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ContentsArticles

Fick's laws of diffusion 1Conservation of mass 7Atom-transfer radical-polymerization 11Living polymerization 14Dispersity 17Molar mass distribution 19Biotechnology 21Biosensor 35Biochemical cascade 41Biocatalysis 49Enzyme 52Active site 72Activation energy 73Oxidoreductase 75Glucose oxidase 77Peroxidase 80Horseradish peroxidase 82Inclusion body 84Protein folding 87Protein purification 95Chromatography 101Gel permeation chromatography 109Size-exclusion chromatography 116Affinity chromatography 122High-performance liquid chromatography 126Electrophoresis 136Gel electrophoresis 139Ion chromatography 149Antibody 151Immunoprecipitation 167Coagulation 174Protease 184Heat equation 187Diffusion 201

Mass diffusivity 212Chemical potential 214Conservation law 221Massenergy equivalence 222Momentum 242Angular momentum 258Charge conservation 266Conservation of energy 269First law of thermodynamics 276Laws of thermodynamics 288Continuity equation 292Fluid mechanics 302NavierStokes equations 307Conserved quantity 319Energy flux 321Mass flow rate 321Fluid dynamics 323

ReferencesArticle Sources and Contributors 330Image Sources, Licenses and Contributors 337

Article LicensesLicense 341

Fick's laws of diffusion 1

Fick's laws of diffusion

Molecular diffusion from a microscopic and macroscopic point ofview. Initially, there are solute molecules on the left side of a barrier(purple line) and none on the right. The barrier is removed, and thesolute diffuses to fill the whole container. Top: A single moleculemoves around randomly. Middle: With more molecules, there is a

clear trend where the solute fills the container more and moreuniformly. Bottom: With an enormous number of solute molecules,

randomness becomes undetectable: The solute appears to movesmoothly and systematically from high-concentration areas to

low-concentration areas. This smooth flow is described by Fick'slaws.

Fick's laws of diffusion describe diffusion and can beused to solve for the diffusion coefficient, D. Theywere derived by Adolf Fick in the year 1855.

Fick's first law

Fick's first law relates the diffusive flux to theconcentration under the assumption of steady state. Itpostulates that the flux goes from regions of highconcentration to regions of low concentration, with amagnitude that is proportional to the concentrationgradient (spatial derivative). In one (spatial) dimension,the law is

where is the "diffusion flux" [(amount of substance) per

unit area per unit time], example . measures the amount of substance that will flowthrough a small area during a small time interval.

is the diffusion coefficient or diffusivity indimensions of [length2 time1], example

(for ideal mixtures) is the concentration in dimensions of [amount of substance per unit volume], example

is the position [length], example is proportional to the squared velocity of the diffusing particles, which depends on the temperature, viscosity of

the fluid and the size of the particles according to the Stokes-Einstein relation. In dilute aqueous solutions thediffusion coefficients of most ions are similar and have values that at room temperature are in the range of 0.6x109

to 2x109 m2/s. For biological molecules the diffusion coefficients normally range from 1011 to 1010 m2/s.

In two or more dimensions we must use , the del or gradient operator, which generalises the first derivative,obtaining

.

The driving force for the one-dimensional diffusion is the quantity

which for ideal mixtures is the concentration gradient. In chemical systems other than ideal solutions or mixtures, thedriving force for diffusion of each species is the gradient of chemical potential of this species. Then Fick's first law(one-dimensional case) can be written as:

where the index i denotes the ith species, c is the concentration (mol/m3), R is the universal gas constant (J/(K mol)),T is the absolute temperature (K), and is the chemical potential (J/mol).

If the primary variable is mass fraction ( , given, for example, in ), then the equation changes to:


where is the fluid density (for example, in ). Note that the density is outside the gradient operator.

Fick's second lawFick's second law predicts how diffusion causes the concentration to change with time:

where

is the concentration in dimensions of [(amount of substance) length3], example is time [s] is the diffusion coefficient in dimensions of [length2 time1], example is the position [length], example It can be derived from Fick's First law and the mass conservation in absence of any chemical reactions:

Assuming the diffusion coefficient D to be a constant we can exchange the orders of the differentiation and multiplyby the constant:

and, thus, receive the form of the Fick's equations as was stated above.For the case of diffusion in two or more dimensions Fick's Second Law becomes

,

which is analogous to the heat equation.If the diffusion coefficient is not a constant, but depends upon the coordinate and/or concentration, Fick's SecondLaw yields

An important example is the case where is at a steady state, i.e. the concentration does not change by time, so thatthe left part of the above equation is identically zero. In one dimension with constant , the solution for theconcentration will be a linear change of concentrations along . In two or more dimensions we obtain

which is Laplace's equation, the solutions to which are called harmonic functions by mathematicians.

Example solution in one dimension: diffusion lengthA simple case of diffusion with time t in one dimension (taken as the x-axis) from a boundary located at position

, where the concentration is maintained at a value is

.

where erfc is the complementary error function. The length is called the diffusion length and provides ameasure of how far the concentration has propagated in the x-direction by diffusion in time t (Bird, 1976).As a quick approximation of the error function, the first 2 terms of the Taylor series can be used:


If is time-dependent, the diffusion length becomes . This idea is useful for estimating a

diffusion length over a heating and cooling cycle, where D varies with temperature.

Generalizations

1. In the inhomogeneous media, the diffusion coefficient varies in space, . This dependence does notaffect Fick's first law but the second law changes:

2. In the anisotropic media, the diffusion coefficient depends on the direction. It is a symmetric tensor .Fick's first law changes to

For the diffusion equation this formula gives

The symmetric matrix of diffusion coefficients should be positive definite. It is needed to make the right handside operator elliptic.3. For the inhomogeneous anisotropic media these two forms of the diffusion equation should be combined in

4. The approach based on the Einstein's mobility and Teorell formula gives the following generalization of Fick'sequation for the multicomponent diffusion of the perfect components:

where are concentrations of the components and is the matrix of coefficients. Here, indexes i,j are related tothe various components and not to the space coordinates.The Chapman-Enskog formulas for diffusion in gases include exactly the same terms. It should be stressed that thesephysical models of diffusion are different from the toy-models which are valid for very small

deviations from the uniform equilibrium. Earlier, such terms were introduced in the MaxwellStefan diffusionequation.

For anisotropic multicomponent diffusion coefficients one needs 4-index quantities, for example, , where i, jare related to the components and , =1,2,3 correspond to the space coordinates.


HistoryIn 1855, physiologist Adolf Fick first reported[1][2] his now-well-known laws governing the transport of massthrough diffusive means. Fick's work was inspired by the earlier experiments of Thomas Graham, which fell short ofproposing the fundamental laws for which Fick would become famous. The Fick's law is analogous to therelationships discovered at the same epoch by other eminent scientists: Darcy's law (hydraulic flow), Ohm's law(charge transport), and Fourier's Law (heat transport).Fick's experiments (modeled on Graham's) dealt with measuring the concentrations and fluxes of salt, diffusingbetween two reservoirs through tubes of water. It is notable that Fick's work primarily concerned diffusion in fluids,because at the time, diffusion in solids was not considered generally possible.[3] Today, Fick's Laws form the core ofour understanding of diffusion in solids, liquids, and gases (in the absence of bulk fluid motion in the latter twocases). When a diffusion process does not follow Fick's laws (which does happen),[4][5] we refer to such processes asnon-Fickian, in that they are exceptions that "prove" the importance of the general rules that Fick outlined in 1855.

ApplicationsEquations based on Fick's law have been commonly used to model transport processes in foods, neurons,biopolymers, pharmaceuticals, porous soils, population dynamics, nuclear materials, semiconductor doping process,etc. Theory of all voltammetric methods is based on solutions of Fick's equation. A large amount of experimentalresearch in polymer science and food science has shown that a more general approach is required to describetransport of components in materials undergoing glass transition. In the vicinity of glass transition the flow behaviorbecomes "non-Fickian". It can be shown that the Fick's law can be obtained from the Maxwell-Stefan equations[6] ofmulti-component mass transfer. The Fick's law is limiting case of the Maxwell-Stefan equations, when the mixture isextremely dilute and every chemical species is interacting only with the bulk mixture and not with other species. Toaccount for the presence of multiple species in a non-dilute mixture, several variations of the Maxwell-Stefanequations are used. See also non-diagonal coupled transport processes (Onsager relationship).

Biological perspectiveThe first law gives rise to the following formula:[7]

in which, is the permeability, an experimentally determined membrane "conductance" for a given gas at a given

temperature. is the difference in concentration of the gas across the membrane for the direction of flow (from to

).Fick's first law is also important in radiation transfer equations. However, in this context it becomes inaccurate whenthe diffusion constant is low and the radiation becomes limited by the speed of light rather than by the resistance ofthe material the radiation is flowing through. In this situation, one can use a flux limiter.The exchange rate of a gas across a fluid membrane can be determined by using this law together with Graham's law.

