^{1,a)}, M. D’Acunzi

^{1}, D. Vollmer

^{1}and G. K. Auernhammer

^{1,b)}

### Abstract

Gelation in colloidalsuspensions is mostly induced by attractive interparticle potentials. Beside these interactions, the mechanical properties of the gel are influenced by morphological aspects like fractality. In suspensions of liquid crystal (LC) and polymeric colloids, solvent-particle interactions dominate and can be changed when the mesogen undergoes phase transition from isotropic to nematic. In case of poly(methyl methacrylate) colloids and 4-pentyl--cyanobiphenyl (5CB), cooling through the isotropic-nematic phase transition results in a cellular network. Such network formation is accompanied by a strong evolution of the mechanical properties. Shear moduli reach values up to for temperatures of 15 K below the transition. Until now, the mechanical response of the gel was attributed to the elastic interactions of the LC with the colloids. However, the dynamic viscoelastic stiffening with decreasing temperature could not be explained satisfactorily. We used a homemade piezorheometer to measure the complex shear modulus of the sample in parallel plate geometry. Since the applied strains are very small, only the linear viscoelastic regime was tested. This limit guarantees a high degree of reproducibility. We gained insight into the underlying processes by measuring the frequency response for the whole cooling process. Temperature and frequency showed a strong correlation allowing for a superposition of the frequency spectra to form a single master curve similar to time-temperature-superposition. We propose that this superposition behavior is connected to the thermodynamics of the isotropic-nematic phase transition of 5CB located in the network walls. Additional experimental observations, such as hysteresis effects, support this assumption. Morphological aspects were found to be of minor relevance.

The authors thank Hans-Jürgen Butt, Mike Cates, George Floudas, and Thomas Palberg for stimulating discussions. SPP 1273 “Kolloidverfahrenstechnik” is gratefully acknowledged for financial support. M.R. also acknowledges the financial and ideational support by the graduate school MAINZ as well as the graduate class of excellence POLYMAT.

I. INTRODUCTION

II. BASIC MODEL DESCRIPTIONS

III. EXPERIMENTAL

A. Piezorheology

B. Samples

IV. RESULTS AND DISCUSSION

A. Reproducibility

B. General temperature dependency

C. Dependency on colloid parameters

D. Influence of the cooling rate and network morphology

E. Reversibility and aging phenomena

F. Time-temperature-superposition

V. CONCLUSIONS

### Key Topics

- Colloidal systems
- 49.0
- Elastic moduli
- 14.0
- Mechanical properties
- 14.0
- Phase separation
- 14.0
- Elasticity
- 12.0

## Figures

Schematic view of the piezorheometer. The scale bar indicates approximate size dimensions.

Schematic view of the piezorheometer. The scale bar indicates approximate size dimensions.

Calibration measurements of Newtonian liquids 2000AW and 100000BW. Graph (a) shows the frequency dependency of the loss modulus of 100000BW at three different temperatures together with the fit according to with as the dynamic viscosity (straight lines with a slope of 1 Pa s). In the left graph (b) the viscosity is plotted against the temperature for both compounds together with the calibration curves (solid lines) provided by the supplier DKD.

Calibration measurements of Newtonian liquids 2000AW and 100000BW. Graph (a) shows the frequency dependency of the loss modulus of 100000BW at three different temperatures together with the fit according to with as the dynamic viscosity (straight lines with a slope of 1 Pa s). In the left graph (b) the viscosity is plotted against the temperature for both compounds together with the calibration curves (solid lines) provided by the supplier DKD.

Temperature dependence of storage and loss moduli (left axis) at 50 Hz in course of network formation for sample PDMS-10. The cooling rate was set to 0.1 K/min, the sample thickness to . The right axis gives the scaling for the loss angle . of pure 5CB at is shifted to lower temperatures of about due to the presence of impurities like alkanes (Ref. 35). Due to resolution limits the values for and above cannot be resolved.

Temperature dependence of storage and loss moduli (left axis) at 50 Hz in course of network formation for sample PDMS-10. The cooling rate was set to 0.1 K/min, the sample thickness to . The right axis gives the scaling for the loss angle . of pure 5CB at is shifted to lower temperatures of about due to the presence of impurities like alkanes (Ref. 35). Due to resolution limits the values for and above cannot be resolved.

Frequency sweeps for samples containing 5% and 10% of PHSA and PDMS-stabilized PMMA colloids dispersed in 5CB. The mixtures were cooled at 0.1 K/min down to and kept constant for several hours before starting the frequency sweeps. Filled symbols represent and open symbols .

Frequency sweeps for samples containing 5% and 10% of PHSA and PDMS-stabilized PMMA colloids dispersed in 5CB. The mixtures were cooled at 0.1 K/min down to and kept constant for several hours before starting the frequency sweeps. Filled symbols represent and open symbols .

