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| In [[polymer chemistry]] the '''kinetic chain length''' of a [[polymer]], ''ν'', is the average number of monomers during [[polymerization]]. During this process, a polymer chain is formed when units called monomers are bonded together to form longer chains known as polymers. Kinetic chain length is defined as the average number of [[monomer]] units consumed for each [[radical initiator]] that begins the polymerization of a chain and is a more general development of the average [[degree of polymerization]]. The kinetic chain length can be calculated several ways, and its value can describe certain characteristics of the material, including chain mobility, [[glass-transition temperature]], and modulus of elasticity.
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| ==Calculating chain length==
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| For [[chain-growth polymerization]], the average kinetic chain length is defined as the ratio of the number of propagation steps to the number of initiation steps:
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| :<math> v = \frac{R_p}{R_i} = \frac{R_p}{R_t}</math>
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| where R<sub>p</sub> is the rate of propagation, R<sub>i</sub> is the rate of initiation of polymerization, and R<sub>t</sub> is the rate of termination of the polymer chain. The second form of the equation is valid at steady-state polymerization, as the chains are being initiated at the same rate they are being terminated (R<sub>i</sub> = R<sub>t</sub>).<ref>Hiemenz, Paul C., and Timothy P. Lodge. Polymer Chemistry. 2nd ed. Boca Raton, FL: CRC Press, 2007. 94-96.</ref>
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| An analogous equation can be written for [[living polymerization]], a type of [[addition polymerization]], and is usually written as:
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| :<math>\ v = \frac{[M]_0-[M]}{[I]_0}</math>
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| where [M]<sub>0</sub>-[M] represents the number of monomer units consumed, and [I]<sub>0</sub> the number of radicals that initiate polymerization. When the reaction goes to completion, [M]=0, and then the kinetic chain length is equal to the number average degree of polymerization of the polymer.
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| ===Notes===
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| * Kinetic chain length is an average quantity, as not all polymer chains are identical in length.
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| * The value of ν depends on the nature and concentration of both the monomer and initiator involved.
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| * Kinetic chain length can be calculated with or without [[chain transfer]] being considered.<ref>{{cite web|last=Hammond|first=Paula T.|title=10.569 Synthesis of Polymers: Fall 2006 materials, MIT OpenCourseWare|url=http://ocw.mit.edu/index.html|publisher=Massachusetts Institute of Technology|accessdate=2007-12-07}}</ref>
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| ==Kinetic chain length without transfer==
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| ===Termination by disproportionation===
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| Termination by [[disproportionation]] occurs when an atom is transferred from one polymer [[free radical]] to another. The atom is usually hydrogen, and this results in two polymer chains.
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| In this situation, the average kinetic chain length is equal to the number average [[degree of polymerization]] (DP<sub>n</sub>):
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| :<math>\ v = DP_n</math>
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| ===Termination by combination===
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| With combination, two radicals are joined together, destroying the radicals on each of the two chains and forming one polymeric chain. Here, the average kinetic chain length is defined as:
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| :<math>\ v = \frac{DP_n}{2}</math>
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| ==Kinetic chain length with chain transfer==
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| In the case of [[chain transfer]], another atom (often hydrogen) is transferred from a molecule in the system to the polymer radical. The original polymer chain is terminated and a new one is initiated.<ref>"Chain Transfer." IUPAC Compendium of Chemical Terminology. 1997. IUPAC. 6 Dec. 2007 <http://www.iupac.org/goldbook/C00963.pdf>.</ref> As a result, the kinetic chain length is shortened. Thus, the kinetic chain length is redefined as:
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| :<math>\ v_{tr} = \frac{R_p}{R_t + R_{tr}}</math>
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| where R<sub>tr</sub> is the rate of transfer. The greater R<sub>tr</sub> is, the shorter the kinetic chain length.
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| ==Significance==
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| The chain length of the polymer is important in many aspects of its properties.
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| * [[Viscosity]] - Chain entanglements are very important in viscous flow behavior ([[viscosity]]) of polymers. As the chain becomes longer, chain mobility decreases; that is, the chains become more entangled with each other.
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| * [[Glass-transition temperature]] - An increase in chain length often leads to an increase in the glass-transition temperature, T<sub>g</sub>. The increased chain length causes the chains to become more entangled at a given temperature. Therefore, a temperature does not need to be as low for the material to act as a solid.
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| * Modulus of Elasticity - A longer chain length is also associated with a material tends to be tougher and has a higher modulus of elasticity, E, also known as the [[Young's modulus]]. The interaction of the chains causes the polymer to become stiffer.
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| ==References== | |
| {{Reflist}}
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| [[Category:Polymer chemistry]]
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The author's title is Belkis Volker. The beloved passion for her and her youngsters is to engage in badminton but she has not manufactured a dime with it. She's usually loved dwelling in New Hampshire. For a long time she's been working as a fiscal officer. Check out out her site here: http://www.circulodeempresariosdegrancanaria.org/documentos.asp?airmax=22
My weblog; Air Max baratas (my sources)