New Applications of an Old Theory ‐ the Rouse Theory ‐ in Polymer Dynamics and Viscoelasticity

Abstract

As re cently shown by a close agree ment be tween the cal cu lated and mea sured viscoelastic spectra of a binary blend so lu tion over a wide fre quency range, the quan ti ta tive va lid ity of the Rouse the ory is dis cussed, point ing out why the tra di tional way of test ing by a sin gle pa ram e ter -the vis cos ity -is mis lead ing. A "bird's-eye" view of the Rouse the ory in re la tion to var i ous as pects of poly mer dy nam ics and viscoelasticity is shown. This rep re sents a fresh way of look ing at some of in ter re la tions be tween fun da mental prob lems in chain dy nam ics. This pa per il lus trates the ap pli ca tion po ten tial of the Rouse the ory by re view ing the re search schemes that make use of the well-tested the ory to elu ci date two fun da men tal prob lems : (1) on set of en tan glement and (2) the mo tions as so ci ated with a sin gle Rouse seg ment. It is shown that through care ful de signs of re search, anal y ses in terms of the Rouse the ory can pro vide vi tally im por tant and in form ing re sults.

Whole Range of Chain Dynamics in Entangled Polystyrene Melts Revealed from Creep Compliance: Thermorheological Complexity between Glassy-Relaxation Region and Rubber-to-Fluid Region. 1

“…In these figures, the locations of the relaxation times, 〈 τ〉 G , (for the normal modes of μ A ( t ); p = 1, 2, ..., 15), τ X , τ B , and τ C are also indicated. The number of normal modes used for μ A ( t ) (i.e., N e − 1 = 15) is a very reasonable choice as it corresponds to the mass for a Rouse segment ( m ) to be about 850, which falls within the range of the values determined by various techniques with small variations. − Segmental motions within a chain section shorter than 850 is regarded as belonging to the glassy relaxation. The { } points as shown in Figures and indicate that the relaxation times of the high Rouse−Mooney modes are closely packed; thus in choosing the number of modes, to differ by one or two basically does not affect the main point that we shall make and discuss below.…”

“…ERT has successfully predicted the characteristics of transformation with molecular weight of the G ( t ) line shape of the nearly monodisperse sample system and the molecular-weight dependence of the zero-shear viscosity η and the steady-state compliance ( J e 0 ) and their respective transition points M c and M c ‘. − , However, the analysis of the relaxation modulus or viscoelastic spectrum in terms of ERT has been limited to the modes of motion associated with length scales above that of a Rouse segment. The main reason is that the smallest structural unit in ERT is the Rouse segment, whose molecular weight ( m ) is estimated to be about 850 for polystyrene. − Experimental limitation also prevents the modes of motion faster than that of a single Rouse segment from being studied. The measurement of G ( t ) in the high modulus region is often limited by the lack of a compliance-free transducer.…”

Motion Associated with a Single Rouse Segment versus the α Relaxation. 2

“…Thus, as far as the fast mode is concerned, one can only show its existence from the MSVD analysis. However, much information about the slow mode 〈 P 2 [ u ( t )· u (0)]〉 has been obtained from the analysis of the experimental results. − It has been shown that the slow mode, with a rather narrow relaxation-time distributionextending over slightly less than two decades, is independent of scattering angle and molecular weight in accordance with eq 8. In the polystyrene melt case, the depolarized photon-correlation function is well-described by the stretched exponential form with the stretching exponent β near 0.4.…”

“…For both the studies of the motion associated with a single Rouse segment and the α-relaxation, the strategy we take is to use the successful description of the slow (low-frequency) viscoelastic propertiesfor instance, the zero-shear viscosity and the viscoelastic spectrum from the low-frequency end of the transition zone to the terminal zonein terms of the molecular theories as the reference frame. − ,− The molecular theory used for analyzing the experimental results depends on whether the system is in the entanglement or entanglement-free region. Then, the frictional factor K thus determined can be used to calculate the time constant of the highest Rouse normal mode for comparison with other dynamic results or be used to “normalize” the α-relaxation time for further comparative analysis.…”

“…The depolarized photon-correlation functions of two entanglement-free concentrated solutions (∼60 wt %) of polystyrene with M w = 9100; M w / M n = 1.02, and M w = 18 100; M w / M n = 1.01 in cyclohexane at the θ condition (i.e., at 35 °C)denoted by samples S1 (59.832 wt %; 0.552 g/cm 3 ) and S2 (60.287 wt %; 0.556 g/cm 3 ), respectivelyhave been measured and analyzed. − Along with the depolarized photon-correlation measurements, two solution samples with accurately determined concentrations in the close neighborhood of the concentration of each of the two samples, S1 and S2, are prepared for viscosity measurements by the falling-ball method, which, with both the ball and solution sealed in a glass tube, is particularly good for studying solution systems as solvent evaporation can be prevented. Then, by interpolation or extrapolation, the viscosity values at the concentrations of samples S1 and S2 can be individually determined; subsequently, their τ v values can be calculated (eqs 6 and 7) for comparison with their depolarized photon-correlation results.…”