Film formation from surfactant-free, slightly crosslinked, Fluorescein-labeled polystyrene particles.

A steady state-fluorescence (SSF) technique for studying film formation from surfactant-free, slightly crosslinked polystyrene (PS) latex particles is reported. The powder films were prepared from fluorescein (F)-labeled PS particles at room temperature. The mechanically strong films were obtained by annealing these films at elevated temperatures in 5, 10, 20, and 30 min time intervals above the glass transition ([T.sub.g]) temperature of polystyrene. Scattered light ([I.sub.s]) and fluorescence ([I.sub.F]) intensities from F were monitored after each annealing step to investigate the three different film formation stages called void closure, healing, and interdiffusion. The evolution of transparency of the latex films was monitored by using a photon transmission technique. Scanning electron microscopy (SEM) was employed to detect the variation in physical structure of the annealed latex films. Onset temperature for void closure, [T.sub.m], and healing temperatures, [T.sub.h], were determined and corresponding activation energies were measured. Void closure and interdiffusion stages were also modeled and the related activation energies were also determined. It was observed that lower energy is needed for the void closure process than interdiffusion of chains across the particle-particle boundaries.

Keywords: Fluorescein, latex film, void closure, interdiffusion, surfactant-free, polystyrene particles

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The interest in polymer latex film formation has grown enormously in recent years due to the need to find alternatives for solvent-based systems with their adverse environmental impacts. This is illustrated in the paint industry where traditional solvent-based paints are seen as environmentally unfriendly, and the increasingly good quality of waterborne coatings is allowing substitution of solvent-based coatings. In the past few years, water-based polymer latexes have gained more attention beyond their current uses in paints, adhesives, coatings, pharmaceuticals, printing inks, etc. over conventional solvent-based systems, mainly due to restrictions imposed by environmental requirements. Several factors are experimentally known to influence latex film formation: the molecular weight and its distribution, (1,2) stabilizers, (3) and surfactants. (4) In addition, the quality of these films, for a given molecular weight, depends on the annealing time and annealing temperature. (5-8)

The formation of a latex film arises from the "coalescence" (i.e., compaction, deformation, cohesion, and polymer chain interdiffusion) of individual latex particles. The term "latex film" normally refers to a film formed from soft latex particles ([T.sub.g] below room temperature) where the forces accompanying the evaporation of solvent are sufficient to compress and deform the particles into a transparent, void-free film. However, latex films can also be obtained by the compression molding of a film of dried latex powder composed of relatively hard polymers, such as polystyrene (PS) or poly(methyl methacrylate) (PMMA) that have [T.sub.g]s above room temperature. Aqueous dispersions of soft latex particles are called low-[T.sub.g], while nonaqueous dispersions of hard polymer particles are generally referred to as high-[T.sub.g]. High-[T.sub.g] latex particles remain essentially discrete and undeformed during drying. The mechanical properties of such films evolve after all the solvent has evaporated by an annealing process which first leads to void closure and then interdiffusion of chains across particle-particle boundaries.

Three steps can be distinguished during the film formation process from low-[T.sub.g] particles that have been observed experimentally (9): In the first step, colloid concentration increases as water evaporates and a uniform shrinkage of the interparticle distance occurs and the voids are gradually filled by particle sliding, until a dense packing of spheres is obtained. In the second step, particle deformation due to the evaporation of the bound water occurs. Finally, in the third step, due to interdiffusion of macromolecules, the mechanical strength increases and the water permeability of the film decreases. Under certain conditions the polymer chains can diffuse through the particle boundaries and a homogeneous, continuous film is formed. However, high-[T.sub.g] particles follow a different line of film formation processes. Particles form a powder after evaporation of water. Annealing of this powder at first causes void closure and then further annealing promotes healing and interdiffusion processes, respectively.

