How is it that ionic diffusion is independent of other ions?

How is it that ionic diffusion is independent of other ions?

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This question arises from the explanation of what the resting potential of a cell membrane is. In the Goldman formula, there is no interaction between different ion types.

If diffusion is caused by random movement of ions and collisions, then how is it that the K+ ions do not seem affected by the very high concentration of Na+ ions outside of the membrane? Shouldn't there be an effect due to the fact that outside, the ion concentration overall is higher than inside? How come they are all independent?

Most importantly, the whole Goldman-Hodgkin-Katz model is, well, a model. It is a way we would like to find and explain phenomena, given pen and paper.

Often, scientists build models in order to explain data in hand, but even then, they will have to add something from their imagination. For example, early astronomers saw planets moving differently from stars, and came up with the idea that, you know, planets do not circle the earth, but maybe around some points in space, which in turn circle the earth. That didn't work well, so they created the heliocentric model, where planets and the Earth circled the sun. That was still perfectible, and Newton suggested the planets do not move on circles, but on ellipses. Each generation of astronomers had almost the same data in hand, but chose to make some assumptions in their models.

The same goes with the lack of interaction between potassium and sodium ions: it is a theoretical assumption. As models go, the GHK model is quite good, because it fits experimental findings better than any other model. Its assumptions have a great chance of being true, of reflecting the physical world. I guess you really asked what are the physical facts that underlie the assumption of ion independence. The fact is, you are looking for explanations for a fact that may be or may not be - so any response you will receive is, to a degree, speculation.

My thought is that the number of water molecules (55 molar) that may collide with an ion is far greater than the number of cations (up to a few hundred nanomolar, about 100 million rarer). Perhaps the number of ion-ion collisions is negligible. There is one bottleneck, in the actual channels, but there different species do not meet, because each has its own channels.

Another, more factual, is that the model is imperfect, and independence is more of a wish than a complete truth. Quoting from : "The rich literature on how ion channels fail to obey the independence principle is reviewed in Chapter 14 of Hille (1991), and some specific models will be studied in the following chapter."

Maybe I'm missing something here (and it's not my area of expertise) but…

the GHK formula includes the parameter Vm which is the transmembrane potential. This parameter is determined by the intracellular and extracellular concentrations of all ions. A high external concentration of Na+ will therefore influence the net movement of K+.

One of the assumptions of the GHK equation is that the ions do not directly interact.

Direct observation of ion dynamics in supercapacitor electrodes using in situ diffusion NMR spectroscopy

Ionic transport inside porous carbon electrodes underpins the storage of energy in supercapacitors and the rate at which they can charge and discharge, yet few studies have elucidated the materials properties that influence ion dynamics. Here we use in situ pulsed field gradient NMR spectroscopy to measure ionic diffusion in supercapacitors directly. We find that confinement in the nanoporous electrode structures decreases the effective self-diffusion coefficients of ions by over two orders of magnitude compared with neat electrolyte, and in-pore diffusion is modulated by changes in ion populations at the electrode/electrolyte interface during charging. Electrolyte concentration and carbon pore size distributions also affect in-pore diffusion and the movement of ions in and out of the nanopores. In light of our findings we propose that controlling the charging mechanism may allow the tuning of the energy and power performances of supercapacitors for a range of different applications.

As renewable energy and green technologies such as electric vehicles become prevalent, we must develop new ways to store and release energy on a range of timescales. Rechargeable batteries are ideal for timescales of minutes or hours (electric cars, portable electronic devices, grid storage and so on), while supercapacitors are more promising for second or subsecond timescales and are increasingly being used for transport applications where rapid charging and discharging are required. The superior power handling and cycle lifetime of supercapacitors comes at the expense of energy density, with recent materials-driven research aiming to address this issue by fine-tuning the nanoporous structure of the carbon electrodes 1,2 , and by using ionic liquid electrolytes that are stable at higher voltages 3,4 . Both approaches have afforded some increases in energy density, though not without sacrificing power density. The delicate balance between energy and power must be understood if supercapacitors are to be used in a wide range of applications.

