So anyone know what amalgam is? It isn’t that way to get that right. One of the components is and you can see why we don’t have so much of this technology any more, mercury. But there was a time when this was the dominant one and probably if you’ve got grandparents or great grandparents, you may even have a scenario where they had silver or gold as their filling, right? So not very cost effective, but it made for a good filling, mostly because it was malleable and inert. So it’s liquid at room temperature, reacts with silver and tin and essentially forms a plastic mass [at times]. So in essence it was the precursor to the bone cement concept, right? You could have something that was workable, shapeable like a dough and then you could plug it in and it would set. So in a matter of moments, you actually had a hard material that was capable of supporting load.
Nickel titanium, which also we call nitinol. So that’s a 50:50 alloy. Gold, again not so common anymore. Probably the acrylic resins at this point dominate. So those are based on polymethyl methacrylate type resin chemistry, very much like bone cement, sets up very, very quickly. Dental works a little bit different from the orthopedics and not — Dr. Reese made a comment about bone cement, I think I made a comment about the bone cements, Dr. Andy Combs made a comment about bone cement, it’s a two-part system, you’ve got pre-polymerized powder and then bring it in except that it’s a chemical hazard to get the monomer in here. You’ve got a monomer that starts that process, you’ve got a liquid vial and then you’ve got a little packet of pre-polymerized powder, put the two together in a bowl, mix it up and you essentially start to dough a mass. So it starts as something that’s almost fully liquid like pancake batter and then ends up something like plateau. And so in a matter of 3 to 5 minutes you move from a liquid to something that feels like plateau. And as it goes through its polymerization process you’ve got a very high temperature increase, so up to 100 degrees or 150 or so degrees Fahrenheit. So it gets so hot you can’t even hold it in your hand any more. So that part of the experiment is great to show the class, it’s the monomer part. So I used to bring it and do in class and I think truly it’s an environmental hazard. So we won’t do that.
Just take my word on it but that same concept really was important but have any of you had filling work in the last few years of any sort? Did you experience that technology? Probably not. So more likely what they did is that they took the same resin chemistry, but they used a UV curable polymer. So more likely they just set something up in your mouth and then a lot of times, they just do UV exposure and this thing sets up in a matter of moments. But they also have quick setting, but yeah, most of us, right, we have our jaws probe tube and probably aren’t seeing anything. But the chemistry is very, very similar to what we’ve seen in orthopedics and the scent is very similar. So if you recall that odor, you can imagine working in the OR, where you’re going to have 12 to 15 packets of bone cement go by. So environmental issues are an issue which probably explains some of the spacesuit technology. You were in surgery recently? Yeah. So they were in full mask, not just for blood contamination, but there’s a lot of — anytime there’s bone cement you have to look at the outgassing of that monomer. So it’s a real environmental concern. It’s really bad. Yeah, you probably weren’t suited up with that protective gear, yeah.
So if you go and watch a surgery, just be prepared for the other side of that. Actually if any of the nurses are expected, I believe they have to leave the room, it’s that bad. Yeah, so it’s a – there are some downsides of medical technology.
Okay. Thermal expansion coefficients, so like I said, it’s the only place in the class where there is an opportunity to talk about thermal stresses because we really don’t have to deal with that anywhere else. Just a simple analysis, here’s our thermal expansion coefficient alpha, which is the length change delta L, normalized by the initial length for a given temperature. So what that means it is we’re looking at a structure for simplicity sake, which is L0, we subject it to a delta T and then moving through that delta T, we get a coefficient of thermal expansion. So there are only a few scenarios where we have materials that give us a negative thermal expansion. So for the most part we apply delta T, that temperature increase, we move from L to a deformed or expanded length L and so it’s alpha is our change now. So this essentially is this differential here, so it’s the total length change delta L normalized by the initial length L0, multiply that by delta T. And the strain that we get as a result of that – and again we’re assuming isotropy. So isotropy is assumed, the way to get around that would be to do this directionally, right? So just take different orientations and then you could get thermal expansion efficient in a longitudinal axial or circumferential direction.
So the strain is just that thermal expansion coefficient times the delta T. And we look at the biometric thermal expansion coefficient we’ve got the biometric strain, which is three times alpha. So again just alpha coming back to give us deltal L over L0 times delta T. So just a very simple expression.
