Dent Mater 8:105-109, March, 1992
Dimensional stability of silicone-based impression materials V. Fano 1, P.U. Gennari 2, I. Ortalli 1 lIstituto di Scienze Fisiche, 2Clinica Odontoiatrica, delI'Universita', Parma, Italy
Abstract. This study attempts to demonstrate that the polymerization reaction is not the only factor that affects the shrinkage of silicone-based impression materials because evaporation of the constituentsalso contributesto the shrinkage.These factors can be evaluated by the study of time-dependent dimensional changes. This is shown both by chemical kinetics and by experimental testing of condensation and addition polymerizing impression materials with different viscosities. Comparison of the different materials shows that the two contributions, polymerization shrinkage, and evaporation shrinkage, can be assessedseparately by analysisof the time-dependentshrinkage diagrams. The instability due to the polymerization reaction is complete after a few hours, but the contribution of the constituent evaporation, if present, can have a significant long-term role. Numerous investigations of the dimensional variations of impression materials have been published in the dental literature. These studies have used a variety of direct and indirect methods of measuring shrinkage. Examples of shrinkage in silicone-based materials were reported by Burdarion (1984). Williams et al. (1984) analyzed the dimensional stability of some elastomers by measuring the gap width of a master coping seated on the dies produced from different impressions materials. Ohsawa and Jcrgensen (1983) measured the curing contraction ofaddition-type silicone impression materials with a mercury bath apparatus. They found the maximum contraction to be more than 0.08% at 15 min after mixing and more than 0.03% during storage from 15 min to 24 h. Clancy et al. (1983) studied the longterm dimensional stability. The ADA Specification No. 19 test block and mold (American Dental Association, 1977) were used. The impressions were measured using a travelingstage reflectingmicroscope and an image -analyzing computer. In this study, a silicone impression material showed significant change (0.14 mm) at 4 h and 0.2 mm after 4 wk. Marcinak and Draughn (1982) measured the linear dimensional change occurring as a function oftime between making the impression and pouring the die. The measured dies were compared to a master model and the linear change in the impression material was determined. Mincham et al. (1981) used holographic interferometry to determine the rate of dimensional change on setting. Lacy et al. (1981) used a technique of measuring stone dies poured sequentially from impressions of simulated preparations in a dental arch configuration. The measurements were made by micrometer. These studies were descriptive and did not give unequivocal conclusions about the origin of the dimensional variation and its time-dependence. Shrinkage was explained as due to the polymerization reaction, a phenomena that is seen in other
dental polymeric materials (Rees and Jacobsen, 1989). However, for dental impression materials, dimensional change can be influenced by other effects that relate to the differences in composition. In fact, the dimensional stability ofimpression materials as a function of time can be affected by several factors: completion of chemical reaction, constituent evaporation, relaxation of stresses due to either a particular shape or type of handling, water imbibition (when the material is not water-repellent; silicones are water-repellent), and temperature variation between body temperature and room temperature. In this work, an attempt has been made to analyze the curves of the linear dimensional change for some siliconebased impression materials. For this purpose, it is worthwhile to consider the intrinsic factors (completion of the polymerization reaction and constituent evaporation) and separate them from the other factors. The influence of the relaxation and water imbibition has been excluded, since simple geometric shapes (parallelepiped) of water-repellent substances were analyzed. Also, these samples were prepared at room temperature (20°C) to avoid the influence of the temperature changes that occur between body temperature and room temperature. Thus, the aim of this work is the following: (a) to demonstrate that, in addition to the polymerization reaction, the dimensional stability is also affected by evaporation of a volatile component; and (b) to find a graphic method for separating the polymerization contribution from the evaporation contribution. For this purpose, we will discuss the possible analytical expressions of the linear dimensional variation due to both polymerization shrinkage and evaporation. Residual Polymerization Reaction. Immediately after making the impression, the polymerization reaction cannot be consideredcompleted. Consequently, the shrinkage behavior as a function of time is dependent upon the kinetics of the polymerization reaction. If the kinetics are not expressed by a linear function, the time-dependent dimensional change cannot be linear. Now we shall examine the kinetics of two very common dental material polymerization reactions as examples of kinetics characterization of these complex reaction systems: (a) polymerization reactions induced by an initiator. In this case, the polymerization process can be represented by the following three principal reactions: I--> R*
(1)
R* + M --> R'*
(2)
2R'* -~ P
(3)
Dental Materials~March 1992 105
