Mesoscale Phenomena in Fluid Systems - American Chemical Society

Chapter 10

Aging of Soft Glassy Materials Probed by Rheology and Light Scattering 1

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EugenePashkovski ,LucaCipelletti ,Suliana Manley , and David Weitz 3

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Colgate Palmolive Company, R&D, Technology Center, 909 River Road, Piscataway, NJ 08855 GDPC UMR 5681, CNRS and Université Montpellier II, Montpellier, France DEAS, Harvard University, 40 Oxford Street, Cambridge, M A 02138

Downloaded by MONASH UNIV on March 6, 2015 | http://pubs.acs.org Publication Date: August 17, 2003 | doi: 10.1021/bk-2003-0861.ch010

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Aging of soft glassy materials studied by rheology, small-angle Dynamic Light Scattering (DLS) and Diffusing Wave Spectroscopy (DWS) is presented. We use these methods to obtain the dynamic signature of aging for various colloidal systems such as compressed water-in-oil emulsions, mixtures of surfactant, oil and water, and xanthan pastes. In all cases, we observe a significant reduction in the colloidal mobility with sample age as derived from measured intensity correlation functions. For all systems, an unusual shape of the age-dependent part of the correlation functions was found, ruling out conventional diffusive mobility. Using an analogy between molecular and colloidal glasses, we analyze a violation of the Generalized Stokes-Einstein Relation using a combination of D W S and rheology.

© 2003 American Chemical Society

In Mesoscale Phenomena in Fluid Systems; Case, F., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2003.

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Rheological properties of soft glassy materials reflect their metastable structure and structural disorder (1). Slow structural relaxation (i.e. aging) of such materials causes rheological responses to depend on the age of the sample, t , defined as the time elapsed since the sample was quenched in the glassy state. Slow dynamics in such systems was recently discussed in terms of jamming (2); the drastic decrease in mobility occurs in the jammed state due to high concentration and/ or inter-particle interactions. Experimentally, slow dynamics can be probed by studying the response of the system to external perturbations or by directly measuring the dynamic structure factor. Experimental evidence of slow relaxations and aging was observed by Struik for polymer glasses (3). His approach was based on mechanical creep measurements that provide information on system's mobility evolution versus its age. Remarkably, very similar aging behavior was observed for many different glassy amorphous polymers as well as for molecular glasses. Molecular mobility that defines the age-dependent


w

relaxation process of these systems diminishes with age t

w

simple power law, M(t )oc w

according to the

M

Ç , where μ is the aging exponent.

This general trend was also found for magnetic glasses; recently, aging of these systems has been the subject of intense theoretical and experimental interest (4). In these experiments, the sample is cooled below the glass transition temperature, T , while an external magnetic field is applied. The age is defined g

as the "waiting" time t

w

spent in the glass phase, before cutting the field. A t

zero field, a rapid decrease of the magnetization is followed by a slow agedependent relaxation. Remarkably, the age-dependent part of the magnetization shows the same scaling behavior as the creep compliance of polymeric glasses. In both cases, the response functions may be scaled as a function of

tlt^

implying that the relaxation time T oc t£. The aging process has been studied theoretically using several approaches, which can be applied for broad classes of systems that display non-stationary dynamics (5-7). One of the main features of non-stationary dynamics is the violation of the fluctuation-dissipation theorem (FDT), which relates the response and correlation functions of the system at equilibrium: z(t,o=jimtj-c(t,t )}

(i)

w

where x(t,t ) is the response at time t to a constant magnetic field applied at w

t, w

C(t,t ) is the correlation function, and Τ is the temperature (6). A t equilibrium, w

a parametric plot of χ(€)

vs. C yields a straight line, whose slope is - 1 / Γ .