And I gave you on this worksheet that you downloaded, what happens as a result of thermal expansion coefficient? So it’s a really simple problem. It’s not to show dissimilar the schematic that we have here. Not so dissimilar from what we had when we talked about transferring stresses or looking at composite type behavior. So we’ve got an internal structure, which is in gray. That’s our filling and we’ve essentially reamed out a hole in the tooth structure. So we’re going to assume that we reamed out a nice cylindrical hole. So again you’d have to account for what the geometry is of the hole itself and so we considered here a 2 mm diameter hole, which is 4 mm in length in a molar tooth. So we’ve got a hole that we’ve created, that’s got 2 mm diameter and it’s sitting in a tooth structure. So here is our tooth but we’re just going to schematically say well, it’s got a boundary and we’re going to be [interested]. So we’ve got a diameter of 2 mm and we’ve got a length of that hole which is 4 mm.
And then we look at what’s going to happen to the coefficient of thermal expansion? So in other words, what’s going to happen if we think about this rigid boundary of the tooth acting on this material? So we’ve got a void space and then we’re going to fill that void space with a material. And then we’re going to subject it to a temperature fluctuation, delta T. And then the question is what’s going to happen to that structure? Well, there’s going to be a thermal expansion of that material as it’s heated and then we have to look at thermal expansion mismatch between the enamel itself and the amalgam or resin. So we’re going to just treat this as enamel, and this is going to be our amalgam or resin. And we just look at the difference between the two.
So this basic problem looks at what happens with the delta T at 53 degree C? So we’ve got a delta T of 50 degree C and then we’ve got different thermal expansion coefficients. So we’ve got the thermal expansion coefficient of the amalgam, so there is our mercury alloy of 25 times 10 to the minus 6, again this is millimeters per millimeter. So it’s a length change per original length per degree C. So it’s unit less per degree C or strain units per degree C or strain units per degree C, alpha of enamel. So again a very small thermal expansion coefficient, which probably makes a lot of sense if we think about what thermal expansion coefficient means. So enamel will be a highly ceramic structure. So we’ve got very little exchange of strain as a function of temperature, so only 8.3. And then you look at the polymer, so again we think back to what polymers were, they were these open structured chain materials that are isotropic for the most part, but they’re also randomly organized in space. So there is lot of room for expansion.
And so even though these are somewhat rigid polymers, you’ve got a coefficient of thermal expansion here for a typical acrylic resin on the order of 81 times 10 to the minus 6. So 81 versus 25 versus 8.3. And then you look at – okay, well what’s the elastic modulus of these materials? So the elastic modulus of that alloy, so again steel versus a polymer, the amalgam is 20 gigapascals for elastic modulus. The resin is two and a half gigapascals, so again a much smaller elastic modulus, it’s a polymer. And then we go back to our expression for what’s the change in volume. So again the volumetric strain took the form of three alpha times delta T, right?
So the volumetric strain took a form of three, so we look at delta V, so that was our volumetric strain, when we look at delta V we’ve got whatever the initial volume is and then we’re multiplying that times – three times alpha times delta T. So we’ve got change in volume is the initial volume times three times thermal expansion coefficient and it’s assuming isotropy times delta T. And then you plug this in, and say, well, what’s going to be the change in volume if we use the mercury-based amalgam? So again just geometry, what’s the cross-sectional areas? We’ve got pi times the radius squared. So pi times one millimeter squared times the length, so we’ve got 4 mm of length, then we’ve got three times that difference now in thermal expansion coefficient. So we’ve got 25, which came from the amalgam, and then we subtract away 8.3, so we subtract away the thermal expansion from the enamel, that was to — 10 to the minus 6 power times the temperature flux 50 degree C. And so you get a volume change of 0.03 mm cube.
