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Sunday, August 31, 2025

Wind turbine design

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Wind_turbine_design

Wind turbine design is the process of defining the form and configuration of a wind turbine to extract energy from the wind. An installation consists of the systems needed to capture the wind's energy, point the turbine into the wind, convert mechanical rotation into electrical power, and other systems to start, stop, and control the turbine.

In 1919, German physicist Albert Betz showed that for a hypothetical ideal wind-energy extraction machine, the fundamental laws of conservation of mass and energy allowed no more than 16/27 (59.3%) of the wind's kinetic energy to be captured. This Betz' law limit can be approached by modern turbine designs which reach 70 to 80% of this theoretical limit.

In addition to the blades, design of a complete wind power system must also address the hub, controls, generator, supporting structure and foundation. Turbines must also be integrated into power grids.

Aerodynamics

Blade shape and dimension are determined by the aerodynamic performance required to efficiently extract energy, and by the strength required to resist forces on the blade.

The aerodynamics of a horizontal-axis wind turbine are not straightforward. The air flow at the blades is not the same as that away from the turbine. The way that energy is extracted from the air also causes air to be deflected by the turbine. Wind turbine aerodynamics at the rotor surface exhibit phenomena that are rarely seen in other aerodynamic fields.

Power control

Rotation speed must be controlled for efficient power generation and to keep the turbine components within speed and torque limits. The centrifugal force on the blades increases as the square of the rotation speed, which makes this structure sensitive to overspeed. Because power increases as the cube of the wind speed, turbines must survive much higher wind loads (such as gusts of wind) than those loads from which they generate power.

A wind turbine must produce power over a range of wind speeds. The cut-in speed is around 3–4 m/s for most turbines, and cut-out at 25 m/s. If the rated wind speed is exceeded the power has to be limited.

A control system involves three basic elements: sensors to measure process variables, actuators to manipulate energy capture and component loading, and control algorithms that apply information gathered by the sensors to coordinate the actuators.

Any wind blowing above the survival speed damages the turbine. The survival speed of commercial wind turbines ranges from 40 m/s (144 km/h, 89 MPH) to 72 m/s (259 km/h, 161 MPH), typically around 60 m/s (216 km/h, 134 MPH). Some turbines can survive 80 metres per second (290 km/h; 180 mph).

Stall

A stall on an airfoil occurs when air passes over it in such a way that the generation of lift rapidly decreases. Usually this is due to a high angle of attack (AOA), but can also result from dynamic effects. The blades of a fixed pitch turbine can be designed to stall in high wind speeds, slowing rotation. This is a simple fail-safe mechanism to help prevent damage. However, other than systems with dynamically controlled pitch, it cannot produce a constant power output over a large range of wind speeds, which makes it less suitable for large scale, power grid applications.

A fixed-speed HAWT (Horizontal Axis Wind Turbine) inherently increases its angle of attack at higher wind speed as the blades speed up. A natural strategy, then, is to allow the blade to stall when the wind speed increases. This technique was successfully used on many early HAWTs. However, the degree of blade pitch tended to increase noise levels.

Vortex generators may be used to control blade lift characteristics. VGs are placed on the airfoil to enhance the lift if they are placed on the lower (flatter) surface or limit the maximum lift if placed on the upper (higher camber) surface.

Furling

Furling works by decreasing the angle of attack, which reduces drag and blade cross-section. One major problem is getting the blades to stall or furl quickly enough in a wind gust. A fully furled turbine blade, when stopped, faces the edge of the blade into the wind.

Loads can be reduced by making a structural system softer or more flexible. This can be accomplished with downwind rotors or with curved blades that twist naturally to reduce angle of attack at higher wind speeds. These systems are nonlinear and couple the structure to the flow field - requiring design tools to evolve to model these nonlinearities.

Standard turbines all furl in high winds. Since furling requires acting against the torque on the blade, it requires some form of pitch angle control, which is achieved with a slewing drive. This drive precisely angles the blade while withstanding high torque loads. In addition, many turbines use hydraulic systems. These systems are usually spring-loaded, so that if hydraulic power fails, the blades automatically furl. Other turbines use an electric servomotor for every blade. They have a battery-reserve in case of grid failure. Small wind turbines (under 50 kW) with variable-pitching generally use systems operated by centrifugal force, either by flyweights or geometric design, and avoid electric or hydraulic controls.

Fundamental gaps exist in pitch control, limiting the reduction of energy costs, according to a report funded by the Atkinson Center for a Sustainable Future. Load reduction is currently focused on full-span blade pitch control, since individual pitch motors are the actuators on commercial turbines. Significant load mitigation has been demonstrated in simulations for blades, tower, and drive train. However, further research is needed to increase energy capture and mitigate fatigue loads.

A control technique applied to the pitch angle is done by comparing the power output with the power value at the rated engine speed (power reference, Ps reference). Pitch control is done with PI controller. In order to adjust pitch rapidly enough, the actuator uses the time constant Tservo, an integrator and limiters. The pitch angle remains from 0° to 30° with a change rate of 10°/second.

As in the figure at the right, the reference pitch angle is compared with the actual pitch angle b and then the difference is corrected by the actuator. The reference pitch angle, which comes from the PI controller, goes through a limiter. Restrictions are important to maintain the pitch angle in real terms. Limiting the change rate is especially important during network faults. The importance is due to the fact that the controller decides how quickly it can reduce the aerodynamic energy to avoid acceleration during errors.

Other controls

Generator torque

Modern large wind turbines operate at variable speeds. When wind speed falls below the turbine's rated speed, generator torque is used to control the rotor speed to capture as much power as possible. The most power is captured when the tip speed ratio is held constant at its optimum value (typically between 6 and 7). This means that rotor speed increases proportional to wind speed. The difference between the aerodynamic torque captured by the blades and the applied generator torque controls the rotor speed. If the generator torque is lower, the rotor accelerates, and if the generator torque is higher, the rotor slows. Below rated wind speed, the generator torque control is active while the blade pitch is typically held at the constant angle that captures the most power, fairly flat to the wind. Above rated wind speed, the generator torque is typically held constant while the blade pitch is adjusted accordingly.

One technique to control a permanent magnet synchronous motor is field-oriented control. Field-oriented control is a closed loop strategy composed of two current controllers (an inner loop and cascading outer loop) necessary for controlling the torque, and one speed controller.

Constant torque angle control

In this control strategy the d axis current is kept at zero, while the vector current aligns with the q axis in order to maintain the torque angle at 90^o. This is a common control strategy because only the Iqs current must be controlled. The torque equation of the generator is a linear equation dependent only on the Iqs current.

So, the electromagnetic torque for Ids = 0 (we can achieve that with the d-axis controller) is now:

$T e = 3 / 2 p (λ p m I q s + (L d s - L q s) I d s I q s) = 3 / 2 p λ p m I q s$

Thus, the complete system of the machine side converter and the cascaded PI controller loops is given by the figure. The control inputs are the duty rations m_ds and m_qs, of the PWM-regulated converter. It displays the control scheme for the wind turbine in the machine side and simultaneously how the I_ds to zero (the torque equation is linear).

Yawing

Large turbines are typically actively controlled to face the wind direction measured by a wind vane situated on the back of the nacelle. By minimizing the yaw angle (the misalignment between wind and turbine pointing direction), power output is maximized and non-symmetrical loads minimized. However, since wind direction varies, the turbine does not strictly follow the wind and experiences a small yaw angle on average. The power output losses can be approximated to fall with (cos(yaw angle))³. Particularly at low-to-medium wind speeds, yawing can significantly reduce output, with wind common variations reaching 30°. At high wind speeds, wind direction is less variable.

Electrical braking

2kW Dynamic braking resistor for small wind turbine.

Braking a small turbine can be done by dumping energy from the generator into a resistor bank, converting kinetic energy into heat. This method is useful if the kinetic load on the generator is suddenly reduced or is too small to keep the turbine speed within its allowed limit.

Cyclically braking slows the blades, which increases the stalling effect and reducing efficiency. Rotation can be kept at a safe speed in faster winds while maintaining (nominal) power output. This method is usually not applied on large, grid-connected wind turbines.

Mechanical braking

A mechanical drum brake or disc brake stops rotation in emergency situations such as extreme gust events. The brake is a secondary means to hold the turbine at rest for maintenance, with a rotor lock system as primary means. Such brakes are usually applied only after blade furling and electromagnetic braking have reduced the turbine speed because mechanical brakes can ignite a fire inside the nacelle if used at full speed. Turbine load increases if the brake is applied at rated RPM.

Turbine size

Turbines come in size classes. The smallest, with power less than 10 kW are used in homes, farms and remote applications whereas intermediate wind turbines (10-250 kW ) are useful for village power, hybrid systems and distributed power. The world's largest wind turbine as of 2021 was Vestas' V236-15.0 MW turbine. The new design's blades offer the largest swept area in the world with three 115.5 metres (379 ft) blades giving a rotor diameter of 236 metres (774 ft). Ming Yang in China have announced a larger 16 MW design.

A person standing beside 15 m long blades.

For a given wind speed, turbine mass is approximately proportional to the cube of its blade-length. Wind power intercepted is proportional to the square of blade-length. The maximum blade-length of a turbine is limited by strength, stiffness, and transport considerations.

Labor and maintenance costs increase slower than turbine size, so to minimize costs, wind farm turbines are basically limited by the strength of materials, and siting requirements.

Low temperature

Utility-scale wind turbine generators have minimum temperature operating limits that apply in areas with temperatures below −20 °C (−4 °F). Turbines must be protected from ice accumulation that can make anemometer readings inaccurate and which, in certain turbine control designs, can cause high structure loads and damage. Some turbine manufacturers offer low-temperature packages at extra cost, which include internal heaters, different lubricants, and different alloys for structural elements. If low-temperatures are combined with a low-wind condition, the turbine requires an external supply of power, equivalent to a few percent of its rated output, for internal heating. For example, the St. Leon Wind Farm in Manitoba, Canada, has a total rating of 99 MW and is estimated to need up to 3 MW (around 3% of capacity) of station service power a few days a year for temperatures down to −30 °C (−22 °F).