We assume that the initiator, I, decomposes and forms an active radical, R* (Eq. 1), which reacts with monomer molecules, M, and immediatelyforms a free radical,R'*(Eq. 2). The termination step is a reaction between two radicals (Eq. 3). The reaction rate of all radicals (regardless of how many monomer units have become incorporated) are hypothesized as being the same. Now we can write the following kinetic reactions: the rate of the initiator reactions = k I [/]
(4)
the reaction rate of the chain growth = k 2 [R'*] [M] (5) the reaction rate of the termination step -- k 3 [R'*] 2 (6) where k,, k 2 and k3 are reaction constants. Under steady-state conditions, it is assumed k 3 [/], k 1[I]. In this case, the R'* concentration is constant; consequently, eqs. 4 and 6 are equal: k 1 [/]
=
k 3 [R'*] 2
(7)
The concentration of free radicals in a steady-state condition can be calculated from Eq. 7: /kl[/]/1/2 (8)
The time-dependent dimensional stability induced by the kinetics of the polymerization reaction, i.e., by rate of [M] decrease, is proportional to the reaction rate of the chain growth (Eq. 5). This evaluation can be made by substituting [R'*], obtained from Eq. 8, in Eq. 5: d[M] _ k 2 dt ~-3)
[I]t/2[M ]
(9)
This equation is not linear. Accordingly, the dimensional change cannot be linear. (b) in the case of competitive-consecutive polymerization reactions typical of the addition polymerization, the following reaction scheme can be established: k 1
R; + R1
R; k2
(10) (11)
k3
(12)
R1
kn n+l
(13)
For these reactions, the following equation set (Szabo, 1969) can be determined:
dR: -- kn_l[R; dt
][R~l]
-
kn[R 1 ] [ R ; ]
106 Fano et aL/Dimensional stability of some impression materials
(14)
This equation type is not linear• Thus, the dimensional change cannot be linear. The same can be demonstrated for all polymerization reactions. The mathematical resolution of equations like Eqs. 9 and 14 was reported (Benson, 1960) as a fractional function (polymerization by initiator) or an exponential function (polymerization by addition). In other words, the linear shrinkage decreases proportionally to a fractional or exponential function, reachinglow values in a comparatively short time. Now we shall examine how to determine the evaporation contribution. The Constituent Evaporation. The followingcomponents are involved in this process: (1) plasticizers--for example, natural inner oils or cycloalkanes, materials that mainly decrease viscosity (with concentrations generally higher in the lowestviscosity materials); (2) liquid catalysts, such as dibutyltin dilaurate; (3) low-molecular-weight starting polymers; and (4) by-products of the condensation polymerization reaction (generally water or alcohol). Large production of by-products is generally reduced when partially polymerized starting materials are used• In all cases, the shrinkage induced by the production and elimination of volatile by-products ceases when the polymerization reaction finishes or immediately thereafter. Thus, the most significant evaporation involves plasticizers and low-molecular-weight polymers. Now we shall examine the possibility of assessing the evaporation and the polymerization contributions separately, if both are present. For this, we shall consider the following: for a sample with fixed stoichiometric composition, the rate of the polymeric reaction is not dependent upon the sample volume and shape, while the rate of evaporation, on the other hand, is strongly dependent on these factors. In other words, the polymerization reaction is always completed within a certain time, regardless of the sample quantity and shape, but the evaporation process can be changed by varying the sample dimensions and shape. The higher the surface to volume ratio (s/v), the sooner the evaporation stops. A quantity of material in film form eliminates volatile substances faster than when it is in bulk form. On the contrary, if large samples having small s/v ratio values are examined (as in this study), the evaporation rate is slow and can be considered constant throughout the experiment. Thus, the dimensional change induced by the evaporation is linear.
MATERIALSAND METHODS Some condensation polymerizing and addition polymerizing silicone-based impression materials were analyzed. Table 1 presents the examined materials• These materials, having different viscosities, were prepared using the same mixing times (2 min, 30 s), after which the materials were put into a 6.5 x 2.5 x 2-cm parallelepiped-shaped mold (Fig. 1A) and kept there for 2 min, 30 s. The bottom of the mold consisted of a die with two parallel straight lines, 49.95 mm apart; oeach. line • . was 5 ~m in width and had constant angles of 60 ; Fig. 1B shows the lines on the die. These lines were recorded by the impression materials. The percent linear shrinkage was calculated by measuring the distance between the two straight lines as a function of time• The calculation was made using the formula: /~2/2) Percent shrinkage = 100 (15)
TABLE 1: MATERIALS
Provil
Polymerization addition
Viscosity very high
Curve Fig. 3a
Manufacturer Bayer, Leverkusen, Germany
Provil Sam
addition addition
high high
Fig. 3b Fig. 3c
Bayer Duebi, Carpi, Italy
7858R, 7864R
Optosil Xantopren
condensation condensation
very high low
Fig. 4a Fig. 4b
Bayer Bayer
0013D 6218E
Polasil Polasil
condensation condensation
very high low
Fig. 4c Fig. 2d
Duebi Duebi
8806 8911
Materials
