Macromolecules zyxwvu 1994,27, 3543-3662 3543 zyxwvutsrqpo Composition Fluctuation Effects on Dielectric Normal-Mode Relaxation in Diblock Copolymers. 1. Weak Segregation Regime zyxwvutsrqpon K. Karatasos, S. H. Anastasiadis,’*+ A. N. Semenov,t G. Fytas, M. Pitsikalis,l and N. Hadjichristidisf Foundation for Research and Technology-Helh, Institute zyxw of Electronic Structure and Laser, zyxwvuts P.O. Box 1527, 711 10 Heraklion, Crete, Greece Received December 14,1993; Revised Manuscript Received April 1, 1994. ABSTRACT: Dielectric relaxation spectroscopy zyxwvu has been used to investigate the normal-mode relaxation in disordered diblock copolymer melts far from the order-to-disorder transition (ODT). The dielectric spectra are analyzed in order to quantitatively obtain the distribution of relaxation times in the disordered diblocks. The width of the relaxation function shows significant broadening relative to the respective homopolymer distributions when the temperature is decreased and/or the molecular weight is increased. The broadening is attributed to composition fluctuation effectson the normal-moderelaxation. These effects are theoretically accounted for by considering both the short-range fluctuations due to chain connectivity and the long-range concentration fluctuations in diblock copolymers due to the proximity to the ODT and their coupling to the individual block segmental dynamics. Theory not only captures the relative features of the distributions but also quantitatively compares very well with the experimental dielectric spectra. I. Introduction Diblock copolymers, consisting of a contiguous linear sequence of polymerized monomers of chemical species A (the A block) covalently bonded to a second contiguous linear sequenceof monomers of a different chemicalspecies B, represent an interesting class of polymeric materials with a rich variety of phase behavior.’ The equilibrium phase morphologies of diblock copolymers are determined by the overall degree of polymerization, N, the overall volume fraction of, e.g., the A block, zyxwvuts f, and the segment- segment Flory-Huggins interaction parameters, x, which depends on temperature as x zyxwvutsrq = (Y + b/Twith b > 0. Since the entropic and enthalpic contributionsto the free energy density scale as N-l and x, respectively, it is the product xN that dictates the equilibrium phase morphology for a certain composition f. For XN C 10, the equilibrium morphology is a melt with uniform composition (homo- geneous or disordered state). However, the unfavorable interactions between the A and B blocks lead to a local segregation of dissimilar monomers, Le., composition fluctuations. The connectivity between the two blocks thus leads to a correlation holelt2 corresponding to a fluctuation length scale of O(Rg), with R = (N/6)l12b being the copolymer radius of gyration and[ b the statistical segment length. As xN increases to 0(10), a delicate balance between entropic and enthalpic factors leads to an order-disorder transition (ODT) toward a microphase characterized by long-range order in its composition with a characteristic size on the order of the size of the molecules. At xN >> 0(10), the domination of enthalpic terms leads to highly organized periodic domain microstructure^.^ In a seminal theoretical work, Leibler2 constructed a Landau expansion of the free energy to fourth order in a compositional order parameter field, $(r) = (pA(r) -f, where (pA(r) is the microscopic volume fraction of A monomers at position r, and he was able to map out the phase diagram * Author to whom correspondence should be addressed. tAlso at Physics Department, University of Crete, 711 10 t Permanent address: Physics Department, Moscow State Uni- Also at Chemistry Department, University of Athens, 157 01 0 Abstract published in Advance ACS Abstracts, May 15, 1994. Heraklion, Crete, Greece. versity, 117234 Moscow, Russia. Zografou, Athens, Greece. of a diblock copolymer near the ODT in the parameter space xN vs f. Leibler also provided an expression for the disordered phase structure factor, S(q) = ($,$-,), with $p being the Fourier transform of $(r), as S(a) = N/[F(x,f) - 2xN3 (1) where F(x,f) is related2 to certain Debye correlation functions of a Gaussian block copolymer (2) with x = q2R,2; this expression predicts a Lorentzian peak at x = x*v> [3/f(l - with the peak intensity diverging at the stability limit, F(x*,f) - 2(xN), = 0. The proximity to the transition point is usually expressed by c = 2N(xs - x). Fredrickson and co-workers5incorporated fluctuation corrections in the effective Hamiltonian for a diblock melt and found that the fluctuation corrections, controlled by a Ginsburg parameter, N, defined6P6 by N = Nb6u-2, where u is the average segmental volume, lead to a suppression of the symmetric critical mean-field point that is replaced by a weak first-order transition at a lower temperature. In the Hartree approximation! the structure factor S(q) for a monodisperse diblock is modified from Leibler’s mean-field result to be given by eq 1 by replacing x with an effective interaction parameter, xetf, which depends on temperature, molecular weight, and composi- tion and is related to the bare parameter.5 The peak intensity does not diverge at the ODT, but it attains a maximum that is O(NP13) at a temperature lower than the mean-field stability limit.s In contrast to the numerous experimental and theoreti- cal investigations on the diblock copolymer morphology, the copolymer equilibrium dynamics only recently has attracted the interest of the scientific community? Rheo- logical measurements on disordered diblock copolymers6 have shown evidence of substantial fluctuation enhance- ment of the shear viscosity and first normal stress coefficients, whereas the composition fluctuations near the orderingtransition lead to a significant departure from thermorheological simplicity at low frequencies even for temperatures much higher than the ODT. Dielectric relaxation spectroscopy (DS)&” and the photon correlation spectroscopy (PCS) techniques of dynamic light scattering in both the depolarized’2J”lB and the polarized17*20-22 g,U,.r) = 2 [fi + e+ - 11/x2 0024-929719412227-3543$04.50/0 Q 1994 American Chemical Society