Nucleation is the first step in the formation of either a new thermodynamic phase or a new structure via self-assembly or self-organization. Nucleation is defined to be the process that determines how long an observer has to wait before the new phase or self-organized structure appears. For example, if a volume of water is cooled below 0° C, it will tend to freeze into ice. Volumes of water cooled only a few degrees below 0° C stay free of ice for long periods. At these conditions, nucleation of ice does not occur at all. However, at lower temperatures ice crystals appear after no delay. At these conditions ice nucleation is fast. Nucleation is how first-order phase transitions start, it is the start of the process of forming a new thermodynamic phase. In contrast, new phases at continuous phase transitions start to form immediately. Nucleation is found to be sensitive to impurities in the system; these impurities may be too small to be seen by the naked eye, but still can control the rate of nucleation.
Because of this, it is important to distinguish between heterogeneous nucleation and homogeneous nucleation. Heterogeneous nucleation occurs at nucleation sites on surfaces in the system. Homogeneous nucleation occurs away from a surface. Nucleation is a stochastic process, so in two identical systems nucleation will occur at different times; this behaviour is similar to radioactive decay. A common mechanism is illustrated in the animation to the right; this shows nucleation of a new phase in an existing phase. In the existing phase microscopic fluctuations of the red phase appear and decay continuously, until an unusually large fluctuation of the new red phase is so large it is more favourable for it to grow than to shrink back to nothing; this nucleus of the red phase grows and converts the system to this phase. The standard theory that describes this behaviour for the nucleation of a new thermodynamic phase is called classical nucleation theory. However, the CNT fails in describing experimental results of vapour to liquid nucleation for model substances like argon by several orders of magnitude.
For nucleation of a new thermodynamic phase, such as the formation of ice in water below 0° C, if the system is not evolving with time and nucleation occurs in one step the probability that nucleation has not occurred should undergo exponential decay as seen in radioactive decay. This is seen for example in the nucleation of ice in supercooled small water droplets; the decay rate of the exponential gives the nucleation rate. Classical nucleation theory is a used approximate theory for estimating these rates, how they vary with variables such as temperature, it predicts that the time you have to wait for nucleation decreases rapidly when supersaturated. It is not just new phases such as crystals that form via nucleation followed by growth; the self-assembly process that forms objects like the amyloid aggregates associated with Alzheimer's disease starts with nucleation. Energy consuming self-organising systems such as the microtubules in cells show nucleation and growth. Heterogeneous nucleation, nucleation with the nucleus at a surface, is much more common than homogeneous nucleation.
For example, in the nucleation of ice from supercooled water droplets, purifying the water to remove all or all impurities results in water droplets that freeze below around - 35 C, whereas water that contains impurities may freeze at - 5 C or warmer. This observation that heterogeneous nucleation can occur when the rate of homogeneous nucleation is zero, is understood using classical nucleation theory; this predicts that the nucleation slows exponentially with the height of a free energy barrier ΔG*. This barrier comes from the free energy penalty of forming the surface of the growing nucleus. For homogeneous nucleation the nucleus is approximated by a sphere, but as we can see in the schematic of macroscopic droplets to the right, droplets on surfaces are not complete spheres and so the area of the interface between the droplet and the surrounding fluid is less than a sphere's 4 π r 2; this reduction in surface area of the nucleus reduces the height of the barrier to nucleation and so speeds nucleation up exponentially.
Nucleation can start at the surface of a liquid. For example, computer simulations of gold nanoparticles show that the crystal phase nucleates at the liquid-gold surface. Classical nucleation theory makes a number of assumptions, for example it treats a microscopic nucleus as if it is a macroscopic droplet with a well-defined surface whose free energy is estimated using an equilibrium property: the interfacial tension σ. For a nucleus that may be only of order ten molecules across it is not always clear that we can treat something so small as a volume plus a surface. Nucleation is an inherently out of thermodynamic equilibrium phenomenon so it is not always obvious that its rate can be estimated using equilibrium properties. However, modern computers are powerful enough to calculate exact nucleation rates for simple models; these have been compared with the classical theory, for example for the case of nucleation of the crystal phase in the model of hard spheres. This is a model of hard spheres in thermal motion, is a simple model of some colloids.
