Diffusion of low molecular weight substances into a laminar film. I: Rigorous solution of the diffusion equation in a composite film of multiple layers

A rigorous solution of the diffusion of penetrant into a laminar film comprised of multilayers of m components is presented by an orthogonal-expansion method. As the simplest practical cases of m ? 2 and m ? 3, with stepwise distribution of both diffusion coefficients and solubility coefficients at the boundary between respective layers, the diffusion properties in the transient state are analyzed in detail. That is, changes in the penetrant concentration distribution within the laminar film and the total amount of penetrant sorbed within the film both with time after exposing the film to an atmosphere of fixed penetrant concentration are calculated for A–B as well as A–B–A type layer arrangements. The calculation is performed while keeping (L₂/L₁) at a constant value of 2.0 but varying the diffusion coefficient ratio of (D₁/D₂) from 10² to 10^?2, and/or varying the solubility coefficient ratio of (S₁/S₂) from 1 to 10, where L₁ and (L₂ ? L₁) are the thickness D₁ and D₂ are the diffusion coefficients of penetrant, and S₁ and S₂ are the solubility coefficients in the A-component and B-component, respectively. The sorption curves deviate considerably from those of Fickian curves of homogeneous film with (D₁/D₂) ? 1 in their respective ways. The results obtained here can be applied to the diffusion in a single component polymer film having a surface layer with different diffusion properties from that of the inner side of the film caused by differing distributions in molecular orientation or degrees of crystallinity.     

Pervaporation of methanol–water mixture by poly(γ-methyl L-glutamate) membrane and synergetic effect of their mixture on diffusion rate

The pervaporation behaviors of methanol–water by poly(γ-methyl L -glutamate) (PMLG) membrane at non-steady- and steady-state permeation were investigated. The values of t_1/2 (time required to reach a half value of steady-state permeation flux) for methanol and water changed and did not change with the component in feed, respectively. Both of the average diffusion coefficients for methanol–and water–PMLG from the mixture changed exponentially with the sorption amount of methanol by the synergetic effect on diffusion. The difference in behavior of non-steady and steady state diffusion was explained by whether D_o (diffusion coefficient at zero penetrant concentration) was influenced by the concentration distribution of penetrant in PMLG membrane.     

Diffusivity of alkanes in polystyrene

Gravimetry is used to study the diffusivity of a homologous series of linear alkanes (C_n, with n = 8, 10, 12, 14 and 16) in amorphous polystyrene at temperatures ranging from 45 °C to 145 °C, i.e. both below and above the polymer glass transition temperature (100 °C). All the mass uptake results obtained are well described by a simple Fickian model (for t < t_1/2) and are used to calculate the corresponding diffusion coefficients (D) using the thin-film approximation of the Fickian equation. For all the alkanes considered, the temperature dependency of the diffusion coefficients is non-Arrhenius in character, over the broad temperature intervals considered. For any particular temperature log(D) varies linearly (R² > 0.993, for all temperatures) with respect to the number of carbon atoms (n) in the alkyl chain, log(D) decreasing when n increases. For each liquid penetrant, over the temperature intervals considered, its log(D) also increases linearly (R² > 0.996 for all the systems) with the decrease in the penetrant’s liquid viscosity.     

Sorption and diffusion of water into melamine–formaldehyde‐incorporated poly(vinyl acetate)–polyester nonwoven fabric composites

A series of composites were fabricated by impregnating a polyester nonwoven fabric with melamine–formol (MF)‐incorporated poly(vinyl acetate) (PVAc) latex. The effect of different weight ratios of MF/PVAc, i.e. 0/100, 5/100, 10, 100, 15/100 and 20/100 (dry, wt/wt), on the water sorption and diffusion into the composites was evaluated. Water sorption studies were carried out at different temperatures, i.e. 30, 50 and 70 °C, based on the immersion weight gain method. From the sorption results, the diffusion (D) and permeation (P) coefficients of water penetrant were calculated. A significant increase in the diffusion and permeation coefficients was observed with an increase in the temperature of sorption. Drastic reductions in diffusion and permeation coefficients were noticed with increasing MF content in the composites. Attempts were made to estimate the empirical parameters like n, which suggests the mode of transport, and K, a constant which depends on the structural characteristics of the composite in addition to its interaction with water. The temperature dependence of the transport coefficients was used to estimate the activation energy parameters for diffusion (E_D) and permeation (E_p) processes from Arrhenius plots. Copyright © 2006 Society of Chemical Industry     

