C

Co (d) 7

Zn 6 Mn 7

Mn Zn

Zn

Mn

 Co8

Zn 3 Mn 9

5

9

13

17

21

25

6 5 4 3 2 1 0

0

1

2

3

4

20

15

10

5

0

0

ρ nSLD solvent 2, n

2

 (10-6 ) -2 Å

nSLD solvent 1, 

ρ

n

1 (10

Information gain, 

Δ

SOFT MATTER

38 NIST CENTER FOR NEUTRON RESEARCH

Structure-property-processing 

relationships of soft viscoelastic materials

J. C.-W Lee,1 K. M. Weigandt,2 E. G. Kelley,2 and S. A. Rogers1

1 University of Illinois at Urbana-Champaign, IL 61801

2 NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899

T

o design the next generation of ‘smart’ soft materials, 

researchers must first understand how rapidly-changing 

flow conditions affect model materials. Soft viscoelastic 

materials, such as synthetic and biological polymers, tend 

to generate complex material responses. The link between 

macroscopic flow and molecular-level microstructural 

rearrangements has long been sought but has remained 

elusive. We show, by experimentally combining new 

rheological techniques with time-resolved rheo-small-angle 

neutron scattering (rheo-SANS), such links can now be 

made, forming nonlinear structure-property-processing 

relations, by considering the evolution of the recoverable 

component of the strain [1].

Oscillatory shearing has been widely used to study a wide array 

of soft materials. In particular, rapidly-changing flow conditions 

that are often encountered in processing and manufacturing 

soft materials can be accurately simulated by large amplitude 

oscillatory shear (LAOS) because of the independent control 

of length and time scales it affords. As such, LAOS has been 

commonly employed as a model transient flow protocol capable 

of eliciting nonlinear responses. In spite of the wide adoption 

of LAOS, the underlying physics and resulting structural 

rearrangements have remained difficult to interpret [2]. In a 

recent study, we show that the recoverable strain, a rheological 

metric first proposed by Weissenberg [3] and Reiner [4], is a key 

to understanding oscillatory shear rheology, in not only complex 

macroscopic responses such as shear and normal stresses, but 

also in how the microstructure reacts to dynamic flows. 

We investigate two distinct polymeric materials, including an 

industrial entangled worm-like micelle (WLM) solution and 

a fibrin network. The LAOS responses from WLMs across a 

wide range of amplitudes at a normalized frequency (Deborah 

number) of 0.25 are presented in Fig. 1. Traditionally, the 

stress response is plotted against the shear strain (Fig.1(a)) or 

shear rate (Fig.1(c)), forming the so-called elastic and viscous 

Lissajous curves. The distorted ellipses and the secondary 

loops are typical features of LAOS in these presentations. 

These presentations, however, view the responses from the 

perspective that the reference state remains fixed at zero strain, 

and ignores the fact that the reference state (or “ground 

state” originally referred by Weissenberg [3]) can be shifted by 

external flow conditions.

Strain can be experimentally decomposed into recoverable and 

unrecoverable components by unloading stresses. Recoverable 

strain is elastic, while viscous properties are dictated by the 

rate at which strain is acquired unrecoverably. The natural 

presentation to display elastic and viscous responses is therefore 

stress versus recoverable strain (Fig.1(b)) and stress versus 

unrecoverable strain rate (Fig.1(d)). Significant differences 

are observed from the traditional Lissajous curves. The curves 

collapse into a straight line at small strains and rates, where the 

slopes naturally correspond to the plateau modulus (Fig.1(b)) 

and zero-shear viscosity (Fig.1(d)) of the WLMs, which are 

traditionally thought not determinable from a single LAOS 

test. Further, the instant when the total strain is maximal 

(star in Fig.1(a)), which is traditionally considered to be the 

most-strained state, actually corresponds to the point of zero 

recoverable strain, indicating there is little-to-no deformation 

from a microscopic perspective. This finding explains the 

origin of observations made in numerous studies of colloidal 

and polymeric materials, where researchers have noted the 

existence of linear elasticity close to total strain extrema (See 

[1] for references). In short, in these new experiments and their 

associated proposed presentations, LAOS naturally presents 

a sequence of physical processes: linear viscoelasticity (LVE) 

is observed when the recoverable strain is small, softening 

and thinning with larger recoverable strains and higher 

unrecoverable strain rates, followed by a recoil process that 

returns the material to the original state. The same sequence 

occurs twice per oscillation, as the materials respond to 

shearing in a symmetric manner. 