Nacelle

The nacelle houses the gearbox and generator connecting the tower and rotor. Sensors detect the wind speed and direction, and motors turn the nacelle into the wind to maximize output.

Gearbox

In conventional wind turbines, the blades spin a shaft that is connected through a gearbox to the generator. The gearbox converts the turning speed of the blades (15 to 20 RPM for a one-megawatt turbine) into the 1,800 (750-3600) RPM that the generator needs to generate electricity. Gearboxes are one of the more expensive components for installing and maintaining wind turbines. Analysts from GlobalData estimate that the gearbox market grew from $3.2bn in 2006 to $6.9bn in 2011. The market leader for Gearbox production was Winergy in 2011. The use of magnetic gearboxes has been explored as a way of reducing maintenance costs.

Generator

For large horizontal-axis wind turbines (HAWT), the generator is mounted in a nacelle at the top of a tower, behind the rotor hub. Older wind turbines generate electricity through asynchronous machines directly connected to the grid. The gearbox reduces generator cost and weight. Commercial generators have a rotor carrying a winding so that a rotating magnetic field is produced inside a set of windings called the stator. While the rotating winding consumes a fraction of a percent of the generator output, adjustment of the field current allows good control over the output voltage.

The rotor's varying output frequency and voltage can be matched to the fixed values of the grid using multiple technologies such as doubly fed induction generators or full-effect converters, which converts the variable frequency current to DC and then back to AC using inverters. Although such alternatives require costly equipment and cost power, the turbine can capture a significantly larger fraction of the wind energy. Most are low voltage 660 Volt, but some offshore turbines (several MW) are 3.3 kV medium voltage.

In some cases, especially when offshore, a large collector transformer converts the wind farm's medium-voltage AC grid to DC and transmits the energy through a power cable to an onshore HVDC converter station.

Hydraulic

Hydraulic wind turbines perform the frequency and torque adjustments of gearboxes via a pressurized hydraulic fluid. Typically, the action of the turbine pressurizes the fluid with a hydraulic pump at the nacelle. Meanwhile, components on the ground can transform this pressure into energy, and recirculate the working fluid. Typically, the working fluid used in this kind of hydrostatic transmission is oil, which serves as a lubricant, reducing losses due to friction in the hydraulic units and allowing for a broad range of operating temperatures. However, other concepts are currently under study, which involve using water as the working fluid because it is abundant and eco-friendly.

Hydraulic turbines provide benefits to both operation and capital costs. They can use hydraulic units with variable displacement to have a continuously variable transmission that adapts in real time. This decouples generator speed to rotor speed, avoiding stalling and allowing for operating the turbine at an optimum speed and torque. This built-in transmission is how these hydraulic systems avoid the need for a conventional gearbox. Furthermore, hydraulic instead of mechanical power conversion introduces a damping effect on rotation fluctuations, reducing fatigue of the drivetrain and improving turbine structural integrity. Additionally, using a pressurized fluid instead of mechanical components allows for the electrical conversion to occur on the ground instead of the nacelle: this reduces maintenance difficulty, and reduces weight and center of gravity of the turbine. Studies estimate that these benefits may yield to a 3.9-18.9% reduction in the levelized cost of power for offshore wind turbines.

Some years ago, Mitsubishi, through its branch Artemis, deployed the Sea Angel, a unique hydraulic wind turbine at the utility scale. The Digital Displacement technology underwent trials on the Sea Angel, a wind turbine rated at 7 MW. This design is capable of adjusting the displacement of the central unit in response to erratic wind velocities, thereby maintaining the optimal efficiency of the system. Still, these systems are newer and in earlier stages of commercialization compared to conventional gearboxes.

Gearless

Gearless wind turbines (also called direct drive) eliminate the gearbox. Instead, the rotor shaft is attached directly to the generator, which spins at the same speed as the blades.

Advantages of permanent magnet direct drive generators (PMDD) over geared generators include increased efficiency, reduced noise, longer lifetime, high torque at low RPM, faster and precise positioning, and drive stiffness. PMDD generators "eliminate the gear-speed increaser, which is susceptible to significant accumulated fatigue torque loading, related reliability issues, and maintenance costs".

To make up for a direct-drive generator's slower rotation rate, the diameter of the generator's rotor is increased so that it can contain more magnets to create the required frequency and power. Gearless wind turbines are often heavier than geared wind turbines. An EU study showed that gearbox reliability is not the main problem in wind turbines. The reliability of direct drive turbines offshore is still not known, given the small sample size.

Experts from Technical University of Denmark estimate that a geared generator with permanent magnets may require 25 kg/MW of the rare-earth element neodymium, while a gearless may use 250 kg/MW.

In December 2011, the US Department of Energy announced a critical shortage of rare-earth elements such as neodymium. China produces more than 95% of rare-earth elements, while Hitachi holds more than 600 patents covering neodymium magnets. Direct-drive turbines require 600 kg of permanent magnet material per megawatt, which translates to several hundred kilograms of rare-earth content per megawatt, as neodymium content is estimated to be 31% of magnet weight. Hybrid drivetrains (intermediate between direct drive and traditional geared) use significantly less rare-earth materials. While permanent magnet wind turbines only account for about 5% of the market outside of China, their market share inside of China is estimated at 25% or higher. In 2011, demand for neodymium in wind turbines was estimated to be 1/5 of that in electric vehicles.

Blades

Blade design

The ratio between the blade speed and the wind speed is called tip-speed ratio. High efficiency 3-blade-turbines have tip speed/wind speed ratios of 6 to 7. Wind turbines spin at varying speeds (a consequence of their generator design). Use of aluminum and composite materials has contributed to low rotational inertia, which means that newer wind turbines can accelerate quickly if the winds pick up, keeping the tip speed ratio more nearly constant. Operating closer to their optimal tip speed ratio during energetic gusts of wind allows wind turbines to improve energy capture from sudden gusts.

Noise increases with tip speed. To increase tip speed without increasing noise would reduce torque into the gearbox and generator, reducing structural loads, thereby reducing cost. The noise reduction is linked to the detailed blade aerodynamics, especially factors that reduce abrupt stalling. The inability to predict stall restricts the use of aggressive aerodynamics. Some blades (mostly on Enercon) have a winglet to increase performance and reduce noise.

A blade can have a lift-to-drag ratio of 120, compared to 70 for a sailplane and 15 for an airliner. In order to optimize the lift-to-drag ratio of a blade, they are typically designed with varying airfoil cross-sections along their length, customized to the varying wind speeds and angles encountered from root to tip.

An additional design improvement is the incorporation of vortex generators, small fins mounted to the surface of the blade, the help to smooth the airflow, preventing flow separation and reducing turbulence, both of which contribute to reducing energy losses. All of these innovations have the end goal of increasing the efficiency of converting wind energy to electricity.

Applications of IMU in Wind Power Generation

Blade Dynamic Deformation and Load Monitoring

The role of the Inertial Measurement Unit (IMU) in wind power generation is to measure the three-axis acceleration and angular velocity of wind turbine blades, hubs, and tower tops in real-time. By using inertial navigation algorithms, it calculates the motion states (position, velocity, and attitude) of these components. IMU captures the global dynamic information of wind turbines and, through data fusion with Kalman filters and GNSS data, reduces cumulative errors. This enables high-precision estimation of blade deflection and loads, providing critical support for monitoring the operational loads of wind turbines.

IMUs measure angular velocity and acceleration, which, combined with navigation algorithms, capture the flexural attitude and positional changes of blades during operation in real time. Through the use of Kalman filters (KF) to fuse data from multiple IMUs, and based on rigid body geometric models and rotor angles, the position of each IMU is determined. Precision is further enhanced by compensating for differences between actual positions and the model.

GNSS Integration:

GNSS plays two key roles:

Time Synchronization: It provides a unified time reference for all IMUs, ensuring sensor data alignment.
Absolute Position Reference: By integrating IMU data, it limits drift errors, ensuring convergence and accuracy in IMU navigation solutions (position and attitude).

Structural Health Monitoring and Fault Prediction

IMU can be combined with other sensors (e.g., vibration and stress sensors) to improve fault detection sensitivity through multi-source data fusion. For example, IMUs installed on the turbine main shaft can extract tower acceleration signals through signal processing and use azimuth information to identify specific faults. Multi-sensor fusion technology can detect blade stress changes and crack risks, reducing downtime losses.

In 2021, Chinese researchers proposed an innovative multi-IMU data fusion algorithm for wind turbine blade dynamic deformation sensing. This algorithm uses a relative motion sensing fusion method that employs an improved Kalman filter and a feedback-based distributed structure to achieve multi-node data fusion.

High-Precision and Low-Precision IMU Collaboration:

High-precision IMUs (main nodes) are placed at the blade root base, serving as a global reference point to provide information on the overall torsional attitude and positional changes of the blade.
Low-precision IMUs (sub-nodes) are distributed at different positions along the blade, sensing local dynamic deformations.
Data from the high-precision IMU is filtered and fused to correct the measurement errors of low-precision IMUs, significantly improving the system's overall measurement accuracy and fault tolerance. Each sub-node independently processes local data, and redundant information is integrated through a global fusion layer to enhance fault tolerance. Even if a single IMU fails, the system can maintain high accuracy.

Application in Blade Dynamic Testing

During wind turbine blade dynamic testing, blades undergo continuous motion under external forces. By combining global reference data from high-precision IMUs with local measurements from low-precision IMUs, multi-node data fusion is achieved through a federated Kalman filter. This enables precise perception of the blade's flexural attitude and position in three-dimensional space.

Simulation results show that the fusion algorithm effectively reduces the measurement errors of low-precision IMUs, significantly decreasing the relative position and attitude errors of local blade nodes while maintaining the accuracy of high-precision IMU nodes. Particularly for complex motions at the blade's middle and tip, the fusion algorithm demonstrates strong robustness and accuracy.

