selectivity

There is no such thing as a "selectivity formula".....it is usually called "education" or "experience". First you must establish your project, like visual properties and strength properties. With that, you can find materials in various technical publications that will allow you to meet these rrequirements. if these cannot be done by yourself, find a friend or a consultant with that background.

Einstein's equation for "selectivity" does exist in the chemical science world! The equation you are looking for is actually the "Stokes-Einstein equation." Stokes-Einstein relation (n = 0.33). Examples: Nitrate Selectivity of Ion-Exchange Resins and of Their Model Compounds. II. Viscosity and Density of Benzyltrialkylammonium Salts in Aqueous Solution and ¹⁴N N.M.R. Relaxation of the Nitrate Ion

G Owens, P Guarilloff and T Kurucsev

Abstract

The densities and viscosities of benzyltrialkylammonium chlorides and nitrates were determined in aqueous solution; the alkyl substituents were methyl, ethyl, propyl , butyl and pentyl . The concentration dependence of the ₁₄N nuclear spin relaxation of the nitrate ion was used to find ion pair association constants for comparison with those derived from conductivity measurements (Part I). Density measurements were used to determine partial molar volumes, and viscosity measurements to find hydrodynamic volumes of the solutes. With the assumption of additivity of ionic volumes, cationic volumes calculated from the two series of chloride and nitrate salts agreed well. The increase in the ratio of hydrodynamic to partial ionic volumes with increasing chain length of the alkyl substituent was interpreted as a corresponding increase in hydrophobic hydration.

Australian Journal of Chemistry 48(8) 1401 - 1411

Full text doi:10.1071/CH9951401

© CSIRO 1995

Environ. Sci. Technol., 37 (7), 1432 -1440, 2003. 10.1021/es0207495 S0013-936X(02)00749-6
Web Release Date: February 28, 2003

Copyright © 2003 American Chemical Society

Ion Exchange Selectivity as a Surrogate Indicator of Relative Permeability of Ions in Reverse Osmosis Processes

Parna Mukherjee and Arup K. SenGupta*

Department of Civil and Environmental Engineering, Lehigh University, 13 East Packer Avenue, Bethlehem, Pennsylvania 18015

Received for review May 22, 2002

Revised manuscript received September 20, 2002

Accepted January 9, 2003

Abstract:

The existing body of experimental data in the open literature clearly indicate that reverse osmosis (RO) processes reject ions of identical valence (i.e., homovalent ions) to different degrees. For example, rejections (or relative permeations) of monovalent anions (such as Cl^-, NO₃^-, Br^-, CH₂ClCOO^-, ClO₄^-, etc.) during RO processes are different under otherwise identical conditions. The same is true for divalent anions (namely, SO₄^2-, HPO₄^2-, SeO₄^2-) or monovalent cations (namely, Li⁺, Na⁺, K⁺, and NH₄⁺). The solution diffusion model with the Nernst-Planck equation is unable to predict the differential permeation behaviors of homovalent ions. It is recognized that hydrated ionic radii data, if available, could be used to compute interdiffusion coefficients (or salt permeability coefficients) of permeating electrolytes. However, a careful scrutiny of the existing body of hydrated ionic radii data in the open literature provide clear evidence that they are unreliable for polyatomic ions such as nitrate, nitrite, selenate, phosphate, chloroacetate, sulfate, etc. Also, ionic diffusivities computed from equivalent conductance data fail to predict the hierarchy of relative permeations of homovalent ions in RO processes. Central to this study is the underlying scientific premise that ion-exchange selectivity can be used as an effective parameter to predict the relative permeability of homovalent ions in a multicomponent system. For two ions of identical valence, ion-exchange selectivity based on Coulombic interaction is dependent only on their relative hydrated ionic radii, which in turn govern the interdiffusion coefficients of permeating electrolytes. The higher the ion-exchange selectivity of a specific ion, the lower is its hydrated ionic radius and, hence, more permeable is the ion. The theoretical relationship between ion-exchange selectivity and permeability can be well explained with the aid of the Stokes-Einstein equation. Experimental results presented in this study with both monovalent and divalent ions show a strong characteristic correlation between ion-exchange selectivity and relative permeation, i.e., a higher ion-exchange selectivity always leads to a greater permeability. One major advantage of this approach is the ease with which ion-exchange selectivity can be determined by ion chromatography and/or batch isotherm technique. A large body of existing experimental data for RO and nanofiltration processes in the open literature, when carefully reviewed, also validate this scientific premise. Type of membrane, solvent dielectric constant, and pH influence the overall solvent and salt permeation fluxes, but the relative permeation of homovalent ions still follows the ion-exchange selectivity sequence.

