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Mallamace F, Mensitieri G, Salzano de Luna M, Lanzafame P, Papanikolaou G, Mallamace D. The Interplay between the Theories of Mode Coupling and of Percolation Transition in Attractive Colloidal Systems. Int J Mol Sci 2022; 23:5316. [PMID: 35628124 PMCID: PMC9141735 DOI: 10.3390/ijms23105316] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2022] [Revised: 05/03/2022] [Accepted: 05/04/2022] [Indexed: 12/04/2022] Open
Abstract
In the recent years a considerable effort has been devoted to foster the understanding of the basic mechanisms underlying the dynamical arrest that is involved in glass forming in supercooled liquids and in the sol-gel transition. The elucidation of the nature of such processes represents one of the most challenging unsolved problems in the field of material science. In this context, two important theories have contributed significantly to the interpretation of these phenomena: the Mode-Coupling theory (MCT) and the Percolation theory (PT). These theories are rooted on the two pillars of statistical physics, universality and scale laws, and their original formulations have been subsequently modified to account for the fundamental concepts of Energy Landscape (EL) and of the universality of the fragile to strong dynamical crossover (FSC). In this review, we discuss experimental and theoretical results, including Molecular Dynamics (MD) simulations, reported in the literature for colloidal and polymer systems displaying both glass and sol-gel transitions. Special focus is dedicated to the analysis of the interferences between these transitions and on the possible interplay between MCT and PT. By reviewing recent theoretical developments, we show that such interplay between sol-gel and glass transitions may be interpreted in terms of the extended F13 MCT model that describes these processes based on the presence of a glass-glass transition line terminating in an A3 cusp-like singularity (near which the logarithmic decay of the density correlator is observed). This transition line originates from the presence of two different amorphous structures, one generated by the inter-particle attraction and the other by the pure repulsion characteristic of hard spheres. We show here, combining literature results with some new results, that such a situation can be generated, and therefore experimentally studied, by considering colloidal-like particles interacting via a hard core plus an attractive square well potential. In the final part of this review, scaling laws associated both to MCT and PT are applied to describe, by means of these two theories, the specific viscoelastic properties of some systems.
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Affiliation(s)
- Francesco Mallamace
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, 00185 Rome, Italy
| | - Giuseppe Mensitieri
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, Piazzale Tecchio 80, 80125 Naples, Italy; (G.M.); (M.S.d.L.)
| | - Martina Salzano de Luna
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, Piazzale Tecchio 80, 80125 Naples, Italy; (G.M.); (M.S.d.L.)
| | - Paola Lanzafame
- Departments of ChiBioFarAm and MIFT—Section of Industrial Chemistry, University of Messina, CASPE-INSTM, V.le F. Stagno d’Alcontres 31, 98166 Messina, Italy; (P.L.); (G.P.)
| | - Georgia Papanikolaou
- Departments of ChiBioFarAm and MIFT—Section of Industrial Chemistry, University of Messina, CASPE-INSTM, V.le F. Stagno d’Alcontres 31, 98166 Messina, Italy; (P.L.); (G.P.)
| | - Domenico Mallamace
- Departments of ChiBioFarAm—Section of Industrial Chemistry, University of Messina, CASPE-INSTM, V.le F. Stagno d’Alcontres 31, 98166 Messina, Italy;
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Schmidtke B, Petzold N, Kahlau R, Hofmann M, Rössler EA. From boiling point to glass transition temperature: transport coefficients in molecular liquids follow three-parameter scaling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:041507. [PMID: 23214591 DOI: 10.1103/physreve.86.041507] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2012] [Revised: 08/03/2012] [Indexed: 06/01/2023]
Abstract
The phenomenon of the glass transition is an unresolved problem in condensed matter physics. Its prominent feature, the super-Arrhenius temperature dependence of the transport coefficients, remains a challenge to be described over the full temperature range. For a series of molecular glass formers, we combined τ(T) collected from dielectric spectroscopy and dynamic light scattering covering a range 10(-12) s < τ(T) < 10(2) s. Describing the dynamics in terms of an activation energy E(T), we distinguish a high-temperature regime characterized by an Arrhenius law with a constant activation energy E(∞) and a low-temperature regime for which E(coop)(T) ≡ E(T)-E(∞) increases exponentially while cooling. A scaling is introduced, specifically E(coop)(T)/E(∞) [proportionality] exp[-λ(T/T(A)-1)], where λ is a fragility parameter and T(A) a reference temperature proportional to E(∞). In order to describe τ(T) still the attempt time τ(∞) has to be specified. Thus, a single interaction parameter E(∞) describing the high-temperature regime together with λ controls the temperature dependence of low-temperature cooperative dynamics.