Fick's flow in liquidsWhen two miscible liquids are brought into contact, and diffusion takes place, the macroscopic (or average) concentration evolves following Fick's law. On a mesoscopic scale, that is, between the macroscopic scale described by Fick's law and molecular scale, where molecular random walks take place, fluctuations cannot be neglected. Such situations can be successfully modeled with Landau-Lifshitz fluctuating hydrodynamics. In this theoretical framework, diffusion is due to fluctuations whose dimensions range from the molecular scale to the macroscopic


scale. [8]

In particular, fluctuating hydrodynamic equations include a Fick's flow term, with a given diffusion coefficient,along with hydrodynamics equations and stochastic terms describing fluctuations. When calculating the fluctuationswith a perturbative approach, the zero order approximation is Fick's law. The first order gives the fluctuations, and itcomes out that fluctuations contribute to diffusion. This represents somehow a tautology, since the phenomenadescribed by a lower order approximation is the result of a higher approximation: this problem is solved only byrenormalizing fluctuating hydrodynamics equations.

Semiconductor fabrication applicationsIC Fabrication technologies, model processes like CVD, Thermal Oxidation, and Wet Oxidation, doping, etc. usediffusion equations obtained from Fick's law.In certain cases, the solutions are obtained for boundary conditions such as constant source concentration diffusion,limited source concentration, or moving boundary diffusion (where junction depth keeps moving into the substrate).

Derivation of Fick's 1st law in 1 dimensionThe following derivation is based on a similar argument made in Berg 1977 (see references).Consider a collection of particles performing a random walk in one dimension with length scale and time scale

. Let be the number of particles at position at time .At a given time step, half of the particles would move left and half would move right. Since half of the particles atpoint move right and half of the particles at point move left, the net movement to the right is:

The flux, J, is this net movement of particles across some area element of area a, normal to the random walk during atime interval . Hence we may write:

Multiplying the top and bottom of the righthand side by and rewriting, we obtain:

We note that concentration is defined as particles per unit volume, and hence .

In addition, is the definition of the diffusion constant in one dimension, . Thus our expression simplifies

to:

In the limit where is infinitesimal, the righthand side becomes a space derivative:


Notes[1] A. Fick, Ann. der. Physik (1855), 94, 59, doi:10.1002/andp.18551700105 (in German).[2] A. Fick, Phil. Mag. (1855), 10, 30. (in English)[3] Jean Philibert, One and a Half Century of Diffusion: Fick, Einstein, before and beyond, Diffusion Fundamentals 2, 2005 1.11.10 (http:/ /

www. uni-leipzig. de/ diffusion/ journal/ pdf/ volume2/ diff_fund_2(2005)1. pdf)[4][4] J. L. Vzquez (2006), The Porous Medium Equation. Mathematical Theory, Oxford Univ. Press.[5] A.N. Gorban, H.P. Sargsyan and H.A. Wahab (2011), Quasichemical Models of Multicomponent Nonlinear Diffusion (http:/ / arxiv. org/ pdf/

1012. 2908v4. pdf), Mathematical Modelling of Natural Phenomena (http:/ / journals. cambridge. org/ action/ displayJournal?jid=MNP),Volume 6 / Issue 05, 184262.

[6] Taylor, Ross; R Krishna (1993). Multicomponent mass transfer. Wiley.[7] Physiology at MCG 3/3ch9/s3ch9_2 (http:/ / web. archive. org/ web/ 20080401093403/ http:/ / www. lib. mcg. edu/ edu/ eshuphysio/

program/ section3/ 3ch9/ s3ch9_2. htm)[8] D. Brogioli and A. Vailati, Diffusive mass transfer by nonequilibrium fluctuations: Fick's law revisited, Phys. Rev. E 63, 012105/1-4 (2001)

(http:/ / arxiv. org/ abs/ cond-mat/ 0006163)

References W.F. Smith, Foundations of Materials Science and Engineering 3rd ed., McGraw-Hill (2004) H.C. Berg, Random Walks in Biology, Princeton (1977) R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, John Wiley & sons, (1976)

External links Diffusion fundamentals (http:/ / www. timedomaincvd. com/ CVD_Fundamentals/ xprt/ intro_diffusion. html) Diffusion in Polymer based Materials (http:/ / www. composite-agency. com/ messages/ 3875. html) Fick's equations, Boltzmann's transformation, etc. (with figures and animations) (http:/ / dragon. unideb. hu/

~zerdelyi/ Diffusion-on-the-nanoscale/ node2. html) Wilson, Bill. Fick's Second Law. Connexions. 21 Aug. 2007 (http:/ / cnx. org/ content/ m1036/ 2. 11/ ) (http:/ / webserver. dmt. upm. es/ ~isidoro/ bk3/ c11/ Mass Transfer. htm)

Conservation of mass 7

Conservation of mass

Antoine Lavoisier's discovery of the Law ofConservation of Mass led to many new findings

in the 19th century. Joseph Proust's Law ofDefinite Proportions and John Dalton's Atomic

Theory branched from the discoveries of AntoineLavoisier. Lavoisier's quantitative experiments

revealed that combustion involved oxygen ratherthan what was previously thought to be

phlogiston.

The law of conservation of mass, also known as the principle ofmass/matter conservation, states that the mass of an isolated system(closed to all transfers of matter and energy) will remain constant overtime. This principle is equivalent to the conservation of energy: whenenergy or mass is enclosed in a system and none is allowed in or out,its quantity cannot otherwise change over time (hence, its quantity is"conserved" over time). The mass of an isolated system cannot bechanged as a result of processes acting inside the system. The lawimplies that mass can neither be created nor destroyed, although it maybe rearranged in space and changed into different types of particles;and that for any chemical process in an isolated system, the mass of thereactants must equal the mass of the products.

The concepts of both matter and mass conservation are widely used inmany fields such as chemistry, mechanics, and fluid dynamics.Historically, the principle of mass conservation, discovered inchemical reactions by Antoine Lavoisier in the late 18th century, wasof crucial importance in progressing from alchemy to the modernnatural science of chemistry.

In a thermodynamically closed system (i.e. one which is closed toexchanges of matter, but open to small exchanges of non-materialenergy (such as heat and work) with the surroundings) mass is onlyapproximately conserved. In this case the input or output of energychanges the mass of the system, according to special relativity,although the change is usually small since relatively large amounts of energy are equivalent to only a small amountof mass. Mass is absolutely conserved in so-called isolated systems, i.e. those completely isolated from all exchangeswith the environment. In special relativity, the mass-energy equivalence theorem states that mass conservation isequivalent to total energy conservation, which is the first law of thermodynamics. In special relativity the differencebetween closed and isolated systems becomes important, since conservation of mass is strictly and perfectly upheldonly for isolated systems. In special relativity, mass is not converted to energy, as such, since energy always retainsits equivalent amount of mass within any isolated system. However, certain types of matter may be converted toenergy, so long as the mass of the system is unchanged in the process. When this energy is removed from systems,they lose mass.

In general relativity, mass (and energy) conservation in expanding volumes of space is a complex concept, subject todifferent definitions, and neither mass nor energy is as strictly and simply conserved as is the case in specialrelativity and in Minkowski space. For a discussion, see mass in general relativity.

HistoryAn important idea in ancient Greek philosophy was that "Nothing comes from nothing", so that what exists now hasalways existed: no new matter can come into existence where there was none before. An explicit statement of this,along with the further principle that nothing can pass away into nothing, is found in Empedocles (approx. 490430BCE): "For it is impossible for anything to come to be from what is not, and it cannot be brought about or heard ofthat what is should be utterly destroyed."[1]


A further principle of conservation was stated by Epicurus (341270 BCE) who, describing the nature of theuniverse, wrote that "the totality of things was always such as it is now, and always will be".[2]

Jain philosophy, a non-creationist philosophy based on the teachings of Mahavira (6th century BCE),[3] states thatthe universe and its constituents such as matter cannot be destroyed or created. The Jain text Tattvarthasutra (2ndcentury) states that a substance is permanent, but its modes are characterised by creation and destruction.[4] Aprinciple of the conservation of matter was also stated by Nasr al-Dn al-Ts (12011274). He wrote that "A bodyof matter cannot disappear completely. It only changes its form, condition, composition, color and other propertiesand turns into a different complex or elementary matter".[5]

The principle of conservation of mass was first outlined by Mikhail Lomonosov (17111765) in 1748. He provedthem by experimentsthough this is sometimes challenged.[6] Antoine Lavoisier (17431794) had expressed theseideas more clearly several years ago. Others who anticipated the work of Lavoisier include Joseph Black(17281799), Henry Cavendish (17311810), and Jean Rey (15831645).[7]

The conservation of mass was obscure for millennia because of the buoyancy effect of the Earth's atmosphere on theweight of gases. For example, a piece of wood weighs less after burning; this seemed to suggest that some of itsmass disappears, or is transformed or lost. This was not disproved until careful experiments were performed in whichchemical reactions such as rusting were allowed to take place in sealed glass ampoules; it was found that thechemical reaction did not change the weight of the sealed container and its contents. The vacuum pump also enabledthe weighing of gases using scales.Once understood, the conservation of mass was of great importance in progressing from alchemy to modernchemistry. Once early chemists realized that chemical substances never disappeared but were only transformed intoother substances with the same weight, these scientists could for the first time embark on quantitative studies of thetransformations of substances. The idea of mass conservation plus a surmise that certain "elemental substances" alsocould not be transformed into others by chemical reactions, in turn led to an understanding of chemical elements, aswell as the idea that all chemical processes and transformations (such as burning and metabolic reactions) arereactions between invariant amounts or weights of these chemical elements.

