Nonlinear polymers, emulsion

Keywords Emulsion polymerization Kinetics Particle nucleation Particle growth Molecular weight distribution Nonlinear polymers... 

Nonlinear polymer formation in emulsion polymerization is a challenging topic. Reaction mechanisms that form long-chain branching in free-radical polymerizations include chain transfer to the polymer and terminal double bond polymerization. Polymerization reactions that involve multifunctional monomers such as vinyl/divinyl copolymerization reactions are discussed separately in Sect. 4.2.2. For simplicity, in this section we assume that both the radicals and the polymer molecules that formed are distributed homogeneously inside the polymer particle. 

Tobita H (2004) Scale-free power-law distribution of emulsion-polymerized nonlinear polymers Free-radical polymerization with chain transfer to polymer. Macromolecules... 

Most common fluids of simple structure are Newtonian (i.e., water, air, glycerine, oils, etc.). However, fluids with complex structures (i.e., high polymer melts or solutions, suspensions, emulsions, foams, etc.) are generally non-Newtonian. Examples of non-Newtonian behavior include mud, paint, ink, mayonnaise, shaving cream, polymer melts and solutions, toothpaste, etc. Many two-phase systems (e.g., suspensions, emulsions, foams, etc.) are purely viscous fluids and do not exhibit significant elastic or memory properties. However, many high polymer fluids (e.g., melts and solutions) are viscoelastic and exhibit both elastic (memory) as well as nonlinear viscous (flow) properties. A classification of material behavior is summarized in Table 5.1 (in which the subscripts have been omitted for simplicity). Only purely viscous Newtonian and non-Newtonian fluids are considered here. The properties and flow behavior of viscoelastic fluids are the subject of numerous books and papers (e.g., Darby, 1976 Bird et al., 1987). 

So far we have considered motion and mass and heat transfer in Newtonian media, which are characterized by proportionality between the tangential stress and the corresponding rate of shear (note that there are no tangential stresses if the rate of shear is zero). Gases and single-phase low-molecular (i.e., simple) liquids obey this law closely. However, in practice one often deals with fluids of more complicated structure, such as polymer solutions and melts and disperse fluid systems (suspensions, emulsions, and pastes), which are characterized by a nonlinear relation between the tangential stress and the rate of shear. Such fluids are said to be non-Newtonian. 

In emulsion polymerization, the molecular weights strongly depend on the average number of radicals per particle. Detailed mathematical models for the calculation of linear [23] and nonlinear [24-34] polymers for any value of n are available. A detailed discussion of this issue is outside the scope of this chapter. Instead, particular solutions for the limiting cases of Smith-Ewart [7] are presented in Table 4.1 where for Case 3, it was considered that the main chain growth termination event was bimolecular termination. 

Tobita H. Molecular-weight distribution in nonlinear emulsion polymerization. J Polym Sci B Polym Phys 1997 35 1515-1532. 

In general, the optimization of polymerization processes [2] focuses on the determination of trade-offs between polydispersity, particle size, polymer composition, number average molar mass, and reaction time with reactor temperature and reactant flow rates as manipulated variables. Certain approaches [3] apply nonhnear model predictive control and online, nonlinear, inferential feedback control [4] to both continuous and semibatch emulsion polymerization. The objectives include the control of copolymer composition. 

Due to the transient nature of the emulsion polymerization process and the inherent nonlinearities in the system, the nonlinear constrained dynamic optimization formulation is best adopted for such process application. The optimization can be carried out to determine optimum operation trajectories to produce polymer latex with specific product characteristics. 

The second large group of chapters spedfically describes the synthetic aspects of ROP/ROMP. In this section, the architecture of polymers prepared by ROMP, functionalization of poly (ethylene oxide), chain extension by ROP, nonlinear polyethers, as wdl as ROP in heterogeneous media are discussed. It also describes methods of polymerization that provide regular and mostly spherical partides, and gives for the first time a review of the kinetics and mechanism of this particular system that resembles emulsion vinyl polymerization. The chapter on polymerization in confined space (encompassing matrix polymerization) summarizes results that may open the way to the replica polymerization, a process that is typical for the matrix synthesis of biomacromolecules in nature. 

In the case of dilute emulsions constitutive modelling of a LAOS experiment based on the Batchelor theory and the Maffettone-Minale Model gave a relation between the nonlinear parameter and structural properties of the emulsion, like the volume averaged droplet radius and the interfacial tension. This relationship was applied to a series of polymer blends to determine their average droplet radius or the interfacial tension. 

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