While the macroscopic physics is more clearly discerned 

by recovery-based rheology, we complete the structureproperty relationship using time-resolved SANS to monitor 

the microstructural evolution. Shown in Fig. 2(a) is the 

stress versus recoverable strain with a color scale reflecting 

the degree of alignment observed in the 2D SANS patterns 

in Fig. 2(b). Given that a natural state of the entangled 

micellar system is isotropic, aligning the micellar segments 

is entropically unfavorable, leading to a macroscopic elastic 

response. The alignment factors in the velocity-gradient 

(1-2) and velocity-vorticity (1-3) planes are presented as 

functions of recoverable strain in Fig. 2(c) and Fig. 2(d), 

where a linear proportionality with a constant prefactor is 

manifested. A clear physical picture therefore emerges. When 
A

12d

A

12d

A

12d

right-h

A

C

6

Å-2

)

solv

ρn

 

0.05

Momen

solv

ρn

 

SOFT MATTER

2019 ACCOMPLISHMENTS AND OPPORTUNITIES 39

the recoverable strain is small, linear viscoelastic responses 

are seen, even under LAOS, and we observe an isotropic 

scattering pattern that is identical to equilibrium conditions 

with no alignment. As the magnitude of the recoverable strain 

increases, so too does the alignment factor. Even when the 

modulus begins to drop at large recoverable strains (points ii 

and iv in Fig. 2(a)), the alignment is still linearly dependent on 

the magnitude of the recoverable strain.

In summary, we have provided key insights into the 

understanding of dynamic flows and how molecular-level 

structure reacts during changing flows. We have shown that, 

by monitoring the evolution of the recoverable component 

of strain, the material physics under dynamic flows can 

be identified as a sequence of processes. Combining with 

experimental evidence from neutron scattering, we have 

established structure-property-processing relationships, 

providing new design criteria for soft materials. Armed with 

such new understandings, researchers now have a clearer path 

for developing advanced materials for a variety of biomedical, 

industrial and environmental applications.

References

[1] J. C.-W. Lee, K. M. Weigandt, E. G. Kelley, S. A. Rogers, 

Phys. Rev. Lett. 122, 248003 (2019).

[2] S. Rogers, Phys. Today 71, 34 (2018).

[3] K. Weissenberg, Nature 159, 310 (1947).

[4] M. Reiner, in Encycl. Phys. VI (Springer-Verlag Berlin 

Heidelberg, 1958), pp. 435–549.

FIGURE 1: LAOS results presented in the traditional (σ-γ, σ-γ ̇ ) and proposed 

(σ-γrec, σ-γ̇ un) frames from WLMs. The lines in the proposed elastic and viscous 

views have slopes equal to the plateau modulus G0 = 180 Pa and the zero-shear 

viscosity η0 = 48 Pa·s. The stars and squares correspond to zero and maximum 

recoverable strain at the largest amplitude, respectively. 

FIGURE 2: Correlation between macroscopic rheology and microscopic 

structure. (a) Proposed elastic Lissajous figure (σ-γrec) coupled with 1-3 

alignment factor A f denoted by the color scale. (b) 2D SANS patterns at zero (i 

and iii) and maximum (ii and iv) recoverable strain in both velocity-gradient and 

velocity-vorticity planes. Alignment factors in the 1-3 (c) and 1-2 (d) planes are 

plotted as functions of the recoverable strain, showing the same proportionality 

constant of 0.045.