Thermodynamic equations

From Wikipedia, the free encyclopedia

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

Thermodynamics is expressed by a mathematical framework of thermodynamic equations which relate various thermodynamic quantities and physical properties measured in a laboratory or production process. Thermodynamics is based on a fundamental set of postulates, that became the laws of thermodynamics.

Introduction

One of the fundamental thermodynamic equations is the description of thermodynamic work in analogy to mechanical work, or weight lifted through an elevation against gravity, as defined in 1824 by French physicist Sadi Carnot. Carnot used the phrase motive power for work. In the footnotes to his famous On the Motive Power of Fire, he states: “We use here the expression motive power to express the useful effect that a motor is capable of producing. This effect can always be likened to the elevation of a weight to a certain height. It has, as we know, as a measure, the product of the weight multiplied by the height to which it is raised.” With the inclusion of a unit of time in Carnot's definition, one arrives at the modern definition for power:

$${\displaystyle P=\frac{W}{t}=\frac{(mg)h}{t}}$$

During the latter half of the 19th century, physicists such as Rudolf Clausius, Peter Guthrie Tait, and Willard Gibbs worked to develop the concept of a thermodynamic system and the correlative energetic laws which govern its associated processes. The equilibrium state of a thermodynamic system is described by specifying its "state". The state of a thermodynamic system is specified by a number of extensive quantities, the most familiar of which are volume, internal energy, and the amount of each constituent particle (particle numbers). Extensive parameters are properties of the entire system, as contrasted with intensive parameters which can be defined at a single point, such as temperature and pressure. The extensive parameters (except entropy) are generally conserved in some way as long as the system is "insulated" to changes to that parameter from the outside. The truth of this statement for volume is trivial, for particles one might say that the total particle number of each atomic element is conserved. In the case of energy, the statement of the conservation of energy is known as the first law of thermodynamics.

A thermodynamic system is in equilibrium when it is no longer changing in time. This may happen in a very short time, or it may happen with glacial slowness. A thermodynamic system may be composed of many subsystems which may or may not be "insulated" from each other with respect to the various extensive quantities. If we have a thermodynamic system in equilibrium in which we relax some of its constraints, it will move to a new equilibrium state. The thermodynamic parameters may now be thought of as variables and the state may be thought of as a particular point in a space of thermodynamic parameters. The change in the state of the system can be seen as a path in this state space. This change is called a thermodynamic process. Thermodynamic equations are now used to express the relationships between the state parameters at these different equilibrium state.

The concept which governs the path that a thermodynamic system traces in state space as it goes from one equilibrium state to another is that of entropy. The entropy is first viewed as an extensive function of all of the extensive thermodynamic parameters. If we have a thermodynamic system in equilibrium, and we release some of the extensive constraints on the system, there are many equilibrium states that it could move to consistent with the conservation of energy, volume, etc. The second law of thermodynamics specifies that the equilibrium state that it moves to is in fact the one with the greatest entropy. Once we know the entropy as a function of the extensive variables of the system, we will be able to predict the final equilibrium state. (Callen 1985)

Notation

Some of the most common thermodynamic quantities are:

The conjugate variable pairs are the fundamental state variables used to formulate the thermodynamic functions.

p

Pressure

V

Volume

T

Temperature

S

Entropy

μ

Chemical potential

N

Particle number

The most important thermodynamic potentials are the following functions:

U

Internal energy

F

Helmholtz free energy

H

Enthalpy

G

Gibbs free energy

Thermodynamic systems are typically affected by the following types of system interactions. The types under consideration are used to classify systems as open systems, closed systems, and isolated systems.

δw

infinitesimal amount of Work (W)

δq

infinitesimal amount of Heat (Q)

m

mass

Common material properties determined from the thermodynamic functions are the following:

ρ

Density is defined as mass of material per unit volume

C_V

Heat capacity at constant volume

C_p

Heat capacity at constant pressure

β_T

Isothermal compressibility

β_S

Adiabatic compressibility

α

Coefficient of thermal expansion

The following constants are constants that occur in many relationships due to the application of a standard system of units.

k_B

Boltzmann constant

R

Ideal gas constant

N_A

Avogadro constant

Laws of thermodynamics

Main article: Laws of thermodynamics

The behavior of a thermodynamic system is summarized in the laws of Thermodynamics, which concisely are:

• Zeroth law of thermodynamics

If A, B, C are thermodynamic systems such that A is in thermal equilibrium with B and B is in thermal equilibrium with C, then A is in thermal equilibrium with C.

The zeroth law is of importance in thermometry, because it implies the existence of temperature scales. In practice, C is a thermometer, and the zeroth law says that systems that are in thermodynamic equilibrium with each other have the same temperature. The law was actually the last of the laws to be formulated.

• First law of thermodynamics

${\displaystyle dU=\delta Q-\delta W}$ where ${\displaystyle dU}$ is the infinitesimal increase in internal energy of the system, ${\displaystyle \delta Q}$ is the infinitesimal heat flow into the system, and ${\displaystyle \delta W}$ is the infinitesimal work done by the system.

The first law is the law of conservation of energy. The symbol ${\displaystyle \delta }$ instead of the plain d, originated in the work of German mathematician Carl Gottfried Neumann and is used to denote an inexact differential and to indicate that Q and W are path-dependent (i.e., they are not state functions). In some fields such as physical chemistry, positive work is conventionally considered work done on the system rather than by the system, and the law is expressed as ${\displaystyle dU=\delta Q+\delta W}$.

• Second law of thermodynamics

The entropy of an isolated system never decreases: ${\displaystyle dS\ge 0}$ for an isolated system.

A concept related to the second law which is important in thermodynamics is that of reversibility. A process within a given isolated system is said to be reversible if throughout the process the entropy never increases (i.e. the entropy remains unchanged).

• Third law of thermodynamics

${\displaystyle S=0}$ when ${\displaystyle T=0}$

The third law of thermodynamics states that at the absolute zero of temperature, the entropy is zero for a perfect crystalline structure.

• Onsager reciprocal relations – sometimes called the Fourth law of thermodynamics

${\displaystyle {\mathbf{J}}_u=L_{uu}\mathrm{\nabla }(1/T)-L_{ur}\mathrm{\nabla }(m/T)}$

${\displaystyle {\mathbf{J}}_r=L_{ru}\mathrm{\nabla }(1/T)-L_{rr}\mathrm{\nabla }(m/T)}$

The fourth law of thermodynamics is not yet an agreed upon law (many supposed variations exist); historically, however, the Onsager reciprocal relations have been frequently referred to as the fourth law.

