Ceiling temperature () is a measure of the tendency of a polymer to revert to its constituent monomers. When a polymer is at its ceiling temperature, the rate of polymerization and depolymerization of the polymer are equal. Generally, the ceiling temperature of a given polymer is correlated to the steric hindrance of the polymer’s monomers. Polymers with high ceiling temperatures are often commercially useful. Polymers with low ceiling temperatures are more readily depolymerizable.
At constant temperature, the reversibility of polymerization can be determined using the Gibbs free energy equation:
where is the change of entropy during polymerization. The change of enthalpy during polymerization, , is also known as the heat of polymerization, which is defined by
where and denote the activation energies for polymerization and depolymerization, respectively, on the assumption that depolymerization occurs by the reverse mechanism of polymerization.
Entropy is the measure of randomness or chaos. A system has a lower entropy when there are few objects in the system and has a higher entropy when there are many objects in the system. Because the process of depolymerization involves a polymer being broken down into its monomers, depolymerization increases entropy. In the Gibbs free energy equation, the entropy term is negative. Enthalpy drives polymerizations. At low temperatures, the enthalpy term is greater than the term, which allows polymerization to occur. At the ceiling temperature, the enthalpy term and the entropy term are equal, so that the rates of polymerization and depolymerization become equal and the net polymerization rate becomes zero. [1] Above the ceiling temperature, the rate of depolymerization is greater than the rate of polymerization, which inhibits the formation of the given polymer. [2] The ceiling temperature can be defined by
This phenomenon was first described by Snow and Frey in 1943. [3] The thermodynamic explanation is due to Frederick Dainton and K. J. Ivin, who proposed that the chain propagation step of the polymerization is reversible. [4] [5]
At the ceiling temperature, there will always be excess monomers in the polymer due to the equilibrium between polymerization and depolymerization. Polymers derived from simple vinyl monomers have such high ceiling temperatures that only a small amount of monomers remain in the polymer at ordinary temperatures. The situation for α-methylstyrene, PhC(Me)=CH2, is an exception to this trend. Its ceiling temperature is around 66 °C. Steric hindrance is significant in polymers derived from α-methylstyrene because the phenyl and methyl groups are bonded to the same carbon. These steric effects in combination with stability of the tertiary benzylic α-methylstyryl radical give α-methylstyrene its relatively low ceiling temperature. When a polymer has a very high ceiling temperature, it degrades via bond cleavage reactions instead of depolymerization. A similar effect explains the relatively low ceiling temperature for polyisobutylene.
| Monomer | Ceiling temperature (°C) [6] | Structure |
|---|---|---|
| 1,3-butadiene | 585 | CH2=CHCH=CH2 |
| ethylene | 610 | CH2=CH2 |
| isobutylene | 175 | CH2=CMe2 |
| isoprene | 466 | CH2=C(Me)CH=CH2 |
| methyl methacrylate | 198 | CH2=C(Me)CO2Me |
| α-methylstyrene | 66 | PhC(Me)=CH2 |
| styrene | 395 | PhCH=CH2 |
| tetrafluoroethylene | 1100 | CF2=CF2 |
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication.
Enthalpy, a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant pressure, which is conveniently provided by the large ambient atmosphere. The pressure–volume term expresses the work required to establish the system's physical dimensions, i.e. to make room for it by displacing its surroundings. The pressure-volume term is very small for solids and liquids at common conditions, and fairly small for gases. Therefore, enthalpy is a stand-in for energy in chemical systems; bond, lattice, solvation and other "energies" in chemistry are actually enthalpy differences. As a state function, enthalpy depends only on the final configuration of internal energy, pressure, and volume, not on the path taken to achieve it.
The enthalpy of vaporization, also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy (enthalpy) that must be added to a liquid substance to transform a quantity of that substance into a gas. The enthalpy of vaporization is a function of the pressure at which that transformation takes place.
The thermodynamic free energy is a concept useful in the thermodynamics of chemical or thermal processes in engineering and science. The change in the free energy is the maximum amount of work that a thermodynamic system can perform in a process at constant temperature, and its sign indicates whether the process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful.
In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 that the van 't Hoff equation for the temperature dependence of equilibrium constants suggests such a formula for the rates of both forward and reverse reactions. This equation has a vast and important application in determining the rate of chemical reactions and for calculation of energy of activation. Arrhenius provided a physical justification and interpretation for the formula. Currently, it is best seen as an empirical relationship. It can be used to model the temperature variation of diffusion coefficients, population of crystal vacancies, creep rates, and many other thermally-induced processes/reactions. The Eyring equation, developed in 1935, also expresses the relationship between rate and energy.
In chemistry, the standard molar entropy is the entropy content of one mole of pure substance at a standard state of pressure and any temperature of interest. These are often chosen to be the standard temperature and pressure.
In thermodynamics, the Gibbs free energy is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions.