If you do the same thing for the resin, so again the same geometry would be pi times one millimeter squared, piR squared times the length 4 mm times three, and then the difference would be instead of having 25 minus 8.3, I’d have 81 minus 8.3, same temperature. And so now the volume change is 0.14 mm cube, so relatively large volume change. If I look at just a one-dimensional force span, you’ve got the forces of the elastic modulus times the strain times the area. So you’ve got the elastic modulus times delta T so that 50 degree C times the change that we have on the amalgam resin minus the enamel. So the difference between thermal expansion coefficient, whether it’s the amalgam or whether it’s the resin and subtract away from that the enamel and then you’ve got the perimeter of your pi DH, there’s your diameter, the height. And so you roll that out and you look at the forces and the amalgam force is 420 Newtons, the force in the resin is 228 Newtons. So the forces are relatively high.
But an interesting thing that I put here in gold is that although the resin expands, so if we look at just the delta V, you’ve got a fourfold increase in volumetric expansion. But the reduced stiffness actually results in a lower force. So again it goes back to — you can’t just look at – just when you look at back of the pockets or back of the envelope calculations, if all you had done (inaudible) to volumetric change, you would’ve said okay, just because of that thermal expansion coefficient of the polymer, the polymer does not look like the way to go because you’ve got a very high thermal expansion coefficient, if I run that into biometric changes you’ve got three times alpha, so there’s your roll right here, we’d have a fourfold increase in that volumetric expansion.
But if I convert that back to a force on the actual system because the modulus is so much stiffer for the polymer versus the metal, you end up equalized in terms of the actual forces. So your gut might have been to say, oh, four times the strain, I am going to expect to see a much greater contribution on stress or force. So just little plays on how some of these relationships work. So polymers because they have a lot of modulus make them very forgiving materials in lot of these applications. Question?
Question: Can you explain why you subtracted the alpha of enamel?
Lisa Pruitt: Because you’re looking at the differential of thermal expansion. So you’re looking at what’s the overall change. So you’re assuming at the boundary, the thermal expansion difference between how much – in other words, the thermal expansion is going to occur in the resin but it’s going to also have a temperature effect that’s going to be balanced by what’s going on in the enamel itself. So if you add delta T, you don’t just have the resin expanding, you also have contribution of what your dental tissue is doing as well. So you subtract that away. The same question, okay. Yeah, so we subtract out the counterpart, so we subtract that away because it’s also experiencing a thermal expansion effect.
So again that was very simplistic approach, just taking a simplistic strain, looking at how we can convert that to a simple force but it gives you perspective of just something we would design for differently in dental applications that we would never see in any of the other materials. So delta T issues are an issue.
So if we look at just some of the environmental effects, chewing forces, I think when you first think about dental applications, you don’t tend to think of the forces in the mouth being very high. And the forces in the jaw are extraordinarily high and if you look at [the bright] enamels, you can get extraordinarily high because it relies on their mechanism for prey and predatory effects. But just for a human a chewing force can be up to 900 Newtons. And so you’ve got a high cyclic loading capability. You can have large temperature differences. So we talked about 37 C being the sub-point and here in the mouth you’re looking at potentially a 50 degree C range. So you can run that through and not just singularly in one day but multiple times a day. So you just think about that effect of having something very, very cold, or something very, very hot and probably every one of you has done that, right, at some point, you’ve had something very cold and very hot or vice versa and you probably get a little tinge of nerve response when you did so. So there’s truly a thermal expansion that occurs and you can actually feel that right down to the innervated part of the tissue.
Large pH differences, so again enormous bodies of literature on the role of pH and the role of different types of a composition of saliva in various foods and how that plays a role of pH in the mouth. And it sounds silly, but it makes an enormous difference, large variety of chemical compositions from food, so I am sipping on my — we all have — some of us have coffee, some of us are chewing gum, we’re all loading our teeth in one way or another. So lots of issues.
Going back to what I started with, you’ve got a number of parameters to think about, you’ve got cyclic loads. So we have to think about fatigue resistance, when designing for these TMJ designs there’s a number of issues. There is overall fracture. So you’ve got a post-scenario, so you wouldn’t want to have fracture of the device. You’ve got again a bearing combination. So you’ve got metal on polymer, so we need to be thinking about wear assistance. You’ve got metal that’s now going to live in the presence of saliva, low pH, so you’ve got moisture, temperature and pH issues. So, you’ve got a big-time corrosion problems. And if we thought we had a corrosion design issue when we got to the Morse taper, you stick something in the mouth and talk about having crevice corrosion issues, you’ve got some design standards to worry about.