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Carretas-Talamante AG, Zepeda-López JB, Lázaro-Lázaro E, Elizondo-Aguilera LF, Medina-Noyola M. Non-equilibrium view of the amorphous solidification of liquids with competing interactions. J Chem Phys 2023; 158:064506. [PMID: 36792503 DOI: 10.1063/5.0132525] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
The interplay between short-range attractions and long-range repulsions (SALR) characterizes the so-called liquids with competing interactions, which are known to exhibit a variety of equilibrium and non-equilibrium phases. The theoretical description of the phenomenology associated with glassy or gel states in these systems has to take into account both the presence of thermodynamic instabilities (such as those defining the spinodal line and the so called λ line) and the limited capability to describe genuine non-equilibrium processes from first principles. Here, we report the first application of the non-equilibrium self-consistent generalized Langevin equation theory to the description of the dynamical arrest processes that occur in SALR systems after being instantaneously quenched into a state point in the regions of thermodynamic instability. The physical scenario predicted by this theory reveals an amazing interplay between the thermodynamically driven instabilities, favoring equilibrium macro- and micro-phase separation, and the kinetic arrest mechanisms, favoring non-equilibrium amorphous solidification of the liquid into an unexpected variety of glass and gel states.
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Affiliation(s)
- Ana Gabriela Carretas-Talamante
- Instituto de Física "Manuel Sandoval Vallarta," Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, Mexico
| | - Jesús Benigno Zepeda-López
- Instituto de Física "Manuel Sandoval Vallarta," Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, Mexico
| | - Edilio Lázaro-Lázaro
- Instituto de Física "Manuel Sandoval Vallarta," Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, Mexico
| | | | - Magdaleno Medina-Noyola
- Instituto de Física "Manuel Sandoval Vallarta," Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, Mexico
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Charbonneau P, Tarzia M. Solution of disordered microphases in the Bethe approximation. J Chem Phys 2021; 155:024501. [PMID: 34266261 DOI: 10.1063/5.0052111] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The periodic microphases that self-assemble in systems with competing short-range attractive and long-range repulsive (SALR) interactions are structurally both rich and elegant. Significant theoretical and computational efforts have thus been dedicated to untangling their properties. By contrast, disordered microphases, which are structurally just as rich but nowhere near as elegant, have not been as carefully considered. Part of the difficulty is that simple mean-field descriptions make a homogeneity assumption that washes away all of their structural features. Here, we study disordered microphases by exactly solving a SALR model on the Bethe lattice. By sidestepping the homogenization assumption, this treatment recapitulates many of the key structural regimes of disordered microphases, including particle and void cluster fluids as well as gelation. This analysis also provides physical insight into the relationship between various structural and thermal observables, between criticality and physical percolation, and between glassiness and microphase ordering.
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Affiliation(s)
| | - Marco Tarzia
- LPTMC, CNRS-UMR 7600, Sorbonne Université, 4 Place Jussieu, F-75005 Paris, France
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Tarzia M, Coniglio A. Lamellar order, microphase structures, and glassy phase in a field theoretic model for charged colloids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:011410. [PMID: 17358153 DOI: 10.1103/physreve.75.011410] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2006] [Indexed: 05/06/2023]
Abstract
In this paper we present a detailed analytical study of the phase diagram and of the structural properties of a field theoretic model with a short-range attraction and a competing long-range screened repulsion. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Tarzia and A. Coniglio, Phys. Rev. Lett. 96, 075702 (2006). The model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions. We employ the self-consistent Hartree approximation and a replica approach, and we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar and a glassy phase. Our results suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales, and emphasize that the formation of microphase structures may play a prominent role in the process of colloidal gelation.