where 11 is the length measured immediately after the extraction from the mold, and 12is the length measured after a given time. To measure this distance between the two impressed parallel straight lines, the samples were located on a slide, which was moved under the stereomicroscope. The slide surface was mirror-like to eliminate probable friction at the sample-slide interface when the sample shrinks. In fact, the comparison among the dimensional change of samples kept on the slide for 24 h, samples dusted with talcum powder, and samples kept for 24 h on mercury did not show any significant differences. Thus, it was not necessary to use the mercury bath apparatus that is frequently used in shrinkage measurements (Lee et al., 1969; Hegdahl and Gjerdet, 1977; Ohsawa and J~rgensen, 1983). An electronic gauge, attached to the slide, (accuracy: 1 pm) was used to measure between the two impressed straight lines.The measurement error was 0.002% (1 ~m/50 mm), significantly lower than that reported in international specifications ISO-4823 (0.04%) (Norme Internationale ISO, 1984) and ADA No. 19 (0.02%) (American Dental Association, 1977). In order to calculate the polymerization contribution
/
B
Batch 6555C, 6518C 8903
separately from the evaporation contribution, the latter value was subtracted from the dimensional change. For this purpose, the graphs as a sum of two functions are considered. In order to know the evaporation contribution at any time during the experiment, a line must be drawn parallel to the (long-term) rectilinear part of the curve and passing through the zero point of the coordinates. At the zero time, the evaporation contribution can be approximated to zero, if the evaporation during the mixing time and during the setting in the mold time is neglected. RESULTS
In Figs. 2 and 3, the different silicone impression materials are compared. Three samples of each material were tested. The curves are repetitive. The experimental errors (0.002%) are too small for the graphic representation in the Figs. The zero time of the curves corresponds to the sample extraction from the mold. The dimensional change is always more rapid at the beginning: during the first 5 h, there is nearly 50% of the decrease for day one. Subsequently, the sample lengths decrease linearly or, in the case of high-viscosity materials, become nearly constant. Owing to the fact that, at the beginning, the dimensional decrease is not linear, the experimental points were checked more frequently for the best curve-fitting (one point every 5-10 min). Otherwise, each experimental point on the rectilinear part of each curve was checked after 1 h or more. Comparing the high-viscosity material obtained by addition reaction to that obtained by condensation reaction, the difference is negligible (compare Fig. 2, curve a, and Fig. 3, curve a). After 5 h, the dimensional change is -0.05% in both cases; after 24 h, the dimensional change is -0.075% for the addition polymers and -0.09% for condensation polymers (the ratio of these two values is 0.83). But when materials from the same manufacturer with different viscosities were compared, the shrinkage difference was significant (the ratio of the dimensional change between materials was much lower than 0.83; see Table 2). In other words, the components involved in the viscosity decrease make a large contribution to the shrinkage. DISCUSSION
Fig. 1. A diagram of the mold (part A) and the die (part B) used to prepare the samples.
The role of evaporation, if present, can be assessed by the analysis of the experimental curves, taking into account that, in our experimental conditions, the shrinkage due to polymerization finishes long before the shrinkage due to evaporation, because of the sample's configuration. On the other hand, the time-dependent shrinkage due to polymerization is closely related to the kinetics of the chemical reaction expressed by Eqs. 9 and 14. Accordingly, the time-dependence of the polymerization shrinkage cannot be linear. Conversely, Dental Materials~March 1992 107
~ -0.08~------------~ C
b
1
0
t
I
I
I
5
I
i0
15
20
25
HOURS
Fig. 2. Shrinkage as a function of time for addition reaction silicone impression materials, comparison of different viscosities: a - very high viscosity (Provil), b - high viscosity (Provil), and c- high viscosity (Sam).
•
-0.08
-o.24
b
< Z
~o.4o ¢,q '
0
5
I0
,
,
15
t
i
20
i
25
HOURS
Fig. 3. Shrinkage as a function of time for condensation reaction silicone impression materials, comparison of different viscosities: a - very high viscosity (Optosil), b - low viscosity (Xantopren), c - very high viscosity (Polasil), and d - low viscosity (Polasil).
when the shrinkage is a linear function of time, i.e., it is expressed by a straight line, this must be ascribed to the evaporation; in this case, no polymerization contribution can be involved. With this fact in mind, all curves of Figs. 2 and 3 can be divided into two parts. The first part (starting from zero time) decreases in a non-linear way and can be approximated to the solution ofEq. 9 (condensation reaction) or Eq. 14 (addition reaction), when the evaporation component has been subtracted. After that, the curves (the second part) take on a behavior following the equation: % length = At + B
(16)
where B is the intercept of the straight-line extension at the % length axis. The characteristic of the second part depends upon the A coefficient of the linear parts of the curves. Numerically, A = Al/At, where A/is the decrease in % length in the At time interval. The larger the A, the larger the h/, due to a larger quantity of evaporated material. The a and b curves of Fig. 2 are materials made by the same manufacturer and having different viscosities: curve a, very high-
