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0342744984
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note
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To be more specific, in the context of filmification from a dispersion of latex particles in water, the cross-linker agent is originally in the aqueous solution, and diffuses inside the polymer particles. We suppose in the text that this diffusion inside the polymer phases and the subsequent attachment reaction (our so-called "first step") are fast processes (compared to the polymer reactions), so that they are completed during the evaporation of the solvent, or very quickly after onset of contacts. Even further, in many real cases, not only the first step is finished at the time of contact, but the polymer-polymer reaction step has already begun inside individual particles, in the dispersed state. Such a premature cross-linking reduces the amount of mobile chains that will be available for interdiffusion when the particles come in contact (at t = 0).
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16
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0342700484
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note
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This statement is, in fact, somewhat inaccurate: when a site reacts, the number of chains that stop as a consequence depends on the nature of the partners of the reaction. If the reaction occurred between one A*X borne by a mobile chain and a A* borne by another mobile chain, then for a single reaction, two chains are stopped. If the reaction occurs between a mobile chain and a fixed one, then only one chain stops, and zero when it occurs between two fixed chains. However, one can show that these subtleties are not very significant at our scaling law level.
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19
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It has been shown by Schnell et al. (Schnell, R.; Stamm, M.; Creton, C. Macromolecules 1998, 31, 2284) that when two glassy samples of a high molecular weight polymer are put into contact and heated above the glass transition during a limited amount of time, so as to allow for a controlled amount of interdiffusion across the junction, the maximum of the adhesion strength is reached when the interpenetration has occurred over a distance comparable to the average length between entanglements (i.e., much earlier than the reptation time). This property highlights the important role of entanglements in the development of adhesion in glassy polymers.
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