A convection–diffusion porous media model for moisture transport in polymer composites: Model development and validation

Moisture may cause many detrimental effects to polymers and their composites, thus inhibiting the applications of polymeric materials in hot and humid environments. In this article, a convection–diffusion porous media model is derived to better characterize rapid moisture transport in polymer composites at high temperatures. The model considers both continuum diffusion in solid and high‐pressure convection taking place in the pore network. Coupling of convection and diffusion is achieved by combining the law of conservation of mass, Darcy's law, the liquid–vapor chemical equilibrium, and the ideal gas law. The presented model is validated by conducting experimental tests on an epoxy compound. It is found that the proposed convection–diffusion model is more effective than diffusion‐only and convection‐only models for interpreting rapid desorption tests at high temperatures. A numerical study is also performed to predict maximum vapor pressure during a rapid heating process. Vapor pressure is found to be as high as 6.5 MPa at a heating rate of 10 K/s. It is concluded that the convection–diffusion model is able to capture both vapor dynamics and diffusion mechanism in porous polymeric materials, and can be potentially used to further investigate polymer‐moisture interactions. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1440–1449     

Oxygen and water vapor permeability of fully substituted long chain cellulose esters (LCCE)

Fully-substituted cellulose esters with acyl substituents ranging in size from C2 to C18 were synthesized using the acyl chloride method. Films were prepared from the purified esters by either solvent-casting or compression-molding at elevated temperatures. Oxygen and water vapor permeability was determined under different conditions of pressure and moisture. The relationship between cellulose ester structure and barrier properties was examined. The results revealed linear relationships between water vapor and oxygen permeabilities and molar ester substituent volume as well as several structural factors relating to polymer polarity and hydrophobicity, such as aliphatic (methylene) content, solubility parameter, and contact angle. Films from long chain cellulose esters (LCCE) with acyl substituents in the size range between C8 and C18 were found to represent effective barriers to water vapor transport while their obstruction to the transfer of oxygen remained low. It was concluded that the hydrophobic nature of LCCEs is responsible for the control of water vapor transport, and that spatial factors dominate the transfer of oxygen.     

Theoretical and experimental study on phase transitions and mass fluxes of supersaturated water vapor onto different insoluble flat surfaces

The heterogeneous nucleation and condensation of water vapor onto three different surfaces (newsprint paper, Teflon, cellulose film) was studied theoretically and experimentally. The theoretical framework included the use of the classical theory of heterogeneous nucleation, diffusion theory corrected with transition regime correction factors, and the theory of heat transfer. Experiments were carried out using an environmental scanning electron microscope (ESEM). The experimental results for newsprint paper were investigated more closely. Our results show that the measured onset supersaturations were smaller than the modeled ones when the experimentally determined contact angle was used. Furthermore, the measured condensational growth rates were smaller than the modeled ones, presumably resulting from the approximations that had to be made in the calculations.     

Water vapor adsorption equilibria and mass transport in unmodified and modified cellulose fiber-based materials

Water vapor adsorption isotherms of different unmodified and coated paper samples were studied to determine their suitability as water barrier packaging materials. The sorption behavior of these samples was compared with commercially available paper. The experimental data were analyzed using the Hailwood–Horrobin (H–H), Guggenheim–Anderson–De Boer (GAB) and BET models for extraction of isotherm parameters and determination of monolayer moisture contents. The H–H and GAB models were found to provide good fits to the experimental data. The monolayer moisture content of modified papers was less than 3.0 % (dry basis) as compared to unmodified paper samples (4.20 %), at saturation. It was also observed that the sorption behavior of modified paper samples differed with substrate type. Water vapor permeability (WVP) of unmodified and coated paper samples at the temperatures of 25 and 38 °C were also measured for a wide range of vapor partial pressure gradients. The permeabilities of the modified samples were found to be generally low compared to the unmodified (reference) paper sample. Among the investigated samples, PLA and PHBV coated paper samples showed higher mass transfer resistance to water vapor transport. Furthermore, the water vapor permeabilities of different samples were found to be relatively constant up to the modest relative humidity levels; however, at the higher humidity levels they showed increasing trend with the further increase in relative humidity. Results of this study confirmed that blocking of active surface sites by coating with PLA and PHBV is the most effective way to increase the water vapor barrier properties of modified papers, thus making them the appropriate candidates for green-based food packaging materials.     

