Stretched Exponential Stress Relaxation in a Thermally Reversible, Physically Associating Block Copolymer Solution
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Stretched Exponential Stress Relaxation in a Thermally Reversible, Physically Associating Block Copolymer Solution Kendra A. Erk1,2 and Jack F. Douglas2 1 2
Department of Materials Science & Engineering, Northwestern University, Evanston, IL 60202 Polymers Division, National Institute of Standards and Technology, Gaithersburg, MD 20899 †
ABSTRACT The shear stress relaxation of a thermally reversible, physically associating solution formed from a triblock copolymer in solvent selective for the mid-block was found to be well described over a broad temperature range by a stretched exponential function with a temperature independent ‘stretching exponent’, E≈ 1/3. This same exponent value has been suggested to have particular significance in describing structural relaxation in a wide range of disordered viscoelastic materials ranging from associating polymer materials (‘gels’) to glass-forming liquids. We quantify the temperature dependence of the high frequency, or short time, shear modulus as function of temperature and find that this property also follows a variation often observed in gels and glass-forming materials. INTRODUCTION Stretched exponential functions are frequently utilized to describe the relaxation dynamics of complex fluids and other strongly interacting materials. [1] In particular, this functional form has been employed to describe the relaxation of polymer networks and gels, including transient telechelic networks in water [2] and symmetric triblock copolymer melts. [3] More recently, the relaxation of triblock copolymer physically associating solutions has been found to display stretched exponential relaxation having the specific form [4]: ª § t ·E º G (t , J 0 ) G (0, J 0 ) exp « ¨ ¸ » , 0 50 °C), the triblock copolymer is fully dissolved in the solvent, forming a free-flowing, low-viscosity solution with a near zero storage modulus (see Figure 1b). At reduced temperatures (< 35 °C), G’ becomes larger than G’’ as the PMMA endblocks self-assemble into spherical aggregates in order to minimize their interaction with the solvent. These end-block aggregates act as physical cross-links, interconnected by flexible PnBA mid-block bridges. Scattering techniques and self-consistent mean field theory simulations have been performed previously to validate the self-assembled transient network structure. [5,6] From small angle x-ray scattering, the end-block aggregates were found to be approximately 5 nm in radius. The mesh size depended on the molecular weight of the midblock and the overall copolymer concentration and was typically tens of nanometers via elastic scaling estimates. [7]
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G' , G'' (Pa)
(b) 400 G' G"
300 200 100 0 5
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25 35 T (oC)
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Figure 1. (a) Cartoon depicting the thermo-reversible self-assembly of physically associating solutions composed of triblock copolymer molecules dissolved in a mid-block-selective solvent. (b) Temperature dependence of the storage (G’) and loss (G’’) shear moduli of the triblock copolymer solution from high frequency oscillatory measurements (Z = 100
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