Handbook of Modern Coating Technologies

Void closure during latex film formation

In consideration of SSF and SEM results together with Monte Carlo simulations, it is evident that the film is optically clearer throughout the process using high-T latexes in relation to the void closure (refer Section 6.3.1). These observations enable us to quantify this phenomenon. In the section above, the maximum Iop has already been made clear with the void closure process through the flow of polymeric substance to cover up the interparticle voids. For observations, Eq. (6.8) can be employed under the assumption that the interparticle voids are dimensionally matching with one another and the quantity of voids remains unchanged throughout the film formation (i.e., p(r)« r—3), and when integrating Eq. (6.8) the following expression is produced:
where C represents a relative density constant p(r).
As mentioned above, the decreased void size (r) extends the mean length of free path (<l>) of a photon, in turn leading to higher Itr and Iop values. Frenkel's neck formation model [149] visualizes this process taking into consideration the identical contacting spheres influ¬enced by surface tension. In this model there is a presumption that the uniform redistribution of displaced volume keep the remaining surfaces spherical with larger radii providing longer mean length of free path (<l>) of a photon on its trip in the latex film. Fig. 6—11 illustrates Frenkel's model for neck formation using latexes [47(b)]. Assume that I(=IP and/or H) is inversely proportionate to the sixth power of void radius r then Eq. (6.11) can be rewritten as
(6.12)
FIGURE 6-11 Geometrical illustration of Frenkel's neck, where C is a constant related to relative density growth model between identical particles: (A) before and (B) after neck growth. R0, R, and r0 are the particle and void radii before and after neck growth, where R > R0 and r < r0.

where r-2 is excluded from the function because of its trivial size, compared with r~2 values measured following the start of void closure process. Eq. (6.12) can be used to solve for IP to evaluate the results in Fig. 6-10 as follows:
3 AH
I (T) = S(t)exp (6.13)
where S(t) = (Yt/2AC)3. At a prespecified time, the logarithmic form of Eq. (6.13) can be rewritten as
3AH
Lnl(T) = LnS(t) - —
As discussed before, the increases in Itr and IoP are caused by void closure. Therefore, Eq. (6.14) was applied to Itr at higher than T0 and to IoP at lower than Th for all the sample films. Fig. 6—12A and B illustrate the curves of LnItr and LnIoP corresponding to T-1 from which the activation energies ДHtr and AHoP are obtained (for the measurements see Table 6—3). It is observed that these remain steady a bit when annealing period is extended, that is, the heating amount needed for one mole of polymer to achieve a jump under the condition of viscosity in flow is stable with help of modifications on the annealing time inter¬val. The activation energies for viscous flow are measured and the variations are observed through several models, that is, AHtr values are observed to be a bit higher than those of AHoP. PS chain is labeled with pyrenes, and it is argued that AHoP values are more realistic to analyze the viscosity. However, AHtr values are generated from turbidity led by viscous flow. Namely, AHtr values were indirectly obtained in comparison to AHoP values.
As presented in Fig. 6—9, the peak values of Isc correspond to the levels for void closure (ta, Tv), hence Eq. (6.11) is rewritten as
Table 6-5 Experimentally produced activation energies.
Annealing time interval, ta (min)
5 10 20 30
AHtr (kJ/mol) 47.7 54.8 53.1 75.2
A HoP (kJ/mol) 35.9 41.4 37.2 32.2
AEb (kJ/mol) 312.2 220.7 309.7 480.7
AHtr, Activation energy of viscous flow (measured from /fr); AHop, activation energy of viscous flow (measured from i0p); AHb, activation energy of backbone motion (measured from /0p).