Sorption of low molar mass silicones in silicone elastomers

Elastomers based on polydimethylsiloxane (PDMS) are used as insulating material in outdoor electrical power applications. It is believed that migration of small molecule PDMS species plays an important role in the recovery of hydrophobicity of oxidized or polluted PDMS elastomer surfaces. This paper reports data on diffusivity and solubility of low molar mass PDMS liquids in PDMS rubbers (8000 < M _c < 16,000 g/mol) obtained by sorption measurements. It was found that the diffusivity (D) of linear PDMS liquids was approximately independent of the concentration of penetrant and that in the molar mass range 400 < M _c < 18,000 g/mol it decreased with molar mass (M _c) of the diffusing liquid according to D α M _c^−0.8. Theory and previous data for other oligomers and elastomers predict that D is proportional to M⁻¹. Linear PDMS liquids of lower molar mass exhibited a stronger molar mass dependence. The diffusivity of a given PDMS liquid increased with increasing elastomer crosslink density. The activation energy of the diffusivity was constant at 15.5 ± 2 kJ/mol for linear PDMS liquids of M _c larger than 1000 g/mol⁻¹ with only a negligible influence of network density and filler content. The activation energy of the lowest molar mass penetrant was considerably lower, 6 to 7 kJ/mol. The solubility increased markedly with decreasing molar mass of the penetrant and with decreasing elastomer crosslink density.     

Water absorption behavior of acrylonitrile‐butadiene (NBR) latex impregnated jute nonwoven fabric composites

Composites were fabricated by impregnating the jute nonwoven fabric in acrylonitrile–butadiene (NBR) latex. The effect of different pickup ratio (dry, wt/wt) of NBR latex to jute nonwoven fabric, viz., 0.5 : 1, 1 : 1.5, 1.5 : 1, 2 : 1, and 2.5 : 1 on the water absorption behavior of the composites were evaluated. Water absorption studies were carried out at different temperatures, viz. 30, 50, and 70°C, based on immersion weight gain method. From the sorption result, the diffusion (D) and permeation (P) coefficients of water penetrant have been calculated. Significant increase in the diffusion and permeation coefficients was observed with increase in the temperature of sorption experiments. Drastic reductions in diffusion and permeation coefficients were noticed with increase in the pickup ratio of NBR on to jute nonwoven fabric. Attempts were made to estimate the empirical parameters like n, which suggests the mode of transport, and K is a constant that depends on the structural characteristics of the composite in addition to its interaction with water. The temperature dependence of the transport coefficients has been used to estimate the activation energy parameter for diffusion (E_D) and permeation processes (E_p) from Arrhenius plots. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 2045–2050, 2006     

Vapor barrier properties of polycaprolactone montmorillonite nanocomposites: effect of clay dispersion

Different compositions of poly(ε-caprolactone) (PCL) and (organo-modified) montmorillonite were prepared by melt blending or catalyzed ring opening polymerization of ε-caprolactone. Microphase composites were obtained by direct melt blending of PCL and sodium montmorillonite (MMT-Na⁺). Exfoliated nanocomposites were obtained by in situ ring opening polymerization of ε-caprolactone with an organo-modified montmorillonite (MMT-(OH)₂) by using dibutyltin dimethoxide as an initiator/catalyst. Intercalated nanocomposites were formed either by melt blending with organo-modified montmorillonite or in situ polymerization within sodium montmorillonite. The barrier properties were studied for water vapor and dichloromethane as an organic solvent. The sorption (S) and the zero concentration diffusion coefficient (D₀) were evaluated for both vapors. The water sorption increases with increasing the MMT content, particularly for the microcomposites containing the unmodified MMT-Na⁺. The thermodynamic diffusion parameters, D₀, were compared to the value of the parent PCL: both microcomposites and intercalated nanocomposites show diffusion parameters very near to PCL. At variance exfoliated nanocomposites show much lower values, even for small montmorillonite content. In the case of the organic vapor, the value of sorption at low relative pressure is mainly dominated by the amorphous fraction present in the samples, not showing any preferential adsorption on the inorganic component. At high relative pressure the isotherms showed an exponential increase of sorption, due to plasticization of the polyester matrix. The D₀ parameters were also compared to those of the unfilled PCL; in this case, both the exfoliated and the intercalated samples showed lower values, due to a more tortuous path for the penetrant molecules.     

