Regulación neuroendocrina del metabolismo

Hardness can be defined as the resistance to localised indentation of a surface by a standard indenter under standard conditions. The smaller the indentation that is made, the harder the material that has been tested. Hardness is a widely measured property of materials. The popularity of the hardness test is due to its simplicity. It is the test usually used in quality control applications and as an indicator of surface durability(^^^). Hardness tests are included in several specifications for the testing of dental materials.

Hardness is not a fundamental property of a materiah^^^). It varies in meaning with the method of measurement and the testing procedure. However, hardness is a resultant effect of several basic properties and appears to be closely related to strength^^^®\ At least the changes in surface hardness should partially reflect the changes in the bulk properties^^^). Measurement of hardness provides a very useful non-destructive method for the determination of the strength and an empirical check on the wear resistance of a material since high hardness appears to be associated with high strength and good wear resistance^^^^).

There are two main hardness measuring methods - static and dynamic indentation tests. The former tests are more important for the routine inspection of the hardness of a material whereas the latter tests are useful for hardness measurements on certain non-metallic materials. The static indentation tests are performed using ‘dead’ or static loading. A standard form of indentation is made in the specimen surface and correlated to the applied load.

Several systems of static indentation tests have been applied as a measurement of hardness, including Brinell, Rockwell, Vickers, Knoop, and Barcol systems. The

selection of the tests depends on the type of materials being investigated. The Brinell and Rockwell tests are classified as macrohardness tests whereas the Vickers and Knoop are microhardness tests(^^\ The latter measures the hardness of very small and thin components.

2 .6 .2 M icroh ard n ess tests (m icro-structure h ard n ess te sts)

Microhardness tests usually employ the diamond pyramid indentation system as the way of determining the hardness of the specimen surface. The diamond indenter used may be either the ‘Vickers’ diamond shape of square pyramid or the ‘Knoop’ diamond shape of rhombus pyramid. The former has the advantage over the latter in that the results can be directly compared with those from the same system of macrohardness tests, although the accuracy of the measurement of the indentation may not be as high. The loads used in this method are usually less than 9.8 N which results in small indentations with depths less than 19 pm("\ This is useful when measuring the hardness in small regions of a small specimen.

There are some differences between the results from small and large indentations using the same shape of indenter as a result of size effect. The elastic recovery of the materials has a greater effect in the small indentations than the larger ones. Measurement of the impression dimensions is also less accurate in small indentations than the larger ones. These contribute to greater hardness values than those obtained from the macrohardness tests.

Microhardness testing is also subject to the danger of results being affected by inhomogeneities in the material. Nevertheless, microhardness indentation tests have been applied for use in dental materials, including composite resins and GICs.

2 .6 .3 V ickers d iam on d pyram id m icroh ard n ess te st

The test utilises the Vickers diamond shape of square pyramid with 136® face angles shown in Figure 2.6-F^^^.

Figure 2.6-1 Vickers diamond

The method of operation is to push the indenter into the surface of the material under a predetermined load for a given period of time, usually 10-15 seconds. The area of the sloping surface of the indentation is calculated using the average of the two diagonals (D). The applied load is then divided by the surface area of the indentation, giving the hardness number - the Vickers Hardness Number (VHN or HV).

2Psin(*/2) _ 1.8544P

VHN = (2.6-1)

where P is the load in kg, (f> is 136°, and D is the average of the two diagonals of the indentation in mm^^^®\

2 .6 .4 The W allace m icro-indentation tester

The Wallace micro-indentation tester utilises the Vickers pyramid diamond indenter principle(^^°). The purpose of the instrument is to measure the depth of penetration of the indenter into a material being tested under a known dead load, the values of which ranging from a fraction of a gram up to 3 kilograms. The depth of penetration is read directly from the dial gauge. The scale on the dial gauge is divided into 100 units, each representing a depth of 0.00001 inches (Wallace indentation number or WN). This is

arbitrary and thus cannot directly compare with other systems. Since the numbers on the dial gauge represent the depth of penetration, the greater the number read on the dial, th e softer the material surface is.

2 .7 W A T E R SO R PT IO N CHARACTERISTICS

W ater sorption of a material is of importance clinically, particularly in relation to the dimensional stability and long-term durability of the restoration. When the material takes up water, its dimensions and structural integrity may be affected. In resin-based materials, expansion as a result of water sorption may be beneficial. This may compensate for any initial contraction and could relieve internal stresses caused by the polymerisation reaction. However, the absorbed water can also act as a plasticiser, weakening the materials. Components of the material may be lost into the water when placed in an aqueous environment. This is referred to as leaching. Leaching of the soluble components from a material into the oral cavity may have an impact on its structural stability and cause undesirable tissue responses. It is therefore desirable that the water sorption and solubility of the materials are as small as possible.

Water sorption by polymers and resin-based materials is a diffusion process(^^\ Diffusion of water is a time-dependent process where water is transported from the environment through the material surface into its body as a function of time(^^\ Rate of diffusion, or rate of mass transport, can be expressed as a diffusion flux (J) which is the mass (dM ) diffusing through and perpendicular to a unit cross-sectional area (A) of a solid per unit time (dt).

J = ~ — (2.7-1)

A dt

If the diffusion flux (J) does not change with time, the condition is known as “steady- state diffusion"(^^^). This occurs when the concentrations of the diffusing species on

both surfaces of the section are held constant. When the concentration ( O is plotted versus the distance across the thickness (%) of the section, the slope of the curve is the concentration gradient ( — ). In the steady-state diffusion, the diffusion flux is

dx

proportional to the concentration gradient or

J = - D — (2.7-2)

dx

Equation 2.7-2 is the “Pick's first law” for one-dimensional diffusion. The term D is the “diffusion coefficient”, with the unit of mV^ or cm^s \ In some cases, e.g. diffusion in dilute solutions, D can be assumed to be constant while in others D depends on the concentration(^^). Equation 2.7-2 is consistent only for an isotropic medium, i.e. one in which the structure and diffusion properties at any point are the same throughout. In a thin plane sheet of thickness L where all diffusing species enter through the cross- sectional area, the rate of duffusion is

/ = - D — = (2.7-3)

dx L

where Ca and Cb, are the constant concentrations on both surfaces of the sheet. D can be obtained if Ca, Cb, L and an observed value of J are known.

