Time evolution of transition points in drying latex films.

The change of minimum film formation temperature (MFFT) with time was studied utilizing a temperature gradient bar. Fitting the data to a theory which assumed that particles deform due to the action of the polymer-air surface tension, the glass transition temperature, [T.sub.g], of the latex was predicted. This [T.sub.g] was compared to the value obtained by differential scanning calorimetry (DSC) and good agreement was observed between the two measurements.

Keywords: Acrylics, drying, flow, levelling, physical properties, thermal properties, latex, water-based

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Latex film formation involves the transition of a stable colloidal dispersion into a coherent, clear polymer film and involves three distinct transitions: (1) Evaporation of water and ordering of particles, deformation of particles to fill voids, and, finally, rupture of particle boundaries with interdiffusion of polymer chains. This is shown schematically in Figure 1. In the first stage, colloidal particles exist as a stable suspension in water, with colloidal stability due to both electrostatic and steric stabilization. As water evaporates, the particles move closer to each other until close packing is obtained at the end of stage 2. (2) During the initial stages of drying, water loss is linear with time for dilute latices regardless of whether the particles are film forming latices or not (drying temperature < [T.sub.g]). (3) Between stages 2 and 3, capillary pressures generated due to further evaporation of water and interparticle van der Waals attractions cause particles to deform to fill the voids between them. At this stage, the film changes from opaque and cloudy to transparent. (4) In the final transition, boundaries between particles blur as interdiffusion of polymer chains occurs, resulting in development of tensile strength.

The minimum film formation temperature (MFFT) is the temperature above which particles will deform. Hard particles will have a higher MFFT compared to softer particles. Experiments are typically performed on an MFFT bar, which is a metal bar with a preassigned temperature gradient. A coating is applied to the bar and MFFT points along the length of the film are identified, after a period of time, using a thermocouple. Winnik (5) defined three distinct MFFT points: the optical MFFT, where turbidity ceases; knife point MFFT, above which the film exhibits mechanical toughness; and crack point MFFT, above which cracking ceases.

[FIGURE 1 OMITTED]

The mechanism of particle deformation during the drying process to form a transparent film has been disputed by academics for many years, with four distinct mechanisms proposed. They are: wet sintering, which is driven by the particle-water surface tension; dry sintering, which is driven by the particle-air surface tension; capillary deformation, which arises from the air-water curvature formed between particles at the surface of the film; and Sheetz's deformation, which occurs if a polymer layer is formed at the surface of the film.

Dillon et al. (6) first suggested that dry sintering plays an important role in particle deformation. They suggested that particles deform due to their viscous flow when the polymer particles in the latex coalesce to reduce their surface energy. In a similar fashion, two isolated viscous particles sintering under surface tension can be described by Frenkel's viscous flow of polymer spheres, [[theta].sup.2] = 3[gamma]t/2[pi][eta]R, where [theta] is the angle formed between two deforming particles, t is the time, [gamma] is the surface tension, R is the particle radius, and [eta] the polymer viscosity. Sperry et al. (7) provided experimental evidence for dry sintering via MFFT measurements. After drying a film well below its MFFT, it was heated up to allow particle deformation. The appearance of these dried films was then compared with films cast wet at the elevated temperature. The cloudy-clear transition temperature for the two films reaches the same value after a time period, indicating that water is not important in particle deformation. Similarly, Chainey et al. (8) observed deformation of particles over a period of one month from latex cast by flash casting, (hence, containing no water). Keddie et al. (9) also supports a dry sintering mechanism in their study of acrylic latices with multiple-angle-of-incidence ellipsometry (MAIE) and environmental scanning electron microscopy (ESEM). They found that at the onset of stage 2, voids were present in the film before particle deformation occurred to yield a film with a high packing density. This implies that particle deformation during this stage is driven by the energy savings from the reduction of the polymer/air surface area. Although they have shown that dry sintering occurs, most of their experiments involve dry films and, hence, do not reflect drying of colloidal polymer dispersions. Lin and Meier (10) argue that even in dry latex films, meniscus rings of water are still present in the contact region between two particles, due to atmospheric humidity. Thus, dry sintering cannot occur.

