Final Report Summary - NFLIQUID (Dynamics and Structure in a Network-Forming Liquid)
The project objectives were focussed on studying the complex dynamic behaviour in soft matter through a network-forming liquid (NFL) that constitutes a paradigm of this behaviour. The main goal was to elucidate the fundamental link between microscopic mechanisms and the strikingly cooperative dynamical behaviour seen in a number of different disordered systems. Using an NFL model system, we also wanted to study the complex interplay between glassy arrest and gelation. The NFL system can be simulated by a hybrid coarse-grained model and studied in detail using a number of different analysis tools. The project objectives were to undertake structural and dynamical characterisation using a number of these different analysis tools and to examine different areas of the phase diagram, in particular the competition between glass and gel. We aimed to communicate and promote our research achievements through participation at international conferences and through the publication of papers in high-impact scientific journals.
In our research we approached the task of finding a link between microscopic mechanisms and complex dynamical behaviour from two different directions. Firstly, we have explored in detail the dynamics of the NFL model and the interplay between glassy arrest and gelation, using results obtained both from experiments and simulations. Secondly, through a collaboration that we have initiated with another group studying systems at the potential energy landscape (PEL) level, we have been working on general methods to analyse the relationship between microscopic mechanisms and observed anomalous behaviour.
In the first part of the project, we have used a simple continuous-time random walk (CTRW) model to investigate the interplay between glassy arrest and gelation in NFLs. Competition results in complex, multi-step decay of correlation functions, controlled by two different localization lengthscales. In our model, particles jump between transient cages which form temporary traps on two different lengthscales. The method is general and we have successfully applied the CTRW description to the original NFL model and also another system. These two systems are characterised by different competing interactions: (1) a hard-core repulsion competes with a very short-range attraction [1], and (2) a soft repulsion competes with an entropic attraction [2]. Both systems can be realised experimentally with colloid-polymer mixtures [3,4]. The former using a non-adsorbing polymer which introduces a short-range interparticle attraction via the depletion effect. In this case, the gel cages formed by polymer ‘bonds’ between particles are smaller than the glass cages formed topologically by nearest neighbours. Conversely, in the latter system, formed by telechelic polymers in an oil-in-water microemulsion, the topological glass cages are smaller than the polymer-bonded cages.
In two highly contrasting systems, we can use a random walk description with trapping in two different cage sizes to faithfully recreate the state diagram, the dynamics in each region and identify boundaries delineating the dominance of different arrest mechanisms.
The second part of the project focussed on characterising structure by studying the Potential Energy Landscape (PEL). The PEL provides a description of the complicated many-particle effects in disordered systems, with information about individual particle configurations and the relationships between different configurations. The properties of a glassy system at low temperature are dominated by long residences near local minima (inherent structures) but at higher temperatures, many dynamic properties are still related to properties of the inherent structures. In glassy systems, the landscape contains many disordered minima with similar energies and has a hierarchical, frustrated appearance with relatively high barriers separating a large number of potential energy funnels. When following an individual trajectory, revisits to individual minima are common. For this reason it is useful to be able to coarse-grain the landscape, for example by defining metabasins. Metabasins are groups of minima within which forward-backward correlations occur and can be identified via the total potential energy of the system [5]. Alternatively, on the microscopic level, important transitions, such as cage-breaks, where an atom leaves its cage of nearest-neighbours can be identified [6].
We have reconciled the two approaches, providing a microscopic description for metabasins within the PEL in the form of productive cage-breaks. Productive (or successful) cage-breaks are cage-breaks that are not later reversed in the course of the trajectory and can be identified for each individual atom. The link between metabasins and cage-breaks allows us to extend the metabasin description to larger systems and to identify lengthscales of cooperative motion. We can also examine in detail the effects of system size on the dynamics.
In a coarse-grained, metabasin description of the PEL, correlation is removed, and the dynamics can be described by a random walk. A temperature-independent elementary lengthscale is uncovered, the hopping distance between metabasins, which corresponds to the distance moved by a cage-breaking atom and its neighbours. The temperature-dependent quantity is the waiting time within each metabasin, the time during which atoms are not able to successfully escape their nearest-neighbour cages. The waiting time determines both the diffusion constant and relaxation timescales. In this way, we have a complete description of the overall dynamics, starting from the atomic level.
The random walk description of competing glass and gel phases and the connection between microscopic mechanisms and dynamic properties elucidated using the Potential Energy Landscape both represent significant progress in understanding the complex dynamic behaviour in soft matter. This work has been disseminated at a number of international conferences through talks and poster presentations. During the project, a number of collaborations were set up and consolidated, and are still ongoing after the end of the project. We have also identified a number of interesting avenues for further research.
[1] E. Zaccarelli and W. C. K. Poon, PNAS 106, 15203 (2009).
[2] P. Chaudhuri, L. Berthier, P. I. Hurtado and W. Kob, Phys. Rev. E 81, 040502(R) (2010).
[3] K. N. Pham, A. M. Puertas, J. Bergenholtz, S. U. Egelhaaf, A. Moussaid, P. N. Pusey, A. B. Schofield, M. E. Cates, M. Fuchs, and W. C. K. Poon, Science 296, 104 (2002).
