Scaling laws for interdiffusion

According to the scaling laws for interdiffusion at a polymer-polymer interface, see Section 11.5.3, the initial diffusion rate as the chain leaves the tube goes as F representing a case of non-Fickian diffusion. An important example involves the interdiffusion of the chains in latex particles to form a film see Section 5.4.4. 

In these relations the reptation time, is related to the molecular weight, Af, via a. Values for r and s are given for the specific molecular properties in Table 1. The properties can be used to explore various molecular models proposed for welding and fracture of polymers. In this paper we investigate the scaling laws for interdiffusion based on the reptation model and examine the fractal nature of polymer interfaces. 

The reptation dynamics and the interface structure relations in Table 2 have been demonstrated experimentally by a series of interdiffusion experiments with selectively deuterated HDH/DHD polymer interfaces using dynamic secondary ion mass spectroscopy (DSIMS - see Secondary ion mass spectrometry) and neutron reflectivity. The scaling laws for interdigitation and the complete concentration profiles for Rouse and reptation dynamics have also been calculated. ... 

An alternative, simpler approach has been proposed in which crack growth is essentially considered the reverse of crack healing (105). In effect, disentanglement is taken to be the reverse of interdiffusion of molecules at the surfaces of two planes in close contact. Thus, assuming scaling laws for characterizing molecular reptation hold, it has been suggested that di/dN is proportional to the quotient of the distance of interpenetration x to too, the time required for complete molecular diffusion and interpenetration. Since and too ocM, then... 

Figure 5.12 Scaling law time dependence for two polystyrene latexes. The H135 material was composed of latexes of 325,000 g/mol polymer having hydrogen end groups. The SI35 material had —SO3 groups at the end of each molecule, with a molecular weight of 325,000 g/mol also. Particle sizes by transmission electron microscopy were in the range of 100-120 nm in all cases. Measurements were by SANS on samples annealed for interdiffusion at 135°C (79).

The fractal characteristics of a polymer diffusion front and the scaling laws, H(t) for interdiffusion were analyzed by a computer simulation of reptating chains. A reptation algorithm was used in which monomers were randomly added and subtracted from the ends of a Gaussian chain of JV-steps in two dimensions. The simulations were done on an... 

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