The effects of lipid chain packing and permeant size and shape on permeability across lipid bilayers have been investigated in gel and liquid crystalline dipalmitoylphosphatidylcholine (DPPC) bilayers by a combined NMR line-broadening/dynamic light scattering method using seven short-chain monocarboxylic acids (formic acid, acetic acid, propionic acid, butyric acid, valeric acid, isovaleric acid, and trimethylacetic acid) as permeants. The experimental permeability coefficients are compared with the predictions of a bulk solubility diffusion model in which the bilayer membrane is represented as a slab of bulk hexadecane. Deviations of the observed permeability coefficients (P_m) from the values predicted from solubility diffusion theory (P_o) lead to the determination of a correction factor, the permeability decrement f (= P_m/P_o), to account for the effects of chain ordering. The natural logarithm of f has been found to correlate linearly with the inverse of the bilayer free surface area with slopes of 25 ± 2, 36 ± 3, 45 ± 8, 32 ± 12, 33 ± 4, 49 ± 12, and 75 ± 6 Ų for formic acid, acetic acid, propionic acid, butyric acid, valeric acid, isovaleric acid, and trimethylacetic acid, respectively. The slope, which measures the sensitivity of the permeability coefficient of a given permeant to bilayer chain packing, exhibits an excellent linear correlation (r = 0.94) with the minimum cross-sectional area of the permeant and a poor correlation (r = 0.59) with molecular volume, suggesting that in the bilayer interior the permeants prefer to move with their long principal axis along the bilayer normal. Based on these studies, a permeability model combining the effects of bilayer chain packing and permeant size and shape on permeability across lipid membranes is developed.

	INTRODUCTION

The passive transport rates of small molecules across biological membranes are often explained, at least qualitatively, by means of a bulk-phase solubility diffusion model (Fettiplace and Haydon, 1980; Finkelstein, 1976; Hanai and Haydon, 1966; Paula et al., 1996). This model, which may be traced to the formulation of Overton's rules nearly a century ago (Overton, 1899), describes the permeation process in terms of the partitioning of the permeant into the membrane, followed by its diffusion through the membrane, where the properties of the membrane are assumed to be adequately represented by a bulk lipid (e.g., hydrocarbon) solvent. It is well known, however, that permeabilities across biological membranes and model lipid bilayers depend strongly on both the degree of lipid chain packing in the membranes (Lande et al., 1995; Worman et al., 1986; Xiang and Anderson, 1995b, 1997) and the size of the permeating solute (Stein, 1986; Walter and Gutknecht, 1986; Xiang and Anderson, 1994c). The effects of lipid chain packing on permeability are most clearly demonstrated by the dramatic increase in transmembrane transport rates that occurs because of a gel-to-liquid crystalline phase transition (Carruthers and Melchior, 1983; Jansen and Blume, 1995; Papahadjopoulos et al., 1973; Xiang and Anderson, 1997). Membranes that are more "ordered" as a result of polar headgroup composition, or because of increased cholesterol concentrations or lower temperatures, or monolayers under high lateral pressures have greater resistances to permeation than predicted from a bulk solubility diffusion model, often by orders of magnitude (Bar-On and Degani, 1985; Brahm, 1983; Finkelstein, 1976; Magin and Niesman, 1984; Peters and Beck, 1983; Sada et al., 1990; Todd et al., 1989a,b). A steep size selectivity is exhibited by both biological membranes and lipid bilayers, as noted by several groups, including Lieb and Stein (1969, 1971, 1986), Walter and Gutknecht (1986), and ourselves (Anderson and Raykar, 1989; Xiang and Anderson, 1994b). These phenomena also cannot be accounted for by bulk solubility diffusion theory.