viscosity material; curve b, high-viscosity material. According to our hypothesis, the A coefficientof the b curve, Ab, must be larger than the A coefficientof the a curve, Aa. In fact, after 5 h , A b = 0.004% h 1 a n d A a = 0.0016% h -1. Thus, the correlation of the straight-line behavior with the evaporation process is confirmed. If we now compare the b and c curves (both curves are ascribed to high-viscosity materials), their behavior is quite different. In fact, the contribution of the non-linear part of the c curve to shrinkage is much larger than that of the b curve, but the b curve material modifies its dimensions chiefly by evaporation, Aa > Ab. Consequently, during the first 2 to 3 h, the b material changes slightly in dimensions when compared with the c material and can be recommended for use when times of under 20 h are necessary. Otherwise, the c material is better. Finally, the condensation polymers are believed to have a higher shrinkage (compared with addition polymers) because of the generation of volatile by-products during the polymerization reaction. As stated in the "Results" section, this difference in behavior can be negligible. On the other hand, it can also be large, for materials obtained by the same polymerization method but having different degrees of viscosity (see the curves of Fig. 2). In other words, the presumed superior precision of the addition polymers must be qualified, because the influence of a long-duration evaporation process can affect the dimensional change in a more significant way than the elimination of the condensation byproduct. Evaluation of the Evaporation Contribution by Graph. Numerically, the evaporation contribution can be evaluated separately from that of polymerization by graph. For this purpose, it is necessary to determine the point of the curve when the polymerization reaction is considered complete. For this, the extension of the rectilinear part of the curve toward zero time must be drawn (see, for example, the d curve of Fig. 3). The A point gives information about the following: (1) the time necessary for completion of the polymerization reaction (7 h); (2) the dimensional change induced by the polymerization reaction (-2.05%, see below); and (3) the dimensional change induced only by evaporation at any time during the experiment (0.275% after 24 h). The last two characteristics are obtained by the drawing a line parallel to the rectilinear part of the d curve, passing through the origin of the coordinates (see the straight line, e, of which only a part has been drawn to simplify the graph). The point B, corresponding to 0.08%, is the contribution due to only evaporation after 7 h. Consequently, the contribution due to polymerization after 7 h is A- B = -0.285% - (-0.08%) = -0.205%. The dimensional change induced by evaporation after 24 h is -0.48% - (-0.205%) = -0.275%. This research has shown: (1) The experimental diagrams of the dimensional stability can be considered as a sum of two contributions: one due to polymerization, the other due to evaporation. The different possibilities in magnitude of the two phenomena explain the great differences in behavior of
2" RATIOOF DIMENSIONALCHANGEBETWEENMATERIALSOF THE SAME MANUFACTURERWITH DIFFERENTDEGREESOF VISCOSITY Material Pairs Polymerization Mechanism Ratio of DimensionalChanges High-viscosity Provil/Iow-viscosityProvil Addition 0.31 Very high-viscosityOptosil/Iow-viscosityXantopren Condensation 0.44 Very high-viscosityPolasil/Iow-viscosityPolasil Condensation 0.66 TABLE
108 Fano et al./Dimensional stability of some impression materials
the materials in practice. (2) The contributions of residual polymerization reaction and constituent evaporation to dimensional stability can be evaluated separately if the dimension change as a function of time is known. (3) The experimental diagrams show that the rate of the dimensional variation, which is maximum at the beginning, decreases rapidly and approaches zero value or becomes constant in a short time (few hours). This is in accordance with the kinetics of the polymerization reactions. (4) The constituent evaporation can play a significant role, depending upon the degree of the viscosity and the bulk dimensions rather than upon the synthesis method. Received August 2, 1990/Accepted September 8, 1991 Address correspondence and reprint requests to: V. Fano Istituto di Scienze Fisiche del|'Universita', Via D'Azeglio, 85 43100 Parma, Italy
REFERENCES American Dental Association (1977). Revised specificationNo. 19 for non-aqueous, elastomeric dental impression materials. JAm Dent Assoc 94:733-741. Benson SW (1960). The foundations ofchemical kinetics. New York: McGraw-Hill, 605. Burdarion G (1984). Biomateriali dentari. Milano, Italy: Masson Italia, 167. Clancy JM, Scandrett FR, Ettinger RL (1983). Long-term dimensional stability of the three current elastomers.
J Oral Rehabil 10:325-333. Hegdahl T, Gjerdet NR (1977). Contraction stresses on composite resin filling materials. Acta Odontol Scand 35:191-195. Lacy AM, Bellmann T. Fukui H, Jendresen MD (1981). Timedependent accuracy of elastomer impression materials. Part I: Condensation silicones. J Prosthet Dent 45:209215. Lee HL, Swartz ML, Smith FF (1969). Physical properties of four thermosetting dental restorative resins. JDent Res 48:526-535. Marcinak CF, Draughn RA(1982). Linear dimensionalchanges in addition curing silicone impression materials. JProsthet Dent 47:411-413. Mincham W, Thurgte SM, Lewis AJ (1981). Measurement of dimensional stability ofelastomeric impression materials by holographic interferometry. Aust Dent J 26:395-399. Norme Internationale ISO 4823 (1984). Produits dentaires-produits pour empreintes ~ base d'elastomers. G~n~ve: Premiere Edition, 6. Ohsawa M, J~rgensen KD (1983). Curing contraction of addition-type silicone impression materials. ScandJDentRes 91:51-54. Rees JS, Jacobsen H (1989). The polymerization shrinkage of composite resins. Dent Mater 5:41-44. Szabo ZG (1969). Kinetic characterization ofcomplexreaction systems. In: Banford CH, editor. Comprehensivechemical kinetics. Amsterdam: Elsevier Publishing Company, 1-79. Williams PT, Jackson DG, Bergman W (1984). An evaluation ofthe time-dependent dimensional stability of eleven elastomeric impression materials. JProsthet Dent 52:120-125.
