Pharma glass properties – Part 2. Thermal expansion

Hello everyone – this is Part 2 of an ongoing series about properties that are included on technical data sheets for pharmaceutical glass packaging.?Part 1 focused on density – you can check it out here.?I briefly mentioned the idea of thermal expansion while discussing the temperature dependence of density, and so let’s pick up there.

Juliet Capulet asked, “What’s in a name?”?This rhetorical question was meant to justify her forbidden love for a Montague.?Juliet believed that a name was just a meaningless label.?As it turns out, engineers were not heavily featured among Shakespeare’s dramatis personae.?Engineers are notoriously good at using descriptive names for things.??In the world of pharmaceutical glass packaging, two common family names are “33 expansion borosilicate” and “51 expansion borosilicate”.?The word “expansion” is actually shorthand for “average linear coefficient of thermal expansion”.?Let’s start by unpacking that terminology.

The coefficient of thermal expansion (CTE) is a measure of the rate at which the dimension of a material changes with temperature (see Footnote 1).?As we previously discussed in Part 1 of this series, most materials expand in size upon heating.?You’re probably associating the volume of an object with the word “size”.?This association is correct, although there’s a practical limitation to this approach.?Measuring the overall volume of an object as a function of temperature can be tricky in practice.?Fortunately, we can rely on an approximation for uniform (otherwise known as “isotropic”) materials like glass by measuring the thermal expansion along a single dimension.?The overall expansion in volume as a function of temperature for an isotropic material is about three times the expansion along a single, linear dimension.?This explains why it’s called a linear CTE.

The units of the linear CTE may look a little unusual at first glance, largely because of some unit cancellation.?The linear CTE is the change in length of an object (let’s say millimeters) per unit length of the object (also in millimeters) and per unit temperature change (degrees Celsius or Kelvin would be typical – see Footnote 2).?As a result, there is a unit of millimeters in the numerator and denominator – these length units can cancel each other out. ?The linear CTE is therefore a measure of some fractional change in dimension for every unit change in temperature.

Next we need to understand how the numerical component of the CTE value is expressed.?Imagine that you have a piece of window glass that is 1 meter wide and heat it by 1 K.?Assuming this a typical window glass, I would expect it’s width to increase by about 9 micrometers, which is equal to 9x10?? meters.?Remembering that the length units cancel out, this would imply that window glass has a linear CTE of about 9x10?? /K.?A “part per million” (abbreviated as ppm) is equal to 1x10?? of some quantity, meaning that the linear CTE of window glass could also be written as 9 ppm/K.?However, there is a historical precedence within the glass industry and technical literature to express the linear CTE on the basis of 10??/K, and so the linear CTE of window glass would instead commonly be written as 90x10??/K.

This was a long walk to explaining why “33 expansion borosilicate” and “51 expansion borosilicate” glasses have the names that they do.?We are casually dropping the factor of 10??/K and assuming that you understand the context.?A good technical data sheet for pharmaceutical glass should unambiguously tell you the basis for reporting the linear CTE value.?This is important – for example, a reported CTE value of just “5” straddles a line that matters in terms of commercially available glasses.?A CTE value of 5x10??/K is presumably referring to fused silica (see Footnote 3), while a value of 5 x10??/K (or 5 ppm/K) could be one of the flavors of Type I borosilicate glass.

The last piece of the puzzle is understanding why we specify an average linear CTE.?The linear thermal expansion curve for a glass might look something like the plot shown in Figure 1.? As expected, this plot is telling us that the length of this hypothetical specimen of glass increases with increasing temperature…to a point (see Footnotes 4 and 5). ?Notice how the segment between points A and B on the curve is not a perfectly straight line.?The extent of curvature depends on the specific type of glass.?One way to read this plot is by finding the instantaneous linear CTE – that is, the linear thermal expansion at a specific temperature.?However, the instantaneous CTE is often not that useful in practice.?Instead, we want to know what happens when changing over some range of temperatures.?This would be equivalent to fitting a slope over some temperature range of the thermal expansion plot.?Assuming that we’re focused on understanding the thermal expansion of solid glass, the upper temperature of this range would ideally not extend beyond approximately point B.?A typical convention is to calculate the average linear CTE over a temperature range of 20 to 300°C.

With that background out of the way, what can we do with this information on thermal expansion??I can think of multiple stages of the fill-finish process where a pharmaceutical glass vial can experience a significant change in temperature – for example, depyrogenation and cold storage.?Assume that a 2R vial made from 51 expansion borosilicate is at 20°C and then heated to 300°C.?For a nominal outer diameter (OD) of 16 mm, we would expect the OD of the heated vial to increase by just 15 μm – not all that much (see Footnote 6).?Let’s go the opposite direction for a drug product requiring cold storage at -80°C.?Starting at 20°C, we would expect the OD of the same vial to decrease by about 8 μm (see Footnote 7).?Once again, not a big apparent change, but now it’s important to recognize that we’re dealing with the full container-closure system.?The CTE of the elastomer stopper is appreciably higher than the glass vial, and it’s rigidity will significantly increase as we approach -80°C (see Footnote 8).?This is where things get interesting – two rigid bodies changing dimensions at different rates as a function of temperature leads to important questions about residual seal force, container-closure integrity (CCI), etc. Given a complete set of fundamental material property data (including but not limited to CTE) and detailed dimensional information, it’s possible to perform computational simulations to predict the compatibility of different packaging components under specific capping and storage conditions.? What I can say in general is that Type I glass vials can routinely be compatible with elastomeric stoppers to storage temperatures on the order of -80°C.? Cooling below that point will likely compromise CCI because the contraction rate of the stopper (now rigid because we’re below the glass transition temperature of the elastomeric material) outpaces the glass vial.