Although substantial progress has been made recently, the molecular mechanisms responsible for the chain-ordering effects on permeability and the role of permeant size have not been well understood historically. It has been common to interpret both the effects of chain ordering on permeability (Lande et al., 1995) and the steep dependence of permeation rates on permeant size (Stein and Nir, 1971; Stein, 1986) exclusively in terms of changes in solute diffusivity within membranes. Walter and Gutknecht (1986) argued, for example, that the effects of solute size on partitioning into a bilayer membrane are unimportant on the basis of the similarity in solubility of short-chain n-alkanes in lipid bilayers (Miller et al., 1977). On the contrary, large size effects on solute partitioning into interphases are evident from the high resolution attainable in chromatographic separations on the basis of subtle differences in size and shape (Wise et al., 1981). More recently, others have shown both theoretically (Marqusee and Dill, 1986) and experimentally (DeYoung and Dill, 1988, 1990; Xiang and Anderson, 1995b) that increasing chain ordering within lipid bilayers substantially reduces solute partitioning into bilayers. These effects are particularly evident in the more ordered regions of the bilayer, as confirmed in neutron diffraction experiments (White et al., 1981) and molecular dynamics simulations (Marrink and Berendsen, 1994, 1996; Xiang and Anderson, 1998). Further complicating the situation, statistical mechanical theory recently developed by the authors (Xiang and Anderson, 1994a) and molecular dynamics simulations conducted in these laboratories (data not shown) suggest that the size selectivity in partitioning is amplified with increases in bilayer chain ordering.

These recent results suggest that structure-transport relationships developed solely on the basis of lipophilicity or hydrogen bonding potential without consideration of molecular size effects and the influence of bilayer composition (i.e., chain ordering) on these size effects may be unreliable. Walter and Gutknecht (1984) noted, for example, that literature data for the incremental free energy changes accompanying the addition of a methylene group to various homologous series of permeants derived from transport studies across a variety of model bilayer and biological membranes were highly variable, ranging from nearly zero to 900 cal/mol. In addition to the inappropriate treatment of unstirred layer effects in some of these studies pointed out by Walter and Gutknecht, the differences in membrane composition and complexity in terms of lipid chain packing (e.g., gel and liquid-crystalline phases) may also have contributed to the variability in the effects of permeant chain length on permeability.

A more systematic characterization of solute permeability with respect to the states of lipid packing in lipid bilayers is essential to a thorough understanding of molecular mechanisms for solute transport across biological membranes. The difficulties in investigating the effects of permeant size on permeability arise from the fact that changes in permeant size are usually accompanied by changes in lipophilicity, with the latter effects often overshadowing the effects of permeant size alone.

In this study we will investigate the effects of permeant size on membrane permeability in a way markedly different from previous studies. Namely, we will examine by means of an NMR line-broadening method the size and shape selectivity of dipalmitoylphosphatidylcholine (DPPC) bilayers for the transport of a series of seven monocarboxylic acids differing in chain length and degree of chain branching (Fig. 1) as a function of lipid bilayer packing, characterized by the bilayer free surface area. The use of a homologous series of monocarboxylic acids minimizes the effects of hydrogen bond potential on the analysis of solute shape and size effects. Our aim, in part, is to examine the hypothesis that increasing lipid chain order will be accompanied by increased membrane selectivity to permeant size and shape. To accomplish this we will apply a chain ordering correction factor to the bulk solubility-diffusion model predicted permeability coefficients to account for the discrepancies between the observed values and those calculated neglecting chain-ordering effects (Xiang and Anderson, 1997). We will then develop an empirical relationship between the permeability decrement due to chain ordering and the bilayer packing properties described by the membrane free surface area. The slope of the linear relationship between the natural logarithm of the chain-ordering correction factor (i.e., the permeability decrement) and the inverse of free surface area will be shown to depend linearly on permeant size when expressed in terms of permeant cross-sectional area.

