Monomer Diffusion Coefficient Research Articles

Precipitation of Zinc Sulfide Particles from Homogeneous Solutions

Zinc sulfide particles were homogeneously precipitated by thermal decomposition of thioacetamide in acidic aqueous solutions in a one-step process. The influence of the operating conditions (initial concentration of zinc ion and TAA) on the nucleation time and number concentration of the generated particles was investigated. The experimental results show that the model of homogeneous nucleation previously developed and successfully tested for silver particle generation by a chemical reduction method can also be applied to the formation of zinc sulfide particles by homogeneous precipitation. Furthermore, in the particle formation method in which the nucleation time t* can be measured, the particle number concentration n* can be predicted by the simple relation n*=1/(4πr*Dt*) (r* is the critical nucleus radius, and D the monomer diffusion coefficient). Thus the particle number concentration can be easily predicted even if the rate expression and the critical supersaturation concentration are unknown.

Modeling of low-temperature depolymerization of poly (methyl methacrylate) promoted by ion beam

The role played by the ion beam in the depolymerization of poly(methyl methacrylate) (PMMA) is the creation of initiators for the unzipping reaction at relatively low temperatures [lower than the ceiling temperature of PMMA (TC=220 °C)]. Monomer (MMA) evolution out of the polymeric film is thus governed by the kinetics of the chemical reaction and also by the diffusion of monomer inside the polymeric film. In this work this phenomenon has been described by using simple models in which both one- and two-dimension monomer diffusion is considered. Exact analytical solutions of the models are provided. The theory fit well the experimental data and allows for the determination of important parameters such as the kinetics constant of the depolymerization and the monomer diffusion coefficient, D, inside the polymer film. Thus, the pulsed ion beam technique, here modeled, is useful not only for extracting D values of slow diffusants in polymers, but even for measuring kinetics constants of depolymerization at a temperature well below that needed for the formation of suitable thermal initiators.

Modeling Insight into the Diffusion-Limited Cause of the Gel Effect in Free Radical Polymerization

The molecular-level cause of the gel effect in free radical polymerization, associated with a decrease in the termination rate parameter with increasing conversion, is studied by experimental and modeling approaches. The predictive Vrentas−Duda free volume theory serves as a basis for modeling as it handles quantitatively the temperature and polymer concentration dependencies of monomer diffusion. The polymer concentration (c) dependencies of various diffusional processes fit an expression of the form [Dm(c)/Dm(0)]ξx,m, where Dm is the monomer diffusion coefficient and ξx,m expresses the power-law dependence of the diffusional process of interest (x) relative to that of monomer (m). Relevant values of ξx,m vary from ∼ 0.8 for segmental mobility, to ∼1−2 or 3 for oligomeric diffusion, to ∼ 3.0−3.5 for unentangled polymer diffusion, and to ∼ 9.5−10 for entangled polymer diffusion. If the very high conversion regime, where issues unrelated to the origin of the gel effect add unnecessary complications, is avoided, the modeling of conversion−time data requires only that the polymer concentration dependence of the termination reaction, caused by a diffusional process cited above, must be taken into account. Comparison of ξx,m values needed to fit various methyl methacrylate conversion−time data (values of 1.1−5.0 were required, increasing with increasing molecular weight of the polymer produced) with those needed for different diffusion types indicates that termination is governed by diffusion of the shortest radical chains present in significant number. In contrast to some “short−long” termination theories that commonly distinguish “short” and “long” as unentangled and entangled, this study finds that entanglements are irrelevant in distinguishing “short” from “long”. Styrene polymerizations yield ξx,m values substantially below 1. This is ascribed to chain transfer, supported by the fact that methyl methacrylate systems with chain transfer agent show similar suppressed gel effect behavior. The very low ξx,m values result in part from the reduced polymer concentration dependence of kt associated with the highly mobile short radical chains obtained in chain transfer reactions. While systems with significant chain transfer must be studied further, this modeling approach should serve as a robust basis for a more complete description of termination under various conditions.

Measuring actin dynamics in endothelial cells.

Cytoplasmic actin distributes between monomeric and filamentous phases in cells. As cells crawl, actin polymerizes near the plasma membrane of expanding peripheral cytoplasm and depolymerizes elsewhere. Thus, the finite actin filament lifetime, the diffusivity of actin monomer, and the distribution of actin between the polymer and monomer phases are key parameters in cell motility. The dynamics of cellular actin can be determined by following the evolution of fluorescence in the techniques of photoactivated fluorescence (PAF) or fluorescence recovery after photobleaching (FRAP) of microinjected actin derivatives. A mathematical model is discussed that measures monomer diffusion coefficients, filament turnover rates, and the fraction of actin polymerized from measurements of the evolution of fluorescence from a photoactivated band [Tardy et al. (1995) Biophys. J., 69:1674-1682; McGrath et al. (1998) Biophys. J., in press]. Applying this model to subconfluent endothelial cells shows that approximately 40% of the actin is polymer and that these filaments turn over on average every 6 minutes. This report discusses how PAF and FRAP can be combined with more traditional biochemistry to probe actin cytoskeleton remodeling in endothelial cells.