The fundamental equation

Main article: Fundamental thermodynamic relation

See also: The fundamental equation

The first and second law of thermodynamics are the most fundamental equations of thermodynamics. They may be combined into what is known as fundamental thermodynamic relation which describes all of the changes of thermodynamic state functions of a system of uniform temperature and pressure. As a simple example, consider a system composed of a number of k  different types of particles and has the volume as its only external variable. The fundamental thermodynamic relation may then be expressed in terms of the internal energy as:

${\displaystyle dU=TdS-pdV+\sum _{i=1}^k{\mu }_{i}d{N}_i}$

Some important aspects of this equation should be noted: (Alberty 2001), (Balian 2003), (Callen 1985)

• The thermodynamic space has k+2 dimensions
• The differential quantities (U, S, V, N_i) are all extensive quantities. The coefficients of the differential quantities are intensive quantities (temperature, pressure, chemical potential). Each pair in the equation are known as a conjugate pair with respect to the internal energy. The intensive variables may be viewed as a generalized "force". An imbalance in the intensive variable will cause a "flow" of the extensive variable in a direction to counter the imbalance.
• The equation may be seen as a particular case of the chain rule. In other words:
  $${\displaystyle dU={\left(\frac{\mathrm{\partial }U}{\mathrm{\partial }S}\right)}_{V,\{N_i\}}dS+{\left(\frac{\mathrm{\partial }U}{\mathrm{\partial }V}\right)}_{S,\{N_i\}}dV+\sum _i{\left(\frac{\mathrm{\partial }U}{\mathrm{\partial }{N}_i}\right)}_{S,V,\{N_{j\ne i}\}}d{N}_i}$$

  
  from which the following identifications can be made:
  $${\displaystyle {\left(\frac{\mathrm{\partial }U}{\mathrm{\partial }S}\right)}_{V,\{N_i\}}=T}$$

  
  $${\displaystyle {\left(\frac{\mathrm{\partial }U}{\mathrm{\partial }V}\right)}_{S,\{N_i\}}=-p}$$

  
  $${\displaystyle {\left(\frac{\mathrm{\partial }U}{\mathrm{\partial }{N}_i}\right)}_{S,V,\{N_{j\ne i}\}}={\mu }_i}$$

  
  These equations are known as "equations of state" with respect to the internal energy. (Note - the relation between pressure, volume, temperature, and particle number which is commonly called "the equation of state" is just one of many possible equations of state.) If we know all k+2 of the above equations of state, we may reconstitute the fundamental equation and recover all thermodynamic properties of the system.
• The fundamental equation can be solved for any other differential and similar expressions can be found. For example, we may solve for ${\displaystyle dS}$ and find that
  $${\displaystyle {\left(\frac{\mathrm{\partial }S}{\mathrm{\partial }V}\right)}_{U,\{N_i\}}=\frac{p}{T}}$$

  

Thermodynamic potentials

Main article: Thermodynamic potential

By the principle of minimum energy, the second law can be restated by saying that for a fixed entropy, when the constraints on the system are relaxed, the internal energy assumes a minimum value. This will require that the system be connected to its surroundings, since otherwise the energy would remain constant.

By the principle of minimum energy, there are a number of other state functions which may be defined which have the dimensions of energy and which are minimized according to the second law under certain conditions other than constant entropy. These are called thermodynamic potentials. For each such potential, the relevant fundamental equation results from the same Second-Law principle that gives rise to energy minimization under restricted conditions: that the total entropy of the system and its environment is maximized in equilibrium. The intensive parameters give the derivatives of the environment entropy with respect to the extensive properties of the system.

The four most common thermodynamic potentials are:

Name	Symbol	Formula	Natural variables
Internal energy	${\displaystyle U}$	${\displaystyle \int \left(T\mathrm{d}S-p\mathrm{d}V+\sum _i{\mu }_i\mathrm{d}{N}_i\right)}$	${\displaystyle S,V,\{N_i\}}$
Helmholtz free energy	${\displaystyle F}$	${\displaystyle U-TS}$	${\displaystyle T,V,\{N_i\}}$
Enthalpy	${\displaystyle H}$	${\displaystyle U+pV}$	${\displaystyle S,p,\{N_i\}}$
Gibbs free energy	${\displaystyle G}$	${\displaystyle U+pV-TS}$	${\displaystyle T,p,\{N_i\}}$

After each potential is shown its "natural variables". These variables are important because if the thermodynamic potential is expressed in terms of its natural variables, then it will contain all of the thermodynamic relationships necessary to derive any other relationship. In other words, it too will be a fundamental equation. For the above four potentials, the fundamental equations are expressed as:

${\displaystyle dU\left(S,V,N_i\right)=TdS-pdV+\sum _i{\mu }_{i}d{N}_i}$

${\displaystyle dH\left(S,p,N_i\right)=TdS+Vdp+\sum _i{\mu }_{i}d{N}_i}$

${\displaystyle dF\left(T,V,N_i\right)=-SdT-pdV+\sum _i{\mu }_{i}d{N}_i}$

${\displaystyle dG\left(T,p,N_i\right)=-SdT+Vdp+\sum _i{\mu }_{i}d{N}_i}$

The thermodynamic square can be used as a tool to recall and derive these potentials.

First order equations

Main article: Equations of state - (general systems)

Main article: Equations of state (particular systems)

Just as with the internal energy version of the fundamental equation, the chain rule can be used on the above equations to find k+2 equations of state with respect to the particular potential. If Φ is a thermodynamic potential, then the fundamental equation may be expressed as:

${\displaystyle d\mathrm{\Phi }=\sum _i\frac{\mathrm{\partial }\mathrm{\Phi }}{\mathrm{\partial }{X}_i}d{X}_i}$

where the ${\displaystyle X_i}$ are the natural variables of the potential. If ${\displaystyle {\gamma }_i}$ is conjugate to ${\displaystyle X_i}$ then we have the equations of state for that potential, one for each set of conjugate variables.

${\displaystyle {\gamma }_i=\frac{\mathrm{\partial }\mathrm{\Phi }}{\mathrm{\partial }{X}_i}}$

Only one equation of state will not be sufficient to reconstitute the fundamental equation. All equations of state will be needed to fully characterize the thermodynamic system. Note that what is commonly called "the equation of state" is just the "mechanical" equation of state involving the Helmholtz potential and the volume:

${\displaystyle {\left(\frac{\mathrm{\partial }F}{\mathrm{\partial }V}\right)}_{T,\{N_i\}}=-p}$

For an ideal gas, this becomes the familiar PV=Nk_BT.