Effect of anodically evolved gas bubbles on the rate of cathodic mass transfer in a vertical cylinder cell

Mass transfer coefficients were measured for the deposition of a copper from acidified copper sulphate solution at a vertical cylinder cathode stirred by oxygen evolved at a coaxial vertical cylinder lead anode placed upstream from the cathode and flush with it. The cathodic mass transfer coefficient was increased by a factor of 2.75–6.7 over the natural convection value depending on the rate of oxygen discharge at the lead anode and height of the cathode. The data were correlated by the equation:J=0.66(F_rR_e)^–0.21 An electrochemical reactor built of a series of vertical coaxial annular cells stirred by the counter electrode gases is proposed as offering an efficient way of stirring with no external stirring power consumption.Nomenclature a, b, c constants - C concentration of copper sulphate, mol cm^–3 - d cylinder diameter, cm - D diffusivity, cm² s^–1 - F Faraday's constant - g acceleration due to gravity, cm² s^–1 - h electrode height, cm - i current density at the oxygen generating anode, A cm^–2 - I _L limiting current density, A cm^–2 - K mass transfer coefficient, cm s^–1 - P gas pressure, atm - R gas constant, atm cm³ mol^–1 K^–1 - T temperature, K - u solution viscosity, poise - V oxygen discharge rate as defined by Equation 9, cm³ cm^–2 s^–1 or cm s^–1 - Z number of electrons involved in the reaction - J mass transferJ factor (S _tS_c ^0.66) - S _t Stanton number (K/V) - S _c Schmidt number (v/D) - S _h Sherwood number (Kh/D) - R _e Reynold's number (/Vh/u) - F _r Froude number (V ² /hg) - G_r Grashof number [gh ³/v² (1–)] - density of the solution, g cm^–3 - kinematic viscosity, cm² s^–1 - void fraction of the gas in the liquid-gas dispersion     

Electrolytic mass transport at a rotating outer cylinder electrode with developing axial flow in the annulus

Mass transport in an experimental horizontal electrochemical reactor with a rotating outer cylinder and axial flow in the annulus has been investigated, and appropriate dimensionless relationships for the estimation of mass transport rates have been developed by employing statistical regression analysis of experimentally measured flow rates and current density.Nomenclature c _O active ion concentration in electrolyte bulk - c _a supporting electrolyte concentration in electrolyte bulk - D electrolyte diffusivity - d _e equivalent diameter - F Faraday's constant - I electric current - i _c cathodic current density - Nu Nusselt number - L electrode length - Pe Peclet number (Re ·Sc) - R ₁ inner cylinder radius (outer) - R ₂ outer cylinder radius (inner) - R ² square of the multiple correlation coefficient - Re Reynolds number (2(R ₂–R ₁)/v) - Sc Schmidt number (v/D) - Sh Sherwood number (2i _c(R ₂–R ₁)/zFDc _o) - Ta _m modified Taylor number (R ₂(R₂–R ₁ ^3/2/vR ₁ ^1/2 ) - axial electrolyte velocity - z valency (z=2 in the current case) - v electrolyte kinematic viscosity - rotation speed     

Dynamic adsorption behaviors between Cu2+ ion and water‐insoluble amphoteric starch in aqueous solutions

Dynamic adsorption behavior between Cu²⁺ ion and water‐insoluble amphoteric starch was investigated. The sorption process occurs in two stages: external mass transport occurs in the early stage and intraparticle diffusion occurs in the long‐term stage. The diffusion rate of Cu²⁺ ion in both stages is concentration dependent. In the external mass‐transport process, the diffusion coefficient (D₁) increases with increasing initial concentration in the low‐ (1 × 10^?3‐4 × 10^?3M) and high‐concentration regions (6 × 10^?3‐10 × 10^?3M). The values of adsorption activation energy (k_d1) in the low‐ and high‐concentration regions are 15.46–24.67 and ?1.80 to ?11.57 kJ/mol, respectively. In the intraparticle diffusion process, the diffusion coefficient (D₂) increases with increasing initial concentration in the low‐concentration region (1 × 10^?3‐2 × 10^?3M) and decreases with increasing initial concentration in the high‐concentration region (4 × 10^?3‐10 × 10^?3M). The k_d2 values in the low‐ and high‐concentration regions are 9.96–15.30 and ?15.53 to ?10.71 kJ/mol, respectively. These results indicate that the diffusion process is endothermic in the low‐concentration region and is exothermic in the high‐concentration region for both stages. The external mass‐transport process is more concentration dependent than the intraparticle diffusion process in the high‐concentration region, and the dependence of concentration for both processes is about equal in the low‐concentration region. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 2849–2855, 2001     

