^{1}and Timothy P. Lodge

^{2,a)}

### Abstract

The tracer diffusion coefficient of unentangled poly(ethylene oxide) (PEO, ) in a matrix of poly(methyl methacrylate) (PMMA, ) has been measured over a temperature range from with forced Rayleigh scattering. The dynamic viscosities of blends of two different high molecular weight PEO tracers ( and ) in the same PMMA matrix were also measured at temperatures ranging from ; failure of time-temperature superposition was observed for these systems. The monomeric friction factors for the PEO tracers were extracted from the diffusion coefficients and the rheological relaxation times using the Rouse model. The friction factors determined by diffusion and rheology were in good agreement, even though the molecular weights of the tracers differed by about three orders of magnitude. The PEO monomeric friction factors were compared with literature data for PEO segmental relaxation timesmeasured directly with NMR. The monomeric friction factors of the PEO tracer in the PMMA matrix were found to be from two to six orders of magnitude greater than anticipated based on direct measurements of segmental dynamics. Additionally, the PEO tracer terminal dynamics are a much stronger function of temperature than the corresponding PEO segmental dynamics. These results indicate that the fastest PEO Rouse mode, inferred from diffusion and rheology, is completely separated from the bond reorientation of PEO detected by NMR. This result is unlike other blend systems in which global and local motions have been compared.

This work was supported by the National Science Foundation, through Awards DMR-9901087 and DMR-0406656. One of the authors (J.C.H.) acknowledges the support by the Graduate School of the University of Minnesota, via a Doctoral Dissertation Fellowship.

INTRODUCTION

EXPERIMENTAL SECTION

Materials

Forced Rayleigh scattering

Rheology

RESULTS AND DISCUSSION

Diffusion

Rheology

Extraction of

Comparison of segmental and global dynamics of the PEO tracer

Comparison of matrix and tracer temperature dependences (test of time-temperature superposition)

Comparison of PEO dynamics with small molecule diffusion in PMMA

Interpretation

SUMMARY

### Key Topics

- Diffusion
- 29.0
- Friction
- 20.0
- Polymers
- 17.0
- Relaxation times
- 15.0
- Photoelectric conversion
- 12.0

## Figures

Results for forced Rayleigh scattering on 0.3% PEO- in a PMMA-10 matrix at selected temperatures. The extracted mean relaxation time is plotted as a function of the squared grating spacing . The solid lines indicate the fit of Eq. (4) to the data.

Results for forced Rayleigh scattering on 0.3% PEO- in a PMMA-10 matrix at selected temperatures. The extracted mean relaxation time is plotted as a function of the squared grating spacing . The solid lines indicate the fit of Eq. (4) to the data.

Zero shear viscosity as a function of temperature for PEO-1 (●) and PMMA-10 (∎). The error bars on the PEO-1 data represent standard deviations from time averaging the experimental viscosity signal.

Zero shear viscosity as a function of temperature for PEO-1 (●) and PMMA-10 (∎). The error bars on the PEO-1 data represent standard deviations from time averaging the experimental viscosity signal.

Complex viscosity as a function of frequency of tracer blends at selected temperatures. (a)–(d) 1% PEO- PMMA-10 blend (filled symbols) and for PMMA-10 homopolymer (open symbols), (e)–(h) 1% PEO- PMMA-10 blend (filled symbols) and for PMMA-10 homopolymer (open symbols). is denoted by circles and by squares. The dotted line is equal to , which is approximately the threshold below which cannot be experimentally resolved. The insets in (c), (d), (g), and (h) plot as a function of ; the frequency range containing the relaxation process attributed to the PEO tracer is designated with arrows in the insets.

Complex viscosity as a function of frequency of tracer blends at selected temperatures. (a)–(d) 1% PEO- PMMA-10 blend (filled symbols) and for PMMA-10 homopolymer (open symbols), (e)–(h) 1% PEO- PMMA-10 blend (filled symbols) and for PMMA-10 homopolymer (open symbols). is denoted by circles and by squares. The dotted line is equal to , which is approximately the threshold below which cannot be experimentally resolved. The insets in (c), (d), (g), and (h) plot as a function of ; the frequency range containing the relaxation process attributed to the PEO tracer is designated with arrows in the insets.

(a) Monomeric friction factor as a function of temperature for the PEO homopolymer, PMMA homopolymer, and the PEO tracers in the PMMA matrix. The error bars for the PEO-1 data are propagated from the reported error for viscosity (see Fig. 2). The error bars for the tracer rheology data points are estimated from the range of frequencies over which the tracer terminal relaxation occurs (see the insets of Fig. 3). The solid line is a fit of the WLF equation to the PEO tracer diffusion and rheology data; the fitting parameters are , , , and . To enable a direct comparison between the temperature dependences of the PEO tracer and the PMMA matrix, the WLF equation was vertically shifted by a factor of 30 (dotted line). (b) Comparison between global and segmental dynamics for the PEO homopolymer and PEO tracer in a PMMA matrix. The monomeric friction factor extracted from terminal dynamics , the apparent monomeric friction factor extracted from segmental dynamics , and the monomeric friction factor for diethyl ether are plotted as a function of temperature. The factor of 3 is an arbitrary shift factor chosen to overlay the PEO homopolymer global dynamics data (●) and the homopolymer segmental dynamics (solid line). The segmental dynamics data are from Ref. 18. The data used to calculate for diethyl ether come from Ref. 21.

(a) Monomeric friction factor as a function of temperature for the PEO homopolymer, PMMA homopolymer, and the PEO tracers in the PMMA matrix. The error bars for the PEO-1 data are propagated from the reported error for viscosity (see Fig. 2). The error bars for the tracer rheology data points are estimated from the range of frequencies over which the tracer terminal relaxation occurs (see the insets of Fig. 3). The solid line is a fit of the WLF equation to the PEO tracer diffusion and rheology data; the fitting parameters are , , , and . To enable a direct comparison between the temperature dependences of the PEO tracer and the PMMA matrix, the WLF equation was vertically shifted by a factor of 30 (dotted line). (b) Comparison between global and segmental dynamics for the PEO homopolymer and PEO tracer in a PMMA matrix. The monomeric friction factor extracted from terminal dynamics , the apparent monomeric friction factor extracted from segmental dynamics , and the monomeric friction factor for diethyl ether are plotted as a function of temperature. The factor of 3 is an arbitrary shift factor chosen to overlay the PEO homopolymer global dynamics data (●) and the homopolymer segmental dynamics (solid line). The segmental dynamics data are from Ref. 18. The data used to calculate for diethyl ether come from Ref. 21.

Attempted time-temperature superposition for PEO tracer blends. is plotted as a function of reduced frequency for (a) the 1% PEO- PMMA-10 blend and (b) the 1% PEO- PMMA-10 blend. In both cases, a reference temperature of is used.

Attempted time-temperature superposition for PEO tracer blends. is plotted as a function of reduced frequency for (a) the 1% PEO- PMMA-10 blend and (b) the 1% PEO- PMMA-10 blend. In both cases, a reference temperature of is used.

## Tables

Diffusion coefficients for PEO- in the PMMA-10 matrix.

Diffusion coefficients for PEO- in the PMMA-10 matrix.

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