Euler integrals

See also: Euler integral (thermodynamics)

Because all of the natural variables of the internal energy U are extensive quantities, it follows from Euler's homogeneous function theorem that

${\displaystyle U=TS-pV+\sum _i{\mu }_i{N}_i}$

Substituting into the expressions for the other main potentials we have the following expressions for the thermodynamic potentials:

${\displaystyle F=-pV+\sum _i{\mu }_i{N}_i}$

${\displaystyle H=TS+\sum _i{\mu }_i{N}_i}$

${\displaystyle G=\sum _i{\mu }_i{N}_i}$

Note that the Euler integrals are sometimes also referred to as fundamental equations.

Gibbs–Duhem relationship

Main article: The Gibbs-Duhem relation

Differentiating the Euler equation for the internal energy and combining with the fundamental equation for internal energy, it follows that:

${\displaystyle 0=SdT-Vdp+\sum _i{N}_{i}d{\mu }_i}$

which is known as the Gibbs-Duhem relationship. The Gibbs-Duhem is a relationship among the intensive parameters of the system. It follows that for a simple system with r components, there will be r+1 independent parameters, or degrees of freedom. For example, a simple system with a single component will have two degrees of freedom, and may be specified by only two parameters, such as pressure and volume for example. The law is named after Willard Gibbs and Pierre Duhem.

Second order equations

There are many relationships that follow mathematically from the above basic equations. See Exact differential for a list of mathematical relationships. Many equations are expressed as second derivatives of the thermodynamic potentials (see Bridgman equations).

Maxwell relations

Maxwell relations are equalities involving the second derivatives of thermodynamic potentials with respect to their natural variables. They follow directly from the fact that the order of differentiation does not matter when taking the second derivative. The four most common Maxwell relations are:

${\displaystyle {\left(\frac{\mathrm{\partial }T}{\mathrm{\partial }V}\right)}_{S,N}=-{\left(\frac{\mathrm{\partial }p}{\mathrm{\partial }S}\right)}_{V,N}}$		${\displaystyle {\left(\frac{\mathrm{\partial }T}{\mathrm{\partial }p}\right)}_{S,N}={\left(\frac{\mathrm{\partial }V}{\mathrm{\partial }S}\right)}_{p,N}}$
${\displaystyle {\left(\frac{\mathrm{\partial }T}{\mathrm{\partial }V}\right)}_{p,N}=-{\left(\frac{\mathrm{\partial }p}{\mathrm{\partial }S}\right)}_{T,N}}$		${\displaystyle {\left(\frac{\mathrm{\partial }T}{\mathrm{\partial }p}\right)}_{V,N}={\left(\frac{\mathrm{\partial }V}{\mathrm{\partial }S}\right)}_{T,N}}$

The thermodynamic square can be used as a tool to recall and derive these relations.

Material properties

Main article: material properties (thermodynamics)

Second derivatives of thermodynamic potentials generally describe the response of the system to small changes. The number of second derivatives which are independent of each other is relatively small, which means that most material properties can be described in terms of just a few "standard" properties. For the case of a single component system, there are three properties generally considered "standard" from which all others may be derived:

• Compressibility at constant temperature or constant entropy
  $${\displaystyle {\beta }_{T\text{ or }S}=-\frac{1}{V}{\left(\frac{\mathrm{\partial }V}{\mathrm{\partial }p}\right)}_{T,N\text{ or }S,N}}$$

  
• Specific heat (per-particle) at constant pressure or constant volume
  $${\displaystyle c_{p\text{ or }V}=\frac{T}{N}{\left(\frac{\mathrm{\partial }S}{\mathrm{\partial }T}\right)}_{p\text{ or }V}}$$

  
• Coefficient of thermal expansion
  $${\displaystyle {\alpha }_p=\frac{1}{V}{\left(\frac{\mathrm{\partial }V}{\mathrm{\partial }T}\right)}_p}$$

  

These properties are seen to be the three possible second derivative of the Gibbs free energy with respect to temperature and pressure.

Thermodynamic property relations

Properties such as pressure, volume, temperature, unit cell volume, bulk modulus and mass are easily measured. Other properties are measured through simple relations, such as density, specific volume, specific weight. Properties such as internal energy, entropy, enthalpy, and heat transfer are not so easily measured or determined through simple relations. Thus, we use more complex relations such as Maxwell relations, the Clapeyron equation, and the Mayer relation.

Maxwell relations in thermodynamics are critical because they provide a means of simply measuring the change in properties of pressure, temperature, and specific volume, to determine a change in entropy. Entropy cannot be measured directly. The change in entropy with respect to pressure at a constant temperature is the same as the negative change in specific volume with respect to temperature at a constant pressure, for a simple compressible system. Maxwell relations in thermodynamics are often used to derive thermodynamic relations.

The Clapeyron equation allows us to use pressure, temperature, and specific volume to determine an enthalpy change that is connected to a phase change. It is significant to any phase change process that happens at a constant pressure and temperature. One of the relations it resolved to is the enthalpy of vaporization at a provided temperature by measuring the slope of a saturation curve on a pressure vs. temperature graph. It also allows us to determine the specific volume of a saturated vapor and liquid at that provided temperature. In the equation below, ${\displaystyle L}$ represents the specific latent heat, ${\displaystyle T}$ represents temperature, and ${\displaystyle \mathrm{\Delta }v}$ represents the change in specific volume.

${\displaystyle \frac{\mathrm{d}P}{\mathrm{d}T}=\frac{L}{T\mathrm{\Delta }v}}$

The Mayer relation states that the specific heat capacity of a gas at constant volume is slightly less than at constant pressure. This relation was built on the reasoning that energy must be supplied to raise the temperature of the gas and for the gas to do work in a volume changing case. According to this relation, the difference between the specific heat capacities is the same as the universal gas constant. This relation is represented by the difference between Cp and Cv:

Cp – Cv = R

 

Ionic compound

From Wikipedia, the free encyclopedia

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

 

The crystal structure of sodium chloride, NaCl, a typical ionic compound. The purple spheres represent sodium cations, Na⁺, and the green spheres represent chloride anions, Cl⁻. The yellow stipples show the electrostatic forces.

In chemistry, an ionic compound is a chemical compound composed of ions held together by electrostatic forces termed ionic bonding. The compound is neutral overall, but consists of positively charged ions called cations and negatively charged ions called anions. These can be simple ions such as the sodium (Na⁺) and chloride (Cl⁻) in sodium chloride, or polyatomic species such as the ammonium (NH⁺
₄) and carbonate (CO²⁻
₃) ions in ammonium carbonate. Individual ions within an ionic compound usually have multiple nearest neighbours, so are not considered to be part of molecules, but instead part of a continuous three-dimensional network. Ionic compounds usually form crystalline structures when solid.