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Affiliation(s)
- Marco Tarzia
- Dipartimento di Scienze Fisiche and INFN sezione di Napoli, Università degli Studi di Napoli "Federico II," Complesso Universitario di Monte Sant'Angelo, via Cinthia, 80126 Napoli, Italy
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Xu A, Gonnella G, Lamura A. Morphologies and flow patterns in quenching of lamellar systems with shear. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:011505. [PMID: 16907098 DOI: 10.1103/physreve.74.011505] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2005] [Revised: 03/02/2006] [Indexed: 05/11/2023]
Abstract
We study the behavior of a fluid quenched from the disordered into the lamellar phase under the action of a shear flow. The dynamics of the system is described by Navier-Stokes and convection-diffusion equations with the pressure tensor and the chemical potential derived by the Brazovskii free energy. Our simulations are based on a mixed numerical method with the lattice Boltzmann equation and a finite difference scheme for Navier-Stokes and order parameter equations, respectively. We focus on cases where banded flows are observed with two different slopes for the component of velocity in the direction of the applied flow. Close to the walls the system reaches a lamellar order with very few defects, and the slope of the horizontal velocity is higher than the imposed shear rate. In the middle of the system the local shear rate is lower than the imposed one, and the system looks like a mixture of tilted lamellae, droplets, and small elongated domains. We refer to this as a region with a shear-induced structures (SIS) configuration. The local behavior of the stress shows that the system with the coexisting lamellar and SIS regions is in mechanical equilibrium. This phenomenon occurs, at fixed viscosity, for shear rates under a certain threshold; when the imposed shear rate is sufficiently large, lamellar order develops in the whole system. Effects of different viscosities have been also considered. The SIS region is observed only at low enough viscosity. We compare the above scenario with the usual one of shear banding. In particular, we do not find evidence for a plateau of the stress at varying imposed shear rates in the region with banded flow. We interpret our results as due to a tendency of the lamellar system to oppose the presence of the applied flow.
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Affiliation(s)
- Aiguo Xu
- Dipartimento di Fisica, Università di Bari, via Amendola 173, 70126 Bari, Italy
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de Candia A, Del Gado E, Fierro A, Sator N, Tarzia M, Coniglio A. Columnar and lamellar phases in attractive colloidal systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:010403. [PMID: 16907047 DOI: 10.1103/physreve.74.010403] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2006] [Revised: 06/06/2006] [Indexed: 05/11/2023]
Abstract
In colloidal suspensions, at low volume fraction and temperature, dynamical arrest occurs via the growth of elongated structures that aggregate to form a connected network at gelation. Here we show that, in the region of parameter space where gelation occurs, the stable thermodynamical phase is a crystalline columnar one. Near and above the gelation threshold, the disordered spanning network slowly evolves and finally orders to form the crystalline structure. At higher volume fractions the stable phase is a lamellar one, which seems to have a still longer ordering time.
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Affiliation(s)
- A de Candia
- Dipartimento di Scienze Fisiche, Università di Napoli Federico II, Complesso Universitario di Monte Sant'Angelo, 80126 Napoli, Italy
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Zhang CZ, Wang ZG. Random isotropic structures and possible glass transitions in diblock copolymer melts. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:031804. [PMID: 16605551 DOI: 10.1103/physreve.73.031804] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2005] [Indexed: 05/08/2023]
Abstract
We study the microstructural glass transition in diblock-copolymer melts using a thermodynamic replica approach. Our approach performs an expansion in terms of the natural smallness parameter--the inverse of the scaled degree of polymerization N--which allows us to systematically study the approach to mean-field behavior as the degree of polymerization increases. We find that in the limit of infinite chain length, both the onset of glassiness and the vitrification transition (Kauzmann temperature) collapse to the mean-field spinodal, suggesting that the spinodal can be regarded as the mean-field signature for glass transitions in this class of microphase-separating system. We also study the order-disorder transition (ODT) within the same theoretical framework; in particular, we include the leading-order fluctuation corrections due to the cubic interaction in the coarse-grained Hamiltonian, which has been ignored in previous studies of the ODT in block copolymers. We find that the cubic term stabilizes both the ordered (body-centered-cubic) phase and the glassy state relative to the disordered phase. In melts of symmetric copolymers the glass transition always occurs after the order-disorder transition (below the ODT temperature), but for asymmetric copolymers, it is possible for the glass transition to precede the ordering transition.