Measuring actin dynamics in endothelial cells

Cytoplasmic actin distributes between monomeric and filamentous phases in cells. As cells crawl, actin polymerizes near the plasma membrane of expanding peripheral cytoplasm and depolymerizes elsewhere. Thus, the finite actin filament lifetime, the diffusivity of actin monomer, and the distribution of actin between the polymer and monomer phases are key parameters in cell motility. The dynamics of cellular actin can be determined by following the evolution of fluorescence in the techniques of photoactivated fluorescence (PAF) or fluorescence recovery after photobleaching (FRAP) of microinjected actin derivatives. A mathematical model is discussed that measures monomer diffusion coefficients, filament turnover rates, and the fraction of actin polymerized from measurements of the evolution of fluorescence from a photoactivated band [Tardy et al. (1995) Biophys. J., 69:1674–1682; McGrath et al. (1998) Biophys. J., in press]. Applying this model to subconfluent endothelial cells shows that ∼40% of the actin is polymer and that these filaments turn over on average every 6 minutes. This report dicusses how PAF and FRAP can be combined with more traditional biochemistry to probe actin cytoskeleton remodeling in endothelial cells. Microsc. Res. Tech. 43:385–394 © 1998 Wiley-Liss, Inc.

Reliable determination of kinetics parameters of adatoms in thin-film epitaxy

We show that in an interrupted step-flow epitaxy on a vicinal surface, the decay of adatom monomer density on terraces after deposition often has a simple dependence on the monomer diffusion coefficient D, the step-edge sticking probability S, and the extra step-edge energy barrier ${E}_{\mathrm{step}}$ (Schwoebel-Ehrlich barrier). One may reliably determine these kinetics parameters by examining the dependence of the decay rate constant on the average terrace width and the temperature. Such a decay can be monitored by either reflection high-energy electron diffraction or optical reflectance difference techniques.

Measurement of Diffusion Coefficients of Oligomeric Penetrants in Rubbery Polymer Matrixes

The diffusion coefficients of oligomeric radicals in monomer-polymer systems have a major influence on properties such as polymerization rates and molecular weight distributions. The present work reports the results of an extensive set of studies of diffusion coefficients of rubbery ternary systems comprising polymer, diluent, and oligomer, determined by pulsed-field-gradient NMR, at 25 and 40 degrees C. Oligomers of methyl methacrylate (MMA) and of butyl methacrylate (BMA) were synthesized by using a catalytic cobalt chain transfer agent to produce macromonomers with a terminal double bond. Where necessary, these were fractionated by preparative GPC to obtain samples ranging from dimeric to decameric; typical polydispersities were 1.08. Pulsed-field gradient NMR is facilitated by being able to monitor the proton NMR of the CH2 hydrogens on the double bond. Matrixes used were high molecular weight polyMMA and polyBMA, the weight fraction of polymer (w(p)) being varied by adding appropriate amounts of diluent (the saturated equivalents of MMA and BMA, viz., methyl isobutyrate and butyl isobutyrate). Above c* (the concentration at which chains start to overlap), all data for diffusion coefficients Di of an oligomer of degree of polymerization i could be fitted with acceptable accuracy by D-1(w(p))/D-i(w(p)) = i(0.664+2.02wp), for both BMA and MMA oligomers in both MMA and BMA matrixes; the same relation also fits earlier data on styrene oligomers in polystyrene. If more accurate scaling parameters are obtained experimentally for smaller oligomers, these can be used to predict data for higher oligomers with even better reliability. For MMA monomer in pMMA, where free-volume parameters are available, the predicted dependences of monomer diffusion coefficient on w(p) and temperature are in accord with experiment.

