Theory of microphase separation in homopolymer-oligomer mixtures

Alexander Olemskoi, Alexey Savelyev

Research output: Contribution to journalReview articlepeer-review

12 Scopus citations


This work starts with the review of theoretical methods proposed, during past decades, for description of phase behavior in different polymer systems, involving variety of linear polymers (regular and polydisperse block (co)polymers, random polymers) and the polymer systems with non-covalent bonds of different strength. Microphase separation (MS) into different ordered mesophases is known to be the principal property of such systems. It is shown that most of the theoretical approaches proposed for description of the MS are based on the simple random phase approximation (RPA). It turns out, however, that mean field RPA method applied to description of the systems with non-covalent bonds does not provide the whole picture of MS. We show that the problem here arises when one treats both Flory-Huggins non-associated interactions and non-covalent bonds (hydrogen, ionic) within the unified RPA scheme, which is obviously rough for description of the latter type of interactions. Such a theory was developed in a few recent papers for the systems involving weak hydrogen bonds between homopolymer chains and the low molecular weight oligomers (surfactants). However, it leaves some experimental data unaccounted. The purpose of this review is to consider more detailed theory which is able to explain not only all the experimental data for the above systems but also to take into account the strength variation of non-bonding interactions. In particular, we consider the strong ionic interactions, weak hydrogen bonding, and the interactions of intermediate strength between polymer chain and short oligomers within our unifying theory. To develop such a description in a self-consistent way we propose to use a general field theory of stochastic systems. The mesoscopic (lamellar) structure of the periodically alternating layers of stretched homopolymer chains surrounded by perpendicularly oriented oligomeric tails is studied for the systems with both strong (ionic) and weak (hydrogen) interactions. We focus on the consideration of the oligomer distribution along the homopolymer chains that is described by the effective equation of motion with the segment number playing the role of imaginary time. In so doing, we eliminate the Flory-Huggins interactions from explicit consideration showing that at strong tendency for polymer/oligomer segregation not Flory parameter but the strength of non-bonding interactions determines the MS transition to lamellar mesophase. The supersymmetry technique is developed to consider associative hydrogen bonding, self-action (nonlinearity) effects, non-homogeneity and temperature fluctuations in the oligomer distribution. Making use of the self-consistent approach allows one to determine experimentally observed temperature dependence of the structure period and the order-disorder transition temperature for different oligomeric fraction in systems with different bonding strength. A whole set of parameters of the model used is found for strong, intermediate, and weak coupled systems being poly(4-vinyl pyridine)-dodecyl benzene sulfonic acid [P4VP-(DBSA)x], P4VP-[Zn(DBS)2]x, and P4VP-3-pentadecyl phenolx [P4VP-(PDP)x], respectively. A passage from the former two to the latter is shown to cause a crucial decrease in the magnitude of both parameters of hydrogen bonding and self-action, as well as the order-disorder transition temperature.

Original languageEnglish
Pages (from-to)145-205
Number of pages61
JournalPhysics Reports
Issue number4-5
StatePublished - Nov 2005


  • Hydrogen bonding
  • Microphase separation
  • Supersymmetry field


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