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Affiliation(s)
- Cheng-Zhong Zhang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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Tarzia M, Coniglio A. Pattern formation and glassy phase in the phi4 theory with a screened electrostatic repulsion. PHYSICAL REVIEW LETTERS 2006; 96:075702. [PMID: 16606111 DOI: 10.1103/physrevlett.96.075702] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2005] [Indexed: 05/08/2023]
Abstract
We study analytically the structural properties of a system with a short-range attraction and a competing long-range screened repulsion. This model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions and provides novel insights on the equilibrium phase diagram of these systems. Within the self-consistent Hartree approximation and by using a replica approach, we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar, and a glassy phase. Our results strongly suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales.
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Affiliation(s)
- Marco Tarzia
- Dipartimento di Scienze Fisiche, INFN sezione di Napoli, Università degli Studi di Napoli Federico II, Complesso Universitario di Monte Sant' Angelo, via Cinthia, 80126 Napoli, Italy
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Portmann O, Vaterlaus A, Pescia D. Observation of stripe mobility in a dipolar frustrated ferromagnet. PHYSICAL REVIEW LETTERS 2006; 96:047212. [PMID: 16486892 DOI: 10.1103/physrevlett.96.047212] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2005] [Indexed: 05/06/2023]
Abstract
We have discovered two novel aspects of the stripe-domain to paramagnetic transition in perpendicularly magnetized Fe films on Cu(100). First, the width of the stripes carrying oppositely oriented spins decreases, close to the transition temperature, with a power law. Second, in a small temperature interval close to the transition temperature, the stripes--which form stationary patterns at low temperatures--become mobile. Various theoretical works have predicted stripe mobility in similar frustrated systems but no direct proof of this phenomenon has been reported so far.
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Affiliation(s)
- O Portmann
- Laboratorium für Festkörperphysik, ETH Zürich, 8093 Zürich, Switzerland
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Westfahl H, Schmalian J. Correlated disorder in random block copolymers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:011806. [PMID: 16089992 DOI: 10.1103/physreve.72.011806] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2005] [Indexed: 05/03/2023]
Abstract
We study the effect of a random Flory-Huggins parameter in a symmetric diblock copolymer melt which is expected to occur in a copolymer where one block is near its structural glass transition. In the clean limit the microphase segregation between the two blocks causes a weak, fluctuation induced first order transition to a lamellar state. Using a renormalization group approach combined with the replica trick to treat the quenched disorder, we show that beyond a critical disorder strength, which depends on the length of the polymer chain, the character of the transition is changed. The system becomes dominated by strong randomness and a glassy rather than an ordered lamellar state occurs. A renormalization of the effective disorder distribution leads to nonlocal disorder correlations that reflect strong compositional fluctuation on the scale of the radius of gyration of the polymer chains. The reason for this behavior is shown to be the chain length dependent role of critical fluctuations, which are less important for shorter chains and become increasingly more relevant as the polymer length increases and the clean first order transition becomes weaker.
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Affiliation(s)
- Harry Westfahl
- Laboratorio Nacional de Luz Sncrotron--ABTLuS, Campinas, São Paulo, Brazil
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Geissler PL, Reichman DR. Nature of slow dynamics in a minimal model of frustration-limited domains. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:021501. [PMID: 14995443 DOI: 10.1103/physreve.69.021501] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2003] [Indexed: 05/24/2023]
Abstract
We present simulation results for the dynamics of a schematic model based on the frustration-limited domain picture of glass-forming liquids. These results are compared with approximate theoretical predictions analogous to those commonly used for supercooled liquid dynamics. Although model relaxation times increase by several orders of magnitude in a non-Arrhenius manner as a microphase separation transition is approached, the slow relaxation is in many ways dissimilar to that of a liquid. In particular, structural relaxation is nearly exponential in time at each wave vector, indicating that the mode-coupling effects dominating liquid relaxation are comparatively weak within this model. Relaxation properties of the model are instead well reproduced by the simplest dynamical extension of a static Hartree approximation. This approach is qualitatively accurate even for temperatures at which the mode-coupling approximation predicts loss of ergodicity. These results suggest that the thermodynamically disordered phase of such a minimal model poorly caricatures the slow dynamics of a liquid near its glass transition.
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Affiliation(s)
- Phillip L Geissler
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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