Dental Materials~March 1992 109
Dimensional stability of silicone-based impression materials V. Fano 1, P.U. Gennari 2, I. Ortalli 1 lIstituto di Scienze Fisiche, 2Clinica Odontoiatrica, delI'Universita', Parma, Italy
Abstract. This study attempts to demonstrate that the polymerization reaction is not the only factor that affects the shrinkage of silicone-based impression materials because evaporation of the constituentsalso contributesto the shrinkage.These factors can be evaluated by the study of time-dependent dimensional changes. This is shown both by chemical kinetics and by experimental testing of condensation and addition polymerizing impression materials with different viscosities. Comparison of the different materials shows that the two contributions, polymerization shrinkage, and evaporation shrinkage, can be assessedseparately by analysisof the time-dependentshrinkage diagrams. The instability due to the polymerization reaction is complete after a few hours, but the contribution of the constituent evaporation, if present, can have a significant long-term role. Numerous investigations of the dimensional variations of impression materials have been published in the dental literature. These studies have used a variety of direct and indirect methods of measuring shrinkage. Examples of shrinkage in silicone-based materials were reported by Burdarion (1984). Williams et al. (1984) analyzed the dimensional stability of some elastomers by measuring the gap width of a master coping seated on the dies produced from different impressions materials. Ohsawa and Jcrgensen (1983) measured the curing contraction ofaddition-type silicone impression materials with a mercury bath apparatus. They found the maximum contraction to be more than 0.08% at 15 min after mixing and more than 0.03% during storage from 15 min to 24 h. Clancy et al. (1983) studied the longterm dimensional stability. The ADA Specification No. 19 test block and mold (American Dental Association, 1977) were used. The impressions were measured using a travelingstage reflectingmicroscope and an image -analyzing computer. In this study, a silicone impression material showed significant change (0.14 mm) at 4 h and 0.2 mm after 4 wk. Marcinak and Draughn (1982) measured the linear dimensional change occurring as a function oftime between making the impression and pouring the die. The measured dies were compared to a master model and the linear change in the impression material was determined. Mincham et al. (1981) used holographic interferometry to determine the rate of dimensional change on setting. Lacy et al. (1981) used a technique of measuring stone dies poured sequentially from impressions of simulated preparations in a dental arch configuration. The measurements were made by micrometer. These studies were descriptive and did not give unequivocal conclusions about the origin of the dimensional variation and its time-dependence. Shrinkage was explained as due to the polymerization reaction, a phenomena that is seen in other
dental polymeric materials (Rees and Jacobsen, 1989). However, for dental impression materials, dimensional change can be influenced by other effects that relate to the differences in composition. In fact, the dimensional stability ofimpression materials as a function of time can be affected by several factors: completion of chemical reaction, constituent evaporation, relaxation of stresses due to either a particular shape or type of handling, water imbibition (when the material is not water-repellent; silicones are water-repellent), and temperature variation between body temperature and room temperature. In this work, an attempt has been made to analyze the curves of the linear dimensional change for some siliconebased impression materials. For this purpose, it is worthwhile to consider the intrinsic factors (completion of the polymerization reaction and constituent evaporation) and separate them from the other factors. The influence of the relaxation and water imbibition has been excluded, since simple geometric shapes (parallelepiped) of water-repellent substances were analyzed. Also, these samples were prepared at room temperature (20°C) to avoid the influence of the temperature changes that occur between body temperature and room temperature. Thus, the aim of this work is the following: (a) to demonstrate that, in addition to the polymerization reaction, the dimensional stability is also affected by evaporation of a volatile component; and (b) to find a graphic method for separating the polymerization contribution from the evaporation contribution. For this purpose, we will discuss the possible analytical expressions of the linear dimensional variation due to both polymerization shrinkage and evaporation. Residual Polymerization Reaction. Immediately after making the impression, the polymerization reaction cannot be consideredcompleted. Consequently, the shrinkage behavior as a function of time is dependent upon the kinetics of the polymerization reaction. If the kinetics are not expressed by a linear function, the time-dependent dimensional change cannot be linear. Now we shall examine the kinetics of two very common dental material polymerization reactions as examples of kinetics characterization of these complex reaction systems: (a) polymerization reactions induced by an initiator. In this case, the polymerization process can be represented by the following three principal reactions: I--> R*
(1)
R* + M --> R'*
(2)
2R'* -~ P
(3)
Dental Materials~March 1992 105
We assume that the initiator, I, decomposes and forms an active radical, R* (Eq. 1), which reacts with monomer molecules, M, and immediatelyforms a free radical,R'*(Eq. 2). The termination step is a reaction between two radicals (Eq. 3). The reaction rate of all radicals (regardless of how many monomer units have become incorporated) are hypothesized as being the same. Now we can write the following kinetic reactions: the rate of the initiator reactions = k I [/]