Investigation of the concentration dependence of mass transfer coefficients in reversed-phase liquid chromatography

In order to investigate the concentration dependence of mass transfer coefficients in RPLC, experimental breakthrough curves obtained by staircase frontal analysis (FA) were fitted to the simplified models such as multiplate (MP) model, equilibrium dispersive (ED) model, and transport model, and the sophisticated models such as lumped pore diffusion (POR) model and general rate (GR) model. The MP model was used to obtain the initial guesses of the parameters of the ED and the transport models. Then the best values were obtained by minimizing the differences between theoretical and experimental values with a nonlinear fitting procedure. The values of the parameters of the POR and the GR models can be calculated by using the expressions derived from the plate height equations, which was further validated by using the fitting method. It was found that the mass transfer coefficients would depend on the solute concentration. This can be ascribed to the surface diffusivity, which correlates with the concentration and is lumped into the mass transfer coefficients for both simplified and sophisticated models.     

About the Dominance of Mesopores in Physisorption in Amorphous Materials

Amorphous, porous materials represent by far the largest proportion of natural and men-made materials. Their pore networks consists of a wide range of pore sizes, including meso- and macropores. Within such a pore network, material moisture plays a crucial role in almost all transport processes. In the hygroscopic range, the pores are partially saturated and liquid water is only located at the pore fringe due to physisorption. Therefore, material parameters such as porosity or median pore diameter are inadequate to predict material moisture and moisture transport. To quantify the spatial distribution of material moisture, Hillerborg’s adsorption theory is used to predict the water layer thickness for different pore geometries. This is done for all pore sizes, including those in the lower nanometre range. Based on this approach, it is shown that the material moisture is almost completely located in mesopores, although the pore network is highly dominated by macropores. Thus, mesopores are mainly responsible for the moisture storage capacity, while macropores determine the moisture transport capacity, of an amorphous material. Finally, an electrical analogical circuit is used as a model to predict the diffusion coefficient based on the pore-size distribution, including physisorption.     

Preparative weak cation-exchange chromatography of monoclonal antibody variants I. Single-component adsorption

The retention behavior of a monoclonal antibody has been characterized on a weak cation exchanger, Fractogel EMD COO(-)(s). This new generation of resin materials comprise of a higher mechanical strength compared to softer gel-type matrices while maintaining elevated capacities, resulting in higher productivity and longer lifetimes. These parameters are extremely important when working with large bio-molecules such as proteins, and in particular monoclonal antibodies. In the first part of this work a parameter estimation strategy is presented to fully characterize the retention behavior of a single monoclonal antibody and determine suitable model parameters. Literature correlations were used for the estimation of mass transfer rates. The transport limiting parameter, pore diffusion, was regressed experimentally. Various methods for the adsorption isotherm determination have been applied, their combinations resulting in little experimental effort and accurate predictions of elution profiles. The process has been modelled with a complete pore diffusion model and the agreement between experimental and predicted profiles is good in general. However, a very marked sensitivity to changes in the effective pore diffusion coefficient has been observed. A correlation describing the effect of the separation conditions on the diffusion rate is therefore needed in order to have a fully predictive mathematical model.     

Heat and moisture transfer in application scale parallel-plates enthalpy exchangers with novel membrane materials

Parallel-plates enthalpy exchangers are one of the most commonly encountered energy recovery devices that are used to simultaneously transfer both sensible heat and moisture between fresh air and exhaust ventilation air. For such equipments, the water vapor sorption properties of the plate materials have tremendous impacts on system performance. In this investigation, three different materials, namely, common paper, CA (cellulose acetate) membrane and a modified CA membrane) are selected as the plate materials for three enthalpy exchangers. Sorption curves and contact angles of these three materials are measured to reflect their hydrophilicity. The steady-state sensible and latent effectiveness of the three exchangers are tested in a special test rig, and the test results are compared with the model predictions. A heat and moisture transfer model for the enthalpy exchangers is proposed. The effects of the varying operating conditions like air flow rates, temperature, and humidity on the sensible and latent effectiveness are evaluated. Both the numerical and experimental results indicate that the moisture resistance through plates is co-determined by thickness, sorption slope, and sorption potential. Moisture diffusivity in various materials is in the same order. So when the plate thickness is fixed, the higher the sorption slopes are, the higher the latent performance is. Of the three exchangers, the exchanger with the modified CA membrane material has the highest performance due to small thickness, steep sorption slope, and large sorption potentials. The paper exchanger has a latent effectiveness of 0.4, while the membranes have latent effectiveness of greater than 0.7.     