Simultaneous Measurements of Actin Filament Turnover, Filament Fraction, and Monomer Diffusion in Endothelial Cells

The analogous techniques of photoactivation of fluorescence (PAF) and fluorescence recovery after photobleaching (FRAP) have been applied previously to the study of actin dynamics in living cells. Traditionally, separate experiments estimate the mobility of actin monomer or the lifetime of actin filaments. A mathematical description of the dynamics of the actin cytoskeleton, however, predicts that the evolution of fluorescence in PAF and FRAP experiments depends simultaneously on the diffusion coefficient of actin monomer, D, the fraction of actin in filaments, FF, and the lifetime of actin filaments, τ (Tardy et al., 1995, Biophys. J. 69:1674–1682). Here we report the application of this mathematical model to the interpretation of PAF and FRAP experiments in subconfluent bovine aortic endothelial cells (BAECs). The following parameters apply for actin in the bulk cytoskeleton of subconfluent BAECs. PAF: D = 3.1 ± 0.4 × 10 −8 cm 2/s, FF = 0.36 ± 0.04, τ = 7.5 ± 2.0 min. FRAP: D = 5.8 ± 1.2 × 10 −8 cm 2/s, FF = 0.5 ± 0.04, τ = 4.8 ± 0.97 min. Differences in the parameters are attributed to differences in the actin derivatives employed in the two studies and not to inherent differences in the PAF and FRAP techniques. Control experiments confirm the modeling assumption that the evolution of fluorescence is dominated by the diffusion of actin monomer, and the cyclic turnover of actin filaments, but not by filament diffusion. The work establishes the dynamic state of actin in subconfluent endothelial cells and provides an improved framework for future applications of PAF and FRAP.

Interpreting photoactivated fluorescence microscopy measurements of steady-state actin dynamics

A continuum model describing the steady-state actin dynamics of the cytoskeleton of living cells has been developed to aid in the interpretation of photoactivated fluorescence experiments. In a simplified cell geometry, the model assumes uniform concentrations of cytosolic and cytoskeletal actin throughout the cell and no net growth of either pool. The spatiotemporal evolution of the fluorescent actin population is described by a system of two coupled linear partial-differential equations. An analytical solution is found using a Fourier-Laplace transform and important limiting cases relevant to the design of experiments are discussed. The results demonstrate that, despite being a complex function of the parameters, the fluorescence decay in photoactivated fluorescence experiments has a biphasic behavior featuring a short-term decay controlled by monomer diffusion and a long-term decay governed by the monomer exchange rate between the polymerized and unpolymerized actin pools. This biphasic behavior suggests a convenient mechanism for extracting the parameters governing the fluorescence decay from data records. These parameters include the actin monomer diffusion coefficient, filament turnover rate, and ratio of polymerized to unpolymerized actin.

A Mathematical Approach to the Analysis of Swollen Emulsion Polymerization of Styrene

Abstract A mathematical model for swollen emulsion polymerization of styrene was derived in this study. The experimental data were obtained using two different swelling agents: cetyl alcohol and lauryl alcohol. In the studied system, potassium persulfate and sodium dodecyl sulfate were used as initiator and emulsifier, respectively. The variation of total monomer conversion with the polymerization time obtained with different swelling agent-emulsifier combinations and data from SEM photographs of the final latexes were evaluated for estimation of the model parameters. In the mathematical model, it was assumed that the polymerization takes place according to first-order kinetics, within the forming latex particles in the presence of monomer diffusion from the monomer droplets to the forming latex particles. The kinetic rate constants and the variation of effective diffusion coefficient of monomer with the polymerization time were estimated using model expressions. Relative rate factor-Thiele modulus diagra...

Monomers in polymer dispersions. III. Diffusion of monomers in poly(vinyl acetate) films

AbstractThe diffusion coefficients of monomers (vinyl acetate, styrene) within poly(vinyl acetate) films were measured by means of infrared attenuated total reflection spectroscopy and gravimetry. The diffusion coefficients obtained by the two methods are almost identical. This is interpreted as an indication that the molecular processes of diffusion of small molecules in bulk and in surface layer regions of the polymer take place in a similar manner.

Swelling of polybutadiene as latex particles and cast films by styrene and acrylonitrile monomers

During emulsion polymerization, the diene structure of butadiene leads to the formation of a network by crosslinking on the residual double bonds. Investigation of the swelling of polybutadiene particles and films cast from latexes, by styrene and acrylonitrile, was carried out in order to get more information on polymer structure and behaviour in the presence of monomers. A thermodynamic approach has permitted us to determine several parameters, such as the average number of butadiene units between two crosslinking points, which represents the crosslink density and was compared with data from simulation of butadiene emulsion polymerization. Swelling by monomer mixtures of various compositions has shown a preferential solvation of styrene as a function of comonomer composition. Comonomer composition in the particles is important in the final structure of an acrylonitrile-butadiene-styrene particle prepared by emulsion polymerization of styrene-acrylonitrile on a polybutadiene seed. Diffusion coefficients of monomers were determined after a kinetic study.

