1 / 49

Microstructure of a soft glass

Microstructure of a soft glass. Béla Joós. Matthew L. Wallace Michael Plischke (SFU). Glass is a phase of matter. Glasses are ubiquitous in nature A glass is a phase such as the solid or gaseous, or liquid phases as opposed to a type of material

manjit
Download Presentation

Microstructure of a soft glass

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Microstructure of a soft glass Béla Joós Matthew L. Wallace Michael Plischke (SFU)

  2. Glass is a phase of matter • Glasses are ubiquitous in nature • A glass is a phase such as the solid or gaseous, or liquid phases as opposed to a type of material • It is a disordered phase, amorphous, like a liquid frozen in time Queen's CSE Colloquium, October 2007

  3. Phase Transitions • In nature there are various kinds of transitions: First order: ex: solid -> liquid, jump in physical observables such as volume, or energy Continuous: ex: Gelling transition as an example of percolation transition (the gel is rigid, i.e. resists shear) Queen's CSE Colloquium, October 2007

  4. Mechanical vs entropic rigidity • Triangular lattice: geometric percolation at p=pc (0.349), rigidity percolation p= pr > pc (pr = 0.66) . • Multiple connectivity required for mechanical rigidity Queen's CSE Colloquium, October 2007

  5. The Glass transition • The glass-maker’s viewpoint: at TG viscosity= 1012 Pa s • A continuous transition characterized by a divergence in viscosity • As to what really happens microscopically, there is really no consensus. There are a number of competing pictures Conference: Mechanical Behaviour of Glassy Materials (UBC, July 2007) Queen's CSE Colloquium, October 2007

  6. The three viewpoints • A transition to an ideal zero entropy state • A dynamical transition resulting from the jamming of particles together • Not a transition but a cross-over where there is a rapid change in viscosity (critical slowing down) Queen's CSE Colloquium, October 2007

  7. Some facts to illustrate the issues • Heat capacity: heat transferred into object as its temperature is raised • In experiments: T raised by increments ΔT during time Δt • Drop in Cp, critical slowing down The three viewpoints have common features (slowing down), but very different views of the glass. How to distinguish them? Queen's CSE Colloquium, October 2007

  8. The challenges • As T decreases, slowing down in the system, increasing run times to simulate anything (also an issue experimentally) • Configuration space very complex often represented as an energy landscape • Glasses age: they continuously evolve Glasses evolve towards lower energy states: consequently longer relaxation times Bouchaud (2000) Have to find clever ways to characterize the glass Queen's CSE Colloquium, October 2007

  9. Our perspective • Model: a short chain polymer melt (10 monomers) (e.g. plastic) • The glass transition and the onset of rigidity • Shearing the glass: the elastic and plastic regimes • Microstructure of the deformed glass: displacements, stresses, Queen's CSE Colloquium, October 2007

  10. Molecular Dynamics of a Polymer Glass L-J • Polymer “melt” of ~1000 particles with chains of length 10. • LJ interactions between all particles • + FENE potential between nearest neighbours in a chain (Kremer and Grest, 1990) • Competing length scales prevent crystallization L-J L-J L-J FENE Queen's CSE Colloquium, October 2007

  11. Approaching the Glass Transition • Instead of approaching the final states along isobars by lowering T (very high cooling rates) • We propose an isothermal compression method (blue curves) for better exploration of phase space • System gets “stuck” in wells of lower potential energy • Below TG, the system is closer to equilibrium (less aging) Queen's CSE Colloquium, October 2007

  12. Numerical algorithms external “piston” force regulates pressure • Equilibrate in the NVT ensemble with Brownian dynamics as a thermostat • Apply a steady compression rate of 0.015 • Final volume realized in the NPT ensemble with a damped-force algorithm Queen's CSE Colloquium, October 2007

  13. The glass transition temperature TG • At TG, there is kinetic arrest, the liquid can no longer change configurations • (expt. time scale issue). TG determined by a change in the volume density. • We obtain TG = 0.465 + 0.005 • But we cannot assume • TG to be the rigidity onset: the viscosity does not diverge at TG. Φ: Packing Fraction Queen's CSE Colloquium, October 2007

  14. Outline • Our way of preparing the polymer melt near the glass transition: pressure quench at constant temperature to improve statistics • Onset of rigidity in the glass: a new angle on the glass transition • Deforming the glass below the rigidity transition: the elastic and plastic regime • Macroscopic signatures • Changes in the microstructure • What is learned, what needs to be learned. Queen's CSE Colloquium, October 2007

