kinetic chain length
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In
polymer chemistry Polymer chemistry is a sub-discipline of chemistry that focuses on the structures of chemicals, chemical synthesis, and chemical and physical properties of polymers and macromolecules. The principles and methods used within polymer chemistry are ...
the kinetic chain length of a
polymer A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
, ''ν'', is the average number of units called
monomer In chemistry, a monomer ( ; ''mono-'', "one" + '' -mer'', "part") is a molecule that can react together with other monomer molecules to form a larger polymer chain or three-dimensional network in a process called polymerization. Classification Mo ...
s added to a growing chain during
chain-growth polymerization Chain-growth polymerization (American English, AE) or chain-growth polymerisation (British English, BE) is a polymerization technique where Unsaturated compound, unsaturated monomer molecules add onto the active site on a growing polymer chain one ...
. During this process, a polymer chain is formed when monomers are bonded together to form long chains known as polymers. Kinetic chain length is defined as the average number of monomers that react with an active center such as a
radical Radical may refer to: Politics and ideology Politics *Radical politics, the political intent of fundamental societal change *Radicalism (historical), the Radical Movement that began in late 18th century Britain and spread to continental Europe and ...
from initiation to termination.Rudin, Alfred ''The Elements of Polymer Science and Engineering'' (Academic Press 1982) pp.209-211 This definition is a special case of the concept of ''chain length'' in
chemical kinetics Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in wh ...
. For any chemical chain reaction, the chain length is defined as the average number of times that the closed cycle of
chain propagation Chain propagation (sometimes referred to as propagation) is a process in which a reactive intermediate is continuously regenerated during the course of a chemical chain reaction. For example, in the chlorination of methane, there is a two-step p ...
steps is repeated. It is equal to the rate of the overall reaction divided by the rate of the
initiation Initiation is a rite of passage marking entrance or acceptance into a group or society. It could also be a formal admission to adulthood in a community or one of its formal components. In an extended sense, it can also signify a transformation ...
step in which the chain carriers are formed.
Keith J. Laidler Keith James Laidler (January 3, 1916 – August 26, 2003), born in England, was notable as a pioneer in chemical kinetics and authority on the physical chemistry of enzymes. Education Laidler received his early education at Liverpool College. H ...
, ''Chemical Kinetics'' (3rd ed., Harper and Row 1987) pp.289-290
For example, the decomposition of
ozone Ozone (), or trioxygen, is an inorganic molecule with the chemical formula . It is a pale blue gas with a distinctively pungent smell. It is an allotrope of oxygen that is much less stable than the diatomic allotrope , breaking down in the lo ...
in water is a chain reaction which has been described in terms of its chain length. In chain-growth polymerization the propagation step is the addition of a monomer to the growing chain. The word ''kinetic'' is added to ''chain length'' in order to distinguish the number of reaction steps in the kinetic chain from the number of monomers in the final macromolecule, a quantity named the
degree of polymerization The degree of polymerization, or DP, is the number of monomeric units in a macromolecule or polymer or oligomer molecule. For a homopolymer, there is only one type of monomeric unit and the ''number-average'' degree of polymerization is given by ...
. In fact the kinetic chain length is one factor which influences the average degree of polymerization, but there are other factors as described below. The kinetic chain length and therefore the degree of polymerization can influence certain physical properties of the polymer, including chain mobility,
glass-transition temperature The glass–liquid transition, or glass transition, is the gradual and reversible transition in amorphous materials (or in amorphous regions within semicrystalline materials) from a hard and relatively brittle "glassy" state into a viscous or rub ...
, and
modulus of elasticity An elastic modulus (also known as modulus of elasticity) is the unit of measurement of an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. The elastic modulus of an object is ...
.


