Handbook of Modern Coating Technologies

Healing and interdiffusion

The entangled Gaussian chain incarcerated in a tube is treated with back-and-forth Brownian motion, in accordance with the reptation model [144]. Immediately after getting out of the tube, its free ends allow for the chain to drift in any direction so that it will become impossible to follow the initial tube position being lost step by step. In consideration of the dimension of length, the first escaper is also called "minor chain” [145,146]. Since this chain is in a form of sphere, its extension simultaneously stretches out the circumference (see Fig. 6—2A). Consequently when time comes to t = Tr, the complete chain is now out of the tube (i.e., forgotten its original configuration).
Assume that there is an interface between the latexes separating the polymer chains at t = 0. Subsequently prolonging minor chains initiate passing the interface to erase the particle—particle (interparticle) boundaries between the particles. This healing process (Fig. 6—2B) can be divided into two phase: first, the growing minor chains lose their ten¬sions and cover all the voids present in the interparticle interfaces. The distinctions between the particles existing at initial position were terminated in this phase, and however several different particles continue to have chains and intermingling has not been completed yet as recognized with the marked interparticle interfaces. Then, these have no memory because of the interdiffusion of chains between neighboring particles.
FIGURE 6-2 Disengagement of a Gaussian chain from its initial tube in reptation model. (A) The emergence and growth of minor chains. (B) Healing at particle-particle junction due to growing of minor chains. Tr, is the tube renewal time and dotted lines represent the tube created by the topological constraints imposed by the neighboring chains. Note that the particle—particle interface is initially rendered as a double line to emphasize the existence of space between the particles. The interface, rendered as a single straight line, is now threaded by a number of minor chains from either side, but not yet completely healed [39b]. 
Prager—Tirrell (PT) [147] makes an explanation for the relaxation of the configuration at the interparticle junction in which each polymer chain within a tube haphazardly under¬goes a reciprocation. The authors describe a homopolymer chain with a number of freely jointed segments N at length L for observation of the motion simply by each segment with a frequency n. The displacement downwards is seen at the bottom of the tube considering the quantity of segments m. The "diffusion coefficient” of m is corresponding to v/2 in one-dimensional movement. Furthermore the probabilistic estimation of the displace¬ment with m during time t in net can be provided with the number of segments equal to the difference between m — Д and m — (Д + dA). For early times a Gaussian probability density function is computed for N segments. The "crossing density” o-(t) refers to the quantity of chains falling to a unit area at the junction surface, and the overall calculation is made using the contributions oy(t) because all the chains are not cleaned inside the first tubes, and a remainder a2(t) to the contribution of any relaxed chains. Considering the reduced time
т 5 2vt/N2
where the diffusion coefficient of freely jointed segment of polymer chain is demonstrated with v, and its quantity with N, and the total crossing density is rewritten as follows:
where the running indexes of the series are represented as n (for the diffusion coefficient) and k (for the quantity). For smaller т values the summation term is negligible on the above equation, and then Eq. (6.9) becomes [145,147]
а(т)/O(N) 5 2n—1 /2T1 /2 (6.10)
This is a prediction of de Gennes based on scaling arguments.
6.3 Experimental results
6.3.1 Film formation from hard (high-7) latexes
6.3.1.1 Poly(methyl methacrylate) latex films
The latex particles used in this study were of high-T fluorescent PMMA and between 1 and 3 pm in diameter. Its molecular proportion to polyisobutylene (PIB) was identified as PMMA: PIB (96:4 per 100 mol), and thus interpenetration was enabled across the particles in a net-work [148]. The solubility of PIB is high in specific hydrocarbon media and its thinness of layer is useful for stabilization. The particles were labeled with P dye. The latex film was pre-pared in a series of procedures. Following dispersing and completely blending the P-labeled
particles in heptane confined to a test tube, a silica window plate round with a 2-cm diame-ter was largely dropped on by the dispersion. Before annealing the films upper than the glass transition temperature of PMMA for a half hour at 110°C—220°C, the heptane was evapo-rated to conduct the fluorescence experiments. LS-50 fluorescence spectrometer (Solid Surface Accessory;a Perkin Elmer Model) [46(b)] was used with the silica plate. The mea-surements were made in the front side of each film by keeping the temperature under the room conditions and the slits at 2.5 mm wide. Prior to casting the films, pre- and postweights of the silica plate were recorded for their thickness. The pyrene excitement was achieved at 345 nm within the fluorescence emission spectra from 340 to 500 nm at room temperature. The samples were all the time shielded from light with an exception of illumination for fluo¬rescence measurements. The maximum heights were designed at 345 nm for the scattered intensity, Isc and 395 nm for P intensity, Iop in each trial.
For a 3.5-layer latex film, Fig. 6—3 presents the typical values of emission (Iop) and scat-tered (Isc) spectra, and Fig. 6—4A and B presents the maximum peak intensities (Iop) and (Isc) corresponding to annealing temperature with a graph. The annealing process increased P intensity (Iop) up to the peak at 150° C where it started to decreased, whereas Isc constantly decreased as the annealing kept the temperature increasing higher than 120°C.
As mentioned in Section 6.2.1, Iop varies by the mean length of optical path s that a pho-ton takes in the film and directly proportionally by its probability of encountering a pyrene molecule. The film is getting annealed by the scattering photons from the latex surfaces. The mean length of free path (< r>) is higher for larger voids between the particles. Following a few steps, the ability of the photons to reemerge from the front surface considerably shortens the mean length of optical path s. In the healing process the photons are mostly scattered from the interfaces between the latexes after the first stage and then these are removed as

FIGURE 6-3 Emission (lop) and scattered (lsc) spectra of pyrene, after a 3.5-layer latex film sample was annealed at 100°C (—), 170°C ( ), and 200°C (...) temperatures for 30-min intervals and excited at 345 nm [21b].
 
well. In the first stage the mean length of free path increases depending on the particle size. With the equal quantity of rescatterings, photons will stay in the film in a prolonged way, increasing Iop. At the end of the second phase, the film gets crystal clear to diverge the mean length of free path r of a photon whose the mean length of optical path s approximates to the film thickness d.
Two-step healing process may account for the maximum Iop [46(b)] at the interparticle interface. Where the healing time (TH) and temperature is 30 min and 150° C, the interparti¬cle voids are covered by the half-way movement of the chains in neighboring particles across the interface surface. And then, the initial boundaries between the latexes disappear to make the latex film semitransparent so that the light photons can excite P molecules. Hence, the emission intensity Iop hits the peak. At 210°C, the film gets completely annealed and the intralatex interfaces disappears with full transparency, in which Iop diminishes again.