An understanding of thermal expansion can also provide insight into the mechanical reliability of glass.?Glass objects can break in response to rapid changes in temperature, a phenomenon known as “thermal shock”. ?The rapid temperature change causes the outer of the surface of the glass object to heat or cool more quickly than the interior.?This also means that the outer surface layer is expanding or contracting to a different extent, thereby creating stress within the glass object.?At a minimum, we can use our knowledge of CTE to predict that a 51 expansion borosilicate vial should be more susceptible to thermal shock than a 33 expansion borosilicate vial of identical geometry.?With some additional material property information (specifically the elastic modulus and Poisson’s ratio), we can even start to estimate the maximum temperature gradient that can be tolerated for a glass vial of given wall thickness and CTE.?However, this is just a rough estimate.?For example, the simplified model that I’m referring to assumes instantaneous cooling – something that is physically impossible, particularly under real fill-finish conditions. ?Thickness also varies considerably as you transition from the wall into the neck and flange of the vial.?Finally, we’re completely ignoring the role of the inherent flaw population on glass strength (the subject of a future post).?Given all of these caveats, I’d be curious to hear from anyone who may have practical experience with thermal shock on their filling lines.?My intuition tells me that thermal shock with converted tubular Type I glass vials in typical formats (anything 30R or smaller) would be unlikely, irrespective of whether it’s a 33 or 51 expansion glass.?I don’t have enough experience with larger format molded vials to provide guidance – it’s something else I’d be curious to learn about from a knowledgeable source.?Also note that I’m ignoring soda lime silicate and so-called “low borosilicate” glass packaging that have higher CTE values.

Got questions??Please contact me directly or leave a comment below.

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Footnotes

1. You may also run into the abbreviation TEC, meaning the thermal expansion coefficient.?It’s the same thing as CTE.

2.?Yes – it’s degrees Celsius (°C) or Kelvin (K).?A quick online search for an explanation as to why it’s not °K may provide a vaguely dissatisfying answer about the Kelvin scale being an absolute temperature scale.?It’s perhaps more useful to consider that: 1) the Celsius temperature scale is arbitrarily defined based on the freezing and boiling temperatures of water at 1 atmosphere of pressure and 2) the word “degree” can also just mean the extent to which something is present.?To say 25 degrees Celsius means that we have moved 25 evenly spaced positions (each position equal to one degree) along a scale anchored at 0 and 100.?In contrast, the Kelvin temperature scale is not based on arbitrary points – it can be directly related to the average energy within a system.

3.?Fused silica is also commonly called fused quartz, quartz glass, or amorphous silica.?This objectively makes sense because a common manufacturing method is based on fusing (i.e., melting) the mineral quartz and quenching the resultant molten liquid to form a glass.?However, this incorrectly implies that the final material is still based on quartz, a crystalline material.

4.?The thermal expansion plot is a preview to other content related to the viscosity of glass -- the subject of another post in this series.?You might be familiar with the concept of annealing a glass, a process by which we hold a newly formed glass object at some temperature for an extended period of time to remove stress.?Point C of the plot is one estimate for determining an appropriate annealing temperature.

5.?Glass science textbooks will often devote some space to discussing how these properties are actually measured.?For example, the linear CTE is often determined using something called a dilatometer or thermomechanical analyzer.?I’m omitting this sort of content for the sake of brevity.?Let me know if you’d be interested in seeing some separate posts dedicated to these topics.

6.?Vials can generally enter the depyrogenation tunnel in two configurations.?One approach is to push single rows of vials into the tunnel with a gap between each row.?It’s less space efficient but limits stress on the vials.?I would expect thermal expansion to be irrelevant here.?In this case, I’m thinking more of densely packed vials within the tunnel.?Even in this configuration, the vial pack can slightly rearrange itself.?I’d be curious to know if anyone is aware of specific instances where mechanically constrained vial packs have led to breakage because of thermal expansion.?That’s not to say that vials can’t break in a depyro tunnel – I’m just not convinced yet that it’s because of this specific root cause.

7. I’m still using an average linear CTE of 51x10-7/K to make this estimate, even though it’s technically outside the appropriate temperature range used to calculate the average CTE.

8. Point C on the thermal expansion plot once again becomes relevant.?This would also be an estimate of the temperature where the rigidity of an elastomer stopper would start to substantially increase upon further cooling.

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