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The formation of foams of biodegradable poly(e-caprolactone) (PCL) from CO2 solutions in molten PCL was investigated. This study included characterization of the CO2 diffusion and equilibrium solubility in molten PCL in contact with supercritical CO2 (scCO2). Experiments were performed at 70, 80, and 90 °C at CO2 pressures up to 25 MPa. The effective mutual diffusivity of CO2 in molten PCL was measured as a function of the CO2 pressure. The data revealed a dramatic increase in apparent effective diffusivity at elevated pressure, likely related to the formation of fluid bubbles, phase-separated from the previously homogeneous, molten PCL solution of CO2. Microcellular PCL foams were produced by starting from an equilibrium CO2−PCL solution at 70 °C over a wide range of initial pressures (from 6.9 to 32 MPa) by quenching down to foaming temperatures (from 24 to 30 °C) followed by rapid depressurization to atmospheric pressure. Foam structures were characterized by scanning electron microscopy, and cell size...

A new approach for modeling sorption and swelling of glassy polymer matrix with carbon dioxide at high pressure has been developed. The ability of the model to predict gas solubility at different operative conditions, with only one adjustable parameter, was investigated through the comparison with experimental data in a wide pressure range.

The isolation of individual proteins from whey would allow production of more consistent and reliable products by the food industry and possibly would also increase their use in the pharmaceutical industry. Alpha-lactalbumin is the second most prevalent protein in bovine milk whey and has many uses including serving as an excellent protein source in infant formulas, power drinks and other beverages that require soluble, nutritional protein. In this study, we describe two methods for production of alpha-lactalbumin from whey protein isolate using bioselective adsorption. The use of a peptide ligand (WHWRKR) attached to a resin allowed production of an alpha-lactalbumin-rich fraction with a purity of 90.6% and a recovery of 47.9%, while also producing other fractions of commercial interest. The combined use of an amino resin followed by the WHWRKR resin produce a highly purified alpha-lactalbumin (100%) with a yield of 35.2%.

Tryptophan enantiomers have been separated by zwitterion pair chromatography using L-leucine-L-leucine-L-leucine peptide as the zwitterion pairing agent. The peptide ligand is adsorbed onto an octadecylsilane support with excess ligand present in bulk solution. This article examines the roles of the hydrophobic matrix and the mobile phase components on tryptophan enantiomer binding and resolution. Capacity factors and enantioselectivites are given for both hydrophobic and hydrophilic matrices using mobile phases containing Leu-Leu-Leu peptide and/or salt. A decrease in selectivity upon the addition of mobile phase salt suggests that quadrupolar ion-pairing contributes to chiral recognition. Results indicate that binding is significantly reduced and separation is not achieved when Leu-Leu-Leu is coupled onto cross-linked or polymerized hydrophilic resins as well as onto macroporous polystyrene resin. However, resin-immobilized Leu-Leu-Asp-Leu-Leu-Leu, Leu-Leu-Glu-Leu-Leu-Leu, and Leu-Leu-Leu-Glu-Leu-Leu peptides, with ion-pairing sites designed to mimic the Leu-Leu-Leu-saturated C18 support, also do not resolve tryptophan enantiomers. This suggests the Leu-Leu-Leu structure is critical for enantiomer resolution. Because D- and L-tryptophan are separated in the absence of bulk Leu-Leu-Leu, chiral discrimination is believed to occur at the surface of the octadecylsilane support.

Affinity chromatography using immobilized S-protein was used for the screening of affinity peptide ligands from two soluble peptide libraries. Peptide library I consisted of octamers with glycine (G) at both termini of each peptide, i.e. GXXXXXXG. The six center positions were constructed using random sequences of six L-amino acids (Y, N, F, E, V, and L). Peptide library II also consisted of octamers but with glycine and valine (V) at both termini of each peptide (GVZZZZVG). The four variable center positions of peptide library II were random sequences of 18 L-amino acids. Peptides that were retained specifically on the immobilized S-protein column were eluted by 2% acetic acid. The peptides in the acid eluate were further separated using reversed-phase HPLC. Each separated peptide fraction was collected and the peptide sequences deconvoluted by mass spectrometry (MS/MS). The screenings of peptide libraries I and II resulted in 12 and 7 affinity peptides, respectively. Eight out of the twelve peptides from peptide library I contained the clear consensus sequence NFEV. Peptide library II resulted in affinity peptides with the sequences GVNFEVVG, GVNFTVVG and GVFFEL(I)VG. The advantages and limitations of affinity chromatography in peptide library screening are discussed.

