Film Formation of Waterborne Coatings

1. Film Formation of Waterborne Coatings Joe Keddie University of Surrey Guildford, UK

2. Close-packing of particles Water loss Deformation of particles Interdiffusion and coalescence Homogenous Film Dodecahedral structure (honey-comb) Idealised View of Latex Film Formation Polymer-in-water dispersion T > MFFT Optical Clarity T > Tg

3. Dark field optical microscopy Atomic force microscopy TEM on C replica Stages of Latex Film Formation

4. Overview • Factors affecting Minimum Film Formation Temperature MFFT • Lateral and vertical drying • Particle packing • Fundamental driving forces for particle deformation • Diffusion and particle coalescence • Factors influencing surfactant distribution

5. Randomly-packed array of deformable particles in dry film Particles are flattened at their boundaries in dry film 1.5 mm x 1.5 mm Source: A. Tzitzinou et al., Macromolecules, 33 (2000) 2695. Typical Morphologies 5 mm x 5 mm AFM Images

6. Typical Morphologies Voids in randomly-packed array of particles: Yet film is optically transparent

7. Percolating Phase within Deformed Particles Latex film formation offers control at the nanometre length scale! From: R. Mezzenga et al., “Templating Organic Semiconductors via Self-Assembly of Polymer Colloids,” Science, 299 (2003) p. 1872.

8. Measuring MFFT Picture courtesy of Dr P. Sperry, Rohm and Haas

9. Hot +10°C Clear Minimum Film Formation Temperature (MFFT) Picture courtesy of Dr P. Sperry Rohm and Haas -10°C Cloudy Cold

10. Factors Affecting MFFT • MFFT has an imprecise definition - subject to human perception •Usually is within a few degrees of the glass transition temperature of the polymer • Optical clarity can increase over time with further coalescence of particles •For the same polymer, MFFT decreases with particle size. Driving force for coalescence is higher for smaller particles. Also, there is an optical effect: less light scattering from smaller voids!

11. Effect of Particle Size on MFT Tg of the latex is ~ 37 - 40 °C Source: D.P. Jensen & L.W. Morgan, J. Appl. Pol. Sci., 42 (1991) 2845.

12. Effect of Particle Size on MFT Blend of 63 nm and 458 nm particles with an average Tg of 38 °C. Source: D.P. Jensen & L.W. Morgan, J. Appl. Pol. Sci., 42 (1991) 2845.

13. Drying of Latex Films

14. E. Sutanto et al., in Film Formation in Coatings, ACS Symposium Series 790 (2001) Ch. 10 Experimental evidence for lateral non-uniformity Cryogenic SEM

15. Films dry first in the thinnest regions Hard particles Film Relevant when coating large surface areas: lateral transport of water is observed

16. P a = particle radius Pcap Capillary pressure: x Reduced capillary pressure: Pressure of Darcy flow

17. • a = particle size • H = film thickness • E = evaporation rate A.F. Routh and W.B. Russel, A.I.Ch.E.J., 44 (1998) 2088. Theory: Reduced capillary pressure controls lateral drying • Reduced capillary pressure, pc, can pin the water at the film edge. Surface tension; viscosity; solids fraction

18. MR imaging of lateral drying 0 hr. 2.6 mm 3 hr. Packed particle bed filled with water Wet, colloidal dispersion 6 hr. 22 mm MR Image J.M. Salamanca et al., Langmuir, 17 (2001) 3202.

19. 2.4mm 22 mm 22 mm 1.1mm Water is pinned at the film edge when there is a high Pc Pc = 1.0 Pc = 420 H = 1.2 mm and a = 25 nm H = 0.32 mm and a = 4.4 mm

20. Experiments support theory • Lower thickness, larger particle size, and slower evaporation rate encourage uniform lateral drying Pc

21. Densely-packed particle layer Experimental Evidence for Vertical Non-Uniformity Cryogenic SEM E. Sutanto et al., in Film Formation in Coatings, ACS Symposium Series 790 (2001) Ch. 10

22. Theory: Peclet number for vertical drying uniformity • Competition between Brownian diffusion that re-distributes particles and evaporation that causes particles to accumulate at the surface

23. Experimental Observation of Brownian Movement Phenomenon was first reported by a Scottish botanist named Brown (19 cent.) Brown observed the motion of pollen grains but realised that they were not living. Brownian motion

24. Peclet number for vertical drying uniformity E Pe >> 1 R Dilute limit E H Pe << 1

25. Scaling Relation for Vertical Drying Uniformity z A.F. Routh and W.B. Zimmerman, Chem. Eng. Sci., 59 (2004) 2961-68.

26. pol Pe = 0.2 Vertical Position Simulations of the Vertical Distribution of Particles fm Close-packed Top fo z