Brown (11) proposed a theory for film formation, which suggests that particle deformation will occur when the force, due to a capillary pressure, is greater than the force resisting deformation. Brown estimated the maximum capillary pressure to be 12.9[gamma]/R by assuming a spherical meniscus between a triangular array of particles. Considering two isolated elastic particles with shear modulus G, Brown proposed a criterion for film formation, G < 35[[gamma].sub.wa]/R, where [[gamma].sub.wa] signifies the water-air surface tension. Later film formation models are mostly based on Brown's capillary deformation model. (12-14) Sheetz (15) proposed a different model, where a layer of dried polymer is formed on the surface of a drying film. Diffusion of water through the skin generates a compressive pressure large enough to cause particle deformation below.

Routh and Russel (2,4) proposed that the mechanism for particle deformation is determined by temperature. Rather than considering isolated particles, pairwise contacts were averaged to give the deformation stress-strain behavior of a packed array of particles. The dimensionless groups that determine this are: the ratio of time for viscous collapse of the particles compared to the evaporation time, [bar.[lambda]] = [[[eta].sub.0]RE]/[[[gamma].sub.wa]H], and the Peclet number, Pe = [6[pi][mu]RH[dot.E]]/kT, which is a ratio of rate of evaporation of water to the rate of diffusion of particles. In the above expressions, [[eta].sub.0] is the polymer low shear viscosity, [dot.E] is the evaporation rate, H is the thickness of the latex film, [mu] is the viscosity of the continuous medium, and kT is thermal energy. Routh and Russel proposed parameter maps that specified when each of the proposed deformation mechanisms would apply.

When deformation of a particle occurs over a long time period, long after evaporation of all water, dry sintering is the responsible mechanism and the time for film formation is

t = [[0.3R[dot.E]]/[H[[gamma].sub.pa]]][[eta].sub.0]([T.sub.g])[a.sub.T.sub.g] (1)

where [[gamma].sub.pa] is the polymer-air surface tension, [[eta].sub.0]([T.sub.g]) is the polymer low shear viscosity at the [T.sub.g] of the polymer and [a.sub.T.sub.g] is a temperature shift factor following from WLF theory (16) as log [a.sub.T.sub.g] = [-[C.sub.1](T - [T.sub.g])]/[[C.sub.2] + T - [T.sub.g]], with [C.sub.1] and [C.sub.2] as material constants. (2) Substituting in the temperature dependence, the time for film formation in the dry sintering regime follows as:

t = [A10.sup.[-[C.sub.1](T - [T.sub.g])]/[[C.sub.2] + T - [T.sub.g]]] (2)

A = [0.3[R.sub.0][dot.E][[eta].sub.0]([T.sub.g])]/[H[[gamma].sub.pa]] (3)

Rearranging, we arrive at the final form:

T - [T.sub.g] = [-[C.sub.2]/[C.sub.1] log (t/A)]/[1 - 1/[C.sub.1] log (t/A)] (4)

The material constants [C.sub.1] and [C.sub.2] referring to the glass transition temperature, [T.sub.g], are material dependent but can be taken as 17.1 and 51.4[degrees]C, respectively. (17) Hence, the temperature of the cloudy-clear transition in a film is time dependent and following it allows for a prediction of the polymer glass transition temperature.

In this article, we report experiments where a known thickness of latex is spread on a temperature gradient bar and left for about a week. Due to viscous deformation, the optical MFFT moves to lower temperatures with time. This time dependence of the MFFT is used to predict the [T.sub.g] of the polymer.

EXPERIMENTAL

Materials

The latices used were poly(ethyl acrylate-co-styrene) (EA/S) and poly(butyl acrylate-co-styrene) (BA/S) copolymers. They were prepared via conventional emulsion polymerization (7) at 85[degrees]C using potassium persulfate as the initiator with 0.2% sodium dodecyl sulfate (SDS) and 1 wt% acrylic acid added based on the weight of the monomer to stabilize the particles. The particles were made as follows: Styrene monomer (Acros Organics) was filtered through aluminum oxide, butyl acrylate; and ethyl acrylate monomers (Acros Organics) were vacuum-distilled to remove inhibitors. Sodium dodecyl sulfate (Sigma Aldrich) and acrylic acid (Acros Organics) were used as received. Initially, distilled water was placed in a four-neck round bottom glass reactor fitted with a stirrer and reflux condenser and heated up under nitrogen in a water bath. Half of the monomers were added with the initiator, surfactant, and acrylic acid to produce a seed for the polymerization process. Finally, the rest of the monomers were added and the reaction was allowed to proceed overnight to ensure complete conversion. The resulting latices were cleaned in dialysis tubing for a week with two changes of water per day. The composition of the polymers was chosen so that the latex glass transition temperature was in the range of 40-60[degrees]C.