Ionic compounds containing basic ions hydroxide (OH⁻) or oxide (O²⁻) are classified as bases. Ionic compounds without these ions are also known as salts and can be formed by acid–base reactions. Ionic compounds can also be produced from their constituent ions by evaporation of their solvent, precipitation, freezing, a solid-state reaction, or the electron transfer reaction of reactive metals with reactive non-metals, such as halogen gases.

Ionic compounds typically have high melting and boiling points, and are hard and brittle. As solids they are almost always electrically insulating, but when melted or dissolved they become highly conductive, because the ions are mobilized.

History of discovery

The word ion is the Greek ἰόν, ion, "going", the present participle of ἰέναι, ienai, "to go". This term was introduced by physicist and chemist Michael Faraday in 1834 for the then-unknown species that goes from one electrode to the other through an aqueous medium.

X-ray spectrometer developed by Bragg

In 1913 the crystal structure of sodium chloride was determined by William Henry Bragg and William Lawrence Bragg. This revealed that there were six equidistant nearest-neighbours for each atom, demonstrating that the constituents were not arranged in molecules or finite aggregates, but instead as a network with long-range crystalline order. Many other inorganic compounds were also found to have similar structural features. These compounds were soon described as being constituted of ions rather than neutral atoms, but proof of this hypothesis was not found until the mid-1920s, when X-ray reflection experiments (which detect the density of electrons), were performed.

Principal contributors to the development of a theoretical treatment of ionic crystal structures were Max Born, Fritz Haber, Alfred Landé, Erwin Madelung, Paul Peter Ewald, and Kazimierz Fajans.^[7] Born predicted crystal energies based on the assumption of ionic constituents, which showed good correspondence to thermochemical measurements, further supporting the assumption.

Formation

Halite, the mineral form of sodium chloride, forms when salty water evaporates leaving the ions behind.

Ionic compounds can be produced from their constituent ions by evaporation, precipitation, or freezing. Reactive metals such as the alkali metals can react directly with the highly electronegative halogen gases to form an ionic product. They can also be synthesized as the product of a high temperature reaction between solids.

If the ionic compound is soluble in a solvent, it can be obtained as a solid compound by evaporating the solvent from this electrolyte solution. As the solvent is evaporated, the ions do not go into the vapor, but stay in the remaining solution, and when they become sufficiently concentrated, nucleation occurs, and they crystallize into an ionic compound. This process occurs widely in nature and is the means of formation of the evaporite minerals. Another method of recovering the compound from solution involves saturating a solution at high temperature and then reducing the solubility by reducing the temperature until the solution is supersaturated and the solid compound nucleates.

Insoluble ionic compounds can be precipitated by mixing two solutions, one with the cation and one with the anion in it. Because all solutions are electrically neutral, the two solutions mixed must also contain counterions of the opposite charges. To ensure that these do not contaminate the precipitated ionic compound, it is important to ensure they do not also precipitate. If the two solutions have hydrogen ions and hydroxide ions as the counterions, they will react with one another in what is called an acid–base reaction or a neutralization reaction to form water. Alternately the counterions can be chosen to ensure that even when combined into a single solution they will remain soluble as spectator ions.

If the solvent is water in either the evaporation or precipitation method of formation, in many cases the ionic crystal formed also includes water of crystallization, so the product is known as a hydrate, and can have very different chemical properties.

Molten salts will solidify on cooling to below their freezing point. This is sometimes used for the solid-state synthesis of complex ionic compounds from solid reactants, which are first melted together. In other cases, the solid reactants do not need to be melted, but instead can react through a solid-state reaction route. In this method, the reactants are repeatedly finely ground into a paste and then heated to a temperature where the ions in neighboring reactants can diffuse together during the time the reactant mixture remains in the oven. Other synthetic routes use a solid precursor with the correct stoichiometric ratio of non-volatile ions, which is heated to drive off other species.

In some reactions between highly reactive metals (usually from Group 1 or Group 2) and highly electronegative halogen gases, or water, the atoms can be ionized by electron transfer, a process thermodynamically understood using the Born–Haber cycle.

Bonding

A schematic electron shell diagram of sodium and fluorine atoms undergoing a redox reaction to form sodium fluoride. Sodium loses its outer electron to give it a stable electron configuration, and this electron enters the fluorine atom exothermically. The oppositely charged ions – typically a great many of them – are then attracted to each other to form a solid.

 

Main article: Ionic bonding

Ions in ionic compounds are primarily held together by the electrostatic forces between the charge distribution of these bodies, and in particular, the ionic bond resulting from the long-ranged Coulomb attraction between the net negative charge of the anions and net positive charge of the cations. There is also a small additional attractive force from van der Waals interactions which contributes only around 1–2% of the cohesive energy for small ions. When a pair of ions comes close enough for their outer electron shells (most simple ions have closed shells) to overlap, a short-ranged repulsive force occurs, due to the Pauli exclusion principle. The balance between these forces leads to a potential energy well with minimum energy when the nuclei are separated by a specific equilibrium distance.

If the electronic structure of the two interacting bodies is affected by the presence of one another, covalent interactions (non-ionic) also contribute to the overall energy of the compound formed. Ionic compounds are rarely purely ionic, i.e. held together only by electrostatic forces. The bonds between even the most electronegative/electropositive pairs such as those in caesium fluoride exhibit a small degree of covalency. Conversely, covalent bonds between unlike atoms often exhibit some charge separation and can be considered to have a partial ionic character. The circumstances under which a compound will have ionic or covalent character can typically be understood using Fajans' rules, which use only charges and the sizes of each ion. According to these rules, compounds with the most ionic character will have large positive ions with a low charge, bonded to a small negative ion with a high charge. More generally HSAB theory can be applied, whereby the compounds with the most ionic character are those consisting of hard acids and hard bases: small, highly charged ions with a high difference in electronegativities between the anion and cation. This difference in electronegativities means that the charge separation, and resulting dipole moment, is maintained even when the ions are in contact (the excess electrons on the anions are not transferred or polarized to neutralize the cations).

Structure

The unit cell of the zinc blende structure

Ions typically pack into extremely regular crystalline structures, in an arrangement that minimizes the lattice energy (maximizing attractions and minimizing repulsions). The lattice energy is the summation of the interaction of all sites with all other sites. For unpolarizable spherical ions, only the charges and distances are required to determine the electrostatic interaction energy. For any particular ideal crystal structure, all distances are geometrically related to the smallest internuclear distance. So for each possible crystal structure, the total electrostatic energy can be related to the electrostatic energy of unit charges at the nearest neighboring distance by a multiplicative constant called the Madelung constant that can be efficiently computed using an Ewald sum. When a reasonable form is assumed for the additional repulsive energy, the total lattice energy can be modelled using the Born–Landé equation, the Born–Mayer equation, or in the absence of structural information, the Kapustinskii equation.