Calculating chain length

For most
chain-growth polymerization Chain-growth polymerization (American English, AE) or chain-growth polymerisation (British English, BE) is a polymerization technique where Unsaturated compound, unsaturated monomer molecules add onto the active site on a growing polymer chain one ...
s, the propagation steps are much faster than the initiation steps, so that each growing chain is formed in a short time compared to the overall polymerization reaction. During the formation of a single chain, the reactant concentrations and therefore the propagation rate remain effectively constant. Under these conditions, the ratio of the number of propagation steps to the number of initiation steps is just the ratio of reaction rates: : \nu = \frac = \frac where Rp is the rate of
propagation Propagation can refer to: *Chain propagation in a chemical reaction mechanism *Crack propagation, the growth of a crack during the fracture of materials *Propaganda, non-objective information used to further an agenda *Reproduction, and other forms ...
, Ri is the rate of
initiation Initiation is a rite of passage marking entrance or acceptance into a group or society. It could also be a formal admission to adulthood in a community or one of its formal components. In an extended sense, it can also signify a transformation ...
of polymerization, and Rt is the rate of
termination Termination may refer to: Science *Termination (geomorphology), the period of time of relatively rapid change from cold, glacial conditions to warm interglacial condition *Termination factor, in genetics, part of the process of transcribing RNA ...
of the polymer chain. The second form of the equation is valid at
steady-state In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ''p'' ...
polymerization, as the chains are being initiated at the same rate they are being terminated (Ri = Rt). An exception is the class of
living polymerization In polymer chemistry, living polymerization is a form of chain growth polymerization where the ability of a growing polymer chain to terminate has been removed. This can be accomplished in a variety of ways. Chain termination and chain transfer r ...
s, in which propagation is much ''slower'' than initiation, and chain termination does not occur until a quenching agent is added. In such reactions the reactant monomer is slowly consumed and the propagation rate varies and is not used to obtain the kinetic chain length. Instead the length at a given time is usually written as: :\nu = \frac where sub>0 – represents the number of monomer units consumed, and sub>0 the number of radicals that initiate polymerization. When the reaction goes to completion, = 0, and then the kinetic chain length is equal to the number average degree of polymerization of the polymer. In both cases kinetic chain length is an average quantity, as not all polymer chains in a given reaction are identical in length. The value of ν depends on the nature and concentration of both the monomer and initiator involved.


Kinetic chain length and degree of polymerization

In chain-growth polymerization, the degree of polymerization depends not only on the kinetic chain length but also on the type of termination step and the possibility of
chain transfer Chain transfer is a polymerization Chemical reaction, reaction by which the activity of a growing polymer chain is transferred to another molecule. :P• + XR' → PX + R'• Chain transfer reactions reduce the average molecular weight of the fi ...
.


Termination by disproportionation

Termination by
disproportionation In chemistry, disproportionation, sometimes called dismutation, is a redox reaction in which one compound of intermediate oxidation state converts to two compounds, one of higher and one of lower oxidation states. More generally, the term can b ...
occurs when an atom is transferred from one polymer
free radical A daughter category of ''Ageing'', this category deals only with the biological aspects of ageing. Ageing Ailments of unknown cause Biogerontology Biological processes Causes of death Cellular processes Gerontology Life extension Metabo ...
to another. The atom is usually hydrogen, and this results in two polymer chains. With this type of termination and no chain transfer, the number average
degree of polymerization The degree of polymerization, or DP, is the number of monomeric units in a macromolecule or polymer or oligomer molecule. For a homopolymer, there is only one type of monomeric unit and the ''number-average'' degree of polymerization is given by ...
(DPn) is then equal to the average kinetic chain length: :DP_n = \nu


Termination by combination

Combination simply means that two radicals are joined together, destroying the radical character of each and forming one polymeric chain. With no chain transfer, the average degree of polymerization is then twice the average kinetic chain length :DP_n = 2 \nu


Chain transfer

Some chain-growth polymerizations include
chain transfer Chain transfer is a polymerization Chemical reaction, reaction by which the activity of a growing polymer chain is transferred to another molecule. :P• + XR' → PX + R'• Chain transfer reactions reduce the average molecular weight of the fi ...
steps, in which 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. The kinetic chain is not terminated if the new radical can add monomer. However the degree of polymerization is reduced without affecting the rate of polymerization (which depends on kinetic chain length), since two (or more) macromolecules are formed instead of one. Harry R. Allcock, Frederick W. Lampe and James E. Mark ''Contemporary Polymer Chemistry'' (3rd ed., Pearson Prentice-Hall 2003) pp.351-2 For the case of termination by disproportionation, the degree of polymerization becomes: :DP_n = \frac < \nu = \frac where Rtr is the rate of transfer. The greater Rtr is, the shorter the final macromolecule.


Significance

The kinetic chain length is important in determining the degree of polymerization, which in turn influences many physical properties of the polymer. *
Viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
- Chain entanglements are very important in viscous flow behavior (
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
) of polymers. As the chain becomes longer, chain mobility decreases; that is, the chains become more entangled with each other. *
Glass-transition temperature The glass–liquid transition, or glass transition, is the gradual and reversible transition in amorphous materials (or in amorphous regions within semicrystalline materials) from a hard and relatively brittle "glassy" state into a viscous or rub ...
- An increase in chain length often leads to an increase in the glass-transition temperature, Tg. The increased chain length causes the chains to become more entangled at a given temperature. Therefore, the temperature does not need to be as low for the material to act as a solid. * 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 Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied leng ...
. The interaction of the chains causes the polymer to become stiffer.


References

{{Reflist Polymer chemistry Chemical kinetics