GeneralizationIn special relativity, the conservation of mass does not apply if the system is open and energy escapes. However, itdoes continue to apply to totally closed (isolated) systems. If energy cannot escape a system, its mass cannotdecrease. In relativity theory, so long as any type of energy is retained within a system, this energy exhibits mass.Also, mass must be differentiated from matter (see below), since matter may not be perfectly conserved in isolatedsystems, even though mass is always conserved in such systems. However, matter is so nearly conserved inchemistry that violations of matter conservation were not measured until the nuclear age, and the assumption ofmatter conservation remains an important practical concept in most systems in chemistry and other studies that donot involve the high energies typical of radioactivity and nuclear reactions.

The mass associated with chemical amounts of energy is too small to measureThe change in mass of certain kinds of open systems where atoms or massive particles are not allowed to escape, butother types of energy (such as light or heat) are allowed to enter or escape, went unnoticed during the 19th century,because the change in mass associated with addition or loss of small quantities of thermal or radiant energy inchemical reactions is very small. (In theory, mass would not change at all for experiments conducted in isolatedsystems where heat and work were not allowed in or out.)The theoretical association of all energy with mass was made by Albert Einstein in 1905. However Max Planck pointed out that the change in mass of systems as a result of extraction or addition of chemical energy, as predicted by Einstein's theory, is so small that it could not be measured with available instruments, for example as a test of


Einstein's theory. Einstein in turn speculated that the energies associated with newly-discovered radioactivity weresignificant enough, compared with the mass of systems producing them, to enable their mass-change to be measured,once the energy of the reaction had been removed from the system. This later indeed proved to be possible, althoughit was eventually to be the first artificial nuclear transmutation reactions in the 1930s, using cyclotrons, that provedthe first successful test of Einstein's theory regarding mass-loss with energy-loss.

Mass conservation remains correct if energy is not lostThe conservation of relativistic mass implies the viewpoint of a single observer (or the view from a single inertialframe) since changing inertial frames may result in a change of the total energy (relativistic energy) for systems, andthis quantity determines the relativistic mass.The principle that the mass of a system of particles must be equal to the sum of their rest masses, even though true inclassical physics, may be false in special relativity. The reason that rest masses cannot be simply added is that thisdoes not take into account other forms of energy, such as kinetic and potential energy, and massless particles such asphotons, all of which may (or may not) affect the mass of systems.For moving massive particles in a system, examining the rest masses of the various particles also amounts tointroducing many different inertial observation frames (which is prohibited if total system energy and momentum areto be conserved), and also when in the rest frame of one particle, this procedure ignores the momenta of otherparticles, which affect the system mass if the other particles are in motion in this frame.For the special type of mass called invariant mass, changing the inertial frame of observation for a whole closedsystem has no effect on the measure of invariant mass of the system, which remains both conserved and invarianteven for different observers who view the entire system. Invariant mass is a system combination of energy andmomentum, which is invariant for any observer, because in any inertial frame, the energies and momenta of thevarious particles always add to the same quantity (the momentum may be negative, so the addition amounts to asubtraction). The invariant mass is the relativistic mass of the system when viewed in the center of momentumframe. It is the minimum mass which a system may exhibit in all possible inertial frames.The conservation of both relativistic and invariant mass applies even to systems of particles created by pairproduction, where energy for new particles may come from kinetic energy of other particles, or from a photon as partof a system. Again, neither the relativistic nor the invariant mass of totally-closed (that is, isolated) systems changeswhen new particles are created. However, different inertial observers will disagree on the value of this conservedmass, if it is the relativistic mass (i.e., relativistic mass is conserved by not invariant). However, all observers agreeon the value of the conserved mass, if the mass being measured is the invariant mass (i.e., invariant mass is bothconserved and invariant).The mass-energy equivalence formula gives a different prediction in non-isolated systems, since if energy is allowedto escape a system, both relativistic mass and invariant mass will escape also. In this case, the mass-energyequivalence formula predicts that the change in mass of a system is associated with the change in its energy due toenergy being added or subtracted: This form involving changes was the form in which thisfamous equation was originally presented by Einstein. In this sense, mass changes in any system are explainedsimply if the mass of the energy added or removed from the system, are taken into account.The formula implies that bound systems have an invariant mass (rest mass for the system) less than the sum of their parts, if the binding energy has been allowed to escape the system after the system has been bound. This may happen by converting system potential energy into some other kind of active energy, such as kinetic energy or photons, which easily escape a bound system. The difference in system masses, called a mass defect, is a measure of the binding energy in bound systems in other words, the energy needed to break the system apart. The greater the mass defect, the larger the binding energy. The binding energy (which itself has mass) must be released (as light or heat) when the parts combine to form the bound system, and this is the reason the mass of the bound system decreases when the energy leaves the system.[8] The total invariant mass is actually conserved, when the mass of the binding


energy that has escaped, is taken into account.

Exceptions or caveats to mass/matter conservation

Matter is not perfectly conservedThe principle of matter conservation may be considered as an approximate physical law that is true only in theclassical sense, without consideration of special relativity and quantum mechanics. It is approximately true except incertain high energy applications.A particular difficulty with the idea of conservation of "matter" is that "matter" is not a well-defined wordscientifically, and when particles that are considered to be "matter" (such as electrons and positrons) are annihilatedto make photons (which are often not considered matter) then conservation of matter does not take place over time,even within isolated systems. However, matter is conserved to such an extent that matter conservation may be safelyassumed in chemical reactions and all situations in which radioactivity and nuclear reactions are not involved.

Open systems and thermodynamically closed systemsMass is also not generally conserved in open systems (even if "closed" which means partly open, i.e. to heat andwork). Such is the case when various forms of energy are allowed into, or out of, the system (see for example,binding energy). However, again unless radioactivity or nuclear reactions are involved, the amount of energyescaping systems as heat, work, or electromagnetic radiation is usually too small to be measured as a decrease insystem mass.The law of mass conservation for isolated systems (totally closed to all mass and energy), as viewed over time fromany single inertial frame, continues to be true in modern physics. The reason for this is that relativistic equationsshow that even "massless" particles such as photons still add mass and energy to isolated systems, allowing mass(though not matter) to be strictly conserved in all processes where energy does not escape the system. In relativity,different observers may disagree as to the particular value of the conserved mass of a given system, but eachobserver will agree that this value does not change over time as long as the system is isolated (totally closed toeverything).

General relativityIn general relativity, the total invariant mass of photons in an expanding volume of space will decrease, due to thered shift of such an expansion (see Mass in general relativity). The conservation of both mass and energy thereforedepends on various corrections made to energy in the theory, due to the changing gravitational potential energy ofsuch systems.

References[1] Fr. 12; see pp.2912 of Kirk, G. S.; J. E. Raven, Malcolm Schofield (1983). The Presocratic Philosophers (2 ed.). Cambridge: Cambridge

University Press. ISBN978-0-521-27455-5.[2] Long, A. A.; D. N. Sedley (1987). "Epicureanism: The principals of conservation". The Hellenistic Philosophers. Vol 1: Translations of the

principal sources with philosophical commentary. Cambridge: Cambridge University Press. pp.2526. ISBN0-521-27556-3.[3] Mahavira is dated 599 BCE - 527 BCE. See. Dundas, Paul; John Hinnels ed. (2002). The Jains. London: Routledge. ISBN0-415-26606-8. p.

24[4] Devendra (Muni.), T. G. Kalghatgi, T. S. Devadoss (1983) A source-book in Jaina philosophy Udaipur:Sri Tarak Guru Jain Gran. p.57. Also

see Tattvarthasutra verses 5.29 and 5.37[5] Farid Alakbarov (Summer 2001). A 13th-Century Darwin? Tusi's Views on Evolution (http:/ / azer. com/ aiweb/ categories/ magazine/

92_folder/ 92_articles/ 92_tusi. html), Azerbaijan International 9 (2).[6] *Pomper, Philip (October 1962). "Lomonosov and the Discovery of the Law of the Conservation of Matter in Chemical Transformations".

Ambix 10 (3): 119127. Lomonosov, Mikhail Vasilevich (1970). Mikhail Vasilevich Lomonosov on the Corpuscular Theory. Henry M. Leicester (trans.). Cambridge,


Mass.: Harvard University Press. Introduction, p.25.[7] An Historical Note on the Conservation of Mass (http:/ / www. eric. ed. gov/ ERICWebPortal/ Home. portal?_nfpb=true&

ERICExtSearch_SearchValue_0=EJ128341& ERICExtSearch_SearchType_0=kw& _pageLabel=ERICSearchResult& newSearch=true&rnd=1194465579133& searchtype=keyword), Robert D. Whitaker, Journal of Chemical Education, 52, 10, 658-659, Oct 75

[8][8] Kenneth R. Lang, Astrophysical Formulae, Springer (1999), ISBN 3-540-29692-1

Atom-transfer radical-polymerizationAtom transfer radical polymerization (ATRP) is an example of a living polymerization or a controlled/livingradical polymerization (CRP). Like its counterpart, ATRA or atom transfer radical addition, it is a means offorming carbon-carbon bond through transition metal catalyst. As the name implies, the atom transfer step is the keystep in the reaction responsible for uniform polymer chain growth. ATRP (or transition metal-mediated living radicalpolymerization) was independently discovered by Mitsuo Sawamoto et al.[1] and by Jin-Shan Wang and KrzysztofMatyjaszewski in 1995.[2] This is a typical ATRP reaction:

General ATRP Reaction. A. Initiation. B. Equilibrium with dormant specie.C.Propagation

ATRP

The uniformed polymer chain growth,which leads to low dispersity, stemsfrom the transition metal basedcatalyst. This catalyst provides anequilibrium between active, andtherefore propagating, polymer and aninactive form of the polymer; knownas the dormant form. Since the dormant state of the polymer is vastly preferred in this equilibrium, side reactions aresuppressed.This equilibrium in turn lowers the concentration of propagating radicals, therefore suppressing unintentionaltermination and controlling molecular weights.ATRP reactions are very robust in that they are tolerant of many functional groups like allyl, amino, epoxy, hydroxyand vinyl groups present in either the monomer or the initiator.[3] ATRP methods are also advantageous due to theease of preparation, commercially available and inexpensive catalysts (copper complexes), pyridine based ligandsand initiators (alkyl halides).[4]

The ATRP with styrene. If all the styrene is reacted (the conversion is 100%) the polymer will have 100 units of styrene built into it.PMDETA stands for N,N,N',N,N pentamethyldiethylenetriamine.