The aggregation of biotin-modified phospholipid vesicles (liposomes) induced by binding the protein avidin in solution is analyzed experimentally and theoretically. Avidin has four binding sites that can recognize biotin specifically, and is able to cross-link the liposomes to form large aggregates. The aggregation kinetics were followed using quasi-elastic light scattering (QLS) to measure the mean particle size, and by measuring the solution turbidity. The rate and extent of aggregation were determined as a function of vesicle concentration, protein concentration, and the biotin density on the surface of the liposomes. A model based on Smoluchowski kinetics, fractal concepts, and Rayleigh and Mie light scattering theory was developed to analyze the experimental observations. Small aggregates (7800 A diameter) may be treated as globular; however, the fractal nature of larger particles must be taken into account. Parameters in the model are taken from molecular simulations, or fit to the experimental observations. The aggregation kinetics are primarily determined by the biotin density on the liposome surface, the stoichiometric ratio of avidin molecules to liposomes, and the liposome concentration. Good agreement is found between the model and the experimental results.

The aggregation of biotinylated phospholipid vesicles (liposomes) cross-linked by antibiotin IgG was studied experimentally and theoretically. The liposomes were either low density liposomes that contained 0.4 mol% biotinylated phospholipid ( approximately 100 exposed biotin molecules per liposome), or high density liposomes that contained 2.7 mol% biotinylated phospholipid ( approximately 1000 exposed biotin molecules per liposome). The solution turbidity and mean particle size measured by quasi-elastic light scattering (QLS) were monitored throughout the aggregation. Three different lots of antibiotin antibodies, each with different association constants and binding heterogeneities, were used. The antibody binding characteristics affected the aggregation rates. The aggregation kinetics were analyzed using a model based on the Smoluchowski theory of aggregation, fractal concepts of aggregate microstructure, and Rayleigh and Mie light scattering theory. The experimental conditions of liposome concentration, protein concentration, and ligand density under which aggregation occurred correlated well with calculated sticking probabilities based on isotherms describing the adsorption of antibiotin antibody to the liposomes. These results are compared with prior observations made when avidin was used as the cross-linking protein.

The Kanai model of a quantum mechanical Brownian particle is used to examine the effect of interactions between particles and their environment. Random forces cause the thermalization of the particle. Reflection of a particle from a step barrier is analyzed. The problem of tunneling of the Brownian particle through a rectangular barrier is solved. Finally, a solution for a Brownian particle in a box is presented.

Mass transfer to the wall and a homogeneous first-order chemical reaction are considered separately for laminar Axial dispersion coefficients for steady-state systems computed from exact solutions for the concentration profiles are shown to be strong functions of axial position. For the homogeneous first-order reaction case, the axial dispersion coefficient is a function of the reaction rate constant.

Escherichia coli beta-D-galactosidase (E.C. 3.2.1.23) was immobilized in cellulose nitrate membrane microcapsules and the reaction kinetics with o-nitrophenyl-beta-D-galactopyranoside (ONPG), lactose, and whole milk were studied using both continuous stirred tank and packed bed reactor configurations. The results of the experiments gave effectiveness factors of 0.3 for ONPG, 0.6 to 0.7 for lactose in solution, and close to unity for lactose in milk. Using a coupled mass transfer and kinetic model, it was possible to estimate the permeability of the microcapsule membrane from the reactor data. Membrane permeabilities on the order of 5 X 10(-3) and 3 X 10(-4) cm/sec were estimated for ONPG and lactose, respectively. It was determined that the membrane was the limiting mass transfer resistance for the overall reaction. The analysis showed that within the microcapsule, the reaction is reaction rate limited for lactose and slightly diffusion limited for ONPG.

Methods based on the density matrix for calculating the time-dependent probability density of a quantum system approaching equilibrium are presented. Explicit expressions are derived for the time-dependent probability density for a double-well potential. The effects of tunneling and transitions between energy levels on the probability density are discussed. For the case of closely spaced energy levels, a partial differential form of the density matrix equation is derived and used to calculate time-dependent probability densities.

A steady‐state form of the master equation is solved to determine rate constants for dissociation of diatomic molecules. A truncated Morse oscillator model describes the vibrational energies and the (SSH) transition probabilities. Single‐quantum vibrational–translational energy exchanges are shown to dominate the rate of dissociation. The theory provides order of magnitude agreement with experimental data for H2, N2, O2, NO, F2, Cl2, Br2, and I2. Anharmonicity of the potential contributes to the lowering of the energy of activation below the bond dissociation energy. Deviations from the Boltzmann distribution cause the energy of activation to decrease at higher temperatures.