  15. Rigidity of Mechanical Structures Queen's CSE Colloquium, October 2007

  16. Onset of mechanical rigidity in disordered systems Triangular lattice: geometric percolation at p=pc (0.349), rigidity percolation p= pr > pc (pr = 0.66) . Multiple connectivity required for mechanical rigidity Queen's CSE Colloquium, October 2007

  17. Entropic rigidity At T>0 K, rigidity sets in at the onset of geometric percolation, through the creation of an entropic spring Plischke and Joos, PRL 1998 Moukarzel and Duxbury, PRE 1999 Queen's CSE Colloquium, October 2007

  18. The entropic spring force = It is a Gaussian spring (zero equilibrium length) whose strength is proportional to the temperature T Queen's CSE Colloquium, October 2007

  19. The onset of rigidity in melts With permanent crosslinks, at a fixed temperature: Well defined point of onset of the entropic rigidity : It is geometric percolation pc where there is a diverging length scale (such as in rubber) Queen's CSE Colloquium, October 2007

  20. Rigidity in melts without crosslinks • Not clear where the onset is • Is it at TG that we have percolating regions of “jammed” or immobile particles that can carry the strain? Wallace, Joos, Plischke, PRE 2004 Queen's CSE Colloquium, October 2007

  21. Calculating the shear viscosity • Using the intrinsic fluctuations in the system: The shear viscosity equals: Queen's CSE Colloquium, October 2007

  22. Viscosity diverges at onset of rigidity • Empirical models of  : • VFT (Vogel-Fulcher-Tamann)(T0 associated with an “ideal” glass state) T0 = 0.41 + 0.02 Tc=0.422 + 0.006 • dynamical scaling (Colby, 2000) •  measured to T=0.49 > TG=0.465 extrapolation required Queen's CSE Colloquium, October 2007

  23. Calculating the shear modulus Two ways: • Applying a finite affine deformation • Using the intrinsic fluctuations in the system driven by temperature to obtain its shear strength, as the limit to ∞ of G(t) called Geq where Queen's CSE Colloquium, October 2007

  24. Geq or extrapolating G(t) to infinity Power law fit of tail: G(t) = Geq + A t- G'eq = G(t=150) Geq = G(t=) Queen's CSE Colloquium, October 2007

  25. The shear modulus : Geq vs s s (=0.1) < < Geq These µ’s are the response of the system to the finite deformation and not the shear modulus of the deformed relaxed system Queen's CSE Colloquium, October 2007

  26. The shear modulus G'eq , Geq , and μs G'eq : short time (t=150) Geq : extrapolated to infinity* μs : applied shear Rigidity onset at T1 =0.44 < TG = 0.465 * using distribution of energy barriers observed during first t=150 Queen's CSE Colloquium, October 2007

  27. Meaning of T1: the onset of rigidity T0 (0.41) and Tc (0.422) gave extrapolated values for the onset of rigidity. Measurement of  stopped at 0.49 (TG = 0.465) T1 = 0.44 is the onset of Geq and s, and the cusp in CP, the heat capacity (is it the appearance of floppy modes with rising T ?) T1 Queen's CSE Colloquium, October 2007

  28. Issues on rigidity in the polymer glass • TG is the temperature at which the melt stops flowing. It is not a point of divergence of the viscosity • (For glass makers: • s= 1012 Pa ·s or  = s / G = 400 s for SiO2 • In simulations: • s= 107 or  = s / G = 105 • (simulations  103, unit of time:  2 ps) • (issues of time scale and aging) • Onset of rigidity: divergence of viscosity, onset of shear modulus, cusp in heat capacity (disappearance of floppy modes) • Comparison with gelation due to permanent crosslinks: no clearly defined length scale, but there could be a dynamical one Queen's CSE Colloquium, October 2007

  29. Polymer glass under deformation • Glasses are heterogeneous • What happens to the glass when deformed: a lot of questions from aging, mechanical properties, and thermal properties • Which properties are we interested in this study? We will focus on the microstructure as a first step in understanding the effect of deformation on the properties of the glass. Main message: deformation reduces heterogeneity Queen's CSE Colloquium, October 2007

  30. Properties of the deformed “rigid” glassy system • Glassy system just below a temperature T1 (“rigidity threshold”): very little cooperative movement (except at long timescales) • Previous study: examining mechanical properties of a polymer glass (e.g. shear modulus) across TG . T1 TMC Samples used to investigate effects of shear (present work) TG Wallace and Joos, PRL 2006 Queen's CSE Colloquium, October 2007

  31. Plastic and elastic deformations • Glassy systems have a clear yield strain • What specific local dynamical and structural changes occur? Plastic Pressure variations in an NVT ensemble Queen's CSE Colloquium, October 2007

