Diffusion/adsorption model of cellulose dyeing. I. The diffusion through never-dry cellulose

The diffusion coefficients D₀, of C.I. Direct Yellow 12, Red 2, Blue 1, and Blue 15 in aqueous NaCl solution were measured at 90°C by the diaphagm cell method. The values of D₀ for Yellow 12 and Red 2 showed a salt concentration dependence and those for Blue 1 and Blue 15 were constant over the ionic strength range from 0.01 to 0.10. In the adsorption/diffusion models proposed so far for the direct dye–cellulose system, the Standing–Warwicker–Willis model was shown to be similar in principle to the Weisz–Zollinger model. The adsorption/diffusion behaviors in never-dry cellophane sheet for C.I. Direct Yellow 12 and Blue 15 were examined by the method of cylindrical film roll at 90°C. The concentration dependence of the apparent diffusion coefficient for these dyes showed an incomplete validity of both the models.     

Effect of microencapsulation on dyeing behaviors of disperse dyes without auxiliary solubilization

Microencapsulated disperse dye can be used to dye hydrophobic fabric in the absence of auxiliaries and without reduction clearing. However, little available information for dyeing practice is provided with respect to the effect of microencapsulation on the dyeing behaviors of disperse dyes. In this research, disperse dyes were microencapsulated under different conditions. The dyeing behaviors and dyeing kinetic parameters of microencapsulated disperse dye on PET fiber, e.g., dyeing curves, build up properties, equilibrium adsorption capacity C_∞, dyeing rate constant K, half dyeing time t_1/2, and diffusion coefficient D were investigated without auxiliary solubilization and compared with those of commercial disperse dyes with auxiliary solubilization. The results show that the dyeing behaviors of disperse dye are influenced greatly by microencapsulation. The diffusion of disperse dyes from microcapsule onto fibers can be adjusted by the reactivity of shell materials and mass ratios of core to shell. The disparity of diffusibility between two disperse dyes can be reduced by microencapsulation. In addition, the microencapsulation improves the utilization of disperse dyes due to no auxiliary solubilization. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Diffusion of dyes in polyester fibers. II. Diffusion coefficients from the radial distribution curves

The computational method of a concentration-dependent diffusion coefficient D(C) of dyes in fibers has been presented. This method is based on concentration profiles determined with the microphotometric technique and the numerical solution of Fick's second law of diffusion for the cylindrical system. Exploiting the grid method and data of experimental concentration profiles, diffusion coefficients of disperse dye Synthene Scarlet P3GL in the anionically modified polyester fiber have been calculated. The results have been compared with those obtained by the Boltzmann–Matano method. It was stated that (1) in the investigated polymer–dye system the relation between D and C is of the form D(C) = D₀ exp(δC); (2) the allowance for the cylindrical symmetry of the fiber leads to the lower values D(C) in the total concentration range than those obtained by the Boltzmann–Matano method; and (3) values of D₀ calculated with both methods are coincident.     

Concentration Dependence of the Diffusion Coefficients of Disperse Dyes in Polyethylene Terephthalate

Diffusion coefficients of disperse dyes have been calculated by Matano's method from diffusion profiles in polyethylene terephthalate(PET). The diffusion coefficients (D_c) clearly indicate concentration-dependence. It has been found, from the densities of the dyed PET and the dye, that there is no overall change in the volume of the PET and dye in dyeing. The instrinsic diffusion coefficients have been calculated from D_c and the volume fraction (φ₁) of penetrant in the amorphous region. From these values, thermodynamic diffusion coefficients (χ?) were obtained. It has been found that the relation between 1/log (χ?/χo) and 1/φ₁ is a straight line, and it therefore seems reasonable to assume that the diffusion of disperse dyes in PET can be described by Fujita's ‘free volume theory’ for the diffusion of low molecular-weight organic compounds in an amorphous high-polymer.     

Mutual diffusion in aqueous gel solutions

Concentration relations for mutual diffusion coefficients D_m(C) in water of polyelectrolyte gelatin macromolecules at different temperatures were studied by optical interferometry. It is shown that D_m(C) values are in agreement with scaling predictions and are similar to those observed for solutions of neutral macromolecules under θ-conditions. However, they are greatly influenced by the square-law term C², having a correlation to the conventional scaling law D_m ∝? C, and the mobility of solution components is influenced by physical gelation processes under certain thermodynamic conditions. It is demonstrated that the temperature relation of the diffusion coefficient at infinite dilution D₀(C → 0) for the three gelating samples with various physico-chemical properties can be described by a universal function.     

