Volume 3 Issue 6

What’s Happening at Missouri S&T:

Spring Short Course Are Coming Up Soon!!!
**These courses are filling up fast! There are still open spots, so register today for Spring courses!!**

This spring we will be offering “Basic Composition of Coatings¿? March 12-16, 2007 and “Introduction to Paint Formulation¿? May 14-18, 2007 . The Basic Composition course is intended for new personnel in the coatings profession. It targets the components of coatings (resin, pigments, extenders, solvents and additives), testing and specifications, general formulation and manufacturing methods. Basic Composition is primarily a lecture course with several laboratory demonstrations. The Introduction to Formulation course is intended to give the person a fundamental knowledge of how to approach a starting formulation and troubleshoot it. This course involves both lecture and laboratory work For more information see our web site at http://coatings.mst.edu and to register contact Michael Van De Mark at coatings@mst.edu or call 573-341-4419. **Both courses held on the Rolla campus**

Summer 2007 Short Course Dates

Next summer we will be offering "Introduction to Coatings Composition and Specifications" July 16-18, 2007 , in St. Louis Missouri.

Thank you for visiting with us at ICE 2006!

We would like to thank everyone who stopped by to visit with us at our booth at ICE! We hope that ICE was beneficial for everyone. If anyone has any questions about our short courses, our academic program, or about working with us on projects or research, we would be happy to answer them, please feel free to email or call us.

Thank you to everyone who entered our ICE 2006 St. Pat's Sweatshirt Drawings! The five winners were:

*Carl Sullivan, Reichhold
*Brian Hope, Trowel Plastics
*Ivan De Lucia, I.D. Art Supplies
*Rudy Berndimaier, King Industries
*David Faherty, Jr., Troy Corporation

We look forward to seeing you all in Toronto for ICE 2007!

Technical Insights on Coatings Science

The Glass Transition Temperature
By Robert Hull, Graduate Student, Missouri S&T Coatings Institute

An interesting property of the polymer materials used in the coatings industry is that they are almost always amorphous in chain orientation. What does that mean, you may ask? Well, that simply means that the molecules making up the material are not together in any particular order. They are just randomly “stuck¿? together. This is why amorphous materials are usually transparent just like glass, which is also amorphous. In materials whose molecular structure is not amorphous, which we call “crystalline,¿? the molecules are regionally ordered together in a certain pattern.

The word glassy is often used to describe the amorphous types of materials. This similarity to a glass gives us the name of a physical change that amorphous polymers go through known as the glass transition. This change occurs at the glass transition temperature, denoted as T_g. The glass transition temperature is specific for each different polymer material and is a very important property for the components of paints and coatings because it contributes to the flexibility of a material at a given temperature, plasticizer activity, and the ability of an additive to act as a volatile plasticizer such as a coalescent aid. Because of the importance of the glass transition temperature of the materials used in our industry, most people could use a little introduction or refresher on what the glass transition temperature is really all about.

The glass transition involves a continuous change in the amorphous, “glassy¿? polymer material, as the temperature increases, from a rigid or even brittle solid into a flexible, slow flowing material whose viscosity decreases by a factor of ten to fourteen orders of magnitude at the transition temperature. The viscosity then continues to decrease at a much slower rate with subsequently increasing temperature. Although this may seem to be the same thing as the melting of what we normally think of as a solid, there is actually an important difference.

When most people think of “melting,¿? they naturally think of ice turning into water. The difference here is that the structure of ice is actually crystalline. When it melts, it changes directly into liquid water and then you have a mixture of melting solid water and liquid water as the melting continues. You can picture this as the individual water molecules leaving the ordered ice structure one by one into the randomly ordered liquid phase. The randomly ordered liquid phase can then flow because the water molecules can move over each other; they have more freedom of motion. So, melting actually describes a change in the order of the molecules in the material. But what if the molecules are already disorded, like they are in amorphous solids? Why then don’t their molecules move past each other and “flow¿??

One of the properties of the water molecules that lets them move from the ordered solid state to the disorded liquid state so easily is that they are very small. Water is a very small molecule relative to polymers, which can be composed of many hundreds or even thousands of units, each of which are themselves larger than a water molecule. So, if you have a solid composed of randomly thrown together large polymer molecules, they are not going to be able to move around each other easily. In fact, they will probably be stuck together most of the time because they will be entangled with each other.

Think of the amorphous solid polymer material as a big bowl of spaghetti. The noodles are not going to move past each other very well, if at all, after you take the bowl out of the refrigerator or even if left out on the counter for a while at room temperature. But, if you chop them up into much smaller pieces, then you will be able to move them around more readily. Thus, the large polymer chains can’t move past each other and so remain “frozen¿? together randomly as a glassy solid.

