Сraig. Dental Materials

characterized by uniform chromaticities. Value (black to white) is denoted as L*, whereas chroma (a*b*)is denoted as red (+a*),green (-a*), yellow (+b% and blue (-by. Differences between two colors can be determined from a color difference formula. One such formula has the form:

where L*, a: and b* depend on the tristimulus values of the specimen and of a perfectly white object. A value of AE" of 1 can be observed visually by half of the observers under standardized conditions. A value of AE* of 3.3 is considered perceptible clinically.

Visual Technique A popular system for the visual determination of color is the Munsell Color System, the parameters of which are represented in three dimensions, as shown in Fig. 3-4. The color considered is compared with a large set of color tabs. Value (lightness) is determined first by the selection of a tab that most nearly corresponds with the lightness or darkness of the color. Value ranges from white (lo/) to black (Oh. Chroma is determined next with tabs that are close to the measured value but are

of increasing saturation of color. Chroma ranges from achromatic or gray ( / O ) to a highly saturated color (/18). The hue of the color is determined last by matching with color tabs of the value and chroma already determined. Hue is measured on a scale from 2.5 to 10 in increments of 2.5 for each of the 10 color families (red, R; yellow-red, YR; yellow, Y; green-yellow, GY; green, G; bluegreen, BG; blue, B; purple-blue, PB; purple, P; red-purple, RP). For example, the color of the attached gingiva of a healthy patient has been measured as 5R 6/4 to indicate a hue of 5R, a value of 6, and a chroma of 4.

Two similar colors also can be compared in the Munsell Color System by a color difference formula such as one derived by Nickerson:

where Cis the average chroma and AH, AT.: and AC are differences in hue, value, and chroma of the two colors. For example, if the color of attached gingiva of a patient with periodontal disease was 2.5R 5/6, the color difference, I, between the diseased tissue and the aforementioned healthy tissue (5R 6/4) would be:

A trained observer can detect a color difference, I, equal to 5 .

Surface Finish and Thickness When white light shines on a solid, some of the light is directly reflected from the surface and remains white light. This light mixes with the light reflected from the body of the material and dilutes the color. As a result, an extremely rough surface appears lighter than a smooth surface of the same material. This problem is associated with unpolished or worn glass ionomer and composite restorations. For example, as the resin matrix of a composite material wears away, the restoration appears lighter and less chromatic (grayer).

The thickness of a restoration can affect its appearance. For example, as the thickness of a composite restoration placed against a white background increases, the lightness and the ex-

citation purity decreases. The most dramatic change observed is the increase in opacity as the thickness increases.

PIGMENTATION

Esthetic effects are sometimes produced in a restoration by incorporating colored pigments in nonmetallic materials such as resin composites, denture acrylics, silicone maxillofacial materials, and dental ceramics. The color observed when pigments are mixed results from the selective absorption by the pigments and the reflection of certain colors. Mercuric sulfide, or vermilion, is a red pigment because it absorbs all colors except red. The mixing of pigments therefore involves the process of subtracting colors. For example, a green color may be obtained by mixing a pigment such as cadmium sulfide, which absorbs

blue and violet, with ultramarine, which absorbs red, orange, and yellow. The only color reflected from such a mixture of pigments is green, which is the color observed.

Inorganic pigments rather than organic dyes are usually used because the pigments are more permanent and durable in their color qualities. When the colors are combined with the proper translucency, the restorative materials may be made to match closely the surrounding tooth structure or soft tissue. To match tooth tissue, various shades of yellow and gray are blended into the white base material, and occasionally some blue or green pigments are added. To match the pink soft tissues of the mouth, various blends of red and white are necessary, with occasional need for blue, brown, and black in small quantities. The color and translucency of human tissue shows a wide variation from patient to patient and from one tooth or area of the mouth to another.

Metameric colors are color stimuli of identical tristimulus values under a particular light source but different spectral energy distributions. The spectral reflectance curves of two such colors would be complicated, with perhaps three or more crossing points. Under some lights such colors would appear to match, but under other lights they would not match.