Comment on “Ionic Conductivity, Diffusion Coefficients, and Degree of Dissociation in Lithium Electrolytes, Ionic Liquids, and Hydrogel Polyelectrolytes”

Publication History

  • Received 4 September 2018
  • Revised 21 October 2018
  • Published online 12 November 2018
  • Published in issue 6 December 2018
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Recently Garrido et al.(1) have published a paper in this journal on the electrical conductivity and ion self-diffusion of lithium salts in water, ionic liquids, and hydrogel polyelectrolytes. The work is intended to demonstrate that the assumption of complete dissociation is not necessary for the proper description of the conductance of such electrolyte solutions in addition to describing conduction in the hydrogels. The authors cite work(2) on the thermodynamic properties of electrolyte solutions based on the so-called Arrhenius model of ion association in strong electrolytes in favor of their approach but ignore the fact that this model has been shown to make incorrect predictions.(3,4)

The arguments employed regarding the transport properties rely on a simple but incorrect model relating ion self-diffusion to the electrical conductivity based on the Nernst–Einstein equation and Arrhenius’ theory of incomplete dissociation. The weaknesses of the Arrhenius theory of conductance were dealt with by MacInnes in his classic monograph many years ago: in essence, it assumes the mobilities are constants independent of concentration.(5) Garrido et al.(1) have ignored a large body of experimental, computational, and theoretical work in the literature showing the inadequacy of their approach, which has no proper theoretical justification. The basic flaws are that correlations between the velocities of different ions, between solvent molecules, and between ions and solvent molecules are neglected and that no distinction is made between the electrical and diffusive mobilities of ions in solution, an important concept in electrochemistry. Unfortunately, these are common misconceptions in the literature, e.g., refs (6−10), all recent publications. This Comment seeks to clarify the issues involved.

The limiting value of the self-diffusion coefficient of an ion (DSi) at infinite dilution (denoted by ∞) is given by Nernst’s relation:(11,12) (1) where λi ∞ is the limiting ionic molar conductivity, F and R are the Faraday and gas constants, and T is the absolute temperature. Since the salt molar conductivity is the sum of the ionic contributions, it can be written in terms of the sum of the ion self-diffusion coefficients as (2) for a solution of a 1:1 salt. This is widely known as the Nernst–Einstein relation.

Garrido et al.(1) apply this equation at concentrations as high as 5 mol/L, by modifying it to include the degree of dissociation of the salt, α: (3)

This neglects ion–solvent interactions and assumes that ion–ion interactions are limited to association to form neutral species. They do not cite any source for this version of the Nernst–Einstein equation nor provide any theoretical justification, but an earlier paper from this group(13) employing the same equation gives a work of Hayamizu(14) as the source. However, both Garrido papers neglect that Hayamizu and co-workers make clear in a still earlier study(15) that eq 2 assumes the neglect of Laity “friction coefficients” or as Laity himself put it, “interionic interference”,(16) or more exactly, correlations between the velocities of the different species in solution, both positive and negative.(17−19) We note that McDaniel and Son have, in a recent work,(20) studied ion dynamics in solutions of ionic liquids from infinite dilution in various solvents to the pure liquid, showing very clearly the crossover from the positive correlation of cation–anion velocities in dilute solution to the anticorrelation of all combinations of ion–ion velocities in the pure ionic liquid. As pointed out by Kashyap et al.,(19) the anticorrelations are a direct result of the law of conservation of momentum.(21,22)

If eq 2 were applicable, then one would expect conductivities and ion self-diffusion coefficients to have a similar concentration dependence at constant temperature. Though one must allow for the degree of association to be composition dependent, the general trend should be the same for the three properties. However, this is not always the case. As Robinson and Stokes point out, “the mobility of ions in diffusion varies much less with concentration than does their mobility in electrolytic conduction and while the latter always decreases with increasing concentration, the former may increase, decrease or remain constant, depending on the salt considered.”(11) An increase of the self-diffusion coefficient with increasing concentration is shown for chloride ion in aqueous cesium chloride, for example, in Figure 8.2 of ref (12). Other examples are given in the work of Hertz and Mills on self-diffusion for a number of “water structure-breaking” electrolytes.(23) Current theories of the transport properties of electrolytes such as those of Bagchi, Turq, and co-workers(24,25) are more appropriate than the application of eq 2.

The relationship between the electrical conductivity and the self-diffusion coefficients for both electrolyte solutions and molten salts (including ionic liquids) was put on a sound basis, combining both nonequilibrium thermodynamics and statistical mechanics, by Schönert,(26) following earlier work by Douglass and Frisch,(27) Hertz,(22) Woolf and Harris,(18) and Miller(28) on electrolyte solutions. Though the Woolf–Harris and Miller versions are consistent with Schönert’s, his has the most comprehensive derivation and has proved very useful in dealing with ionic liquids.

