Mills' constant: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>Kc kennylau
No edit summary
en>David Eppstein
m →‎Mills primes: rm stray apostrophe
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
[[File:PolycaprolactoneSynthesis.svg|300px|thumbnail|An example of chain-growth polymerization by ring opening to [[polycaprolactone]]]]
Bryan is a celebrity from the earning as well as the career  [http://www.museodecarruajes.org meet and greet with luke bryan] growth initial second to his 3rd place recording,  And , may be the resistant.  [http://lukebryantickets.flicense.com where to buy luke bryan tickets] He broken on the scene in 2008 along with his unique mixture of lower-residence availability, movie celebrity great seems and words, is set t in the main way. The newest album Top in the nation chart and #2  [http://www.hotelsedinburgh.org jason aldeen] on the pop charts, earning it the 2nd highest first appearance at that time of 2010 to get a region performer. <br><br><br><br>The boy of any , knows persistence and willpower are key elements when it comes to a successful  profession- . His very first record, Keep Me, made the best  strikes “All My Buddies Say” and “Country Guy,” whilst his  hard work, Doin’  Point, discovered the singer-3 directly No. 8 singles:  In addition Phoning Is a Wonderful Issue.<br><br>From the fall of 2013, Concert tours: Luke Bryan  & which in fact had an amazing selection of , including Downtown. “It’s much like you’re receiving a  approval to go to a higher level, states those performers that had been an element of the  Concertsmore than right into a greater degree of performers.” It packaged as among the best  trips in their ten-12 months background.<br><br>Feel free to surf to my website: buy tickets ([http://lukebryantickets.pyhgy.com pyhgy.com])
'''Chain-growth polymerization''' or '''chain polymerization''' is a [[polymerization]] technique where [[Unsaturated compound|unsaturated]] [[monomer]] molecules add onto the active site on a growing [[polymer]] chain one at a time.<ref>''Introduction to Polymers'' 1987 R.J. Young Chapman & Hall ISBN 0-412-22170-5</ref> Growth of the polymer occurs only at one (or possibly more) ends. Addition of each monomer unit regenerates the active site.<ref>{{cite journal|title=Glossary of basic terms in polymer science (IUPAC Recommendations 1996)|journal=[[Pure and Applied Chemistry]]|year=1996|volume=68|issue=12|pages=2287–2311|doi=10.1351/pac199668122287|url=http://pac.iupac.org/publications/pac/pdf/1996/pdf/6812x2287.pdf}}</ref>
 
[[Polyethylene]], [[polypropylene]], and [[polyvinyl chloride]] (PVC) are common types of plastics made by chain-growth polymerization. They are the primary component of four of the plastics specifically labeled with [[Resin identification code|recycling codes]] and are used extensively in packaging.
 
==Mechanism==
Chain-growth polymerization can be understood with the [[chemical equation]]:
 
:<math> (-M-)_n (polymer) + M (monomer) \rightarrow (-M-)_{n+1}</math>
 
where n is the [[degree of polymerization]] and M is some form of [[unsaturated compound]]: an [[alkene]] ([[vinyl polymer]]s) or [[alicyclic compound]] ([[ring-opening polymerization]]) containing molecule.
 
This type of polymerization result in high molecular weight polymer being formed at low conversion. This final weight is determined by the rate of propagation compared to the rate of individual chain termination, which includes both chain transfer and chain termination steps. Above a certain [[ceiling temperature]], no polymerization occurs.
 
===Steps===
Chain-growth polymerization usually has the following steps:
# [[initiation (chemistry)|chain initiation]], usually by means of an [[Radical initiator|initiator]] which starts the chemical process.  Typical initiators include any organic compound with a labile group: e.g. azo (-N=N-), disulfide (-S-S-), or peroxide (-O-O-). Two examples are [[benzoyl peroxide]] and [[Azobisisobutyronitrile|AIBN]].
# [[chain propagation]]
# [[chain transfer reaction|chain transfer]], terminates the chain, but the active site is transferred to a new chain. This can occur with the solvent, monomer, or other polymer. This process increases the [[Branching (polymer chemistry)|branching]] of the resulting polymer.
# [[chain termination]], which occurs either by '''combination''' or '''[[disproportionation]]'''. Termination, in radical polymerization, is when the free radicals combine and is the end of the polymerization process.
 