The quality and intensity of light are factors that must be controlled in matching colors in dental restorations. Because light from incandescent lamps, fluorescent lamps, and the sun differs, the match in color between a pigmented dental material and tooth structure may also vary. Whenever possible, colors should be matched in light corresponding to that of use.

FLUORESCENCE

Fluorescence is the emission of luminous energy by a material when a beam of light is shone on it. The wavelength of the emitted light usually is longer than that of the exciting radiation. Typically, blue or ultraviolet light produces fluores-

cent light that is in the visible range. Light from most fluorescent substances is emitted in a single, broad, well-shaped curve, the width and peak depending on the fluorescing substance.

Sound human teeth emit fluorescent light when excited by ultraviolet radiation (365nm), the fluorescence being polychromatic with the greatest intensity in the blue region (450nm) of the spectrum. Some anterior restorative materials and dental porcelains are formulated with fluorescing agents (rare earths excluding uranium) to reproduce the natural appearance of tooth structure.

OPACITY, TRANSLUCENCY,

AND TRANSPARENCY

The color of an object is modified not only by the intensity and shade of the pigment or coloring agent but also by the translucency or opacity of the object. Body tissues vary in the degree of opacity that they exhibit. Most possess a degree of translucency. This is especially true of tooth enamel and the supporting soft tissues surrounding the teeth.

Opacity is a property of materials that prevents the passage of light. When all of the colors of the spectrum from a white light source such as sunlight are reflected from an object with the same intensity as received, the object appears white. When all the spectrum colors are absorbed equally, the object appears black. An opaque material may absorb some of the light and reflect the remainder. If, for example, red, orange, yellow, blue, and violet are absorbed, the material appears green in reflected white light.

Translucency is a property of substances that permits the passage of light but disperses the light, so objects cannot be seen through the material. Some translucent materials used in dentistry are ceramics, resin composites, and denture plastics.

Transparent materials allow the passage of light in such a manner that little distortion takes place and objects may be clearly seen through them. Transparent substances such as glass may be colored if they absorb certain wavelengths and transmit others. For example, if a piece of

glass absorbed all wavelengths except red, it would appear red by transmitted light. If a light beam containing no red wavelengths were shone on the glass, it would appear opaque, because the remaining wavelengths would be absorbed.

Measurement of Contrast Ratio The opacity of a dental material can be determined instrumentally or by visual comparison with opal glass standards. Opacity is represented by a contrast ratio, which is the ratio between the daylight apparent reflectance of a specimen (typically 1 mm thick) when backed by a black standard and the daylight apparent reflectance of the specimen when backed by a white standard having a daylight apparent reflectance of 70% (or sometimes 100%) relative to magnesium oxide. The contrast ratio (C,,,,) for a resin composite should lie between the values of 0.55 and 0.70. The spectral reflectance curves of a composite resin backed by black and white standards are shown in Fig. 3-1. The contrast ratio can also be calculated from optical constants, as discussed later.

INDEX OF REFRACTION

The index of refraction (5) for any substance is the ratio of the velocity of light in a vacuum (or air) to its velocity in the medium. When light enters a medium, it slows from its speed in air (300,000 km/sec) and may change direction. For example, when a beam of light traveling in air strikes a water surface at an oblique angle, the light rays are bent toward the normal. The normal is a line drawn perpendicular to the water surface at the point where the light contacts the water surface. If the light is traveling through water and contacts a water-air surface at an oblique angle, the beam of light is bent or refracted away from the normal. The index of refraction is a characteristic property of the substance (Table 3-2) and is used extensively for identification. One of the most important applications of refraction is the control of the refractive index of the dispersed and matrix phases in materials such as resin composites and dental ceramics, designed to have the translucent appearance of tooth tissue. A perfect match in the

refractive indices results in a transparent solid, whereas large differences result in opaque materials.

