchanged.

Fig. 2.18 Assessment of setting time by determination of resistance to penetration. (a) Material is unset.

(b) Material is set.

by a probe of known weight and tip diameter (Fig. 2.18). It can be seen that in Fig. 2.18a the material is readily penetrated by the probe indicating that it has not set, whilst in Fig. 2.18b the probe is supported by the material, indicating that it is now set. As with most other methods of setting-time evaluation, this one is to some extent arbitrary in that the value obtained depends on the weight and tip diameter of the probe.

Further consideration of the arrangement illustrated in Fig. 2.18 suggests that the setting time determined by this method is the time required to produce a particular value of yield stress within the setting material. For this test to be meaningful the critical yield stress which corresponds to the applied load and probe tip diameter should have some practical significance related to the intended use of the material. Some products develop elastic properties during setting. These working times and setting times can be determined through measurement of the initial onset of elastic behaviour and the attainment of the final, optimum elastic state.

2.4 Thermal properties

Wide temperature fluctuations occur in the oral cavity due to the ingestion of hot or cold food and drink. In addition, more localized temperature increases may occur due to the highly exothermic nature of the setting reaction for some dental materials. The dental pulp is very sensitive to temperature change and in the healthy tooth is surrounded by dentine and enamel, which are relatively good thermal insulators. It is important that materials which are used to restore teeth should not only offer a similar degree of insulation but also should not undergo a large temperature rise when setting in situ.

Another consequence of thermal change is dimensional change. Materials generally expand when heated and contract when cooled. These dimensional changes may cause serious problems for filling materials, particularly in the region of the tooth/restorative interface.

Thermal conductivity: Thermal conductivity is defined as the rate of heat flow per unit temperature gradient. Thus, good conductors have high values of conductivity. Table 2.3 gives values of thermal conductivity for some dental materials along with those for enamel and dentine. It is clear that heat is conducted through metals and alloys more readily than through polymers such as acrylic resin. The relatively high value of conductivity for dental amalgam indicates that this material could not provide satisfactory insulation of the pulp. For this reason it is normal practice to use a cavity base of a cement such as zinc phosphate which has a lower thermal conductivity value.

Table 2.3 Thermal conductivity values of some selected dental materials.

Thermal conductivity is an equilibrium property and since most thermal stimuli encountered in the mouth are transitory in nature the value of thermal diffusivity may be of more practical use in predicting materials behaviour.

Thermal diffusivity: Thermal diffusivity (D) is defined by the equation

where K is the thermal conductivity, Cp is the heat capacity and r the density. This property gives a better indication of the way in which a material responds to transient thermal stimuli. Thus, if a cold drink is taken and the cooling effect on any tooth or restoration surface is maintained for only a second or two, the diffusivity allows calculation of the temperature change in the pulp. This should, naturally, be as small as possible. The diffusivity value recognizes that when transient thermal stimuli are applied a certain amount of heat will be absorbed in raising the temperature of the material itself. This will effectively reduce the quantity of heat available to be transported through the material.

Measurements of thermal diffusivity are often made by embedding a thermocouple in a specimen of material and plunging the specimen into a hot or cold liquid (Fig. 2.19a). If the temperature recorded by the thermocouple rapidly reaches that of the liquid, this indicates a high value of diffusivity. A slow response, on the other hand, indicates a lower value of diffusivity (Fig. 2.19b). In many circumstances a low value of diffusivity is

preferred. However, there are occasions on which a high value is beneficial. For example, a denture base material, ideally, should have a high value of thermal diffusivity in order that the patient retains a satisfactory response to hot and cold stimuli in the mouth.

Exothermic reactions: Many dental materials involve the mixing of two or more components followed by setting. The setting process often occurs in situ and very often the chemical reaction occurring during setting is exothermic in nature. For industrial production processes, exothermic reactions must be closely controlled in order to avoid explosions. For dental materials this is not a problem due to the relatively small sample sizes used. However, the heat liberated and the associated rise in temperature may cause clinical problems.

Table 2.4 gives typical values of temperature rise recorded for small samples of some dental materials. Naturally, the temperature rise increases with an increasing amount of material. Hence, due regard must be paid to the possible effect that

Fig. 2.19 (a) Measuring thermal diffusivity by embedding a thermocouple in a sample of the material. The sample is plunged into a hot or cold fluid and (b) temperature change plotted against time.

Table 2.4 Temperature rise during setting of some selected materials (100 mg sample).

such materials may have on the dental pulp when used as restoratives, particularly when a large bulk of material is used.

Following the course of an exothermic chemical reaction using a calorimeter is an accurate way of evaluating the setting characteristics of some dental materials. Consideration of the temperature against time curve which results from such experiments may produce a convenient method for measuring working times and setting times. The temperature rise occurring during setting has become even more significant with the growing number of light-activated materials used in