(4)
the reaction rate of the chain growth = k 2 [R'*] [M] (5) the reaction rate of the termination step -- k 3 [R'*] 2 (6) where k,, k 2 and k3 are reaction constants. Under steady-state conditions, it is assumed k 3 [/], k 1[I]. In this case, the R'* concentration is constant; consequently, eqs. 4 and 6 are equal: k 1 [/]
=
k 3 [R'*] 2
(7)
The concentration of free radicals in a steady-state condition can be calculated from Eq. 7: /kl[/]/1/2 (8)
The time-dependent dimensional stability induced by the kinetics of the polymerization reaction, i.e., by rate of [M] decrease, is proportional to the reaction rate of the chain growth (Eq. 5). This evaluation can be made by substituting [R'*], obtained from Eq. 8, in Eq. 5: d[M] _ k 2 dt ~-3)
[I]t/2[M ]
(9)
This equation is not linear. Accordingly, the dimensional change cannot be linear. (b) in the case of competitive-consecutive polymerization reactions typical of the addition polymerization, the following reaction scheme can be established: k 1
R; + R1
R; k2
(10) (11)
k3
(12)
R1
kn n+l
(13)
For these reactions, the following equation set (Szabo, 1969) can be determined:
dR: -- kn_l[R; dt
][R~l]
-
kn[R 1 ] [ R ; ]
106 Fano et aL/Dimensional stability of some impression materials
(14)
This equation type is not linear• Thus, the dimensional change cannot be linear. The same can be demonstrated for all polymerization reactions. The mathematical resolution of equations like Eqs. 9 and 14 was reported (Benson, 1960) as a fractional function (polymerization by initiator) or an exponential function (polymerization by addition). In other words, the linear shrinkage decreases proportionally to a fractional or exponential function, reachinglow values in a comparatively short time. Now we shall examine how to determine the evaporation contribution. The Constituent Evaporation. The followingcomponents are involved in this process: (1) plasticizers--for example, natural inner oils or cycloalkanes, materials that mainly decrease viscosity (with concentrations generally higher in the lowestviscosity materials); (2) liquid catalysts, such as dibutyltin dilaurate; (3) low-molecular-weight starting polymers; and (4) by-products of the condensation polymerization reaction (generally water or alcohol). Large production of by-products is generally reduced when partially polymerized starting materials are used• In all cases, the shrinkage induced by the production and elimination of volatile by-products ceases when the polymerization reaction finishes or immediately thereafter. Thus, the most significant evaporation involves plasticizers and low-molecular-weight polymers. Now we shall examine the possibility of assessing the evaporation and the polymerization contributions separately, if both are present. For this, we shall consider the following: for a sample with fixed stoichiometric composition, the rate of the polymeric reaction is not dependent upon the sample volume and shape, while the rate of evaporation, on the other hand, is strongly dependent on these factors. In other words, the polymerization reaction is always completed within a certain time, regardless of the sample quantity and shape, but the evaporation process can be changed by varying the sample dimensions and shape. The higher the surface to volume ratio (s/v), the sooner the evaporation stops. A quantity of material in film form eliminates volatile substances faster than when it is in bulk form. On the contrary, if large samples having small s/v ratio values are examined (as in this study), the evaporation rate is slow and can be considered constant throughout the experiment. Thus, the dimensional change induced by the evaporation is linear.
MATERIALSAND METHODS Some condensation polymerizing and addition polymerizing silicone-based impression materials were analyzed. Table 1 presents the examined materials• These materials, having different viscosities, were prepared using the same mixing times (2 min, 30 s), after which the materials were put into a 6.5 x 2.5 x 2-cm parallelepiped-shaped mold (Fig. 1A) and kept there for 2 min, 30 s. The bottom of the mold consisted of a die with two parallel straight lines, 49.95 mm apart; oeach. line • . was 5 ~m in width and had constant angles of 60 ; Fig. 1B shows the lines on the die. These lines were recorded by the impression materials. The percent linear shrinkage was calculated by measuring the distance between the two straight lines as a function of time• The calculation was made using the formula: /~2/2) Percent shrinkage = 100 (15)
TABLE 1: MATERIALS
Provil
Polymerization addition
Viscosity very high
Curve Fig. 3a
Manufacturer Bayer, Leverkusen, Germany
Provil Sam
addition addition
high high
Fig. 3b Fig. 3c
Bayer Duebi, Carpi, Italy
7858R, 7864R
Optosil Xantopren
condensation condensation
very high low
Fig. 4a Fig. 4b
Bayer Bayer
0013D 6218E
Polasil Polasil
condensation condensation
very high low
Fig. 4c Fig. 2d
Duebi Duebi
8806 8911
Materials