However, most diffusion processes are “non steady-state”; the diffusion flux and the concentration gradient vary with time. Non steady-state diffusion also occurs in a non- homogeneous medium where the diffusion coefficient varies from point to poinb^). For these conditions, the “Pick's second law” of diffusion is used.

— = -^ (D — ) (2.7-4)

dt âc âc

This equation is for one-dimensional diffusion where the concentration gradient is along the x-axis only. If the diffusion coefficient is independent of concentration, then

In the case of diffusion through a thin plane sheet of thickness 2 L where the region

- L < x < L is initially at a uniform concentration Coand the surfaces are maintained at a constant concentration Ca,the concentration C at any point in the region - L < x < L

is given by

= i - ± z t î ï L „ p f D(2n

— Cq 7C n~Q 2n+1 4L 2L

Experimentally, it is more convenient to determine the diffusing species as a function of t i m e ^ ^ - 34)^ I f j i f , i s the total amount of diffusing species entering the sheet at time t and

Moo is that after an infinite time or at equilibrium, then(^^)

\2^2,

For a small period of time, i.e. at the early stages of diffusion, C can be expressed as(^)

= S + Z (-ITerfc (2.7-8)

C ^ - C o n=0 2y/Dt n=0 2ylDt

and hence Æ = +2 Z H ) " i e r / c - ^ } (2.7-9)

M o o 1 L \ 7T n=I \ D t

Fickian diffusion is controlled by a concentration-dependent diffusion coefficient, i.e. the diffusion coefficient increases as the concentration of diffusing species increases, but does not depend on any other factors^^-^^. The representative plots for the Fickian and non-Fickian diffusion are given in Figure 2.7-1.

M t/M i

Square ro o t o f Tim e

Mt/M 00

S q u are r o o t o f Tim e

Figure 2 .7 -1 Fickian (a) and non-Fickian (b) sorption curves

In the early stages of Fickian diffusion, the amount sorbed or desorbed is directly proportional to the square root of time, t ^ . The linear sorption or desorption curve may extend well beyond 50% of the final equilibrium uptake or loss. When the curves cease to be linear, they become concave towards the axis and steadily approach the final equilibrium values {Figure 2.7-1 (a)). Pseudo-Fickian diffusion is used to describe the sorption-desorption curves of similar shape to the Fickian diffusion but of shorter initial linear portion.

The diffusion behaviour of some polymers, such as a glassy polymer, cannot be described adequately by a concentration-dependent form of Fick's law with constant boundaiy conditions, particularly when the diffusing species cause extensive swelling of the polymer. The properties of these polymers are time-dependent, i.e. they respond

slowly to the changes in their conditions. As a result, their behaviour deviates from that of Fick's law due to the slow rate of response to the sorption or desorption of diffusing molecules^^^^ and the curve has no initial linear portion ^Figure 2.7-1 (b)).

Quantitative measurements of the rate at which a diffusion process occurs are usually expressed in terms of a diffusion coefficient (D). In practice, a restorative material with a small value of D is desired since it takes longer time to take up water into its mass. There are many experimental techniques for measuring D , some of which assume that D is constant. When these methods are applied to systems where D is not constant, only a mean value of D is obtained. The following methods involve observing the over­ all rate of uptake or loss of diffusing substance by specimens of known size and shape. In these techniques, it is assumed that D is constant and the sheet does not swell.

a) Use o f Equation 2.7-7

From Equation 2.7-7 for a sheet of thickness 2L, only n = 0 (the first term in the series) is used since the subsequent terms become negligibly small for n ^ . Substituting n = 0 into Equation 2.7-7 gives

^ = (2.7-10)

n* 4L

If M,/M« = ^ t h e n

and if the value for which M, ^ is (tyj4L ^) then

If the half-time of a sorption process is observed experimentally, the value of D can be determined from Equation 2.7-11.

It can be seen that tj4l} for any given value of (Equation 2.7-10), and ( ty j4 Û ) {Equation 2.7-11) are independent of M«when D is constant. However, it has been shown experimentally that both terms decreases as increases, indicating that D is not constant but increases as the concentration of the diffusing species increases. Therefore, an approximation of D is used. A simple way to approximate D is to use the average value of D from both sorption and desorption data.

D = i( D , + Dj) (2.7-12)

b) Use o f Equation 2.7-9

It is also possible to obtain D from the initial gradients of the sorption or desorption curves when plotted against t ^ . For the early stages of diffusion where t is small, the first term of Equation 2.7-9 gives

If the initial gradient then d = — R^ (2.7-14)

d(t/4U)'^2 16

If MjMao is plotted against and an approximately linear portion of the curve is

obtained for MJM^ up to 0.5, then the initial ingredient R =---^ ^ and hence

Equation 2.7-15 gives similar value of D as in Equation 2.7-11.

If MJM^ is plotted against for up to 0.5 and a straight line is obtained, the slope of the straight line is given by

s = i J ^ (2.7-16)

The diffusion coefficient can be calculated by

D = (2.7-17)

4 16

Equation 2.7-17 should give similar value of D as in Equation 2.7-15.

The most practical approach to determine D is by using Equation 2.7-17. This equation will be used in this thesis.