[FIGURE 1 OMITTED]

Various experimental techniques have been used to study latex film formation stages and mechanisms, which are given below. Small-angle neutron scattering (SANS) has been used to study latex film formation at the molecular level. Extensive studies using SANS have been performed by Sperling and co-workers on compressionmolded polystyrene film. (10) Direct-nonradiative energy transfer (DET) method has been employed to investigate the film formation process from dye-labeled polymeric particles. (11-13) Steady state fluorescence (SSF) technique, combined with DET, has been used to examine healing and interdiffusion processes in the dye-labeled PMMA latex systems. (14,15) Recently, photon transmission method has been performed to study latex film formation from PMMA and PS particles, using the UV-visible (UVV) technique as a function temperature and time. (16-18)

[FIGURE 2 OMITTED]

In this work, the SSF technique was used to study the evolution of latex film formation from surfactant-free, slightly crosslinked PS particles, by monitoring the scattered excited light ([I.sub.s]) from the film surface and fluorescence emission intensity ([I.sub.F]) from fluorescein. The films were prepared by annealing latex powder above the glass transition temperature of PS for 5, 10, 20, and 30 min time intervals at temperatures ranging from 100[degrees] to 250[degrees]C. As a supporting experiment, transmitted photon intensity, [I.sub.tr], from films was monitored to study the evolution of transparency. Void closure and interdiffusion processes were modeled and the relations between intensities ([I.sub.s], [I.sub.tr], and [I.sub.F]) and annealing temperature were derived to produce the related activation energies. Scanning electron microscopy (SEM) was used to justify the variation in the transparency of the latex films during annealing processes.

EXPERIMENTAL

Slightly crosslinked polystyrene (PS) latex was produced via a surfactant-free emulsion polymerization process. The polymerization was performed batch-wise using a thermostatted reactor equipped with a condenser, thermocouple, mechanical stirring paddle, and nitrogen inlet. The agitation rate was 300 rpm and the polymerization temperature was controlled at 70[degrees]C. Water (50 ml), styrene (5 g), and the crosslinker (0.006 g of fluorescent Fluorescein dimethacrylate, PolyFluor[R] 511) were first mixed in the polymerization reactor and when the temperature was constant (at 70[degrees]C), KPS initiator (0.06 g), dissolved in a small amount of water (3 ml), was introduced in order to induce styrene polymerization. The polymerization was conducted during 17 hours.

Scanning electron micrographs of PS latex particles were taken at 10-15 kV in a JEOL JSM microscope. A hummer VII sputtering system was used for gold coating of latex films. Figure 1 presents an SEM micrograph of a powder film prepared from PS particles at room temperature.

Four different latex films were prepared from the dispersion of PS particles by placing the same number of drops on a glass plate measuring 0.8 X 2.5 [cm.sup.2] and allowing the water to evaporate. Then, the samples were separately annealed above the [T.sub.g] of PS, 105[degrees]C, for 5, 10, 20, and 30 min time intervals at temperatures ranging from 100[degrees] to 250[degrees]C. The temperature was maintained within [+ or -] 2[degrees]C during annealing. Samples were weighed before and after film casting to determine the latex contents and film thickness. The average particles size was taken to be 0.6 [micro]m to calculate the thickness of the films.

After annealing, each sample was placed in the solid surface accessory of a Perkin-Elmer Model LS-50 fluorescence spectrometer. Fluorescein was excited at 323 nm and scattered light and fluorescence emission were detected between 300-500 nm. All measurements were carried out in the front-face position at room temperature. Slit widths were adjusted to give a wavelength resolution of 8 nm during all SSF measurements. The sample position, incident, [I.sub.0], and scattered light, [I.sub.s], intensities are shown in Figure 2a, where [I.sub.F] presents the emission of fluorescein intensity from fluorescein.

[FIGURE 3 OMITTED]

Photon transmission experiments were carried out using a model DU 530 Life Science UV-Visible (UVV) spectrometer from Beckman. The transmittances of the films were detected between 300 and 400 nm. A glass plate was used as a standard for all UVV experiments and the measurements were carried out at room temperature after each annealing process. The sample position and the transmitted light intensity, [I.sub.tr], are presented in Figure 2b.

