This award supports theoretical research and education on polymer crystallization.
The long-chain nature of polymer molecules dictates that polymeric crystals adopt a chain-folded lamellar form, but the basic question of how the crystals nucleate is ill understood. There is experimental evidence that polyethylene, the most common semicrystalline polymer, actually nucleates via an intermediate ?rotator" mesophase. However, no theoretical basis yet exists to assess this intriguing hypothesis, or to ascertain how widespread this phenomenon might be in other polymers. Progress requires a theory of the mesophases, able to compute not only their free energy relative to the melt and crystal phases, but also the free energy of the interface between the melt and the mesophase or crystal.
An effective theory of the crystal-melt interface in semicrystalline polymers would also predict the concentration of ?tie chains", which link together adjacent crystalline lamellae and lead to the toughness and ductility of plastics. Also, there is much current interest in the effect of flow on crystallization kinetics and morphology. This is crucial in commercial use of semicrystalline polymers, which are very sensitive to flow effects. Without a good theory of quiescent crystallization, any effort to understand how flow speeds up nucleation is severely handicapped.
The PI aims to develop the theoretical basis to understand the mesophases in polyethylene. It will lead to predictions for bulk and surface free energies, and it will determine whether nucleation in polyethylene can indeed occur via a mesophase. Given the inherently multiscale nature of the problem, a transformative synthesis of techniques will be employed: atomistic simulation of ordered phases, novel use of ?solid-state simulations" to characterize mesophase domain walls, mesoscopic discrete-spin simulation of partially ordered mesophases, and a new adaptation of grafted chain ?brush" theory of the interface between ordered polymer phases and adjacent melt. This unique combination of strategies will lead to a better understanding of how polymer crystals nucleate, and will bring us closer to achieving optimal properties of these truly modern materials.
This intellectually rich problem of practical importance provides an excellent opportunity for education, offering students and postdocs broad exposure to theory, analytical methods, atomistic and mesoscale simulation. The PI is developing an undergraduate course for Fall 2009 in Polymers and Complex Fluids, which is well aligned with the multiscale approach of this proposal. The Chemical Engineering Department has a strong record of minority and gender representation among its graduate students, with about 30 percent women. The College of Engineering has an active Women In Engineering Program and a Multicultural Engineering Program. All simulations will be performed with open source software, to remove any barrier to use by others.
NON-TECHNICAL SUMMARY This award supports theoretical and computational research and education on how polymers crystallize.
Semicrystalline polymers, although relatively young, are the most ubiquitous materials of the modern age. The mass of such materials now produced worldwide each year exceeds the production of steel. Even so, their ultimate potential for desirable mechanical and physical properties is as yet unfulfilled. This is because, in contrast to the centuries-old field of metallurgy, the science base for semicrystalline polymers is still very much a work in progress, with many key results obtained only in the past few decades. Likewise, improved control of polymer molecular structure through advances in catalysis has emerged only relatively recently.
The PI will use theoretical techniques to explore a possible microscopic mechanism for crystallization through an intermediate polymer phase.
This intellectually rich problem of practical importance provides an excellent opportunity for education, offering students and postdocs broad exposure to theory, analytical methods, atomistic and mesoscale simulation. The PI is developing an undergraduate course for Fall 2009 in Polymers and Complex Fluids, which is well aligned with the multiscale approach of this proposal. The Chemical Engineering Department has a strong record of minority and gender representation among its graduate students, with about 30 percent women. The College of Engineering has an active Women In Engineering Program and a Multicultural Engineering Program. All simulations will be performed with open source software, to remove any barrier to use by others.
Trapped twists that make plastics plastic. Polyethylene, that most common of common plastics, "gives" when you pull on it, rather than snapping in two. To the hand and eye, that’s what makes a plastic plastic. But how does a solid material manage to "give" rather than snap, the way plastics do? To find out, we use computer simulations to look inside the crystals that make up polyethylene, in which the long-chain molecules line up together like pencils in a box. But there can be defects in the crystal — trapped twists, that can move along the length of the molecule, like a bump under a rug. These trapped twists — "twist solitons" — can move inside the crystal; when they slide from one end of the molecule to the other, they shift that molecule over by one atom. (Fig. 1) That process, repeated many times, allows crystals to change shape in response to stress, instead of snapping. Understanding how to make this process more or less facile, may give insight into how to tailor inexpensive, weight-saving polymer materials for a wider range of uses. How entangled is an entangled melt? A melt or solution of long entangled polymer chains flows like honey — very viscous, and even "elastic", for example snapping back when you cut a flowing stream with scissors. This behavior comes from the stretchy, springy nature of the long molecules, and the fact that they are entangled together, like a bowl of cooked spaghetti. Different kinds of polymers — made from different chemical "beads" strung together in a long necklace — are more or less elastic in this way, depending on how entangled they are. To study this with computer simulation, we made "movies" of how the molecules wiggle about in an entangled melt. The molecules try to move sideways, but run into neighboring chains oriented crossways, and bounce back. The molecule acts as if it is trapped in a soft "tube". The more entangled it is, the wider the tube. We can use simulations to see this, by averaging over all the ways the chain can wiggle from the same starting arrangement. The set of places the chain can wiggle to, appears as a "cloud" of points around an average entangled path. (Fig. 2) The width of the cloud reveals the diameter of the tube. It turns out that stiff, skinny polymer chains are more entangled — they can get closer to each other, and get in each other’s way more effectively — while flexible, bulky chains take up more room around themselves, which keeps the entangling effects of other chains further away. Another way to ask how entangled is a polymer melt, is to ask how many different knots it can tie, if allowed to explore all possible arrangements. Mathematicians who study topology know a lot about knots, how many different kinds there are, and how to tell them apart. (Fig. 3) We programmed a computer to use their tools to count how many of each kind of knot that a small polymer melt could randomly tie. We found that the more narrow the "tube", the more different kinds of knots the melt can tie. The tube, in other words, is a result of the uncrossability of chains, the same thing that makes knots so difficult to untie. Undergraduate research. Computer simulations are a great way for undergraduates to begin to do research into the molecular origins of material properties. These tools couple to visual insight — you can "see" what happens, which stimulates new questions, in a rapid cycle of discovery. And undergraduate research is a proven effective way to encourage bright students to pursue advanced work in STEM (science, technology, engineering, and mathematics) fields. Over the past four years, I have mentored eight undergraduate research students, who together have written eight published papers, five as first author. Two of these students are now pursuing PhD studies at leading institutions in the U.S.
