Dynamic Mechanical Analysis part 8 potx

©1999 CRC Press LLC FIGURE 6.3 Effects of staging on the curing of resins. Staging is done to improve handling properties during lay-up but also changes the cure profile. ©1999 CRC Press LLC Another special area of concern is paints and coatings, 9 where the material is used in a thin layer. This can be addressed experimentally by either employing a braid as above or coating the material on a thin sheet of metal. The metal is often run first and its scan subtracted from the coated sheet’s scan to leave only the scan of the coating. This is also done with thin films and adhesive coatings. A sample cure profile for a commercial two-part epoxy resin is shown in Figure 6.6. From this scan, we can determine the minimum viscosity ( h * min ), the time to h * min and the length of time it stays there, the onset of cure, the point of gelation where the material changes from a viscous liquid to a viscoelastic solid, and the beginning of vitrification. The minimum viscosity is seen in the complex viscosity curve and is where the resin viscosity is the lowest. A given resin’s minimum viscosity is determined by the resin’s chemistry, the previous heat history of the resin, the rate at which the temperature is increased, and the amount of stress or stain applied. Increasing the rate of the temperature ramp is known to decrease the h * min , the time to h * min , and the gel time. The resin gets softer faster, but also cures faster. The degree of flow limits the type of mold design and when as well as how much pressure can be applied to the sample. The time spent at the minimum viscosity plateau is the result of a competitive relationship between the material’s softening or melting as it heats and its rate of curing. At some point, the material begins curing faster than it softens, and that is where we see the viscosity start to increase. As the viscosity begins to climb, we see an inversion of the E ≤ and E ¢ values as the material becomes more solid-like. This crossover point also corresponds to where the tan d equals 1 (since E ¢ = E ≤ at the crossover). This is taken to be the gel point, 10 where the cross-links have progressed to forming an “infinitely” long net- FIGURE 6.4 Relationship of T g to cure time and the stages of a cure. Note that for thermosets, it is often difficult to impossible to see the T g by DSC in the latter half of region 3. ©1999 CRC Press LLC (a) (b) FIGURE 6.5 T g and E¢¢ ¢¢ for post-cure times. (a) Data collected by DMA on chip encapsu- lation material plotted as time of post cure vs. measured values listed in the table. T g was measured as the peak of the tan d , the onset of tan d , and the onset of the drop in E ¢ . Storage modulus was measured at 50 ∞ C and is reported as e 9 Pa. (b) The measurement of T g by tan d peak values for the data in (a) is shown. All the T g ’s except the 0 hour of post-cure T g were undetectable by DSC. ©1999 CRC Press LLC this again in Chapter 7.) At the gel point, the frequency dependence disappears 14 (see Figure 6.7). My own experience is that this value is only a few degrees different from the one obtained in a normal scan and not worth the additional time. During this rapid climb of viscosity in the cure, the slope for h * increase can be used to calculate an estimated E act (activation energy). 15 We will discuss this below, but the fact that the slope of the curve here is a function of E act is important. Above the gel temperature, some workers estimate the molecular weight, M c , between cross-links as (6.1) where R is the gas constant, T is the temperature in Kelvin, and r is the density. At some point the curve begins to level off, and this is often taken as the vitrification point, T vf . The vitrification point is where the cure rate slows because the material has become so viscous that the bulk reaction has stopped. At this point, the rate of cure slows significantly. The apparent T vf , however, is not always real: any analyzer in the world has an upper force limit. When that force limit is reached, the “topping out” of the analyzer can pass as the T vf . Use of a combined technique such as DMA–DEA 16 to see the higher viscosities, or removing a sample from parallel plate and sectioning it into a flexure beam, is often necessary to see the true vitrification point (Figure 6.8). A reaction can also completely cure without vitrifying and will level off the same way. One should be aware that reaching vitrification or complete cure too quickly could be as bad as too slowly. Often a overly aggressive cure cycle will result in a weaker material, as it does not allow for as much network develop- ment, but gives a series of hard (highly cross-linked) areas among softer (lightly cross-linked) areas. On the way to vitrification, I have marked a line at 10 6 Pa. s. This is the viscosity of bitumen 17 and is often used as a rule of thumb for where a material is stiff enough to support its own weight. This is a rather arbitrary point, but is chosen to allow the removal of materials from a mold, and the cure is then continued as a post-cure step. As an example, Table 6.1 gives the viscosities of common materials. As we shall see below, the post-cure is often a vital part of the curing process. The cure profile is both a good predictor of performance as well as a sensitive probe of processing conditions. We will discuss the former case under Section 6.4 below and the latter as part of Section 6.7. A final note on cure profiles is that a volume change occurs during the cure. 18 This shrinkage of the resin is important and can be studied by monitoring the probe position of some DMAs as well as by TMA and dilatometry. 6.3 PHOTO-CURING A photo-cure in the DMA is run by applying a UV light source to a sample that is held at a specific temperature or subjected to a specific thermal cycle. 19 Photo-curing is done for dental resin, contact adhesives, and contact lenses. UV exposure studies are also run on cured and thermoplastic samples by the same techniques as photo- GRTM¢= r c GRTM¢= r c ©1999 CRC Press LLC (a) (b) FIGURE 6.9 Photo-cure of a UV curing adhesive in the DMA. Note the similarity to the materials in Figure 6.1a and b. ©1999 CRC Press LLC FIGURE 6.10 Multistep cure cycles: A multiple step cure cycle with two ramps and two isothermal holds is used to model processing conditions. Run on an RDA 2 by the author. ©1999 CRC Press LLC collected. It is also how rubber samples are cross-linked, how initiated reactions are run, and how bulk polymerizations are performed. Industrially, continuous processes, as opposed to batch, require an isothermal approach. Figure 6.11 shows the isother- mal cure of a rubber (a) and three isothermal polymerizations (b) that were used for a kinetic study. UV light and other forms of nonthermal initiation also use isothermal studies for examining the cure at a constant temperature. 