A New Formula to Calculate a Polymer’s Elasticity

21 September 2016

Polymer manufacturers and designers are naturally interested in how elastic their polymers are, but up to now they have not had a way to accurately predict how stretchy or rigid new polymer designs will be. This is because, whilst a theoretical level of elasticity is calculable, the flaws and defects that are found in real world polymeric molecular chains are an unknown factor that prevents a precise formula being created.

That is until now, for a research team from MiT have created a method to calculate how elastic a new polymer will be; a key discovery that polymer engineers have been trying to make for more than a century. As Jeremiah Johnson, a Professor of Chemistry at MiT and a key player in the research explained, “This is the first time anyone has developed a predictive theory of elasticity in a polymer network, which is something that many have said over the years was impossible to do.”

Previous calculations to predict how flexible a polymer would be were very theoretical, as they did not compute how many of the molecular chains were defective. In theory all of the molecular chains in a polymer bind with another chain, however some of them inevitably bind with themselves to create ‘floppy loops’ that weaken the material.

Seeing that this was the root of a problem, Johnson and his colleague Bradley Olson, an Associate Professor of Chemical Engineering at MiT, came up with a way of measuring the number of defects in a polymer.

A discovery the online journal Phys.Org reports the discovery as follows;

“The researchers designed polymer chains that incorporate at a specific location a chemical bond that can be broken using hydrolysis. Once the polymers link to form a gel, the researchers cleave the bonds and measure the quantity of different types of degradation products.” Developing this research further, the team have made a breakthrough as, “By comparing that measurement with what would be seen in a defect-free material, they can figure out how much of the polymer has formed loops.”

The result is a formula for predicting a polymer’s elasticity. As Anne Trafton explains on the MiT website, “First, they calculated how a single defect would alter the elasticity. This number can then be multiplied by the total number of defects measured, which yields the overall impact on elasticity.”

You can watch the video of MiT’s explanation of the discovery here.

Olsen described the process himself, when he said, “We do one complicated calculation for each type of defect to calculate how it perturbs the structure of the network under deformation, and then we add up all of those to get an adjusted elasticity.”

The process has already been tested out on numerous materials and has held true, proving it to be a far more accurate predictor than the previous methods (known as the affine network theory and the phantom network model), neither of which factored defects into their calculations.

Now the team has published their results in the peer review journal, Science, where the research team reported how, “The results led to a real elastic network theory (RENT) that describes how loop defects affect bulk elasticity. Given knowledge of the loop fractions, RENT provides predictions of the shear elastic modulus.”

The research is already being hailed as a massive step forward in our understanding of polymer dynamics and will be a massive boon to both polymer manufacturers and designers. Something that Sanat Kumar, professor of chemical engineering at Columbia University, who was not part of the research, agreed with when he said, “They have taken an age-old problem and done very clear experiments and developed a very nice theory that moves the field up a whole quantum leap.”

But the researchers have not yet finished their work, as they plan to expand their predictive process to cover other materials, with Olsen stating that, “I think within a few years you’ll see it broaden rapidly to cover more and more types of networks.”

Meanwhile the Phys.org website explains how the researchers, “are also interested in exploring other features of polymers that affect their elasticity and strength, including a property known as entanglement, which occurs when polymer chains are wound around each other like Christmas tree lights without chemically binding to each other.”

But for now polymer traders and plastic producers are looking forward to the improved products that it is hoped will be developed now that much of the guesswork of polymer design has been removed.

As Trafton explains, “This theory could make it much easier for scientists to design materials with a specific elasticity, which is currently more of a trial-and-error process.”

 

 

Photo credit: Jose-Luis Olivares/MIT