Jumping random walks: a stochastic description for the modelling of glass-like materials
Is glass a solid or a liquid? You’d probably say it’s a solid, because in our day-to-day lives, that’s how it acts, unless your bottles strangely splash about! Scientifically, glass stands on both sides, having the disordered structure of a liquid while acting like a solid most of its time. How we can observe this behaviour was the focus of Dr Bart Vorselaars’ seminar on Wednesday 26th November, “Jumping random walks: a stochastic description for the modelling of glass-like materials.” His talk discussed how the simple idea of random walks helps us understand these materials that are used in our regular lives.
We determine if a material is glass or not by checking its viscosity, which is how easily something flows. Water has a viscosity of 10-3 Pas (pascal-second), whilst for a material to be considered glass, its viscosity must exceed 1012 Pas, meaning it flows so slow to the point it seems solid. A good example to demonstrate this behaviour is the pitch-drop experiment; an extremely thick fluid with a viscosity of 108 Pas, that shatters if hit with force, but if left for long periods of time will eventually drip. The experiment showed “it took eight years for the first drop to fall, and more than 40 years for another five to follow.” [1], so just imagine how long it’d take for glassy materials with a higher viscosity!
Many glass-like materials are polymers, which we can view as identical building blocks put together into a long chain and they’re seen used in our disposable coffee cups, or the plastic used for your phone case! To understand their behaviour such as their deformation, scientists run molecular simulations, and to keep it simple, researchers introduce the idea of random walks to model these polymers mathematically.
So, what is a random walk? The idea is in the name: a path taken where the direction of every step is random. It has a strong correlation to the behaviour of molecules in liquids, constantly moving and bouncing into each other. Take watching particles move in diluted milk under a microscope, the way each one jiggles around is a random walk. By now, a question may have come to mind: if every step is purely random, how can we generalise this? The chances of an atom moving forwards versus backwards is equal, so its average displacement becomes zero as they cancel each other out. However, the size of the walk grows with the square root of the number of steps taken. These factors help scientists generalise how particles diffuse in a liquid and change overtime.
However, there is an extra obstacle for particles in glass-like materials. They can get trapped in cages made by their neighbours. It takes time and sufficient energy for a particle to make a sudden jump out of the cage and into the next since all these particles typically repel each other, so it must overcome a barrier. An easy way of modelling this is imagining a ball rolling up and down a line of hills: it is a lot more comfortable for the ball to reside in the troughs since it needs a push to make its way up the hill, only to reside in the next dip. To word it more mathematically (so you can sound fancier!) is to refer to the hills as a sine wave as it has the same shape. Like with actual steep landscape, the higher a climb a particle has, the longer it will be trapped there as it needs more energy to overcome the barrier, a lot like if you had to climb a gentle hill compared to Mount Everest; you could do the hill many times back-to-back, but Everest maybe once at a push. This model is simple but an easy way to represent the motion observed in real polymer glasses.
These simple, one-dimensional stochastic models capture the key characteristics of materials, such as polystyrene, which is used in packaging such as takeaway boxes. This model can also teach us about the switching of magnetic field of the earth, electrical circuits and laser physics!
This talk concludes that by using random walks to model atoms in glass, we can understand their key characteristics of both acting like a solid and liquid using this one-dimensional mathematical model. Researchers can then know what materials are the most ideal for certain uses by seeing how they behave in different temperatures and predict when they will deform. All from just comparing glass-like materials to walking in random directions like headless chickens!
[1] “Pitch Drop experiment”, The University of Queensland, Australia, [Online] Available: https://smp.uq.edu.au/pitch-drop-experiment
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Presentation: Date, title and name of speaker were present. Good grammar. No improvements needed.
Content: Seminar content covered accurately. No improvements needed.
Context: Societal context adressed. Reseach context not adressed. To improve, explain the research context of the seminar.
Style: Blog is suitable for a lay audience and engaging. No improvements needed.
External source: Evidence of external source with quote. No improvements needed.
41058
Your blog discusses the seminar in a non-confusing way and it is enjoyable to read. The introduction gives a good overview of the content.
The main important concepts have been covered such as random walks and viscosity.
The content is correct and can be understood by a wide range of audience. Real life examples have also been included to verify the content.
The societal and research contexts have been covered and also the wider scientific applications have been covered too. Even though it is a blog it could come across as a bit more informal, an improvement could be making it not highly formal but a bit more formal.
External sources have been used correctly but I would recommend maybe including one more link to research in the scientific world that relates to this seminar.
69356
Following the marking scheme for the seminar reports, provided in the module handbook:
Name of speaker and title are clearly stated. I believe there are no mistakes in your grammar. The overall presentation of the blog is more than clear enough. - 3/3
Your report accurately report’s the take-home message of the seminar, covering most of the content on the seminar. - 3/3
There is an accurate contextualization of the research topic, for both research and society, with the use of simple examples that break down tougher terminology and links to everyday life. - 3/3
There are additional findings within the report from external sources, including a direct quote. However, the additional findings are quite scarce within the message of the seminar, therefore I believe a very small improvement could be the addition of a few more external sources that complement the seminar. - 2/3
The level of the writing style is appropriate for a lay audience and consistent throughout the report. - 3/3
Overall mark - 14/15
Very good report with minimal changes to be made!
31842
- Blog overall presentation (3/3)
Well presented in terms of the specification, all relevant information is included and grammar looks good.
- Accurate reporting of the seminar’s take-home message (3/3)
The seminar message is well covered.
- Accurate contextualisation of the research topic (3/3)
Good information is provided around the topic of research.
- Additional assessment using external sources with a direct quote (2/3)
The included references are okay, but I feel they may be lacking depth into the original topic of the seminar.
- Writing style and technical level for a lay audience (3/3)
Perfect and consistent writing style for a more complicated scientific area of study