where 11 is the length measured immediately after the extraction from the mold, and 12is the length measured after a given time. To measure this distance between the two impressed parallel straight lines, the samples were located on a slide, which was moved under the stereomicroscope. The slide surface was mirror-like to eliminate probable friction at the sample-slide interface when the sample shrinks. In fact, the comparison among the dimensional change of samples kept on the slide for 24 h, samples dusted with talcum powder, and samples kept for 24 h on mercury did not show any significant differences. Thus, it was not necessary to use the mercury bath apparatus that is frequently used in shrinkage measurements (Lee et al., 1969; Hegdahl and Gjerdet, 1977; Ohsawa and J~rgensen, 1983). An electronic gauge, attached to the slide, (accuracy: 1 pm) was used to measure between the two impressed straight lines.The measurement error was 0.002% (1 ~m/50 mm), significantly lower than that reported in international specifications ISO-4823 (0.04%) (Norme Internationale ISO, 1984) and ADA No. 19 (0.02%) (American Dental Association, 1977). In order to calculate the polymerization contribution
/
B
Batch 6555C, 6518C 8903
separately from the evaporation contribution, the latter value was subtracted from the dimensional change. For this purpose, the graphs as a sum of two functions are considered. In order to know the evaporation contribution at any time during the experiment, a line must be drawn parallel to the (long-term) rectilinear part of the curve and passing through the zero point of the coordinates. At the zero time, the evaporation contribution can be approximated to zero, if the evaporation during the mixing time and during the setting in the mold time is neglected. RESULTS
In Figs. 2 and 3, the different silicone impression materials are compared. Three samples of each material were tested. The curves are repetitive. The experimental errors (0.002%) are too small for the graphic representation in the Figs. The zero time of the curves corresponds to the sample extraction from the mold. The dimensional change is always more rapid at the beginning: during the first 5 h, there is nearly 50% of the decrease for day one. Subsequently, the sample lengths decrease linearly or, in the case of high-viscosity materials, become nearly constant. Owing to the fact that, at the beginning, the dimensional decrease is not linear, the experimental points were checked more frequently for the best curve-fitting (one point every 5-10 min). Otherwise, each experimental point on the rectilinear part of each curve was checked after 1 h or more. Comparing the high-viscosity material obtained by addition reaction to that obtained by condensation reaction, the difference is negligible (compare Fig. 2, curve a, and Fig. 3, curve a). After 5 h, the dimensional change is -0.05% in both cases; after 24 h, the dimensional change is -0.075% for the addition polymers and -0.09% for condensation polymers (the ratio of these two values is 0.83). But when materials from the same manufacturer with different viscosities were compared, the shrinkage difference was significant (the ratio of the dimensional change between materials was much lower than 0.83; see Table 2). In other words, the components involved in the viscosity decrease make a large contribution to the shrinkage. DISCUSSION
Fig. 1. A diagram of the mold (part A) and the die (part B) used to prepare the samples.
The role of evaporation, if present, can be assessed by the analysis of the experimental curves, taking into account that, in our experimental conditions, the shrinkage due to polymerization finishes long before the shrinkage due to evaporation, because of the sample's configuration. On the other hand, the time-dependent shrinkage due to polymerization is closely related to the kinetics of the chemical reaction expressed by Eqs. 9 and 14. Accordingly, the time-dependence of the polymerization shrinkage cannot be linear. Conversely, Dental Materials~March 1992 107
~ -0.08~------------~ C
b
1
0
t
I
I
I
5
I
i0
15
20
25
HOURS
Fig. 2. Shrinkage as a function of time for addition reaction silicone impression materials, comparison of different viscosities: a - very high viscosity (Provil), b - high viscosity (Provil), and c- high viscosity (Sam).
•
-0.08
-o.24
b
< Z
~o.4o ¢,q '
0
5
I0
,
,
15
t
i
20
i
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Fig. 3. Shrinkage as a function of time for condensation reaction silicone impression materials, comparison of different viscosities: a - very high viscosity (Optosil), b - low viscosity (Xantopren), c - very high viscosity (Polasil), and d - low viscosity (Polasil).
when the shrinkage is a linear function of time, i.e., it is expressed by a straight line, this must be ascribed to the evaporation; in this case, no polymerization contribution can be involved. With this fact in mind, all curves of Figs. 2 and 3 can be divided into two parts. The first part (starting from zero time) decreases in a non-linear way and can be approximated to the solution ofEq. 9 (condensation reaction) or Eq. 14 (addition reaction), when the evaporation component has been subtracted. After that, the curves (the second part) take on a behavior following the equation: % length = At + B
(16)
where B is the intercept of the straight-line extension at the % length axis. The characteristic of the second part depends upon the A coefficient of the linear parts of the curves. Numerically, A = Al/At, where A/is the decrease in % length in the At time interval. The larger the A, the larger the h/, due to a larger quantity of evaporated material. The a and b curves of Fig. 2 are materials made by the same manufacturer and having different viscosities: curve a, very high-
