Exponential Phase Freezing

Exponential phase freezing is a cryopreservation method that preserves actively dividing cells during the exponential, or logarithmic, phase of growth, when cultures typically show strong viability and recovery potential. The process involves harvesting cells before nutrients become limiting, suspending them in a cryoprotective medium, and cooling them under controlled conditions to limit intracellular ice formation and membrane damage. Cryogenically stored cells can later be thawed and returned to culture for characterization, expansion, or experimental use. In medicine and biomedical research, this approach supports reproducible cell banking, preservation of therapeutic or diagnostic cell lines, and consistent starting material for studies and manufacturing.

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JoVE Core - Chemistry

Phase Transitions: Melting and Freezing

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2020

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...

Exponential Growth

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2026

Bacterial populations exhibit exponential growth when conditions such as nutrient availability and temperature are favorable. In this phase, cells reproduce through binary fission, where each cell divides into two identical daughter cells. This process causes the population to double at regular intervals, resulting in a growth rate that is directly proportional to the current number of cells. As the population increases, the number of new cells formed during each generation also grows, creating...

Freezing Point Depression and Boiling Point Elevation

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2020

Boiling Point Elevation The boiling point of a liquid is the temperature at which its vapor pressure is equal to ambient atmospheric pressure. Since the vapor pressure of a solution is lowered due to the presence of nonvolatile solutes, it stands to reason that the solution’s boiling point will subsequently be increased. Vapor pressure increases with temperature, and so a solution will require a higher temperature than will pure solvent to achieve any given vapor pressure, including one...

Exponential Functions with Base e

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2025

Exponential functions with base e are essential for modeling continuous processes of growth and decay. The constant e, approximately 2.718, naturally arises in systems where change occurs proportionally to the current value. A positive exponent represents continuous growth, while a negative exponent represents continuous decay. These functions are especially useful for describing situations where change happens smoothly over time rather than in discrete steps.One clear example of exponential...

Exponential and Sinusoidal Signals

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2024

The exponential function is crucial for characterizing waveforms that rise and decay rapidly. This continuous-time exponential function is defined using exponential terms with constants α and A. When both constants are real, the function is represented as, and can be graphically depicted to show exponential growth or decay. When the constant α is purely imaginary, the result is a complex exponential, expressed as, where j is the imaginary unit and ω0 is the angular frequency. This function is...

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