Particle sizes were determined by dynamic light scattering (Brookhaven's Zeta Plus). Particle wt% was determined from the dry mass of the sample; a known mass of sample was dried at 60[degrees]C overnight and the remaining mass of sample determined.

MFFT Measurements

Experiments were performed on a temperature gradient bar. The temperature across the bar ranged from room temperature to 30[degrees]C above the [T.sub.g] of the polymers used. The temperature at specific points was measured using a thermocouple with an accuracy of about [+ or -] 0.5[degrees]C. Latices were cast onto a glass plate pre-equilibrated to the temperature of the gradient bar. The latices were spread using an adjustable micrometer film applicator so that the thickness of the wet film was known. Time was measured from the moment latex was cast onto the glass plate. Measurement of MFFT was carried out after the film was dried, which usually takes one to two hours. Three different MFFTs were measured: the cloudy-clear transition, the crack point, and the knife point MFFT. The knife point MFFT was taken as the point where the latex film started to exhibit brittleness when stabbed with a knife. With operator consistency in selecting the transition is taken into account, the precision of determination was estimated to be [+ or -] 1[degrees]C for the cloudy-clear transition and [+ or -] 2[degrees]C for the knife point MFFT, due to difficulty in estimating the brittleness of the film. The thicknesses of the wet films were varied, from 1.0 mm to 2.5 mm.

Differential Scanning Calorimeter 

The [T.sub.g] of the polymer blends was obtained using a PerkinElmer diamond differential scanning calorimeter (DSC). DSC measures the difference in heat flux required to keep a sample and reference at the same temperature. The two specimens are cooled and heated at a controlled rate. The amount of energy required to maintain system equilibrium is directly proportional to the energy changes occurring in the sample. Calibration of the instrument for a 5[degrees]C/min heating rate was done using two reference samples, containing zinc and indium, respectively. The two latex samples were placed in separate aluminum pans and film formed in an oven at 100[degrees]C for 24 hr. Then the mass of latex film inside each sample was determined before sealing the sample pans with aluminum lids. The samples were placed next to a reference cell, which was an identical empty aluminum pan. The cells were allowed to equilibrate to the starting temperature (20[degrees]C) before heating/cooling commenced. The cells were cooled to -50[degrees]C and then heated to 100[degrees]C. The cells were then held at 100[degrees]C for 10 min before being cooled to 20[degrees]C again, to ensure that no crystallization took place. The cooling and heating rate were controlled at 5[degrees]C/min. The same cycles were applied to the two different latices.

[FIGURE 2 OMITTED]

RESULTS AND DISCUSSION

Materials

Latices used in these experiments were poly(ethyl acrylate-co-styrene) (EA/S) and poly(butyl acrylate-co-styrene) (BA/S). Their properties are shown in Table 1.

MFFT Measurements

Figure 2 shows a photograph of a film casting. The left-hand side of the latex, the low temperature end, is highly turbid due to scattering of light from the voids between particles. The right-hand side of the film is transparent due to the particles having deformed to fill voids, at the higher temperature. Bubbles are visible under the surface of the film, especially in the higher temperature end. This is due to vertical in-homogeneities and a faster coalescence rate at the surface of the film. The crack point is a few degrees higher than the cloudy-clear transition and does not change with time. Figures 3 and 4 show the evolution of the MFFTs with time. The temperature where the cloudy-clear and knife point transitions take place seems to vary linearly with time. The change in MFFT long after water has evaporated from the film indicates that dry sintering is continuing particle deformation. Considering the precision in reproducing the readings with casting of different thicknesses, from Figures 3(a) and (b) and Figure 5, our results demonstrate that the MFFTs do not seem to be affected by the casting thickness. The optical and knife point MFFTs change with a similar slope irrespective of the film thickness, as shown in Figures 5(a) and (b). The knife point of the BA/S films could only be determined at a much later time after casting, since at early times the film was too soft and sticky.