where S(rv) = 2AC/Yrv2 here rv is the minimum value of the void radius where Isc is at the highest level. The curve of ta corresponding to Tv and the logarithmic function of these fac¬tors are illustrated in Fig. 6—13A and B, respectively. The linearity slope in Fig. 6—13B offers AHv = 34.0 kJ/mol where fit goodness is obtained with the AHoP values in Table 6—5. This outcome is supportive for our arguments presented in the previous paragraphs.
The association of the decreased IP at higher than Th with the disappearance of the inter-particle interface is already achieved in Fig. 6—9. For the annealing temperatures higher than Th, a part of the polymer chains may jump over to the junction surface, the latexes start to lose their boundaries, and then IoP decreases when the mean length of optical path s of a photon is shorter. For comparative analysis of the observations in this study considering the crossing density of the PT model, the temperature dependence of а(т)/а( <х ) is determined for the linear diffusion coefficient using the Arrhenius relation
v = voexp( — AE/kT) (6.16)
where AE represents the activation energy variations for backbone motion between the tem-perature intervals.
The combination of Eqs. (6.10) and (6.16) provides an attractive expression as follows:
O(T)/O(N) = Roexp( - A.E/2kT) (6.17)
where the coefficient of Ro = (8vot/nN2)1/2 is independent from temperature.
From now on, an assumption can be made that there is an inverse proportion of IoP values and the crossing density a(T) and hence the phenomenological Eq. (6.17) can be rewritten as
І0Р (T)/IP (да) = R0-1exp( AE/2kBT) (6.18)
Fig. 6—15 displays the logarithmic graphs of IoP versus T-1 for annealing time intervals of 5 and 20 min, respectively. The activation energy of backbone motion ДЕ is generated by least squares method, fitting the data in Fig. 6—14 to Eq. (6.18) as listed in Table 6—5. The average value is computed as 330.8 kJ/mol, which is the activation energy much larger than required for void closure. It can be inferred that a single chain requires higher energy to carry out the interparticle interface diffusion than to accomplish by viscous flow.
The maximum values of IoP refer to the healing point (ta, Th) where the minor chain of (1 — 1/e) jumps over to the interparticle interface. To analyze the data of (ta, Th), Eq. (6.10) is rewritten at the healing point as
ta = Bexp( ДEh/kTh) (6.19)
where B = (a(T)/o-(x>))(nN2/8V0) is fixed at a given time and temperature. Eq. (6.19) can be applied to generate the healing activation energy, ДЕЙ. Fitting Eq. (6.19) to the data of (ta, Th) is obtained in Fig. 6—15A, where the tangent of the straight line gives the ДЕЙ value as 49.4 kJ/ mol, which is expectedly lower than ДЕЪ. There is a requirement of the minor chain to have lower energy for its achievement of traveling across the polymer—polymer interface than the whole chain, and thus the correctness holds for the mentioned proposition at any trial.
Consequently the minimum temperature of film formation, T0 is found via the Arrhenius function:

rh1(°K1)x!03 Г01(0К1)х103
ta = Bexp( ДД, /kT(j) (6.20)
to find out the minimum energy ДЕ0 required for the latex particles to create a film. Fig. 6—15(B) exhibits the fitness of (ta, T0) to Eq. (6.20). As shown in Fig. 6—15(B), the curve slope gives the minimum activation energy ДЕ0 appeared as 34.9 kJ/mol in film formation. ДЕ0 is actually so approximate to the activation energy for viscous flow, ДНоР, that is, the minimum energy of film formation is the energy necessary to make the polymeric substance more viscous. We conclude that the ideal fit is established between the basic kinetics of void closure, healing and interdiffusion and the fluorescence and UV visible (UVV) data.
6.3.1.3 Film formation using nanosized polystyrene latexes
The surfactant-free latex particles can be obtained from the nanosized (100 nm) PS material using emulsion polymerization technique [66]. Pyrenes are exclusive markers to label their surfaces. Five different films are obtained through dispersion of latex particles by means of water evaporation at room temperature (refer Section 6.3.1.2). Afterwards, the annealing times are defined as 5, 10, 15, 20, and 30 min for each sample, with varying temperatures from 90°C to 350°C. The annealing process excites P at 345 nm, and the detectible range of monomer (IP) and excimer (IE) fluorescence emission spectra are observed to be between 300 and 600 nm for the latex films by annealing for 10 min with rising temperatures (see Fig. 6—16). IE increases as the thermal degree is raised in the film annealing. By the way, the IP value of the latex film decreases for the excimer formation at the first phase. Going ahead to anneal the latex film results in a decrease in the intensity IE and an increase in the inten¬sity IP. The ratio of IE/IP is plotted in Fig. 6—17A and Itr values in Fig. 6—17B corresponding to annealing temperature T in a 10-min period for annealing. It is observed that with rising temperature, the IE/IP ratio first increases to a certain point (at Th) and then decreases while Itr values decreases to a certain point and then increases. The only temperature of sudden
FIGURE 6-16 Monomer (/P) and excimer (lE) spectra of latex films after being annealed for 10 min at (A) 100°C, (B) 150°C, and (C) 250°C [64c].

