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SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 62 , Issue 10 : 107007(2019) https://doi.org/10.1007/s11433-018-9403-3

Interplay between the glass and the gel transition

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  • ReceivedDec 21, 2018
  • AcceptedMar 28, 2019
  • PublishedJun 5, 2019
PACS numbers

Abstract

By changing the control parameters, many physical systems reach a slow dynamics regime followed by an arrested or a quasi-arrested state. Examples, among others, are gels and glasses. In this paper, we discuss some experimental and theoretical results in polymer and colloidal systems, where gel and glass transitions interfere, and use models from Mode Coupling Theory (MCT) to illustrate the rich phenomenology observed. The continuous and the discontinuous transition lines, found in the MCT models, are considered suitable to describe respectively the gel and the glass transitions, so we suggest that the interplay between gel and glass may be interpreted in terms of the $F_{13}$ MCT model, clarifying also the origin of logarithmic decays often observed in such systems. In particular, the theoretical predictions of the MCT in the $F_{13}$ model are compared with Molecular Dynamics simulations in model systems for chemical gels and charged colloids.


Acknowledgment

This work was supported by the CNR-NTU joint laboratory of amorphous materials for energy harvesting applications. The authors would like to thank Arenzon, De Arcangelis, Del Gado, Chen, Khalil, Mallamace, Pica Ciamarra, and Sellitto, for valuable collaborations on various papers on which a significant part of this work is based.


References

[1] P. J. Flory, Principles of Polymer Chemistry (Cornell University Press, Ithaca, NY, 1954). Google Scholar

[2] P. G. de Gennes P. G., Scaling Concepts in Polymer Physics, (Cornell University Press, Ithaca, NY, 1993). Google Scholar

[3] Gotze W., Sjogren L.. Rep. Prog. Phys., 1992, 55: 241-376 CrossRef ADS Google Scholar

[4] G?tze W.. J. Phys.-Condens. Matter, 1999, 11: A1-A45 CrossRef Google Scholar

[5] W. Götze, Complex dynamics of glass-forming liquids (Oxford University Press, Oxford, 2009). Google Scholar

[6] Mallamace F., Corsaro C., Stanley H. E., Mallamace D., Chen S. H.. J. Chem. Phys., 2013, 139: 214502-214502 CrossRef PubMed ADS Google Scholar

[7] Mallamace F., Corsaro C., Vasi C., Vasi S., Mallamace D., Chen S. H.. J. Non-Crystalline Solids, 2015, 407: 355-360 CrossRef ADS Google Scholar

[8] Mallamace F., Chen S. H., Coniglio A., de Arcangelis L., Del Gado E., Fierro A.. Phys. Rev. E, 2006, 73: 020402 CrossRef PubMed ADS Google Scholar

[9] Fierro A., Abete T., Coniglio A.. J. Chem. Phys., 2009, 131: 194906-194906 CrossRef PubMed ADS arXiv Google Scholar

[10] Coniglio A., Arenzon J. J., Fierro A., Sellitto M.. Eur. Phys. J. Spec. Top., 2014, 223: 2297-2306 CrossRef ADS Google Scholar

[11] Arenzon J. J., Coniglio A., Fierro A., Sellitto M.. Phys. Rev. E, 2014, 90: 020301 CrossRef PubMed ADS arXiv Google Scholar

[12] Fredrickson G. H., Andersen H. C.. Phys. Rev. Lett., 1984, 53: 1244-1247 CrossRef ADS Google Scholar

[13] Sellitto M., Biroli G., Toninelli C.. Europhys. Lett., 2005, 69: 496-502 CrossRef ADS Google Scholar

[14] de Candia A., Fierro A., Coniglio A.. Sci Rep, 2016, 6: 26481 CrossRef PubMed ADS arXiv Google Scholar

[15] G\"{o}tze W., Sperl M.. Phys. Rev. E, 2002, 66: 011405 CrossRef PubMed ADS Google Scholar

[16] G?tze W., Haussmann R.. Z. Physik B - Condensed Matter, 1988, 72: 403-412 CrossRef ADS Google Scholar

[17] Khalil N., de Candia A., Fierro A., Ciamarra M. P., Coniglio A.. Soft Matter, 2014, 10: 4800 CrossRef PubMed ADS arXiv Google Scholar

[18] D. Stauffer, and A. Aharony, Introduction to percolation theory, (Taylor & Francis, London, 1992). Google Scholar

[19] Abete T., de Candia A., Gado E. D., Fierro A., Coniglio A.. Phys. Rev. Lett., 2007, 98: 088301 CrossRef PubMed ADS Google Scholar

[20] Candia A., Fierro A., Pastore R., Pica Ciamarra M., Coniglio A.. Eur. Phys. J. Spec. Top., 2017, 226: 323-329 CrossRef ADS arXiv Google Scholar

[21] Chaudhuri P., Berthier L., Hurtado P. I., Kob W.. Phys. Rev. E, 2010, 81: 040502 CrossRef PubMed ADS arXiv Google Scholar