Synthesis and Self-Aggregation of a Hydroxyl-Functionalized Imidazolium-Based Ionic Liquid Surfactant in Aqueous Solution

This paper deals with the synthesis and self-aggregation of a hydroxyl-functionalized imidazolium-based ionic liquid (IL) surfactant, namely 1-hydroxyethyl-3-dodecylimidazolium chloride ([C₂OHC₁₂im]Cl). The molecular structure was confirmed by means of electrospray ionization mass spectrometry (ESI–MS), ¹H nuclear magnetic resonance (¹H NMR) and elemental analysis. Many important physicochemical parameters, such as the critical micelle concentration (CMC), the surface tension at CMC (γ_CMC), the adsorption efficiency (pC ₂₀), the surface pressure at CMC (Π_CMC), the maximum surface excess (Γ _m ), the minimum molecular cross-sectional area (A _min), the value of CMC/C ₂₀, the average number of aggregation (N _m ) and the micellar microenvironment polarity were determined by surface tension-concentration curves, fluorescence spectra, and electrical conductivity. The phenomena of the second CMC, the concentration dependence of N _m , and the critical average aggregation number (N _m,c) of imidazolium-based IL surfactants are reported for the first time in this paper.     

Pore diffusion: Dependence of the effective diffusivity on the initial sorbate concentration in single and multisolute batch adsorption systems

The present work studies the intraparticle diffusivity in batch adsorption systems as a function of the initial sorbate concentration. The systems under investigation are basic dyes, namely Basic Blue 69, Basic Red 22 and Basic Yellow 21 and their binary and ternary combinations, all adsorbing onto activated carbon Filtrasorb 400. They study is based on the film-pore diffusion model and the output is a combination of the external mass transfer coefficient, k_f and the effective diffusivity, D_eff that yields congruent experimental and theoretical kinetic data. It has been found the D_eff varies with C_o in an exponential decay function. Furthermore. D_eff values undergo a general reduction in the multisolute systems compared to the single component systems. Also, the relative diffusion rates in the multisolute systems are found to change such that D_eff of the slower diffuser is enhanced and that D_eff of the faster diffuser is inhibited.     

Diffusion with simultaneous reaction of reactive dyes in cellulose. II. Effect of hydrolysis

Theoretical equations that describe the concentration profiles of immobilized and active species for reactive dyes were derived from the diffusion equation accompanied by the reaction with cellulose and water in the substrate. The diffusion coefficient D and the rate constant of the reaction with cellulose, k_cell, and that with water in cellulose, k_w, were estimated by using the theoretical equations and the cylindrical film roll method. The theory predicted that the apparent diffusion coefficients decreased with the hydrolysis of active species in cellulose. Results from diffusion experiments with C.I. Reactive Yellow 4 and Orange 1 show that the ratio P of k_w to k_cell for Orange 1 increased with increase in pH to about pH 13 and that the P for Yellow 4 was smaller than unity. Using an alternative experiment to diffusion, P of Orange 1 was measured to be 1.0–1.5, and that of Yellow 4 was smaller than unity at pH 11.6 at 30°C. It was therefore concluded that the D of active species was constant to a highly alkaline region and that the decrease in the apparent diffusion coefficient of Orange 1 was mainly due to the hydrolysis of active species in cellulose.     

Probing the state of absorbed water by diffusion technique

The diffusion coefficient of water, D_wm, across homogeneous cellulose acetate membranes of graded porosity ε (water content) are measured. At high values of porosity, D_wm varies monotonously as ε is varied. At a certain porosity ε_c, however, there is a sudden change in D_wm; and thereafter the change becomes linear again, but with a different slope. Diffusion coefficients are interpreted, through the Stokes-Einstein relation, in terms of the overall microscopic viscosities η_wm of the membrane matrix. The values of η_wm are then correlated with the equivalent pore size r of the membranes. It is discovered that the sudden change in D_wm (or η_wm) at ε_c correlates with similar changes in other properties such as hydraulic permeability and selectivity of the membrane. All these observations are then attributed to the water structure inside the membranes.     

Diffusion of dyes in polyester fibers. IV. Anomalous sorption of disperse dye synthene scarlet P3GL

The investigations on dyeing of poly(ethylene terephthalate) fibers with disperse dye Synthene Scarlet P3GL have revealed anomalous sorption of the dye in heat-treated samples. In the mathematical solution of the process it has been assumed that anomalous sorption can be treated as superposition in time of two stages of Fickian sorption. The contents of absorbed dye at quasiequilibrium C_I, at the final equilibrium C_II, and the apparent diffusion coefficients D_I, and D_II have been calculated using Hill's equation.     