Using an even simpler approximation of the ions as impenetrable hard spheres, the arrangement of anions in these systems are often related to close-packed arrangements of spheres, with the cations occupying tetrahedral or octahedral interstices. Depending on the stoichiometry of the ionic compound, and the coordination (principally determined by the radius ratio) of cations and anions, a variety of structures are commonly observed, and theoretically rationalized by Pauling's rules.

Some ionic liquids, particularly with mixtures of anions or cations, can be cooled rapidly enough that there is not enough time for crystal nucleation to occur, so an ionic glass is formed (with no long-range order).

Defects

Frenkel defect

 

Schottky defect

 

See also: crystallographic defect

Within an ionic crystal, there will usually be some point defects, but to maintain electroneutrality, these defects come in pairs. Frenkel defects consist of a cation vacancy paired with a cation interstitial and can be generated anywhere in the bulk of the crystal, occurring most commonly in compounds with a low coordination number and cations that are much smaller than the anions. Schottky defects consist of one vacancy of each type, and are generated at the surfaces of a crystal, occurring most commonly in compounds with a high coordination number and when the anions and cations are of similar size. If the cations have multiple possible oxidation states, then it is possible for cation vacancies to compensate for electron deficiencies on cation sites with higher oxidation numbers, resulting in a non-stoichiometric compound. Another non-stoichiometric possibility is the formation of an F-center, a free electron occupying an anion vacancy. When the compound has three or more ionic components, even more defect types are possible. All of these point defects can be generated via thermal vibrations and have an equilibrium concentration. Because they are energetically costly but entropically beneficial, they occur in greater concentration at higher temperatures. Once generated, these pairs of defects can diffuse mostly independently of one another, by hopping between lattice sites. This defect mobility is the source of most transport phenomena within an ionic crystal, including diffusion and solid state ionic conductivity. When vacancies collide with interstitials (Frenkel), they can recombine and annihilate one another. Similarly, vacancies are removed when they reach the surface of the crystal (Schottky). Defects in the crystal structure generally expand the lattice parameters, reducing the overall density of the crystal. Defects also result in ions in distinctly different local environments, which causes them to experience a different crystal-field symmetry, especially in the case of different cations exchanging lattice sites. This results in a different splitting of d-electron orbitals, so that the optical absorption (and hence colour) can change with defect concentration.

Properties

Acidity/basicity

Ionic compounds containing hydrogen ions (H⁺) are classified as acids, and those containing electropositive cations and basic anions ions hydroxide (OH⁻) or oxide (O²⁻) are classified as bases. Other ionic compounds are known as salts and can be formed by acid–base reactions. If the compound is the result of a reaction between a strong acid and a weak base, the result is an acidic salt. If it is the result of a reaction between a strong base and a weak acid, the result is a basic salt. If it is the result of a reaction between a strong acid and a strong base, the result is a neutral salt. Weak acids reacted with weak bases can produce ionic compounds with both the conjugate base ion and conjugate acid ion, such as ammonium acetate.

Some ions are classed as amphoteric, being able to react with either an acid or a base. This is also true of some compounds with ionic character, typically oxides or hydroxides of less-electropositive metals (so the compound also has significant covalent character), such as zinc oxide, aluminium hydroxide, aluminium oxide and lead(II) oxide.

Melting and boiling points

Electrostatic forces between particles are strongest when the charges are high, and the distance between the nuclei of the ions is small. In such cases, the compounds generally have very high melting and boiling points and a low vapour pressure. Trends in melting points can be even better explained when the structure and ionic size ratio is taken into account. Above their melting point ionic solids melt and become molten salts (although some ionic compounds such as aluminium chloride and iron(III) chloride show molecule-like structures in the liquid phase). Inorganic compounds with simple ions typically have small ions, and thus have high melting points, so are solids at room temperature. Some substances with larger ions, however, have a melting point below or near room temperature (often defined as up to 100 °C), and are termed ionic liquids. Ions in ionic liquids often have uneven charge distributions, or bulky substituents like hydrocarbon chains, which also play a role in determining the strength of the interactions and propensity to melt.

Even when the local structure and bonding of an ionic solid is disrupted sufficiently to melt it, there are still strong long-range electrostatic forces of attraction holding the liquid together and preventing ions boiling to form a gas phase. This means that even room temperature ionic liquids have low vapour pressures, and require substantially higher temperatures to boil. Boiling points exhibit similar trends to melting points in terms of the size of ions and strength of other interactions. When vapourized, the ions are still not freed of one another. For example, in the vapour phase sodium chloride exists as diatomic "molecules".

Brittleness

Most ionic compounds are very brittle. Once they reach the limit of their strength, they cannot deform malleably, because the strict alignment of positive and negative ions must be maintained. Instead the material undergoes fracture via cleavage. As the temperature is elevated (usually close to the melting point) a ductile–brittle transition occurs, and plastic flow becomes possible by the motion of dislocations.

Compressibility

The compressibility of an ionic compound is strongly determined by its structure, and in particular the coordination number. For example, halides with the caesium chloride structure (coordination number 8) are less compressible than those with the sodium chloride structure (coordination number 6), and less again than those with a coordination number of 4.

Solubility

When ionic compounds dissolve, the individual ions dissociate and are solvated by the solvent and dispersed throughout the resulting solution. Because the ions are released into solution when dissolved, and can conduct charge, soluble ionic compounds are the most common class of strong electrolytes, and their solutions have a high electrical conductivity.

The aqueous solubility of a variety of ionic compounds as a function of temperature. Some compounds exhibiting unusual solubility behavior have been included.

The solubility is highest in polar solvents (such as water) or ionic liquids, but tends to be low in nonpolar solvents (such as petrol/gasoline). This is principally because the resulting ion–dipole interactions are significantly stronger than ion-induced dipole interactions, so the heat of solution is higher. When the oppositely charged ions in the solid ionic lattice are surrounded by the opposite pole of a polar molecule, the solid ions are pulled out of the lattice and into the liquid. If the solvation energy exceeds the lattice energy, the negative net enthalpy change of solution provides a thermodynamic drive to remove ions from their positions in the crystal and dissolve in the liquid. In addition, the entropy change of solution is usually positive for most solid solutes like ionic compounds, which means that their solubility increases when the temperature increases. There are some unusual ionic compounds such as cerium(III) sulfate, where this entropy change is negative, due to extra order induced in the water upon solution, and the solubility decreases with temperature.