Atom-transfer radical-polymerization 12

Components of ATRPThere are five important variable components of Atom Transfer Radical Polymerizations. They are the monomer,initiator, catalyst, solvent and temperature. The following section breaks down the contributions of each componentto the overall polymerization.

MonomerMonomers that are typically used in ATRP are molecules with substituents that can stabilize the propagatingradicals; for example, styrenes, (meth)acrylates, (meth)acrylamides, and acrylonitrile.[5] ATRP are successful atleading to polymers of high number average molecular weight and a narrow polydispersity index when theconcentration of the propagating radical balances the rate of radical termination. Yet, the propagating rate is uniqueto each individual monomer. Therefore, it is important that the other components of the polymerization (initiator,catalysts, ligands and solvents) are optimized in order for the concentration of the dormant species to be greater thanthe concentration of the propagating radical and yet not too great to slow down or halt the reaction.[6][7]

InitiatorThe number of growing polymer chains is determined by the initiator. The faster the initiation, the fewerterminations and transfers, the more consistent the number of propagating chains leading to narrow molecular weightdistributions.[7] Organic halides that are similar in the organic framework as the propagating radical are often chosenas initiators.[6] Most initators for ATRP are alkyl halides.[8] Alkyl halides such as alkyl bromides are more reactivethan alkyl chlorides and both have good molecular weight control.[6][7] The shape or structure of your initiator candetermine the architecture of your polymer. For example, initiators with multiple alkyl halide groups on a single corecan lead to a star-like polymer shape.[9]

Illustration of a star initiator for ATRP

CatalystThe catalyst is the most important component of ATRP because it determines the equilibrium constant between theactive and dormant species. This equilibrium determines the polymerization rate and an equilibrium constant toosmall may inhibit or slow the polymerization while an equilibrium constant too large leads to a high distribution ofchain lengths.[7]

There are several requirements for the metal catalyst:1.1. there needs to be two accessible oxidation states that are separated by one electron2.2. the metal center needs to have a reasonable affinity for halogens3.3. the coordination sphere of the metal needs to be expandable when its oxidized so to be able to accommodate the

halogen


4. a strong ligand complexation.[6]

The most studied catalysts are those that polymerizations involving copper, which has shown the most versatility,showing successful polymerizations regardless of the monomer.

SolventToluene,1,4-dioxane, xylene, anisole, DMF, DMSO, water, methanol, acetonitrile, chloroform, bulk monomer

Reverse ATRPIn reverse ATRP, the catalyst is added in its higher oxidation state. Chains are activated by conventional radicalinitiators (e.g. AIBN) and deactivated by the transition metal. The source of transferrable halogen is the copper salt,so this must be present in concentrations comparable to the transition metal. A mixture of radical initiator and active(lower oxidation state) catalyst allows for the creation of block copolymers (contaminated with homopolymer) whichis impossible using standard reverse ATRP. This is called SR&NI (simultaneous reverse and normal initiationATRP).

AGET ATRPActivators generated by electron transfer uses a reducing agent unable to initiate new chains (instead of organicradicals) as regenerator for the low-valent metal. Examples are metallic Cu, tin(II), ascorbic acid, or triethylamine. Itallows for lower concentrations of transition metals, and may also be possible in aqueous or dispersed medium.

Hybrid and bimetallic systemsThis technique uses a variety of different metals/oxidation states, possibly on solid supports, to act asactivators/deactivators, possibly with reduced toxicity or sensitivity. Iron salts can, for example, efficiently activatealkyl halides but requires an efficient Cu(II) deactivator which can be present in much lower concentrations(35mol%)

ICAR ATRPInitiators for continuous activator regeneration is a technique that uses large excesses of initiator to continuouslyregenerate the activator, lowering its required concentration from thousands of ppm to around 1 ppm; making it anindustrially relevant technique. Styrene is especially interesting because it generates radicals when sufficientlyheated.

ARGET ATRPActivators regenerated by electron transfer can be used to make block copolymers using a method similar to AGETbut requiring strongly reduced amounts of metal, since the activator is regenerated from the deactivator by a largeexcess of reducing agent (e.g. hydrazine, phenoles, sugars, ascorbic acid, etc...) It differs from AGET ATRP in thatAGET uses reducing agents to generate the active catalyst (in quasi stoichiometric amounts) while in ARGET a largeexcess is used to continuously regenerate the activator allowing transition metal concentrations to drop to ~1 ppmwithout loss of control.


Polymers Made by ATRP Polystyrene Poly (methyl methacrylate) Polyacrylamide

References[1] Kato, M; Kamigaito, M; Sawamoto, M; Higashimura, T (1995). "Polymerization of Methyl Methacrylate with the Carbon

Tetrachloride/Dichlorotris-(triphenylphosphine)ruthenium(II)/Methylaluminum Bis(2,6-di-tert-butylphenoxide) Initiating System: Possibilityof Living Radical Polymerization". Macromolecules 28: 17211723. Bibcode1995MaMol..28.1721K. doi:10.1021/ma00109a056.

[2] Wang, J; Matyjaszewski, K (1995). "Controlled/"living" radical polymerization. Atom transfer radical polymerization in the presence oftransition-metal complexes". J. Am. Chem. Soc. 117: 56145615. doi:10.1021/ja00125a035.

[3] Cowie, J. M. G.; Arrighi, V. In Polymers: Chemistry and Physics of Modern Materials; CRC Press Taylor and Francis Group: Boca Raton, Fl,2008; 3rd Ed., pp. 8284 ISBN 0849398134

[4] Matyjaszewski, K. Fundamentals of ATRP Research (http:/ / www. chem. cmu. edu/ groups/ maty/ about/ research/ 03. html) (accessed01/07, 2009).

[5] Patten, T. E; Matyjaszewski, K (1998). "Atom Transfer Radical Polymerization and the Synthesis of Polymeric Materials". Adv. Mater. 10:901. doi:10.1002/(SICI)1521-4095(199808)10:123.0.CO;2-B.

[6] Odian, G. In Radical Chain Polymerization; Principles of Polymerization; Wiley-Interscience: Staten Island, New York, 2004; Vol. , pp316321.

[7] Matyjaszewski, K; Xia, J (2001). "Atom Transfer Radical Polymerization". Chem. Rev. 101 (9): 29212990. doi:10.1021/cr940534g.ISSN0009-2665. PMID11749397.

[8] Matyjaszewski, Krzysztof; Nicolay V. Tsarevsky (2009). "Nanostructured functional materials prepared by atom transfer radicalpolymerization". Nature Chemistry 1 (4): 276288. Bibcode2009NatCh...1..276M. doi:10.1038/NCHEM.257.

[9] Jakubowski, Wojciech. "Complete Tools for the Synthesis of Well-Defined Functionalized Polymers via ATRP" (http:/ / www. sigmaaldrich.com/ materials-science/ polymer-science/ atrp. html). Sigma-Aldrich. . Retrieved 21 July 2010.

Living polymerizationIn polymer chemistry, living polymerization is a form of addition polymerization where the ability of a growingpolymer chain to terminate has been removed.[1][2] This can be accomplished in a variety of ways. Chain terminationand chain transfer reactions are absent and the rate of chain initiation is also much larger than the rate of chainpropagation. The result is that the polymer chains grow at a more constant rate than seen in traditional chainpolymerization and their lengths remain very similar (i.e. they have a very low polydispersity index). Livingpolymerization is a popular method for synthesizing block copolymers since the polymer can be synthesized instages, each stage containing a different monomer. Additional advantages are predetermined molar mass and controlover end-groups.Living polymerization in the literature is often called "living" polymerization or controlled polymerization. Livingpolymerization was demonstrated by Michael Szwarc in 1956 in the anionic polymerization of styrene with an alkalimetal / naphthalene system in tetrahydrofuran (THF). He found that after addition of monomer to the initiator systemthat the increase in viscosity would eventually cease but that after addition of a new amount of monomer after sometime the viscosity would start to increase again.[3]

The main living polymerization techniques are: Living anionic polymerization Living cationic polymerization Ring opening metathesis polymerization Living free radical polymerization Group transfer polymerization living Ziegler-Natta polymerization

Living polymerization 15

Living anionic polymerizationAs early as 1936, Karl Ziegler proposed that anionic polymerization of styrene and butadiene by consecutiveaddition of monomer to an alkyl lithium initiator occurred without chain transfer or termination. Twenty years later,living polymerization was demonstrated by Szwarc through the anionic polymerization of styrene in THF usingsodium naphthalenide as celerator.[4][5][6]

Living cationic polymerizationMonomers for living cationic polymerization are electron-rich alkenes such as vinyl ethers, isobutylene, styrene, andN-vinylcarbazole. The initiators are binary systems consisting of a electrophile and a Lewis acid. The method wasdeveloped around 1980 with contributions from Higashimura, Sawamoto and Kennedy.

