Intraparticle polymers

Before scattering intensity measurements can be converted to molecular weights, the two corrections previously discussed—the dissymmetry correction for intraparticle interference and the extrapolation to zero concentration—must be introduced, or established to be negligible. The relationships given in the preceding sections unfortunately account rigorously for either only in the absence of the other. The theory of the concentration dependence of the scattered intensity applies to the turbidity corrected for dissymmetry, and the treatment of dissymmetry is strictly valid only at zero concentration (where interference of radiation scattered by different polymer molecules vanishes). 

Polymer-supported catalysts often have lower activities than the soluble catalysts because of the intraparticle diffusion resistance. In this case the immobilization of the complexes on colloidal polymers can increase the catalytic activity. Catalysts bound to polymer latexes were used in oxidation reactions, such as the Cu-catalyzed oxidation of ascorbic acid,12 the Co-catalyzed oxidation of tetralin,13 and the CoPc-catalyzed oxidation of butylphenol14 and thiols.1516 Mn(III)-porphyrin bound to colloidal anion exchange resin was... 

The effect of pore size on CEC separation was also studied in detail [70-75]. Figure 9 shows the van Deemter plots for a series of 7-pm ODS particles with pore size ranging from 10 to 400 nm. The best efficiency achieved with the large pore packing led to a conclusion that intraparticle flow contributes to the mass transfer in a way similar to that of perfusion chromatography and considerably improves column efficiency. The effect of pore size is also involved in the CEC separations of synthetic polymers in size-exclusion mode [76]. 

Following the intrusion branch with increasing pressure (Fig. 1.16A), the steep initial rise at low pressures is caused by the filling of interparticle spaces. The breakthrough pressure, i.e. the pressure when the voids between the particles are filled, follows in principle the theory of Mayer and Stowe [94], and is inversely proportional to the particle size [95]. The demarcation between interparticle spaces and actual intraparticle pores may be unclear for microparticles, but in the case of polymer beads from suspension polymerization having particle sizes between 50-500 pm, usually no interference occurs. The second rise of the intrusion branch is caused by pores inside the particles. Shown in Fig. 1.16A is a porous material of rather narrow pore size distribution. 

At one extreme diffusivity may be so low that chemical reaction takes place only at suface active sites. In that case p is equal to the fraction of active sites on the surface of the catalyst. Such a polymer-supported phase transfer catalyst would have extremely low activity. At the other extreme when diffusion is much faster than chemical reaction p = 1. In that case the observed reaction rate equals the intrinsic reaction rate. Between the extremes a combination of intraparticle diffusion rates and intrinsic rates controls the observed reaction rates as shown in Fig. 2, which profiles the reactant concentration as a function of distance from the center of a spherical catalyst particle located at the right axis, When both diffusion and intrinsic reactivity control overall reaction rates, there is a gradient of reactant concentration from CAS at the surface, to a lower concentration at the center of the particle. The reactant is consumed as it diffuses into the particle. With diffusional limitations the active sites nearest the surface have the highest turnover numbers. The overall process of simultaneous diffusion and chemical reaction in a spherical particle has been described mathematically for the cases of ion exchange catalysis,63 65) and catalysis by enzymes immobilized in gels 66-67). Many experimental parameters influence the balance between intraparticle diffusional and intrinsic reactivity control of reaction rates with polymer-supported phase transfer catalysts, as shown in Fig. 1. 

The affinity of the polymer-bound catalyst for water and for organic solvent also depends upon the structure of the polymer backbone. Polystyrene is nonpolar and attracts good organic solvents, but without ionic, polyether, or other polar sites, it is completely inactive for catalysis of nucleophilic reactions. The polar sites are necessary to attract reactive anions. If the polymer is hydrophilic, as a dextran, its surface must be made less polar by functionalization with lipophilic groups to permit catalytic activity for most nucleophilic displacement reactions. The % RS and the chemical nature of the polymer backbone affect the hydrophilic/lipophilic balance. The polymer must be able to attract both the reactive anion and the organic substrate into its matrix to catalyze reactions between the two mutually insoluble species. Most polymer-supported phase transfer catalysts are used under conditions where both intrinsic reactivity and intraparticle diffusion affect the observed rates of reaction. The structural variables in the catalyst which control the hydrophilic/lipophilic balance affect both activity and diffusion, and it is often not possible to distinguish clearly between these rate limiting phenomena by variation of active site structure, polymer backbone structure, or % RS. 

Intraparticle diffusion limits rates in triphase catalysis whenever the reaction is fast enough to prevent attaiment of an equilibrium distribution of reactant throughout the gel catalyst. Numerous experimental parameters affect intraparticle diffusion. If mass transfer is not rate-limiting, particle size effects on observed rates can be attributed entirely to intraparticle diffusion. Polymer % cross-linking (% CL), % ring substitution (% RS), swelling solvent, and the size of reactant molecule all can affect both intrinsic reactivity and intraparticle diffusion. Typical particle size effects on the... 

Variation in % CL of the catalyst support most likely affects intraparticle diffusion more than it affects intrinsic reactivity. Increased cross-linking causes decreased swelling of the polymer by good solvents. Thus the overall contents of the gel become more polystyrene-like and less solvent-like as the % CL is increased. Fig. 5 shows the... 