EXPERIMENTAL

Materials

DPPC was purchased from Avanti Polar Lipids (Pelham, AL). Formic acid (99%) and [¹⁴C]formic acid (>98%) were purchased from Sigma Chemical Co. (St. Louis, MO). [³H]Acetic acid, [¹⁴C]propionic acid, and [¹⁴C]butyric acid were obtained from American Radiolabeled Chemical (St. Louis, MO). Acetic acid (99.8%), propionic acid (99+%), butyric acid (99+%), valeric acid (99+%), isovaleric acid (99%), trimethylacetic acid (99%), deuterium oxide (99%), and hexadecane (99%) were purchased from Aldrich Chemical Co. (Milwaukee, WI). All other reagents were obtained commercially and were of analytical reagent grade. Polycarbonate membranes and membrane holders were obtained from Nuclepore (Pleasanton, CA).

Large unilamellar vesicle liposome preparation

A detailed description of the experimental procedure has been published elsewhere (Xiang and Anderson, 1995a). In brief, large unilamellar vesicles (LUVs) were prepared by a modified combined technique of Bangham et al. (1965) and Olson et al. (1979). The DPPC lipids were accurately weighed, dissolved in chloroform, evaporated to a dry thin film under nitrogen gas, and left under vacuum for 2 h at ~50°C. A deuterated aqueous solution containing 5-30 mM permeant was then added to a final lipid concentration of 10 mg/ml. The lipids were then hydrated by repeated vortexing and shaking above the main transition temperature (41°C). The multilamellar vesicles formed were then forced through a 0.1-0.2-µm polycarbonate membrane filter 18 times to form LUVs before the NMR transport experiments.

Permeability coefficient determinations

The permeability coefficients for the seven monocarboxylic acids across DPPC bilayers were determined at various temperatures by the ¹H-NMR line-broadening method developed by Alger and Prestegard (1979) and further validated in a recent study by the authors (Xiang and Anderson, 1995a). The experiments were performed on a Bruker-200 NMR spectrometer (Bruker Instruments, Billerica, MA) operated in the Fourier transform mode at 200 MHz. Samples were equilibrated for 20 min at a given temperature controlled by a standard variable-temperature accessory (BVT1000; Bruker). Each spectrum was the average of 32-1000 acquisitions separated by 2-5-s pulse delays. The spectra were Fourier transformed and phased with an Aspect 3000 computer. The resonance frequencies of selected protons in the permeants located inside and outside the vesicles, _i and _o, were separated by adding an impermeable shift reagent, Pr(NO₃)₃ (final concentration, 0.5-3 mM), to the sample before the spectral acquisitions. The binding capacity of the chemical shift reagent (Pr³⁺) and its effects on solute permeability have been studied previously (Xiang and Anderson, 1995a). The DPPC main transition temperature was found to remain constant (41 ± 0.5°C) upon the addition of 5 mM Pr³⁺, and the permeability coefficient for acetic acid in DMPC/CHOL was shown to be independent of [Pr³⁺] up to 40 mM. The concentration of free Pr³⁺ available for binding to the outer vesicle surface is lower than the total Pr³⁺ concentration because of complex formation between carboxylic acids and Pr³⁺. For example, at [Pr³⁺] = 5 mM and an acetic acid concentration of 0.05 M (pD 6.32), only ~25% of the total Pr³⁺ would exist in the uncomplexed form.

The proton peak(s) for the methylene group adjacent to the carboxylic acid group in acetic acid, propionic acid, butyric acid, and valeric acid exhibit the greatest chemical shift in the presence of paramagnetic ions and thus were used for the permeability determinations. However, proton coupling in propionic acid, butyric acid, valeric acid, and isovaleric acid splits the proton resonances into two to four peaks, precluding an accurate determination of the line broadening due to solute transport. This was minimized by irradiating these protons through a separate decoupling channel. The collapsed singlet peak had a linewidth of 1.0-2.2 Hz in LUVs in the absence of chemical shift reagent. For isovaleric acid and trimethylacetic acid, the proton peak(s) for the methyl groups are the strongest and most symmetrical and thus were used for the permeability determinations.

