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Concentration fluctuation in binary polymer blends: chi parameter, spinodal and Ginzburg criterion

Wang, Zhen-Gang (2002) Concentration fluctuation in binary polymer blends: chi parameter, spinodal and Ginzburg criterion. Journal of Chemical Physics, 117 (1). pp. 481-500. ISSN 0021-9606. https://resolver.caltech.edu/CaltechAUTHORS:WANjcp02

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Abstract

A theory for concentration fluctuations in binary polymer blends is developed using field-theoretic techniques. The theory provides a simple, unified framework for addressing a number of important issues. First, consideration of the fluctuation and correlation effects on different length scales leads to a clarification of three different chi parameters and their interrelationship. By incorporating interaction (modeled by the bare χb) and packing effects up to the polymer size, an effective chie emerges as the natural parameter for characterizing the molecular compatibility of the two polymer species. The measured quantity in small-angle neutron scattering (SANS) experiments is an apparent chia that includes long wavelength critical and spinodal fluctuations, and is related to χe through a self-consistent equation. χa exhibits the typical upward parabolic composition dependence observed in experiments and computer simulations. Second, a unified Ginzburg criterion involving both the composition and temperature (or temperaturelike variable) is derived that is applicable to both the critical and the off-critical spinodal regimes. The common characterization of the Ginzburg criterion in terms of a range of temperature (or temperaturelike variable) alone is generally inadequate. The molecular weight scaling proposed by de Gennes and Binder in the respective critical and off-critical spinodal regimes are recovered as special cases in the limit of large molecular weights. For typical molecular weights used in experiments the Ginzburg region is larger than commonly believed. Finally, the nature of the thermodynamic spinodal is examined. It is shown that a true off-critical thermodynamic spinodal does not exist in spatial dimensions less than 4. In its place, a pseudo-spinodal can be defined where the susceptibility reaches a finite maximum. The pseudo-spinodal precedes the mean-field spinodal but approaches the latter in the limit of infinite molecular weights. The pseudo-spinodal correlates strongly with the free energy barrier for nucleation becoming order kT. Thus it provides a kinetic limit for the physically accessible metastable state, beyond which phase separation may exhibit features characteristic of spinodal decomposition. The calculated location of the pseudo-spinodal for two samples used in a recent experiment of Balsara and co-workers agrees with the onset of spinodal-decomposition-like nucleation observed in the experiment.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.1481761DOIArticle
http://link.aip.org/link/?JCPSA6/117/481/1PublisherArticle
ORCID:
AuthorORCID
Wang, Zhen-Gang0000-0002-3361-6114
Additional Information:©2002 American Institute of Physics. (Received 22 January 2002; accepted 5 April 2002) This work is supported in part by the National Science Foundation (DMR-9970589) and by the China Natural Science Foundation. Helpful discussions with Nitash Balsara, Frank Bates, Karl Freed, Igal Szleifer, and Andrew Spakowitz are gratefully acknowledged.
Funders:
Funding AgencyGrant Number
NSFDMR-9970589
National Natural Science Foundation of ChinaUNSPECIFIED
Subject Keywords:polymer blends; polymer solutions; fluctuations; neutron diffraction
Issue or Number:1
Record Number:CaltechAUTHORS:WANjcp02
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:WANjcp02
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3840
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:14 Jul 2006
Last Modified:12 Dec 2019 17:06

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