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Introduction to Radiative Transfer
Published in John R. Howell, M. Pinar Mengüç, Kyle Daun, Robert Siegel, Thermal Radiation Heat Transfer, 2020
John R. Howell, M. Pinar Mengüç, Kyle Daun, Robert Siegel
The connection between Eλb and temperature can be conceptualized if we remember that thermal radiation originates from random fluctuations in the quantized energy levels of matter, which coincides with the emission or absorption of a photon due to the First Law of Thermodynamics (i.e. the conservation of radiative energy when no other modes of energy transfer are present). The transition probability between two energy states, i and j, depends on three things: The population of each state, the difference in energy between the states, and the temperature. States are populated according to a Boltzmann distribution, Equation (1.1), so higher temperatures permit a broader distribution of energy states and occupation of higher energy states. Therefore, transitions involving larger energy changes become possible, which corresponds to a shift toward emission at higher frequencies/lower wavelengths through Ei→j = Ei − Ej = hn. The transition probability also increases with temperature, meaning that the transitions become more frequent; this accounts for the increase in spectral intensity or spectral emissive power.
Basic statistical concepts
Published in Nils O. Petersen, Foundations for Nanoscience and Nanotechnology, 2017
The Maxwell-Boltzmann distribution of speeds is a special case of the Boltzmann distribution which describes the fraction of molecules, f(v), in an ideal gas with a particular speed, v, which corresponds to a kinetic energy of Ekin=12mv2 $ E_{kin} = \frac{1}{2}mv^{2} $ where m is the mass of the molecule. This is a continuous distribution which has the form f(v)=(m2πkT)324πv2e-12mv2kT $$ f(v) = (\frac{m}{{2\pi kT}})^{{\frac{3}{2}}} 4\pi v^{2} e^{{ - \frac{{\frac{1}{2}mv^{2} }}{{kT}}}} $$
Nanothermodynamics: Fundamentals and Applications
Published in Klaus D. Sattler, 21st Century Nanoscience – A Handbook, 2020
Vladimir García-Morales, Javier Cervera, José A. Manzanares
The Boltzmann distribution describes the occupation probability of different microstates of a system that only interacts thermally with an ideal reservoir that is able to fix the temperature by virtue of its practically infinite heat capacity and an instantaneous energy transfer between different parts of the system. However, deviations from this ideal situation may occur. For example, the “effective” number of degrees of freedom of the bath can be finite, as far as the thermal interaction with the system is concerned. Hence, corrections to the Boltzmann factor are necessary, as described in the next section.
The effects of synthesized silver nanowires on the structure and esterase-like activity of human serum albumin and their impacts on human endometrial stem cells
Published in Inorganic and Nano-Metal Chemistry, 2022
Azadeh Hekmat, Shadie Hatamie, Ali Akbar Saboury
At different temperatures, the values of KA are different. Based on the Boltzmann distribution law, when the temperature is increased, the higher energy molecular levels are employed. Subsequently, the probability for AgNW-HSA interaction is increased and the values of KA are increased.[35] Increasing the temperature may induce some conformational alterations in the structure of HSA which facilitates the binding of AgNWs to HSA molecule (increasing “KA”). Furthermore, this phenomenon shows an association of hydrophobic interactions in the HSA-AgNWs binding process, because the temperature tends to improve the strength of hydrophobic interactions in an aqueous medium and then enlarges the KA value.[36,37] On the contrary, if the binding process is primarily initiated by hydrogen-bonding and/or electrostatic interactions, reducing the KA value is expected to be observed because the temperature tends to disfavor the binding.[38] The evaluation of the modified Stern–Volmer binding constant (KA) between HSA and a ligand is vital to realize its distribution in plasma and organs because it defines the unbound concentration of a drug/ligand in the blood and consequently impacts on the distribution and efficacy of a ligand/drug. A too-weak binding (low KA value) can produce a poor distribution of the ligand/drug in the human body (possibly increased metabolism), whereas strong binding (high KA value) reduces the concentration of free ligand/drug in plasma. As a result, a moderate binding constant value can be set as the best parameter to attain the desired biological activity for several ligands/drugs. As shown in Table 1, at 310 K and 320 K, the values of KA are in the order of 104 M−1, demonstrating a moderate binding between AgNWs and HSA.[38] It is important to mention that the common binding constants of ligands/drugs for HSA are in the range of 104–106 M−1.[39] However, at 300 K, the KA value is in the order of 103 M−1, displaying a weak binding between AgNWs and HSA at a lower temperature. More interestingly, the value of KA at 310 K is in agreement with that of Zhang et. al., who have revealed that KA of AgNWs − BSA at 298 K was 1.23 × 104.[4] Thus, the value of KA obtained for the AgNWs and HSA system at 310 K (physiologic temperature) is desirable for the transportation of AgNWs in circulation, as well as its release at the whole body.[40] Numerous drugs have been revealed to bind proteins with a similar binding affinity.[38,40]