FIGURE 6-17 Plot of (A) /E//P and (b) ltr versus annealing temperature for the films annealed in 10 min time
decrease in Itr is called as void closure temperature Tv, and the temperature where the ratio of IE/Ip hits the peak as the healing temperature Th.
For any probability, the higher IE/IP agrees to the void closure up to the healing tempera-ture Th [66]. The lower values of IE/Ip at higher than Th indicate the polymer chain interdiffu-sion. Fig. 6—18 illustrates the behavior of IE/IP using the diagrams. As for Fig. 6—18A, the powder film contains a great amount of voids and fluorescence emission occurs with the pyr-ene monomers at the beginning of film formation. Fig. 6—18B displays an image of film where the interparticle voids disappear after annealing and excimer emission partly starts so that pyrenes become adjacent in greater quantity.
Immediately after filling the voids, healing process starts coupling most of the pyrenes [66] emitting only excimer fluorescence as presented in Fig. 6—18C. This phase experiences the maxima of IE/IP. With the interdiffusion process the pyrenes are completely blended across the latex film upon further annealing and begin to emit only monomer fluorescence and show a lower value of IE/IP. However, void closure process ends with disappearance of the p—p interfaces and scattering of most of the incident light at the lowest Itr value. After

FIGURE 6-18 Pictorial representation of film formation from PS particles (A) before annealing, (B) film with no voids, (C) film with no particle-particle interfaces, and (D) film after interdiffusion process is completed. PS, Polystyrene [64c].
FIGURE 6-19 AFM micrograph of PS particles (A) before and (B) after annealed at 170°C for 10 min. AFM, Atomic force microscopy; PS, polystyrene [64c].
that, film turns pellucid in the interdiffusion process with rising Itr at high temperatures of annealing. Pre- and postannealing AFM images of the latex film (at 170° C) are displayed in Fig. 6—19A and B, respectively, all the interfaces are eliminated by annealing processes.
As stated above, the decreased void size (radius, r) increases the IE/Ip ratios. Assume that the ratio of IE/IP is inversely proportionate to the sixth power of void radius r, Eq. (6.11) is rewritten where S(t) = (jt/2AC)3. In accordance with the previous argument, the increase in IE/IP is derived from void closure process
IE 3AH
T™ = S»“4"5r (6'21)
then Eq. (6.21) is used for IE/I at lower than Th for the sample films. Fig. 6—20A and B exhi¬bits the curve of ln(IE/I ) corresponding to T21 following the annealing at both temporal intervals of 10 and 15 min, and the computed activation energies (Дй) are presented in
FIGURE 6-20 Logarithmic plots of IE/IP data below the healing point versus inverse of annealing temperatures (T21) for the films annealed at (A) 10 min and (B) 15 min time intervals. Slopes of the straight lines produce AH values which are listed in Table 6-6 [64c].
Table 6-6 Experimentally produced activation energies.
Annealing time interval, ta (min)
5 10 15 20 30 Average
AH (kJ/mol) 7.3 8.9 11.5 10.6 13.0 10.3
A E (kJ/mol) 51.1 57.1 18.0 38.4 86.9 50.3
AH, Activation energy of viscous flow; AE, activation energy of backbone motion.