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Affiliation(s)
- B Schmidtke
- Universität Bayreuth, Experimentalphysik II, D-95440 Bayreuth, Germany
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Rössler E, Börner K, Tauchert J, Taupitz M, Pöschl M. Reorientational Correlation Functions of Simple Supercooled Liquids as Revealed by NMR Studies. ACTA ACUST UNITED AC 2010. [DOI: 10.1002/bbpc.19910950925] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Chong SH, Chen SH, Mallamace F. A possible scenario for the fragile-to-strong dynamic crossover predicted by the extended mode-coupling theory for glass transition. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:504101. [PMID: 21836212 DOI: 10.1088/0953-8984/21/50/504101] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
It is argued that the extended mode-coupling theory for glass transition predicts a dynamic crossover in the α-relaxation time and in the self-diffusion constant as a general implication of the structure of its equations of motion. This crossover occurs near the critical temperature T(c) of the idealized version of the theory, and is caused by the change in the dynamics from the one determined by the cage effect to that dominated by hopping processes. When combined with a model for the hopping kernel deduced from the dynamical theory for diffusion-jump processes, the dynamic crossover can be identified as the fragile-to-strong crossover (FSC) in which the α-relaxation time and the self-diffusion constant cross over from a non-Arrhenius to an Arrhenius behavior. Since the present theory does not resort to the existence of the so-called Widom line, to which the FSC in confined water has been attributed, it provides a possible explanation of the FSC observed in a variety of glass-forming systems in which the existence of the Widom line is unlikely. In addition, the present theory predicts that the Stokes-Einstein relation (SER) breaks down in different ways on the fragile and strong sides of the FSC, in agreement with the experimental observation in confined water. It is also demonstrated that the violation of the SER in both the fragile and strong regions can be fitted reasonably well by a single fractional relation with an empirical exponent of 0.85.
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Affiliation(s)
- S-H Chong
- Institute for Molecular Science, Okazaki 444-8585, Japan
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Huang W, Richert R. Dynamics of glass-forming liquids. XI. Fluctuating environments by dielectric spectroscopy. J Chem Phys 2006; 124:164510. [PMID: 16674149 DOI: 10.1063/1.2191491] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The dielectric relaxation of a 1 wt % mixture of di-n-butylether in 3-methylpentane has been measured across a range of eight decades, in which the characteristic relaxation time varies from 5 s to 50 ns. Each loss spectrum is a superposition of the dispersive solvent peak and a Debye peak which is one decade slower and readily assigned to the larger and more dipolar solute molecules. Fluctuating environments or rate exchange is made responsible for the Debye nature of probe rotation, implying that the environmental relaxation times fluctuate on time scales which are faster than the rotational correlation decay of the probe molecule. Within the experimental range from 2.2 s to 42 ns regarding the mean alpha-relaxation time, the results are consistent with the exchange time matching the upper limit of structural relaxation times or two to three times their average value. As T(g) is approached, no indication for a variation in exchange behavior or for slower environmental fluctuations is found.
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Affiliation(s)
- Wei Huang
- Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287-1604, USA
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Ruth AA, Nickel B. Spin-Lattice Relaxation and Rotational Motion of Aromatic Triplet-State Molecules in Supercooled Alkane Solvents (Part 1). J Phys Chem A 2005; 110:3138-50. [PMID: 16509637 DOI: 10.1021/jp0545546] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The phosphorescence of phenazine (PZ) and quinoxaline (QX) was investigated after pulsed laser excitation in the glass-transition range of several alkane solvents. Three relaxation processes of PZ and QX in the metastable triplet state, T1, were studied as a function of temperature: (1) the decay of the selective population of the strongly phosphorescent triplet substate T1x due to spin-lattice relaxation (SLR), (2) the time-dependent red shift of the phosphorescence spectrum due to the solvation of triplet-state molecules, and (3) the decay of the phosphorescence polarization due to orientational relaxation (OR). Various aspects and connections of the mechanisms governing the three relaxation phenomena are discussed. The relaxation dynamics were characterized at temperatures above the glass-transition temperature of the respective solvent, where the fundamental processes involved are strongly dependent upon the solvent viscosities. For the systems treated here, OR and solvation were satisfactorily described by a Vogel-Fulcher-Tammann temperature behavior. SLR also depends on properties of the alkane solvent above the glass transition. Upon cooling, SLR becomes independent of the specific solvent properties and is based on mechanisms that are typical for amorphous glasses or solids. (This particular aspect will be the subject of a subsequent publication, part 2).
