Related Experiment Video
Updated: Oct 2, 2025
09:12
A Method for Studying the Temperature Dependence of Dynamic Fracture and Fragmentation
Published on: June 28, 2015
8.7K
Stochastic Theory of Discrete Binary Fragmentation-Kinetics and Thermodynamics
1Department of Chemical Engineering, Pennsylvania State University, State College, PA 16802, USA.
Entropy (Basel, Switzerland)
|February 25, 2022
Summary
Binary fragmentation, a process where mass splits into smaller pieces, is modeled as a discrete stochastic process. Shattering is identified as a phase transition, analogous to gelation, occurring when stability conditions are violated.
Area of Science:
- Physics
- Chemistry
- Materials Science
Background:
- Binary fragmentation is a fundamental process across various scientific disciplines.
- Understanding fragmentation dynamics is crucial for predicting material behavior and system evolution.
- Previous models often simplify the complex stochastic nature of fragmentation.
Purpose of the Study:
- To formulate binary fragmentation as a discrete stochastic process.
- To derive the ensemble of possible mass distributions and their probabilities.
- To analyze the stability of fragmentation and identify phase transitions.
Main Methods:
- Modeling binary fragmentation as a discrete stochastic process with a fragmentation kernel.
- Constructing the ensemble of distributions formed over a fixed number of steps.
- Utilizing thermodynamic tools to determine the stability of the partition function.
Main Results:
- Derived probabilities for all possible distributions based on the fragmentation kernel.
- Obtained the partition function, mean distribution, and its temporal evolution.
- Demonstrated that shattering is a phase transition linked to partition function instability.
Conclusions:
- Binary fragmentation can be rigorously modeled as a discrete stochastic process.
- Shattering represents a critical phase transition in fragmentation systems.
- A strong analogy exists between fragmentation-aggregation and shattering-gelation processes.
Related Concept Videos
02:39Entropy
31.8K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
31.8K
02:24Predicting Reaction Outcomes
8.7K
Kinetics describes the rate and path by which a reaction occurs. In contrast, thermodynamics deals with state functions and describes the properties, behavior, and components of a system. It is not concerned with the path taken by the process and cannot address the rate at which a reaction occurs. Although it does provide information about what can happen during a reaction process, it does not describe the detailed steps of what appears on an atomic or a molecular level. On the other hand,...
8.7K
02:38Third Law of Thermodynamics
19.8K
A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
19.8K
01:14The Second Law of Thermodynamics
5.9K
In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
5.9K
01:20Mass Spectrometry: Molecular Fragmentation Overview
4.0K
The ionization of a molecule into a molecular ion inside the mass spectrometer causes instability in the molecule's structure due to the loss of an electron. This eventually leads to the fragmentation or breaking of some bonds in the molecule. The fragmentation occurs predominantly at specific bonds to yield relatively stable fragments.
One type of fragmentation pattern is the cleavage of a single bond in the molecular ion. The cleavage leads to a radical and a cation. The cleavage can...
One type of fragmentation pattern is the cleavage of a single bond in the molecular ion. The cleavage leads to a radical and a cation. The cleavage can...
4.0K
01:20Entropy and the Second Law of Thermodynamics
3.3K
The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
3.3K