When the system is cooled below T , it stays out of equilibrium, and the g

dependence of χ(€) is non-linear. Thus, the slope of the curve z(C) the F D T violation factor X(C) :


defines

163 dz(C)

X(C)

dC

Τ

(2)

The concept of "effective temperature", T f[ = T/X(Q, defines the physical meaning of X(C) for systems with slow dynamics. As the violation occurs for X(QT. e

eff

During aging, the system "cools", i.e. X(C) - » 1 for t -> .Violations of F D T were analyzed for spin (7) and molecular glasses such as glycerol below the glass transition (8,9). In these measurements, the weak violation of F D T was observed such that X(C) increased and T decreased with aging time. Thus, F D T - violation is certainly a signature of aging behavior of broad classes of glassy systems. w


eff

Jammed colloidal systems as "soft glasses Jammed colloidal systems have many common features with polymer, spin or structural glasses. This similarity was recognized by Sollich (10). His theory on the rheology of "soft glassy materials" (SGM) allows one to incorporate the so called "trap model" (77) developed for glasses. The rheological response of S G M depends on age as a result of inherent metastability and restricted mobility. Experimental studies of soft microgels (72) and concentrated silica suspensions (73) have shown that the low frequency data can be scaled similarly to the magnetization curves for spin glasses, or the creep curves for polymers. These analogies suggest that aging phenomena in colloids may be studied by investigating the violation of the FDT, as it is done for magnetic and molecular glasses. For colloidal systems, a convenient way to do so is to study the violation of the Generalized Stokes-Einstein Relation (GSER). At equilibrium, the G S E R provides the relationship between the mean square displacement of particles of radius a and the viscoelastic properties of the complex fluid (14). The viscoelastic spectrum G(s)

as a function of Laplace

frequency (75) s is given by:

transform. The time-domain creep compliance can be obtained from eq. (3) and the simple relationship between the shear modulus and the shear creep

compliance , J = l/(sG) (15): 2

J(0~

(4)


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Measurements of the mean square displacements of monodisperse tracer particles allows viscoelastic parameters of complex liquids to be calculated (1417). In these experiments, the value of < Ar*(t) > is obtained by dynamic light scattering (DLS) techniques, either diffusing wave spectroscopy (DWS) (16) or single scattering (17). This approach, i f used for such systems as semi-dilute polymer solutions or moderately concentrated colloidal dispersions, allows one to calculate the viscoelastic properties, as the G S E R is not violated.


Violation of Generalized Stokes-Einstein Relation using light scattering study Jammed systems such as foams, colloidal gels and concentrated pastes are metastable systems for which G S E R is generally violated. The violation factor depends on the observation timescale, and increases with time (decreases with frequency). Despite the metastability, the system slowly evolves towards the equilibrium state and therefore its rheological properties depend on age. A s a result, there are two different time scales to be considered, the observation time t and the aging time t . Typically, for t «c t G S E R is not violated and therefore w

w

high-frequency responses may be age-independent. For instance, a good estimate of the high-frequency rheological response was obtained from D W S measurements of the mean square displacement of monodisperse droplets in concentrated emulsions (18). To investigate the violation of G S E R in jammed systems, one should extend the measurements of to much longer times, t > t . For traditional detection schemes that use a single detector (19), the value of g (t) must be extensively averaged over time; the measurement time is typically several orders of magnitude longer than the system relaxation time. The single-detection scheme becomes impractical for t> t ; the dynamics may be age-dependent for aging systems. To probe the slow dynamics, so-called multi-speckle detection schemes (20- 22) based on a 2D C C D camera detector have been developed. These techniques allow one to decrease the measurement time by several orders of magnitude, down to the order of the system relaxation time. Aging effects probed by multi-speckle techniques can be compared with age-dependent rheology. This gives information on aging at different time and length scales. The displacement that is resolved in our rheological experiments is 0.5-1 microns, whereas D W S can resolve displacements of particles as low as a few nanometers. Comparing the dynamic behaviors on meso and micro scales allows investigating violation of G S E R for colloidal systems, in analogy with F D T violation for magnetic and molecular glasses. 2

w

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w


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Aging of jammed systems One of the important features discovered for colloids, is the unusual shape of the intensity correlation function which decays faster than an exponential function, g (q,t)l. This unusual shape was discovered p

{

using multi-speckle D L S for low-volume fraction colloidal gels formed by 10nm polystyrene particles (21). The parameter ρ that defines the shape of the "compressed" exponential was p=l.5. Furthermore, the relaxation time was found to depend on the scattering vector as τ oc q~ , The latter rules out the x

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diffusive motion of particles that sets rocq' .