The active center can be one of a number of different types:
* [[free radical]] in [[radical polymerization]], for example, [[polystyrene]], sometimes seen as [[Foam peanut|packing peanuts]], is produced by polymerizing [[styrene]] with [[Benzoyl peroxide]] as its [[radical initiator]]
* [[carbocation]] in [[cationic addition polymerization|cationic polymerization]], an example is Isobutyl [[synthetic rubber]], initiated by [[Aluminium chloride]] ionizing [[isobutylene]]
* [[carbanion]] in [[anionic polymerization]]
* [[organometallic]] complex in [[coordination polymerization]].
Under the necessary reaction conditions, an [[addition polymer]]ization can be considered a [[living polymerization]]. This is most often seen with anionic polymerization as it can be easy to perform without termination steps.
 
==Comparison with other polymerization methods==
The distinction between [[step-growth polymerization]] and chain-growth polymerization was instead introduced by [[Paul Flory]] in 1953, and refers to the difference in [[reaction mechanism]]s with step-growth using the functional groups of the monomer compared to the free-radical or ion groups used in chain-growth polymerization.<ref>Susan E. M. Selke, John D. Culter, Ruben J. Hernandez, [http://books.google.com/books?id=1aM9n0hovOoC "Plastics packaging: Properties, processing, applications, and regulations"], Hanser, 2004, p.29. ISBN 1-56990-372-7</ref>
 
Chain growth polymerization and addition polymerization (also called polyaddition) are two different concepts. In fact [[polyurethane]] polymerizes with addition polymerization (because its polymerization does not produce any small molecules, called "condensate"), but its [[reaction mechanism]] is a step-growth polymerization.
 
The distinction between "addition polymerization" and "condensation polymerization" was introduced by [[Wallace Hume Carothers]] in 1929, and refers to the type of product produced.<ref>{{cite journal | author=W. H. Carothers | journal=Journal of American Chemical Society | doi=10.1021/ja01383a041 | title=Studies On Polymerization And Ring Formation. I. An Introduction To The General Theory Of Condensation Polymers | year = 1929 | volume = 51 | issue =8  | pages=2548–59 }}</ref><ref>Paul J. Flory, [http://books.google.com/books?id=CQ0EbEkT5R0C&pg=PA37&lpg=PA37&dq=Carothers+polymer+addition+condensation&source=bl&ots=13v-5Uxvju&sig=h1RcDqB_plK0WR__xwxwjuLybC4&hl=it&ei=wdJUSuKSKY2angPIt4SMDA&sa=X&oi=book_result&ct=result&resnum=1 "Principles of Polymer Chemistry"], Cornell University Press, 1953, p.39. ISBN 0-8014-0134-8</ref> Addition polymerization produces only a polymer molecule, while condensation polymerization produces a polymer as well as a molecule with a low molecular weight, usually water.
 
==References==
{{Reflist}}
 
==External links==
* [http://www.daviddarling.info/encyclopedia/A/addition_reaction.html Internet Encyclopedia of Science]
 
{{DEFAULTSORT:Chain Growth Polymerisation}}
[[Category:Polymer chemistry]]
[[Category:Polymerization reactions]]
 
[[ja:重合反応#付加縮合]]

Latest revision as of 21:04, 5 November 2014

Bryan is a celebrity from the earning as well as the career meet and greet with luke bryan growth initial second to his 3rd place recording, And , may be the resistant. where to buy luke bryan tickets He broken on the scene in 2008 along with his unique mixture of lower-residence availability, movie celebrity great seems and words, is set t in the main way. The newest album Top in the nation chart and #2 jason aldeen on the pop charts, earning it the 2nd highest first appearance at that time of 2010 to get a region performer.



The boy of any , knows persistence and willpower are key elements when it comes to a successful profession- . His very first record, Keep Me, made the best strikes “All My Buddies Say” and “Country Guy,” whilst his hard work, Doin’ Point, discovered the singer-3 directly No. 8 singles: In addition Phoning Is a Wonderful Issue.”

From the fall of 2013, Concert tours: Luke Bryan & which in fact had an amazing selection of , including Downtown. “It’s much like you’re receiving a approval to go to a higher level, states those performers that had been an element of the Concertsmore than right into a greater degree of performers.” It packaged as among the best trips in their ten-12 months background.

Feel free to surf to my website: buy tickets (pyhgy.com)