For a binary electrolyte with salt cation, C, denoted by 1, and anion, A, denoted by 2, in a neutral solvent (0), where the salt ionizes as (4) and where the measurement of self-diffusion coefficients can be made by either tracer or spin–echo NMR methods, the fluxes (J) of the ions and solvent can be written in the mass-fixed frame of refs (28) and (29) as (5) The thermodynamic force driving diffusion or ion migration in an electric field in direction x for species j is (6) where μj and ϕj are the chemical potential and electrical potential, respectively. F is the Faraday constant. The Onsager phenomenological coefficients Ωij satisfy the reciprocal relations, the basis of nonequilibrium thermodynamics: (7)

Statistical mechanical linear response theory, however, employs Kubo–Green velocity cross-correlation coefficients (VCC) between different particles α and β of species i and j: (8) written in terms of velocities v, also in the mass-fixed reference frame. The brackets indicate an average over all the particles in the system. The term within the brackets, the velocity cross-correlation function (VCF), grows from a negative value to a positive maximum and then decays in an oscillatory fashion with time due to interparticle collisions in a fluid at typical liquid densities. This can be calculated through molecular dynamics simulations and the VCC obtained by averaging over the ensemble and integrating over the time of the simulation.(19)

When i and j are identical components or species and α and β refer to the same particle, the integral of the VCF is a velocity autocorrelation coefficient and directly related to the self-diffusion coefficient in a pure substance or the self-diffusion coefficient of species i in a solution or mixture: (9) The single-particle VCF here is necessarily positive at zero time and also decays in an oscillatory fashion with time as interparticle collisions randomize the velocity of a given particle. It can be readily shown that self-diffusion coefficients have the same values in all frames of reference when the experimentally observed (e.g., radio-tracer or NMR-resonant) species has the same properties as the nominated species of interest.(29,30)

In a binary electrolyte there are six measurable, independent transport properties that can be given in terms of velocity correlation coefficients: the mutual diffusion coefficient, DV, either ion transport number, t1 or t2, the electrical conductivity, κ, or the molar conductivity, Λ, and three self-diffusion coefficients, one for each ion, DS1 and DS2, and that for the solvent, DS0. Accordingly, there are six independent Onsager coefficients and six velocity cross-correlation coefficients. For a molten salt or ionic liquid, these are reduced to just three independent transport properties, the electrical conductivity and the two ion self-diffusion coefficients. [Despite many assertions to the contrary in the ionic liquid literature due to misunderstandings of electrochemistry, one cannot define a transport number in a pure molten salt, only in a binary mixture or solution.(31−33) The assertion in the Results and Discussion section, on p 8304, that the transport number of the cation is equal to DS1/(DS1 + DS2) is incorrect. Again, this relation only applies at infinite dilution where the diffusive and electrical mobilities are equal.(11,12,34) The correct form for an ion transport number in a binary electrolyte solution at finite concentrations is given by eq 41 of ref (18).]

The relations between the VCC, the experimental transport numbers, and the Onsager coefficients have been given by Schönert, his eq 24. For the purposes of this Comment, only three of these expressions for the ion–ion VCC are required. Using the following notation(35) (10) for the VCC (NA is Avogadro’s number), these are (11) (12) and (13) Note that the (obsolete) equivalent conductivity Λeq = Λ/(ν1z1) appears in these expressions. The ti are transport numbers in the solvent-fixed or Hittorf frame of reference as measured in the laboratory, D, is given by (14) where DV is the binary or mutual interdiffusion coefficient in the volume-fixed frame of reference, again as measured in the laboratory, m is the salt molality, γ is the mean activity coefficient on the molality composition scale, and ci are molarities, with the density ρ given in terms of the partial densities by (15) Mi being molar masses.

With a little algebra, the full relation between the conductivity and ion self-diffusion coefficients can be obtained from eqs 11–13: (16) with the deviation, Δ, from the Nernst–Einstein expression, ΛNE, given in terms of the VCC by (17) This result, using equivalent but slightly different definitions of the fij, was previously derived by Hertz(22) and by Woolf and Harris.(18) Importantly, exactly the same equation applies to molten salts and ionic liquids.(35−39) However, in this case the fij are always negative, representing anticorrelations between the velocities of the ions, for both ion couples of the same and opposite charges,(19) whereas, in binary solutions, the fij may be positive or negative.(18,19) It has been found that, in aqueous solutions of simple salts (e.g., alkali and alkaline earth halides), f12 values for the unlike ion interactions are positive at low to moderate concentrations that is, the velocities of cations and anions are correlated as one would expect. This is possible as momentum is also exchanged with the solvent molecules, whereas in a molten salt there is no solvent and, as a consequence, conservation of momentum results in negative f12, albeit somewhat smaller in magnitude than the fii., the VCC for like ion interactions.(40−42) Where ion association occurs, as for aqueous ZnCl2(43) and Na2SO4,(44)f12 values are strongly positive, much more so than for typical unassociated salts such as MgCl2. This is actually a useful diagnostic for ion association in strong electrolytes where other methods such as neutron scattering can give ambiguous results.

