Master’s project (30 ECTS): Describing small systems
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The science education community has recently
proposed that nanoscience and technology should be included
in secondary school. This can be a challenge, as the properties of small
systems often don’t comply with the paradigms of classical physics students
learn about in school. Indeed, small systems can display unusual behavior,
such as the surprising and mystifying thermophilic motion recently observed
in proteins and other small biological systems. This seems to be contrary to
classical laws, which state that particles will be pushed away from higher
temperatures. These discrepancies force us towards new insights, new ways of
thinking. A more systematic understanding of small systems and their
seemingly anomalous properties will enable us to modernize the curriculum and
demystify nanotechnology. What makes a system small then? Systems are always in contact with an environment
that influences their energy, volume, and mass. In certain cases, the
presence of the environment is of little significance, and, for simplicity,
the system may be described as though it were isolated. In other cases,
surroundings significantly affect the properties of systems, and external
interactions need to be considered. Systems subject to the latter scenario may be
referred to as small, where small is not an attribute
determined by the system’s sheer size, but rather by how the size compares to
the range of the interactions affecting the system. From this point of view,
a solar system may be thought of as small; indeed, two adjacent identical
solar systems would not have twice the energy as one of them would have on
its own. Yet a water droplet may well be thought of as large; as far as we
can measure, a water droplet has twice the internal energy as an isolated
droplet half the size. In contrast to large systems, small systems are non-extensive,
i.e. doubling the size of the system does not simply double its
energy. And, as a result, non-additive, i.e. the system cannot
be expressed as the sum of its parts (interactions between subsystems are far
from negligible and must also be considered). In other words: small systems escape the paradigms
of classical thermodynamics. Yet many such systems are still too large to be
conveniently described by quantum theory. Too small for classical
thermodynamics and too large for quantum theory. It appears a modified
thermostatistical description is in order. In this master’s project, the student will identify
different approaches to this problem, and how they can help us model the
seemingly anomalous properties exhibited by small systems. The student must be familiar with quantum,
statistical and thermal physics or physical chemistry (TFY2045+TFY4230+TFY4165 or TKJ4170+TKJ4215+TKJ4162 or equivalent
coursework). Before starting the project, the student will make him/herself
familiar with this publication: Nanomaterials 2020, 10(12),
2471. It is expected that the student will invest a
minimum of 700-800 hours from his/her start in the project to the oral
defense. Interested students may send their academic profile (with a list of relevant coursework) and a statement of motivation to rodrigo.demiguel@ntnu.no. Other inquiries may be directed at the same address. |