In polymer chemistry, step-growth polymerization is a type of polymerization mechanism in which bi-functional or multifunctional monomers react to form first dimers, then trimers, longer oligomers, and eventually long-chain polymers. Many naturally occurring and some synthetic polymers are produced by step-growth polymerization, such as polyesters, polyamides, polyurethanes, etc. Due to the nature of the polymerization mechanism, a high extent of reaction is required to achieve high molecular weight. The easiest way to visualize the mechanism of a step-growth polymerization is a group of people reaching out to hold their hands to form a human chain—each person has two hands (reactive sites). There also is the possibility to have more than two reactive sites on a monomer: In this case branched-polymer production takes place.
IUPAC has deprecated the term step-growth polymerization, and recommends use of the terms polyaddition (when the propagation steps are addition reactions and molecules are not evolved during these steps) and polycondensation (when the propagation steps are condensation reactions and molecules are evolved during these steps).
Historical aspects Most natural polymers employed at early stages of human society are of condensation type. The synthesis of first truly synthetic polymeric material, bakelite, was announced by Leo Baekeland in 1907, through a typical step-growth polymerization fashion of phenol and formaldehyde. The pioneer of synthetic polymer science, Wallace Carothers, developed a new means of making polyesters through step-growth polymerization in 1930s as a research group leader at DuPont. It was the first reaction designed and carried out with the specific purpose of creating high-molecular-weight polymer molecules, as well as the first polymerization reaction whose results had been predicted by scientific theory. Carothers developed a series of mathematical equations to describe the behavior of step-growth polymerization systems which are still known as the Carothers equations today. Collaborating with Paul Flory, a physical chemist, they developed theories that describe more mathematical aspects of step-growth polymerization including kinetics, stoichiometry, molecular-weight distribution, etc. Carothers is also well-known for his invention of Nylon.
Condensation polymerization
Step-growth polymerization and condensation polymerization are two different concepts, not always identical. In fact polyurethane polymerizes with addition polymerization (because its polymerization produces no small molecules), but its reaction mechanism corresponds to a step-growth polymerization.
The distinction between addition polymerization and condensation polymerization was introduced by Wallace Carothers in 1929, and refers to the type of products, respectively: a polymer only (addition), and a polymer and a molecule with a low molecular weight (condensation).
The distinction between step-growth polymerization and chain-growth polymerization was introduced by Paul Flory in 1953, and refers to the reaction mechanisms, respectively: by functional groups (step-growth polymerization), and by free-radical or ion (chain-growth polymerization).
Differences from chain-growth polymerization
This technique is usually compared with chain-growth polymerization to show its characteristics.
Step-growth polymerizationChain-growth polymerizationChain growth profileGrowth throughout matrixGrowth by addition of monomer only at one end or both ends of chainUsage of monomer in the reactionRapid loss of monomer early in the reactionSome monomer remains even at long reaction timesReaction stepsSimilar steps repeated throughout reaction processDifferent steps operate at different stages of mechanism (i.e. initiation, propagation, termination, and chain transfer)Average molecular weightAverage molecular weight increases slowly at low conversion and high extents of reaction are required to obtain high chain lengthMolar mass of backbone chain increases rapidly at early stage and remains approximately the same throughout the polymerizationActive chain remains after reaction?Ends remain active (no termination)Chains not active after terminationInitiators required?No initiator necessaryInitiator required
Classes of step-growth polymers
Classes of step-growth polymers are: Polyester has high glass-transition temperature Tg and high melting point Tm, good mechanical properties to about 175 °C, and good resistance to solvents and chemicals. It can exist as fibers and films. The former is used in garments, felts, tire cords, etc. The latter appears in magnetic recording tape and high-grade films. Polyamide (nylon) has good balance of properties: high strength, good elasticity, abrasion resistance, good toughness, favorable solvent resistance. The applications of polyamide include rope, belting, fiber cloths, thread, substitute for metal in bearings, jackets on electrical wire, and more. Polyurethane can exist as elastomers with good abrasion resistance, hardness, good resistance to grease, and good elasticity, as fibers with excellent rebound, as coatings with good resistance to solvent attack and abrasion, and as foams with good strength, good rebound, and high impact strength. Polyurea shows high Tg, fair resistance to greases, oils, and solvents. It can be used in truck bed liners, bridge coatings, caulk, and decorative designs. Polysiloxane, siloxane-based polymers available in a wide range of physical states—from liquids to greases, waxes, resins, and rubbers. Due to perfect thermal stability (thanks to silicon), uses of this material include antifoam and release agents, gaskets, seals, cable and wire insulation, hot liquids and gas conduits, etc. Polycarbonates are transparent, self-extinguishing materials. They possess properties like crystalline thermoplasticity, high impact strength, and good thermal and oxidative stability. They can be