Electrical conductivity

Although ionic compounds contain charged atoms or clusters, these materials do not typically conduct electricity to any significant extent when the substance is solid. In order to conduct, the charged particles must be mobile rather than stationary in a crystal lattice. This is achieved to some degree at high temperatures when the defect concentration increases the ionic mobility and solid state ionic conductivity is observed. When the ionic compounds are dissolved in a liquid or are melted into a liquid, they can conduct electricity because the ions become completely mobile. This conductivity gain upon dissolving or melting is sometimes used as a defining characteristic of ionic compounds.

In some unusual ionic compounds: fast ion conductors, and ionic glasses, one or more of the ionic components has a significant mobility, allowing conductivity even while the material as a whole remains solid. This is often highly temperature dependent, and may be the result of either a phase change or a high defect concentration. These materials are used in all solid-state supercapacitors, batteries, and fuel cells, and in various kinds of chemical sensors.

Colour

Anhydrous cobalt(II) chloride, CoCl₂

 

Cobalt(II) chloride hexahydrate, CoCl₂·6H₂O

 

See also: Color of chemicals

The colour of an ionic compound is often different from the colour of an aqueous solution containing the constituent ions, or the hydrated form of the same compound.

The anions in compounds with bonds with the most ionic character tend to be colorless (with an absorption band in the ultraviolet part of the spectrum). In compounds with less ionic character, their color deepens through yellow, orange, red, and black (as the absorption band shifts to longer wavelengths into the visible spectrum). 

The absorption band of simple cations shifts toward a shorter wavelength when they are involved in more covalent interactions. This occurs during hydration of metal ions, so colorless anhydrous ionic compounds with an anion absorbing in the infrared can become colorful in solution.

Uses

Ionic compounds have long had a wide variety of uses and applications. Many minerals are ionic. Humans have processed common salt (sodium chloride) for over 8000 years, using it first as a food seasoning and preservative, and now also in manufacturing, agriculture, water conditioning, for de-icing roads, and many other uses. Many ionic compounds are so widely used in society that they go by common names unrelated to their chemical identity. Examples of this include borax, calomel, milk of magnesia, muriatic acid, oil of vitriol, saltpeter, and slaked lime.

Soluble ionic compounds like salt can easily be dissolved to provide electrolyte solutions. This is a simple way to control the concentration and ionic strength. The concentration of solutes affects many colligative properties, including increasing the osmotic pressure, and causing freezing-point depression and boiling-point elevation. Because the solutes are charged ions they also increase the electrical conductivity of the solution. The increased ionic strength reduces the thickness of the electrical double layer around colloidal particles, and therefore the stability of emulsions and suspensions.

The chemical identity of the ions added is also important in many uses. For example, fluoride containing compounds are dissolved to supply fluoride ions for water fluoridation.

Solid ionic compounds have long been used as paint pigments, and are resistant to organic solvents, but are sensitive to acidity or basicity. Since 1801 pyrotechnicians have described and widely used metal-containing ionic compounds as sources of colour in fireworks. Under intense heat, the electrons in the metal ions or small molecules can be excited. These electrons later return to lower energy states, and release light with a colour spectrum characteristic of the species present.

In chemistry, ionic compounds are often used as precursors for high-temperature solid-state synthesis.

Many metals are geologically most abundant as ionic compounds within ores. To obtain the elemental materials, these ores are processed by smelting or electrolysis, in which redox reactions occur (often with a reducing agent such as carbon) such that the metal ions gain electrons to become neutral atoms.

Nomenclature

See also: IUPAC nomenclature of inorganic chemistry

According to the nomenclature recommended by IUPAC, ionic compounds are named according to their composition, not their structure. In the most simple case of a binary ionic compound with no possible ambiguity about the charges and thus the stoichiometry, the common name is written using two words. The name of the cation (the unmodified element name for monatomic cations) comes first, followed by the name of the anion. For example, MgCl₂ is named magnesium chloride, and Na₂SO₄ is named sodium sulfate (SO²⁻
₄, sulfate, is an example of a polyatomic ion). To obtain the empirical formula from these names, the stoichiometry can be deduced from the charges on the ions, and the requirement of overall charge neutrality.

If there are multiple different cations and/or anions, multiplicative prefixes (di-, tri-, tetra-, ...) are often required to indicate the relative compositions, and cations then anions are listed in alphabetical order. For example, KMgCl₃ is named magnesium potassium trichloride to distinguish it from K₂MgCl₄, magnesium dipotassium tetrachloride (note that in both the empirical formula and the written name, the cations appear in alphabetical order, but the order varies between them because the symbol for potassium is K). When one of the ions already has a multiplicative prefix within its name, the alternate multiplicative prefixes (bis-, tris-, tetrakis-, ...) are used. For example, Ba(BrF₄)₂ is named barium bis(tetrafluoridobromate).

Compounds containing one or more elements which can exist in a variety of charge/oxidation states will have a stoichiometry that depends on which oxidation states are present, to ensure overall neutrality. This can be indicated in the name by specifying either the oxidation state of the elements present, or the charge on the ions. Because of the risk of ambiguity in allocating oxidation states, IUPAC prefers direct indication of the ionic charge numbers. These are written as an arabic integer followed by the sign (... , 2−, 1−, 1+, 2+, ...) in parentheses directly after the name of the cation (without a space separating them). For example, FeSO₄ is named iron(2+) sulfate (with the 2+ charge on the Fe²⁺ ions balancing the 2− charge on the sulfate ion), whereas Fe₂(SO₄)₃ is named iron(3+) sulfate (because the two iron ions in each formula unit each have a charge of 3+, to balance the 2− on each of the three sulfate ions). Stock nomenclature, still in common use, writes the oxidation number in Roman numerals (... , −II, −I, 0, I, II, ...). So the examples given above would be named iron(II) sulfate and iron(III) sulfate respectively. For simple ions the ionic charge and the oxidation number are identical, but for polyatomic ions they often differ. For example, the uranyl(2+) ion, UO²⁺
₂, has uranium in an oxidation state of +6, so would be called a dioxouranium(VI) ion in Stock nomenclature. An even older naming system for metal cations, also still widely used, appended the suffixes -ous and -ic to the Latin root of the name, to give special names for the low and high oxidation states. For example, this scheme uses "ferrous" and "ferric", for iron(II) and iron(III) respectively, so the examples given above were classically named ferrous sulfate and ferric sulfate.