The lifetime of the permeant inside the vesicle, _i, was obtained using the following linewidth expression in the slow exchange limit, |_{i o}|T_2,i 1 (Piette and Anderson, 1959):

(1)

where is the full linewidth at one-half the maximum peak height, and T_2,i is the spin-spin relaxation time, which includes heterogeneous line broadening in the absence of exchange. The linewidth in the absence of exchange (1/T_2,i = 2.6-5.0 Hz) was obtained at a low temperature and/or high pD, where the permeation rate is negligible.

Previous studies in these laboratories have shown that the permeabilities of ionized carboxylic acid permeants are negligible in the pD range of interest (Xiang and Anderson, 1995a). Thus the permeability coefficient for the neutral species, P_m, can be expressed as

(2)

where V is the entrapped volume, A_t is the vesicle surface area, and K_a is the dissociation constant in D₂O. The V/A_t ratio was determined from the vesicle hydrodynamic diameter (d), as obtained from dynamic light scattering (DLS) measurements according to the formula V/A_t = d/6. DLS experiments were conducted with a goniometer/autocorrelator (model BI-2030AT; Brookhaven, Holtsville, NY) and an Ar⁺ ion laser (M95; Cooper Laser Sonics, Palo Alto, CA) operated at 514.5-nm wavelength. One drop of LUV suspension was placed in a 13 × 75 mm cleaned glass test tube and brought to a volume of 2 ml with the same filtered buffer solution. The sample was placed in a temperature-controlled cuvette holder with a toluene index-matching bath. Autocorrelation functions were determined for a period of 100 s with a 10-80-µs duration at 90° and analyzed by the method of cumulants.

Partition coefficient determinations

Hexadecane/water partition coefficients for the series of monocarboxylic acids were measured using the shake flask method at a pH 2 units below the pK_a of the corresponding acid to ensure that >99% was in its un-ionized form. The organic solvent was first washed three times with an equal amount of de-ionized water. The organic solvent (2-3 ml) and 1 ml of an aqueous solution containing 3 × 10² to 1 × 10⁴ M of "cold" permeant or 1-20 µCi of radiolabeled permeant were placed in a test tube and mixed with magnetic stirring in an incubator at a preset temperature (25-50°C) for 24 h. The sample was then centrifuged to remove any emulsified water from the organic phase. Aliquots of both phases were carefully taken for high-performance liquid chromatography (HPLC) analyses of "cold" compounds (acetic acid, propionic acid, butyric acid, valeric acid, isovaleric acid, and trimethylacetic acid) or for liquid scintillation counting (LS1801; Beckman Instrument Co., Fullerton, CA) of radiolabeled compounds (formic acid, acetic acid, propionic acid, and butyric acid). Duplicate measurements were performed with two different permeant concentrations to evaluate the effects of permeant self-association in hexadecane on the measured partition coefficients. To minimize the potential effects of more lipophilic impurities in the radiolabeled compounds (not a problem if HPLC is used for concentration analyses), the organic phase was replaced with fresh solvent, and the above experimental procedure was repeated until the radioactivity in the organic phase reached a plateau value. The partition coefficient was calculated as the ratio between the molar concentrations in the hydrocarbon solvent and water.

The partition coefficients obtained using both "hot" and "cold" compounds and two different solute concentrations were generally within the experimental error, suggesting that self-association was not a significant factor in the partition coefficient determinations.

An HPLC system consisting of a syringe-loaded sample injector (Rheodyne model 7125; Rainin Instrument Co., Woburn, MA), a solvent delivery system (110B; Beckman Instrument Co., San Ramon, CA) operated at a flow rate of 1.0-1.2 ml/min, a dual-wavelength absorbance detector (model 441, Water Associates, Milford, MA) operated at 214 nm, an integrator (model 3392A; Hewlett-Packard Co., Avondale, PA), and a reversed-phase column packed with 5-µm C18 300 Å (Jupiter, 4.6 mm i.d. × 25 cm; Phenomenex Co., Torrance, CA) was used at ambient temperature for the analyses of the "cold" monocarboxylic acids taken during the partition experiments. Mobile phases containing 2.5%-40% acetonitrile, depending on the analyte lipophilicity, and 0.01 M phosphate buffer (pH 3.0) were employed.

