The Transition to Diffusion Limited Kinetics Investigated by Neutron Scattering

Transcription

1 The Transition to Diffusion Limited Kinetics Investigated by Neutron Scattering Richard A. Livingston Material Science & Engineering Dept. University of Maryland

2 Collaborators Dan Neumann, NIST Center for Neutron Research Andrew Allen, NIST, Materials Science & Engineering Laboratory Walairat Bumrongjaroen, Vitreous State Laboratory, Catholic U. of America Norbert Nemes, Instituto de Ciencia de Materials de Madrid -CISC, Madrid, Spain Jeff Thomas, Civil & Environmental Engineering Department, Northwestern U. Stephen FitzGerald, Physics Dept. Bowling Green College

3 Outline Introduction Quasi-elastic Neutron Scattering Hydration kinetics models Role of the A parameter Effects of w/c ratio and temperature Conclusions

4 Typical C 3 S Hydration Kinetics

5 MASS PERCENT INDUCTION PERIOD REACTION PROGRESS (Alpha) HYDRATION PRODUCTS FREEWATER INDEX FREE WATER W/C = PORTLAND CEMENT LOG TIME (days) 1.0 after GLASSER et al. (1987)

6 Free Water Water of Hydration Hydroxyl Group Oxygen Hydrogen

7 COUNTS DATA GAUSSIAN LORENTZIAN ENERGY SHIFT (mev)

8 Gaussian Lorentzian 1 ω Sinc Q,ω A exp B σ 2π σ 2 2 π ω 2 2 Freewater Index: FWI B A B Capillary Water Total Water Boundwater Index: BWI = 1 - FWI Gel + Chemically Bound Total Water

9 BWI Time (hrs)

10 Nucleation and Growth model ( t) ( t ) A 1 exp k t t o o m β(t) = boundwater fraction or BWI t o = induction time A = asymptotic volume fraction k = rate constant m = dimensionality

11 Nucleation and Growth Models KAMJ (Kolmogorov Avrami Mehl Johnson) ( t) ( t ) 1 exp k t t o o m Double Logarithmic fit ln ln 1 ( t ) ( t) mln k mln t t o o 4-Parameter Model ( t) ( t ) A 1 exp k t t o o m

12 BWI Time (hrs)

13 Fujii-Kondo Diffusion-limited Model: Unreacted C 3 S C-S-H gel 1/3 1/3 2 D* d t t R d 1/ 2 R = Mean initial particle radius D* = Effective diffusion constant t d = Time at start of diffusion-limited period β d = BWI

14 Fujii-Kondo Diffusion-limited Model: Unreacted C 3 S C-S-H gel 1/3 1/3 2 D* d t t R d 1/ 2 dr D * dt r

15 BWI Modeling C 3 S Hydration Kinetics 0.4 Diffusion-limited 0.3 t D Nucleation and Growth A Time (hrs)

16 BWI QENS Measurement of C 3 S Hydration Kinetics 0.4 Topochemical kinetics 0.3 Inner Product Through solution, diffusionlimited aggregation Outer Product Time (hrs)

17 Diffusion-limited Aggregation D v 2.7 Livingston, 2000

18 C 3 S vs w/c ratio Unpublished data

19 C 3 S vs w/c Master Curve

20 Results The parameters k, t i, m and t D are independent of w/c ratio The A parameter decreases with increasing w/c There is significant amount of free water at t D

21 Scaling Factor vs w/c ratio Bleeding? D40/ D D40/ D = w/c R 2 1 Self-desiccation?

22 / / D40 D w c D40 A 1 exp k t t w/ c D D o m A D w / c m 1 exp k t t 0.1 w / c D o

23 Eliminating the A parameter: ( t) ( to) 1 exp k t t 0.1 w/ c o m Master Curve Rescaling the BWI data: 0.1 w / c ( t) ( t ) o 1 exp k t t o m KAMJ Model

24 0.1 w / c ( t) ( to) () t w b c β t Water in hydration products Total water w h w ( t) w 1 wh w 1 wh 1 boundwater b c b w c b c b cement

25 1 w b c h 1 exp k t t o m w h c b t Therefore the new asymptote, b, is the total mass of boundwater that can fill the available pore space, normalized by the cement mass.