OPTICAL CONSTANTS

Esthetic dental materials such as ceramics, resin composites, and human tooth structure are intensely light-scattering or turbid materials. In a turbid material the intensity of incident light is diminished considerably when light passes through the specimen. The optical properties of these materials are described by the KubelkaMunk equations, which develop relations for monochromatic light between the reflection of an infinitely thick layer of a material and its absorption and scattering coefficients. These equations can be solved algebraically by hyperbolic functions derived by Kubelka.

Secondary optical constants (a and bj can be calculated as follows:

and

where R, is the reflectance of a dark backing (the black standard), R,is reflectance of a light backing (the white standard), R(B) is the light reflectance of a specimen with the dark backing, and R(W) is the light reflectance of the specimen with the light backing.

These equations are used under the assumptions that (1) the material is turbid, dull, and of constant finite thickness; ( 2 ) edges are neglected;

(3) optical inhomogeneities are much smaller than the thickness of the specimen and are distributed uniformly; and (4)illumination is homogeneous and diff~~sed.

Scattering Coefficient The scattering coefficient is the fraction of incident light flux lost by reversal of direction in an elementary layer. The scattering coefficient, S, for a unit thickness of a material is defined as follows:

S = (l/bX) Ar ctgh [l- a(R + R,) +

RR,/b(R - R,)], mm-'

where Xis the actual thickness of the specimen, Ar ctgh is an inverse hyperbolic cotangent, and R is the light reflectance of the specimen with the backing of reflectance, Rg.

The scattering coefficient varies with the wavelength of the incident light and the nature of the colorant layer, as shown in Fig. 3-5 for several shades of a resin composite. Composites with larger values of the scattering coefficient are more opaque.

Absorption Coefficient The absorption coefficient is the fraction of incident light flux lost by absorption in an elementary layer. The absorption coefficient, K, for a unit thickness of a material is defined as follows:

The absorption coefficient also varies with the wavelength of the incident light and the nature of the colorant layer, as shown in Fig. 3-6 for several shades of a resin composite. Composites with larger values of the absorption coefficient are more opaque and more intensely colored.

Light Reflectivity The light reflectivity, RI, is the light reflectance of a material of infinite thickness, and is defined as follows:

Wavelength (nm)

Fig. 3-5 Scattering coefficient versus wavelength for shades of a composite, C. Shades are 0, opaque;

I, light; U, universal; ): yellow; D):dark yellow; T, translucent; and G, gray.

(From Yeh CL, Miyagawa Y, Powers JM: J Dent Res 61:797, 1982.)

This property also varies with the wavelength of the incident light and the nature of the colorant layer.

The light reflectivity can be used to calculate a thickness, XI, at which the reflectance of a material with an ideal black background would attain 99.9% of its light reflectivity. The infinite optical thickness, XI, is defined for monochromatic light as follows:

XI = (l/bS) Ar ctgh [(I - 0.999aRI)/0.999bRIl,mm

The variation of XI with wavelength is shown in Fig. 3-7 for a composite resin. It is interesting that composites are more opaque to blue than to red light, yet blue light is used to cure light-activated composites.

Once a, b, and S are obtained, the light reflectance (R)for a specimen of

Fig. 3-6 Absorption coefficient versus wavelength for shades of a composite, C. Shades are D): dark yellow; 0, opaque; ):yellow; G, gray; 1, light;

T, translucent; and U, universal.

(From Yeh CL, Miyagawa Y, Powers JM: 1 Dent Res 61:797, 1982.)

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any thickness (XIin contact with a backing of any reflectance (Rg) can be calculated by:

R = [l- R,(a - b ctgh bSX)I/

(a + b ctgh bSX - R,)

An estimate of the opacity of a 1-mm-thick specimen can then be calculated from the contrast ratio (C) as:

where R, is the computed light reflectance of the specimen with a black backing. If R, is 0.70, then C,,,, can be calculated (see Measurement of contrast ratio).