RESULTS AND DISCUSSION

The emission spectra of fluorescein from PS latex films, annealed at various temperatures for 10 min time intervals and excited at 323 nm, are shown in Figure 3 where the scattered light intensities are also presented. It is observed that [I.sub.s] decreased continuously with increasing annealing temperature; however, [I.sub.F] first increased and then decreased after reaching a maximum. This behavior was repeated in all film samples. Here it has to be noted that the low [I.sub.F] values, as compared to [I.sub.s], most probably come from the low molar extinction coefficient of fluorescein. (19) On the other hand, transmitted light intensity, [I.sub.tr], increased above a certain onset temperature, upon annealing. The behavior of [I.sub.tr] and [I.sub.s] versus annealing temperature, [T.sub.an], is presented in Figure 4a and b, respectively, for all film samples. The shifts of the maxima for [I.sub.F] to the lower annealing temperatures with increasing annealing time are shown in Figure 5.

The increase in [I.sub.tr] and decrease in [I.sub.s] upon annealing can be explained by the evaluation of transparency of the PS films. Increase in [I.sub.tr] and decrease in [I.sub.s] starts above a certain temperature, which may be called minimum film forming temperature, [T.sub.m], above which polystyrene starts to flow upon annealing and voids between particles can be filled. Further annealing makes the PS film totally transparent to the light, [I.sub.s] drops to its minimum, and [I.sub.tr] reaches its maximum values. SEM photographs in Figure 6 confirm this picture where at 140[degrees]C (Figure 6b) void closure starts due to an increase in viscous flow in the necks. At 150[degrees]C (Figure 6c), complete void closure is reached where [I.sub.s] shows a sharp drop and [I.sub.tr] increases dramatically. Finally, above 150[degrees]C, the film becomes totally transparent (Figure 6d) due to interdiffusion.

On the other hand, the increase in [I.sub.F] above [T.sub.m] presumably corresponds to the void closure process up to the [T.sub.h] point where healing process takes place. The decrease in [I.sub.F] above [T.sub.h] can be understood by the interdiffusion processes between polymer chains. The variation in [I.sub.F] depends on the mean optical path, s, of a photon in the film. This mean optical path is directly proportional to the probability of the photon encountering a fluorescein molecule. Before annealing, the photon is scattered from the particle surfaces. That is, the mean free path (<a>) is of the order of the size of the interparticle voids. After a few steps, the photon reemerges from the front surface of the film. Thus, the mean optical path, s, is very short. After the void closure process is completed, scattering takes place predominantly from the interparticle interfaces and the mean free path is of the order of the particle size. In this regime (with the same number of rescatterings), a photon will stay for a much longer time in the film, and [I.sub.F] will increase. After the completion of the healing process, these interfaces are also removed. The film becomes essentially transparent to the photon, the mean free path diverges, and s is of the order of the film thickness.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

The maximum in [I.sub.F] can be explained by the healing process at the particle-particle interface. The time ([t.sub.an]) can be referred to as the healing time during which the chains in adjacent particles move halfway across the interface surface. At this temperature and time ([t.sub.an], [T.sub.h]), the original particle boundaries disappear and the latex film starts to become semitransparent to the exciting light for F molecules. As a result, the emission intensity, [I.sub.F], reaches a maximum well above [T.sub.h], complete transparency is reached due to the complete annealing of the latex film with the disappearance of all interparticle interfaces. It is here that the [I.sub.F] once more decreases.

These speculations were modeled and the behavior of [I.sub.F] and [I.sub.s] were interpreted by the results of Monte Carlo simulations. (14) The behavior of [I.sub.s], [I.sub.tr], and [I.sub.F] can be explained with the schematic picture in Figure 7. In Figure 7a, at the early stage of film formation, the powder film possesses many voids, which results in short mean free, <a>, and optical <s> paths of a photon. At this stage the film scatters the light totally, which yields low [I.sub.F]. Figure 7b presents a film in which, due to the annealing, interparticle voids disappear, which give rise to a long mean free (<a>) and the longest optical (s) paths. As soon as the voids are filled, a healing process takes place and <a> and s get even longer than before. At this stage, [I.sub.F] reaches its maximum value where [I.sub.s] drops to minima. Finally, Figure 7c presents a fully transparent film with the longest <a> but shorter s values. This film has low [I.sub.F] and [I.sub.s] intensities. This fully transparent film transmits the light totally, giving the highest [I.sub.tr] value.