Once you start to heat the material up though, segments of the chain begin to wiggle around more and more as the temperature increases. As the chain segments wiggle around more about their positions, they create more “free volume¿? by bumping into other chain segments and pushing the chains farther apart. This is why we see an increase in volume as the temperature goes up. At a certain temperature there will be enough free volume for the polymer chain segments to start to be able to wiggle past each other and the material is no longer “glassy.¿? The chain segments can then “flow¿? past each other and the viscosity drops by ten to fourteen orders of magnitude, though it is still extremely high.

The temperature at which the molecules can start to move around each other is then called the glass transition temperature. The transition at this temperature is denoted by a change in rate of increase of volume with temperature. When the sample being heated undergoes a “transition¿? there is a change either in the rate of change of volume or there is a discontinuity in the rate of change; that is, a large sudden change in the volume at a certain temperature. A discontinuity is called a melting point transition. The former is a second order transition, the glass transition, which is defined as occurring at the temperature where the coefficient of thermal expansion changes.

Since we would rather not go too much further into physical chemistry than this though, we will move on from here to a basic overview of what determines the glass transition temperature on the chain segment level. If you are interested in learning more, please see the excellent book referenced at the end of this article. [1]

Factors Affecting the Glass Transition Temperature

There are four main types of factors that affect the glass transition temperature: molecular weight (MW), chemical structure, diluents and copolymers, and cross-linking. Each of these can be explained by the basic free volume definition given above.

An equation showing the effect of molecular weight on a polymers T_g, was given by Fox and Flory in the 1950s [2] as the relationship:

T_g = T_g ⁸ - K / MW

where T_g ⁸ is the glass transition of an infinitely large polymer chain (infinite molecular weight) and K is a constant which is related to the free volume. From this we see that the glass transition temperature increases with molecular weight. This makes sense in terms of the free volume: as the molecular size increases more free volume is necessary for the molecules to move past each other, which in turn requires higher temperatures. Also, we can consider low MW polymers to contain more chain ends per unit volume, which have a greater range of motion and hence more free volume at lower temperatures.

In reality though, this equation does have a limit. After a molecular weight reaches about 100,000 g/mol the T_g pretty much stops increasing. This is because the mobility of the chain segments doesn’t significantly change above this molecular weight since chain entanglement has been maximized.

The effect of chemical structure on the T_g can be slightly more complicated. Obviously, polymers with groups that have a tendency to have strong intermolecular interactions will have a higher T_g. This is seen in polymers with even slightly polar groups, such as halogens, showing increases in T_g because the chains are attracted to each other and do not want to move apart. The polymer chain stiffness is similarly straight forward: stiffer chains are less mobile and so show a higher T_g.

Chain branching, however, is a bit more complicated. Initially this appears simple: bulky pendant groups will raise the T_g by sterically hindering bond rotations, thus requiring higher temperatures for the required free volume to undergo the glass transition. This effect increases with group size becoming less pronounced as the distance from the polymer chain increases.

As the length of the pendant chain increases though, an actual decrease in T_g is seen because the secondary chain causes a decrease in how closely the chains are packed together. The side chains are also then long enough to bend in different directions and move out of the way of the main chain as it moves. Thus, an increase in T_g is observed only for short or very rigid pendant groups with longer more flexible side chains acting to decrease T_g. As with the effect of increasing molecular weight though, this also has a limit. If the side chains get too long then they are able to organize themselves into packing orders or get entangled with other chains and then T_g again goes up.

Dilution of a polymer with another polymer having a different T_g leads to a T_g of the mixture being somewhere between the two, provided that they are miscible. This is very common in the manufacture of polymer materials to adjust a product’s flexibility by the addition of a plasticizing resin or a plasticizer, which is a low molecular weight material. The exception would be for a polyblend in which the two distinct polymer chains have very strong mutual affinities or repulsions. Similarly, chemical copolymerization of different monomer species (different monomers mixed in the same chain) yields an intermediate T_g, calculable by the Fox equation [3]:

1/T_g = W₁ / T_g1 + W₂ / T_g2 + …

Note here that the temperature is in degrees Kelvin, K, and that Wi means the weight fraction of a particular polymer in the mixture or copolymer.

Lastly, the effect of cross-linking does not require a whole lot of detail. Cross-linking basically ties the polymer chains together. As you would expect then, it decreases both the free volume and the chain mobility, leading to a higher T_g.

Thanks for reading! We hope this helps.

References:

1. P. C. Painter and M. M. Coleman, Fundamentals of Polymer Science: An Introductory Text, 2^nd Ed.; CRC Press, 1997.
2. T. G. Fox and P. J. Flory, J. Appl. Phys., 21, 581 (1950); J. Polym Sci., 14, 315 (1954)
3. T. G. Fox, Bull. Am. Phys. Soc., 1, 123 (1956)

Is there a topic you would like discussed? Contact us by e-mail at coatings@mst.edu.