Relaxation (science)

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In the natural sciences, relaxation refers to the transition of a system via relaxation processes into its basic state or into a state of equilibrium (often after a stimulus or an external disturbance).

The relaxation time (more precisely relaxation time constant ) describes the characteristic time in which a system (mostly exponentially ) approaches the stationary state. Obviously, after the duration of a relaxation time constant, the system has moved noticeably towards its state of equilibrium; after the duration of three to six relaxation time constants one can usually assume a largely complete relaxation. The reciprocal of the relaxation time constant is called the relaxation rate.

Mathematical description

Exponential relaxation of a quantity from the initial value to the equilibrium value in the case . ${\displaystyle f(t)}$ ${\displaystyle f_{0}}$ ${\displaystyle f_{\infty }}$ ${\displaystyle f_{\infty }>f_{0}}$

If the relaxation of a quantity from the initial value to the asymptotic final value follows an exponential law: ${\displaystyle f(t)}$ ${\displaystyle f_{0}}$ ${\displaystyle f_{\infty }}$

${\displaystyle f(t)=f_{\infty }+(f_{0}-f_{\infty })\cdot \mathrm {e} ^{-{\frac {t}{\tau }}}}$,

then the associated relaxation time constant and the relaxation rate. ${\displaystyle \tau }$ ${\displaystyle R=1/\tau }$

After the time ( half-life ) the size has approached the final value up to half, after about 36.8% ( ), after down to about 13.5% and after down to about 5.0%; d. That is, the system is approximately 95% (almost completely) relaxed at this point. ${\displaystyle t=\ln(2)\cdot \tau \approx 0{,}69\cdot \tau }$ ${\displaystyle t=\tau }$ ${\displaystyle =1/e}$ ${\displaystyle t=2\tau }$ ${\displaystyle t=3\tau }$

In the case of more complicated (for example stretched-exponential ) time dependencies, the relaxation time can be defined as

${\displaystyle \langle \tau \rangle =\int _{0}^{\infty }{\frac {f(t)-f_{\infty }}{f_{0}-f_{\infty }}}\mathrm {d} t}$.

Examples

• The heat transfer with the thermal relaxation time ; this describes how quickly the temperature of a body adapts to the changed ambient temperature ( Newton's law of cooling ). Here is the mass of the body, the specific heat capacity , the heat transfer coefficient and the interface. ${\displaystyle t_{\text{R}}={\tfrac {mc}{\alpha A}}}$ ${\displaystyle m}$ ${\displaystyle c}$ ${\displaystyle \alpha }$ ${\displaystyle A}$
• The magnetization relaxation in the nuclear magnetic resonance (NMR) or electron spin resonance (ESR) with the relaxation times and the longitudinal and transverse magnetization. ${\displaystyle T_{1}}$ ${\displaystyle T_{2}}$
• The charging and discharging process of the capacitor of an RC element in electronics with the relaxation time , see time constant . ${\displaystyle \tau =R\cdot C}$
• The violent relaxation of the kinetic energy of a star gas or galaxy cluster , so that a thermal equilibrium is established.
• The time sequence of a chemical reaction measured with the relaxation method , see also Kinetics (chemistry) .
• The decrease in mechanical stress over time with constant elongation in strength theory , see relaxation experiment .
• If an ion (central ion) of a salt solution moves in the electric field together with its ion cloud of "counter-ions", it has to build up the ion cloud again in the direction of movement and break it down again "behind". This process takes time, the so-called relaxation time. As a result, the ion is slowed down by its ion cloud. This effect is known as the relaxation effect or asymmetry effect and reduces the electrolytic conductivity of the solution. This effect disappears at high frequencies (above 1 MHz). The latter is known as the dispersion effect or Debye-Falkenhagen effect .
• for gas discharge tubes : ionization time (ignition delay time / switch-on time / build-up time) and deionization time (recovery time / switch-off time) are relaxation times. Occurrence z. B. with: glow lamps , gas discharge tubes , barrier tubes , cold cathode relay tubes , thyratrons , ignitrons gas rectifiers / mercury vapor rectifiers and counter tubes , as well as high pressure lamps and high pressure lamps and flash tubes . The usual ionization time for cold cathode tubes with / without auxiliary discharge is below 0.1 ms / significantly above 0.1 ms. The deionization time is between 0.1 and 10 ms, if high currents have previously flowed it is also higher. Because of the longer deionization time (switch-off time), this mostly determines the cut-off frequency of a gas discharge tube. The cut-off frequency of cold cathode tubes is usually in the range of 0.5 to 2 kHz. With gas-filled counter tubes for radioactivity , the deionization time determines the maximum possible counting frequency.
• for semiconductor components :
  • for diodes : blocking delay time ( reverse recovery time ) and the associated maximum operating frequency ${\displaystyle t_{rr}}$ ${\displaystyle f_{G}}$
  • for thyristors and triacs : ignition delay time or the identical switch-on time ; and the off time or the identical recovery time ${\displaystyle t_{gd}}$ ${\displaystyle t_{\text{on}}}$ ${\displaystyle t_{\text{off}}}$ ${\displaystyle t_{q}}$
  • for bipolar transistors : switch-on time , which is made up of the additive delay time and rise time; as well as the switch-off time , which is made up of the storage time and fall time ${\displaystyle t_{\text{on}}}$ ${\displaystyle t_{a}}$ ${\displaystyle t_{r}}$ ${\displaystyle t_{\text{off}}}$ ${\displaystyle t_{s}}$ ${\displaystyle t_{f}}$
• Time constant in control technology , especially for real PID controllers with a first-order delay element ${\displaystyle T_{P}}$