Living ring-opening metathesis polymerizationGiven the right reaction conditions ring-opening metathesis polymerization (ROMP) can be rendered living. The firstsuch systems were described by Robert H. Grubbs in 1986 based on norbornene and Tebbe's reagent and in 1978Grubbs together with Richard R. Schrock describing living polymerization with a tungsten carbene complex.[7]

Living free radical polymerizationStarting in the 1970s several new methods were discovered which allowed the development of living polymerizationusing free radical chemistry. These techniques involved catalytic chain transfer polymerization, iniferter mediatedpolymerization, stable free radical mediated polymerization (SFRP), atom transfer radical polymerization (ATRP),reversible addition-fragmentation chain transfer (RAFT) polymerization, and iodine-transfer polymerization.

Living group-transfer polymerizationGroup-transfer polymerization also has characteristics of living polymerization.[8] It is applied to alkylatedmethacrylate monomers and the initiator is a silyl ketene acetal. New monomer adds to the initiator and to the activegrowing chain in a Michael reaction. With each addition of a monomer group the trimethylsilyl group is transferredto the end of the chain. The active chain-end is not ionic as in anionic or cationic polymeriation but is covalent. Thereaction can be catalysed by bifluorides and bioxyanions such as tris(dialkylamino)sulfonium bifluoride or tetrabutylammonium bibenzoate. The method was discovered in 1983 by O.W. Webster[9] and the name first suggested byBarry Trost.

Living Ziegler-Natta polymerizationSeveral reported methods exist that introduce livingness in Ziegler-Natta polymerization.[10] The monomer in thistype of polymerization (a subset of coordination polymerization) is an alpha-olefin and the active site contains analkyl to metal bond. Chain growth is based on the Cossee-Arlman mechanism. An early method (Doi, 1979)describes propene polymerization in toluene at 50C using diethylaluminium chloride and a vanadium catalyst forexample V(acac)3 to syndiotactic polypropylene with a polydispersity index of 1.05 to 1.4.

[11][12] Another livingsystem as described by McConville in 1996 is based on titanium using 1-hexene, [RN(CH2)3NR]TiMe2 andtris(pentafluorophenyl)boron[13]

Living polymerization 16

External links IUPAC Gold Book Definition [14]

precise definitions from the American Chemical Society [15]

Living Ziegler-Natta Polymerization Article [16]

Living polymers 50 years of evolution Article [17]

References[1] Halasa, A. F. Rubber Chem. Technol., 1981, 54, 627.[2] (2006) The Chemistry of Radical Polymerization - Second fully revised edition (Graeme Moad & David H. Solomon). Elsevier. ISBN

0-08-044286-2[3] Webster, O. W. Science, 1991, 251, 8877.[4] M. Szwarc, Nature 1956, 178, 1168.[5] Szwarc, M.; Levy, M.; Milkovich, R. J. Am. Chem. Soc. 1956, 78, 2656.[6][6] US 4 158 678 (priority date 30 June 1976).[7] "Ring-opening polymerization of norbornene by a living tungsten alkylidene complex" R. R. Schrock, J. Feldman, L. F. Cannizzo, R. H.

Grubbs Macromolecules; 1987; 20(5); 11691172. doi:10.1021/ma00171a053[8] Polymer chemistry: a practical approach 2004 Fred J. Davis[9] "Group-transfer polymerization. 1. A new concept for addition polymerization with organosilicon initiators" O. W. Webster, W. R. Hertler,

D. Y. Sogah, W. B. Farnham, T. V. RajanBabu J. Am. Chem. Soc., 1983, 105 (17), pp. 57065708 doi:10.1021/ja00355a039[10] organicdivision.org Essay: Living Ziegler-Natta Polymerization 2002 Richard J. Keaton PDF (http:/ / www. organicdivision. org/ ama/ orig/

Fellowship/ 2002_2003_Awardees/ Essays/ keaton. pdf)[11] "'Living' Coordination Polymerization of Propene Initiated by the Soluble V(acac)3-Al(C2H5)2Cl System" Yoshiharu Doi, Satoshi Ueki,

Tominaga Keii Macromolecules, 1979, 12 (5), pp. 814819 doi:10.1021/ma60071a004[12] "Living coordination polymerization of propene with a highly active vanadium-based catalyst" Yoshiharu Doi, Shigeo Suzuki, Kazuo Soga

Macromolecules, 1986, 19 (12), pp. 28962900 doi:10.1021/ma00166a002[13] "Living Polymerization of -Olefins by Chelating Diamide Complexes of Titanium" John D. Scollard and David H. McConville J. Am.

Chem. Soc., 1996, 118 (41), pp. 1000810009 doi:10.1021/ja9618964[14] http:/ / www. iupac. org/ goldbook/ L03597. pdf[15] http:/ / www. polyacs. org/ nomcl/ mnn12. html[16] http:/ / organicdivision. org/ essays_2002/ keaton. pdf[17] http:/ / www. weizmann. ac. il/ ICS/ booklet/ 18/ pdf/ levy. pdf

Dispersity 17

Dispersity

A monodisperse collection

A polydisperse collection

In physical and organic chemistry, the dispersity is a measure of theheterogeneity of sizes of molecules or particles in a mixture. Acollection of objects is called monodisperse if the objects have thesame size, shape, or mass. A sample of objects that have aninconsistent size, shape and mass distribution is called polydisperse.The objects can be in any form of chemical dispersion, such asparticles in a colloid, droplets in a cloud,[1] crystals in a rock,[2] orpolymer molecules in a solvent.[3] Polymers can possess a distributionof molecular mass; particles often possess a wide distribution of size,surface area and mass; and thin films can possess a varied distributionof film thickness.

IUPAC has deprecated the use of the term polydispersity index havingreplaced it with the term dispersity, represented by the symbol andcalculated using the equation = Mm/Mn, where Mm is themass-average molar mass and Mn is the number-average molar mass.IUPAC has also deprecated the terms monodisperse, which isconsidered to be self-contradictory, and polydisperse, which isconsidered redundant, preferring the terms uniform and non-uniforminstead.[4]

OverviewA monodisperse, or uniform, polymer is composed of molecules of the same mass.[5] Natural polymers are typicallymonodisperse.[6] Synthetic monodisperse polymer chains can be made by processes such as anionic polymerization,a method using an anionic catalyst to produce chains that are similar in length. This technique is also known as livingpolymerization. It is used commercially for the production of block copolymers. Monodisperse collections can beeasily created through the use of template-based synthesis, a common method of synthesis in nanotechnology.A polymer material is denoted by the term polydisperse, or non-uniform, if its chain lengths vary over a wide rangeof molecular masses. This is characteristic of man-made polymers.[7]. Natural organic matter produced by thedecomposition of plants and wood debris in soils (humic substances) also has a pronounced polydispersed character.It is the case of humic acids and fulvic acids, natural polyelectrolyte substances having respectively higher and lowermolecular weights. Another interpretation of polydispersity index is explained in the article Dynamic light scattering(cumulant method subheading). In this sense, the PDI values are in the range from 0 to 1.

Dispersity 18

IUPAC definition of dispersity

The polydispersity index (PDI) or heterogeneity index, or simply dispersity(), is a measure of the distribution of molecular mass in a given polymersample. The PDI calculated is the weight average molecular weight ( )divided by the number average molecular weight ( ). It indicates thedistribution of individual molecular masses in a batch of polymers. The PDIhas a value equal to or greater than 1, but as the polymer chains approachuniform chain length, the PDI approaches unity (1).[8] For some naturalpolymers PDI is almost taken as unity. The PDI from polymerization is oftendenoted as:

,where is the weight average molecular weight and is the numberaverage molecular weight. is more sensitive to molecules of lowmolecular mass, while is more sensitive to molecules of high molecular mass.

Effect of polymerization mechanismTypical dispersities vary based on the mechanism of polymerization and can be affected by a variety of reactionconditions. In synthetic polymers, it can vary greatly due to reactant ratio, how close the polymerization went tocompletion, etc. For typical addition polymerization, values of the PDI can range around 10 to 20. For typical steppolymerization, most probable values of the PDI are around 2 Carothers' equation limits PDI to values of 2 andbelow.Living polymerization, a special case of addition polymerization, leads to values very close to 1. Such is the casealso in biological polymers, where the dispersity can be very close or equal to 1, indicating only one length ofpolymer is present.

Determination methods Gel permeation chromatography (also known as size exclusion chromatography) Light scattering measurements such as dynamic light scattering Direct measurement via mass spectrometry using MALDI or ESI-MS

References[1] Martins, J. A.; Silva Dias, M. A. F. (2009). "The impact of smoke from forest fires on the spectral dispersion of cloud droplet size

distributions in the Amazonian region". Environmental Research Letters 4: 015002. doi:10.1088/1748-9326/4/1/015002.[2] Higgins, Michael D. (2000). "Measurement of crystal size distributions" (http:/ / wwwdsa. uqac. ca/ ~mhiggins/ am_min_2000. pdf).