Zinc removal from dilute solutions using a rotating cylinder electrode reactor

Mine residue recycling processes produce dilute zinc solutions suitable for metal recovery. The rotating cylinder electrode reactor behaviour sequentially followed charge transfer and diffusion control mechanisms, even with solutions contaminated with metals or organic substances. Zinc removal at low pH (0) and low concentration (2 mg dm^–3) is demonstrated. Under galvanostatic operation, the zinc deposition current efficiency in the charge transfer control region attains values up to 77.3%, whereas in the diffusion control region it decreases rapidly to values as low as 0.1%. When a potentio-static mode is used, less energy is required to deposit zinc, even at low current efficiency. The results and possible problems for continuous reactor operation under conditions of powder formation are identified and discussed using knowledge from other zinc industries such as electrowinning, plating and batteries.List of symbols A _c cylinder electrode active surface (cm²) - A _d disc electrode active surface (cm²) - c _H analytical sulfuric acid concentration (mol cm^–3) - c _Zn analytical zinc sulphate concentration (mol cm^–3) - d cylinder electrode diameter (cm) - D zinc diffusion coefficient (cm² s^–1) - F Faraday constant (96 500 C mol^–1) - I total current (A) - I _H hydrogen production current (A) - I ₁ zinc deposition limiting current (A) - j critical hydrogen current density (A cm^–2) - k zinc mass transfer coefficient (cm s^–1) - K Wark's rule constant - n number of electrons exchanged in the zinc deposition reaction - Re Reynolds number (d ²/2) - Sc Schmidt number (/D) - Sh Sherwood number (kd/D) - t time (s) - V electrolyte volume in the RCER (cm³) - solution kinematic viscosity (cm² s^–1) - zinc deposition current efficiency - rotation speed (rad s^–1)     

Diffusion of saturated hydrocarbons in low density polyethylene (LDPE) films

The diffusion coefficients at zero penetrant concentration, D₀, of n-heptane, n-heptane, n-octane, n-decane, and 2,2,4-trimethylpentane (TMP) in LDPE were obtained in the range of 25–50°C, using the desorption method. The dependence of D₀ on the size and shape of the penetrant is reported. It was found that D₀ decreases with increasing penetrant molecule size. The activation energies of diffusion in the temperature range of 25–50°C increase with increasing penetrant molecule size and are independent of temperature. The results are interpreted in terms of the free volume theory and semiquantitative estimates of the free volume parameters are reported.     

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.     

Molecular transport characteristics of a chlorosulfonated polyethylene geomembrane in the presence of aromatic esters

Results of a study on sorption and diffusion of chlorosulfonated polyethylene geomembrane with methyl benzoate, ethyl benzoate, methyl salicylate, iso-butyl salicylate, phenyl acetate, and diethyl phthalate in the temperature range 25–60°C are presented. A gravimetric sorption method is used to calculate the diffusion and permeation coefficients from the Fickian relationship. The diffusion results are dependent on penetrant–membrane interactions, temperature, and on penetrant concentration. The values of diffusion coefficients range from 0·02 × 10^?7 cm² s^?1 for diethyl phthalate at 25°C to 1·81 × 10^?7 cm² s^?1 for ethyl benzoate at 60°C. The activation energies for diffusion range from 21 to 50 kJ mol^?1. The values of heat of sorption ranged between 2·2 and 6·4 kJ mol^?1. Sorption results are also analyzed using a first-order sorption kinetic equation. Experimental results and calculated parameters are used to discuss the transport behavior. None of the esters used have shown any chemical attack toward the geomembrane.     

