Molecular diffusion polymer

A first limit rate expression is obtained when surface rate contributions are rate determining.The concentration profile is plotted in Fig. 18.22. Although the use of Henry s law (Equation [18.1]) as boundary conditions is usually limited to the case of molecular diffusion (polymer membranes), it can also be used to describe permeation across metallic membranes with surface rate-determining step (rds). In such cases, the dissociative physisorption step of H2 into H is assumed to be fast and at equilibrium. Steps (3) and (5) of the sorption mechanism are rds and the relationship between surface hydrogen ad-atoms and pressure is given by Equation [18.8] ... 

Plate count should always be tested with a monodisperse sample of low molecular weight. Polymers can also be used, but they show much lower plate counts because their diffusion coefficients are much smaller than those of low molecular weight compounds. 

Measurements of diffusion of tracer polymers in ordered block copolymer fluids is another potentially informative activity, since molecular diffusion is one of the most basic dynamic characteristics of a molecule. Balsara, et al. have measured the retardation of diffusion due to ordering in the diffusion of polystyrene tracer homopolymers in polystyrene-polyisoprene matrices of various domain sizes [167]. Measurement of the tracer diffusion of block copolymer molecules will also be important. Several interesting issues are directly addressable via measurements... 

Attempts were made to determine number average molecular weights (Mn) by osmometry (Mechrolab Model 502, high speed membrane osmometer, 1 to 10 g/1 toluene solution at 37 °C), however, in many instances irreproducible data were obtained, probably due to the diffusion of low molecular weight polymer through the membrane. This technique was abandoned in favor of gel permeation chromatography (GPC). 

Optimization requires that a-rtjl have some reasonably high value so that the wall temperature has a significant influence on reactor performance. There is no requirement that 3>AtlR be large. Thus, the method can be used for polymer systems that have thermal diffusivities typical of organic liquids but low molecular diffusivities. The calculations needed to solve the optimization are much longer than those needed to solve the ODEs of Chapter 6, but they are still feasible on small computers. 

Polymerizations often give such high viscosities that laminar flow is inevitable. A t5rpical monomer diffusivity in a polymerizing mixture is 1.0 X 10 ° m/s (the diffusivity of the polymer will be much lower). A pilot-scale reactor might have a radius of 1 cm. What is the maximum value for the mean residence time before molecular diffusion becomes important What about a production-scale reactor with R= 10 cm ... 

The second phase of polymer degradation is characterized by a decrease in the rate of chain scission (Fig. 19) and the onset of weight loss. Weight loss has been attributed to (1) the increased probability that chain scission of a low molecular weight polymer will produce a fragment small enough to diffuse out of the polymer bulk and (2) the breakup of the polymer mass to produce smaller particles with an increased probability of phagocytosis. The decrease in the rate of chain scission, as well as the increased brittleness of the polymer, is the result of an increase in the crystallinity of PCL,... 

A quite different approach to rheo-NMR was taken by Xia and Callaghan [12], in an NMR microscopy measurement of the velocity profile of a high molecular weight polymer solution flowing through a capillary. In this study anomalous polymer diffusion was found at a radius within the pipe at which the local shear rate exceeded... 

The basic biofilm model149,150 idealizes a biofilm as a homogeneous matrix of bacteria and the extracellular polymers that bind the bacteria together and to the surface. A Monod equation describes substrate use molecular diffusion within the biofilm is described by Fick s second law and mass transfer from the solution to the biofilm surface is modeled with a solute-diffusion layer. Six kinetic parameters (several of which can be estimated from theoretical considerations and others of which must be derived empirically) and the biofilm thickness must be known to calculate the movement of substrate into the biofilm. 

JS Vrentas, JL Duda. Molecular diffusion in polymer solutions, AIChE J 25 1-24, 1979. 

Many polymers solidify into a semi-crystalline morphology. Their crystallization process, driven by thermodynamic forces, is hindered due to entanglements of the macromolecules, and the crystallization kinetics is restricted by the polymer s molecular diffusion. Therefore, crystalline lamellae and amorphous regions coexist in semi-crystalline polymers. The formation of crystals during the crystallization process results in a decrease of molecular mobility, since the crystalline regions act as crosslinks which connect the molecules into a sample spanning network. 

The separation is not totally orthogonal, as shown in Fig. 18.1, and is typical of most 2DLC separations (Kilz et al., 1995). Low molecular weight polymers that can diffuse into the packing pores exhibit both hydrophobic and size exclusion mechanisms in RPLC, and this mixed mechanism is shown by the Brij 70 series of peaks, dl through d3. The lower molecular weight material (dl) is more retained on the RPLC column since it can further diffuse into the pores. 

The monomers get absorbed in micelles resulting in their swelling. Water soluble initiators are used which form free radicals. Inorganic persulphates are commonly used as initiators. The initiator diffuses into a micelle and polymerisation proceeds. As more monomer is polymerised monomers from outside the micelle diffuse inside and the process continues when another radical enters the micelle the polymerisation stops. This technique can give high Molecular weight polymers. 

NMR is the most fundamental molecular specific probe of diffusion. Polymer motions and the spectroscopic signature of a given nucleus can be unambiguously related to a particular morphological domain. The size and time scale of the experiments are such that the fundamental hopping events of diffusing molecules can be sampled. 

Emulsion polymerisation is a special case of heterogeneous addition polymerisation in which the reaction kinetics are modified because the A are compartmentalised in small polymer particles [48, 49]. These particles are usually dispersed in water and reaction (78) occurs in the aqueous phase. Initiating radicals diffuse to the particles which are stabilised by surfactant material. Chain termination becomes retarded physically and a relatively high polymerisation rate is obtained. If chain transfer is not prominent, a high molecular weight polymer is produced. The polymerisation rate is given by the expression... 

Hirao A, Nishizawa H, Sugiuchi M (1995) Diffusion and drift of charge carriers in molecularly doped polymers. Phys Rev Lett 75 1787... 

Nonporous gel membranes - these membranes do not contain a porous structure and thus diffusion occurs through the space between the polymer chains (the mesh). Obviously in this case, molecular diffusion rather than convective transport is the dominant mechanism of diffusion in these membranes. 

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