Effects of ionic strength and pH on the diffusion coefficients and conformation of chitosans molecule in solution

The effects of ionic strength and pH on the diffusion coefficients and gross conformation of chitosan molecules in solution were studied. Chitosan with 83% degree of deacetylation (DD) was prepared from red shrimp (Solemocera prominenitis) processing waste. Ten different molecular weight chitosans were prepared by ultrasonic degradation, and their molecular weights were determined by static light scattering. The weight-average molecular weight (M_w) were between 78 to 914 kilo dalton (KDa). Solution of different ionic strengths (I = 0.01, 0.10, and 0.20) but the same pH (2.18) and different pHs (2.37, 3.10, and 4.14) but the same ionic strength (I = 0.05) were prepared to measure their mutual diffusion coefficient (D_m). The diffusion coefficients for standard condition (D_20,w) were derived from D_m. Intrinsic viscosities ([η]) were determined by a capillary viscometer in different pH solutions. The Mark–Houwink exponents a and ε were obtained from plots of Log [η] and Log D_20,w versus Log M_w, respectively. The results show that diffusion coefficients increased with increasing ionic strength or with increasing pH or with decreasing M_w. Value of ε and a were between 0.503 to 0.571 and ranged from 0.543 to 0.632, respectively. The results indicates that chitosans conformation were in random coil in solutions in the ranges of ionic strength and pH studied. The values of a*, ε* and a**, ε**, Mark–Houwink exponents of smaller and higher than 223 KDa chitosans, respectively, were between 0.752 to 0.988 and 0.585 to 0.777 for smaller M_w chitosans and 0.406 to 0.428 and 0.430 to 0.518 for larger M_w chitosans, respectively. Molecular-weight-induced conformational transition occurred because smaller M_w chitosans was more extended than higher M_w chitosans. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 2041–2050, 1999     

Nonlinear phase‐separation behavior of poly(methyl methacrylate)/poly(styrene‐co‐maleic anhydride) blends

The nonlinear phase‐separation behavior of poly(methyl methacrylate)/poly(styrene‐co‐maleic anhydride) (PMMA/SMA) blends over wide appropriate temperature and heating rate ranges was studied using time‐resolved small‐angle laser light scattering. During the non‐isothermal process, a quantitative logarithm function was established to describe the relationship between cloud point (T_c) and heating rate (k) as given by T_c = Alnk + T₀, in which the parameter A, reflecting the heating rate dependence, is much different for different compositions due to phase‐separation rate and activation energy difference. For the isothermal phase‐separation process, an Arrhenius‐like equation was successfully applied to describe the temperature dependence of the apparent diffusion coefficient (D_app) and the relaxation time (τ) of the early stage as well as the late stage of spinodal decomposition (SD) of PMMA/SMA blends. Based on the successful application of the Arrhenius‐like equation, the related activation energies could be obtained from D_app and τ of the early and late stages of SD, respectively. In addition, these results indicate that it is possible to predict the temperature dependence of the phase‐separation behavior of binary polymer mixtures during isothermal annealing over a range of 100 °C above the glass transition temperature using the Arrhenius‐like equation. © 2012 Society of Chemical Industry     

Multi-domain binding of cytochrome c peroxidase by cytochrome c: Thermodynamic vs. microscopic binding constants

We have demonstrated that cytochrome c (Cc) binds to cytochrome c peroxidase (Cc P) with a 2:1 stoichiometry, and that: (i) Cc reacts at two distinct and non-exclusive surface domains of Cc P; (ii) two molecules of Cc can bind simultaneously to Cc P; and (iii) the ternary complex is more reactive than the binary complex for the heme—heme reaction. The quenching studies, however, provide only stoichiometric (thermodynamic) parameters. They do not directly probe the microscopic properties of the individual domains, and thus do not apportion the reactivity due to 1:1 stoichiometry between the two types of binary complexes: one with Cc bound at the high-affinity domain and one with Cc bound at a low-affinity domain. We describe here a method for analyzing the stoichiometric parameters obtained from triplet quenching titrations to partition the quenching of ZnCc by Cc P into contributions from the binary and ternary complexes, and also to give limits on the partition of the quenching into contributions from the low- and high-affinity binding domains. By applying this method to the experimental quenching titration data for the multi-domain binding of Cc to Cc P, we were able to evaluate, for the first time, the functional relevance of the low-affinity domain in the binary and ternary complexes at both low and high ionic strength. At low ionic strength, essentially no Cc binds at the low-affinity domain in a binary complex. However, reactivity at this domain is significant and indeed can be dominant, in the ternary complex, which does form with measureable concentration. At higher, more physiologically-relevant ionic strengths, very little ternary complex forms, but now the situation is changed, and there is significant reactivity from the 1:1 complex with Cc bound at the low-affinity domain. In other words, there is substantial reactivity from Cc bound at the weakly binding domain over a wide range of ionic strengths, either in a binary or a ternary complex. Finally, we suggest that at high ionic strength, interactions between the two bound Cc are shielded such that it is easier to bind the second Cc molecule when one domain is occupied already.     

