Polymer spinning model

R.M. Patel, A.K. Doufas and R.R Raradkar, Raman spectroscopy for spinline crystallinity measurements. II. Validation of fundamental fiber-spinning models, J. Appl. Polym. Sci., 109, 3398-3412 (2008). 

While the 0 -theory discussed in section 3.3 does not provide such averages it is essential that these can be performed in the framework of the MH model. With the effective Hamiltonian derived in section 2.4 it turns out that the moments correspond to the propagators of this theory with masses rk that reflect the fact that there is a distinct critical point associated to each moment, i.e. there is no multicritical point as in the spin models with finite numbers of components and as suggested by the d > 4 interpretation of the (j> polymer theory [39] in sect. 3.3. In extracting the scaling behavior of the moments gw or equivalently of the masses r the central quantities will be the terms linear in k in an expansion in A as suggested by Eq. (115). 

There still are challenges which have come about in extending the Edwards model to tethered membranes D = 2) [3]. The demonstration of the renormalizability of the resulting model is a topic of current research [10]. In this context there does not appear to be an equivalent spin model which describes self-avoidance in such objects. Further extension of these models to membranes and charged species is expected to be an important problem in the general area of soft-condensed-matter physics. A perusal of the literature on these topics is sufficient to appreciate the deep influence of the two landmark papers [4, 8] on polymer physics. 

LATTICE SPIN MODELS OF POLYMER-DISPERSED LIQUID CRYSTALS... 

Abstract Monte Carlo simulations of lattice spin models are a powerful method for the investigation of confined nematic liquid crystals and allow for a study of the molecular organization and thermod3mamics of these systems. Investigations of models of polymer-dispersed liquid cr3rstals are reviewed devoting particular attention to the calculation of deuterium NMR spectra from the simulation data. 

We have described lattice spin models for the simulation of polymer-dispersed liquid crystals. The biggest advantage of Monte Carlo simulations is the possibility of investigating the system at a microscopic level, and to calculate thermodynamic properties and their specific order parameters suitable for different types of PDLC. Molecular organizations can be investigated by calculating the order parameters point by point across the droplet. Moreover, it is possible to calculate experimental observables like optical textures and, as discussed here, NMR line shapes. We have given an overview of the method and some applications to models of PDLC with radial and bipolar boundary conditions, and considered the effect of orientational and translational diffusion on the spectra. We have examined in particular under what conditions the NMR spectra of the deuterated nematic can provide reliable information on the actual boundaries present in these submicron size droplets. 

NEMATICS WITH DISPERSED POLYMER NETWORKS FROM LATTICE SPIN MODELS TO EXPERIMENTAL OBSERVABLES... 

The main topics in lattice theories, which are relevant for the polymer subject are avoided random walk, lattice percolation [3] and lattice spin models. In this work we shall put the emphasis on the numerical investigation of the systems in the framework of lattice percolation methodologies and avoided random walks on square and cubic lattices. 

Several of functional Fe(III)- and Co(II)-phthalocyanines and their polymers as models for catalase, peroxidase, oxidase and oxygenase enzymes were synthesized ([265] and references cited therein). Copolyesters 62 containing Fe(III)- and Cu(II) phthalocyanines were obtained by polycondensation of phthalocyanine dicarboxylic acid dichlorides with terephthalic acid dichloride and aliphatic diols. Green or blue colored fibres could be obtained by melt spinning of the copolyesters containing below 1 mol% of the metal complex [265]. The polymers were investigated as catalysts for the thiol oxidation. 

Figure 23.15 for results obtained with the inside labeled polymers). The model provided an excellent prediction of the segmental dynamics of the PCHMA, while the experimental values for PCHA were somewhat higher than the predicted values. Nevertheless, these results implied that the region explored by the spin-label was comparable to the cube of the Kuhn length, as suggested by Lodge and McLeish. 

Figure 19.14 Schematic illustration of the basic setup for electrospinning, (a) The typical SEM image of nonwoven mat of polymer nanofibers, (b) CCD image of the stable con-jet spinning model. Photographs illustrating the instability region of a liquid jet and the capture time was on two different scales (c) 1/250 s and, (d) 18 ns. (Reprinted from Polymer, 42, Y.M. Shin, M.M. Hohman, M.P. Brenner and G.C. Rutledge Experimental characterization of electrospinning The electrically forced jet and instabilities, 9955-9967, 2001, with permission from Elsevier.)...

A relation between polymer statistics and phase transition was established by de Gennes (1979) and des Cloiseaux (1974) showing a correspondence between the polymer chain modeled by SAWs and the n-vector spin model of magnetization in the limit n 0. Similarities between correlation length (0 and the end-to-end distance (Re) can be noticed by compar-ing O Eqs. 8.12 and O 8.13. Correspondence between 1/N and -jr- is viewed as 0 and... 

We relate the high-temperature expansion of a one-dimensional w-component axis spin model to a polymer problem, as has been discussed elsewhere by us [50,107,... 

Application of Raman spectroscopy to obtain crystallinity data, on-line, during fiber spininning of polypropylene polymers is described. These data were obtained to develop validated fundamental fiber spinning models. These validated fiber spinning models will be used to guide fiber spinning for rapid product development. 

Fiber crystallinity data for fibers spun from two polypropylene resins was obtained, on a commercial fiber line, using on-line Raman spectroscopy. The experimental data presented here will be used to validate fundamental fiber spinning models. Results from the model validation/refinement will be are presented in a separate paper. The validated models and experimental observations can be used to guide fiber spinning of hPP polymers for rapid product development. Some key results obtained from the online Raman measurements can be summarized as follows... 

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