Reptation Dynamics of Asymmetric Diblock Copolymer Melts via the Dynamic Random Phase Approximation

Abstract

A calculation of the intermediate scattering function of an entangled melt of asymmetric diblock copolymers is presented. On the basis of the reptation model of polymer dynamics and the dynamic random phase approximation, it is shown that the spectrum of relaxation rates for an asymmetric diblock copolymer consists of two sets of modes. In the noninteracting case, both sets of modes have relaxation rates that are independent of the diblock composition. The relative mode amplitudes, however, depend strongly on composition. In the noninteracting case, one set has relaxation rates given by Γ p,β ) βp 2 /t*, with 4t* the disengagement time and βp given by the pth positive root of βp cot βp -(qRg) 2 /2 ) 0, p ) 1, 2, 3, .... The other set only appears in the asymmetric case, and, in both the small-qRg and large-qRg limits, has relaxation rates given by Γp,R ) (π 2 /4t*)(2p -2) 2 , p ) 2, 3, 4, ....

Condensed Exponential Correlation Functions in Multicomponent Polymer Blends Measured by X-ray Photon Correlation Spectroscopy

“…This kind of behavior is anticipated in disordered fluctuating phases near a critical point and is sometimes called de Gennes narrowing . Such a peak in τ( q ) has been observed in a wide variety of systems including polymer systems. − In Figure c we plot 1/τ q 2 as a function of q at different temperatures for B20. We observe a minimum in this plot as anticipated from systems exhibiting de Gennes narrowing.…”

“…71 Such a peak in τ(q) has been observed in a wide variety of systems including polymer systems. [72][73][74][75][76][77] In Figure 7c we plot 1/τq 2 as a function of q at different temperatures for B20. We observe a minimum in this plot as anticipated from systems exhibiting de Gennes narrowing.…”

Polymers: When S(Q,t) is not what you think! The role of dynamic RPA

“…While in the last decades some approaches on the use of dynamical RPA have been made [5][6][7][8][9][10] these did not directly yield a way to routinely describe the full resulting intermediate scattering curves as e.g. obtained in NSE experiments and allow model fitting within this framework.…”

The Static and Dynamic Structure Factor of a Diblock Copolymer Melt via Small-Angle X-ray Scattering and X-ray Photon Correlation Spectroscopy

“…Diblock copolymer dynamics have been studied using dielectric spectroscopy, forced Rayleigh scattering, and nuclear magnetic resonance spectroscopy . In an important study, Semenov et al focused on the relaxation modes of compositional fluctuations in disordered symmetric diblock copolymer solutions, both theoretically and experimentally. − They found that they could account for their light scattering measurements via a linear summation of reptation and Rouse relaxation modes.…”

“…Such emphatically stretched exponential relaxations stand outside what is expected theoretically. Semenov et al 44 and Mochrie 45 showed that compositional fluctuations in BCPs undergoing reptational motion are expected to decay as a sum of exponentials, which could in principle mimic stretched exponential relaxations. However, close to the MST, the theoretically predicted relaxations are dominated by a single exponential, which is not what we observe experimentally.…”