Hub design

In simple designs, the blades are directly bolted to the hub and are unable to pitch, which leads to aerodynamic stall above certain windspeeds. In more sophisticated designs, they are bolted to the pitch bearing, which adjusts their angle of attack with the help of a pitch system according to the wind speed. Pitch control is performed by hydraulic or electric systems (battery or ultracapacitor). The pitch bearing is bolted to the hub. The hub is fixed to the rotor shaft, which drives the generator directly or through a gearbox.

Blade count

The number of blades is selected for aerodynamic efficiency, component costs, and system reliability. Noise emissions are affected by the location of the blades upwind or downwind of the tower and the rotor speed. Given that the noise emissions from the blades' trailing edges and tips vary by the 5th power of blade speed, a small increase in tip speed dramatically increases noise.

Wind turbines almost universally use either two or three blades. However, patents present designs with additional blades, such as Chan Shin's multi-unit rotor blade system. Aerodynamic efficiency increases with number of blades but with diminishing return. Increasing from one to two yields a six percent increase, while going from two to three yields an additional three percent. Further increasing the blade count yields minimal improvements and sacrifices too much in blade stiffness as the blades become thinner.

Theoretically, an infinite number of blades of zero width is the most efficient, operating at a high value of the tip speed ratio, but this is not practical.

Component costs affected by blade count are primarily for materials and manufacturing of the turbine rotor and drive train. Generally, the lower the number of blades, the lower the material and manufacturing costs. In addition, fewer blades allow higher rotational speed. Blade stiffness requirements to avoid tower interference limit blade thickness, but only when the blades are upwind of the tower; deflection in a downwind machine increases tower clearance. Fewer blades with higher rotational speeds reduce peak torque in the drive train, resulting in lower gearbox and generator costs.

System reliability is affected by blade count primarily through the dynamic loading of the rotor into the drive train and tower systems. While aligning the wind turbine to changes in wind direction (yawing), each blade experiences a cyclic load at its root end depending on blade position. However, these cyclic loads when combined at the drive train shaft are symmetrically balanced for three blades, yielding smoother operation during yaw. One or two blade turbines can use a pivoting teetered hub to nearly eliminate the cyclic loads into the drive shaft and system during yawing. In 2012, a Chinese 3.6 MW two-blade turbine was tested in Denmark.

Blade size

Increasing blade length pushed power generation from the single megawatt range to upwards of 10 megawatts. A larger area effectively increases tip-speed ratio at a given wind speed, thus increasing its energy extraction. Software such as HyperSizer (originally developed for spacecraft design) can be used to improve blade design.

As of 2015 the rotor diameters of onshore wind turbine blades reached 130 meters, while the diameter of offshore turbines reached 170 meters. In 2001, an estimated 50 million kilograms of fiberglass laminate were used in wind turbine blades.

Blade weight

An important goal is to control blade weight. Since blade mass scales as the cube of the turbine radius, gravity loading constrains systems with larger blades. Gravitational loads include axial and tensile/ compressive loads (top/bottom of rotation) as well as bending (lateral positions). The magnitude of these loads fluctuates cyclically and the edgewise moments (see below) are reversed every 180° of rotation. Typical rotor speeds and design life are ~10 and 20 years, respectively, with the number of lifetime revolutions on the order of 10^8. Considering wind, it is expected that turbine blades go through ~10^9 loading cycles.

Wind is another source of rotor blade loading. Lift causes bending in the flatwise direction (out of rotor plane) while airflow around the blade cause edgewise bending (in the rotor plane). Flaps bending involves tension on the pressure (upwind) side and compression on the suction (downwind) side. Edgewise bending involves tension on the leading edge and compression on the trailing edge.

Wind loads are cyclical because of natural variability in wind speed and wind shear (higher speeds at top of rotation).

Failure in ultimate loading of wind-turbine rotor blades exposed to wind and gravity loading is a failure mode that needs to be considered when the rotor blades are designed. The wind speed that causes bending of the rotor blades exhibits a natural variability, and so does the stress response in the rotor blades. Also, the resistance of the rotor blades, in terms of their tensile strengths, exhibits a natural variability. Given the increasing size of production wind turbines, blade failures are increasingly relevant when assessing public safety risks from wind turbines. The most common failure is the loss of a blade or part thereof. This has to be considered in the design.

In light of these failure modes and increasingly larger blade systems, researchers seek cost-effective materials with higher strength-to-mass ratios.

Blade materials

In general, materials should meet the following criteria:

wide availability and easy processing to reduce cost and maintenance
low weight or density to reduce gravitational forces
high strength to withstand wind and gravitational loading
high fatigue resistance to withstand cyclic loading
high stiffness to ensure stability of the optimal shape and orientation of the blade and clearance with the tower
high fracture toughness
the ability to withstand environmental impacts such as lightning strikes, humidity, and temperature

History

Wood and canvas sails were used on early windmills due to their low price, availability, and ease of manufacture. These materials, however, require frequent maintenance. Wood and canvas construction limits the airfoil shape to a flat plate, which has a relatively high ratio of drag to force captured (low aerodynamic efficiency) compared to solid airfoils. Construction of solid airfoil designs requires inflexible materials such as metals or composites.

Advances in turbine blade materials mirrored the progression of materials science as a broader subject. The first large turbine blades were predominantly made from metals like steel and aluminum due to their availability and robustness. However, their heavy weight and low flexibility restricted turbine size and decreased efficiency, requiring more energy to maintain blade rotation.

The wind energy sector eventually moved onto lighter materials, namely fiberglass, a marked improvement over the excessive weight of metals. However, fiberglass possessed its own set of disadvantages, notably durability and sustainability issues. They were susceptible to environmental damages including UV radiation and moisture, leading to delamination and loss of structural integrity. Additionally, fiberglass is difficult to recycle, making the end-of-life impact of fiberglass blades quite high.

As a response to these challenges, the wind energy industry looked to carbon fiber as a blade material, the specific stiffness and durability of which are greater than both metal and carbon fiber. The superior stiffness-to-weight ratio allows for the use of larger blades, increasing efficiency (see size section). In recent research, bio-based composites and nanostructure enhancements have been utilized to further reduce weight and increase strength and stiffness.

Polymer

The majority of commercialized wind turbine blades are made from fiber-reinforced polymers (FRPs), which are composites consisting of a polymer matrix and fibers. The long fibers provide longitudinal stiffness and strength, and the matrix provides fracture toughness, delamination strength, out-of-plane strength, and stiffness. Material indices based on maximizing power efficiency, high fracture toughness, fatigue resistance, and thermal stability are highest for glass and carbon fiber reinforced plastics (GFRPs and CFRPs).

In turbine blades, matrices such as thermosets or thermoplastics are used; as of 2017, thermosets are more common. These allow for the fibers to be bound together and add toughness. Thermosets make up 80% of the market, as they have lower viscosity, and also allow for low-temperature cure, both features contributing to ease of processing during manufacture. Thermoplastics offer recyclability that the thermosets do not, however their processing temperature and viscosity are much higher, limiting the product size and consistency, which are both important for large blades. Fracture toughness is higher for thermoplastics, but the fatigue behavior is worse.

Fiberglass-reinforced epoxy blades of Siemens SWT-2.3-101 wind turbines. The blade size of 49 meters is in comparison to a substation behind them at Wolfe Island Wind Farm.

Manufacturing blades in the 40 to 50-metre range involves proven fiberglass composite fabrication techniques. Manufacturers such as Nordex SE and GE Wind use an infusion process. Other manufacturers vary this technique, some including carbon and wood with fiberglass in an epoxy matrix. Other options include pre-impregnated ("prepreg") fiberglass and vacuum-assisted resin transfer moulding. Each of these options uses a glass-fiber reinforced polymer composite constructed with differing complexity. Perhaps the largest issue with open-mould, wet systems is the emissions associated with the volatile organic compounds ("VOCs") released. Preimpregnated materials and resin infusion techniques contain all VOCs, however these contained processes have their challenges, because the production of thick laminates necessary for structural components becomes more difficult. In particular, the preform resin permeability dictates the maximum laminate thickness; also, bleeding is required to eliminate voids and ensure proper resin distribution. One solution to resin distribution is to use partially impregnated fiberglass. During evacuation, the dry fabric provides a path for airflow and, once heat and pressure are applied, the resin may flow into the dry region, resulting in an evenly impregnated laminate structure.

Epoxy

Epoxy-based composites have environmental, production, and cost advantages over other resin systems. Epoxies also allow shorter cure cycles, increased durability, and improved surface finish. Prepreg operations further reduce processing time over wet lay-up systems. As turbine blades passed 60 metres, infusion techniques became more prevalent, because traditional resin transfer moulding injection times are too long compared to resin set-up time, limiting laminate thickness. Injection forces resin through a thicker ply stack, thus depositing the resin in the laminate structure before gelation occurs. Specialized epoxy resins have been developed to customize lifetimes and viscosity.

Carbon fiber-reinforced load-bearing spars can reduce weight and increase stiffness. Using carbon fibers in 60-metre turbine blades is estimated to reduce total blade mass by 38% and decrease cost by 14% compared to 100% fiberglass. Carbon fibers have the added benefit of reducing the thickness of fiberglass laminate sections, further addressing the problems associated with resin wetting of thick lay-up sections. Wind turbines benefit from the trend of decreasing carbon fiber costs.

Although glass and carbon fibers have many optimal qualities, their downsides include the fact that high filler fraction (10-70 wt%) causes increased density as well as microscopic defects and voids that can lead to premature failure.

Carbon nanotubes

Carbon nanotubes (CNTs) can reinforce polymer-based nanocomposites. CNTs can be grown or deposited on the fibers or added into polymer resins as a matrix for FRP structures. Using nanoscale CNTs as filler instead of traditional microscale filler (such as glass or carbon fibers) results in CNT/polymer nanocomposites, for which the properties can be changed significantly at low filler contents (typically < 5 wt%). They have low density and improve the elastic modulus, strength, and fracture toughness of the polymer matrix. The addition of CNTs to the matrix also reduces the propagation of interlaminar cracks.