Using the expression for film formation by dry sintering, equation (4), we ploted the temperature of the cloudy-clear transition versus [-51.4/17.1log(t/A)]/[1 - 1/17.1log(t/A)]. We expected an intercept of [T.sub.g] at the point where the horizontal axis is zero, allowing for the prediction of the glass transition temperature. The value of A is dependent on each particular experiment and was calculated from A = [0.3R[dot.E][[eta].sub.0]([T.sub.g])]/[H[[gamma].sub.pa]] where [[eta].sub.0]([T.sub.g]) had a value of 10 (12) Ns/[m.sup.2], [dot.E] was 0.3 cm/day, and [[gamma].sub.pa] was 0.02 N/m. (13)

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

From Figures 6(a) and (b), the [T.sub.g] obtained for the EA/S polymer was between 49.7[degrees]C and 52.4[degrees]C, while the [T.sub.g] for the BA/S was in the range of 41.8[degrees]C to 49.0[degrees]C. We therefore had a prediction of [T.sub.g] ~ 51.1 [+ or -] 1.5[degrees]C for the EA/S particles and a [T.sub.g] ~ 45.5 [+ or -] 3.5[degrees]C for the BA/S particles. Changing the values of [C.sub.1] and [C.sub.2] had little effect on the [T.sub.g] values.

[FIGURE 7 OMITTED]

It is important to recognize the large amount of scatter in the data. This is most pronounced in Figures 5(a) and 6(a). This is typical of MFFT measurements and shows the variability of latex systems. Contrary to this, however, is the narrowness of the prediction of the glass transition temperature. This was calculated from the best fit lines, shown on the graphs, and hence, the MFFT measurement variability was somewhat averaged out.

DSC Measurements

Figures 7(a) and (b) show the heat flux versus temperature for the two samples. An abrupt increase in heat flux shows the glass transition temperature of the latex. The sample absorbs more heat because of its higher heat capacity. (18) We chose to use the midpoint of the inflection as the [T.sub.g] of the latex. From the DSC measurements, we determined the [T.sub.g] of the polymers to be 56.1[degrees]C for EA/S and 43.2[degrees]C for BA/S.

Ascribing a particular value to the glass transition temperature is inherently difficult. The DSC curves are very broad, give a range of values, and are dependant on the rate of heating/cooling. Using Fox's equation, we can get an estimate of the [T.sub.g] of a random copolymer from the wt% of each polymer used. Taking [T.sub.g] for styrene, butyl acrylate, and ethyl acrylate as 100[degrees]C, -43[degrees]C and -8[degrees]C, respectively, (19) the [T.sub.g] calculated from Fox's equation, 1/[T.sub.g] = [wt.sub.1]/[T.sub.g1] + [wt.sub.2]/[T.sub.g2], is shown in Table 2. (20) Application of this equation assumes a perfect random copolymer and the reaction yield to be the same for each monomer. Nevertheless, it is striking that the Fox equation fails to adequately predict the [T.sub.g], while the MFFT bar experiments are within 3[degrees]C of the DSC measurements.

CONCLUSION

In this article, we have shown that deformation of particles at the cloudy-clear transition occurs by a dry sintering mechanism. Applying the data obtained to a dry sintering model, the glass transition temperature for latices can be obtained. These results compare well with the glass transition temperature obtained from differential scanning calorimetry. The glass transition temperature obtained was higher than that predicted from Fox's equation, indicating either segregation of the monomers during polymerization, or more likely, incomplete incorporation of the acrylate during the emulsion polymerization.

ACKNOWLEDGMENT

This work was supported by EPSRC through grant number GR/S05885/01. The authors are very grateful to the EPSRC equipment pool for the loan of a DSC.

Reference

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(3) Steward, P.A., Hearn, J., and Wilkinson, M.C., "An Overview of Polymer Latex Film Formation and Properties," Adv. Colloid Interface Sci., 86, 195 (2000).