[4] E. Michel, M. Filali, R. Aznar, G. Porte, and J. Appell, Langmuir 16, 8702 (2000).
[5] B. Doliwa and A. Heuer, Phys. Rev. E 67, 030501 (2003)
[6] V.K. de Souza and D. J. Wales, J. Chem. Phys. 129, 164507 (2008)
In our research we approached the task of finding a link between microscopic mechanisms and complex dynamical behaviour from two different directions. Firstly, we have explored in detail the dynamics of the NFL model and the interplay between glassy arrest and gelation, using results obtained both from experiments and simulations. Secondly, through a collaboration that we have initiated with another group studying systems at the potential energy landscape (PEL) level, we have been working on general methods to analyse the relationship between microscopic mechanisms and observed anomalous behaviour.
In the first part of the project, we have used a simple continuous-time random walk (CTRW) model to investigate the interplay between glassy arrest and gelation in NFLs. Competition results in complex, multi-step decay of correlation functions, controlled by two different localization lengthscales. In our model, particles jump between transient cages which form temporary traps on two different lengthscales. The method is general and we have successfully applied the CTRW description to the original NFL model and also another system. These two systems are characterised by different competing interactions: (1) a hard-core repulsion competes with a very short-range attraction [1], and (2) a soft repulsion competes with an entropic attraction [2]. Both systems can be realised experimentally with colloid-polymer mixtures [3,4]. The former using a non-adsorbing polymer which introduces a short-range interparticle attraction via the depletion effect. In this case, the gel cages formed by polymer ‘bonds’ between particles are smaller than the glass cages formed topologically by nearest neighbours. Conversely, in the latter system, formed by telechelic polymers in an oil-in-water microemulsion, the topological glass cages are smaller than the polymer-bonded cages.
In two highly contrasting systems, we can use a random walk description with trapping in two different cage sizes to faithfully recreate the state diagram, the dynamics in each region and identify boundaries delineating the dominance of different arrest mechanisms.
The second part of the project focussed on characterising structure by studying the Potential Energy Landscape (PEL). The PEL provides a description of the complicated many-particle effects in disordered systems, with information about individual particle configurations and the relationships between different configurations. The properties of a glassy system at low temperature are dominated by long residences near local minima (inherent structures) but at higher temperatures, many dynamic properties are still related to properties of the inherent structures. In glassy systems, the landscape contains many disordered minima with similar energies and has a hierarchical, frustrated appearance with relatively high barriers separating a large number of potential energy funnels. When following an individual trajectory, revisits to individual minima are common. For this reason it is useful to be able to coarse-grain the landscape, for example by defining metabasins. Metabasins are groups of minima within which forward-backward correlations occur and can be identified via the total potential energy of the system [5]. Alternatively, on the microscopic level, important transitions, such as cage-breaks, where an atom leaves its cage of nearest-neighbours can be identified [6].
We have reconciled the two approaches, providing a microscopic description for metabasins within the PEL in the form of productive cage-breaks. Productive (or successful) cage-breaks are cage-breaks that are not later reversed in the course of the trajectory and can be identified for each individual atom. The link between metabasins and cage-breaks allows us to extend the metabasin description to larger systems and to identify lengthscales of cooperative motion. We can also examine in detail the effects of system size on the dynamics.
In a coarse-grained, metabasin description of the PEL, correlation is removed, and the dynamics can be described by a random walk. A temperature-independent elementary lengthscale is uncovered, the hopping distance between metabasins, which corresponds to the distance moved by a cage-breaking atom and its neighbours. The temperature-dependent quantity is the waiting time within each metabasin, the time during which atoms are not able to successfully escape their nearest-neighbour cages. The waiting time determines both the diffusion constant and relaxation timescales. In this way, we have a complete description of the overall dynamics, starting from the atomic level.
The random walk description of competing glass and gel phases and the connection between microscopic mechanisms and dynamic properties elucidated using the Potential Energy Landscape both represent significant progress in understanding the complex dynamic behaviour in soft matter. This work has been disseminated at a number of international conferences through talks and poster presentations. During the project, a number of collaborations were set up and consolidated, and are still ongoing after the end of the project. We have also identified a number of interesting avenues for further research.
[1] E. Zaccarelli and W. C. K. Poon, PNAS 106, 15203 (2009).
[2] P. Chaudhuri, L. Berthier, P. I. Hurtado and W. Kob, Phys. Rev. E 81, 040502(R) (2010).
[3] K. N. Pham, A. M. Puertas, J. Bergenholtz, S. U. Egelhaaf, A. Moussaid, P. N. Pusey, A. B. Schofield, M. E. Cates, M. Fuchs, and W. C. K. Poon, Science 296, 104 (2002).
[4] E. Michel, M. Filali, R. Aznar, G. Porte, and J. Appell, Langmuir 16, 8702 (2000).
[5] B. Doliwa and A. Heuer, Phys. Rev. E 67, 030501 (2003)
[6] V.K. de Souza and D. J. Wales, J. Chem. Phys. 129, 164507 (2008)