^{1,a)}, Jeffrey L. Hutter

^{1}and John R. de Bruyn

^{1,b)}

### Abstract

Physically cross-linked blends of concentrated poly(vinyl alcohol) (PVA) and poly(ethylene glycol) (PEG) undergo microphase separation and gel as they age. We investigate the microrheology and microstructure of these materials by using particle tracking and dynamic light scattering to measure the thermal motion of small polystyrene spheres suspended in the blends. Dynamic light scattering probes the ensemble-averaged motion of all the probe particles over a wide range of time scales, while video-based particle tracking follows the motion of many individual tracer particles. Dynamic light scattering shows that the tracer particles move diffusively at short and long time scales, while their motion is restricted by materialelasticity at intermediate time scales. The particle tracking experiments show a wide distribution of mean square displacements at a given lag time, indicating spatial heterogeneity on the micron length scale. We separate the particles into three populations according to their behavior. We extract information about the local microrheological environments probed by each population and study their dependence on PEG concentration and aging time. We find that addition of PEG to the PVA solutions influences the microrheological environment significantly, and that phase separation occurs prior to gelation as the blends age. The gelation time determined from the microrheological measurements is later than the bulk gel time, indicating that the different phase-separated regions age differently. Our results are consistent with a model in which the PVA/PEG blends consist of PVA-poor pores within a continuous PVA-rich domain.

This research was supported by the Natural Sciences and Engineering Research Council of Canada.

I. INTRODUCTION

II. EXPERIMENT

A. Sample preparation

B. Dynamic light scattering

C. Video-based particle tracking

D. Microrheology

III. RESULTS

A. Dynamic light scattering

B. Video-based particle tracking

IV. DISCUSSION

V. CONCLUSION

### Key Topics

- Light scattering
- 39.0
- Gels
- 37.0
- Elastic moduli
- 32.0
- Elasticity
- 32.0
- Viscosity
- 25.0

## Figures

Mean square displacements of 110 nm microspheres measured from dynamic light scattering experiments in water (filled circles), 10% PVA solution (diamonds) and 10% PVA/PEG blends with PEG concentrations of 3% (squares), 5% (circles) and 7% (triangles). The dynamic light scattering experiments were performed 1 h after each sample was prepared. The dashed line has a slope of 1.

Mean square displacements of 110 nm microspheres measured from dynamic light scattering experiments in water (filled circles), 10% PVA solution (diamonds) and 10% PVA/PEG blends with PEG concentrations of 3% (squares), 5% (circles) and 7% (triangles). The dynamic light scattering experiments were performed 1 h after each sample was prepared. The dashed line has a slope of 1.

The filled circles show the microscopic viscosity , computed from the data of Fig. 1 at short lag times. The local elasticity obtained from the plateau of in Fig. 1 is plotted as open squares. Both are plotted as a function of PEG concentration.

The filled circles show the microscopic viscosity , computed from the data of Fig. 1 at short lag times. The local elasticity obtained from the plateau of in Fig. 1 is plotted as open squares. Both are plotted as a function of PEG concentration.

for dynamic light scattering experiments using microspheres of different sizes in (a) a 10% PVA solution and (b) a 10% PVA/7% PEG blend. The sample age in both cases was 1 day. Scaled data for 110 nm and 210 nm microspheres in water are also shown in (a) for comparison (circles).

for dynamic light scattering experiments using microspheres of different sizes in (a) a 10% PVA solution and (b) a 10% PVA/7% PEG blend. The sample age in both cases was 1 day. Scaled data for 110 nm and 210 nm microspheres in water are also shown in (a) for comparison (circles).

Mean square displacements of 110 nm microspheres measured from dynamic light scattering experiments in a 10% PVA/7% PEG blend at different aging times as indicated. The dashed line has a slope of 1. The line segments with slopes , and schematically represent the behavior of at short, intermediate, and long lag times, respectively.

Mean square displacements of 110 nm microspheres measured from dynamic light scattering experiments in a 10% PVA/7% PEG blend at different aging times as indicated. The dashed line has a slope of 1. The line segments with slopes , and schematically represent the behavior of at short, intermediate, and long lag times, respectively.