For the crystallization of hard spheres the classical theory is a reasonable approximate theory. So for the simple models we can study, classical nucleation theory works quite well, but we do not know if it works well for complex molecules crystallising out of solution. Phase-
This is a list of heads of state, heads of governments, other rulers in the year 1680. Kingdom of Bamum – Koutou, Sultan of Bamum Kingdom of Dahomey – Houegbadja Ethiopian Empire – Yohannes I Wolof Empire – Bakar Penda Ayutthaya Kingdom – Narai China - Kangxi Emperor Empire of Japan – Monarch – Reigen Tokugawa shogunate - Tokugawa Ietsuna Tokugawa Tsunayoshi Ryukyu Kingdom – Shō Tei Joseon – Sukjong Mughal Empire – Aurangzeb Kingdom of Mysore – Chikka Devaraja Sirmoor State – Budh Prakash, Raja of Sirmoor Sintang – Sri Paduka Sultan Muhammad Shams ud-din Sa'id ul-Khairiwaddien Sultan Nata, Sultan of Sintang Taiwan - Zheng Jing Tibet - Dalai Lama- Ngawang Lobsang Gyatso Desi - Sangye Gyatso Kingdom of Denmark–Norway – Christian V Kingdom of England – Charles II Kingdom of France – Louis XIV Holy Roman Empire – Leopold I Electors Electorate of Bavaria – Maximilian II Emanuel Kingdom of Bohemia - Leopold I Brandenburg - Frederick William, Elector of Brandenburg, 1640–1688 Electorate of Cologne – Electorate of Mainz – Electorate of Saxony - Electorate of Trier – Kingdom of Hungary – Leopold I Kingdom of Ireland – Charles II Duchy of Mantua – Carlo IV Gonzaga Duchy of Modena – Francesco II Kingdom of Naples – Charles V Ottoman Empire Sultan - Mehmed IV, the Hunter, Ottoman Sultan Grand Vizier - Kara Mustafa Pasha Papal States – Pope Innocent XI Duchy of Parma – Ranuccio II Farnese Polish–Lithuanian Commonwealth – Jan III Sobieski, King of Poland Kingdom of Portugal and the Algarves – Monarch – Afonso VI Prince-Regent – Peter, Duke of Beja Duchy of Prussia – Frederick William Tsardom of Russia – Feodor III Duchy of Savoy – Victor Amadeus II Kingdom of Scotland – Charles II Kingdom of Sicily – Charles III Kingdom of Spain – Charles II Kingdom of Sweden – Charles XI Grand Duchy of Tuscany – Cosimo III de' Medici United Provinces Estates of Friesland, Guelders, Overijssel, Zeeland Stadtholder - Prince William III of Orange, Stadtholder of Guelders, Overijssel and Zeeland Holland – Grand Pensionary Gaspar Fagel of Holland Republic of Venice - Alvise Contarini, Doge of Venice Sultanate of Morocco – Al-Harrani, Abu'l Abbas Ahmad I, Ismail, Joint Sultan of Morocco Safavid Empire – Suleiman I of Persia Shah of Iran
Jane Worcester was a biostatistician and epidemiologist who became the second tenured female professor, after Martha May Eliot, the first female chair of biostatistics in the Harvard School of Public Health. Worcester graduated from Smith College in 1931, with a bachelor's degree in mathematics, was hired by Harvard biostatistician Edwin B. Wilson to become a human computer at Harvard, they continued to work together on theoretical research in biostatistics until Wilson retired as chair of the department in 1945 publishing 27 papers together. Worcester completed a Ph. D. in epidemiology at Harvard under Wilson's supervision in 1947. She joined the Harvard faculty, was granted tenure in 1962, served as chair from 1973 to 1977, when she retired, she became a Fellow of the American Statistical Association in 1960. In 1968, Smith College awarded her an honorary doctorate