Nucleation and growth kinetics and the density of C-S-H. -Shashank Bishnoi & Karen L. Scrivener
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1 Nucleation and growth kinetics and the density of C-S-H -Shashank Bishnoi & Karen L. Scrivener
2 About μic Stands for Microstructure A modelling platform for resolution-free modelling of cement microstructure Allows users to define materials, particle types, reactions and models Enables studying hypothesis through customised simulations of cement hydration Available for free in open source 2
3 Here we use μic to study nucleation and growth kinetics 3
4 Nucleation and growth Simple 3D nucleation and growth: growth surface available 4
5 Inputs Rate of nucleation dn =k k 0 dt Rate of growth dm dr free surface =constant dt dt 5
6 Result vs. Avrami equation Fraction fill =1 e n kt Parameters calculated from input; no fitting needed. 6
7 Moving closer to cement... Random nucleation and growth on surface of spherical particles Similar nucleation and growth dn =k k 0 dt dm dr free surface =constant dt dt 7
8 Moving closer to cement... 8
9 Calculated rates Fitting needed; parameters not related to inputs 9
10 Calculated rates Fitting needed; parameters not related to inputs 10
11 This means 11 The Avrami equation does not work for alite-like systems Overlap between nuclei growing on the same particle can stop acceleration Only overlap between nuclei from different particles can lead to deceleration
12 What does this mean for alite? We studied the hydration rates of alites of different particle size distributions* Different models of hydration kinetics were used to reproduce the measured calorimetry curves *All experimental data from Mercedes Costoya 12
13 Particle size distributions *All experimental data from Mercedes Costoya 13
14 Measured calorimetry curves 14 *From Mercedes Costoya
15 Nucleation and growth 15
16 Important assumptions The Nucleation and Growth process is demand based: 16 Reactants are available in sufficient amounts in the solution Rate is governed only by the surface available for growth
17 When we fit N&G kinetics Instead of having actual nuclei, we simulate them numerically We derived an equation to calculate the fraction of surface covered and got... well... the Avrami equation again! Include an outwards growth rate and integrate in 3D for each particle... r 0 G 2 t mi= r0 17 r r 0 4 r 1 exp k 1 t G2 2 n f dr free
18 The fits 18
19 Snapshot at peak And these are the outer boundaries of the rough surfaces 19
20 Fit factors Fraction t1/2(hours) n G2(μm/hour) α0(%) A-38 μm B-83 μm C-38 μm D-18 μm Only t2/3 and G2 are fit factors 20 E-15 μm
21 Diffusion regime One of the explanations of the deceleration is diffusion controlled hydration dr in = dt 21 k diff 1 1 r r in r out 2 in
22 Still we try to fit... 22
23 Fit parameters Fraction k1 (hours-n) n kdiff (μm2/h) A-38 μm B-83 μm C-38 μm D-18 μm E-15 μm A large variation in transport properties of C-S-H has to be assumed 23
24 Heat-rate vs. thickness of product 24
25 Why not diffusion from peak? 25 A large variation in transport properties has to be assumed when density is constant Very little product present Particle surface is not fully covered if nucleation and growth on cement particles is assumed
26 Why doesn't this work? 26 Too little product at peak to have reduction in growth area due to overlaps Diffusion controlled process seems unlikely The acceleration can be modelled but post-peak behaviour can't be modelled
27 So let's try a lower density product We assume that the product formed has a low density (dry bulk density) at first It grows outwards due to a surface growth process Its packing improves with time First order assumption: 27 The rate of improvement of packing reduces exponentially with density
28 This is what it looks like 28
29 Product around a single particle: r0 G 2 t mi= r0 r r 0 4 r 1 exp k 1 t G2 2 n r f free dr o k den t r = max max min exp max min 29
30 The fits 30
31 Fit factors Fraction t1/2 (hours) n G2 (μm/hour) kden (g/cm3/hour) ρmin (g/cm3) α0 (%) A-38 μm B-83 μm C-38 μm D-18 μm E-15 μm ρmin (bulk dry density) is low ~0.2 g/cm3 G2 shows a wide spread... are the fits meaningless or can it mean something? 31
32 The most variable factor This means the product spreads faster in systems where inter-particle distances are larger 32
33 Redundancy in parameters Fraction D-18 μm t1/2 (hours) n G2 (μm/hour) kden (g/cm3/hour) ρmin (g/cm3) α0 (%) Two sets of parameters, similar curves 33 D-18 μm alternative
34 Snapshot at peak... Only outer boundary of growth shown 34
35 Results indicate 35 A loosely packed product is formed The product forms a fine mesh in the microstructure and fills a large part of the microstructure within a few hours The packing of the product improves with time
36 Evidence to support Different densities of C-S-H (Jennings 2004) No capillary pores observed in NMR (Halperin et al. 1994) Setting when very little product is formed Why not seen in SEM? 36 Drying will collapse the fine, water-filled mesh of product
37 Low-density in micrographs 37 De Jong et al. 1967
38 Low-density in micrographs 38 Richardson 1999
39 Low-density in micrographs 39 Mathur 2007
40 High-resolution SEM 40 From Patrick Juilland
41 To conclude (1/2) 41 Nucleation and growth can explain the acceleration Post-peak behaviour is not explained Large variations in transport properties have to be assumed to explain using diffusion mechanism The formation of a low-density product spreading outwards and densifying with time can reproduce the experimental results
42 To conclude (2/2) We currently do not have conclusive evidence... but the results point towards a direction to investigate Can explain various other phenomena: 42 Early setting when the volume of products is small Visco-elastic behaviour Invisible capillary pores in NMR
43 Thank you! Available in open source 43
44 Homogenous nucleation and growth N0 I G k n Sim. A Sim. B
45 Boundary nucleation and growth Simulation Final number of nuclei Sim. C Sim. D 45 I 79, ,643,311 Avrami eq. G S k1 n BN eq. I G S
46 PSDs used Name A B C D E Dmode Ds-vmd Has Dv10 (μm) (μm) fines (μm) Yes No No No Yes 2.0 Dv50 (μm) Dv90 (μm) Blaine (m2/kg) BET (m2/kg) N.A. 1 Fraction A-38 μm No. of particles Size (μm) B-83 μm C-38 μm D-18 μm E-15 μm
47 Simulations with diffusion equation Fraction k1 (hours-n) n kdiff (μm2/h) t0 (hours) α0 (%) hp,min (μm) hp,max(μm) hp,mean (μm) 47 A-38 μm B-83 μm C-38 μm D-18 μm E-15 μm
48 Dependence on parameters 48
49 Equations... n f =1 exp k 1 t [ [ G t f =1 exp S G t 2y 1 exp I y 2 t 3 3G dv dv * = 1 V V =1 exp V * dt dt 49 ] dy ]
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