[22] Chaudhuri P., Hurtado P. I., Berthier L., Kob W.. J. Chem. Phys., 2015, 142: 174503 CrossRef PubMed ADS arXiv Google Scholar

[23]

[24] Caiazzo A., Coniglio A., Nicodemi M.. Phys. Rev. Lett., 2004, 93: 215701 CrossRef PubMed ADS Google Scholar

[25] Mallamace F., Gambadauro P., Micali N., Tartaglia P., Liao C., Chen S. H.. Phys. Rev. Lett., 2000, 84: 5431-5434 CrossRef PubMed ADS Google Scholar

[26] Chen S. H.. Science, 2003, 300: 619-622 CrossRef PubMed ADS Google Scholar

[27] de Candia A., Del Gado E., Fierro A., Sator N., Coniglio A.. Physica A-Statistical Mech. its Appl., 2005, 358: 239-248 CrossRef ADS Google Scholar

[28] de Candia A., Del Gado E., Fierro A., Sator N., Tarzia M., Coniglio A.. Phys. Rev. E, 2006, 74: 010403 CrossRef PubMed ADS Google Scholar

[29] Fierro A., Del Gado E., de Candia A., Coniglio A.. J. Stat. Mech., 2008, 2008(04): L04002 CrossRef ADS arXiv Google Scholar

[30] de Candia A., Del Gado E., Fierro A., Coniglio A., Pastore R., de Candia A., Fierro A., Pica Ciamarra M., Coniglio A.. J. Stat. Mech., 2009, 2009(02): P02052 CrossRef ADS Google Scholar

[31] Sciortino F., Tartaglia P., Zaccarelli E.. J. Phys. Chem. B, 2005, 109: 21942-21953 CrossRef PubMed Google Scholar

[32] J. N. Israelachvili, Intermolecular and surface forces (Academic Press, London, 1985). Google Scholar

[33] Crocker J. C., Grier D. G.. Phys. Rev. Lett., 1994, 73: 352-355 CrossRef PubMed ADS Google Scholar

[34] Campbell A. I., Anderson V. J., van Duijneveldt J. S., Bartlett P.. Phys. Rev. Lett., 2005, 94: 208301 CrossRef PubMed ADS Google Scholar

  • Figure 1

    (Color online) Phase diagram of the $F_{12}$ model. The horizontal line is an arrested state line. Crossing such line the order parameter, characterised by the plateau of the correlator in the long time limit, grows continuously from zero. The other line is an arrested line where the order parameter jumps discontinuously. The two lines meet at a higher order critical point.

  • Figure 2

    (Color online) Phase diagram of the $F_{13}$ model. The horizontal line corresponds to a continuous transition, while the other line corresponds to a discontinuous transition, where the order parameter jumps, like in Figure 1. The difference with the phase diagram of Figure 1is that the second line penetrates in the arrested state ending at the $A_3$ singular point, where the jump of the order parameter goes to zero.

  • Figure 3

    (Color online) Structural arrest diagram obtained in a model for chemical gel, by varying the volume fraction, $\phi$, and the bonding probability, $p$. At low values of $p$, by increasing $\phi$, the transition from sol to glass is crossed. At large values of $p$, by increasing $\phi$, the sol-gel transition, first, and then the gel-glass transition are crossed. So open symbols are obtained after introducing bonds in an out-of-equilibrium monomer suspension. Solid lines are guides to the eye. Reproduced from ref. [17]with permission from the Royal Society of Chemistry.

  • Figure 4

    (Color online) The structural relaxation time, $\tau(k)$, at $p=0.4$ as function of the volume fraction $\phi$, for $k=1$ and $k=6.28$. The continuous lines are power law fitting functions.

  • Figure 5

    (Color online) The self ISF, $F_{\rm~s}(k,t)$, for $p=0.5$, $\phi=0.52$, and wave-vector $k=1$, $2$, $3$, $4$, $5$, $6.28$ (from top to bottom). Continuous lines are logarithmic functions. Reproduced from ref. [17]with permission from the Royal Society of Chemistry.

  • Figure 6

    (Color online) The self ISF, $F_{\rm~s}(k,t)$, at different values of $p$ as indicated, moving along the glass line, for $k~=~k_{\text{max}}$ (a) and for $k~=~3$ (b). The plateau associated with the gel and the glass are indicated by an arrow. Reproduced from ref. [17]with permission from the Royal Society of Chemistry.

  • Figure 7

    (Color online) The structural relaxation time, $\tau(k)$ (circles), compared with the bond relaxation time, $\tau_b$ (stars), for $T=0.15$ and $k=0.36,~1.88,~7.52$ (from top to bottom). The curves are power law fits, $\tau_0*(0.14-\phi)^{-3.3}$, with different $\tau_0$ (from ref. [30]).

  • Figure 8

    (Color online) The self-ISF, $F_{\rm~s}(k,t)$, for $T~=~0.15$, $\phi=0.12$ and $k=1.53,~1.88,~2.89,~3.76,~6.27$ (from top to bottom). Continuous lines are logarithmic functions, $A-B~\log(t)$.

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