Research on a low-cost carbon fiber (LCCF) at Oak Ridge National Laboratory gained attention in 2020, because it can mitigate the structural damage from lightning strikes. On glass fiber wind turbines, lightning strike protection (LSP) is usually added on top, but this is effectively deadweight in terms of structural contribution. Using conductive carbon fiber can avoid adding this extra weight.

Bio-composites

A significant concern in materials criteria for a turbine blade is its manufacturing and end-of-life environmental impact, as well its recyclability. While there are methods for manufacturing of fiberglass and carbon fiber composites into turbine blades have a lower carbon footprint than aluminum, for example, they still have a noticeable impact (30–100 kg CO₂ equivalent per kg). Additionally, fiberglass is incredibly difficult to recycle and carbon fiber composites, while possible to recycle, require additional research to yield fibers that are suitable for reusing as turbine materials (as opposed to the fibers being so degraded that they are only suitable for downcycling). The development of bio-composite materials with sufficient mechanical properties aims to address these issues.

Bio-composite materials use natural fibers and fillers as reinforcement instead of synthetic glass or carbon fibers. Approaches vary from partial to complete replacement of synthetics, with varying levels of success. Unfortunately, plant-based natural fibers, while having extremely low environmental impact, possess issues in their structural properties. Namely, they have high cellulosic content and large oxygen reaction sites, both of which contribute to issues in mechanical and thermal performance. As such, other natural fibers, such as non-moisture attractive basalt, have become the focus of bio-composite research.

Research

Some polymer composites feature self-healing properties. Since the blades of the turbine form cracks from fatigue due to repetitive cyclic stresses, self-healing polymers are attractive for this application, because they can improve reliability and buffer various defects such as delamination. Embedding paraffin wax-coated copper wires in a fiber reinforced polymer creates a network of tubes. Using a catalyst, these tubes and dicyclopentadiene (DCPD) then react to form a thermosetting polymer, which repairs the cracks as they form in the material. As of 2019, this approach is not yet commercial.

Further improvement is possible through the use of carbon nanofibers (CNFs) in the blade coatings. A major problem in desert environments is erosion of the leading edges of blades by sand-laden wind, which increases roughness and decreases aerodynamic performance. The particle erosion resistance of fiber-reinforced polymers is poor when compared to metallic materials and elastomers. Replacing glass fiber with CNF on the composite surface greatly improves erosion resistance. CNFs provide good electrical conductivity (important for lightning strikes), high damping ratio, and good impact-friction resistance.

For wind turbines, especially those offshore, or in wet environments, base surface erosion also occurs. For example, in cold climates, ice can build up on the blades and increase roughness. At high speeds, this same erosion impact can occur from rainwater. A useful coating must have good adhesion, temperature tolerance, weather tolerance (to resist erosion from salt, rain, sand, etc.), mechanical strength, ultraviolet light tolerance, and have anti-icing and flame retardant properties. Along with this, the coating should be cheap and environmentally friendly.

Super hydrophobic surfaces (SHS) cause water droplets to bead, and roll off the blades. SHS prevents ice formation, up to -25 C, as it changes the ice formation process.; specifically, small ice islands form on SHS, as opposed to a large ice front. Further, due to the lowered surface area from the hydrophobic surface, aerodynamic forces on the blade allow these islands to glide off the blade, maintaining proper aerodynamics. SHS can be combined with heating elements to further prevent ice formation.

Lightning

Lightning damage over the course of a 25-year lifetime goes from surface level scorching and cracking of the laminate material, to ruptures in the blade or full separation in the adhesives that hold the blade together. It is most common to observe lightning strikes on the tips of the blades, especially in rainy weather due to embedded copper wiring. The most common method countermeasure, especially in non-conducting blade materials like GFRPs and CFRPs, is to add lightning "arresters", which are metallic wires that ground the blade, skipping the blades and gearbox entirely.

Blade repair

Wind turbine blades typically require repair after 2–5 years. Notable causes of blade damage comes from manufacturing defects, transportation, assembly, installation, lightning strikes, environmental wear, thermal cycling, leading edge erosion, or fatigue. Due to composite blade material and function, repair techniques found in aerospace applications often apply or provide a basis for basic repairs.

Depending on the nature of the damage, the approach of blade repairs can vary. Erosion repair and protection includes coatings, tapes, or shields. Structural repairs require bonding or fastening new material to the damaged area. Nonstructural matrix cracks and delaminations require fills and seals or resin injections. If ignored, minor cracks or delaminations can propagate and create structural damage.

Four zones have been identified with their respective repair needs:

Zone 1- the blade's leading edge. Requires erosion or crack repair.
Zone 2- close to the tip but behind the leading edge. Requires aeroelastic semi-structural repair.
Zone 3- Middle area behind the leading edge. Requires erosion repair.
Zone 4- Root and near root of the blade. Requires semi-structural or structural repairs

After the past few decades of rapid wind expansion across the globe, wind turbines are aging. This aging brings operation and maintenance(O&M) costs along with it, increasing as turbines approach their end of life. If damages to blades are not caught in time, power production and blade lifespan are decreased. Estimates project that 20-25% of the total levelized cost per kWh produced stems from blade O&M alone.

Blade recycling

The Global Wind Energy Council (GWEC) predicted that wind energy will supply 28.5% of global energy by 2030. This requires a newer and larger fleet of more efficient turbines and the corresponding decommissioning of older ones. Based on a European Wind Energy Association study, in 2010 between 110 and 140 kilotonnes of composites were consumed to manufacture blades. The majority of the blade material ends up as waste and requires recycling or downcycling. As of 2020, most end-of-use blades are stored or sent to landfills rather than recycled. It is also important to note that recent studies predict that nearly 52,000 tons of turbine blades are to be decommissioned every year until 2030. Typically, glass-fiber-reinforced polymers (GFRPs) comprise around 70% of the laminate material in the blade. GFRPs are not combustible and so hinder the incineration of combustible materials. The following methods are the major EOL paths for turbine blades, with methods varying depending on whether individual fibers are to be recovered and the requisite temperature/catalysts.

Mechanical recycling: This method doesn't recover individual fibers. Initial processes involve shredding, crushing, or milling. The crushed pieces are then separated into fiber-rich and resin-rich fractions. These fractions are ultimately incorporated into new composites either as fillers or reinforcements.
Pyrolysis: Thermal decomposition of the composites recovers individual fibers. For pyrolysis, the material is heated up to 500 °C in an environment without oxygen, causing it to break down into lower-weight organic substances and gaseous products. The glass fibers generally lose 50% of their strength and can be downcycled for fiber reinforcement applications in paints or concrete. This can recover up to approximately 19 MJ/kg at relatively high cost. It requires mechanical pre-processing, similar to that involved in purely mechanical recycling.
Solvolysis: This method involves the polymer matrix undergoing chemical decomposition via solvents including but not limited to acetone, nitric acid, ammonia, and alcohols. Advantages of solvolysis include a lower operation compared to pyrolysis and its ability to yield fibers with favorable surface and mechanical properties. Solvolysis has a significant number of operational considerations, including solvent flow, solvent diffusion, phase transitions, etc., that depend heavily on the polymer structure of the blades, which are notably heterogeneous and contain relatively high numbers of defects and voids. As such, current research focuses on computational modeling of solvolysis to allow for more complete and efficient recycling.
Direct structural recycling of composites: The general idea is to reuse the composite as is, without altering its chemical properties, which can be achieved especially for larger composite material parts by partitioning them into pieces that can be used directly in other applications.

Start-up company Global Fiberglass Solutions claimed in 2020 that it had a method to process blades into pellets and fiber boards for use in flooring and walls. The company started producing samples at a plant in Sweetwater, Texas.

Tower

Height

Wind velocities increase at higher altitudes due to surface aerodynamic drag (by land or water surfaces) and air viscosity. The variation in velocity with altitude, called wind shear, is most dramatic near the surface. Typically, the variation follows the wind profile power law, which predicts that wind speed rises proportionally to the seventh root of altitude. Doubling the altitude of a turbine, then, increases the expected wind speeds by 10% and the expected power by 34%. To avoid buckling, doubling the tower height generally requires doubling the tower diameter, increasing the amount of material by a factor of at least four. As of July 2025, the world's tallest wind turbine, at 300 metres (980 ft) hub height with 3.8 MW capacity, was under construction in Germany.

During the night, or when the atmosphere becomes stable, wind speed close to the ground usually subsides whereas at turbine hub altitude it does not decrease that much or may even increase. As a result, the wind speed is higher and a turbine will produce more power than expected from the 1/7 power law: doubling the altitude may increase wind speed by 20% to 60%. A stable atmosphere is caused by radiative cooling of the surface and is common in a temperate climate: it usually occurs when there is a (partly) clear sky at night. When the (high altitude) wind is strong (a 10-meter wind speed higher than approximately 6 to 7 m/s) the stable atmosphere is disrupted because of friction turbulence and the atmosphere turns neutral. A daytime atmosphere is either neutral (no net radiation; usually with strong winds and heavy clouding) or unstable (rising air because of ground heating—by the sun). The 1/7 power law is a good approximation of the wind profile. Indiana was rated as having a wind capacity of 30,000 MW, but by raising the expected turbine height from 50 m to 70 m raised the wind capacity to 40,000 MW, and could be double that at 100 m.

For HAWTs, tower heights approximately two to three times the blade length balance material costs of the tower against better utilisation of the more expensive active components.

Road restrictions make tower transport with a diameter of more than 4.3 m difficult. Swedish analyses showed that the bottom wing tip must be at least 30 m above the tree tops. A 3 MW turbine may increase output from 5,000 MWh to 7,700 MWh per year by rising from 80 to 125 meters. A tower profile made of connected shells rather than cylinders can have a larger diameter and still be transportable. A 100 m prototype tower with TC bolted 18 mm 'plank' shells at the wind turbine test center Høvsøre in Denmark was certified by Det Norske Veritas, with a Siemens nacelle. Shell elements can be shipped in standard 12 m shipping containers.