Gel electrophoresis of nucleic acids

From Wikipedia, the free encyclopedia

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

 

Digital printout of an agarose gel electrophoresis of cat-insert plasmid DNA

 

DNA electropherogram trace

Nucleic acid electrophoresis is an analytical technique used to separate DNA or RNA fragments by size and reactivity. Nucleic acid molecules which are to be analyzed are set upon a viscous medium, the gel, where an electric field induces the nucleic acids (which are negatively charged due to their sugar-phosphate backbone) to migrate toward the anode (which is positively charged because this is an electrolytic rather than galvanic cell). The separation of these fragments is accomplished by exploiting the mobilities with which different sized molecules are able to pass through the gel. Longer molecules migrate more slowly because they experience more resistance within the gel. Because the size of the molecule affects its mobility, smaller fragments end up nearer to the anode than longer ones in a given period. After some time, the voltage is removed and the fragmentation gradient is analyzed. For larger separations between similar sized fragments, either the voltage or run time can be increased. Extended runs across a low voltage gel yield the most accurate resolution. Voltage is, however, not the sole factor in determining electrophoresis of nucleic acids.

The nucleic acid to be separated can be prepared in several ways before separation by electrophoresis. In the case of large DNA molecules, the DNA is frequently cut into smaller fragments using a DNA restriction endonuclease (or restriction enzyme). In other instances, such as PCR amplified samples, enzymes present in the sample that might affect the separation of the molecules are removed through various means before analysis. Once the nucleic acid is properly prepared, the samples of the nucleic acid solution are placed in the wells of the gel and a voltage is applied across the gel for a specified amount of time.

The DNA fragments of different lengths are visualized using a fluorescent dye specific for DNA, such as ethidium bromide. The gel shows bands corresponding to different nucleic acid molecules populations with different molecular weight. Fragment size is usually reported in "nucleotides", "base pairs" or "kb" (for thousands of base pairs) depending upon whether single- or double-stranded nucleic acid has been separated. Fragment size determination is typically done by comparison to commercially available DNA markers containing linear DNA fragments of known length.

The types of gel most commonly used for nucleic acid electrophoresis are agarose (for relatively long DNA molecules) and polyacrylamide (for high resolution of short DNA molecules, for example in DNA sequencing). Gels have conventionally been run in a "slab" format such as that shown in the figure, but capillary electrophoresis has become important for applications such as high-throughput DNA sequencing. Electrophoresis techniques used in the assessment of DNA damage include alkaline gel electrophoresis and pulsed field gel electrophoresis.

For short DNA segments such as 20 to 60 bp double stranded DNA, running them in polyacrylamide gel (PAGE) will give better resolution (native condition). Similarly, RNA and single-stranded DNA can be run and visualised by PAGE gels containing denaturing agents such as urea. PAGE gels are widely used in techniques such as DNA foot printing, EMSA and other DNA-protein interaction techniques.

The measurement and analysis are mostly done with a specialized gel analysis software. Capillary electrophoresis results are typically displayed in a trace view called an electropherogram.

Factors affecting migration of nucleic acids

A number of factors can affect the migration of nucleic acids: the dimension of the gel pores, the voltage used, the ionic strength of the buffer, and the concentration intercalating dye such as ethidium bromide if used during electrophoresis.

Size of DNA

The gel sieves the DNA by the size of the DNA molecule whereby smaller molecules travel faster. Double-stranded DNA moves at a rate that is approximately inversely proportional to the logarithm of the number of base pairs. This relationship however breaks down with very large DNA fragments and it is not possible to separate them using standard agarose gel electrophoresis. The limit of resolution depends on gel composition and field strength. and the mobility of larger circular DNA may be more strongly affected than linear DNA by the pore size of the gel. Separation of very large DNA fragments requires pulse field gel electrophoresis (PFGE). In field inversion gel electrophoresis (FIGE, a kind of PFGE), it is possible to have "band inversion" - where large molecules may move faster than small molecules.

Gels of plasmid preparations usually show a major band of supercoiled DNA with other fainter bands in the same lane. Note that by convention DNA gel is displayed with smaller DNA fragments near the bottom of the gel. This is because historically DNA gel were run vertically and the smaller DNA fragments move downwards faster.

Conformation of DNA

The conformation of the DNA molecule can significantly affect the movement of the DNA, for example, supercoiled DNA usually moves faster than relaxed DNA because it is tightly coiled and hence more compact. In a normal plasmid DNA preparation, multiple forms of DNA may be present, and gel from the electrophoresis of the plasmids would normally show a main band which would be the negatively supercoiled form, while other forms of DNA may appear as minor fainter bands. These minor bands may be nicked DNA (open circular form) and the relaxed closed circular form which normally run slower than supercoiled DNA, and the single-stranded form (which can sometimes appear depending on the preparation methods) may move ahead of the supercoiled DNA. The rate at which the various forms move however can change using different electrophoresis conditions, for example linear DNA may run faster or slower than supercoiled DNA depending on conditions, and the mobility of larger circular DNA may be more strongly affected than linear DNA by the pore size of the gel. Unless supercoiled DNA markers are used, the size of a circular DNA like plasmid therefore may be more accurately gauged after it has been linearized by restriction digest.

DNA damage due to increased cross-linking will also reduce electrophoretic DNA migration in a dose-dependent way.

Concentration of ethidium bromide

Circular DNA are more strongly affected by ethidium bromide concentration than linear DNA if ethidium bromide is present in the gel during electrophoresis. All naturally occurring DNA circles are underwound, but ethidium bromide which intercalates into circular DNA can change the charge, length, as well as the superhelicity of the DNA molecule, therefore its presence during electrophoresis can affect its movement in gel. Increasing ethidium bromide intercalated into the DNA can change it from a negatively supercoiled molecule into a fully relaxed form, then to positively coiled superhelix at maximum intercalation. Agarose gel electrophoresis can be used to resolve circular DNA with different supercoiling topology.

Gel concentration

The concentration of the gel determines the pore size of the gel which affects the migration of DNA. The resolution of the DNA changes with the percentage concentration of the gel. Increasing the agarose concentration of a gel reduces the migration speed and improves separation of smaller DNA molecules, while lowering gel concentration permits large DNA molecules to be separated. For a standard agarose gel electrophoresis, 0.7% gel concentration gives good separation or resolution of large 5–10kb DNA fragments, while 2% gel concentration gives good resolution for small 0.2–1kb fragments. Up to 3% gel concentration can be used for separating very tiny fragments but a vertical polyacrylamide gel would be more appropriate for resolving small fragments. High concentrations gel, however, requires longer run times (sometimes days) and high percentage gels are often brittle and may not set evenly. High percentage agarose gels should be run with PFGE or FIGE. Low percentage gels (0.1−0.2%) are fragile and may break. 1% gels are common for many applications.