(a) Mean square displacement at three different lag times as a function of aging time for 110 nm tracer particles in a 10% PVA/7% PEG blend. The error bars are based on the uncertainty in the light scattering measurements; where not shown they are smaller than the plotted symbols. (b) The logarithmic slopes at short, intermediate, and long lag times as a function of aging time for tracer particles in a 10% PVA/7% PEG blend. The lines are to guide the eye.

(a) Mean square displacement at three different lag times as a function of aging time for 110 nm tracer particles in a 10% PVA/7% PEG blend. The error bars are based on the uncertainty in the light scattering measurements; where not shown they are smaller than the plotted symbols. (b) The logarithmic slopes at short, intermediate, and long lag times as a function of aging time for tracer particles in a 10% PVA/7% PEG blend. The lines are to guide the eye.

The effective microscopic viscous modulus (dashed lines) and elastic modulus (solid lines) calculated from the data shown in Fig. 1 using Eqs. (7) and (8) for fresh samples of (a) 10% PVA solution, (b) 10% PVA/3% PEG, (c) 10% PVA/5% PEG, and (d) 10% PVA/7% PEG. + and × are the bulk values of and , respectively, measured using small-amplitude oscillatory shear with a rheometer.

The effective microscopic viscous modulus (dashed lines) and elastic modulus (solid lines) calculated from the data shown in Fig. 1 using Eqs. (7) and (8) for fresh samples of (a) 10% PVA solution, (b) 10% PVA/3% PEG, (c) 10% PVA/5% PEG, and (d) 10% PVA/7% PEG. + and × are the bulk values of and , respectively, measured using small-amplitude oscillatory shear with a rheometer.

The open symbols show the crossover frequencies and at which , obtained from the data in Fig. 6. The solid symbols show , the minimum value of the , and , the microelastic modulus at the same frequency. The lines are to guide the eye.

The open symbols show the crossover frequencies and at which , obtained from the data in Fig. 6. The solid symbols show , the minimum value of the , and , the microelastic modulus at the same frequency. The lines are to guide the eye.

The effective microscopic viscous modulus (dashed lines) and elastic modulus (solid lines) calculated from the data shown in Fig. 4 for a 10% PVA/7% PEG blend. The sample ages are (a) 0 day, (b) 1 day, (c) 8 days, and (d) 27 days. + and × are the bulk values of and , respectively, measured with a rheometer using small amplitude oscillatory shear.

The effective microscopic viscous modulus (dashed lines) and elastic modulus (solid lines) calculated from the data shown in Fig. 4 for a 10% PVA/7% PEG blend. The sample ages are (a) 0 day, (b) 1 day, (c) 8 days, and (d) 27 days. + and × are the bulk values of and , respectively, measured with a rheometer using small amplitude oscillatory shear.

Mean square displacements of 110 nm microspheres measured from video-based particle tracking experiments in freshly prepared samples of: 10% PVA (diamonds), 10% PVA with 3% PEG (squares), 10% PVA with 5% PEG (circles), and 10% PVA with 7% PEG (triangles). The dashed line has a slope of one.

Mean square displacements of 110 nm microspheres measured from video-based particle tracking experiments in freshly prepared samples of: 10% PVA (diamonds), 10% PVA with 3% PEG (squares), 10% PVA with 5% PEG (circles), and 10% PVA with 7% PEG (triangles). The dashed line has a slope of one.

(a) Mean square displacements of individual 110 nm tracer particles in the 10% PVA solution. The measurements were performed 1 h after the sample was prepared. The dashed lines are for particles with nearly diffusive motion and the solid lines for particles that are strongly subdiffusive at short τ. (b) Distribution of particle displacements at a lag time of 1 s for the particles labeled (i)–(iii) in (a). (c) The particle displacement distributions averaged over all particles at lag times (squares) and (circles). The dashed lines in (b) and (c) are fits to Gaussian functions. (d) Trajectories of particles (i)–(iii).