The hydrophobic interaction of beta-galactosidase with Sepharose 4B substituted with 3,3'-diaminodipropylamine was studied in both batch and column experiments. The equilibrium and the binding rate constants were determined for different phosphate buffer concentrations. The equilibrium constants exhibit a hysteresis effect, i.e., desorption constants are less than adsorption constants, and the higher the ionic strength to start the desorption, the larger the effect. The rate data are not satisfactorily described by a simple reversible first-order model. The column chromatographic data are semiquantitatively described by a local equilibrium theory without axial dispersion or intraparticle diffusion.

The tunneling of a hydrogen atom through the barrier of a three-dimensional double-well potential is considered. From the time-dependent Schrodinger equation, expressions are derived for the ensemble-averaged probability density and for the probability that the hydrogen atom is in the reactant region, in the barrier region, or in the product region. It is found that when thermal vibrations are not taken into account, the ensemble-averaged probability density may oscillate with time about its equilibrium value. When thermal vibrations are included, the oscillations become damped and the probability density approaches equilibrium. The tunneling rate is found to decrease considerably for increasing barrier thickness and barrier height.

This review article surveys representative literature on enzyme kinetics and engineering published form January 1969 to August 1971. Particlar attention is given to methods of attaching enzymes to solid supports, and to factors, such as pH and temperature, which affect the reaction rate. Recent theories accounting for the high selectivity and high rate of enzyme reactions, calculations taking into consideration the effects of diffusion, methods for analysing kinitic data, and proposals for enzyme reactors are evaluated. Also reviewed are recent methods for extraction of enzymes from cells, procedures for synthesizing enzymes artificailly, and techniques for isolating and purifying enzymes.

A method that takes into account both tunneling and transitions is presented for calculating the rate constant for transfer reactions. An exothermic proton transfer reaction with a large energy of activation is considered, and the rate constant is computed as a function of temperature. It is found that at high temperatures the Arrhenius plot for the rate constant is nearly linear, but at low temperatures, where quantum effects become especially important, the plot is nonlinear.

The hydrophobic interaction of beta-galactosidase with Sepharose 4B substituted with 3,3'-diaminodipropylamine was studied in both batch and column experiments. The equilibrium and the binding rate constants were determined for different phosphate buffer concentrations. The equilibrium constants exhibit a hysteresis effect, i.e., desorption constants are less than adsorption constants, and the higher the ionic strength to start the desorption, the larger the effect. The rate data are not satisfactorily described by a simple reversible first-order model. The column chromatographic data are semiquantitatively described by a local equilibrium theory without axial dispersion or intraparticle diffusion.

An analysis of relaxation phenomena in diatomic molecules, based on a harmonic oscillator master equation formalism, can accurately predict induction times for O2 dissociation in shock tubes, in the temperature range 2850° to 18 000°K, using measured vibrational relaxation times. In this case, the induction times are the direct result of relaxation of lower vibrational states prior to chemical reaction. Transient times for chemical reactions in temperature jump or shock tube experiments are shown to depend on the magnitude of the difference between initial and final temperatures. The phenomenological rate expression is valid for times greater than the transient times for large temperature jumps, and for practically all times for small temperature jumps.

The formation of foams of biodegradable poly(ƒÕ-caprolatone) (PCL) from CO2 solutions in molten PCL was investigated. This study included characterization of the CO2 diffusion and equilibrium solubility in molten PCL in contact with supercritical CO2 (scCO2). Experiments were performed at 70, 80 and 90¢XC at CO2 pressures up to 25 MPa. Diffusion kinetics were studied as a function of the CO2 pressure and the data revealed a dramatic increase in apparent effective diffusivity at elevated pressure consistent with the incipient phase separation in the gas-molten PCL solution. Microcellular PCL foams were produced starting from an equilibrium CO2-PCL solution at 70 ¢XC over a wide range of initial pressures (from 6,5 to 32 MPa) by rapid depressurization and quenching of the polymer solution down to foaming temperatures ranging from 24 to 30„aC. Foam structures were characterized by scanning electron microscopy and cell sizes and density were determined quantitatively. The various foam structures were analyzed and interpreted in connection with the independently measured kinetics and equilibrium of CO2 sorption in PCL by considering the effects of starting pressure and foaming temperature on bubble nucleation and growth.