Nonlinear step polymerization

Yet another possiblity for the nonlinearity in the low conversion region is the decrease in the volume of the reaction mixture with conversion due to loss of one of the products of reaction (water in the case of esterification). This presents no problem if concentration is plotted against time as in Eq. 2-20. However, a plot of 1/(1 — p j2 against time (Eq. 2-22) has an inherent error since the formulation of Eq. 2-21 assumes a constant reaction volume (and mass) [Szabo-Rethy, 1971]. Elias [1985] derived the kinetics of step polymerization with correction for loss of water, but the results have not been tested. It is unclear whether this effect alone can account for the nonlinearity in the low conversion region of esterification and polyesterification. 

Additional Step 12 polymeric nonlinear optical chromophores and electrooptic devices were prepared by the author [1] in earlier investigations. 

Floiy Statistics of the Molecular Weight Distribudon. The solution to the complete set (j= 1toj = 100,000) of coupled-nonlinear ordinary differential equations needed to calculate the distribution is an enormous undertaking evai with the fastest computers. However, we can use probability theory to estimate the distribution. This theory was developed by Nobel laureate Paul Flory. We have shown that for step polymerization and for free radical polymerization in which termination is by isproportionation the mole fraction of polymer with chain lengthy is... 

Polymer growth J(c) showed nonlinear monomer concentration dependence in the presence of ATP (Carrier et al., 1984), while in the presence of ADP, the plot of J(c) versus monomer concentration for actin was a straight line, as expected for reversible polymerization. The data imply that newly incorporated subunits dissociate from the filament at a slower rate than internal ADP-subunits in other words, (a) the effect of nucleotide hydrolysis is to decrease the stability of the polymer by increasing k and (b) nucleotide hydrolysis is uncoupled from polymerization and occurs in a step that follows incorporation of a ATP-subunit in the polymer. Newly incorporated, slowly dissociating, terminal ATP-subunits form a stable cap at the ends of F-actin filaments. 

During isothermal polymerization below Tg, the molecular weight and T, increase, and eventually T, will equal Tjure The main purpose of this section is to discuss the calculation of the time to vitrification, where vitrification is defined to occur when Tj, equals T ure- The concepts of vitrification and the TTT cure diagram are extended to linear systems for both step growth and chain reaction mechanisms, although most of the discussion will focus on the nonlinear step growth case, of which the cure of epoxy resins is an example. 

Fig. 17. Extent of reaction at vitrification vs. reaction temperature for nonlinear step-growth polymerization (A + 2B2). All kinetic orders have the same p at vitrification. For mpdel parameters and system, see Fig. 16 caption. [Aronhime,...

Molecular dynamics employs Newtonian mechanics to model the time evolution of the system. The positions, velocities, and accelerations of each atom in the system are calculated from the force-field potential. Newtonian mechanics describes the relationship between the potential felt by each atom, the forces on each atom, and, therefore, the accelerations, velocities, and positions of each atom at each time step of the simulation. From the time evolution of the system, we can calculate many properties of the system. In this chapter, we describe the history, methods, and results of the work on the electric field poling of nonlinear optical polymeric guest-host systems. 

Figure 12-3 Plots of the degree of polymerization versus the cumulative number of synthetic steps for various repetitive syntheses (a) conventional linear solid-phase synthesis (b) nonlinear straight-chain sequence synthesis (c) dendrimer synthesis (branching multiplicity of three) (d) double exponential den-drimer synthesis (branching multiplicity of three). In all cases, the degree of polymerization is defined as the total number of monomer units per polymer molecule.

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