Hoffman nucleation theory
Hoffman nucleation theory is a theory developed by John D. Hoffman and coworkers in the 1970s and 80s that attempts to describe the crystallization of a polymer in terms of the kinetics and thermodynamics of polymer surface nucleation.
Polymers contain different morphologies on the molecular level which give rise to their macro properties.
Above the Tm, the polymer chains lose their molecular ordering and exhibit reptation, or mobility.
Below the Tm, but still above the Tg, the polymer chains lose some of their long-range mobility and can form either crystalline or amorphous regions.
Below the Tg, molecular motion is stopped and the polymer chains are essentially frozen in place.
The transition from an amorphous to a crystalline single polymer chain is related to the random thermal energy required to align and fold sections of the chain to form ordered regions titled lamellae, which are a subset of even bigger structures called spherulites.
Nucleation is the formation and growth of a new phase with or without the presence of external surface.
Heterogeneous nucleation occurs in cases where there are pre-existing nuclei present, such as tiny dust particles suspended in a liquid or gas or reacting with a glass surface containing SiO2.
Homogeneous nucleation begins with small clusters of molecules forming from one phase to the next.
The size continues to increase and ultimately form macroscopic droplets (or bubbles depending on the system).
Also the nucleation barrier, in polymer crystallization, consists of both enthalpic and entropic components that must be over come.
This barrier consists of selection processes taking place in different length and time scales which relates to the multiple regimes later on.
[2] This barrier is the free energy required to overcome in order to form nuclei.
It is the formation of the nuclei from the bulk to a surface that is the interfacial free energy.
The interfacial free energy is always a positive term and acts to destabilize the nucleus allowing the continuation of the growing polymer chain.
[3] It can be used to describe the rate at which secondary nucleation competes with lateral addition at the growth front among the different temperatures.
This theory can be used to help understand the preferences of nucleation and growth based on the polymer's properties including its standard melting temperature.
For many polymers, the change between the initial lamellar thickness at Tc is roughly the same as at Tm and can thus be modeled by the Gibbs–Thomson equation fairly well.
However, since it implies that the lamellar thickness over the given supercooling range (Tm–Tc) is unchanged, and many homogeneous nucleation of polymers implies a change of thickness at the growth front, Hoffman and Weeks pursued a more accurate representation.
Applying this experimentally for a constant β allows for the determination of the equilibrium melting temperature, Tm° at the intersection of Tcand Tm.
[3] The crystallization process of polymers does not always obey simple chemical rate equations.
[5] The Lauritzen–Hoffman growth theory breaks the kinetics of polymer crystallization into ultimately two rates.
In this instance of g >> i, monolayers are formed one at a time so that if the substrate has a length of Lp and thickness, b, the overall linear growth can be described through the equation
Lastly, Regime III in the L-H model depicts the scenario where lateral growth is inconsequential to the overall rate, since the nucleation of multiple sites causes i >> g. This means that the growth rate can be modeled by the same equation as Regime I,
where GIII° is the prefactor for Regime III and can be experimentally determined through applying the Lauritzen–Hoffman Plot.
[7] A reza's crystallization depends on the time it takes for layers of its chains to fold and orient themselves in the same direction.
Many additional tests have since been run to apply and compare Hoffman's principles to reality.
Among the experiments done, some of the more notable secondary nucleation tests are briefly explained in the table below.
