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Related Concept Videos

Carrier Transport01:21

Carrier Transport

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The generation of electrical current in semiconductors is fundamentally driven by two mechanisms: drift and diffusion. These processes are essential for the functionality and performance of semiconductor-based devices.
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
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Passive Diffusion: Overview and Kinetics01:17

Passive Diffusion: Overview and Kinetics

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Passive diffusion is a critical process that allows small lipophilic drugs to cross the cell membrane along a concentration gradient. This mechanism's efficiency depends on four primary factors: the membrane's surface area, the drug's lipid-water partition coefficient, the concentration gradient, and the membrane's thickness.
When administered orally, drugs establish a substantial concentration gradient between the gastrointestinal (GI) lumen and the bloodstream, expediting...
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Proteins show rotational as well as lateral diffusion across the membrane. The lateral diffusion of proteins was confirmed through the cell fusion experiment where mouse and human cells were fused, resulting in hybrid cells. When the human and mouse cells fused, the specific membrane proteins on human and mouse cells were marked with the red and green-fluorescent markers, respectively. Initially, the red and green fluorescence was located on the respective hemisphere of the cell. As time...
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Theories of Dissolution: Diffusion Layer Model01:15

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Dissolution, the process by which drug particles dissolve in a solvent, is explained by the diffusion layer model, a theoretical framework that simulates the absorption of oral drugs and allows us to analyze experimental data.
This process starts with a thin layer, saturated with the drug, forming at the interface between the solid and liquid. The solute then diffuses from this layer into the main solution. The Noyes-Whitney equation suggests that the rate of dissolution relies on the diffusion...
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Diffusion01:12

Diffusion

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Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
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Diffusion01:21

Diffusion

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Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
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Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
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Exploring Nonlinear Diffusion Equations for Modelling Dye-Sensitized Solar Cells.

Benjamin Maldon1, Ngamta Thamwattana1, Maureen Edwards2

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|December 8, 2020
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Summary

This study presents mathematical models for dye-sensitized solar cells (DSSCs), offering analytical and numerical solutions for electron diffusion. These models enhance understanding of DSSC performance for renewable energy applications.

Keywords:
Lie symmetrydye-sensitized solar cellsefficiencyelectron densitynonlinear diffusion

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Area of Science:

  • Renewable Energy
  • Materials Science
  • Mathematical Physics

Background:

  • Dye-sensitized solar cells (DSSCs) are a promising renewable energy technology.
  • Comprehensive mathematical modeling of DSSCs is currently lacking.
  • Existing models often rely on diffusion equations for electron density.

Purpose of the Study:

  • To develop and analyze mathematical models for DSSCs.
  • To provide analytical solutions for electron diffusion under linear conditions.
  • To explore solutions for nonlinear diffusion equations using Lie symmetry analysis.

Main Methods:

  • Analytical solutions for linear diffusion and recombination equations.
  • Lie symmetry analysis for nonlinear diffusion equations.
  • Numerical solutions for complex cases.

Main Results:

  • Analytical solutions were derived for simplified DSSC models.
  • Lie symmetry analysis yielded insights into nonlinear diffusion behavior.
  • Numerical solutions demonstrated good agreement with existing literature.

Conclusions:

  • The study provides valuable mathematical frameworks for DSSC analysis.
  • The developed models can aid in optimizing DSSC design and efficiency.
  • Further research can build upon these modeling techniques for advanced solar cell development.