Applied field

At low voltages, the rate of migration of the DNA is proportional to the voltage applied, i.e. the higher the voltage, the faster the DNA moves. However, in increasing electric field strength, the mobility of high-molecular-weight DNA fragments increases differentially, and the effective range of separation decreases and resolution therefore is lower at high voltage. For optimal resolution of DNA greater than 2kb in size in standard gel electrophoresis, 5 to 8 V/cm is recommended. Voltage is also limited by the fact that it heats the gel and may cause the gel to melt if a gel is run at high voltage for a prolonged period, particularly for low-melting point agarose gel.

The mobility of DNA however may change in an unsteady field. In a field that is periodically reversed, the mobility of DNA of a particular size may drop significantly at a particular cycling frequency. This phenomenon can result in band inversion whereby larger DNA fragments move faster than smaller ones in PFGE.

Mechanism of migration and separation

The negative charge of its phosphate backbone moves the DNA towards the positively charged anode during electrophoresis. However, the migration of DNA molecules in solution, in the absence of a gel matrix, is independent of molecular weight during electrophoresis, i.e. there is no separation by size without a gel matrix. Hydrodynamic interaction between different parts of the DNA are cut off by streaming counterions moving in the opposite direction, so no mechanism exists to generate a dependence of velocity on length on a scale larger than screening length of about 10 nm. This makes it different from other processes such as sedimentation or diffusion where long-ranged hydrodynamic interaction are important.

The gel matrix is therefore responsible for the separation of DNA by size during electrophoresis, however the precise mechanism responsible the separation is not entirely clear. A number of models exists for the mechanism of separation of biomolecules in gel matrix, a widely accepted one is the Ogston model which treats the polymer matrix as a sieve consisting of randomly distributed network of inter-connected pores. A globular protein or a random coil DNA moves through the connected pores large enough to accommodate its passage, and the movement of larger molecules is more likely to be impeded and slowed down by collisions with the gel matrix, and the molecules of different sizes can therefore be separated in this process of sieving.

The Ogston model however breaks down for large molecules whereby the pores are significantly smaller than size of the molecule. For DNA molecules of size greater than 1 kb, a reptation model (or its variants) is most commonly used. This model assumes that the DNA can crawl in a "snake-like" fashion (hence "reptation") through the pores as an elongated molecule. At higher electric field strength, this turned into a biased reptation model, whereby the leading end of the molecule become strongly biased in the forward direction, and this leading edge pulls the rest of the molecule along. In the fully biased mode, the mobility reached a saturation point and DNA beyond a certain size cannot be separated. Perfect parallel alignment of the chain with the field however is not observed in practice as that would mean the same mobility for long and short molecules. Further refinement of the biased reptation model takes into account of the internal fluctuations of the chain.

The biased reptation model has also been used to explain the mobility of DNA in PFGE. The orientation of the DNA is progressively built up by reptation after the onset of a field, and the time it reached the steady state velocity is dependent on the size of the molecule. When the field is changed, larger molecules take longer to reorientate, it is therefore possible to discriminate between the long chains that cannot reach its steady state velocity from the short ones that travel most of the time in steady velocity. Other models, however, also exist.

Real-time fluorescence microscopy of stained molecules showed more subtle dynamics during electrophoresis, with the DNA showing considerable elasticity as it alternately stretching in the direction of the applied field and then contracting into a ball, or becoming hooked into a U-shape when it gets caught on the polymer fibres. This observation may be termed the "caterpillar" model. Other model proposes that the DNA gets entangled with the polymer matrix, and the larger the molecule, the more likely it is to become entangled and its movement impeded.

Visualization

DNA gel electrophoresis

The most common dye used to make DNA or RNA bands visible for agarose gel electrophoresis is ethidium bromide, usually abbreviated as EtBr. It fluoresces under UV light when intercalated into the major groove of DNA (or RNA). By running DNA through an EtBr-treated gel and visualizing it with UV light, any band containing more than ~20 ng DNA becomes distinctly visible. EtBr is a known mutagen, and safer alternatives are available, such as GelRed, produced by Biotium, which binds to the minor groove.

SYBR Green I is another dsDNA stain, produced by Invitrogen. It is more expensive, but 25 times more sensitive, and possibly safer than EtBr, though there is no data addressing its mutagenicity or toxicity in humans.

SYBR Safe is a variant of SYBR Green that has been shown to have low enough levels of mutagenicity and toxicity to be deemed nonhazardous waste under U.S. Federal regulations. It has similar sensitivity levels to EtBr, but, like SYBR Green, is significantly more expensive. In countries where safe disposal of hazardous waste is mandatory, the costs of EtBr disposal can easily outstrip the initial price difference, however.

Since EtBr stained DNA is not visible in natural light, scientists mix DNA with negatively charged loading buffers before adding the mixture to the gel. Loading buffers are useful because they are visible in natural light (as opposed to UV light for EtBr stained DNA), and they co-sediment with DNA (meaning they move at the same speed as DNA of a certain length). Xylene cyanol and Bromophenol blue are common dyes found in loading buffers; they run about the same speed as DNA fragments that are 5000 bp and 300 bp in length respectively, but the precise position varies with percentage of the gel. Other less frequently used progress markers are Cresol Red and Orange G which run at about 125 bp and 50 bp, respectively.

Visualization can also be achieved by transferring DNA after SDS-PAGE to a nitrocellulose membrane followed by exposure to a hybridization probe. This process is termed Southern blotting.

For fluorescent dyes, after electrophoresis the gel is illuminated with an ultraviolet lamp (usually by placing it on a light box, while using protective gear to limit exposure to ultraviolet radiation). The illuminator apparatus mostly also contains imaging apparatus that takes an image of the gel, after illumination with UV radiation. The ethidium bromide fluoresces reddish-orange in the presence of DNA, since it has intercalated with the DNA. The DNA band can also be cut out of the gel, and can then be dissolved to retrieve the purified DNA. The gel can then be photographed usually with a digital or polaroid camera. Although the stained nucleic acid fluoresces reddish-orange, images are usually shown in black and white (see figures). UV damage to the DNA sample can reduce the efficiency of subsequent manipulation of the sample, such as ligation and cloning. Shorter wavelength UV radiations (302 or 312 nm) cause greater damage, for example exposure for as little as 45 seconds can significantly reduce transformation efficiency. Therefore if the DNA is to be use for downstream procedures, exposure to a shorter wavelength UV radiations should be limited, instead higher-wavelength UV radiation (365 nm) which cause less damage should be used. Higher wavelength radiations however produces weaker fluorescence, therefore if it is necessary to capture the gel image, a shorter wavelength UV light can be used a short time. Addition of Cytidine or guanosine to the electrophoresis buffer at 1 mM concentration may protect the DNA from damage. Alternatively, a blue light excitation source with a blue-excitable stain such as SYBR Green or GelGreen may be used.

Gel electrophoresis research often takes advantage of software-based image analysis tools, such as ImageJ.