As of 2003, typical modern wind turbine installations used 65 metres (213 ft) towers. Height is typically limited by the availability of cranes. This led to proposals for "partially self-erecting wind turbines" that, for a given available crane, allow taller towers that locate a turbine in stronger and steadier winds, and "self-erecting wind turbines" that could be installed without cranes.

Materials

Currently, the majority of wind turbines are supported by conical tubular steel towers. These towers represent 30% – 65% of the turbine weight and therefore account for a large percentage of transport costs. The use of lighter tower materials could reduce the overall transport and construction cost, as long as stability is maintained. Higher grade S500 steel costs 20%-25% more than S355 steel (standard structural steel), but it requires 30% less material because of its improved strength. Therefore, replacing wind turbine towers with S500 steel offer savings in weight and cost.

Another disadvantage of conical steel towers is meeting the requirements of wind turbines taller than 90 meters. High performance concrete may increase tower height and increase lifetime. A hybrid of prestressed concrete and steel improves performance over standard tubular steel at tower heights of 120 meters. Concrete also allows small precast sections to be assembled on site. One downside of concrete towers is the higher CO
₂ emissions during concrete production. However, the overall environmental impact should be positive if concrete towers can double the wind turbine lifetime.

Wood is another alternative: a 100-metre tower supporting a 1.5 MW turbine operates in Germany. The wood tower shares the same transportation benefits of the segmented steel shell tower, but without the steel. A 2 MW turbine on a wooden tower started operating in Sweden in 2023.

Another approach is to form the tower on site via spiral welding rolled sheet steel. Towers of any height and diameter can be formed this way, eliminating restrictions driven by transport requirements. A factory can be built in one month. The developer claims 80% labor savings over conventional approaches.

Grid connection

Grid-connected wind turbines, until the 1970s, were fixed-speed. As recently as 2003, nearly all grid-connected wind turbines operated at constant speed (synchronous generators) or within a few percent of constant speed (induction generators). As of 2011, many turbines used fixed-speed induction generators (FSIG). By then, most newly connected turbines were variable speed.

Early control systems were designed for peak power extraction, also called maximum power point tracking—they attempted to pull the maximum power from a given wind turbine under the current wind conditions. More recent systems deliberately pull less than maximum power in most circumstances, in order to provide other benefits, which include:

Spinning reserves to produce more power when needed—such as when some other generator drops from the grid
Variable-speed turbines can transiently produce slightly more power than wind conditions support, by storing some energy as kinetic energy (accelerating during brief gusts of faster wind) and later converting that kinetic energy to electric energy (decelerating). either when more power is needed, or to compensate for variable windspeeds.
damping (electrical) subsynchronous resonances in the grid
damping (mechanical) tower resonances

The generator produces alternating current (AC). The most common method in large modern turbines is to use a doubly fed induction generator directly connected to the grid. Some turbines drive an AC/AC converter—which converts the AC to direct current (DC) with a rectifier and then back to AC with an inverter—in order to match grid frequency and phase.

A useful technique to connect a PMSG (Permanent Magnet Synchronous Generator) to the grid is via a back-to-back converter. Control schemes can achieve unity power factor in the connection to the grid. In that way the wind turbine does not consume reactive power, which is the most common problem with turbines that use induction machines. This leads to a more stable power system. Moreover, with different control schemes a PMSG turbine can provide or consume reactive power. So, it can work as a dynamic capacitor/inductor bank to help with grid stability.

The diagram shows the control scheme for a unity power factor :

Reactive power regulation consists of one PI controller in order to achieve operation with unity power factor (i.e. Q_grid = 0 ). I_dN has to be regulated to reach zero at steady-state (I_dNref = 0).

The complete system of the grid side converter and the cascaded PI controller loops is displayed in the figure.

Construction

As wind turbine usage has increased, so have companies that assist in the planning and construction of wind turbines. Most often, turbine parts are shipped via sea or rail, and then via truck to the installation site. Due to the massive size of the components involved, companies usually need to obtain transportation permits and ensure that the chosen trucking route is free of potential obstacles such as overpasses, bridges, and narrow roads. Groups known as "reconnaissance teams" will scout the way up to a year in advance as they identify problematic roads, cut down trees, and relocate utility poles. Turbine blades continue to increase in size, sometimes necessitating brand new logistical plans, as previously used routes may not allow a larger blade. Specialized vehicles known as Schnabel trailers are custom-designed to load and transport turbine sections: tower sections can be loaded without a crane and the rear end of the trailer is steerable, allowing for easier maneuvering. Drivers must be specially trained.

Foundations

Wind turbines, by their nature, are very tall, slender structures, and this can cause a number of issues when the structural design of the foundations are considered. The foundations for a conventional engineering structure are designed mainly to transfer the vertical load (dead weight) to the ground, generally allowing comparatively unsophisticated arrangement to be used. However, in the case of wind turbines, the force of the wind's interaction with the rotor at the top of the tower creates a strong tendency to tip the wind turbine over. This loading regime causes large moment loads to be applied to the foundations of a wind turbine. As a result, considerable attention needs to be given when designing the footings to ensure that the foundation will resist this tipping tendency.

One of the most common foundations for offshore wind turbines is the monopile, a single large-diameter (4 to 6 metres) tubular steel pile driven to a depth of 5-6 times the diameter of the pile into the seabed. The cohesion of the soil, and friction between the pile and the soil provide the necessary structural support for the wind turbine.

In onshore turbines the most common type of foundation is a gravity foundation, where a large mass of concrete spread out over a large area is used to resist the turbine loads. Wind turbine size & type, wind conditions and soil conditions at the site are all determining factors in the design of the foundation. Prestressed piles or rock anchors are alternative foundation designs that use much less concrete and steel.

Costs

A wind turbine is a complex and integrated system. Structural elements comprise the majority of the weight and cost. All parts of the structure must be inexpensive, lightweight, durable, and manufacturable, surviving variable loading and environmental conditions. Turbine systems with fewer failures require less maintenance, are lighter and last longer, reducing costs.

The major parts of a turbine divide as: tower 22%, blades 18%, gearbox 14%, generator 8%.

Specification

Turbine design specifications contain a power curve and availability guarantee. The wind resource assessment makes it possible to calculate commercial viability. Typical operating temperature range is −20 to 40 °C (−4 to 104 °F). In areas with extreme climate (like Inner Mongolia or Rajasthan) climate-specific versions are required.

Wind turbines can be designed and validated according to IEC 61400 standards.

RDS-PP (Reference Designation System for Power Plants) is a standardized system used worldwide to create structured hierarchy of wind turbine components. This facilitates turbine maintenance and operation cost, and is used during all stages of a turbine creation.

Carbon farming

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Carbon_farming

Carbon farming is a set of agricultural methods that aim to store carbon in the soil, crop roots, wood and leaves. The technical term for this is carbon sequestration. The overall goal of carbon farming is to create a net loss of carbon from the atmosphere. This is done by increasing the rate at which carbon is sequestered into soil and plant material. One option is to increase the soil's organic matter content. This can also aid plant growth, improve soil water retention capacity and reduce fertilizer use. Sustainable forest management is another tool that is used in carbon farming. Carbon farming is one component of climate-smart agriculture. It is also one way to remove carbon dioxide from the atmosphere.

Agricultural methods for carbon farming include adjusting how tillage and livestock grazing is done, using organic mulch or compost, working with biochar and terra preta, and changing the crop types. Methods used in forestry include reforestation and bamboo farming. As of 2016, variants of carbon farming reached hundreds of millions of hectares globally, of the nearly 5 billion hectares (1.2×10¹⁰ acres) of world farmland.

Carbon farming tends to be more expensive than conventional agricultural practices. Depending on the region, carbon farmings costs US$3-130 per tonne of carbon dioxide sequestered. Some countries provide subsidies to farmers to use carbon farming methods. While the implementation of carbon farming methods can reduce/sequester emissions, it is important to also consider the effects of land use changes with respect to the conversion of forests to agricultural production.

Aims

The overall aim of carbon farming is to store carbon in the soil, crop roots, wood and leaves. It is one of several methods for carbon sequestration. It can be achieved by modification of agricultural practices because soil can act as an effective carbon sink and thus offset carbon dioxide emissions.

Agricultural sequestration practices may have positive effects on soil, air, and water quality, be beneficial to wildlife, and expand food production. On degraded croplands, an increase of one ton of soil carbon pool may increase crop yield by 20 to 40 kilograms per hectare of wheat, 10 to 20 kg/ha for maize, and 0.5 to 1 kg/ha for cowpeas.

Mechanism

Compared to natural vegetation, cropland soils are depleted in soil organic carbon (SOC). When a soil is converted from natural land or semi natural land, such as forests, woodlands, grasslands, steppes and savannas, the SOC content in the soil reduces by about 30–40%. The loss of carbon through agricultural practices can eventually lead to the loss of soil suitable for agriculture. The carbon loss from the soil is due to the removal of plant material containing carbon, via harvesting. When land use changes, soil carbon either increases or decreases. This change continues until the soil reaches a new equilibrium. Deviations from this equilibrium can also be affected by varying climate. The decrease can be counteracted by increasing carbon input. This can be done via several strategies, e.g. leaving harvest residues on the field, using manure or rotating perennial crops. Perennial crops have a larger below ground biomass fraction, which increases the SOC content. Globally, soils are estimated to contain >8,580 gigatons of organic carbon, about ten times the amount in the atmosphere and much more than in vegetation.

In part, soil carbon is thought to accumulate when decaying organic matter was physically mixed with soil. Small roots die and decay while the plant is alive, depositing carbon below the surface. More recently, the role of living plants has been emphasized where carbon is released as plants grow. Soils can contain up to 5% carbon by weight, including decomposing plant and animal matter and biochar.

About half of soil carbon is found within deep soils. About 90% of this is stabilized by mineral–organic associations.

Scale

Carbon farming can offset as much as 20% of 2010 carbon dioxide emissions annually. As of 2016, variants of carbon farming reached hundreds of millions of hectares globally, of the nearly 5 billion hectares (1.2×10¹⁰ acres) of world farmland.