A phenomenological model

explaining this behavior introduces local stress sources that appear as a result of shrinking of the gel (21). A more rigorous model developed by Bouchaud and Pitard (23) computes the dynamic structure factor based on random appearance of micro-collapses in a gel, resulting in motions of particles that contribute to the decorrelation of the scattered light intensity. Bouchaud and Pitard also found that p=l.5 in an early-time regime; however, for intermediate-time regime p-1.25 and for long-time regime, the "compressing" exponent reaches ρ -> 1. Though both models (21J3) were developed for particulate gels, the same unusual shape of the correlation function was observed for widely different colloidal systems, such as compressed emulsions, "onion" phases, and micellar cubic phase (24). For these systems, D L S measurements have reproduced the "compressed" exponential shape of the dynamic structure factor /(#>0«&(?>0 exp[--(i/r) ]. Note, that the D W S measurements for oc

p

Laponite gels also reproduce this behavior (25). In this case, the tracer micro particles were dispersed in the gel to induce multiple scattering. For a given q in D L S , the relaxation time increases with sample's age as τ oc ίζ. The aging exponent μ appears to be system-dependent and, in some cases, it changes with t . A l l this observations reveal the universality of slow dynamics of jammed colloidal systems having different structural organization. In this Chapter, we discuss aging behavior of compressed emulsions, multiphase oil-in water emulsions, and microgel suspensions studied by D L S , DWS, and by rheological methods. D L S has been a very useful tool to characterize slow dynamics but it is limited to the single-scattering regime. Multispeckle D W S may be applied to a much wider class of systems, including compressed emulsions with nonmatching refractive indices in their continuous and dispersed phases and concentrated colloidal suspensions and gels. However, characterization of aging behavior using D W S is still poorly understood. As observed in D L S experiments, D W S measurements reveal similar aging effects that occur for very w


166 different systems. To demonstrate this, we compare transparent compressed emulsions with two turbid systems, a mixture of Pluronic F108, water and mineral oil and a xanthan paste with dispersed tracer particles.

Compressed emulsions When the volume fraction of droplets ^exceeds the critical packing volume fraction φ an emulsion system becomes compressed with elasticity 0\φ)κ(σΙ α)·(φΙ φ -ϊ)(26). The Laplace pressure ( σ / α ) , the ratio of surface tension to the droplet radius, depends on preparation conditions and the nature and the concentration of the surfactant which stabilizes the droplets. In our study, the water phase (^=0.77) was dispersed in the oil phase (cyclomethicone), which contained a silicon-based polymeric surfactant, (Copolyol, Dow Corning 522C, c=0.25 wt. %). Refractive indices of water and oil phases were matched by adding PEG-600 and a salt (NaCl) to the water phase. The two phases were separately prepared, than mixed using high-speed lab mixer. The speed was selected such that the average particle size was 1.0±0.2μιη. Confocal microscopy shows no coalescence of droplets during aging for this polydisperse emulsion. The emulsion was centrifuged for 15 min at rate between 1500 and 1900 rpm, to avoid scattering from air bubbles entrapped in the optical cell. The end of the centrifugation was set as f = 0. ζ


€

w

Figure l a shows the dynamic structure factors measured simultaneously for scattering vectors parallel to the acceleration imposed by centrifugation for i =300s. The dynamic structure factor decays as w

ex

i/T

P

/(

Mesoscale Phenomena in Fluid Systems - American Chemical Society

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