polymer chemistry Polymer chemistry is a sub-discipline of chemistry that focuses on the structures, chemical synthesis, and chemical and physical properties of polymers and macromolecules. The principles and methods used within polymer chemistry are also applic ...

, the kinetic chain length () of a

polymer A polymer () is a chemical substance, substance or material that consists of very large molecules, or macromolecules, that are constituted by many repeat unit, repeating subunits derived from one or more species of monomers. Due to their br ...

is the average number of units called

monomer A monomer ( ; ''mono-'', "one" + '' -mer'', "part") is a molecule that can react together with other monomer molecules to form a larger polymer chain or two- or three-dimensional network in a process called polymerization. Classification Chemis ...

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 monomer molecules add onto the active site on a growing polymer chain one at a time. There are a limited n ...

. 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 (from Latin: ', root) may refer to: Politics and ideology Politics *Classical radicalism, the Radical Movement that began in late 18th century Britain and spread to continental Europe and Latin America in the 19th century *Radical politics ...

from

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 transformatio ...

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 different from chemical thermodynamics, which deals with the direction in which a ...

. For any chemical chain reaction, the chain length is defined as the average number of times that the closed cycle of

chain propagation In chemistry, chain propagation (sometimes just referred to as propagation) is a process in which a reactive intermediate is continuously regenerated during the course of a Chain reaction#Chemical chain reactions, chemical chain reaction. For exa ...

steps is repeated. It is equal to the rate of the overall reaction divided by the rate of the initiation 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 compound, 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 , break ...

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 structural unit, 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 polymeriza ...

. 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, and

modulus of elasticity An elastic modulus (also known as modulus of elasticity (MOE)) is a quantity that describes an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. Definition The elastic modu ...

Calculating chain length

For most

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 rate The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per u ...

\nu = \frac = \frac

where is the rate of propagation, is the rate of

of polymerization, and is the rate of termination 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 (). 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 transf ...

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 represents the number of monomer units consumed, and the number of radicals that initiate polymerization. When the reaction goes to completion, , 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 In polymer chemistry, chain transfer is a polymerization reaction by which the activity of a growing polymer chain is transferred to another molecule: \ce^\bullet + \ce^\bullet where • is the active center, P is the initial polymer chain, X i ...

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 state. The reverse of disproportionatio ...

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 Biogerontology Biological processes Causes of death Cellular processes Gerontology Life extension Metabolic disorders Metabolism ...

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

(DP_n) 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

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 R_tr is the rate of transfer. The greater R_tr 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 Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...

- Chain entanglements are very important in viscous flow behavior (

viscosity Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...

) of polymers. As the chain becomes longer, chain mobility decreases; that is, the chains become more entangled with each other. * Glass-transition temperature - An increase in chain length often leads to an increase in the glass-transition temperature, T_g. 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 (or the Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the modulus of elasticity for tension or axial compression. Youn ...

. The interaction of the chains causes the polymer to become stiffer.

References

{{Reflist Polymer chemistry Chemical kinetics