Void Closure

In order to quantify the behavior of [I.sub.s] and [I.sub.tr] above [T.sub.m], a phenomenological void closure model was introduced. Particle deformation and void closure between particles can be induced by shearing stress which is generated by the surface tension of the polymer, i.e., polymer-air interfacial tension. The void closure kinetics can determine the time for optical transparency and latex film formation. (20) In order to relate the shrinkage of spherical void of radius, r, to the viscosity of surrounding medium, [eta], an expression was derived and given by the following relation. (20)

[FIGURE 6 OMITTED]

[dr]/[dt] = -[[gamma]/[2[eta]]](1/[[rho](r)]) (1)

where [gamma] is surface energy, t is time, and [rho](r) is the relative density. It has to be noted that, here, surface energy causes a decrease in void size and the term [rho](r) varies with the microstructural characteristics of the material, such as the number of voids, the initial particle size, and packing. Here, [rho](r) can be defined as a volume ratio of polymeric material to voids, whereas r goes to zero [rho](r) increases. However, for larger r values [rho](r) decreases. Equation (1) is similar to one which was used to explain the time dependence of the minimum film formation temperature during latex film formation. (21, 22) If the viscosity is constant in time, integration of equation (1) gives the relation as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where [r.sub.0] is the initial void radius at time t = 0.

The dependence of the viscosity of the polymer melt on temperature is affected by the overcoming energy barrier induced by the forces of macromolecular interaction which must be overcome to enable the segments of polymer chain to jump over from one equilibration position to another. This process happens at temperatures when the free volume becomes large enough and is connected with passage over the potential barrier. The Frenkel-Eyring (23, 24) theory produces the following relation for the temperature dependence of viscosity

[eta] = [[[N.sub.0]h]/V]exp([DELTA]G/kT) (3)

Where [N.sub.0] is Avagadro's number, h is Planck's constant, V is molar volume, and k is Boltzmann constant. It is known that [DELTA]G = [DELTA]H - T[DELTA]S, then equation (3) can be written as

[eta] = A exp ([DELTA]H/kT) (4)

Where [DELTA]H is the activation energy of viscous flow, i.e., the amount of heat which must be given to one mole of material for creating the act of a jump during viscous flow; [DELTA]S is the entropy of activation of viscous flow. Here A represents a constant for the related parameters. Combining equations (2) and (4), the following useful equation is obtained

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

In order to quantify the above results, equation (5) can be employed by assuming that the interparticle voids are spherical and in equal size and that the number of voids stay constant during film formation (i.e., [rho](r) [proportional][r.sup.-3]), then the integration of equation (5) gives the relation

t = [[2AC]/[gamma]]exp ([[DELTA]H]/[kT]) ([1/[r.sup.2]] - [1/[r.sub.0.sup.2]]) (6)

where, C is a constant related to relative density [rho](r). As we stated before, a decrease in void size (r) causes an increase in mean free path <a> of a photon, which then results in an increase in [I.sub.tr] and [I.sub.0P] intensities. This picture can also be visualized by Frenkel's neck formation model, (24) which takes into account the identical contacting spheres under the influence of surface tension. Frenkel's model assumes that the displaced volume is redistributed uniformally such that the remaining surfaces keep their spherical shapes but of larger radii, which offers a larger mean free path <a> of a photon during its journey in the latex film. Since the scattering intensity, [I.sub.s], varies with volume squared ([I.sub.s][alpha][v.sup.2]) of the scattering object (25) then it can be assumed that emission and transmitted light intensities ([I.sub.F] and [I.sub.tr]) are inversely proportional to the 6th-power of void radius, r. Equation (6) can be written as

[FIGURE 7 OMITTED]

t = [[2AC]/[gamma]]exp ([[DELTA]H]/[kT])[I.sup.1/3] (7)

Here, [r.sub.0.sup.-2] is omitted from the relation since it is very small compared to the [r.sup.-2] values after the void closure processes start. Equation (7) can be solved for I to interpret the results in Figures (4-7) as

I(T) = S(t) exp (-[3[DELTA]H]/[kT]) (8)

where S(t)=([gamma]t/2AC)[.sup.3]. For a given time, the logarithmic form of equation (8) can be written as follows

In I(T) = InS(t)-[[3[DELTA]H]/[kT]] (9)