However, the effects of soil sequestration can be reversed. If the soil is disrupted or intensive tillage practices are used, the soil becomes a net source of greenhouse gases. Typically after several decades of sequestration, the soil becomes saturated and ceases to absorb carbon. This implies that there is a global limit to the amount of carbon that soil can hold.

Methods used in agriculture

All crops absorb CO
₂ during growth and release it after harvest. The goal of agricultural carbon removal is to use the crop and its relation to the carbon cycle to permanently sequester carbon within the soil. This is done by selecting farming methods that return biomass to the soil and enhance the conditions in which the carbon within the plants will be reduced to its elemental nature and stored in a stable state. Methods for accomplishing this include:

Use cover crops such as grasses and weeds as a temporary cover between planting seasons
Concentrate livestock in small paddocks for days at a time so they graze lightly but evenly. This encourages roots to grow deeper into the soil. Stock also till the soil with their hooves, grinding old grass and manures into the soil.
Cover bare paddocks with hay or dead vegetation. This protects soil from the sun and allows the soil to hold more water and be more attractive to carbon-capturing microbes.
Restore degraded, marginal, and abandoned land, which slows carbon release while returning the land to agriculture or other use. Degraded land with low soil carbon pool has particularly high potential to store soil carbon, which can be farther enhanced by proper selection of vegetation.

Adjusting livestock grazing

Livestock, like all animals, are net producers of carbon. Ruminants like cows and sheep produce not only CO₂, but also methane due to the microbes residing in their digestive system. A small amount of carbon may be sequestered in grassland soils through root exudates and manure. By regularly rotating the herd through multiple paddocks (as often as daily) the paddocks can rest/recover between grazing periods. This pattern produces stable grasslands with significant fodder. Annual grasses have shallower roots and die once they are grazed. Rotational grazing leads to the replacement of annuals by perennials with deeper roots, which can recover after grazing. By contrast, allowing animals to range over a large area for an extended period can destroy the grassland.

Silvopasture involves grazing livestock under tree cover, with trees separated enough to allow adequate sunlight to nourish the grass. For example, a farm in Mexico planted native trees on a paddock spanning 22 hectares (54 acres). This evolved into a successful organic dairy. The operation became a subsistence farm, earning income from consulting/training others rather than from crop production.

However, many researchers have argued argue the approach is unable to provide the benefits claimed. Moreover, several peer-reviewed studies have found that excluding livestock completely from semi-arid grasslands can lead to significant recovery of vegetation and soil carbon sequestration.

Adjusting tillage

Carbon farming minimizes disruption to soils over the planting/growing/harvest cycle. Tillage is avoided using seed drills or similar techniques. Livestock can trample and/or eat the remains of a harvested field. The reduction or complete halt of tilling will create an increase in the soil carbon concentrations of topsoil allowing for regeneration of the soil. Plowing splits soil aggregates and allows microorganisms to consume their organic compounds. The increased microbial activity releases nutrients, initially boosting yield. Thereafter the loss of structure reduces soil's ability to hold water and resist erosion, thereby reducing yield.

Using organic mulch and compost

Mulching covers the soil around plants with a mulch of wood chips or straw. Alternatively, crop residue can be left in place to enter the soil as it decomposes.

Compost sequesters carbon in a stable (not easily accessed) form. Carbon farmers spread it over the soil surface without tilling. A 2013 study found that a single compost application significantly and durably increased grassland carbon storage by 25–70%. The continuation sequestration likely came from increased water-holding and "fertilization" by compost decomposition. Both factors support increased productivity. Both tested sites showed large increases in grassland productivity: a forage increase of 78% in a drier valley site, while a wetter coastal site averaged an increase of 42%. CH
₄ and N
₂O and emissions did not increase significantly. Methane fluxes were negligible. Soil N
₂O emissions from temperate grasslands amended with chemical fertilizers and manures were orders of magnitude higher. Another study found that grasslands treated with .5" of commercial compost began absorbing carbon at an annual rate of nearly 1.5 tons/acre and continued to do so in subsequent years. As of 2018, this study had not been replicated.

Working with biochar and terra preta

Mixing anaerobically burned biochar into soil sequesters approximately 50% of the carbon in the biomass. Globally up to 12% of the anthropogenic carbon emissions from land use change (0.21 gigatonnes) can be off-set annually in soil, if slash-and-burn is replaced by slash-and-char. Agriculture and forestry wastes could add some 0.16 gigatonnes/year. Biofuel production using modern biomass can produce a bio-char by-product through pyrolysis sequestering 30.6 kg for each gigajoule of energy produced. Soil-sequestered carbon is easily and verifiably measured.

Adjusting crop type

Cover crops are fast-growing species planted to protect soils from wind and water erosion during the off-growing season. The cover crop may be incorporated into the soil to increase soil organic matter. Legume cover crops can also produce a small amount of nitrogen. The carbon content of a soil should not be increased without also ensuring that the relative amount of nitrogen also increases to maintain a healthy soil ecosystem.

Perennial crops offer potential to sequester carbon when grown in multilayered systems. One system uses perennial staple crops that grow on trees that are analogs to maize and beans, or vines, palms and herbaceous perennials.

Methods used in forestry

Reforestation

Forestry and agriculture are both land-based human activities that add up to contribute approximately a third of the world's greenhouse gas emissions. There is a large interest in reforestation, but in regards to carbon farming most of that reforestation opportunity will be in small patches with trees being planted by individual land owners in exchange for benefits provided by carbon farming programs. Forestry in carbon farming can be both reforestation, which is restoring forests to areas that were deforested, and afforestation which would be planting forests in areas that were not historically forested. Not all forests will sequester the same amount of carbon. Carbon sequestration is dependent on several factors which can include forest age, forest type, amount of biodiversity, the management practices the forest is experiences and climate. Biodiversity is often thought to be a side benefit of carbon farming, but in forest ecosystems increased biodiversity can increase the rate of carbon sequestration and can be a tool in carbon farming and not just a side benefit.

Bamboo farming

A bamboo forest will store less total carbon than most types of mature forest. However, it can store a similar total amount of carbon as rubber plantations and tree orchards, and can surpass the total carbon stored in agroforests, palm oil plantations, grasslands and shrublands. A bamboo plantation sequesters carbon at a faster rate than a mature forest or a tree plantation. However it has been found that only new plantations or plantations with active management will be sequestering carbon at a faster rate than mature forests. Compared with other fast-growing tree species, bamboo is only superior in its ability to sequester carbon if selectively harvested. Bamboo forests are especially high in potential for carbon sequestration if the cultivated plant material is turned into durable products that keep the carbon in the plant material for a long period because bamboo is both fast growing and regrows strongly following an annual harvest.

While bamboo has the ability to store carbon as biomass in cultivated material, more than half of the carbon sequestration from bamboo will be stored as carbon in the soil. Carbon that is sequestered into the soil by bamboo is stored by the rhizomes and roots which is biomass that will remain in the soil after plant material above the soil is harvested and stored long-term. Bamboo can be planted in sub-optimal land unsuitable for cultivating other crops and the benefits would include not only carbon sequestration but improving the quality of the land for future crops and reducing the amount of land subject to deforestation. The use of carbon emission trading is also available to farmers who use bamboo to gain carbon credit in otherwise uncultivated land. Therefore, the farming of bamboo timber may have significant carbon sequestration potential.

Costs and financial incentives

Many factors affect the costs of carbon sequestration including soil quality, transaction costs and various externalities such as leakage and unforeseen environmental damage. Because reduction of atmospheric CO
₂ is a long-term concern, farmers can be reluctant to adopt more expensive agricultural techniques when there is not a clear crop, soil, or economic benefit.

Carbon farming methods might have additional costs. Individual land owners are sometimes given incentives to use carbon farming methods through government policies. Governments in Australia and New Zealand are considering allowing farmers to sell carbon credits once they document that they have sufficiently increased soil carbon content.

Approved practices may make farmers eligible for federal funds. Not all carbon farming techniques have been recommended.

Challenges

Carbon farming is not without its challenges or disadvantages. When ecosystem restoration is used as a form of carbon farming, there can be a lack of knowledge that is disadvantageous in project planning. Ecosystem services are often a side benefit of restoring ecosystems along with carbon farming, but often ecosystem services are ignored in project planning because, unlike carbon sequestration, is not a global commodity that can be traded. If and how carbon farming's additional sequestration methods can affect ecosystem services should be researched to determine how different methods and strategies will impact the value an ecosystem service in particular areas. One concern to note is that if policy and incentives are only aimed towards carbon sequestration, then carbon farming could actually be harmful to ecosystems. Carbon farming could inadvertently cause an increase of land clearing and monocultures when species diversity is not a goal of the landscapes project, so there should be attempts to balance the goals of carbon farming and biodiversity should be attempted.

Critics say that the related regenerative agriculture cannot be adopted enough to matter or that it could lower commodity prices. The impact of increased soil carbon on yield has yet to be settled.

Another criticism says that no-till practices may increase herbicide use, diminishing or eliminating carbon benefits.

Composting is not an NRCS-approved technique and its impacts on native species and greenhouse emissions during production have not been fully resolved. Further, commercial compost supplies are too limited to cover large amounts of land.

Carbon farming may consider related issues such as groundwater and surface water degradation.

Related concepts

Climate-smart agriculture

Climate-smart agriculture (CSA) (or climate resilient agriculture) is a set of farming methods that has three main objectives with regards to climate change. Firstly, they use adaptation methods to respond to the effects of climate change on agriculture (this also builds resilience to climate change). Secondly, they aim to increase agricultural productivity and to ensure food security for a growing world population. Thirdly, they try to reduce greenhouse gas emissions from agriculture as much as possible (for example by following carbon farming approaches). Climate-smart agriculture works as an integrated approach to managing land. This approach helps farmers to adapt their agricultural methods (for raising livestock and crops) to the effects of climate change.