Table 6-6. It is observed that activation energies change a bit through the extensions of annealing time, that is, varying these intervals remain ineffective for the heating requirement by one mole polymer so that it can jump along with viscous flow.
The AH values here are observed to be three times smaller compared with the PS latex films (from 1-pm particles) as mentioned in Section 6.3.1.2. With this, it is realized that the energy requirement are much lower for viscosity of nanoparticles than that for micron-sized systems within the process of film formation.
Fig. 6—17B graphs the minima of Itr corresponding to the void closure coordinates (tv, Tv), then Eq. (6.11) is rewritten as:
tv = S(rv)exp (AHv/kTv) (6.22)
S(rv) = 2AC/7^ is present where rv is the minimum length of void radius in which Itr is the lowest and tv is corresponding to the annealing period at Tv. Fig. 6—21A displays tv curve corresponding to Tv, and their logarithmic function is shown in Fig. 6—21B. The increasing annealing temperatures expectedly diminish tv values, that is, at higher temperatures the annealing intervals should be less for void closure.
In Fig. 6—21B the slope of the linear function is equal to AHv = 27.9 kJ/mol which is three times greater than the value calculated using the excimer data. In this phase, it is
inappropriate to judge the gap between ДН and ДИ values calculated using the data of IE/ IP and Itr, respectively.
The decreased values of IE/IP at higher than Th have been associated with the disappear-ance of the interparticle interfaces, that is, with rising temperatures for annealing, the cross-ing density o-(T) becomes higher since a greater amount of chains release across the junction surface. Thus, it could be presumed that the ratio of IE/IP is inversely proportionate to o-(T), and so this phenomenon can be rewritten as:
!EI!P!T\ 5 Vexp (ДЕ/2квТ) (6.23)
IE/IP t N)
Logarithmic curve of IE/IP corresponding to T-1 are illustrated in Fig. 6—22A and B where the annealing time intervals are 10 and 15 min, respectively. The values of ДЕ are estimated through least squares method by means of the data in Fig. 6—22 fitted to Eq. (6.23) as listed
(A)
0
180 210 240 270 1.9 2.0 2.1 2.2
Th(C) Th 1xl03(°K1)
in Table 6-6. The mean value is computed as 50 kJ/mol, highly greater than the activation energies for void closure.
This result is understood in accordance with the statements given in the previous section. However, the obtained value, AE for the nanosized PS system (100 nm) is six times lower than the micron-sized (1 pm) PS system [66] (see Section 6.3.1.2). This discrepancy may account for high degrees in annealing temperature for the nanosized PS system because of less energy requirement for the chains to fulfill reptation across the interparticle interface.
The relationship of the maximum values of 1E/1P to the healing point (th, Th) has been stated in Section 6.3.1.2, and these are plotted in Fig. 6—23A. It can be observed that as th increases, Th decreases to run the healing process with minor chains throughout film forma-tion. The fit of Eq. (6.19) to the information in Fig. 6—23A is shown in Fig. 6—23B, where AEh can be determined with the tangent of the straight line as 38.5 kJ/mol expectedly lower than AE. The minor chain requires less energy than the whole chain for movability across the interparticle interface.
6.3.1.4 Fast transient fluorescence technique in latex film formation
6.3.1.4.1 Vapor—induced latex film formation using fluorescence quenching method
PMMA—PIB latexes are individually prepared in two phases. The detailed information are released in another report [150]. The high-Tg dispersion is stable using polymer spherical particles varying from 1 to 3 pm in radius. Both 1H-NMR and UV analyses reveal that these particles contain 6 mol.% PIB and 0.037 mmol of any compound included in the pyrene group per gram of polymer. The latex film preparation is completed in the way that the dis-persion is made using equal amounts of pyrene-labeled particles in heptane inside a test tube containing solids at the rate of 0.24%. And then the sample films are provided with a specific number of dispersion drops on a glass plates (2.5 X 0.8 cm2), monitoring the heptane evaporation. The samples are weighed pre- and postcasting to quantify the thickness. In the study, each film was observed to be c. 20 pm thick on average. For seven trials, each of seven
films whose latex content was the same were prepared using P-labeled PMMA particles as described above and exposed to vapor of different blends of chloroform and heptane.
For the group of pyrenes, the fluorescence lifetime is monitored throughout the process of film formation induced by vaporization. The strobe method attributed to fast transient fluorescence (FTRF) is used for estimation of these durations. In this technique or pulse sampling [151] a pulsed light source excites each sample. Its name is originated from the fact that a voltage pulse gates or strobes the PMT in synchronization with the light source pulsed. For fluorescence emission, the intensity can be digitally measured based on a time window that is very narrow on each pulse. Every time window is changed following a pulse. PMT is forced to be off by the strobe which enables to measure the emission intensity in a time win¬dow with short period. The sampling out of the population within a proper time interval can establish a decay curve to graph the trend of fluorescence intensity by time. The primary advantage of the strobe technique [151] is the time requirement for each trial, which is just a couple of few seconds. By means of such an advantage lifetime experiments (more than 40 or 50) were conducted for the formation of latex films which lasts one hour at least. All the measurements were vertically made in this study, and slit breadths were maintained at 20 nm. The quartz cells (1 X 1 cm2) placed in the SMS were used for trials. The decay curve of fluorescence represents the three-decade data of decay days [152]. Each sample was placed in a quartz cell containing a blend of chloroform and heptane present at the bottom. When the films were illuminated with 345-nm excitation light, P fluorescence emission became detectible at 395 nm. As a supportive trial, the intensity data of transmitted lights Itr from the films were recorded throughout the formation process, as well.
Fluorescence quenching: an organic dye is electronically excited by light absorption;then fluorescence appears from the lowest excited singlet state and decays in a couple of nanose-conds as usual [133]. Besides the unimolecular decay pathways for inversion of the excited states, different bimolecular interactions may also allow for deactivation. All these quenching processes promote the decay rate of an excited state intensity I represented by
I = Aexp ^ (6.24)
where A represents the preexponential factor, and т the lifetime that specifies the decay time for individual excited state. In Eq. (6.24) this is defined by the observable decay intensity. The decays are commonly exponential for the diluted dispersions of dye molecules on the isotropic media. What is frequently observed in higher complex systems is a set of deviations. Under these circumstances the mean decay time <T > determines the state of decay.
Fluorescence emission refers to a radiative transition from its singlet excited state to its ground state of an electronically excited molecule [136]. Fluorescence quenching typically means any bimolecular process occurring between the excited singlet states of a fluorescence dye and an alternative species to accelerate the decay rate of the excited state. This process may schematically represented as
kf ;knr

