Condensation polymers functionality theory

The theories of Miller and Macosko are used to derive expressions for pre-gel and post-gel properties of a crosslinking mixture when two crosslinking reactions occur. The mixture consists of a polymer and a crosslinker, each with reactive functional groups. Both the polymer and crosslinker can be either collections of oligomeric species or random copolymers with arbitrary ratios of M /Mj. The two independent crosslinking reactions are the condensation of a functional group on the polymer with one on the crosslinker, and the self-condensation of functional groups on the crosslinker. 

Although dimethylberyllium is a coordination polymer in the solid state,27 it has long been known to be monomeric in the gas phase.28 It has also been found to be monomeric when synthesized from the co-condensation of laser-ablated beryllium atoms and a methane/argon mixture at 10 K.11 Formed in conjunction with several other species, including hydrides (see Section 2.02.2.4), (CH3)2Be was identified from its infrared absorption bands, which were compared to DFT-calculated frequencies (DFT = density functional theory). 

HCP-l,4-benzenedimethanol (HCP-BDM) and HCP-ben l alcohol (HCP-BA) networks synthesized by the Friedel-Crafts self-condensation method have shown high selectivity for CO2 over N2, measured by nitrogen adsorption isotherm at two different temperatures, 273 and 298 Nonlocal density functional theory (NLDFT) calculations confirmed the pore sizes to be below 2 nm for both of the networks. Such small pore sizes, as well as the high ojq gen content in both the polymers, is most probably tbe reason for the strong interactions with polar CO2 rather than N2, making these good candidates for the selective separation of CO2 from N2. 

The theory of polymer gel phase transition provides a novel paradigm of remarkable predictive power to explain both condensation and decondensation in secretion. It assigns specific functional roles to the polyanionic-network/ cation pairs ubiquitously found in secretory granules, and provides a working framework to formulate new, testable questions to investigate further the mechanisms of storage and release in secretion. 

The field of generating functions was actually opened to polymer science with the work of Burchard [1], DuSek [2], and Gordon [4]. Gordon introduced the cascade theory [5] to derive finally the degree of polymerization in various systems. In contrast to radical polymerization the concept of directionality [6] is not of importance for equilibrium condensation reactions. Extensive work on the subject has been done by Tang [26, 27]. 

The theory of cyciization in condensation polymerization was first investigated by Kuhn in the 1930s with the introduction of the concept of effective concentration (Ceff), which is the local concentration of two chain ends of the same molecule for a Gaussian chain. This measurement provides a relationship between the end-to-end length of a polymer chain and that same chain s propensity to cyclize. Therefore, C s provides a method of quantification for the propensity of intramolecular interactions and cyciization, and Kuhn predicted that the cyciization probability decreases as where N is the number of bonds in the chain. Several other treatments have addressed the calculation of C s as a function of chain length using either random-flight statistics or a particle-in-a-sphere approximation. ... 

The first theory of polyelectrolyte complex formation was proposed by Voom and Overbeek [14, 15]. This mean field model was used to describe the binodal compositions, the water content and the critical salt concentration as a function of the polymer chain length. This theoretical description uses the Debye-Hiickel approximation the approximations within the derivation of the electrostatic interaction free energy are therefore only valid at low charge densities. The correlation effects at high concentrations of salt and monomeric units are neglected, and ion pairing effects such as counterion condensation are not taken into account. Despite these limitations, the experimental results could be described reasonably well [13]. 

The time-to-failure models, derived on the basis of the electrochemistry of solutions, theory of adsorption and condensation, and transport through water films and polymers are characterized by the product of four functions ... 

Rg. 17. Ratio between our SCF results for the nucleation barrier AG and the predictions of the classical theory (using Ap) as a function of the reduced distance from the binodal. Curves correspond to different pressures as indicated in the key. The circle marks the condensation of the solvent-vapor into a solvent-rich liquid inside the critical bubble. The inset shows the data for all pressures versus the scaled distance in the chemical potential of the polymer. From [164]... 

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