Diffusion of water vapour in cellulose acetate: 2. Permeation and integral sorption kinetics

A series of permeation and integral sorption kinetic experiments were performed under both absorption and desorption conditions on membranes of cellulose acetate prepared by the same methods and conditions as before¹. Alternative methods of data treatment are presented. The slow approach to steady state as well as analysis of time lag data suggest that the limiting value of the thermodynamic permeability coefficient is approached at a slow rate. In view of a comparable time-variability already observed in the solubility coefficient¹, these results indicate that the mobility of penetrant molecules does not decrease with time; hence they imply that the effect of partial immobilisation of the water molecules in clusters is offset by polymer plastisization caused by the penetrant. The diffusion coefficient D is shown to increase with concentration in all cases, thus confirming the conclusions based on differential sorption data. D measured in absorption is, at any concentration, lower than in desorption, but in desorption it shows satisfactory agreement between the two limbs of the equilibrium isotherm.     

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.     

Enhanced mass transfer at the rotating cylinder electrode: III. Pilot and production plant experience

Enhanced mass transfer at a rotating cylinder electrode, due to the development of surface roughness of a metal deposit, has been studied in a range of commercial and pilot scale reactors known as ECO-CELLS. The data obtained for relatively restricted ranges of process parameters show reasonable agreement with the more definitive data obtained under laboratory conditions. With scale-up factors of approximately six times in terms of the rotating cylinder diameter, enhanced mass transfer factors of up to 30 times are reported (in comparison with hydrodynamically smooth electrodes) due to the development of roughened deposits during the process of metal extraction from aqueous solution.Nomenclature a, b, c constants in Equation 15 - A active area of rotating cylinder (cm²) - C (bulk) concentration of metal (mol cm^–3 or mg dm–3) - c concentration change over reactor (mol cm^–3 or mg dm^–3) - C _IN,C _OUT,C _CELL inlet, outlet and reactor concentrations of metal (mol cm^–3 or mgdm^–3) - d diameter of rotating cylinder (cm) - D diffusion coefficient (cm₂ s_–1) - f _R fractional conversion - F Faraday constant=96 500 A s (mo1^–1) - I current (A) - I _L limiting current (A) - I _o useful current (A) - j _D ^' mass transport factor (=St Sc ^c) - K constant in Equation 27 - K _L mass transport coefficient (cm s^–1) - m slope of Fig. 8 (s^–1) - M molar mass of copper = 63.54 g mol^–1 - n number of elements in the cascade - N volumetric flow rate (cm^{3 –1}) - P Reynolds number exponent for powder formation (Equation 28) - R total cell resistance (Q) - t time (s) - U peripheral velocity of cylinder (cm s^–1) - V _cell cell voltage (V) - V _R,V _T effective cell, reservoir volume (cm³) - W electrolytic power consumption (W) - x velocity index in Equation 27 - z number of electrons - Re Reynolds number=Ud/v - Sc Schmidt number=v/D - St Stanton number=K _L/U - gu kinematic viscosity (cm² s^–1) - cathode current efficiency - rotational speed (revolutions min^–1) - peak to valley roughness (cm)     

The role of mass transfer in the electrolytic reduction of hexavalent chromium at gas evolving rotating cylinder electrodes