Quasielastic light scattering studies of tubulin aggregation

A quasielastic light scattering study of purified tubulin has resulted in a monomer diffusion coefficient of 6.0 × 10 −7 cm 2/s. In an attempt to characterize the small tubulin oligomers which are predicted to form as intermediates in the self-assembly into double rings, magnesium ions (10 m m) were incorporated into the PG (10 m m NaP i, 0.1 m m GTP, pH 7.0) buffer. With magnesium-containing buffers, a second slow diffusing species was identified with D = 0.56 × 10 −7 cm 2/ s. This corresponds to the tubulin double rings. A study of the small oligomers was precluded by the presence in all preparations of traces of aggregates resulting from the slow aging process of the protein ( V. Prakash and S. N. Timasheff (1982) J. Mol. Biol. 160, 499–515 ). While colchicine was shown to inhibit this aging process, the presence of these irreversible aggregates, even to the extent of 1% by mass, precludes equilibrium studies of the self-association of tubulin into small oligomers.

Translational diffusion of lipid monomers determined by spin label electron spin resonance

The collision rates between spin-labelled valeric acid in water, and between the corresponding mixed-chain, spin-labelled phosphatidylcholine in water-methanol mixtures, and also between spin-labelled phosphatidylcholine monomers and micelles in water have been determined from the spin-spin broadening of the electron spin resonance spectrum. In each case the second order rate constants are consistent with a diffusion-controlled process. For spin-labelled valeric acid in water the translational diffusion coefficient at 20°C is 3.4 · 10 −6 cm 2 · s −1, and for spin-labelled phosphatidylcholine varies between 2.3 · 10 −6 and 3.8 · 10 −6 cm 2 · s −1 within the range 44 to 88 wt% methanol. The spin-labelled phosphatidylcholine monomer diffusion coefficient in water at 20°C is 2.4 · 10 −6 cm 2 · s −1, deduced from the monomer-micelle association rate, with an activation energy of 4.0 kcal · mol −1. The much slower on-rates for association of lipid monomers with phospholipid bilayer vesicles reported in the literature, therefore indicate that incorporation into bilayers is not a diffusion-controlled process.

Transport of monomer surfactant molecules and hindered diffusion of micelles through porous membranes

Diffusion of Triton X-100 through Celgard 2500 membranes was examined. The pore permeability for monomers was 5.0 × 10 −6 cm 2/sec and it was measured for upstream concentrations below the CMC value of 2.29 × 10 −4 M at 30°C. This value is close to the monomer diffusion coefficient in bulk suggesting that the monomers do not experience significant hindrance due to the pore walls. The permeability of the surfactant drops abruptly within a narrow range of reservoir solution concentrations in the vicinity of the CMC. At concentrations 10 × CMC, the permeability coefficient becomes constant and equal to 3.9 × 10 −7 cm 2/sec which is the pore permeability for the Triton X-100 micelles. Compared to the diffusion coefficient of micelles in bulk water, the transport of micelles is hindered by the pore walls. In a 10-fold concentration range the micellar pore permeability is practically constant indicating no large change in micelle size. The chemical equilibrium model applied to surfactant diffusion in pores shows reasonable agreement over the entire range of the experimental data for reservoir concentrations from one-fifth times the CMC to 100 times the CMC.

Mobility of gold clusters on amorphous carbon substrates II: Evaluation of surface diffusion coefficients

Computer simulation of film growth is carried out for the system consisting of gold on amorphous carbon on the basis of the generalized Zinsmeister equations derived in Part I. If it is assumed that i-mers move about over the substrate with a diffusion coefficient D i = i - x D 1 where D 1 is the monomer diffusion coefficient and x is a constant ( x ≈ 1.5), values of τ (the monomer residence time) and σ D 1 (σ is the collision cross section) that give densities n i of i-mers reasonably consistent with the observed cluster size distributions and n = Σn i versus time relations can be found.

Conformational studies of BSA using laser light scattering

AbstractThe usefulness of laser light scattering as a technique for determining protein conformation has been investigated by studying the self‐association and drug binding of bovine serum albumin (BSA). The diffusion coefficients of BSA monomers and dimers have been measured and the ratio of these two quantities indicates that in the dimer, the subunit separation is 2.2 times the monomeric hydrodynamic radius. The binding of salicylate to BSA causes an increase in its diffusion coefficient corresponding to a reduction in the frictional drag of the solvent on the protein molecules. It has been found that data obtained using laser light scattering may be interpreted confidently only when proper care has been taken in sample preparation and the scattered intensity autocorrelation function has been appropriately analyzed.

Study of the diffusion of monomers of acrylic series in polyvinylchloride

A study was made of the diffusion of monomers of acrylic series in PVC, the relations which govern this process and the relation between diffusion coefficients of acrylic monomers and their chemical structure was established.