where F represents the fluorescent molecule, and F* its excited form, Q the quencher, and kf, knr, and kq the fluorescence, nonradiative, and quenching rate constants, respectively. Quenching can be led by different types of processes. In kinetics, there are dynamic and static quenching processes. For dynamic category, diffusion occurs to form a facing pair dur¬ing excited state lifetime of the dye, whereas for static one, diffusion is found unattractive by researchers. Fluid solution is necessary for occurrence of the first category since the dye or quencher is freely portable. When a single rate coefficient (kq) and a unique lifetime (T0) determine the quenching rate and the unquenched decay rate of F, respectively, the quench-ing kinetics will follow the Stern—Volmer equation:
T-1 = T-1 1 kq[Q] (6.27a)
where [Q] stands for the Quencher concentration, and kq is calculated using the expression such as:
kq = 4nNADR X 10 3 (6.27b)
In Eq. (6.27b), D is the sum of the mutual diffusion coefficients of the dye and quencher, inversely depending on the medium viscosity via the Stokes—Einstein function [133]. R is the total of their interaction radii while NA represents Avogadro's number.
Fig. 6—24 displays the fluorescence decay profiles of P on different stages of film forma-tion. It is determined that the excited P decays faster with increasing the vapor exposure time te and thus the excited P quenches at a higher level. The quasicontinuum of states can be achieved with the help of the solvent molecules for satisfying the energy resonance condi-tions; that is, the vapor molecules support rapid vibrational relaxation as an energy sink, which occurs following the rate controlling transition from the initial state. Birks et al. [153] investigated the effects of solvent viscosity on the fluorescence behavior of P solutions in dif-ferent solvents and concluded that the monomer internal quenching rate depends on solvent quality. To query the film formation caused by vaporization, the fluorescence decay curves are evaluated and fitted to Eq. (6.27a). Linear least-squares analytical technique is used to estimate the values of A and T at each step of film formation.
Lifetimes: Fig. 6—25A—C presents the measurements T for the trials of film formation while the chloroform contents are 30%, 50%, and 80%, where exponential decrease is viewed with rising te.
For quantification of the behavioral outcomes, a Stern—Volmer quenching mechanism is suggested for the P fluorescence decay in latex film during the formation process resulted from vaporization potentially using Eq. (6.27a). For poor efficiency of quenching, T0kq[M] < 1;Eq. (6.27a) becomes
where [M] represents the quencher or vapor concentration at the time te. The association of the P lifetime and [M] in the film can be almost captured through integration of the volume of Eq. (6.28) and the relationship
Ст > M
= 1 - C
. T 0 > MN
where = T0kqMN/v (v, the volume of the film). The differential volume equation offers the estimation of vapor sorption using the following equality:
where dv is the differential volume in the film, and the integration is made in the range from 0 to d, the film thickness, and MN the amount of vapor sorption at an infinite time.
When comparing our findings with the crossing density of the PT model, we can rewrite Eq. (6.10) as
a(r)/a( N ) = Rt1/2 (6.31)
where R = (8u/n) 1/2N-1. In combination of Eq. (6.30) with Eq. (6.31) it is assumed that there is a proportion between vapor penetration and the chain interdiffusion based on plasticiza¬tion, that is, the increased vapor sorption also increases crossing density, we get the relation
1 - < T > = Bt1/2 (6.32)
< T0 >
where B = CR. The data from Fig. 6—25A—C are plotted in accordance with Eq. (6.32) as illustrated in Fig. 6—26A—C, respectively. The slopes of the linear functions in Fig. 6—26 result in the values of B where the reptation frequency, и is the sole parameter while the others in C and R are fixed throughout the film formation process. Fig. 6—27 displays a dia-gram of B values corresponding to percentage chloroform; B values increase with rising frac-tion of chloroform.
This behavior can be interpreted through a proposal that polymer chains reptate at high-er frequencies within the processes of film formation, resulting in large B values, when the exposure level of chloroform vaporization is high. It is very likely that greater B values are led by higher values of crossing density because of fast reptation of polymer chains.
Transmitted light intensities: the intensity values related to light transmission were col-lected to prove the abovementioned observations;that is, the higher the chloroform content
FIGURE 6-26 Plots of the data in Fig. 6—25 according to Eq. (6.32), where linear least squares fits are performed [152].