pK_a determinations in D₂O

The ionization constants for the series of monocarboxylic acids in deuterated water were measured by a pD titration. An accurately weighed amount of each acid was dissolved in 2.0 ml D₂O to yield a final concentration of 0.03 M. pK_a determinations were carried out at 24°C under nitrogen by slow addition of 0.03 M NaOD while monitoring the apparent pH with a standard pH meter (PHM82; Radiometer, Copenhagen, Denmark) calibrated with standard buffer solutions. The pD values were obtained by adding 0.40 units to the corresponding pH readings (Glasoe and Long, 1960). Plots of the pD values versus the titrant volumes added were fitted numerically, including a correction for changes of the ionic strength using Davies' equation (Perrin and Dempsey, 1974). The dissociation constants obtained are presented in Table 1.

Transport experiments were conducted in large unilamellar vesicles composed of DPPC. The chain packing properties within these DPPC bilayers, as characterized by the bilayer free surface area (see Eq. 8), were varied by changes in temperature, which also brought about changes in bilayer phase structure (gel and liquid crystalline phases). Seven monocarboxylic acids differing in chain length and the degree of chain branching as shown in Fig. 1 were used as permeants. This permeant series offered several advantages for the purposes of this study. One was the technical advantage of being able to determine the permeability coefficients for this series of relatively lipophilic permeants by the NMR line-broadening method, in contrast to other, slower transport methods that rely on separations of intravesicular permeants from the external solution (e.g., size exclusion chromatography, ultrafiltration, or dialysis). Moreover, the size and shape of permeants within this series could be varied in a more systematic manner. Furthermore, the structural changes involved only variations in the number of methylene groups, which have relatively small and well-documented effects on solute lipophilicity in comparison to most substituents. This rendered less problematic the selection of an appropriate bulk reference solvent to correct for the effects of changes in permeant lipophilicity on permeability, as the incremental free energy for the transfer of a single methylene group from water to various bulk organic solvents is essentially independent of the nature of the solvent (849 cal/mol in heptane compared with 712 cal/mol in octanol; Davis et al., 1972, 1974).

Permeability coefficients: expectations from bulk solubility-diffusion theory

As noted earlier, bulk solubility-diffusion theory assumes that solute partitioning from water into and diffusion through a lipid bilayer or biomembrane resembles that within a homogeneous slab of bulk solvent such as olive oil, octanol, or hydrocarbon. The permeability coefficient predicted from this model (P_o) can be expressed as

(3)

where K_hc/w and D_o are the organic solvent (i.e., hexadecane)/water partition coefficient and the diffusion coefficient in the organic solvent, respectively, and is the effective thickness of the homogeneous layer of organic solvent.

To use bulk solubility-diffusion theory to predict permeability coefficients as temperature is varied, the temperature dependence for permeant partitioning into (and diffusion through) an organic solvent that most closely mimics the physicochemical properties of the barrier domain in the bilayer membrane under investigation must be known. A large body of evidence has shown that the barrier domain in lipid bilayers behaves like a hydrocarbon solvent with respect to intermolecular electrostatic interactions (Stein, 1986; Xiang and Anderson, 1994c). Moreover, certain dynamic properties in the bilayer interior, including chain reorientation rates and microviscosity resemble those in bulk hexadecane (Bell, 1981; Brown et al., 1986; Venable et al., 1993). Thus hexadecane, which resembles the lipid chains in DPPC in terms of chain length and degree of saturation, was used as a model solvent in this study. Fig. 2 shows the Arrhenius plots of the hexadecane/water partition coefficients for the series of monocarboxylic acids used in this study. The molar free energies, enthalpies (obtained from the slopes of linear fits of the data in Fig. 2), and entropies of transfer from water to hexadecane are presented in Table 1. The transfer enthalpies (H°) are in the range of 3.2-5.4 kcal/mol and generally increase with the chain length, suggesting that permeant dehydration contributes only a small fraction of the large activation energies observed for permeability of the monocarboxylic acids across DPPC bilayers (vide infra). Increases in H° with chain length were also found for the transfer of short-chain alkanols (C₁-C₅) from water to hydrocarbons (Nemethy et al., 1963). These values are approximations, as they are assumed to be constant over the entire temperature range explored (25-50°C). Large transfer heat capacities are typically observed (DeYoung and Dill, 1990), however, which may change the slopes of Arrhenius plots from which the molar enthalpies of transfer were obtained. The partition coefficient for valeric acid is slightly larger than that for isovaleric acid, which is consistent with the view that chain branching decreases the molecular surface area and thereby reduces the partition coefficient due to the reduced hydrophobic interaction in water (Grant and Higuchi, 1990). However, the partition coefficient for trimethylacetic acid is about twice as large as that for valeric acid, whereas H°_hc/w is smaller for trimethylacetic acid. These results may be attributed to the fact that the three methyl groups in trimethylacetic acid may interfere with solvation of the carboxylic acid group by water, effectively making it less hydrophilic. Steric hindrance of solvation of the ion produced on ionization of highly hindered aliphatic acids also decreases acid strength (Hine, 1975), as demonstrated by a 0.2-unit higher pK_a value for trimethylacetic acid than that for valeric acid.

