Effect of Chain Length and Topological Constraints on Segmental Relaxation in Cyclic PDMS

Abstract

We present a detailed investigation of local dynamics of linear and cyclic poly­(dimethylsiloxane) (PDMS) covering a wide range of molar masses. To aid interpretation of the experimental data, QENS measurements in the time scale from 2 to 200 ps and at Q = 0.3 to 1.8 Å–1 are complemented by theoretical calculations. These make use of a methodology developed by us elsewhere applicable to both simple chain models and real chains and applied here, for the first time, to cyclic PDMS. Analysis of the incoherent dynamic structure factor at T < T m shows that the rotational motion of the methyl groups is unaffected by polymer topology. At higher temperatures, the QENS data are described by a model that consists of two dynamic contributions: methyl group rotation and segmental motion, the latter described by a stretched exponential function. Relaxation times of both linear and cyclic PDMS increase with increasing molar mass. Several features predicted by theory are also reproduced by the experimental data. We show, unambiguously, that rings have higher relaxation times for the segmental motion compared to linear chains of the same number of monomer units. Theoretical calculations support the idea that such slowing down of local dynamics is due to the topological constraint imposed by the ring closure, a constraint which becomes negligible for very large molar masses. Our calculations suggest that due to its albeit small conformational rigidity, cyclic PDMS undergoes an additional constraint which further increases the relaxation time, producing a shallow maximum for N ≈ 50 repeat units. A similar feature is also observed in the experimental QENS data. Values of activation energy, E a, are derived from analysis of the temperature dependence of the quasi-elastic broadening and are found to be in agreement with viscosity measurements reported in the literature. Although the pronounced molar mass dependence of E a for linear PDMS is certainly linked to the presence of mobile chain ends, for the cyclic polymers the behavior appears to be more complex than anticipated.

Local Effects of Ring Topology Observed in Polymer Conformation and Dynamics by Neutron Scattering—A Review

“…As shown in Figure 13 , rings have longer relaxation times compared to linear chains of the same number of monomer units, a result that is also supported by theory [ 105 ]. Furthermore, relaxation times of both linear and cyclic PDMS increase with increasing molar mass.…”

“…The experimental QENS data [ 104 , 105 , 113 ] and theoretical calculations [ 105 ] are supported by bulk viscosity [ 12 , 13 , 14 ], self-diffusion, and spin-spin relaxation measurements [ 17 ], according to which, rings have slower dynamics (higher viscosities or smaller diffusion coefficients) compared to linear chains at low molar mass. As noted by Semlyen et al, configurational restrictions in rings are likely responsible for a slowing down of the segmental mobility, resulting in higher viscosity at low molecular weight [ 12 , 13 , 14 ].…”

“…To date, neutron scattering investigations of ring dynamics are very limited [ 44 , 54 , 88 , 104 , 105 ]. In the following sections, NSE and QENS measurements will be reviewed.…”

“…QENS has been extensively used over many years to study local dynamics in polymers. However, there is little in the literature on the comparison between cyclics and linear chains, except for QENS measurements on PDMS [ 104 , 105 , 113 ]. The local dynamics of linear PDMS has been investigated extensively by neutron scattering [ 114 , 115 , 116 ], dielectric spectroscopy [ 117 , 118 , 119 , 120 ], NMR [ 17 ], as well as simulations [ 121 ], and these studies provide a starting point for a detailed comparison with ring dynamics.…”

“…This followed the trend predicted by theoretical calculations of Ganazzoli et al, applicable to both simple chain models and real chains [ 124 ]. The same methodology was used to compare experimental QENS data of linear and cyclic PDMS with theoretical predictions based on a realistic representation of a PDMS chain within the Rotational Isomerical State approach [ 105 ].…”