Blue carbon

Blue carbon is a concept within climate change mitigation that refers to "biologically driven carbon fluxes and storage in marine systems that are amenable to management". Most commonly, it refers to the role that tidal marshes, mangroves and seagrass meadows can play in carbon sequestration.These ecosystems can play an important role for climate change mitigation and ecosystem-based adaptation. However, when blue carbon ecosystems are degraded or lost, they release carbon back to the atmosphere, thereby adding to greenhouse gas emissions.

By country or region

Australia

In 2011 Australia started a cap-and-trade program. Farmers who sequester carbon can sell carbon credits to companies in need of carbon offsets. The country's Direct Action Plan states "The single largest opportunity for CO
₂ emissions reduction in Australia is through bio-sequestration in general, and in particular, the replenishment of our soil carbons." In studies of test plots over 20 years showed increased microbial activity when farmers incorporated organic matter or reduced tillage. Soil carbon levels from 1990 to 2006 declined by 30% on average under continuous cropping. Incorporating organic matter alone was not enough to build soil carbon. Nitrogen, phosphorus and sulphur had to be added as well to do so.

Canada

By 2014 more than 75% of Canadian Prairies' cropland had adopted "conservation tillage" and more than 50% had adopted no-till. Twenty-five countries pledged to adopt the practice at the December 2015 Paris climate talks. The Canadian government has allocated CAD$885M to spend between 2021-31 on adopting climate solutions in agriculture as part of the CAD$2B Natural Climate Solutions Fund.

France

The largest international effort to promote carbon farming is "four per 1,000", led by France. Its goal is to increase soil carbon by 0.4% per year through agricultural and forestry changes. In 2016, France implemented a cap on the amount of energy crops that could be used to produce biofuels to limit competition with food crop production. Cover crops are exempted from this cap in order to create a financial incentive to adopt cover cropping.

United States of America

In California multiple Resource Conservation Districts (RCDs) support local partnerships to develop and implement carbon farming, In 2015 the agency that administers California's carbon-credit exchange began granting credits to farmers who compost grazing lands. In 2016 Chevrolet partnered with the US Department of Agriculture (USDA) to purchase 40,000 carbon credits from ranchers on 11,000 no-till acres. The transaction equates to removing 5,000 cars from the road and was the largest to date in the US.^[26] In 2017 multiple US states passed legislation in support of carbon farming and soil health.

California appropriated $7.5 million as part of its Healthy Soils Program. The objective is to demonstrate that "specific management practices sequester carbon, improve soil health and reduce atmospheric greenhouse gases." The program includes mulching, cover crops, composting, hedgerows and buffer strips. Nearly half of California counties have farmers who are working on carbon-farming.
Maryland's Healthy Soils Program supports research, education and technical assistance.
Massachusetts funds education and training to support agriculture that regenerates soil health.
Hawaii created the Carbon Farming Task Force to develop incentives to increase soil carbon content. A 250-acre demonstration project attempted to produce biofuels from the pongamia tree. Pongamia adds nitrogen to the soil. Similarly, one ranch husbands 2,000 head of cattle on 4,000 acres, using rotational grazing to build soil, store carbon, restore hydrologic function and reduce runoff.

Other states are considering similar programs.

Saturday, August 30, 2025

Franck–Condon principle

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Franck%E2%80%93Condon_principle

The Franck–Condon principle describes the intensities of vibronic transitions, or the absorption or emission of a photon. It states that when a molecule is undergoing an electronic transition, such as ionization, the nuclear configuration of the molecule experiences no significant change.

Overview

**Figure 2.** Schematic representation of the absorption and fluorescence spectra corresponding to the energy diagram in Figure 1. The symmetry is due to the equal shape of the ground and excited state potential wells. The narrow lines can usually only be observed in the spectra of dilute gases. The darker curves represent the inhomogeneous broadening of the same transitions as occurs in liquids and solids. Electronic transitions between the lowest vibrational levels of the electronic states (the 0–0 transition) have the same energy in both absorption and fluorescence.

**Figure 3.** Semiclassical pendulum analogy of the Franck–Condon principle. Vibronic transitions are allowed at the classical turning points because both the momentum and the nuclear coordinates correspond in the two represented energy levels. In this illustration, the 0–2 vibrational transitions are favored.

The Franck–Condon principle has a well-established semiclassical interpretation based on the original contributions of James Franck. Electronic transitions are relatively instantaneous compared with the time scale of nuclear motions, therefore if the molecule is to move to a new vibrational level during the electronic transition, this new vibrational level must be instantaneously compatible with the nuclear positions and momenta of the vibrational level of the molecule in the originating electronic state. In the semiclassical picture of vibrations (oscillations) of a simple harmonic oscillator, the necessary conditions can occur at the turning points, where the momentum is zero.

Classically, the Franck–Condon principle is the approximation that an electronic transition is most likely to occur without changes in the positions of the nuclei in the molecular entity and its environment. The resulting state is called a Franck–Condon state, and the transition involved, a vertical transition. The quantum mechanical formulation of this principle is that the intensity of a vibronic transition is proportional to the square of the overlap integral between the vibrational wavefunctions of the two states that are involved in the transition.

— IUPAC Compendium of Chemical Terminology, 2nd Edition (1997)

In the quantum mechanical picture, the vibrational levels and vibrational wavefunctions are those of quantum harmonic oscillators, or of more complex approximations to the potential energy of molecules, such as the Morse potential. Figure 1 illustrates the Franck–Condon principle for vibronic transitions in a molecule with Morse-like potential energy functions in both the ground and excited electronic states. In the low temperature approximation, the molecule starts out in the v = 0 vibrational level of the ground electronic state and upon absorbing a photon of the necessary energy, makes a transition to the excited electronic state. The electron configuration of the new state may result in a shift of the equilibrium position of the nuclei constituting the molecule. In Figure 3 this shift in nuclear coordinates between the ground and the first excited state is labeled as q₀₁. In the simplest case of a diatomic molecule the nuclear coordinates axis refers to the internuclear separation. The vibronic transition is indicated by a vertical arrow due to the assumption of constant nuclear coordinates during the transition. The probability that the molecule can end up in any particular vibrational level is proportional to the square of the (vertical) overlap of the vibrational wavefunctions of the original and final state (see Quantum mechanical formulation section below). In the electronic excited state molecules quickly relax to the lowest vibrational level of the lowest electronic excitation state (Kasha's rule), and from there can decay to the electronic ground state via photon emission. The Franck–Condon principle is applied equally to absorption and to fluorescence.

The applicability of the Franck–Condon principle in both absorption and fluorescence, along with Kasha's rule leads to an approximate mirror symmetry shown in Figure 2. The vibrational structure of molecules in a cold, sparse gas is most clearly visible due to the absence of inhomogeneous broadening of the individual transitions. Vibronic transitions are drawn in Figure 2 as narrow, equally spaced Lorentzian line shapes. Equal spacing between vibrational levels is only the case for the parabolic potential of simple harmonic oscillators, in more realistic potentials, such as those shown in Figure 1, energy spacing decreases with increasing vibrational energy. Electronic transitions to and from the lowest vibrational states are often referred to as 0–0 (zero zero) transitions and have the same energy in both absorption and fluorescence.

Development of the principle

In a report published in 1926 in Transactions of the Faraday Society, James Franck was concerned with the mechanisms of photon-induced chemical reactions. The presumed mechanism was the excitation of a molecule by a photon, followed by a collision with another molecule during the short period of excitation. The question was whether it was possible for a molecule to break into photoproducts in a single step, the absorption of a photon, and without a collision. In order for a molecule to break apart, it must acquire from the photon a vibrational energy exceeding the dissociation energy, that is, the energy to break a chemical bond. However, as was known at the time, molecules will only absorb energy corresponding to allowed quantum transitions, and there are no vibrational levels above the dissociation energy level of the potential well. High-energy photon absorption leads to a transition to a higher electronic state instead of dissociation. In examining how much vibrational energy a molecule could acquire when it is excited to a higher electronic level, and whether this vibrational energy could be enough to immediately break apart the molecule, he drew three diagrams representing the possible changes in binding energy between the lowest electronic state and higher electronic states.

Diagram I. shows a great weakening of the binding on a transition from the normal state n to the excited states a and a'. Here we have D > D' and D' > D". At the same time the equilibrium position of the nuclei moves with the excitation to greater values of r. If we go from the equilibrium position (the minimum of potential energy) of the n curve vertically [emphasis added] upwards to the a curves in Diagram I. the particles will have a potential energy greater than D' and will fly apart. In this case we have a very great change in the oscillation energy on excitation by light...

— James Franck, 1926

James Franck recognized that changes in vibrational levels could be a consequence of the instantaneous nature of excitation to higher electronic energy levels and a new equilibrium position for the nuclear interaction potential. Edward Condon extended this insight beyond photoreactions in a 1926 Physical Review article titled "A Theory of Intensity Distribution in Band Systems".^[3] Here he formulates the semiclassical formulation in a manner quite similar to its modern form. The first joint reference to both Franck and Condon in regard to the new principle appears in the same 1926 issue of Physical Review in an article on the band structure of carbon monoxide by Raymond Birge.

Quantum mechanical formulation

Consider an electrical dipole transition from the initial vibrational state (υ) of the ground electronic level (ε), $| ϵ v ⟩$ , to some vibrational state (υ′) of an excited electronic state (ε′), $| ϵ^{'} v^{'} ⟩$ (see bra–ket notation). The molecular dipole operator μ is determined by the charge (−e) and locations (r_i) of the electrons as well as the charges (+Z_je) and locations (R_j) of the nuclei:

μ = μ_{e} + μ_{N} = - e \sum_{i} r_{i} + e \sum_{j} Z_{j} R_{j} .

The probability amplitude P for the transition between these two states is given by

P = ⟨ ψ^{'} | μ | ψ ⟩ = \int ψ^{' *} μ ψ d τ,

where $ψ$ and $ψ^{'}$ are, respectively, the overall wavefunctions of the initial and final state. The overall wavefunctions are the product of the individual vibrational (depending on spatial coordinates of the nuclei) and electronic space and spin wavefunctions:

ψ = ψ_{e} ψ_{v} ψ_{s} .