(a) Microscopic images of the network structure of sample PHSA-10 at a sample thickness of and various cooling rates. For increasing cooling rate the size of the nematic droplets decreased. (b) Image analysis: for each data point the average droplet size and its variance are calculated on the base of more than 50 droplets. Besides PHSA-10 the samples PHSA-05 and PDMS-05 were analyzed. The data are consistent with a power-law dependency (straight lines as guide to the eye). Areas with different hatchings separate parameter constellations for which the domain size exceeds the sample thickness and vice versa.

(a) Microscopic images of the network structure of sample PHSA-10 at a sample thickness of and various cooling rates. For increasing cooling rate the size of the nematic droplets decreased. (b) Image analysis: for each data point the average droplet size and its variance are calculated on the base of more than 50 droplets. Besides PHSA-10 the samples PHSA-05 and PDMS-05 were analyzed. The data are consistent with a power-law dependency (straight lines as guide to the eye). Areas with different hatchings separate parameter constellations for which the domain size exceeds the sample thickness and vice versa.

Dependency of the shear moduli on the cooling rate for sample PHSA-10. The transition from a 2D structure to a 3D one in Fig. 5(b) is reflected in a convergence of the mechanical spectra. For cooling rates of 0.2 and 0.5 K/min nearly no difference in the spectra could be seen.

Dependency of the shear moduli on the cooling rate for sample PHSA-10. The transition from a 2D structure to a 3D one in Fig. 5(b) is reflected in a convergence of the mechanical spectra. For cooling rates of 0.2 and 0.5 K/min nearly no difference in the spectra could be seen.

The sample PDMS-05 was kept inside the rheometer for successive heating-cooling cycles. (a) The temperature dependent storage modulus is plotted for three different frequencies and for the first nine subsequent cycles. A pronounced hysteresis with respect to cooling and heating is revealed. The maximal cooling rate between the turning points was 0.5 K/min. (b) Different shaded symbols represent the relative storage modulus at for maximal temperatures of 29.5 and , respectively, in course of 20 cycles. The temperatures are held constant for 50 min before each measurement.

The sample PDMS-05 was kept inside the rheometer for successive heating-cooling cycles. (a) The temperature dependent storage modulus is plotted for three different frequencies and for the first nine subsequent cycles. A pronounced hysteresis with respect to cooling and heating is revealed. The maximal cooling rate between the turning points was 0.5 K/min. (b) Different shaded symbols represent the relative storage modulus at for maximal temperatures of 29.5 and , respectively, in course of 20 cycles. The temperatures are held constant for 50 min before each measurement.

Aging behavior of the network exemplary shown for PDMS-10 for stopping temperatures of about 32 and . The filled and open symbols represent the storage and loss modulus, respectively. The data were normalized to the initial moduli.

Aging behavior of the network exemplary shown for PDMS-10 for stopping temperatures of about 32 and . The filled and open symbols represent the storage and loss modulus, respectively. The data were normalized to the initial moduli.

a) Frequency dependence of the shear moduli for four different temperatures. Filled symbols represent and open symbols , respectively. Characteristic features of the single curves, such as crossing points of and , are common to all curves. Shifts in frequency correspond to different sample temperatures and are indicated by arrows. (b) Temperature dependence of the frequency of the phase maximum for colloids stabilized with PDMS and PHSA at a weight fraction of 10%. For each temperature this frequency was determined by a parabolic fit to the data (see inset for a temperature of ). The dashed curve serves as a guide to the eye suggesting an exponential dependency.

a) Frequency dependence of the shear moduli for four different temperatures. Filled symbols represent and open symbols , respectively. Characteristic features of the single curves, such as crossing points of and , are common to all curves. Shifts in frequency correspond to different sample temperatures and are indicated by arrows. (b) Temperature dependence of the frequency of the phase maximum for colloids stabilized with PDMS and PHSA at a weight fraction of 10%. For each temperature this frequency was determined by a parabolic fit to the data (see inset for a temperature of ). The dashed curve serves as a guide to the eye suggesting an exponential dependency.

Superposition of the frequency spectra of Fig. 9(a) according to the shift factors of Fig. 9(b). Along the whole frequency axis the overlap of adjacent spectra is reasonably good. Deviations are most apparent for the loss angle at low and intermediate frequencies and in the moduli for the highest frequencies.

Superposition of the frequency spectra of Fig. 9(a) according to the shift factors of Fig. 9(b). Along the whole frequency axis the overlap of adjacent spectra is reasonably good. Deviations are most apparent for the loss angle at low and intermediate frequencies and in the moduli for the highest frequencies.

## Tables

Particle parameters: for each synthesis method one single batch was used to prepare samples at PMMA contents of 5 and . Radii and standard deviations were determined by SEM on the basis of 50 particles. Both radii and densities were comparable for the two types of colloids.

Particle parameters: for each synthesis method one single batch was used to prepare samples at PMMA contents of 5 and . Radii and standard deviations were determined by SEM on the basis of 50 particles. Both radii and densities were comparable for the two types of colloids.

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