  32. Decay of the shear stress after deformation Shows both the initial stress and the subsequent decay in the system Queen's CSE Colloquium, October 2007

  33. Structural changes (1) • Changes in the energy of the inherent structures (eIS) are relevant to subtle structural changes • Initial decrease / increase in polymer bond length for elastic / plastic deformations • Plastic deformations create a new “well” in the PEL – different from those explored by slow relaxations in a normal aging process • In “relaxed”, deformed system, changes in the energy landscape are entirely due to L-J interactions Immediately after deformation After tw=103 time units Queen's CSE Colloquium, October 2007

  34. Local bond-orientational order parameter Q6 • Q6 measures subtle angular correlations (towards an FCC structure) between particles at long time tw after deformations • We can resolve a clear increase in Q6 for elastic deformations, but limited impact on system dynamics Queen's CSE Colloquium, October 2007

  35. Diffusion Effect of "caging" observed near the transition (T G = 0.465). At TG, still possibility to rearrange under deformation. Queen's CSE Colloquium, October 2007

  36. Glasses are heterogeneous Widmer-Cooper, Harrowel, Fynewever, PRL 2004 Propensity: Mean squared deviation of the displacements of a particle in different iso-configurations The propensity reveals more acurately the fast and slow regions than a single run Queen's CSE Colloquium, October 2007

  37. Mobility and “sub-diffusion” • Initially, plastic shear forces the creation of “mobile” regions of mobile particles • Once the system is allowed to relax, cooperative re-arrangements remain possible • Rearrangements from plastic deformations allow cage escape in more regions • In the case of elastic deformations, new mobile particles can be created, but only temporarily Queen's CSE Colloquium, October 2007

  38. Heterogeneous dynamics • The non-Gaussian parameter α2(t) measures deviations from Gaussian behavior • Deviations from a Gaussian distribution become less apparent for plastic deformations Queen's CSE Colloquium, October 2007

  39. Cooperative movement • The dynamical heterogeneity is spatially correlated • The peak of α2(t) coincides with the beginning of sub-diffusive behavior – can indicate a maximum in “mobile cluster” size Snapshots of dynamically heterogeneous systems. Left: the clusters are localized. Right: as cluster size increases, significant large-scale relaxation is possible. Queen's CSE Colloquium, October 2007

  40. Effect of shear on the microstructure • Based on changes in L-J potentials and the formation of larger mobile clusters, plastic deformations must induce substantial local reconfigurations Queen's CSE Colloquium, October 2007

  41. Fraction of nearest neighbours which are the fastest 5% the slowest 5% ε = 0, reference system, ε = 0.2, smaller domains of fast and slow particles Queen's CSE Colloquium, October 2007

  42. Fraction of n-n’s on the same chain which are the fastest which are the slowest 5% This means that the islands of fast particles are getting smaller Queen's CSE Colloquium, October 2007

  43. Average distance between fast particles slow particles fast particles • Evidence of reduction in size of mobile regions and increase in size of jammed regions with increasing deformation • Increasing jamming in elastic region, as seen in slowest particle Queen's CSE Colloquium, October 2007

  44. Distances between particles There is homogenization with applied deformation, most evident with the fast particles Queen's CSE Colloquium, October 2007

  45. Glasses age! Kob, 2000 Glasses evolve towards lower energy states: consequently longer relaxation times Incoherent intermediate scattering function: Bouchaud, 2000 Queen's CSE Colloquium, October 2007

  46. On route to irreversible changes Statistics of big jumps show accelerated equilibrium for large ε, but also that fast regions become smaller. More stable glass, less aging? Queen's CSE Colloquium, October 2007

  47. Irreversible microstructural changes Polymers shrink after deformation Reduction in grain size or correlations in inhomogeneities Queen's CSE Colloquium, October 2007

  48. Conclusion (1) • Real glasses versus glasses on the computer: time scales and a better grasp on the computer of the microstructure • At the latest conference at UBC on glasses, there was a growing consensus that this is really an issue of critical slowing down, in other words not a real transition Queen's CSE Colloquium, October 2007

  49. Conclusion (2) • We have presented attempts to characterize the effect of deformations on the structure of the glass that did not require huge computing times • The net effect of deformations appears to be connected to general “jamming” phenomena, and what the deformations can do to un-jam the structure • What they reveal is a more homogeneous glass with a smaller “grain” structure • More studies are required (highly computer intensive) • Currently working on applying oscillating shear to the glass, and monitoring the aging of the glasses prepared by shear deformation Queen's CSE Colloquium, October 2007

More Related