This separation of the electronic and vibrational wavefunctions is an expression of the Born–Oppenheimer approximation and is the fundamental assumption of the Franck–Condon principle. Combining these equations leads to an expression for the probability amplitude in terms of separate electronic space, spin and vibrational contributions:

P = ⟨ ψ_{e}^{'} ψ_{v}^{'} ψ_{s}^{'} | μ | ψ_{e} ψ_{v} ψ_{s} ⟩ = \int ψ_{e}^{' *} ψ_{v}^{' *} ψ_{s}^{' *} (μ_{e} + μ_{N}) ψ_{e} ψ_{v} ψ_{s} d τ

= \int ψ_{e}^{' *} ψ_{v}^{' *} ψ_{s}^{' *} μ_{e} ψ_{e} ψ_{v} ψ_{s} d τ + \int ψ_{e}^{' *} ψ_{v}^{' *} ψ_{s}^{' *} μ_{N} ψ_{e} ψ_{v} ψ_{s} d τ

= \underset{\binom{Franck–Condon}{factor}}{\underset{⏟}{\int ψ_{v}^{' *} ψ_{v} d τ_{n}}} \underset{\binom{orbital}{selection rule}}{\underset{⏟}{\int ψ_{e}^{' *} μ_{e} ψ_{e} d τ_{e}}} \underset{\binom{spin}{selection rule}}{\underset{⏟}{\int ψ_{s}^{' *} ψ_{s} d τ_{s}}} + \underset{0}{\underset{⏟}{\int ψ_{e}^{' *} ψ_{e} d τ_{e}}} \int ψ_{v}^{' *} μ_{N} ψ_{v} d τ_{v} \int ψ_{s}^{' *} ψ_{s} d τ_{s} .

The spin-independent part of the initial integral is here approximated as a product of two integrals:

\iint ψ_{v}^{' *} ψ_{e}^{' *} μ_{e} ψ_{e} ψ_{v} d τ_{e} d τ_{n} \approx \int ψ_{v}^{' *} ψ_{v} d τ_{n} \int ψ_{e}^{' *} μ_{e} ψ_{e} d τ_{e} .

This factorization would be exact if the integral $\int ψ_{e}^{' *} μ_{e} ψ_{e} d τ_{e}$ over the spatial coordinates of the electrons would not depend on the nuclear coordinates. However, in the Born–Oppenheimer approximation $ψ_{e}$ and $ψ_{e}^{'}$ do depend (parametrically) on the nuclear coordinates, so that the integral (a so-called transition dipole surface) is a function of nuclear coordinates. Since the dependence is usually rather smooth it is neglected (i.e., the assumption that the transition dipole surface is independent of nuclear coordinates, called the Condon approximation is often allowed).

The first integral after the plus sign is equal to zero because electronic wavefunctions of different states are orthogonal. Remaining is the product of three integrals. The first integral is the vibrational overlap integral, also called the Franck–Condon factor. The remaining two integrals contributing to the probability amplitude determine the electronic spatial and spin selection rules.

The Franck–Condon principle is a statement on allowed vibrational transitions between two different electronic states; other quantum mechanical selection rules may lower the probability of a transition or prohibit it altogether. Rotational selection rules have been neglected in the above derivation. Rotational contributions can be observed in the spectra of gases but are strongly suppressed in liquids and solids.

It should be clear that the quantum mechanical formulation of the Franck–Condon principle is the result of a series of approximations, principally the electrical dipole transition assumption and the Born–Oppenheimer approximation. Weaker magnetic dipole and electric quadrupole electronic transitions along with the incomplete validity of the factorization of the total wavefunction into nuclear, electronic spatial and spin wavefunctions means that the selection rules, including the Franck–Condon factor, are not strictly observed. For any given transition, the value of P is determined by all of the selection rules, however spin selection is the largest contributor, followed by electronic selection rules. The Franck–Condon factor only weakly modulates the intensity of transitions, i.e., it contributes with a factor on the order of 1 to the intensity of bands whose order of magnitude is determined by the other selection rules. The table below gives the range of extinction coefficients for the possible combinations of allowed and forbidden spin and orbital selection rules.

**Intensities of electronic transitions**
	Range of extinction coefficient (ε) values (mol⁻¹ cm⁻¹)
Spin and orbitally allowed	10³ to 10⁵
Spin allowed but orbitally forbidden	10⁰ to 10³
Spin forbidden but orbitally allowed	10⁻⁵ to 10⁰

Franck–Condon metaphors in spectroscopy

The Franck–Condon principle, in its canonical form, applies only to changes in the vibrational levels of a molecule in the course of a change in electronic levels by either absorption or emission of a photon. The physical intuition of this principle is anchored by the idea that the nuclear coordinates of the atoms constituting the molecule do not have time to change during the very brief amount of time involved in an electronic transition. However, this physical intuition can be, and is indeed, routinely extended to interactions between light-absorbing or emitting molecules (chromophores) and their environment. Franck–Condon metaphors are appropriate because molecules often interact strongly with surrounding molecules, particularly in liquids and solids, and these interactions modify the nuclear coordinates of the chromophore in ways closely analogous to the molecular vibrations considered by the Franck–Condon principle.

Franck–Condon principle for phonons

The closest Franck–Condon analogy is due to the interaction of phonons (quanta of lattice vibrations) with the electronic transitions of chromophores embedded as impurities in the lattice. In this situation, transitions to higher electronic levels can take place when the energy of the photon corresponds to the purely electronic transition energy or to the purely electronic transition energy plus the energy of one or more lattice phonons. In the low-temperature approximation, emission is from the zero-phonon level of the excited state to the zero-phonon level of the ground state or to higher phonon levels of the ground state. Just like in the Franck–Condon principle, the probability of transitions involving phonons is determined by the overlap of the phonon wavefunctions at the initial and final energy levels. For the Franck–Condon principle applied to phonon transitions, the label of the horizontal axis of Figure 1 is replaced in Figure 6 with the configurational coordinate for a normal mode. The lattice mode $q_{i}$ potential energy in Figure 6 is represented as that of a harmonic oscillator, and the spacing between phonon levels ( $ℏ Ω_{i}$ ) is determined by lattice parameters. Because the energy of single phonons is generally quite small, zero- or few-phonon transitions can only be observed at temperatures below about 40 kelvins.

See Zero-phonon line and phonon sideband for further details and references.

Franck–Condon principle in solvation

Franck–Condon considerations can also be applied to the electronic transitions of chromophores dissolved in liquids. In this use of the Franck–Condon metaphor, the vibrational levels of the chromophores, as well as interactions of the chromophores with phonons in the liquid, continue to contribute to the structure of the absorption and emission spectra, but these effects are considered separately and independently.

Consider chromophores surrounded by solvent molecules. These surrounding molecules may interact with the chromophores, particularly if the solvent molecules are polar. This association between solvent and solute is referred to as solvation and is a stabilizing interaction, that is, the solvent molecules can move and rotate until the energy of the interaction is minimized. The interaction itself involves electrostatic and van der Waals forces and can also include hydrogen bonds. Franck–Condon principles can be applied when the interactions between the chromophore and the surrounding solvent molecules are different in the ground and in the excited electronic state. This change in interaction can originate, for example, due to different dipole moments in these two states. If the chromophore starts in its ground state and is close to equilibrium with the surrounding solvent molecules and then absorbs a photon that takes it to the excited state, its interaction with the solvent will be far from equilibrium in the excited state. This effect is analogous to the original Franck–Condon principle: the electronic transition is very fast compared with the motion of nuclei—the rearrangement of solvent molecules in the case of solvation. We now speak of a vertical transition, but now the horizontal coordinate is solvent-solute interaction space. This coordinate axis is often labeled as "Solvation Coordinate" and represents, somewhat abstractly, all of the relevant dimensions of motion of all of the interacting solvent molecules.

In the original Franck–Condon principle, after the electronic transition, the molecules which end up in higher vibrational states immediately begin to relax to the lowest vibrational state. In the case of solvation, the solvent molecules will immediately try to rearrange themselves in order to minimize the interaction energy. The rate of solvent relaxation depends on the viscosity of the solvent. Assuming the solvent relaxation time is short compared with the lifetime of the electronic excited state, emission will be from the lowest solvent energy state of the excited electronic state. For small-molecule solvents such as water or methanol at ambient temperature, solvent relaxation time is on the order of some tens of picoseconds whereas chromophore excited state lifetimes range from a few picoseconds to a few nanoseconds. Immediately after the transition to the ground electronic state, the solvent molecules must also rearrange themselves to accommodate the new electronic configuration of the chromophore. Figure 7 illustrates the Franck–Condon principle applied to solvation. When the solution is illuminated by light corresponding to the electronic transition energy, some of the chromophores will move to the excited state. Within this group of chromophores there will be a statistical distribution of solvent-chromophore interaction energies, represented in the figure by a Gaussian distribution function. The solvent-chromophore interaction is drawn as a parabolic potential in both electronic states. Since the electronic transition is essentially instantaneous on the time scale of solvent motion (vertical arrow), the collection of excited state chromophores is immediately far from equilibrium. The rearrangement of the solvent molecules according to the new potential energy curve is represented by the curved arrows in Figure 7. Note that while the electronic transitions are quantized, the chromophore-solvent interaction energy is treated as a classical continuum due to the large number of molecules involved. Although emission is depicted as taking place from the minimum of the excited state chromophore-solvent interaction potential, significant emission can take place before equilibrium is reached when the viscosity of the solvent is high, or the lifetime of the excited state is short. The energy difference between absorbed and emitted photons depicted in Figure 7 is the solvation contribution to the Stokes shift.

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Saturday, August 30, 2025

Franck–Condon principle

Overview

Development of the principle

Quantum mechanical formulation

Franck–Condon metaphors in spectroscopy

Franck–Condon principle for phonons

Franck–Condon principle in solvation

Existence