Synthesis and Relaxation Dynamics of Multiarm Polybutadiene Melts L. A. Archer* Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843 S. K. Varshney Polymer Source Inc., Dorval, PQ, Canada H9P 1G7 Received February 20, 1998; Revised Manuscript Received May 26, 1998 ABSTRACT: We describe synthesis and nonlinear relaxation dynamics of various multiarm entangled polybutadiene molecules of the general type A 3-A-A3. In low-amplitude oscillatory shear, entangled multiarm polymers display broader relaxation spectra than linear polybutadienes of comparable molecular weight. Dramatic slowing down of cross-bar (A) relaxation by the entangled arms (A) is believed to be the source of this behavior. In nonlinear step strain experiments the A arms have a rather remarkable effect on polymer dynamics. At a critical shear strain γ of around 6.0, 〈|E‚u|〉 ) 3.2, the nonlinear relaxation modulus G(t;γ) abruptly decreases in value but retains similar time dependence to G(t;γ) at strains below the critical value. The sudden drop in G(t;γ) is reflected in the damping function and appears to be a consequence of arm withdrawal into the tube confining the cross-bar. This behavior is in near perfect agreement with a recent theoretical proposal for branched polymer dynamics. That this proposal is based on the notion of tensile forces on individual macromolecules due to tube confinement supports the existence of such forces and provides new circumstantial evidence for the existence of a mean-field tube. For all multiarm polymers studied we find time-strain separability at all strains with a separability time λ k that appears insensitive to the arm withdrawal process. This last finding is not in agreement with current descriptions of multiarm polymer dynamics. 1.0. Introduction Linear viscoelastic properties and relaxation dynam- ics of branched macromolecules has attracted consider- able research interest in the last several years. This interest is sustained by the commercial importance of branched polymers and by the challenge of generalizing to other architectures theoretical constructs such as the tube that appears to capture linear polymer dynamics. Detailed rheology studies have emerged for architec- tures including multiarm stars, 1-4 comb polymers, 5,6 and H-shaped molecules. 7-9 In all cases material properties such as zero shear viscosity and terminal molecular relaxation time manifest exponential depend- ences on arm molecular weight. When arm molecular weights are large enough to form entanglements, orders of magnitude enhancements in zero shear viscosity and stress relaxation times are found relative to linear polymers of comparable molecular weight. McLeish 9 and recently Bick and McLeish 10 and Bish- ko et al. 11 proposed a molecular theory for multiarm polymer dynamics that provides a promising starting point for describing the nonlinear rheology of entangled branched polymers. The theory is based on the tube model picture, which assumes that neighboring polymer molecules entangle with each other and thereby impose topological constraints that restrict motion of individual macromolecules to a tubelike region of diameter a )  N e b that follows the molecular contour. N e is the number of chain segments between entanglement points, and b is the segment length. The main innovation in the theory of McLeish et al. 9-11 concerns the way arm friction is introduced into the nonlinear relaxation modulus. Specifically, for a multiarm polymer molecule as in Figure 1 these authors contend that the nonlinear relaxation modulus should change dramatically when the effective tube strain 〈|E‚u|〉 approaches the priority i (minimum number of arms) of the molecule. At strains such that 〈|E‚u|〉 < i retraction of the central portion of the molecule (cross-bar) is thought to be prevented by a Pincus law tensile force that pulls the outermost segments of the arms away from the branch point. For fully relaxed arms this force is F eq ) 3k B T/a per arm, which is large enough to overcome the affine tension in the cross bar F ) 3(k B T/a)〈|E‚u|〉. 12 As a result, the contour length of the cross-bar retains it instantaneous affine value L ) L o 〈|E‚u|〉 even after the arms have relaxed completely. This situation changes when the tube strain exceeds the priority of the molecule, 〈|E‚u|〉 g i. In this case the affine tension in the cross-bar becomes large enough to overcome the total outward force F eq;T ) 3i(k B T/a) on the arms, allowing the arms to be withdrawn into the central tube. Assuming time strain facotorability occurs after some period of time, the effect of strain on the nonlinear modulus can be separated into two parts, h el (γ) ) [〈|E‚u|〉/(4/15)γ] 〈(E‚u)(E‚u)/|E‚u|〉 and h DE (γ) ) [1/(4/15)γ- 〈|E‚u|〉]〈(E‚u)(E‚u)/|E‚u|〉 for 〈|E‚u|〉 < i and 〈|E‚u|〉 > i, respectively. 10 The predicted discontinuity in the shear damping function is smoothed out in real branched polymers by an inevitable distribution of priorities. For Figure 1. Molecular architecture of A3-A-A3 multiarm poly- butadiene. The central portion of the molecule (cross-bar) is 55% 1,4-polybutadiene and the arms are >92% 1,4-polybuta- diene. 6348 Macromolecules 1998, 31, 6348-6355 S0024-9297(98)00273-3 CCC: $15.00 © 1998 American Chemical Society Published on Web 08/19/1998