Polyfunctional Cross-Linking of Existing Polymer Chains

Abstract

Polyfunctional cross-linking of polydisperse copolymer primary chains is described theoretically, and dependences of structural parameters on conversion (R) before and after the gel point are derived. In particular, concentrations and average molecular weights of the sol, the elastically active network chains and their backbone chains, and dangling chains are given as functions of R. The theory can be used for chemical as well as physical gelation processes. A generalized theory of branching processes (TBP) is used, in which two sets of variables are introduced, for units and for links.

Cross-Linking Behavior of Diskotic Side-Chain Polymers in Solution

“…Nevertheless, Flory demonstrated the possibility of modeling tetrafunctional cross-linking of polymer molecules with a monodisperse distribution of the molecular weights at and beyond the gel point. Much later, te Nijenhuis generalized the model to comply with cross-links of any functionality and a polydisperse distribution of the molecular weights. − It has to be mentioned that there is much agreement between the results of the cross-linking process of high molecular weight polymer calculated with this model and those more specific presented in the literature (e.g., Charlesby et al, , Langley et al, − Graessley et al., , Šomvársky et al, and Peppas et al , ). For a so-called accumulated Schulz−Flory distribution with M̄ w / M̄ n ≥ 2 the relationship between the equilibrium shear modulus, G e (determined with oscillatory rheological measurements), and the sol fraction, w s , is found to be where and and where f is the functionality of the cross-links (i.e., the number of polymers leaving the cross-links), c is the mass concentration of polymer (kg/m 3 ), R is the gas constant (J/(mol K)), T is the absolute temperature (K), M̄ w is the weight-average molecular weight of the polymer molecules before cross-linking (kg/mol), and α is the monomer conversion during preparation of the polymer, which can be calculated from the polydispersity index ( D = M̄ w / M̄ n , where M̄ n is the number-average molecular weight (kg/mol)): …”

Soft micron-sized polypeptide microgels: preparation, crosslink density, topography and nanomechanics in swollen state

“…40 The application of TBP on multifunctional crosslinking chains is explained in detail in the work. 41 Briefly, applying the TBP, one examines all the possible connections between units existing at a given state of the crosslinking process. The units are distinguished according to their number of bonds in all reaction states: unreacted bonds, bonds reacted but issued to a finite structure, and bonds reacted and issued to an infinite network structure.…”

Applicability of Statistical Theories of Network Formation

“…Existence of hard clusters and their size distribution affect the mechanical and optical properties. Transient (physical) networks is the domain most suitable for implementation of a statistical theory because of reversibility of the crosslinking reaction and independence of the history of structure build-up, Also attractive is the possibility of coupling gelation and phase separation [38][39][40] Multistage network formation is a process which can be very well described by statistical theories distinguishing bonds formed within different stages. The products in one stage are converted to starting components of the following stage.…”