Viscoelasticity of Near-Critical Gels

Martin, James E.; Adolf, Douglas Brian; Wilcoxon, J. P.

doi:10.1103/physrevlett.61.2620

Cited by 301 publications

(267 citation statements)

References 14 publications

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“…This value is quite close to the one experimentally measured in silica gels [7,19] and interestingly these systems are characterized by a polyfunctional condensation mechanism with tetrafunctional monomers, which is actually very similar to the case simulated here. This result is also close to the value obtained by recent accurate measurements in PDMS [3].…”

supporting

confidence: 75%

“…Within the study of diffusion properties in the system an interesting picture is obtained with a simple scaling argument on the diffusion coefficients as presented in [19]: the sol at the sol-gel transition is a heteregenous medium formed by the solvent and all the other clusters 1 The same agreement with the random percolation critical exponents has already been obtained in the d = 2 version of the model [18]. Here it is worth to mention that this case on a cubic lattice with monomer functionality f = 4 is rather the problem of a restricted valence percolation.…”

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confidence: 99%

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Viscosity critical behaviour at the gel point in a 3d lattice model

2000

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confidence: 99%

Viscosity critical behaviour at the gel point in a 3d lattice model

2000

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“…In focusing on the small displacements associated with the relaxation of structure and stress, the coupling of the motion of different clusters is neglected. Such coupling is described in the gel transition by Martin et al (35,36) in which a cluster of size R diffuses in a medium whose viscosity has contributions from the clusters of size less than R and whose confinement is determined by clusters of size greater than R. Within the constraint network picture, an explicit, but partial, treatment of collective motion and its cooperative character emerges quite naturally. Collective motions arise here because constraints induce local rigidity, which compels a group of particles to move as one while pivots link these clusters so that motion of one can only occur with the cooperative motion of the other clusters in the pivot group.…”

Section: Discussionmentioning

confidence: 99%

Rigidity percolation and the spatial heterogeneity of soft modes in disordered materials

Souza

Harrowell

2009

Proc. Natl. Acad. Sci. U.S.A.

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We show how the spatial character of unconstrained motion in a network of bonds can be directly inferred from the topological arrangement of constraints. Relaxation time scales of these soft modes are determined, and from this information we generate spatial maps of the heterogeneous distribution of relaxation times in the disordered network. We show that the nature of the dynamic heterogeneity and its sensitivity to changes in bond configuration depends dramatically on the proximity of the system to the rigidity percolation point.dynamic heterogeneity ͉ glass transition ͉ inherent structure ͉ local mode ͉ supercooled liquid T he kinetic behavior of supercooled liquids is dominated by those configurations, known as inherent structures (1), which correspond to the local minima of the potential energy. This perspective, articulated by Goldstein (2) in 1969, is now generally accepted (3-6). The inherent structures can be regarded as zero-temperature disordered solids. The continuous transition from fluidity to rigidity that characterizes the glass transition is accomplished by the supercooled liquid sampling these disordered solids at nonzero temperatures for durations that increase as the temperature drops. Eventually, a low enough temperature is reached such that 1 local minimum persists indefinitely. To understand the kinetic and structural features of the transitions between different inherent structures we must understand the types of motion available to disordered solids. In this article we start from the proposal that constraint networks provide a general description of such solids and then develop a method for identifying the spatial distribution of the motions that remain unconstrained in such materials (i.e., the soft modes) and the spectrum of relaxation times associated with these modes.In the absence of explicit structural correlates for dynamics, the descriptive approach of dynamic heterogeneities has proved a powerful way forward in developing microscopic accounts of glassy relaxation and in articulating questions about determining dynamics from structure (7). Recently, it was shown that the spatial distribution of low-frequency quasi-localized normal modes is strongly correlated with the spatial distribution of irreversible reorganization (8). This study and related work (9-13) underline the importance of understanding the relation between local soft modes and structure in disordered solids. Understanding how features of an inherent structure determine the spatial pattern of motions is of central importance in developing a useful microscopic treatment of glass transitions and is the goal of this article.Faced with the daunting variety of particle arrangements that typically comprise a disordered solid, geometrical characterizations of such solids are difficult to both perform and interpret. An alternative treatment of amorphous rigidity is based on networks of constraints. The constraint approach to rigidity focuses on topology, instead of geometry, and the global balance between constraints and deg...

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“…8,9 Rubinstein et al 21 applied this dynamic scaling theory to dynamic moduli data of several stopped samples from condensation of diesters with alcohol. The theory, with its prediction of a constant n value, does not result in particularly good agreement between model and experimental data.…”

Section: Discussionmentioning

confidence: 99%

“…Due to the critical nature of the liquid-solid transition, transient rheological properties such as zero-shear viscosity and equilibrium modulus show a distinct scaling behavior in the vicinity of the gel point: 5,6 Dynamic scaling based on percolation theory [7][8][9] predicts different values for s and z, depending on the specific model assumption. Martin and Adolf 10 report n ) 2 / 3 , s ) 4 / 3 , and z ) 8 / 3 in the case of Rouse behavior (complete screening of hydrodynamic interactions), n ) 1, s ) 0, and z ) 8 / 3 for Zimm behavior (hydrodynamic interactions included), and n ) 0.71, s ) 0.75, and z ) 1.94 if the electrical network analogy introduced by de Gennes 11 is used.…”

Section: Introductionmentioning

confidence: 99%

Relaxation Patterns of Nearly Critical Gels

Mours¹,

Winter²

1996

Macromolecules

142

116

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We measure the complex rheological behavior of nearly critical gels and analyze the data by searching for characteristic patterns and abstracting those patterns into a self-consistent model. The sample is a linear, flexible, nearly monodisperse polybutadiene which gets cross-linked on its vinyl side groups. The dynamic mechanical storage and loss moduli of cross-linking polymers change smoothly during the liquid-solid transition, while equilibrium rheological properties (e.g., zero-shear viscosity and equilibrium compliance) diverge. During gelation, the relaxation occurs in a distinct pattern which can be described in a quantitative way with a minimum number of parameters. The pattern can be understood as a combination of the BSW spectrum (representing the precursor relaxation behavior) and the selfsimilar Chambon-Winter gel spectrum (modeling the terminal relaxation due to growing clusters). The spectrum is cut off at the material's longest relaxation time, λmax. Our model parameters, λmax and Ge (equilibrium modulus), exhibit characteristic scaling behavior with respect to the distance from the gel point, |p -pc|. The relaxation exponent, n, in the terminal zone is a function of the extent of reaction. Hence, dynamic scaling (requires constant n values) is not valid for our system. The proposed model passes the self-consistency test by predicting the mechanical behavior (at different frequencies) as a function of the extent of reaction and other rheological observations during the sol-gel transition.

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Viscoelasticity of Near-Critical Gels

Cited by 301 publications

References 14 publications

Viscosity critical behaviour at the gel point in a 3d lattice model

Viscosity critical behaviour at the gel point in a 3d lattice model

Rigidity percolation and the spatial heterogeneity of soft modes in disordered materials

Relaxation Patterns of Nearly Critical Gels

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