Concentration dependence of the diffusion coefficient in polymer solution and molecular weight distribution determined by the diffusion method

The effects of the concentration dependence of the diffusion coefficient of a polymer solution (polystyrene in benzene and cyclohexane) in determining molecular weight distribution by the diffusion method are briefly discussed. The value of the ratio D_m0/D_A0 in a good solvent was found to be close to 1.0 for a polydisperse polymer and less than 1.0 for monodisperse polymers. Molecular weight distribution curves of the polydisperse sample were obtained by the diffusion method in cyclohexane and benzene, respectively. The molecular weight distribution curve obtained for the polymer used in benzene solution looked as if the polymer had a narrow molecular weight distribution. The phenomena cited above were interpreted in the light of the concentration dependence of the diffusion coefficient of polymer solutions.     

A new method for the measurement of the diffusivity of carbon in alpha-iron using an electrochemical cell

A new method has been employed to measure the diffusivity of carbon in alpha iron. The method involves the measurement of ionic current of a carbon concentration cell which employs an iron cylinder as the anode. The design of the cell is such that when a constant external potential is applied, the ionic current is determined by the concentration polarization of carbon in the two electrodes. From the values of ionic current, the diffusivity of carbon (D _c) is calculated by the application of Fick's law. The results in the temperature range 854–975 K have been fitted by regression analysis to obtain the expression:D _c = 2.448 × 10^–5 exp(–102900.7/RT) withD _c in m² s^–1 andR in JK^–1 mol^–1. The results agree well with data in the literature.     

Adsorption Behavior of Fatty Alcohol Ether Sulfonate at Different Interfaces

The equilibrium surface tension, dynamic surface tension, and interfacial tension (IFT) of fatty alcohol ether sulfonates (C_mE_nSO) were measured to investigate their adsorption behavior. The effect of NaCl and CaCl₂ concentrations on the IFT was also studied. The results showed that the number of EO units has no significant effect on the critical micelle concentration (CMC) and CMC decreases with increasing the length of the hydrophobic group. The surface tension at the CMC increases with the increase of the number of EO units and the length of the hydrophobic group. At dilute surfactant concentration, the adsorption process for C_mE_nSO is controlled by diffusion; at higher concentration, it becomes a mixed diffusion‐kinetic adsorption mechanism. The IFT between C_mE_nSO solution and dodecane remains around 10^?1 mN/m over a wide range of electrolyte concentrations (NaCl concentration from 25 to 210 g/L, CaCl₂ concentration from 0.1 to 10 g/L).     

Relationship between segmental dynamics and tracer diffusion of low mass compounds in polyacrylates

We studied the relationship between segmental dynamics of matrix polymers and tracer diffusion of low mass compounds by the use of forced Rayleigh scattering and dielectric spectroscopy. Specifically poly(methyl acrylate), poly(ethyl acrylate) and poly(n-butyl acrylate) were used as the polymer matrices and six azobenzene derivatives with various substituents as the diffusant. The temperature dependence of the tracer diffusion coefficient D was measured on methylyellow (MY)/polyacrylate blends at the MY concentration of 1 wt%. The results indicate that the temperature dependence of D is weaker than the dielectric loss maximum frequencies f_m for the α processes of the matrices. The effect of volume of the dye molecules on D was also investigated at 305 K. Comparison of the tracer diffusion coefficients among various dye/polymer systems indicates that log D in the same matrix decreases linearly with the molar volume of the dyes.     