American Mineralogist 85: 11051116. .[3] Okita, K.; Teramoto, A.; Kawahara, K.; Fujita, H. (1968). "Light scattering and refractometry of a monodisperse polymer in binary mixed

solvents". The Journal of Physical Chemistry 72: 278. doi:10.1021/j100847a053.[4] Stepto, R. F. T.; Gilbert, R. G.; Hess, M.; Jenkins, A. D.; Jones, R. G.; Kratochvl P. (2009). " Dispersity in Polymer Science (http:/ / media.

iupac. org/ publications/ pac/ 2009/ pdf/ 8102x0351. pdf)" Pure Appl. Chem. 81 (2): 351353. DOI:10.1351/PAC-REC-08-05-02.[5] "monodisperse polymer (See: uniform polymer)" (http:/ / goldbook. iupac. org/ M04012. html). IUPAC Gold Book. International Union of

Pure and Applied Chemistry. . Retrieved 25 January 2012.[6] Brown, William H.; Foote, Christopher S.; Iverson, Brent L.; Anslyn, Eric V. (2012). Organic chemistry (http:/ / books. google. ca/

books?id=rxRHzOS-3xoC& pg=PT1193) (6 ed.). Cengage Learning. p.1161. ISBN978-0-8400-5498-2. .[7] http:/ / www. chemicool. com/ definition/ polydisperse. html[8] Peter Atkins and Julio De Paula, Atkins' Physical Chemistry, 9th edition (Oxford University Press, 2010, ISBN 978-0-19-954337-3)

Dispersity 19

External links Polymer structure (http:/ / openlearn. open. ac. uk/ mod/ resource/ view. php?id=196629)

Molar mass distributionIn linear polymers the individual polymer chains rarely have exactly the same degree of polymerization and molarmass, and there is always a distribution around an average value. The molar mass distribution (or molecular weightdistribution) in a polymer describes the relationship between the number of moles of each polymer species (Ni) andthe molar mass (Mi) of that species.

[1] The molar mass distribution of a polymer may be modified by polymerfractionation.

Definition of molar mass averagesDifferent average values can be defined depending on the statistical method that is applied. The weighted mean canbe taken with the weight fraction, the mole fraction or the volume fraction: Number average molar mass or Mn Weight average molar mass or Mw Viscosity average molar mass or Mv Z average molar mass or Mz

[2]

Here a is the exponent in the Mark-Houwink equation that relates the intrinsic viscosity to molar mass.

MeasurementThese different definitions have true physical meaning because different techniques in physical polymer chemistryoften measure just one of them. For instance, osmometry measures number average molar mass and small-anglelaser light scattering measures weight average molar mass. Mv is obtained from viscosimetry and Mz bysedimentation in an analytical ultracentrifuge. The quantity a in the expression for the viscosity average molar massvaries from 0.5 to 0.8 and depends on the interaction between solvent and polymer in a dilute solution. In a typicaldistribution curve, the average values are related to each other as follows: Mn < Mv < Mw < Mz. Polydispersity of asample is defined as Mw divided by Mn and gives an indication just how narrow a distribution is.

[2]

The most common technique for measuring molecular weight used in modern times is a variant of high-pressureliquid chromatography (HPLC) known by the interchangeable terms of size exclusion chromatography (SEC) andgel permeation chromatography (GPC). These techniques involve forcing a polymer solution through a matrix ofcross-linked polymer particles at a pressure of up to several thousand psi. The limited accessibility of stationaryphase pore volume for the polymer molecules results in shorter elution times for high-molecular-weight species. Theuse of low polydispersity standards allows the user to correlate retention time with molecular weight, although theactual correlation is with the Hydrodynamic volume. If the relationship between molar mass and the hydrodynamicvolume changes (i.e., the polymer is not exactly the same shape as the standard) then the calibration for mass is inerror.The most common detectors used for size exclusion chromatography include online methods similar to the bench methods used above. By far the most common is the differential refractive index detector that measures the change in refractive index of the solvent. This detector is concentration-sensitive and very molecular-weight-insensitive, so it is ideal for a single-detector GPC system, as it allows the generation of mass v's molecular weight curves. Less

Molar mass distribution 20

common but more accurate and reliable is a molecular-weight-sensitive detector using multi-angle laser-lightscattering - see Static Light Scattering. These detectors directly measure the molecular weight of the polymer and aremost often used in conjunction with differental refractive index detectors. A further alternative is either low-anglelight scattering, which uses a single low angle to determine the molar mass, or Right-Angle-Light Laser scattering incombination with a viscometer, although this latter technique does not give an absolute measure of molar mass butone relative to the structural model used.The molar mass distribution of a polymer sample depends on factors such as chemical kinetics and work-upprocedure. Ideal step-growth polymerization gives a polymer with polydispersity of 2. Ideal living polymerizationresults in a polydispersity of 1. By dissolving a polymer an insoluble high molar mass fraction may be filtered offresulting in a large reduction in Mw and a small reduction in Mn thus reducing polydispersity.

Number average molecular weightThe number average molecular weight is a way of determining the molecular weight of a polymer. Polymermolecules, even ones of the same type, come in different sizes (chain lengths, for linear polymers), so the averagemolecular weight will depend on the method of averaging. The number average molecular weight is the ordinaryarithmetic mean or average of the molecular weights of the individual macromolecules. It is determined bymeasuring the molecular weight of n polymer molecules, summing the weights, and dividing by n.

The number average molecular weight of a polymer can be determined by gel permeation chromatography,viscometry via the (Mark-Houwink equation), colligative methods such as vapor pressure osmometry, end-groupdetermination or proton NMR.[3]

An alternative measure of the molecular weight of a polymer is the weight average molecular weight. The ratio ofthe weight average to the number average is called the polydispersity index.High Number-Average Molecular Weight Polymers may be obtained only with a high fractional monomerconversion in the case of step-growth polymerization, as per the Carothers' equation.

Weight average molecular weightThe weight average molecular weight is a way of describing the molecular weight of a polymer. Polymermolecules, even if of the same type, come in different sizes (chain lengths, for linear polymers), so we have to takean average of some kind. For the weight average molecular weight, this is calculated by

where is the number of molecules of molecular weight .If the weight average molecular weight is w, and one chooses a random monomer, then the polymer it belongs to willhave a weight of w on average (for a homopolymer).The weight average molecular weight can be determined by light scattering, small angle neutron scattering (SANS),X-ray scattering, and sedimentation velocity.An alternative measure of molecular weight for a polymer is the number average molecular weight; the ratio of theweight average to the number average is called the polydispersity index.The weight-average molecular weight, Mw, is also related to the fractional monomer conversion, p, in step-growthpolymerization as per Carothers' equation:

, where Mo is the molecular weight of the repeating unit.

Molar mass distribution 21

References[1][1] I. Katime "Qumica Fsica Macromolecular". Servicio Editorial de la Universidad del Pas Vasco. Bilbao[2][2] R.J. Young and P.A. Lovell, Introduction to Polymers, 1991[3] Polymer Molecular Weight Analysis by 1H NMR Spectroscopy Josephat U. Izunobi and Clement L. Higginbotham J. Chem. Educ., 2011, 88

(8), pp 10981104 doi:10.1021/ed100461v

Biotechnology

Insulin crystals.

Biotechnology (sometimes shortened to "biotech") is generallyaccepted as the use of living systems and organisms to develop ormake useful products, or "any technological application that usesbiological systems, living organisms or derivatives there of, to make ormodify products or processes for specific use" (UN Convention onBiological Diversity)[1] . For thousands of years, humankind has usedbiotechnology in agriculture, food production and medicine.[2] Theterm itself is largely believed to have been coined in 1919 byHungarian engineer Karl Ereky. In the late 20th and early 21st century,biotechnology has expanded to include new and diverse sciences suchas genomics, recombinant gene technologies, applied immunology, and development of pharmaceutical therapiesand diganostic tests.[3]

Various definitions of 'biotechnology'The concept of 'biotech' or 'biotechnology' encompasses a wide range of procedures (and history) for modifyingliving organisms according to human purposes going back to domestication of animals, cultivation of plants, and"improvements" to these through breeding programs that employ artificial selection and hybridization. Modern usagealso includes genetic engineering as well as cell and tissue culture technologies. The United Nations Convention onBiological Diversity defines 'biotechnology' as: "Any technological application that uses biological systems, livingorganisms, or derivatives thereof, to make or modify products or processes for specific use."[4] In other words,biotechology can be defined as the mere application of technical advances in life science to develop commercialproducts.Biotechnology also draws on the pure biological sciences (genetics, microbiology, animal cell culture, molecularbiology, biochemistry, embryology, cell biology). And in many instances it is also dependent on knowledge andmethods from outside the sphere of biology including: chemical engineering, bioprocess engineering, bioinformatics, a new brand of information technology, and biorobotics.Conversely, modern biological sciences (including even concepts such as molecular ecology) are intimately entwined and dependent on the methods developed through biotechnology and what is commonly thought of as the life sciences industry. Biotechnology is the research and development in the laboratory using bioinformatics for exploration, extraction, exploitation and production from any living organisms and any source of biomass by means of biochemical engineering where high value-added products could be planned (reproduced by biosynthesis, for example), forecasted, formulated, developed, manufactured and marketed for the purpose of sustainable operations (for the return from bottomless initial investment on R & D) and gaining durable patents rights (for exclusives rights for sales, and prior to this to receive national and international approval from the results on animal experiment and

Biotechnology 22

human experiment, especially on the pharmaceutical branch of biotechnology to prevent any undetected side-effectsor safety concerns by using the products), for more about the biotechnology industry, see.[5][6][7][8][9][10]

By contrast, bioengineering is generally thought of as a related field with its emphasis more on higher systemsapproaches (not necessarily altering or using biological materials directly) for interfacing with and utilizing livingthings.