26 Finally: where: b h V CSH OP h = mass fraction of water in CSH gel ρ CSH = density of CSH gel V OP = Asymptotic value of outer product volume SANS Contrast Measurement: h = 0.174(4) ρ CSH = 2.605(24) Mg m 3 Allen, Thomas & Jennings, 2007 V OP = cm 3 /g

27 Reflectivity Master curve w/c t D hrs T. Voigt et al. Cem. and Conc. Res. 35 (2005)

28 Model of Hydrated Cement Grains T. Voigt et al. Cem. and Conc. Res. 35 (2005)

29 C 3 S Hydration, w/c =0.4

30 C 3 S Hydration, w/c =0.4, Time-shifted

31 Nucleation Regime: Effect of Particle Size Distribution on A Hydration Reaction Parameter, A O BW I, 20 C CB, 20 C BW I, 30 C CB, 30 C BW I, 40 C CB, 40 C Mean C S Particle Diameter ( m) 3 Fig. 4 Allen et al. JMR 2004

32 Results The dimensionality m is independent of temperature The rate constant k increases with temperature The parameters A, t i and t D decrease with increasing temperature There is significant amount of free water at t D Implies a decrease of C-S-H water content and or density with temperature

33 Diffusion-limited Aggregation D v 2.7 Livingston, 2000

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35 d d (cm -1 sr -1 ) SANS Data Plot ~Q -3.4 surface-fractal BP6 data BP6 model fit SANS data with fit background scattering removed ~Q -2.6 volume-fractal Scattering from gel particle 0.1 Q -4 Porod scattering Q (A) -1

36 Topochemical or Shrinking Core Model Outer Product Unreacted fly ash core Volume Fractal Gel Layer Surface Fractal Inner Product

37 Fractal Ratio S VF = Area of volume fractal-type interface per unit volume, m 2 /cm 3 S SF = Area of surface fractal-type interface per unit volume, m 2 /cm 3 S VF / S SF = Fractal ratio, non-dimensional

38 Fractal Ratio vs Time Bumrongjaroen et al., 2009

39 Fractal Ratio vs Volume Fractal

40 Map of C-S-H gel density nonoindenter data. LD= Low density; HD= High Density; UHD =Ultra High Density (Ulm and Vandamme, 2009)

41 Conclusions Transition occurs when topochemical reaction dominates over through-solution The through-solution reaction is limited to the available pore space The initial pore space is a function of the w/c ratio The transition time t D is independent of w/c ratio, but depends on temperature

42 Conclusions,contd A fourth parameter, A, must be introduced to model the nucleation and growth kinetics of the boundwater index The parameter A represents the asymptotic value of the amount of outer product that can be formed The parameter A has an inverse relationship with w/c ratio Scaling the boundwater index by the w/c ratio eliminates A The resulting boundwater/cement ratio has an asymptotic value determined by the water content of the C-S-H gel The parameter A decreases with temperature indicating a lower water content of the gel with temperature

43 Conclusions,contd II The observed C-S-H gel density is a bulk average, but there may be several gels with different densities. The outer product be less dense than the inner product due to the reaction mechanism The outer product phase forms first and the inner product subsequently. Therefore the bulk average may be changing over time. The outer and inner products may mix physically or chemically

44 Conclusions,contd III The ultrasonic reflectivity data has a similar master curve with respect to the w/c ratio However, the invariant is the gel surface contact area, not the t D This implies that the growth-limiting mechanism of the boundwater differs from the reflectivity

45 Thank you for your attention! Merci beaucoup pour votre attention! Richard A. Livingston:

46 QUASI-ELASTIC NEUTRON SCATTERING

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