The diffusion coefficients of monocarboxylic acids in bulk solvents are determined primarily by their molecular sizes (Albery et al., 1967), whereas the polar carboxylic acid residue is expected to play a minor role, at least in nonpolar hydrocarbons (Chan, 1983). As a result, the diffusion coefficients for the monocarboxylic acids used in this study were estimated from a relation developed from the experimental diffusivity data for a series of alkane homologs in hexadecane at 25°C (Hayduk and Ioakimidis, 1976) and the assumption that the diffusion coefficient varies inversely with solvent viscosity:

(4)

where is the viscosity (cp) of hexadecane and V_s is the solute volume (ų). The molecular volumes for the series of diffusants were calculated from an atomic additivity method (Edward, 1970). The size dependence in Eq. 4 (n = 0.83) is stronger than that predicted by the Stokes-Einstein relation (n = 0.33), though less than that typically observed for solute diffusion in polymers (n = 1.1-3.8) (Lieb and Stein, 1969).

Because of the small changes of bilayer density with temperature, the thickness of the acyl chain region in the bilayer, , is related to the bilayer reduced surface density (vide infra) by = l_o, where l_o (= 38.4 Å) is the end-to-end length of a fully extended DPPC molecule.

The permeability coefficients (P_o) from bulk solubility-diffusion theory are calculated at different temperatures by combining the sets of partition coefficients, diffusion coefficients, and bilayer thickness data described above. These results are presented in Fig. 3 for later comparison with the experimental permeability coefficients. Bulk solubility diffusion theory predicts a weak dependence of permeability on temperature, as indicated by the relatively small activation energies E_a derived from the slopes of the ln P_o versus 1/T data in Fig. 3, which are listed in Table 1 (10.3-12.7 kcal/mol).

Membrane permeability coefficients: deviations from bulk solubility-diffusion theory

Fig. 4 shows the proton magnetic resonance peak(s) for the methylene group adjacent to the carboxylic group in butyric acid in DPPC LUVs in the absence and presence of chemical shift reagent (Pr³⁺) and with and without coupling to the neighboring methylene group. In the absence of Pr³⁺, decoupling of the methylene group by irradiating at a radio frequency corresponding to the central position of the adjacent methylene group leads to a narrow singlet peak (~1.5 Hz) for the methylene group (Fig. 4 B). Addition of Pr³⁺ shifts the proton peaks of the extravesicular permeant downfield (~140 Hz), whereas that of the permeant entrapped in the internal aqueous space is broadened (Fig. 4, C and D). The degree of line broadening, which is attributed to the exchange of permeant across the LUVs, was found to depend on pD and temperature. The permeability coefficient can be calculated according to Eqs. 1 and 2 from the observed linewidth and solution pD.

And so forth! Brian Wenzel - Satre, TE/PM, NORDIC Engineering International

Blimey!!! another copy and paster!!

I little paste is a dangerous thing!

He could have just put a couple of links and been good. Basically, we all know that ion selective exchange depends on a number of variables, including the composition of the resin/membrane employed, what the material contacted with to "regenerate" it, etc.