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Affiliation(s)
- Albert A Ruth
- Department of Physics, National University of Ireland, University College Cork, Cork, Ireland.
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Wang LM, Velikov V, Angell CA. Direct determination of kinetic fragility indices of glassforming liquids by differential scanning calorimetry: Kinetic versus thermodynamic fragilities. J Chem Phys 2002. [DOI: 10.1063/1.1517607] [Citation(s) in RCA: 262] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
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Vogel M, Brinkmann C, Eckert H, Heuer A. Two-dimensional 109Ag NMR and random-walk simulation studies of silver dynamics in glassy silver ion conductors. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2002; 22:344-362. [PMID: 12469819 DOI: 10.1006/snmr.2002.0089] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
By applying one- and two-dimensional 109Ag NMR, we demonstrate that silver diffusion in silver iodide/silver phosphate glasses is governed by a very broad, continuous distribution of correlation times G(lg tau). As a consequence, over a wide temperature range, the 109Ag NMR spectra can be described by a weighted superposition of a Gaussian and a Lorentzian where these line-shape components result from the slow and the fast silver ions in G(lg tau), respectively. For the 109Ag NMR two-time correlation functions F2(t), measured as a stimulated echo, a very stretched decay to F2SS(t(m)) = 0 is observed. When fitting to a Kohlrausch function, exp[-(t/tau)beta], a stretching parameter beta approximately = 0.2 is found. The temperature dependence of the mean correlation time of silver dynamics is described by an Arrhenius law where the activation energy is consistent with the one reported for the dc conductivity sigma(dc). In addition, it is shown that the effect of complex dynamical processes on NMR multi-time correlation functions can easily be calculated when performing random-walk simulations for schematic models such as the random-barrier model and the random-energy model. Based on these models it is possible to simulate various NMR observables and the mean square displacement, thus revealing the information content of multi-dimensional NMR experiments on solid ion conductors.
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Affiliation(s)
- M Vogel
- Institut für Physikalische Chemie and SFB 458, Westfalische Wilhelms-Universität, Schlossplatz 7, D 48149 Münster, Germany
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Brace DD, Gottke SD, Cang H, Fayer MD. Orientational dynamics of the glass forming liquid, dibutylphthalate: Time domain experiments and comparison to mode coupling theory. J Chem Phys 2002. [DOI: 10.1063/1.1427711] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
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Aouadi A, Dreyfus C, Massot M, Pick RM, Berger T, Steffen W, Patkowski A, Alba-Simionesco C. Light scattering study of the liquid–glass transition of meta-toluidine. J Chem Phys 2000. [DOI: 10.1063/1.481642] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Miller DP, de Pablo JJ, Corti HR. Viscosity and Glass Transition Temperature of Aqueous Mixtures of Trehalose with Borax and Sodium Chloride. J Phys Chem B 1999. [DOI: 10.1021/jp984736i] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Danforth P. Miller
- Department of Chemical Engineering, University of Wisconsin-Madison, 1415 Engineering Drive, Madison, Wisconsin 53706, Instituto de Química Física de Materiales, Ambiente y Energía, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón II, 1428 Buenos Aires, Argentina, and Unidad de Actividad Química, Comisión Nacional de Energía Atómica, Av. Libertador 8250, 1429 Buenos Aires, Argentina
| | - Juan J. de Pablo
- Department of Chemical Engineering, University of Wisconsin-Madison, 1415 Engineering Drive, Madison, Wisconsin 53706, Instituto de Química Física de Materiales, Ambiente y Energía, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón II, 1428 Buenos Aires, Argentina, and Unidad de Actividad Química, Comisión Nacional de Energía Atómica, Av. Libertador 8250, 1429 Buenos Aires, Argentina
| | - Horacio R. Corti
- Department of Chemical Engineering, University of Wisconsin-Madison, 1415 Engineering Drive, Madison, Wisconsin 53706, Instituto de Química Física de Materiales, Ambiente y Energía, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón II, 1428 Buenos Aires, Argentina, and Unidad de Actividad Química, Comisión Nacional de Energía Atómica, Av. Libertador 8250, 1429 Buenos Aires, Argentina
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Comez L, Fioretto D, Palmieri L, Verdini L, Rolla PA, Gapinski J, Pakula T, Patkowski A, Steffen W, Fischer EW. Light-scattering study of a supercooled epoxy resin. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:3086-96. [PMID: 11970116 DOI: 10.1103/physreve.60.3086] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/1998] [Revised: 04/08/1999] [Indexed: 04/18/2023]
Abstract
The dynamics of the fragile glass-forming liquid diglycidyl ether of bisphenol-A was studied by depolarized Rayleigh-Brillouin light-scattering and photon correlation spectroscopy above the glass transition, in the temperature range from 261 to 473 K and in the frequency range from 1 Hz to 300 GHz. The structural (alpha-) relaxation process was revealed and no signature of the secondary relaxation previously evidenced by dielectric spectroscopy at about 0.1 GHz was observed. The characteristic time of the alpha process differs from that determined by dielectric spectroscopy of an amount, which increases with increasing temperature. The relaxation times were compared with viscosity data to test the predictions of the classic Stokes-Einstein-Debye model. The tau proportional, variant eta behavior was verified for dielectric data, while a fractional power law of viscosity tau proportional, variant eta(0.89) was obtained for light-scattering relaxation times, extending over more than seven decades in viscosity and time. This deviation of light scattering from viscosity data could be interpreted in terms of cooperative motion in the supercooled liquid with a characteristic length xi(a) proportional, variant(T-T0)(-v) where T(0)=229 K is the Vogel temperature and v is close to 2 / 3 which is consistent with the prediction of the fluctuation theory of glass transition.