History

Brewing was an early application ofbiotechnology

Although not normally what first comes to mind, many forms ofhuman-derived agriculture clearly fit the broad definition of "using abiotechnological system to make products". Indeed, the cultivation ofplants may be viewed as the earliest biotechnological enterprise.

Agriculture has been theorized to have become the dominant way ofproducing food since the Neolithic Revolution. Through earlybiotechnology, the earliest farmers selected and bred the best suitedcrops, having the highest yields, to produce enough food to support agrowing population. As crops and fields became increasingly large anddifficult to maintain, it was discovered that specific organisms andtheir by-products could effectively fertilize, restore nitrogen, andcontrol pests. Throughout the history of agriculture, farmers haveinadvertently altered the genetics of their crops through introducingthem to new environments and breeding them with other plants oneof the first forms of biotechnology.

These processes also were included in early fermentation of beer.[11]

These processes were introduced in early Mesopotamia, Egypt, and India, and still use the same basic biologicalmethods. In brewing, malted grains (containing enzymes) convert starch from grains into sugar and then addingspecific yeasts to produce beer. In this process, carbohydrates in the grains were broken down into alcohols such asethanol. Later other cultures produced the process of lactic acid fermentation which allowed the fermentation andpreservation of other forms of food, such as soy sauce. Fermentation was also used in this time period to produceleavened bread. Although the process of fermentation was not fully understood until Louis Pasteur's work in 1857, itis still the first use of biotechnology to convert a food source into another form.

For thousands of years, humans have used selective breeding to improve production of crops and livestock to usethem for food. In selective breeding, organisms with desirable characteristics are mated to produce offspring with thesame characteristics. For example, this technique was used with corn to produce the largest and sweetest crops.[12]

In the early twentieth century scientists gained a greater understanding of microbiology and explored ways ofmanufacturing specific products. In 1917, Chaim Weizmann first used a pure microbiological culture in an industrialprocess, that of manufacturing corn starch using Clostridium acetobutylicum, to produce acetone, which the UnitedKingdom desperately needed to manufacture explosives during World War I.[13]

Biotechnology has also led to the development of antibiotics. In 1928, Alexander Fleming discovered the moldPenicillium. His work led to the purification of the antibiotic by Howard Florey, Ernst Boris Chain and NormanHeatley, penicillin. In 1940, penicillin became available for medicinal use to treat bacterial infections in humans.[12]

The field of modern biotechnology is generally thought of as having been born in 1971 when Paul Berg's (Stanford) experiments in gene splicing had early success. Herbert W. Boyer (Univ. Calif. at San Francisco) and Stanley N. Cohen (Stanford) significantly advanced the new technology in 1972 by transferring genetic material into a bacterium, such that the imported material would be reproduced. The commercial viability of a biotechnology industry was significantly expanded on June 16, 1980, when the United States Supreme Court ruled that a genetically

Biotechnology 23

modified microorganism could be patented in the case of Diamond v. Chakrabarty.[14] Indian-born AnandaChakrabarty, working for General Electric, had modified a bacterium (of the Pseudomonas genus) capable ofbreaking down crude oil, which he proposed to use in treating oil spills. (Chakrabarty's work did not involve genemanipulation but rather the transfer of entire organelles between strains of the Pseudomonas bacterium.Revenue in the industry is expected to grow by 12.9% in 2008. Another factor influencing the biotechnology sector'ssuccess is improved intellectual property rights legislationand enforcementworldwide, as well as strengtheneddemand for medical and pharmaceutical products to cope with an ageing, and ailing, U.S. population.[15]

Rising demand for biofuels is expected to be good news for the biotechnology sector, with the Department of Energyestimating ethanol usage could reduce U.S. petroleum-derived fuel consumption by up to 30% by 2030. Thebiotechnology sector has allowed the U.S. farming industry to rapidly increase its supply of corn and soybeansthemain inputs into biofuelsby developing genetically modified seeds which are resistant to pests and drought. Byboosting farm productivity, biotechnology plays a crucial role in ensuring that biofuel production targets are met.[16]

Applications

A rose plant that began as cells grown in a tissueculture

Biotechnology has applications in four major industrial areas,including health care (medical), crop production and agriculture, nonfood (industrial) uses of crops and other products (e.g. biodegradableplastics, vegetable oil, biofuels), and environmental uses.

For example, one application of biotechnology is the directed use oforganisms for the manufacture of organic products (examples includebeer and milk products). Another example is using naturally presentbacteria by the mining industry in bioleaching. Biotechnology is alsoused to recycle, treat waste, cleanup sites contaminated by industrialactivities (bioremediation), and also to produce biological weapons.

A series of derived terms have been coined to identify several branchesof biotechnology; for example: Bioinformatics is an interdisciplinary field which addresses

biological problems using computational techniques, and makes therapid organization and analysis of biological data possible. The fieldmay also be referred to as computational biology, and can bedefined as, "conceptualizing biology in terms of molecules and thenapplying informatics techniques to understand and organize theinformation associated with these molecules, on a large scale."[17]

Bioinformatics plays a key role in various areas, such as functional genomics, structural genomics, andproteomics, and forms a key component in the biotechnology and pharmaceutical sector.

Blue biotechnology is a term that has been used to describe the marine and aquatic applications of biotechnology,but its use is relatively rare.

Green biotechnology is biotechnology applied to agricultural processes. An example would be the selection anddomestication of plants via micropropagation. Another example is the designing of transgenic plants to growunder specific environments in the presence (or absence) of chemicals. One hope is that green biotechnologymight produce more environmentally friendly solutions than traditional industrial agriculture. An example of thisis the engineering of a plant to express a pesticide, thereby ending the need of external application of pesticides.An example of this would be Bt corn. Whether or not green biotechnology products such as this are ultimatelymore environmentally friendly is a topic of considerable debate.

Biotechnology 24

Red biotechnology is applied to medical processes. Some examples are the designing of organisms to produceantibiotics, and the engineering of genetic cures through genetic manipulation.

White biotechnology, also known as industrial biotechnology, is biotechnology applied to industrial processes.An example is the designing of an organism to produce a useful chemical. Another example is the using ofenzymes as industrial catalysts to either produce valuable chemicals or destroy hazardous/polluting chemicals.White biotechnology tends to consume less in resources than traditional processes used to produce industrialgoods.{{Citation needed|date=October 2009} http:/ / www. bio-entrepreneur. net/ Advance-definition-biotech.pdf}

The investment and economic output of all of these types of applied biotechnologies is termed as bioeconomy.

MedicineIn medicine, modern biotechnology finds promising applications in such areas as drug production pharmacogenomics gene therapy genetic testing (or genetic screening): techniques in molecular biology detect genetic diseases. To test the

developing fetus for Down syndrome, Amniocentesis and chorionic villus sampling can be used.[12]

Pharmacogenomics

DNA microarray chip some can do as many asa million blood tests at once

Pharmacogenomics is the study of how the genetic inheritance of anindividual affects his/her body's response to drugs. It is a portmanteauderived from the words "pharmacology" and "genomics". It is hencethe study of the relationship between pharmaceuticals and genetics.The vision of pharmacogenomics is to be able to design and producedrugs that are adapted to each person's genetic makeup.[18]

Pharmacogenomics results in the following benefits:[18]

1. Development of tailor-made medicines. Using pharmacogenomics,pharmaceutical companies can create drugs based on the proteins,enzymes and RNA molecules that are associated with specific genesand diseases. These tailor-made drugs promise not only to maximize therapeutic effects but also to decreasedamage to nearby healthy cells.

2.2. More accurate methods of determining appropriate drug dosages. Knowing a patient's genetics will enabledoctors to determine how well his/ her body can process and metabolize a medicine. This will maximize the valueof the medicine and decrease the likelihood of overdose.

3.3. Improvements in the drug discovery and approval process. The discovery of potential therapies will be madeeasier using genome targets. Genes have been associated with numerous diseases and disorders. With modernbiotechnology, these genes can be used as targets for the development of effective new therapies, which couldsignificantly shorten the drug discovery process.

4.4. Better vaccines. Safer vaccines can be designed and produced by organisms transformed by means of geneticengineering. These vaccines will elicit the immune response without the attendant risks of infection. They will beinexpensive, stable, easy to store, and capable of being engineered to carry several strains of pathogen at once.

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Pharmaceutical products

Computer-generated image of insulin hexamershighlighting the threefold symmetry, the zinc ions

holding it together, and the histidine residuesinvolved in zinc binding.

Most traditional pharmaceutical drugs are relatively small moleculesthat bind to particular molecular targets and either activate ordeactivate biological processes. Small molecules are typicallymanufactured through traditional organic synthesis, and many can betaken orally. In contrast, Biopharmaceuticals are large biologicalmolecules such as proteins that are developed to address targets thatcannot easily be addressed by small molecules. Some examples ofbiopharmaceutical drugs include Infliximab, a monoclonal antibodyused in the treatment of autoimmune diseases, Etanercept, a fusionprotein used in the treatment of autoimmune diseases, and Rituximab,a chimeric monoclonal antibody used in the treatment of cancer. Dueto their larger size, and corresponding difficulty with surviving thestomach, colon and liver, biopharmaceuticals are typically injected.