Adsorption kinetics and mechanism of cationic methyl violet and methylene blue dyes onto sepiolite

The use of low-cost and ecofriendly adsorbents was investigated as an ideal alternative to the current expensive methods of removing dyes from wastewater. Sepiolite was used as an adsorbent for the removal of methyl violet (MV) and methylene blue (MB) from aqueous solutions. The rate of adsorption was investigated under various parameters such as contact time, stirring speed, ionic strength, pH and temperature for the removal of these dyes. Kinetic study showed that the adsorption of dyes on sepiolite was a gradual process. Quasi-equilibrium reached within 3 h. Adsorption rate increased with the increase in ionic strength, pH and temperature. Pseudo-first-order, the Elvoich equation, pseudo-second-order, mass transfer and intra-particle diffusion models were used to fit the experimental data. The sorption kinetics of MV and MB onto sepiolite was described by the pseudo-second-order kinetic equation. Intra-particle diffusion process was identified as the main mechanism controlling the rate of the dye sorption. The diffusion coefficient, D, was found to increase when the ionic strength, pH and temperature were raised. Thermodynamic activation parameters such as ΔG¹, ΔS¹ and ΔH¹ were also calculated.     

Effects of the orientation of smectite particles and ionic strength on diffusion and activation enthalpies of I and Cs ions in compacted smectite

The apparent diffusion coefficients (D_a) for I⁻ and Cs⁺ ions in compacted Na-smectite which is a major constituent clay mineral of bentonite were studied as a function of smectite's dry density (0.9–1.4 Mg/m³), ionic strength ([NaCl] = 0.01, 0.51 M), temperature (22–60 °C) and diffusion direction to the orientated direction of smectite particles. The Na-smectite was prepared by ion-exchanging with Na⁺ ions a Na-bentonite, Kunipia-F®, of which smectite content is over 99 wt.%. The D_a-values for both ions showed a tendency to be higher in the parallel direction than in the perpendicular direction to the orientated direction of smectite particles at a low-ionic strength of [NaCl] = 0.01 M. The D_a-values for I⁻ ions showed different trends depending on diffusion direction and dry density at a high-ionic strength of [NaCl] = 0.51 M. Namely, although the D_a-values for I⁻ ions showed a tendency to be higher in the parallel direction than in the perpendicular direction to the orientated direction of smectite particles at a high-dry density of 1.4 Mg/m³, these showed a reciprocal tendency at dry densities of 0.9–1.0 Mg/m³. The D_a-values for Cs⁺ ions uniformly increased with an increase of ionic strength in both diffusion directions. Considering electrostatic effect from smectite surface and the change in tortuosity on dry density, ionic strength and diffusion direction to the orientated direction of smectite particles, I⁻ ions are considered to mainly diffuse in interstitial pores. While, Cs⁺ ions can diffuse in both interlayer and interstitial pores, and the D_a-values are considered to have elevated by competing with Na⁺ ions. The activation enthalpies (ΔE_a) for I⁻ ions, slightly higher (ΔE_a = 19.8−20.0 kJ/mol) than that of the diffusion coefficient in free water (D^o) for I⁻ ions (ΔE_a = 17.36 kJ/mol) at a low-ionic strength of [NaCl] = 0.01 M, decreased with an increase of ionic strength, became of similar level to that of the D^o at a high-ionic strength of [NaCl] = 0.51 M, increased with an increase of dry density. On the contrary, the ΔE_a-values for Cs⁺ ions, clearly higher (ΔE_a = 25.6−28.4 kJ/mol) than that of the D^o for Cs⁺ ions (ΔE_a = 16.47 kJ/mol) even in low-dry density over the ionic strength, increased with an increase of dry density. The ΔE_a-values for Cs⁺ ions are considered to be due to the decrease in the activity of porewater in addition to the effect of ion exchange enthalpy between Cs⁺ and Na⁺ ions in smectite.     

Effect of penetrant size and shape on its transport through a thermoset adhesive: I. n-alkanes

The diffusion behaviors of a series of n-alkanes, ranging from C₆ to C₁₇, through a polyamide-type polymeric matrix have been investigated by means of mass uptake measurements. Since n-alkanes are known to display negligible interactions with the polymer matrix, this study serves to isolate the effects of penetrant size and shape on the transport process without undue interference from polymer-penetrant interactions. It is established that the diffusion of the n-alkanes through the polymer matrix studied is Fickian and proceeds via a Henry's law-type mechanism. The diffusion coefficients, D, are evaluated based on a thin-film approximation of the Fickian equation. The activation energies of diffusion, E_d, are determined from the temperature dependence of D, using the Arrhenius equation. Correlations between the Arrhenius terms, E_d and D₀, are also established which enable the prediction of diffusion coefficients for similar polymer-penetrant systems. It is also demonstrated by means of activation energy calculations and molecular simulations that the n-alkanes assume a linear geometry within the polymer matrix and diffuse along their long axes.