The rate of electrolytic reduction of hexavalent chromium from acidic solution at a hydrogen-evolving rotating cylinder lead cathode was studied under conditions of different current densities, Cr⁶⁺ concentrations and rotation speeds. The rate of the reaction was found to follow a first order rate equation. The specific reaction rate constant was found to increase with increasing rotation speed until a limiting value was reached with further increase in rotation speed. Mechanistic study of the reaction has shown that at relatively low rotation speeds the reduction of Cr⁶⁺ is partially diffusion controlled, at higher speeds the reaction becomes chemically controlled. The limiting specific reaction rate constant was related to the operating current density by the equationK=0.044i ^1.385. The current efficiency of Cr⁶⁺-reduction was measured as a function of current density, initial Cr⁶⁺ concentration and rotation speed. Possible practical applications are discussed.Nomenclature A electrode area (cm²) - a, b constants in Equations 5 and 13, respectively - C bulk concentration of Cr⁶⁺ at timet(M) - C _o initial concentration of Cr⁶⁺ (M) - C _i interfacial concentration of Cr⁶⁺ (M) - d cylinder diameter (cm) - D diffusivity of Cr⁶⁺ (cm² s^–1) - e _o standard electrode potential (V) - F Faraday's constant (96 487 C) - current consumed in hydrogen discharge (A) - i current density (A cm^–2) - I cell current (A) - K _l mass transfer coefficient (cm s^–1) - K _r mass transfer coefficient due to cylinder rotation (cm s^–1) - K _o natural convection mass transfer coefficient (cm s^–1) - K _g mass transfer coefficient due to hydrogen stirring (cm s^–1) - K ₂ specific reaction rate constant (cm s^–1) - K overall rate constant (cm s^–1) - m theoretical amount of Cr⁶⁺ reduced during electrolysis (g) - P gas pressure (atm) - R gas constant (atm cm³ mol^–1 K^–1) - T temperature (K) - t time (s) - V linear speed of the rotating cylinder (cm s^–1) - hydrogen discharge rate (cm³ cm^–2 s^–1) - V _s solution volume (cm³) - z electrochemical equivalent (g C^–1) - Z number of electrons involved in the reaction - Re Reynolds number (Vd/v) - Sh Sherwood number (K _r d/D) - Sc Schmidt number (v/D) - rotation speed (r.p.m.) - kinematic viscosity (cm² s^–1)     

Diffusion of m-nitroaniline into polyacylonitrile

The diffusion of nonionic penetrant, m-nitroaniline, into polyacrylonitrile was studied in detail on a range of temperature from 50.6°C to 95.0°C. The penetrant distribution in polymer is Fickian, which is different from that of cationic dye, Malachite Green reported earlier. The diffusion coefficient D increases with the rise of temperature. The sharp inflection point (72°C) of the Arrhenius plot, log D versus 1/T, corresponds to T_g of polyacrylonitrile in the presence of water, which is lower than that measured in the dry state by a dynamic mechanical testing method. The activation energy is constant below T_g (ca. 10 kcal/mole), suddenly reaches a maximum at T_g and then gradually decreases with increasing temperature. General trends of Arrhenius plot for different polymer–penetrant systems are discussed. The temperature dependence of penetrant diffusion above T_g can be described by a general form of the WLF equation, log a_T = log (D_Tg/D_T) = ? C₁^g(T ? T_g)/(C₂^g + T ? T_g), where the values of C₁^g and C₂^g were calculated to be 4.03 and 24.54, respectively. A comparison was made between m-nitroaniline and Malachite Green. The difference in the respective T_g and the constants C₁^g and C₂^g of the WLF equation in polyacrylonitrile is attributed to the size of the penetrants and their ionic character. The surface concentration increases below T_g and decreases above T_g with rise in temperature.     

Diffusion of ethyl acetate vapor in strained low density polyethylene

At a fixed vapor pressure p of the penetrant and constant temperature of the experiment, the sorption S = c/p or concentration c of the ethylacetate vapor in the uniaxially strained low density polyethylene (LDPE) increases most rapidly at low strains. If, however, on the basis of strain relaxation one separates the total strain ? into an elastic ?_e, and a plastic ?_pl, deformation, one obtains an almost linear increase of the concentration c or sorption S of the sorbate with elastic strain ?_e. The separation of ? = ?_e + ?_pl depends very much on the time t_h the sample is kept elongated and the vapor pressure p of the sorbate. The elastic component decreases and the complementary plastic fraction increases with t_h and p. An almost stationary state is reached after t_h of about 1/2 h. The calculation of the diffusion coefficient D_s1 from the first sorption immediately after the stretching is affected by this slow adjustment in the interval 0 ≤ t_h ≤ ½h and shows a pseudo maximum at a strain of ?～ = 10 percent. The first desorption experiment and all the later sorptions and desorptions yield the same D_D = D_S < D_S1 that is the correctly calculated diffusion coefficient D. The coefficient D decreases with the strain ? or ?_e in contrast with the expected increase of D_a of the amorphous component. Such an increase of D_a is expected as a consequence of the fractional free volume (FFV) increase caused by the elongation. According to the FFV concept, a decrease of the measured apparent diffusion coefficient D = ψD_a requires that with increasing ?, the tortuosity factor ψ decreases faster than the increase in D_a.