Analysis of diffusion models for protein adsorption to porous anion-exchange adsorbent

The ion-exchange adsorption kinetics of bovine serum albumin (BSA) and gamma-globulin to an anion exchanger, DEAE Spherodex M, has been studied by batch adsorption experiments. Various diffusion models, that is, pore diffusion, surface diffusion, homogeneous diffusion and parallel diffusion models, are analyzed for their suitabilities to depict the adsorption kinetics. Protein diffusivities are estimated by matching the models with the experimental data. The dependence of the diffusivities on initial protein concentration is observed and discussed. The adsorption isotherm of BSA is nearly rectangular, so there is little surface diffusion. As a result, the surface and homogeneous diffusion models do not fit to the kinetic data of BSA adsorption. The adsorption isotherm of gamma-globulin is less favorable, and the surface diffusion contributes greatly to the mass transport. Consequently, both the surface and homogeneous diffusion models fit to the kinetic data of gamma-globulin well. The adsorption kinetics of BSA and gamma-globulin can be very well fitted by parallel diffusion model, because the model reflects correctly the intraparticle mass transfer mechanism. In addition, for both the favorably bound proteins, the pore diffusion model fits the adsorption kinetics reasonably well. The results here indicate that the pore diffusion model can be used as a good approximate to depict protein adsorption kinetics for protein adsorption systems from rectangular to linear isotherms.     

Effects of type of adsorption isotherms on parallel diffusion of sulfonated dyes into porous cellulose membrane

Transport phenomenon of three sulfonated azo dyes, C.I. Acid Red 88, C.I. Direct Yellow 12, and C.I. Direct Blue 15 into water-swollen cellulose membranes has been analyzed on the basis of parallel transport theory by surface and pore diffusion. Langmuir equation was applied into the mass balance equation to estimate dye concentration in the pores. The results were compared with the results obtained by applying Freundlich equation in our previous papers. The surface diffusivity (D _s) and the pore diffusivity (D _p) for the parallel diffusion model obtained by applying Langmuir equation agreed with those obtained by applying Freudlich equation. The theoretical concentration profiles for parallel diffusion calculated usingD _s andD _p coincided accurately with the experimental data when we applied either Langmuir or Freundlich equations.     

Mass transport model for semiconductor nanowire growth

We present a mass transport model based on surface diffusion for metal-particle-assisted nanowire growth. The model explains the common observation that for III/V materials thinner nanowires are longer than thicker ones. We have grown GaP nanowires by metal-organic vapor phase epitaxy and compared our model calculations with the experimental nanowire lengths and radii. Moreover, we demonstrate that the Gibbs-Thomson effect can be neglected for III/V nanowires grown at conventional temperatures and pressures.     

紫外光固化的聚氨酯－丙烯酸酯－纤维素复合膜

再生纤维素膜(甘蔗渣浆制)表面直接用紫外光固化聚氨酯-丙烯酸酯制备出防水性复合膜。由红外光谱和扫描电镜研究了复合膜的结构。同时,测定了膜的防水性、力学性能、水汽透过性和尺寸稳定性。实验结果表明,当聚氨酯：丙烯酸酯为40:55(质量比),在400W紫外光下固化5min制得的复合膜具有致密的表面结构和较好的性能,该膜经水浸泡后其断裂强度可达干膜的90%,浸水收缩率和膨胀率均小于2.5%,水汽渗透量仅为再生纤维素膜的1/4.由此表明复合膜的防水性和尺寸稳定性明显提高。此外,该复合膜在可见光区的透光率在80%～90%之间,而且对紫外光有屏蔽作用。     

Investigation of gas transport through porous membranes based on nonlinear frequency response analysis

Theoretical development of a new experimental method for investigation of mass transport in porous membranes, based on the principle of the modified Wicke-Kallenbach diffusion cell and the nonlinear frequency response analysis is presented. The method is developed to analyze the transport of a binary gas mixture in a porous membrane. The mixture is assumed to consist of one adsorbable and one inert component. Complex mass transfer mechanism in the membrane, where bulk or transition diffusion in the pore volume and surface diffusion take place in parallel, is assumed. Starting from the basic mathematical model equations and following a rather standardized procedure, the frequency response functions (FRFs) up to the second order are derived. Based on the derived FRFs, correlations between some characteristic features of these functions on one side, and the whole set of equilibrium and transport parameters of the system, on the other, are established. As the FRFs can be estimated directly from different harmonics of the measured outputs, these correlations give a complete theoretical basis for the proposed experimental method. The method is illustrated by quantifying the transport of helium (inert gas) and C₃H₈ and CO₂ (adsorbable gases) through a porous Vycor glass membrane.     