Equation (9) was applied to [I.sub.s] and [I.sub.tr] above [T.sub.m] and [I.sub.F] below [T.sub.h] for all film samples. Figures 8 and 9 present the Ln[I.sub.tr] and Ln[I.sub.s] versus [T.sup.-1] plots, respectively, from which [DELTA][H.sub.tr] and [DELTA][H.sub.s] activation energies were obtained. The measured [DELTA][H.sub.tr] and [DELTA][H.sub.s] activation energies are listed in Table 1 where it is seen that [DELTA][H.sub.s] values were found to be smaller than [DELTA][H.sub.tr] values. The cartoons in Figure 2a and b can be used to explain these differences. Since [I.sub.s] sees only the latex particles at the surface, the smaller [DELTA][H.sub.s] values predict that surface latexes need less energy than latexes in the inner part of the film to execute void closure processes. However both [I.sub.s] and [I.sub.tr] intensities behave in a similar fashion upon annealing, i.e., both intensities measure the degree of transparency during film formation.

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

On the other hand, the increase in [I.sub.F] above [T.sub.m] in Figure 5 was mentioned previously. Now, data in Figure 5 below [T.sub.h] can be quantified by using equation (9). The produced [DELTA][H.sub.F] values from the fits are given in Table 1. The observed viscous flow activation energies, [DELTA][H.sub.F], were found to be smaller than [DELTA][H.sub.tr] values. Here, one may argue that since [DELTA][H.sub.F] values are produced at a molecular level in comparison to [DELTA][H.sub.tr] values, which are produced using a macroscopic treatment, it is believed that [DELTA][H.sub.F] values are more reliable and can be trusted. Besides, [I.sub.tr] carries two different pieces of information: void closure and interdiffusion which has to be separated (see next section).

It is seen in Figure 4 that minimum film forming temperature [T.sub.m] (i.e., onset temperatures for void closure) shifted to higher temperatures for smaller annealing time intervals for both [I.sub.tr] and [I.sub.s]. These increases and decreases in [I.sub.tr] and [I.sub.s] in Figure 4 probably correspond to the minimum film formation (void closure) point ([t.sub.an], [T.sub.m]). Equation (6) now can be written as

[t.sub.an] = S([r.sub.v]) exp ([DELTA][H.sub.m]/k[T.sub.m]) (10)

where S([r.sub.v]) = 2AC/[gamma][r.sub.v.sup.2]. Here [r.sub.v] is the minimal void radius at which [I.sub.tr] starts to increase (i.e., [I.sub.s] starts to decrease). Time ([t.sub.an]) versus [T.sub.m] and their logarithmic forms from the data in Figure 4a and b are shown in Figure 10a and b and Figure 11a and b, respectively. The slopes of the linear relation in Figures 10b and 11b produced [DELTA][H.sub.m] = 8.4 and 9.6 kcal/mol, which are slightly larger than [DELTA][H.sub.F] values.

[FIGURE 10 OMITTED]

Interdiffusion

The decrease in [I.sub.F] was already explained by the increase in transparency of latex film due to the disappearance of deformed particle-particle interfaces. As the annealing temperature is increased above [T.sub.h], some part of the polymer chains may cross the junction surface and the particle boundaries start to disappear; as a result, [I.sub.F] decreases due to the shorter optical path, s, of a photon. In order to quantify these results, the Prager-Tirrell (PT) model (26,27) for the chain crossing density can be employed. These authors used de Gennes's "reptation" model to explain configurational relaxation at the polymer-polymer junction where each polymer chain is considered to be confined to a tube in which it executes a random back and forth motion. A homopolymer chain with N freely jointed segments of length L was considered by PT, which moves back and forth by one segment with a frequency v. In time, the chain displaces down the tube by a number of segments, m. Here, v/2 is called the "diffusion coefficient" of m in one-dimensional motion. PT calculated the probability of the net displacement with m during time t in the range of n-[DELTA] to n-([DELTA] + d[DELTA]) segments. A Gaussian probability density was obtained for small times and large N. The total "crossing density" [sigma](t) (chains per unit area) at the junction surface was then calculated from the contributions [[sigma].sub.1](t) due to chains still retaining some portion of their initial tubes, plus a remainder, [[sigma].sub.2](t). Here, the [[sigma].sub.2](t) contribution comes from chains which have relaxed at least once. Figure 12 shows the pictoral representation of [[sigma].sub.1] and [[sigma].sub.2] contributions at the particle-particle interface, where the small segments present the part of the polymer chain called minor chain. In terms of reduced time, [tau] = 2vt/[N.sup.2], the total crossing density can be written as