THERMAL PROPERTIES

a'*+,, ra"

TEMPERATURE

The temperature of a substance can be measured with a thermometer or a thermocouple. An important application of temperature measurement in dentistry is the measurement of heat during the shaping of cavities in teeth. Numerous studies have been made of the effect of speed and force on the rise of temperature in teeth. The increase in temperature during the cutting of tooth structure with various types of steel burs, carbide burs, and rotary diamond instruments also has been investigated. In addition, the rise in temperature in the tooth at various distances from the cutting instrument has been determined. Examples of the effect of the speed of rotation and coolants on the increase in temperature in tooth structure are shown in Fig. 3-8. The temperature was measured by a thermocouple inserted into a small opening that extended into the dentoenamel junction. The tooth was then cut in the direction of the thermocouple and the maximum temperature recorded.

TRANSITION TEMPERATURES

The arrangement of atoms and molecules in materials is influenced by the temperature; as a

result, thermal techniques are important in understanding dental materials. These techniques are differential thermal analysis, differenti, I scanning calorimetry, thermogravimetric analysis, thermomechanical analysis, and dynamic inechanical analysis. Differential thermal analysis has been used to locate the temperature of transitions and to study the effect of variables, such as composition and heat treatment, on these transitions. Differential scanning calorimetry can determine the heats of transition and reaction. Thermogravirnetric analysis measures the change in weight of materials as a function of temperature and environment and gives information related to the thermal decomposition of materials or their stability in various environments. Thermomechanical analysis measures the dimensional change with or without load as a function of temperature. Changes in the ease of deformation as the temperature increases indicate the presence of transitions. This method can also measure the coefficient of thermal expansion as a function of temperature. Dynamic mechanical analysis measures the changes in modulus of elasticity and loss tangent as a function of temperature. This technique can be used to measure the glass transition temperature of polymers.

Differential thermal analysis (DTA) has been used to stud37 waxes used in the compounding of dental waxes. The DTA curve of a mixture of paraffin and carnauba wax is shown in Fig. 3-9. The thermogram was obtained when the difference in temperature between the wax and a standard was recorded under the same heating conditions in which thermocouples were used. The difference in temperature was recorded as a function of the temperature of the surroundings. A decrease in the value of AT indicated an endothermic process in the specimen. The endotherms at 31.5" and 35" C are solid-solid transitions occurring in the paraffin wax as the result of a change of crystal structure. The endotherm at 52" C represents the solid-liquid transition of paraffin wax, whereas the endotherms at 68.7" and 80.2" C result from the melting of carnauba wax. The heat of transition of the two solid-solid transitions is about 8 cal/g, and the

melting transition of paraffin and carnauba wax is approximately 39 and 11 cal/g, respectively. These and other thermograms show that 25% carnauba wax added to paraffin wax has no effect on the melting point of paraffin wax but increases the melting range about 28" C.

Thermomechanical analysis (TMA) of the carnauba-paraffin wax mixture is also shown in Fig. 3-9. The percent penetration of the wax mixture by a cylindrical probe is shown for two stresses of 0.013 and 0.26 MPa. The penetration of the wax at the lower stress was controlled by the melting transition of the carnauba wax component, whereas the penetration at the higher stress was dominated by the solid-solid and solid-liquid transitions of the paraffin wax components. About 44% penetration, which is related to flow, occurred before the melting point of the paraffin wax was reached.

Other properties correlate with thermograms. The coefficient of thermal expansion of paraffin

tion, and the flow increases greatly in this temperature range.

Dynamic mechanical analysis (DMA) of a dimethacrylate copolymer is shown in Fig. 3-10. A thin film of the copolymer was subjected to a sinusoidal tensile strain at a frequency of 11 Hz. As temperature was increased, values of modulus of elasticity (E') and loss tangent (tan 6) were obtained. The glass transition temperature (Td was determined from identification of the beginning of a rapid decrease in E' with temperature. The value of T, identifies the temperature at which a glassy polymer goes to a softer, rubbery state upon heating. A lower value of T, can result from a lower degree of conversion of