In polymer chemistry, ring-opening polymerization (ROP) is a form of chain-growth polymerization, in which the terminus of a polymer chain attacks cyclic monomers to form a longer polymer. The reactive center can be radical, anionic or cationic. Some cyclic monomers such as norbornene or cyclooctadiene can be polymerized to high molecular weight polymers by using metal catalysts. ROP is a versatile method for the synthesis of biopolymers.
In thermodynamics, an isentropic process is an idealized thermodynamic process that is both adiabatic and reversible. The work transfers of the system are frictionless, and there is no net transfer of heat or matter. Such an idealized process is useful in engineering as a model of and basis of comparison for real processes. This process is idealized because reversible processes do not occur in reality; thinking of a process as both adiabatic and reversible would show that the initial and final entropies are the same, thus, the reason it is called isentropic. Thermodynamic processes are named based on the effect they would have on the system. Even though in reality it is not necessarily possible to carry out an isentropic process, some may be approximated as such.
In surface science, surface free energy quantifies the disruption of intermolecular bonds that occurs when a surface is created. In solid-state physics, surfaces must be intrinsically less energetically favorable than the bulk of the material, otherwise there would be a driving force for surfaces to be created, removing the bulk of the material. The surface energy may therefore be defined as the excess energy at the surface of a material compared to the bulk, or it is the work required to build an area of a particular surface. Another way to view the surface energy is to relate it to the work required to cut a bulk sample, creating two surfaces. There is "excess energy" as a result of the now-incomplete, unrealized bonding at the two surfaces.
Steric effects arise from the spatial arrangement of atoms. When atoms come close together there is a rise in the energy of the molecule. Steric effects are nonbonding interactions that influence the shape (conformation) and reactivity of ions and molecules. Steric effects complement electronic effects, which dictate the shape and reactivity of molecules. Steric repulsive forces between overlapping electron clouds result in structured groupings of molecules stabilized by the way that opposites attract and like charges repel.
In polymer chemistry, free-radical polymerization (FRP) is a method of polymerization by which a polymer forms by the successive addition of free-radical building blocks. Free radicals can be formed by a number of different mechanisms, usually involving separate initiator molecules. Following its generation, the initiating free radical adds (nonradical) monomer units, thereby growing the polymer chain.
In polymer chemistry, an ideal chain is the simplest model to describe polymers, such as nucleic acids and proteins. It only assumes a polymer as a random walk and neglects any kind of interactions among monomers. Although it is simple, its generality gives insight about the physics of polymers.
Flory–Huggins solution theory is a lattice model of the thermodynamics of polymer solutions which takes account of the great dissimilarity in molecular sizes in adapting the usual expression for the entropy of mixing. The result is an equation for the Gibbs free energy change for mixing a polymer with a solvent. Although it makes simplifying assumptions, it generates useful results for interpreting experiments.
In thermodynamics, the entropy of mixing is the increase in the total entropy when several initially separate systems of different composition, each in a thermodynamic state of internal equilibrium, are mixed without chemical reaction by the thermodynamic operation of removal of impermeable partition(s) between them, followed by a time for establishment of a new thermodynamic state of internal equilibrium in the new unpartitioned closed system.
The Van 't Hoff equation relates the change in the equilibrium constant, Keq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, ΔrH⊖, for the process. It was proposed by Dutch chemist Jacobus Henricus van 't Hoff in 1884 in his book Études de Dynamique chimique.
Thermodynamic databases contain information about thermodynamic properties for substances, the most important being enthalpy, entropy, and Gibbs free energy. Numerical values of these thermodynamic properties are collected as tables or are calculated from thermodynamic datafiles. Data is expressed as temperature-dependent values for one mole of substance at the standard pressure of 101.325 kPa, or 100 kPa. Unfortunately, both of these definitions for the standard condition for pressure are in use.
Depolymerization is the process of converting a polymer into a monomer or a mixture of monomers. This process is driven by an increase in entropy.
Lattice diffusion refers to atomic diffusion within a crystalline lattice. Diffusion within the crystal lattice occurs by either interstitial or substitutional mechanisms and is referred to as lattice diffusion. In interstitial lattice diffusion, a diffusant, will diffuse in between the lattice structure of another crystalline element. In substitutional lattice diffusion, the atom can only move by substituting place with another atom. Substitutional lattice diffusion is often contingent upon the availability of point vacancies throughout the crystal lattice. Diffusing particles migrate from point vacancy to point vacancy by the rapid, essentially random jumping about. Since the prevalence of point vacancies increases in accordance with the Arrhenius equation, the rate of crystal solid state diffusion increases with temperature. For a single atom in a defect-free crystal, the movement can be described by the "random walk" model.
Depolymerizable polymers or Low-Ceiling Temperature Polymers refer to polymeric materials that can undergo depolymerization to revert the materials to their monomers at relatively low temperatures, such as room temperature. For example, the ceiling temperature Tc for formaldehyde is 119 °C, and that for acetaldehyde is -39 °C.