[FIGURE 11 OMITTED]

[sigma]([tau])/[sigma]([infinity])= 2[[pi].sup.-1/2][[[tau].sup.1/2] + 2[[infinity].summation over (k=0)][(-1).sup.n][[[tau].sup.1/2]exp([-k.sup.2]/[tau]) - [[pi].sup.-1/2]erfc(k/[[tau].sup.1/2])]] (11)

For small [tau] values, the summation term of equation (11) is very small and can be neglected, which then results in

[sigma]([tau])/[sigma]([infinity]) = 2[[pi].sup.-1/2][[tau].sup.-1/2] (12)

This was predicted by de Gennes (28) on the basis of scaling arguments. In order to compare our results with the crossing density of the PT model, the temperature dependence of [sigma]([tau])/[sigma]([infinity]) can be modeled by taking into account the following Arrhenius relation for the linear diffusion coefficient

v = [v.sub.o]exp(-[DELTA][E.sub.b]/kT) (13)

Here, [DELTA][E.sub.b] is defined as the activation energy for backbone in our case depending on the temperature interval. Combining equations (12) and (13), a useful relation is obtained as

[FIGURE 12 OMITTED]

[sigma]([tau])/[sigma]([infinity]) = [R.sub.o]exp(-[DELTA][E.sub.b]/2kT) (14)

where [R.sub.o] = (8[v.sub.o]t)/[pi][N.sup.2])[.sup.1/2] is a temperature independent coefficient.

The decrease in [I.sub.F] in Figure 5 above the [T.sub.h] value is already related to the disappearance of particle-particle interface, i.e., as annealing temperature increased, more chains relaxed across the junction surface and, as a result, the crossing density increases. In other words, photons stay shorter in the transparent film due to the increase in crossing density, so that the probability of the photon encountering a fluorescein molecule decreases, which results in the decrease in fluorescence intensity, [I.sub.F]. Now it can be assumed that [I.sub.F] is inversely proportional to the crossing density [sigma](T) and, then, the phenomenological equation can be written as

[I.sub.F](T)/[I.sub.F]([infinity]) = [R.sub.0.sup.-1]exp([DELTA][E.sub.bF]/2kT) (15)

The activation energy of backbone motion, [DELTA][E.sub.bF] is produced from the logarithmic plots of [I.sub.F] versus [T.sub.an.sup.-1] by least squares fitting the data in Figure 5 to equation (15) and are listed in Table 1. The averaged value is found to be 14.8 kcal/mol, which is larger than the void closure activation energy ([DELTA][H.sub.F] = 5.6 kcal/mol). This result is understandable because a single chain needs more energy to execute diffusion across the polymer-polymer interface than a latex particle needs to accomplish the viscous flow process. In other words, a single chain needs more energy to cross over the barrier junction than the polymer melt needs to jump over from one equilibration position to other because the later process is a collective phenomenon.

It has already been mentioned that both [I.sub.tr] and [I.sub.s] data possess two different pieces of information, namely void closure and interdiffusion. Now equation (14) can be written in the following manner

[I.sub.tr](T)/[I.sub.tr]([infinity]) = [R.sub.0]exp(-[DELTA][E.sub.btr]/2kT) (16a)