Diffusion in complementary pore spaces

The rate of mass transfer is among the key numbers determining the efficiency of nanoporous materials in their use for matter upgrading by heterogeneous catalysis or mass separation. Transport enhancement by pore space optimization is, correspondingly, among the main strategies of efficiency promotion. Any such activity involves probing and testing of the appropriate routes of material synthesis and post-synthesis modification just as the exploration of the transport characteristics of the generated material. Modelling and molecular simulation is known to serve as a most helpful tool for correlating these two types of activities and their results. The present paper reports about a concerted research activity comprising these three types of activities. Recent progress in producing pore space replicas enabled focusing, in these studies, on “complementary” pore spaces, i.e. on pairs of material, where the pore space of one sample did just coincide with the solid space of the other. We report about the correlations in mass transfer as observable, in this type of material, by pulsed field gradient NMR diffusion studies, with reference to the prediction as resulting from a quite general, theoretical treatment of mass transfer in complementary pore spaces.     

Comparative study between a CMS membrane and a CMS adsorbent: Part II. Water vapor adsorption and surface chemistry

The adsorption/desorption equilibria of water vapor in a carbon molecular sieve (CMS) membrane and a commercial CMS adsorbent were determined, exhibiting S-shaped, type V isotherms. The fits of several models found in the literature to the experimental data were evaluated. The results obtained led to the development of a new model accounting for both adsorption and desorption and essentially based on the work of Lagorsse et al. (2005) [15]. Furthermore, the adsorption kinetics was also assessed for both materials and well described by a linear driving force model. The existence of hydrophilic groups responsible for water vapor adsorption in such carbonaceous materials has been related to the surface chemistry by means of X-ray microanalysis and by thermogravimetry. It was concluded from X-ray microanalyses that the carbon membrane presents a lower C/O ratio and is thus more sensitive towards water vapor exposure, as evidenced by the measured water adsorption at lower relative pressures. It was also observed that the diffusion rates are higher for the CMS membrane than for the CMS adsorbent.     

Separation characteristics of some phenoxy herbicides from aqueous solution

The adsorption and desorption characteristics of some phenoxy herbicides (CPA 2,4-D, and MCPA) from an aqueous solution on the active carbon materials (GAC, F-400) were studied. Adsorption equilibrium capacities of the phenoxy herbicides increased with a decrease in pH of the solution. Adsorption equilibrium isotherms were represented by the Sips equation. Kinetic parameters were measured in a batch adsorber to analyze the adsorption rates of the phenoxy herbicides. The internal diffusion coefficients were determined by comparing the experimental concentration curves with those predicted from the surface diffusion model and the pore diffusion model. The adsorption model based on the linear driving force approximation (LDFA) was used to simulate the adsorption behavior of the phenoxy herbicides in a fixed bed adsorber. Over 95 percent desorption of the phenoxy herbicides was obtained using distilled water.     

Transport phenomena of sulfonated dyes into cellulose membrane: Effects of urea on parallel diffusion of mono azo dyes

 Effects of urea on transport phenomena of sulfonated azo dyes with different aggregation constants into water-swollen cellulose membrane have been studied at 25–55 °C. The results were analyzed on the basis of a parallel transport theory of surface and pore diffusion. Addition of urea decreased equilibrium adsorption of the dyes onto cellulose and increased the surface and pore diffusivities for the parallel diffusion model of the dye with high aggreg-ation constant. Temperature dependence of the effects was also discussed. Received: 30 November 1996 Accepted: 7 April 1997     

Effects of affinity and aggregation on parallel diffusion of tri-sulfonated azo compounds into water-swollen cellulose membranes

Adsorption and diffusion of tri-sulfonated azo dyes, C.I. Acid Red 18 and C.I. Acid Red 27 onto waterswollen cellulose membrane has been studied at 25°C. Affinities of these dyes onto cellulose were evaluated by the coefficients of Freundlich equation. Diffusion behavior of these days was analyzed on the basis of a parallel transport theory by surface and pore diffusion. The results could be described by the parallel diffusion model provided that adsorption was stimulated by addition of NaCl. The surface diffusivities for the parallel diffusion model were correlated by the affinity of the dyes, on the other hand, the pore diffusivities for the model were affected by aggregation of the dye depending on its structure and NaCl concentration.     

Comparative modeling of breakthrough curves of bovine serum albumin in anion-exchange chromatography

The experimental results of a previous study of the mass transfer kinetics of bovine serum albumin (BSA) in ion-exchange chromatography, under nonlinear conditions, were reevaluated using the general rate model of chromatography. Solutions of this model were obtained numerically. The influences of axial dispersion, the resistance to mass transfer from the bulk mobile phase to the surface of the packing particles, and the intraparticle mass transfer resistances on the profiles of the breakthrough curves of BSA were investigated. The results obtained are compared to those of a previous investigation of the same data, using the simple transport-dispersive model and the lumped pore diffusion model. The results obtained show that the use of an oversimplified model for the analysis of chromatographic data can lead to erroneous interpretations of the experimental data and to misunderstandings of the fundamentals of the processes involved. Finally, a theoretical comparison between the properties and the range of application of the three models is provided.