(a) Mean square displacements of individual 110 nm tracer particles in the 10% PVA solution. The measurements were performed 1 h after the sample was prepared. The dashed lines are for particles with nearly diffusive motion and the solid lines for particles that are strongly subdiffusive at short τ. (b) Distribution of particle displacements at a lag time of 1 s for the particles labeled (i)–(iii) in (a). (c) The particle displacement distributions averaged over all particles at lag times (squares) and (circles). The dashed lines in (b) and (c) are fits to Gaussian functions. (d) Trajectories of particles (i)–(iii).

(a) Mean square displacements of individual 110 nm tracer particles in the 10% PVA/7% PEG blend. The measurements were performed 1 h after the sample was prepared. The solid lines are for particles that are subdiffusive at short τ, while the dotted-dashed lines are for particles, whose curves are nearly flat over all the accessible times. (b) Distribution of particle displacements at a lag time of 1 s for the particles labeled (iv) and (v) in (a). (c) The particle displacement distributions averaged over all particles at lag times (squares) and (circles). The dashed lines in (b) and (c) are fits to Gaussian functions. (d) Trajectories of particles (iv) and (v).

(a) Mean square displacements of individual 110 nm tracer particles in the 10% PVA/7% PEG blend. The measurements were performed 1 h after the sample was prepared. The solid lines are for particles that are subdiffusive at short τ, while the dotted-dashed lines are for particles, whose curves are nearly flat over all the accessible times. (b) Distribution of particle displacements at a lag time of 1 s for the particles labeled (iv) and (v) in (a). (c) The particle displacement distributions averaged over all particles at lag times (squares) and (circles). The dashed lines in (b) and (c) are fits to Gaussian functions. (d) Trajectories of particles (iv) and (v).

Elasticity as a function of aging time for (a) particles which show dynamic confinement effects (group 2) and (b) particles which show permanent confinement (group 3). is estimated from the plateau of measured in the video particle tracking experiments. The uncertainties include those from the temperature fluctuation, the probe-size polydispersity, and the mean squared displacement measurements in the particle tracking experiments. Note that there are no particles in group 3 in the pure PVA solution at age 0.

Elasticity as a function of aging time for (a) particles which show dynamic confinement effects (group 2) and (b) particles which show permanent confinement (group 3). is estimated from the plateau of measured in the video particle tracking experiments. The uncertainties include those from the temperature fluctuation, the probe-size polydispersity, and the mean squared displacement measurements in the particle tracking experiments. Note that there are no particles in group 3 in the pure PVA solution at age 0.

Effective microscopic viscous (open symbols) and elastic moduli (filled symbols) calculated from video particle tracking data for particles in a 10% PVA sample. (a)–(d) are for particles in group 2, which show dynamic confinement, and (e)–(g) are for group 3, which show permanent confinement. The different plots are for different aging times: (a) 0 day; (b) and (e) 1 day; (c) and (f) 4 days; (d) and (g) 10 days. There are no permanently confined particles in the pure PVA solution at age 0. The solid lines in (c) are fits to a Maxwell model.

Effective microscopic viscous (open symbols) and elastic moduli (filled symbols) calculated from video particle tracking data for particles in a 10% PVA sample. (a)–(d) are for particles in group 2, which show dynamic confinement, and (e)–(g) are for group 3, which show permanent confinement. The different plots are for different aging times: (a) 0 day; (b) and (e) 1 day; (c) and (f) 4 days; (d) and (g) 10 days. There are no permanently confined particles in the pure PVA solution at age 0. The solid lines in (c) are fits to a Maxwell model.

Effective viscous (open symbols) and elastic moduli (filled symbols) calculated from video particle tracking data for particles in a 10% PVA/7% PEG blend. (a)–(d) are for particles in group 2, which show dynamic confinement, and (e)–(g) are for group 3, which show permanent confinement. The different plots are for different aging times: (a) and (e) 0 day, (b) and (f) 1 day, (c) and (g) 4 days, and (d) and (h) 10 days.

Effective viscous (open symbols) and elastic moduli (filled symbols) calculated from video particle tracking data for particles in a 10% PVA/7% PEG blend. (a)–(d) are for particles in group 2, which show dynamic confinement, and (e)–(g) are for group 3, which show permanent confinement. The different plots are for different aging times: (a) and (e) 0 day, (b) and (f) 1 day, (c) and (g) 4 days, and (d) and (h) 10 days.

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