Gaussian string model

Macromolecules are modeled as Gaussian strings of beads and described using the same path-integral formalism as in SCFT. For a multicomponent system, the time-dependent distribution of bead density (r,t) is assumed to obey the following set of functional Langevin equations of motion ... 

Analysis of Eq. 3.6 reveals that the function C =/(f) tends to be Gaussian and approaches the Taylor model when N increases. On the other hand, the validity of this equation is dubious for low N values, as the shape of the curve skews. This means that the model provides good results when applied to unsegmented-flow systems with long reactors but fails to describe sample dispersion in short reactors. This limitation of the model is not as relevant to efficient mixing devices such as the single bead string reactor [5,52],... 

As discussed in Chapter 1, a Gaussian chain is physically equivalent to a string of beads connected by harmonic springs with the elastic constant ikT/lP (Eq. (1.47) with 6 given by Eq. (1.44)). Here each bead is regarded as a Brownian particle in modeling the chain d3mamics. Such a model was first proposed by Rouse and has been the basis of molecular theories for the dynamics of polymeric liquids. 34... 

An analytical approximation [23] can be found for the Gaussian chain melt by taking either the so-called thread or string limits. The thread-like chain model has been discussed in depth elsewhere [23]. Mathematically, it corresponds to the limit that all microscopic length scales approach zero but their ratios remain finite. In particular, the site hard core diameter d 0, but the site density pm - oo such that the reduced density, pmd , is non-zero and finite. In... 

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