used in machinery, auto-industry, and medical applications. For example, the cockpit canopy of the F-22 Raptor is made of high-optical-quality polycarbonate. Polysulfides have outstanding oil and solvent resistance, good gas impermeability, and good resistance to aging and ozone. However, they smell bad, and they shows low tensile strength as well as poor heat resistance. They can be used in gasoline hoses, gaskets, and places that require solvent resistance and gas resistance. Polyether shows good thermoplastic behavior, water solubility, generally good mechanical properties, and moderate strength and stiffness. It is applied in sizing for cotton and synthetic fibers, stabilizers for adhesives, binders, and film formers in pharmaceuticals. Phenol formaldehyde resin (Bakelite) have good heat resistance and dimensional stability as well as good resistance to most solvents. It also shows good dielectric properties. These materials are typically used in molding applications, electrical, radio, televisions, and automotive parts, where their good dielectric properties are of use. Some other uses include impregnating paper, varnishes, and decorative laminates for wall coverings. Polytriazole polymers are produced from monomers which bear both an alkyne and azide functional group. The monomer units are linked to each other by the a 1,2,3-triazole group, which is produced by the 1,3-dipolar cycloaddition, also called the azide-alkyne Huisgen cycloaddition. These polymers can take on the form of a strong resin or a gel. With oligopeptide monomers containing a terminal alkyne and terminal azide, the resulting clicked peptide polymer will be biodegradable due to action of endopeptidases on the oligopeptide unit.
Branched polymers A monomer with functionality of 3 or more will introduce branching in a polymer and will ultimately form a cross-linked macrostructure or network even at low fractional conversion. The point at which a tree-like topology transits to a network is known as the gel point because it is signalled by an abrupt change in viscosity. One of the earliest so-called thermosets is known as Bakelite. It is not always water that is released in step-growth polymerization: in acyclic diene metathesis or ADMET, dienes polymerize with loss of ethene.
Kinetics
The kinetics and rates of step-growth polymerization can be described using a polyesterification mechanism. The simple esterification is an acid-catalyzed process in which protonation of the acid is followed by interaction with the alcohol to produce an ester and water. However, there are a few assumptions needed with this kinetic model. The first assumption is water (or any other condensation product) is efficiently removed. Secondly, the functional group reactivities are independent of chain length. Finally, it is assumed that each step only involves one alcohol and one acid.
This is a general rate law degree of polymerization for polyesterification, where n is the reaction order.
Self-catalyzed polyesterification If no acid catalyst is added, the reaction will still proceed because the acid can act as its own catalyst. The rate of condensation at any time t can then be derived from the rate of disappearance of groups and
The second-order [COOH] term arises from its use as a catalyst, and k is the rate constant. For a system with equivalent quantities of acid and glycol, the functional group concentration can be written simply as
After integration and substitution from Carothers equation, the final form is
For a self-catalyzed system, the number average degree of polymerization (Xn) grows proportionally with .
External catalyzed polyesterification The uncatalyzed reaction is rather slow, and a high Xn is not readily attained. In the presence of a catalyst, there is an acceleration of the rate, and the kinetic expression is altered to
which is kinetically first-order in each functional group. Hence,
and integration gives finally
For an externally catalyzed system, the number average degree of polymerization grows proportionally with t.
Molecular weight distribution in linear polymerization The product of a polymerization is a mixture of polymer molecules of different molecular weights. For theoretical and practical reasons, it is of interest to discuss the distribution of molecular weights in a polymerization. The molecular weight distribution (MWD) had been derived by Flory by a statistical approach based on the concept of equal reactivity of functional groups.
Probability Step-growth polymerization is a random process, so we can use statistics to calculate the probability of finding a chain with x-structural units ("x-mer") as a function of time or conversion.
The probability that an A functional group has reacted is , and the probability of finding an A unreacted is . Therefore
where Px is the probability of finding a chain that is x units long and has an unreacted A. As x increases, the probability decreases.
Number fraction distribution
The number fraction distribution is the fraction of x-mers in any system and equals the probability of finding it in solution:
where N is the total number of polymer molecules present in the reaction.
Weight fraction distribution
The weight fraction distribution is the fraction of x-mers in a system and the probability of finding them in terms of mass fraction:
where Mo is the molar mass of the repeat unit, No is the initial number of monomer molecules, and N is the number of unreacted functional groups. Substituting from the Carothers equation
we can now obtain
Polydispersity index The polydispersity index (PDI) is a measure of the distribution of molecular mass in a given polymer sample:
However, for step-growth polymerization, the Carothers equation can be used to substitute and rearrange this formula into
Therefore, in step-growth when p=1, then the PDI=2.
Molecular weight control in linear polymerization
Need for stoichiometric control