Macroporous and isoporous polystyrene supports have been used for onium ion catalysts in attempts to overcome intraparticle diffusional limitations on catalyst activity. A macroporous polymer may be defined as one which retains significant porosity in the dry state68-71 . The terms macroporous and macroreticular are synonomous in this review. Macroreticular is the term used by the Rohm and Haas Company to describe macroporous ion exchange resins and adsorbents 108). The terms microporous and gel have been used for cross-linked polymers which have no macropores. Both terms can be confusing. The micropores are the solvent-filled spaces between polymer chains in a swollen network. They have dimensions of one or a few molecular diameters. When swollen by solvent a macroporous polymer has both solvent-filled macropores and micropores created by the solvent within the network. A gel is defined as a solvent-swollen polymer network. It is a macroscopic solid, since it does not flow, and a microscopic liquid, since the solvent molecules and polymer chains are mobile within the network. Thus a solvent-swollen macroporous polymer is also microporous and is a gel. Non-macroporous is a better term for the polymers usually called microporous or gels. A sample of 200/400 mesh spherical non-macroporous polystyrene beads has a surface area of about 0.1 m2/g. Macroporous polystyrenes can have surface areas up to 1000 m2/g. 

Rates with 34 depended slightly on the particle size, whereas rates with 35 and 41 depended significantly on particle size. These results indicate that reactivity with 34 is limited mainly by intrinsic reactivity, and reactivity with 35 and 41 is limited by a combination of intraparticle diffusion and intrinsic reactivity. Such 1/r dependences of k0b8d are similar to those with polymer-supported benzyltrimethylammonium ion 2 and benzyltri-n-butylphosphonium ion 1. (See Fig. 4 and Table 1 in Sect. 3.1.2). 

As with polymer-supported onium ions the degree of cross-linking of the polymer support is likely to affect mainly intraparticle diffusion in reactions with polymer-supported crown ethers or cryptands. The activity of catalyst 37 decreased by a factor of about 3 as % CL with divinylbenzene changed from 1 % to 4.5 % 146). 

The introduction of a spacer chain between the polymer backbone and the active site is expected to facilitate intraparticle diffusion. Increased swelling power of sol-... 

The activity of polymer-supported crown ethers depends upon the degree of substitution of the polymer support. Fig. 11 reports dependence of kobsd on % RS and solvent for iodide displacement reactions (Eq. (4)) with catalysts 34,35 and 41149). The rate with 6% RS 41 was smaller than that with 17 % RS 35, though the former catalyst had a 7-atom spacer. Reduced % RS makes the catalysts more lipophilic, and results in the slower intraparticle diffusion of the KL Therefore, the lowest % RS catalysts... 

The activity of polymer-supported crown ethers is a function of % RS as shown in Fig. 11 149). Rates for Br-I exchange reactions with catalysts 34, 35, and 41 decreased as % RS increased from 14-17% to 26-34%. Increased % RS increases the hydro-philitity of the catalysts, and the more hydrated active sites are less reactive. Less contribution of intraparticle diffusion to rate limitation was indicated by less particle size dependence of kohMi with the higher % RS catalysts149). 

The activity of polymer-supported crown ethers depends on solvent. As shown in Fig. 11, rates for Br-I exchange reactions with catalysts 34 and 41 increased with a change in solvent from toluene to chlorobenzene. Since the reaction with catalyst 34 is limited substantially by intrinsic reactivity (Fig. 10), the rate increase must be due to an increase in intrinsic reactivity. The reaction with catalyst 41 is limited by both intrinsic reactivity and intraparticle diffusion (Fig. 10), and the rate increase from toluene to chlorobenzene corresponds with increases in both parameters. Solvent effects on rates with polymer-supported phase transfer catalysts differ from those with soluble phase transfer catalysts60. With the soluble catalysts rates increase (for a limited number of reactions) with decreased polarity of solvent60), while with the polymeric catalysts rates increase with increased polarity of solvent74). Solvents swell polymer-supported catalysts and influence the microenvironment of active sites as well as intraparticle diffusion. The microenvironment, especially hydration... 

Kim H, Kaczmarski K, Guiochon G (2006) Isotherm parameters and intraparticle mass transfer kinetics on molecularly imprinted polymers in acetonitrile/buffer mobile phases. Chem Eng Sci 61(16) 5249-5267... 

The situation becomes more complex if light scattering measurements are made at larger angles where there is intraparticle interference in the scattered light. The angular variation of intensity is related to the radius of gyration RG of the polymer. 

McKay G. and McConvey I.F., The external mass transfer of basic and acidic dyes by wood. J Chem Technol Biotechnol 31 (1981) pp. 401-408 McKay G., Blair H.S. and Gardner J., The adsorption of dyes in diitin II. intraparticle diffiision processes. JAppl Polymer Sci 28 (1983) pp. 1767-1778 Staszczuk P., Stefaniak E. and Dobrowolski R., Characterisation of thermally treated dolomite. Powder Technol 92 (1997) 257... 

Termination rate coefficients can be measured using the y-radiolysis relaxation method. This involves initiation using y-radiation, followed by removal of the reaction vessel from the y-source. Conversion during the relaxation period is monitored by dilatometry, and the decay in polymerization rate over time is related to the rate of radical loss. When large particles are used, radical loss is dominated by intraparticle termination, rather than exit into the aqueous phase, and the rate coefficient for termination can be determined from the decay curve. By using multiple insertions and removals, the termination rate coefficient is determined over a wide range of polymer mass fraction (wp). 

Petruzzelli, D., et al., Kinetics of ion exchange with intraparticle rate control Models accounting for interactions in the solid phase, Reactive Polymers, 7, 1, 1987. 

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