(4) Routh, A.F. and Russel, W.B., "Deformation Mechanism During Latex Film Formation: Experimental Evidence," Ind. Eng. Chem. Res., 40, 4302 (2001).

(5) Winnik, M.A., Latex Film Formation, Current Opinion in Colloid and Interface Science, 2, 192 (1997b).

(6) Dillon, R.E., Matheson L.A., and Bradford E.B., "Sintering of Synthetic Latex Particles," J. Colloid Sci., 6, 108 (1951).

(7) Sperry, P.R., Snyder, B.S., O'Dowd, M.L., and Lesco, P.M., "Role of Water in Particle Deformation and Compaction in Latex Film Formation," Langmuir, 10, 2619 (1994).

(8) Chainey, M., Wilkinson, M.C., and Hearn, J. "Preparation of Polymer Latex Films by a Flash Casting Technique," J. Appl. Polym. Sci., 30(11) 4273-4285 (1985).

(9) Keddie, J.L., Meredith, P., Jones, R.A.L., and Donald, A.M., "Kinetics of Film Formation in Acrylic Latices Studied with Multiple Angle of Incidence Ellipsometry and Environmental SEM," Macromolecules, 28, 2673, (1995).

(10) Lin, F. and Meier, D.J., "A Study of Latex Film Formation by Atomic Force Microscopy," Langmuir, 11, 2726, (1995).

(11) Brown, G.L., "Formation of Films from Polymer Dispersions," J. Polym. Sci., 22, 423 (1956).

(12) Vanderhoff, J.W., Bradford, E.B., and Carrington, W.K., "Transport of Water Through Latex Films," J. Polym. Sci., Polym. Symp., 41, 155 (1973).

(13) Mason G., "Formation of Films from Polymer Latexes: A Theoretical Treatment," Br. Polym. J., 5, 101 (1973).

(14) Eckersley, S.T. and Rudin, A., "Mechanism of Film Formation from Polymer Latexes," J. COAT. TECHNOL., 62, No. 780, 89 (1990).

(15) Sheetz, D.P., "Formation of Films by Drying of Latex," J. Appl. Poly. Sci., 9, 3759 (1965).

(16) Williams, M.L., Landel, R.F., and Ferry, J.D., The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-forming Liquids. Mechanical Properties of Substances of High Molecular Weight, 3701 (1955).

(17) Graessley, W.W., Polymeric Liquid and Networks: Structure and Properties, Garland Science, 2004.

(18) Rabek, J.L., Experimental Methods in Polymer Chemistry: Physical Principles and Applications, John Wiley and Sons Ltd., New York, 1980.

(19) Penzel, E., Rieger, J., and Schneider, H.A., "The Glass Transition Temperature of Random Copolymers: 1. Experimental Data and the Gordon-Taylor Equation," Polymer, 38, 325 (1997).

(20) M' Bareck, C.O., Nguyen, Q.T., Metayer, M., Saiter, J.M., and Garda, M.R., "Poly (Acrylic Acid) and Poly (Sodium Styrene-sulfonate) Compatibility by Fourier Transform Infrared and Differential Scanning Calorimetry," Polymer, 45, 4181 (2004).

Wai Peng Lee and Alexander F. Routh ([dagger]) -- University of Sheffield*

* Particle Products Group, Department of Chemical Engineering, Mappin Street, Sheffield, S1 3JD, United Kingdom.

([dagger]) Present address: BP Institute and Department of Chemical Engineering, University of Cambridge, Madingley Rise, Madingley Rd., Cambridge, CB3 OEZ, United Kingdom. Email: [e-mail].

Table 1 -- Properties of Latices Used in the MFFT Experiments

Sample  Composition (wt%)    Diameter (nm)  Particle wt%

EA/S    42 EA / 57 S / 1 AA  190 nm         18.6
BA/S    35 BA / 64 S / 1 AA  160 nm         20.0

Table 2 -- [T.sub.g] for the Polymer Blends Calculated Using Fox's
Equation, MFFT Bar, and DSC

                        Fox's's Equation  MFFT Bar      DSC
Latex                   ([degrees]C)      ([degrees]C)  ([degrees]C)

Poly(ethyl
  acrylate-co-styrene)  45.0              51            56
Poly(butyl
  acrylate-co-styrene)  32.7              45            43