Liquid-Solid Phase Transition vs. Glass Transition

According to statistical physics, a clear change in a measurable physical quantity accompanies the transition between solid and liquid phases. For instance, when a solid is heated, its volume increases. At the melting point, there is an abrupt increase in volume, and a latent heat associated with the solid-to-liquid phase change. This energy is necessary to overcome molecular attractions at constant temperature, allowing the material to transition abruptly from solid to liquid. But how does this differ from the liquid to glass transition?

A liquid approaching the glass transition skips the melting point and remains a liquid even at lower temperatures. This state is termed supercooled. Supercooled liquids exhibit very high viscosities that increase further as the temperature drops.

Pitch, from the earlier discussed experiment, serves as a prime example of a supercooled liquid. Scientists have estimated pitch's viscosity to be 230 billion times that of water, highlighting its extreme thickness.

Once temperatures drop significantly, we confront the dilemma of the glass transition:

> If a liquid is so viscous that it behaves like a solid over geological timescales, how do we classify it?

Glassblowing has been practiced since the 1st century BC. When glass is blown and cooled, it eventually solidifies. However, it may take millions of years to reach a stable state, as evidenced by studies on 20-million-year-old amber fossils. In comparison, the pitch drop experiment is a mere infant!

The Dilemma:

> In crystalline structures, molecules are arranged in a specific order, leading to infinite viscosity: solids cannot be spread (you can't spread butter on toast without deforming it). Is there a similar glass transition temperature below which viscosity becomes infinite? How can we experimentally verify this, given that a liquid near the glass transition might take eons to flow?

Is There Hidden Order Within Disorder?

At the glass transition, processes slow down logarithmically. Cooling freshly blown glass may lead to a rapid increase in viscosity. The time taken to increase viscosity by factors of 10, 20, or even 60 can stretch into minutes, hours, or even millions of minutes. Researchers humorously note that the first data point takes a minute, the second ten minutes, and by the fifth or sixth data point, you exceed a PhD student's study time.

However, determining the presence of a glass transition doesn't solely rely on waiting for infinity. The transition from liquid to crystal features a distinct structural change: from disordered liquid to ordered crystal.

On the surface, liquid and glass appear structurally similar, while crystals display molecular order.

> The ongoing debate centers on whether disordered glass possesses any hidden order that is not immediately evident.

Various theories contend that there might be an abrupt ideal glass transition temperature, below which all molecular motion ceases. At this temperature, molecules become completely locked in place, with their movements correlated. This scenario resembles spheres densely packed together with no apparent order, yet no sphere is able to move. However, measuring such hidden order remains an unresolved challenge.

Hidden Order in Our Everyday World?

A compelling question arises: does our world possess some hidden order? This inquiry extends to phenomena such as stock market fluctuations, housing market trends, and epidemics: can these emergent behaviors reveal underlying order, making them predictable?

Recent findings indicate the existence of a specialized order amid disorder, termed hyperuniformity. In 2014, it was discovered that a chicken's eyes possess differently colored receptors arranged in a seemingly random pattern, yet exhibit hidden order.

While it might appear that similar order exists in other disordered systems, such as traffic jams and crowded gatherings, it is crucial to remember that hyperuniformity has only been confirmed in specific contexts. In our exploration for hidden order, we must remain mindful of our original purpose.

> What should we do when the laws of physics fail to predict numerous everyday occurrences, from liquid-solid transitions to traffic congestion and stock market dynamics?

When Do the Laws of Physics Fail? What Are the Practical Implications?

We must recognize that physical laws are as vital as the phenomena they aim to describe. While these laws may seem unchangeable, they too can evolve. Statistical physics was created to comprehend materials and their transitions, relying on averages. Individual atomic and molecular behaviors are inherently random and unpredictable. Nevertheless, centuries of research have shown that statistical physics serves as a solid approximation of collective molecular behavior in solids, liquids, and gases. Yet, these laws are merely approximations.

> Physical laws are approximations of reality, not the other way around.

When conditions deviate from the norm, the laws of physics can falter. Consider a lawn: while it may appear uniformly green, small bare patches may not alter that perception. However, if those patches are replaced with highly infectious weeds, the entire landscape changes.

Several factors contribute to the inadequacy of established laws in statistical physics to describe many everyday phenomena:

1. Lack of Averaging Out: In traditional crystals, atomic motions average out to form orderly lattices, whereas in glasses, motions do not average as neatly. This principle can be extended to larger societal phenomena; a single erratic driver or accident can lead to massive traffic jams.
2. Finite Size Effects: The world is not infinitely sized, whereas materials can be approximated as containing an infinite number of molecules.
3. Timescales: The transition from solid to liquid can be approximated as instantaneous. Conversely, the transition from liquid to glass may take millions of years, complicating predictions given our limited lived experiences.

Despite these challenges, there is potential for accurate approximations of reality, enabling us to better predict and shape future events. For instance, many scientists anticipated COVID-19 would escalate into a major pandemic, but pinpointing the exact timing proved more complex.

> Physics offers a significant advantage:

> Physical approximations are grounded in causation, rather than mere correlation.

While vast data collections have led to advancements in data science and machine learning methods to forecast events like stock markets and housing trends, many of these approaches falter with minor disturbances due to their reliance on correlation instead of causation. For example, slight modifications to stop signs can mislead complex neural networks that were not trained on such variations.

In conclusion, physical laws falter when their foundational assumptions are not met. In some instances, new laws may emerge to replace outdated ones; in others, no singular law may exist to encapsulate everything.

The essence of this discussion serves as a poignant reminder of this ongoing challenge: can we determine whether pitch is a solid or a liquid—a material that behaves like a liquid yet acts as a solid in practical terms? Additionally, is there hidden order within the apparent disorder? If so, does this suggest that beneath the unpredictability of our daily lives lies a profound order?

Alternatively, could it be that some phenomena are inherently more predictable than others? Instead of categorizing events as predictable or unpredictable, perhaps we need to consider a spectrum of predictability.

Regardless of the outcome, it is crucial to understand why existing laws may fail, as this knowledge can enhance our comprehension of the intricate world around us. A balanced approach in seeking accurate approximations for complex emergent phenomena will help us forge sustainable and resilient futures.

If you found this article engaging, consider following the Emergent Phenomena publication, where we delve into how complex everyday occurrences—from materials to societal interactions—emerge.