User:Chem538w10grp6/sandbox dynamics

kinetics
In typical chain growth polymerization, the reaction rate for initaition, propagation and termination can be described as follows.


 * $$v_i={\operatorname{d}[M\cdot]/\operatorname{d}t}=2k_df[I]$$
 * $$v_p=k_p[M][M\cdot]$$
 * $$v_t={-\operatorname{d}[M\cdot]/\operatorname{d}t}=2k_t[M\cdot]^2$$

where f is the efficiency of the initiator, kd kp kt is the constant for initiator dissociation, chain propagation and termination, respectly. [I], [M] and [M\cdot] is the concentration of the initiator, monomer and the active growing chain.

Under the steady state approximation, the concentration of the active growing chains remains constant, i.e. the rate of initiation and termination is the same. In this case, the rate of chain propagation can be further described using a function of the initiator and monomer concentration


 * $$rate={k_p}(\frac{fk_d}{k_t})^{1/2}[I]^{1/2}[M]$$

The kinetic chain length \bar{v} is a measure of the average number of monomer units reacting with an active center during its life time and is related to the molecular weight through the mechanism of the termination.

thermodynamics
In chain growth polymerization, the position of the equilibrium between polymer and monomers can be determined by the thermodynamics of the polymerization. The Gibbs free energy (ΔGp) of the polymerization is commonly used to quantified the tendency of a polymeric reaction. The polymerization will be favoured if ΔGp < O; if ΔGp > 0, the polymer will undergo depolymerization. According to the thermodynamic equation ΔG = ΔH - TΔS, a negative enthalpy and an increasing entropy will shift the equillibrium towards polymerization.

In general, the polymerization is an exothermal process, i.e. negative enthalpy change, since they involve the conversion of π bonds into σ bonds or an ring opening reaction that releases the ring tension in a cyclic monomer. Meanwhile, during polymerization, a large amount of small molecules are associated, losing rotation and translational degress of freedom. As a result, the entroply decreases in the system, ΔSp < O for nearly all polymerization processes. Since depolymerization is almost always entropically favored, the ΔHp must then be sufficiently negative to composite for the unfavorable entropic term. Only then will polymerization be thermodynamically favored by the resulting negative ΔGp. • In practice,Polymerization is favored at low temperatures: TΔSp is small Depolymerization is favored at high temperatures: TΔSp is large As the temperature increases, Gp become less negative. At certain temperature, the polymerization reaches equilibrium (rate of polymerization = rate of depolymerization) This temp is called the ceiling temperature (Tc). Gp = 0

stereochemistry of polyermization
The physical behavior of a polymer depends not only on the general chemical composition but also on the more subtle differences in microstructure. Atactic polymers are amorphous (noncrystalline), soft materials with lower physical strength. The corresponding isotactic and syndiotactic polymers are usually obtained as highly crystalline materials. The ordered structures are capable of packing into a crystal lattice, while the unordered structures are not. Crystallinity leads to high physical strength and increased solvent and chemical resistance as well as differences in other properties that depend on crystallinity. The prime example of the industrial utility of stereoregular polymers is polypropene. Isotactic polypropene is a high-melting (165 C), strong, crystalline polymer, which is used as both a plastic and fiber (Sec. 8-11) [Juran, 1989; Lieberman and Barbe, 1988]. Atactic polypropene is an amorphous material with an oily to waxy soft appearance that finds use in asphalt blends and formulations for lubricants, sealants, and adhesives, but the volumes are minuscule compared to that of isotactic polypropene.