27. Pe = 1 pol Vertical Position Simulations of the Vertical Distribution of Particles Close-packed

28. Pe = 10 pol Vertical Position Simulations of the Vertical Distribution of Particles

29. B1 Gy B0 Film Sample Coverslip RF Coil GARFielddepth profiling magnet for planar samples Characteristics : • 0.7 T permanent magnet (B0) • 17.5 T.m-1 gradient in the vertical direction (Gy) Abilities : • accommodates samples of 2 cm by 2 cm area • achieves better than 10 m pixel resolution! P. M. Glover, et al., J. Magn. Reson. (1999) 139, 90. position Gravity Signal intensity

30. Experiments partially agree with simulations H= 255 m, E = 0.2 x 10-8 ms-1, D = 3.23 x 10-12 m2s-1 High humidity Pe  0.2 w z • Slow evaporation rate, small particle size, low film thickness and low serum viscosity favor uniform vertical drying. J.-P. Gorce et al., Eur Phys J E, 8 (2002) 421

31. Experiments partially agree with simulations H = 340 m, E = 15 x 10-8 ms-1, D = 3.23 x 10-12 m2s-1 Flowing Air Pe  16 w fw=0.15 z • High evaporation rate, large particle size, high film thickness and high serum viscosity favor non-uniform vertical drying. There is no discontinuity in the water concentration.

32. Mixed modes of drying Flowing air: High E and vertical uniformity of water Static air: Low E and non-uniformity of water vertically Time

33. Particle Packing

34. Particle Packing Defects Requires monodisperse particle sizes BCC Slow drying favours ordering FCC Packing defects are often associated with particles of differing size! Particles of “wrong” size

35. Solids Fraction of Packed Particles • If monosized particles pack into a face-centered array, the volume fraction of solids, , is 0.74 - the densest possible for hard spheres. •If the particles are randomly-packed,  0.6 • If smaller particles fit into the void space between larger particles, then  will be higher. • Also, if an electric double-layer prevents particle-particle contact, then  will be lower at “close packing”.

36. Effect of Double-Layers Confinement of particles but without particle/particle contact

37. Solids fraction is 74 vol% for FCC packing of both small and large particles • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Solids Fractions of Hard Particles If small particles fit into the voids between large particles, the packing fraction can be increased!

38. Formation of Colloidal Crystals These size ratios are required to create various types of colloidal crystal: Cubic # Nearest Large/Small Crystal Structure Neighbors Ratio . CsCl (Simple) 8 1.37:1 NaCl (Face-centred) 6 2.41:1 ZnS (Diamond) 4 4.45:1 This strategy requires tight control of particle sizes and controlled drying conditions. An alternative approach is to disperse large particles in a continuous phase of small particles.

39. MRS Bulletin, Feb 2004, p. 86 Ordered Arrays of Particle Blends

40. Critical Volume of Particle to Achieve a Continuous Phase Enough small particles to percolate around larger particles Large/Small Ratio

41. Example of Morphology from the Packing of Bimodal Particles Atomic force microscopy images of a latex film made by blending 80 wt% 300 nm particles with 20 wt% 50 nm particles 1.5 mm x 1.5 mm Source: A. Tzitzinou et al., Macromolecules, 33 (2000) 2695.

42. In Latex with Bimodal Size Distribution: Number Fraction  Weight Fraction Example:10:1 ratio of Large:Small Particles Weight/Vol. Fraction LargeNumber Fraction Large 0.01 0.00001 0.10 0.00011 0.50 0.00100 0.95 0.01865 0.97 0.03132 0.99 0.90082 Actual sizes are irrelevant. Calculations assume large and small particles have the same density.

43. Under a shear stress Effects of Shear Stress on Colloidal Dispersions With no shear Confocal Microscope Images MRS Bulletin, Feb ‘04, p. 88

44. Mechanisms for Particle Deformation and Coalescence

45. 2 2 3 • 3 4 1 1 4 • • 5 6 6 5 Face-centered cubic array of particles: 12 neighbours for each particle Typical Morphologies • • •

46. Typical Morphologies Particles are deformed to fill all available space: dodecahedra Y. Wang et al., Langmuir8 (1992) 1435.

47. Particle Coalescence Same polymer volume before and after coalescence: r R Surface area of particle made from coalesced particles:4pR2 Surface area of N particles:4Npr2 Change in area, DA = - 4pr2(N-N2/3) In 1 L of latex (50% solids), with a particle diameter of 200 nm, N is ~ 1017 particles. Then DA = -1.3 x 104 m2

48. Driving Force for Coalescence: Reduction in Free Energy Decrease in Gibbs Free Energy, DG, with particle coalescence: DG = gDA g= interfacial energy (J m-2) DA = change in interfacial area Coalescence is favorable when G is reduced (DG < 0). For coalescence of N = 1017 particles with a 200 nm diameter, with g = 3 x 10-2 J m-2,DG = - 390 J.

49. Concept of Energy Balance Energy “gained” by the reduction in surface area with particle deformation is “spent” on the deformation of particles: Deformation is either elastic, viscous (i.e. flow) or viscoelastic (i.e. both)

50. Typical Values of Interfacial Energy Interface Water/Air Polymer/Water Polymer/Air g (10-3 J m-2) 72 5 - 10 20 - 35