Modern biotechnology is often associated with the use of geneticallyaltered microorganisms such as E. coli or yeast for the production ofsubstances like synthetic insulin or antibiotics. It can also refer totransgenic animals or transgenic plants, such as Bt corn. Genetically altered mammalian cells, such as ChineseHamster Ovary cells (CHO), are also used to manufacture certain pharmaceuticals. Another promising newbiotechnology application is the development of plant-made pharmaceuticals.

Biotechnology is also commonly associated with landmark breakthroughs in new medical therapies to treat hepatitisB, hepatitis C, cancers, arthritis, haemophilia, bone fractures, multiple sclerosis, and cardiovascular disorders. Thebiotechnology industry has also been instrumental in developing molecular diagnostic devices that can be used todefine the target patient population for a given biopharmaceutical. Herceptin, for example, was the first drugapproved for use with a matching diagnostic test and is used to treat breast cancer in women whose cancer cellsexpress the protein HER2.Modern biotechnology can be used to manufacture existing medicines relatively easily and cheaply. The firstgenetically engineered products were medicines designed to treat human diseases. To cite one example, in 1978Genentech developed synthetic humanized insulin by joining its gene with a plasmid vector inserted into thebacterium Escherichia coli. Insulin, widely used for the treatment of diabetes, was previously extracted from thepancreas of abattoir animals (cattle and/or pigs). The resulting genetically engineered bacterium enabled theproduction of vast quantities of synthetic human insulin at relatively low cost.[19] According to a 2003 studyundertaken by the International Diabetes Federation (IDF) on the access to and availability of insulin in its membercountries, synthetic 'human' insulin is considerably more expensive in most countries where both synthetic 'human'and animal insulin are commercially available: e.g. within European countries the average price of synthetic 'human'insulin was twice as high as the price of pork insulin.[20] Yet in its position statement, the IDF writes that "there is nooverwhelming evidence to prefer one species of insulin over another" and "[modern, highly purified] animal insulinsremain a perfectly acceptable alternative.[21]

Modern biotechnology has evolved, making it possible to produce more easily and relatively cheaply human growthhormone, clotting factors for hemophiliacs, fertility drugs, erythropoietin and other drugs.[22] Most drugs today arebased on about 500 molecular targets. Genomic knowledge of the genes involved in diseases, disease pathways, anddrug-response sites are expected to lead to the discovery of thousands more new targets.[22]

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Genetic testing

Gel electrophoresis

Genetic testing involves the direct examination of the DNA moleculeitself. A scientist scans a patient's DNA sample for mutated sequences.

There are two major types of gene tests. In the first type, a researchermay design short pieces of DNA ("probes") whose sequences arecomplementary to the mutated sequences. These probes will seek theircomplement among the base pairs of an individual's genome. If themutated sequence is present in the patient's genome, the probe willbind to it and flag the mutation. In the second type, a researcher mayconduct the gene test by comparing the sequence of DNA bases in apatient's gene to disease in healthy individuals or their progeny.Genetic testing is now used for: Carrier screening, or the identification of unaffected individuals who carry one copy of a gene for a disease that

requires two copies for the disease to manifest; Confirmational diagnosis of symptomatic individuals; Determining sex; Forensic/identity testing; Newborn screening; Prenatal diagnostic screening; Presymptomatic testing for estimating the risk of developing adult-onset cancers; Presymptomatic testing for predicting adult-onset disorders.Some genetic tests are already available, although most of them are used in developed countries. The tests currentlyavailable can detect mutations associated with rare genetic disorders like cystic fibrosis, sickle cell anemia, andHuntington's disease. Recently, tests have been developed to detect mutation for a handful of more complexconditions such as breast, ovarian, and colon cancers. However, gene tests may not detect every mutation associatedwith a particular condition because many are as yet undiscovered.

Controversial questions

The bacterium Escherichia coli is routinelygenetically engineered.

The absence of privacy and anti-discrimination legal protections inmost countries can lead to discrimination in employment or insuranceor other use of personal genetic information. This raises questions suchas whether genetic privacy is different from medical privacy.[23]

1. Reproductive issues. These include the use of genetic informationin reproductive decision-making and the possibility of geneticallyaltering reproductive cells that may be passed on to futuregenerations. For example, germline therapy changes the geneticmake-up of an individual's descendants. Thus, any error intechnology or judgment may have far-reaching consequences(though the same can also happen through natural reproduction).Ethical issues like designed babies and human cloning have also given rise to controversies between and amongscientists and bioethicists, especially in the light of past abuses with eugenics (see reductio ad hitlerum).

2.2. Clinical issues. These center on the capabilities and limitations of doctors and other health-service providers,people identified with genetic conditions, and the general public in dealing with genetic information.

3.3. Effects on social institutions. Genetic tests reveal information about individuals and their families. Thus, testresults can affect the dynamics within social institutions, particularly the family.

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4.4. Conceptual and philosophical implications regarding human responsibility, free will vis--vis geneticdeterminism, and the concepts of health and disease.

Gene therapy

Gene therapy using an Adenovirus vector. A newgene is inserted into an adenovirus vector, which

is used to introduce the modified DNA into ahuman cell. If the treatment is successful, the new

gene will make a functional protein.

Gene therapy may be used for treating, or even curing, genetic andacquired diseases like cancer and AIDS by using normal genes tosupplement or replace defective genes or to bolster a normal functionsuch as immunity. It can be used to target somatic cells (i.e., those ofthe body) or gamete (i.e., egg and sperm) cells. In somatic genetherapy, the genome of the recipient is changed, but this change is notpassed along to the next generation. In contrast, in germline genetherapy, the egg and sperm cells of the parents are changed for thepurpose of passing on the changes to their offspring.

There are basically two ways of implementing a gene therapytreatment:1. Ex vivo, which means "outside the body" Cells from the patient's

blood or bone marrow are removed and grown in the laboratory.They are then exposed to a virus carrying the desired gene. The virus enters the cells, and the desired genebecomes part of the DNA of the cells. The cells are allowed to grow in the laboratory before being returned to thepatient by injection into a vein.

2. In vivo, which means "inside the body" No cells are removed from the patient's body. Instead, vectors are usedto deliver the desired gene to cells in the patient's body.

As of June 2001, more than 500 clinical gene-therapy trials involving about 3,500 patients have been identifiedworldwide. Around 78% of these are in the United States, with Europe having 18%. These trials focus on varioustypes of cancer, although other multigenic diseases are being studied as well. Recently, two children born withsevere combined immunodeficiency disorder ("SCID") were reported to have been cured after being givengenetically engineered cells.Gene therapy faces many obstacles before it can become a practical approach for treating disease.[23] At least four ofthese obstacles are as follows:1. Gene delivery tools. Genes are inserted into the body using gene carriers called vectors. The most common

vectors now are viruses, which have evolved a way of encapsulating and delivering their genes to human cells in apathogenic manner. Scientists manipulate the genome of the virus by removing the disease-causing genes andinserting the therapeutic genes. However, while viruses are effective, they can introduce problems like toxicity,immune and inflammatory responses, and gene control and targeting issues. In addition, in order for gene therapyto provide permanent therapeutic effects, the introduced gene needs to be integrated within the host cell's genome.Some viral vectors effect this in a random fashion, which can introduce other problems such as disruption of anendogenous host gene.

2. High costs. Since gene therapy is relatively new and at an experimental stage, it is an expensive treatment toundertake. This explains why current studies are focused on illnesses commonly found in developed countries,where more people can afford to pay for treatment. It may take decades before developing countries can takeadvantage of this technology.

3. Limited knowledge of the functions of genes. Scientists currently know the functions of only a few genes. Hence,gene therapy can address only some genes that cause a particular disease. Worse, it is not known exactly whethergenes have more than one function, which creates uncertainty as to whether replacing such genes is indeeddesirable.

Biotechnology 28

4. Multigene disorders and effect of environment. Most genetic disorders involve more than one gene. Moreover,most diseases involve the interaction of several genes and the environment. For example, many people withcancer not only inherit the disease gene for the disorder, but may have also failed to inherit specific tumorsuppressor genes. Diet, exercise, smoking and other environmental factors may have also contributed to theirdisease.

Human Genome Project

DNA Replication image from the HumanGenome Project (HGP)

The Human Genome Project is an initiative of the U.S. Department ofEnergy ("DOE") and the National Institutes of Health ("NIH") thataims to generate a high-quality reference sequence for the entire humangenome and identify all the human genes.

The DOE and its predecessor agencies were assigned by the U.S.Congress to develop new energy resources and technologies and topursue a deeper understanding of potential health and environmentalrisks posed by their production and use. In 1986, the DOE announcedits Human Genome Initiative. Shortly thereafter, the DOE and NationalInstitutes of Health developed a plan for a joint Human GenomeProject ("HGP"), which officially began in 1990.The HGP was originally planned to last 15 years. However, rapidtechnological advances and worldwide participation accelerated thecompletion date to 2003 (making it a 13 year project). Already it hasenabled gene hunters to pinpoint genes associated with more than 30disorders.[24]

Cloning

Cloning involves the removal of the nucleus from one cell and itsplacement in an unfertilized egg cell whose nucleus has either beendeactivated or removed.There are two types of cloning:1.1. Reproductive cloning. After a few divisions, the egg cell is placed

into a uterus where it is allowed to develop into a fetus that isgenetically identical to the donor of the original nucleus.

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