Thermodynamics and Phase Behavior of Block CopolymerHomopolymer Blends with Attractive and Repulsive

1
Thermodynamics and Phase Behavior of Block
Copolymer/Homopolymer Blends with Attractive and
Repulsive Interactions

• Andrey Tataurov

2
Introduction

• Polymer blends are excellent model systems for
  fundamental studies of liquid state
  thermodynamics. 1
• Predicting the thermodynamic properties of
  individual chains requires knowledge of two
  parameters 1. The statistical segment length,
  l2. The chain length, N (number of monomers per
  chain) 2
• The interactions between different chains are
  characterized by a Flory-Huggins interaction
  parameter, ?. 2
• Knowledge of these parameters (?, N, and l)
  enables prediction of the thermodynamic
  properties of any multicomponent mixture in the
  mean-field limit. 2

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Difficulties

• In many systems, the ? parameters depend on
  blend composition in an unpredictable way.
• In complex, multicomponent systems characterized
  by a multitude of ? parameters, chain lengths,
  and statistical segment lengths, methods for
  identifying the subset of parameters that govern
  the thermodynamics of mixing have not been
  established. 2
• The presence of large concentration fluctuations
  leads to departures from mean-field behavior, and
  such effects have only been studied in a few
  systems.

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The Problem

• We focus on A-B/C diblock copolymer/homopolymer
  blends wherein ? AC is positive and a decreasing
  function of temperature, while ? BC is negative
  and an increasing function of temperature. In
  other words, A/C interactions are repulsive while
  B/C interactions are attractive in the
  temperature range of interest. 2

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The Technique

• The problem discussed here are based on
  observations of phase behavior by electron
  microscopy and
• Small-angle neutron scattering (SANS)
  experiment (radiation is elastically
  scattered by a sample and the resulting
  scattering pattern is analysed to provide
  information about the size, shape and orientation
  of some component of the sample) 3

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Example of Polymer blend
poly(ethylene-block-headto-head propylene)
copolimer (PE-PP)
polyisobutylene (PIB) 2
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Theory of Scattering from HomogeneousMixtures

• We use random phase approhimation (RPA) 2
• In RPA the coherent scattering intensity, I(q)
  I(q)BTS(q)BS(q) - an n by n structure
  factor matrix whose elements, Sij, describe
  correlations between components i and j. 2
• We assume that the mixture is incompressible, and
  this eliminates the correlations of one of the
  components.
• The column vector, B Bibi/vi b0/v0
  (i1,2)where bi is the scattering length of
  component i and vi is the monomer volume of
  component i.

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Theoretical Predictions for a Simplified A-B/C
System

• A single-phase mixture is stable when the
  determinant of the structure factor matrix is
  positive detS(q) gt 0. The stability limit
  (spinodal) of the single phase mixture is given
  by detS(q) ) 0at any positive q. 2
• If q is zero it indicates macrophase separation.
  2
• A finite value of q indicates the formation of
  an ordered phase with a periodic length scale
  (2pi/q). 2

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Example of spinodal
Spinodal locus for the model A-B/C blend shown by
plotting ?N vs the statistical segment length of
the B block (l). 2
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Conclusion

• There are important connections between phase
  behavior and pretransitional concentration
  fluctuations. These fluctuations are
  announcements of the nature of impending phase
  transitions. 2
• The phase behavior of A-B/C blends is determined
  by an intricate interplay between ? parameters
  and statistical segment lengths. 2
• Using RPA we can obtain effective interaction
  parameters and statistical segment lengths by
  fitting multicomponent results to the
  experimental data in particular temperature
  range. 2

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References

• Paul, D. R., Bucknall, C. B., Eds. Polymer
  Blends John Wiley New York, 2000
• Lee, J. H. Balsara N. P. Chakraborty A. K.
  Macromolecules 2002, 35, 7748-7757
• http//www.isis.rl.ac.uk/largescale/loq/documents/
  sans.htm