Other meanings

In solid-state physics and surface chemistry , the existence of changed atomic distances on or near the solid-state surface is referred to as (surface) relaxation . This is not a dynamic relaxation process in the sense of the description given above.

Remarks

1. ↑ The distinction between "relaxation time" and "relaxation time constant" is useful, since in experiments for observing or quantifying the relaxation, the freely selectable duration during which a system is allowed to relax is referred to as the "relaxation time".
2. ↑ Since a system that strives towards its equilibrium value asymptotically (e.g. exponentially) needs an infinite amount of time until equilibrium is fully established, this duration is not defined as the relaxation time, but the period after which a certain percentage value of the equilibrium value is reached.

literature

• Ernst Schmutzer : Basics of Theoretical Physics . 3rd revised edition. Wiley-VCH-Verlag, Weinheim 2005, ISBN 3-527-40555-0 , pp. 1911–1913 ( limited preview in Google Book Search).
• Hans-Albert Kurzhals (Ed.): Lexicon of food technology . B. Behr's Verlag, Hamburg 2003, ISBN 3-86022-973-7 , p. 904 ( limited preview in Google Book search).
• Klaus Dransfeld , Paul Kienle , Georg Michael Kalvius : Physics I. Mechanics and heat . 10th, revised and expanded edition. Oldenbourg Wissenschaftsverlag, Munich 2005, ISBN 3-486-57810-3 , p. 314–315 ( limited preview in Google Book search).

Individual evidence

1. ↑ Hans Keune: "chimica, Ein Wissensspeicher", Volume II, VEB Deutscher Verlag für Grundstoffindindustrie Leipzig, 1972, conductivity coefficient p. 148.
2. ↑ Heinz Greif: cold cathode, VEB Verlag Technik Berlin, 1970, GDR, S. 34 and S. 43
3. ↑ ddv1, A-ZZY, diode comparison table and data dictionary, ECA GmbH Munich, 1993, pp. "1-7"
4. ↑ tht thyristors AZ-60000, comparison table and data dictionary, ECA GmbH Munich, 1988, p. "1-8"
5. ↑ tdv1 A-BUZ transistors, comparison table and data dictionary, ECA GmbH Munich, 1991, pp. "1-7" and "1-8"