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Affiliation(s)
- L Comez
- INFM and Department of Physics, University of Perugia, via Pascoli, 06123 Perugia, Italy
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Jeffrey KR, Wieczorek W, Raducha D, Stevens JR. Dynamics of the hydrogen and phosphate ions in proton conducting gel/D3PO4 electrolytes: A 2H and 31P nuclear magnetic resonance study. J Chem Phys 1999. [DOI: 10.1063/1.478650] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Fu CYS, Lackritz HS, Priddy, DB, McGrath JE. Effects of Chromophore Functionalization and Physical Aging during Poling on Chromophore Orientational Dynamics in Poly(arylene ether)s for Second-Order Nonlinear Optics. Macromolecules 1996. [DOI: 10.1021/ma9512869] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Maekawa H, Inagaki Y, Shimokawa S, Yokokawa T. Dynamics of a glass‐forming system: 11B NMR of B2O3. J Chem Phys 1995. [DOI: 10.1063/1.469604] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Rössler E, Eiermann P. Reorientational dynamics in supercooledm‐tricresyl phosphate: Its relation to main and secondary relaxation—31Pnuclear magnetic resonance study of relaxation, line shape, and stimulated echo. J Chem Phys 1994. [DOI: 10.1063/1.467188] [Citation(s) in RCA: 68] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Fluorescence lifetime measurements and hole-burning experiments on J-aggregates of a benzimidocarbocyanine dye. Chem Phys 1993. [DOI: 10.1016/0301-0104(93)85081-i] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Wuttke J, Kiebel M, Bartsch E, Fujara F, Petry W, Sillescu H. Relaxation and phonons in viscous and glassy orthoterphenyl by neutron scattering. ACTA ACUST UNITED AC 1993. [DOI: 10.1007/bf01344065] [Citation(s) in RCA: 103] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Nayak SK, Murthy SSN. Dielectric relaxation studies of glass formation in some esters of phthalic acid. J Chem Phys 1993. [DOI: 10.1063/1.465329] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Inagaki Y, Maekawa H, Yokokawa T, Shimokawa S. Nuclear-magnetic-resonance study of the dynamics of network-glass-forming systems: xNa2O. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:674-680. [PMID: 10005540 DOI: 10.1103/physrevb.47.674] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Floudas G, Fytas G, Brown W. Solvent mobility in poly(methyl methacrylate)/toluene solutions by depolarized and polarized light scattering. J Chem Phys 1992. [DOI: 10.1063/1.462068] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Pavlatou EA, Rizos AK, Papatheodorou GN, Fytas G. Dynamic light scattering study of ionic KNO3–Ca(NO3)2mixtures. J Chem Phys 1991. [DOI: 10.1063/1.460731] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Fytas G, Rizos A, Floudas G, Lodge TP. Solvent mobility in polystyrene/Aroclor solutions by depolarized Rayleigh scattering. J Chem Phys 1990. [DOI: 10.1063/1.459670] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Rössler E. Indications for a change of diffusion mechanism in supercooled liquids. PHYSICAL REVIEW LETTERS 1990; 65:1595-1598. [PMID: 10042310 DOI: 10.1103/physrevlett.65.1595] [Citation(s) in RCA: 184] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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