viscosity material; curve b, high-viscosity material. According to our hypothesis, the A coefficientof the b curve, Ab, must be larger than the A coefficientof the a curve, Aa. In fact, after 5 h , A b = 0.004% h 1 a n d A a = 0.0016% h -1. Thus, the correlation of the straight-line behavior with the evaporation process is confirmed. If we now compare the b and c curves (both curves are ascribed to high-viscosity materials), their behavior is quite different. In fact, the contribution of the non-linear part of the c curve to shrinkage is much larger than that of the b curve, but the b curve material modifies its dimensions chiefly by evaporation, Aa > Ab. Consequently, during the first 2 to 3 h, the b material changes slightly in dimensions when compared with the c material and can be recommended for use when times of under 20 h are necessary. Otherwise, the c material is better. Finally, the condensation polymers are believed to have a higher shrinkage (compared with addition polymers) because of the generation of volatile by-products during the polymerization reaction. As stated in the "Results" section, this difference in behavior can be negligible. On the other hand, it can also be large, for materials obtained by the same polymerization method but having different degrees of viscosity (see the curves of Fig. 2). In other words, the presumed superior precision of the addition polymers must be qualified, because the influence of a long-duration evaporation process can affect the dimensional change in a more significant way than the elimination of the condensation byproduct. Evaluation of the Evaporation Contribution by Graph. Numerically, the evaporation contribution can be evaluated separately from that of polymerization by graph. For this purpose, it is necessary to determine the point of the curve when the polymerization reaction is considered complete. For this, the extension of the rectilinear part of the curve toward zero time must be drawn (see, for example, the d curve of Fig. 3). The A point gives information about the following: (1) the time necessary for completion of the polymerization reaction (7 h); (2) the dimensional change induced by the polymerization reaction (-2.05%, see below); and (3) the dimensional change induced only by evaporation at any time during the experiment (0.275% after 24 h). The last two characteristics are obtained by the drawing a line parallel to the rectilinear part of the d curve, passing through the origin of the coordinates (see the straight line, e, of which only a part has been drawn to simplify the graph). The point B, corresponding to 0.08%, is the contribution due to only evaporation after 7 h. Consequently, the contribution due to polymerization after 7 h is A- B = -0.285% - (-0.08%) = -0.205%. The dimensional change induced by evaporation after 24 h is -0.48% - (-0.205%) = -0.275%. This research has shown: (1) The experimental diagrams of the dimensional stability can be considered as a sum of two contributions: one due to polymerization, the other due to evaporation. The different possibilities in magnitude of the two phenomena explain the great differences in behavior of
2" RATIOOF DIMENSIONALCHANGEBETWEENMATERIALSOF THE SAME MANUFACTURERWITH DIFFERENTDEGREESOF VISCOSITY Material Pairs Polymerization Mechanism Ratio of DimensionalChanges High-viscosity Provil/Iow-viscosityProvil Addition 0.31 Very high-viscosityOptosil/Iow-viscosityXantopren Condensation 0.44 Very high-viscosityPolasil/Iow-viscosityPolasil Condensation 0.66 TABLE
108 Fano et al./Dimensional stability of some impression materials
the materials in practice. (2) The contributions of residual polymerization reaction and constituent evaporation to dimensional stability can be evaluated separately if the dimension change as a function of time is known. (3) The experimental diagrams show that the rate of the dimensional variation, which is maximum at the beginning, decreases rapidly and approaches zero value or becomes constant in a short time (few hours). This is in accordance with the kinetics of the polymerization reactions. (4) The constituent evaporation can play a significant role, depending upon the degree of the viscosity and the bulk dimensions rather than upon the synthesis method. Received August 2, 1990/Accepted September 8, 1991 Address correspondence and reprint requests to: V. Fano Istituto di Scienze Fisiche del|'Universita', Via D'Azeglio, 85 43100 Parma, Italy
REFERENCES American Dental Association (1977). Revised specificationNo. 19 for non-aqueous, elastomeric dental impression materials. JAm Dent Assoc 94:733-741. Benson SW (1960). The foundations ofchemical kinetics. New York: McGraw-Hill, 605. Burdarion G (1984). Biomateriali dentari. Milano, Italy: Masson Italia, 167. Clancy JM, Scandrett FR, Ettinger RL (1983). Long-term dimensional stability of the three current elastomers.
J Oral Rehabil 10:325-333. Hegdahl T, Gjerdet NR (1977). Contraction stresses on composite resin filling materials. Acta Odontol Scand 35:191-195. Lacy AM, Bellmann T. Fukui H, Jendresen MD (1981). Timedependent accuracy of elastomer impression materials. Part I: Condensation silicones. J Prosthet Dent 45:209215. Lee HL, Swartz ML, Smith FF (1969). Physical properties of four thermosetting dental restorative resins. JDent Res 48:526-535. Marcinak CF, Draughn RA(1982). Linear dimensionalchanges in addition curing silicone impression materials. JProsthet Dent 47:411-413. Mincham W, Thurgte SM, Lewis AJ (1981). Measurement of dimensional stability ofelastomeric impression materials by holographic interferometry. Aust Dent J 26:395-399. Norme Internationale ISO 4823 (1984). Produits dentaires-produits pour empreintes ~ base d'elastomers. G~n~ve: Premiere Edition, 6. Ohsawa M, J~rgensen KD (1983). Curing contraction of addition-type silicone impression materials. ScandJDentRes 91:51-54. Rees JS, Jacobsen H (1989). The polymerization shrinkage of composite resins. Dent Mater 5:41-44. Szabo ZG (1969). Kinetic characterization ofcomplexreaction systems. In: Banford CH, editor. Comprehensivechemical kinetics. Amsterdam: Elsevier Publishing Company, 1-79. Williams PT, Jackson DG, Bergman W (1984). An evaluation ofthe time-dependent dimensional stability of eleven elastomeric impression materials. JProsthet Dent 52:120-125.
Dental Materials~March 1992 109