6.6 KINETICS BY DMA Several approaches have been developed to studying the chemorheology of thermo- setting systems. MacKay and Halley (Table 6.2) recently reviewed chemorheology and the more common kinetic models. 22 A fundamental method is the Williams–Lan- del–Ferry (WLF) model, 23 which looks at the variation of T g with degree of cure. This has been used and modified extensively. 24 A common empirical model for curing has been proposed by Roller. 25 This method will be discussed in depth, as well as some of the variations on it. Samples of the thermoset are run isothermally as described above, and the viscosity versus time data are plotted as shown in Figure 6.11b. This is replotted in Figure 6.12 as log h * vs. time in seconds, where a change in slope is apparent in the curve. This break in the data indicates the sample is approaching the gel time. From these curves, we can determine the initial viscosity, h o and the apparent kinetic factor, k. By plotting the log viscosity vs. time for each isothermal run, we get the slope, k, and the viscosity at t = 0. The initial viscosity and k can be expressed as (6.2) (6.3) Combining these allows us to set up the equation for viscosity under isothermal conditions as (6.4) By replacing the last term with an expression that treats temperature as a function of time, we can write (6.5) This equation can be used to describe viscosity–time profiles for any run where the temperature can be expressed as a function of time. Returning to the data plotted in Figure 6.12, we can determine the activation energies we need as follows. The plots of the natural log of the initial viscosity (determined above) vs. 1/ T and the natural hh h o = • e ERTD hh h o = • e ERTD kke ERT k o = • D kke ERT k o = • D ln ( ) lnhh h tERTtk e ERT k =+ + •• D D ln ( ) lnhh h tERTtk e ERT k =+ + •• D D ln ( , ) lnhh h Tt E RT ke dt ERT t k =+ + •• Ú D D 0 ln ( , ) lnhh h Tt E RT ke dt ERT t k =+ + •• Ú D D 0 ©1999 CRC Press LLC 6.7 MAPPING THERMOSET BEHAVIOR: THE GILLHAM–ENNS DIAGRAM Another approach to attempt to fully understand the behavior of a thermoset was developed by Gillham 30 and is analogous to the phase diagrams used by metallurgists. The time-temperature–transition diagram (TTT) or the Gilham–Enns diagram (after its creators) is used to track the effects of temperature and time on the physical state of a thermosetting material. Figure 6.14 shows an example. These can be done by running isothermal studies of a resin at various temperatures and recording the changes as a function of time. One has to choose values for the various regions, and Gillham has done an excellent job of detailing how one picks the T g , the glass, the gel, the rubbery, and the charring regions. 31 These diagrams are also generated from DSC data, 32 and several variants, 33 such as the continuous heating transformation and conversion-temperature-property diagrams, have been reported. Surprisingly easy to do, although a bit slow, they have not yet been accepted in industry despite their obvious utility. A recent review 34 will hopefully increase the use of this approach. FIGURE 6.14 The Gillham–Enns or TTT diagram. (From J. K. Gillham and J. B. Enns, Trends in Polymer Science, 2(12), 406–419, 1994. With permission from Elsevier Science.) ©1999 CRC Press LLC 6.8 QC APPROACHES TO THERMOSET CHARACTERIZATION Quality control (QC) is still one of the biggest applications of the DMA in industry. For thermosets, this normally involves two approaches to examining incoming mate- rials or checking product quality. First is the very simple approach of fingerprinting a resin. Figure 6.15 shows this for two adhesives; a simple heating run under standardized conditions allows one to compare the known good material with the questionable material. This can be done as simply as described or by measuring various quantities. A second approach is to run the cure cycle that the material will be processed under in production and check the key properties for acceptable values. Figure 6.16 shows three materials run under the same cycle. Note the differences in the minimum viscosity, in the length and shape of the minimum viscosity plateau, the region of increasing viscosity associated with curing, and both the time required to exceed 1 ¥ 10 6 Pa. s and to reach vitrification. These materials, sold for the same application, would require very different cure cycles to process. If we estimate the activation energy, E act , by taking the values of h* at various temperatures and plotting them versus 1/T, we get very different numbers. (This is a fast way of estimating the E act , where we will assume the viscosity obtained from the temperature ramp is close to the initial viscosity of the Roller method. This is not a very accurate assumption, but for materials cured under the same conditions, it works.) This indicates, as did the shape of the cures, different times are required to complete the cures. The differences in the minimum viscosity mean the material will have different flow characteristics and, for the same pressure cycle, give different thicknesses. As dif- ferent times are required to reach a viscosity equal to or exceeding 10 6 Pa. s, the materials will need to be held for different times before they are solid enough to FIGURE 6.15 QC comparisons. Fingerprinting of materials for QC is often done. Good and bad hot melt adhesives were scanned using a constant heating rate cure profile. ©1999 CRC Press LLC FIGURE 6.17 Results and analysis of a “gel” time test from a DMA run. Note the “gel time” here is really the time to vitrification, not gelation. . case under Section 6.4 below and the latter as part of Section 6.7. A final note on cure profiles is that a volume change occurs during the cure. 18 This shrinkage of the resin is important and. sectioning it into a flexure beam, is often necessary to see the true vitrification point (Figure 6 .8) . A reaction can also completely cure without vitrifying and will level off the same way. One. gives the viscosities of common materials. As we shall see below, the post-cure is often a vital part of the curing process. The cure profile is both a good predictor of performance as well as a