[I.sub.s](T)/[I.sub.s]([infinity]) = [R.sub.0.sup.-1]exp(-[DELTA][E.sub.bs]/2kT) (16b)

by assuming that [I.sub.tr] and [I.sub.s] are directly and inversely proportional to the crossing density as the annealing temperature is increased, i.e., more chains cross the boundary as the temperature is increased, as a result [I.sub.tr] increases and [I.sub.s] decreases. Using equations (16a) and (16b) and data in Figures 4a and 4b, [DELTA][E.sub.b] values were produced and are listed in Table 1. It is observed that [DELTA][E.sub.btr] values for [I.sub.tr] are much larger than [DELTA][E.sub.bs] values for [I.sub.s]. A similar argument can be given as was done in the previous section, i.e., surface latexes need more energy than the latexes in the inner part of the film to execute the interdiffusion processes. As far as the backbone activation energies are concerned, we have to emphasize that [DELTA][E.sub.bF] values are trusted more than [DELTA][E.sub.btr] values because [DELTA][E.sub.bF] were obtained using molecular level data. Besides, [DELTA][E.sub.btr] carries information for both void closure and interdiffusion.

[FIGURE 13 OMITTED]

In Figure 5, the maxima of [I.sub.F] can be attributed to the healing point ([t.sub.an], [T.sub.h]) where minor chain crosses the particle-particle interface. Plotted in Figure 13a are ([t.sub.an], [T.sub.h]) pairs where it is seen that as [t.sub.an] is increased [T.sub.h] decreased to execute the healing process using minor chains during film formation. In order to interpret the data in Figure 13a, equation (12) is written at the healing point as

[t.sub.an] = B.exp([DELTA][E.sub.h]/k[T.sub.h]) (17)

where B = ([[sigma](T)]/[[sigma]([infinity])])([[pi][N.sup.2]]/[8[v.sub.0]]), which is constant for a given time and temperature. Equation (17) can be used to produce healing activation energy [DELTA][E.sub.h]. The fit of equation (17) to the data in Figure 13a is presented in Figure 13b, where the slope of the straight line produces the [DELTA][E.sub.h] value as 10.7 kcal/mol, which is smaller than [DELTA][E.sub.bF] as expected, since the minor chain always needs smaller energy than the whole chain to accomplish its motion across the polymer-polymer interface.

CONCLUSION

In summary, film formation processes from surfactant-free slightly crosslinked polystyrene latexes were investigated in conjugation with the morphological evolution of the films at elevated annealing temperatures. We have shown that simple kinetic models for void closure, healing, and interdiffusion mechanisms are fitted quite well to our fluorescence and UVV data. Transmitted, scattered, and fluorescence light were used to produce void closure, healing, and backbone activation energies. It is understood that fluorescence emission from the fluorescein produces more reliable results than [I.sub.tr] and [I.sub.s] lights. We have learned that the slightly branched polystyrene chains can interdiffuse across the particle-particle junctions during the film formation process.

Table 1 -- Experimentally Produced, Backbone, and Viscous Flow
Activation Energies

[I.sub.tr]  (kcal.mo[l.sup.-1])  [DELTA][E.sub.btr] (a)
                                 [DELTA][H.sub.tr] (b)
[I.sub.s]   (kcal.mo[l.sup.-1])  [DELTA][E.sub.bs]
                                 [DELTA][H.sub.s]
[I.sub.F]   (kcal.mo[l.sup.-1])  [DELTA][H.sub.F]
            (kcal.mo[l.sup.-1])  [DELTA][E.sub.bF]

             Annealing Time Interval [t.sub.an] (min)
                  5    10    20     30    Average

[I.sub.tr]      61.0  32.0  59.0   47.0   49.7
                10.1   6.0   9.9    7.5    8.4
[I.sub.s]       33.0  26.0  40.0   36.0   33.7
                 5.5   4.1   5.6    6.0    5.3
[I.sub.F]        5.6   4.7   6.8    5.3    5.6
                23.4   7.3  10.1   18.5   14.8

(a) [DELTA][E.sub.b] values were produced by using equation (15).
(b) [DELTA]H values were produced by using equation (9).

ACKNOWLEDGMENTS

O. Pekcan would like to thank the Turkish Academy of Sciences (TUBA) for their partial support.

References

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S. Ugur and O. Pekcan -- Istanbul Technical University*

A. Elaissari -- Macromolecular Systems & Human Immunovirology ([dagger])

*Dept. of Physics, 80626 Maslak, Istanbul, Turkey.

([dagger]) CNRS-bioMerieux, UMR-2142 ENS de Lyon 46 allee d'Italie 69364 Lyon Cedex, France.