Chloroform (%)
FIGURE 6-27 Plot of B values versus percentage chloroform in the solvent mixture [152].

is the more the interparticle interfaces disappear due to interdiffusion of chains in higher densities. Namely, crossing density increases with enlarging chloroform content. Standardized intensities of transmitted light, Itr, are plotted in a graph corresponding to vapor exposure time, te, as illustrated in Fig. 6—28 for seven different latex films with seven separate contents of chloroform vapor. Fig. 6—28 shows that Itr values increase when te values are raised, which indicates that the latex films turn higher transparent to light. Lower Itr values with less chloroform (30% and 40%) imply that the film formation induced by vaporization has remained incomplete for these samples. With greater chloroform, Itr values increase faster and the saturation values are greater. It is subjectively assessed that such behavior of Itr tends to help the sample films turn pellucid in much quickness due to their exposure to more chloroform vapors. From now on, it is assumed that Itr is proportionate to the crossing density, o-(t), in Eq. (6.10), provided that the following phenomenological equa-tion is rewritten [152]:
5 Rtl'2 (6.33)
Itr (t„) e v J
This assumption involves the disappearance of the interparticle interfaces thanks to chain interdiffusion so that Itr can become higher. The curves plotted the data from Fig. 6—28 using Eq. (6.33) are displayed in Fig. 6—29A—C for the samples with 30%, 50%, and 80% chloroform content, respectively. The void closure mechanisms in the film formation process underlies the early deviations. The slopes of linear parts in Fig. 6—29 give R values which are plotted corresponding to chloroform (%) in Fig. 6—30A. As expected, R values increase at higher chloroform in the solvent mixture, which indicates that reptation frequency и esca-lates with increasing role of plasticization. By comparison of the obtained results based on
the data of lifetime and transmitted light intensity, the normalization of BN and RN values are shown in a plot corresponding to chloroform (%) in Fig. 6—30B, where these parameters exhibit resemblance in their acts.