Equations 16 and 17 show that deviations from the simple Nernst–Einstein equation involve correlations between the velocities of ions in solution, not just simple association as proposed by Garrido et al.(1) The simple NE or, more properly Nernst–Hartley,(11,12) expression only applies at infinite dilution or for the artificial condition that f12 is the arithmetic mean of fii. (Similar conditions for simple expressions such as the Darken or Hartley–Crank equation relating mutual and self-diffusion coefficients in nonelectrolyte solutions have long been known.(12,21,45)) The investigation of electrolyte solutions requires more than ion self-diffusion and conductivity measurements but must encompass mutual diffusion, solvent self-diffusion, and transport number measurements in order to obtain a full picture. The use of ionic liquids as solutes permits examination of the whole composition range in principle, from infinite dilution to pure ionic liquid, as in the simulations of McDaniel and Son,(20) which represent a more sophisticated approach, in step with the experimental determination of VCC. However, the latter is a formidable task at high concentrations due to the high viscosity of such solutions, which almost excludes classical techniques for determining mutual diffusion(12,46) (though light scattering is a possibility) or transport numbers.(47) Notwithstanding this, one should resist the temptation to use inappropriate approaches in the analysis of transport property measurements.

External ligands

External ligands (shown here in green) bind to a site on the extracellular side of the channel.

  • Acetylcholine (ACh). The binding of the neurotransmitter acetylcholine at certain synapses opens channels that admit Na + and initiate a nerve impulse or muscle contraction.
  • Gamma amino butyric acid (GABA). Binding of GABA at certain synapses &mdash designated GABAA &mdash in the central nervous system admits Cl - ions into the cell and inhibits the creation of a nerve impulse. [More]

Internal ligands

Internal ligands bind to a site on the channel protein exposed to the cytosol.

  • "Second messengers", like cyclic AMP (cAMP) and cyclic GMP (cGMP), regulate channels involved in the initiation of impulses in neurons responding to odors and light respectively.
  • ATP is needed to open the channel that allows chloride (Cl - ) and bicarbonate (HCO3 - ) ions out of the cell. This channel is defective in patients with cystic fibrosis. Although the energy liberated by the hydrolysis of ATP is needed to open the channel, this is not an example of active transport the ions diffuse through the open channel following their concentration gradient.

Properties Shared by Ionic Compounds

The properties of ionic compounds relate to how strongly the positive and negative ions attract each other in an ionic bond. Iconic compounds also exhibit the following properties:

  • They form crystals.
    Ionic compounds form crystal lattices rather than amorphous solids. Although molecular compounds form crystals, they frequently take other forms plus molecular crystals typically are softer than ionic crystals. At an atomic level, an ionic crystal is a regular structure, with the cation and anion alternating with each other and forming a three-dimensional structure based largely on the smaller ion evenly filling in the gaps between the larger ion.
  • They have high melting points and high boiling points.
    High temperatures are required to overcome the attraction between the positive and negative ions in ionic compounds. Therefore, a lot of energy is required to melt ionic compounds or cause them to boil.
  • They have higher enthalpies of fusion and vaporization than molecular compounds.
    Just as ionic compounds have high melting and boiling points, they usually have enthalpies of fusion and vaporization that can be 10 to 100 times higher than those of most molecular compounds. The enthalpy of fusion is the heat required melt a single mole of a solid under constant pressure. The enthalpy of vaporization is the heat required for vaporize one mole of a liquid compound under constant pressure.
  • They're hard and brittle.
    Ionic crystals are hard because the positive and negative ions are strongly attracted to each other and difficult to separate, however, when pressure is applied to an ionic crystal then ions of like charge may be forced closer to each other. The electrostatic repulsion can be enough to split the crystal, which is why ionic solids also are brittle.
  • They conduct electricity when they are dissolved in water.
    When ionic compounds are dissolved in water the dissociated ions are free to conduct electric charge through the solution. Molten ionic compounds (molten salts) also conduct electricity.
  • They're good insulators.
    Although they conduct in molten form or in aqueous solution, ionic solids do not conduct electricity very well because the ions are bound so tightly to each other.

Fiori, G. et al. Electronics based on two-dimensional materials. Nat. Nanotech. 9, 768–779 (2014).

Mak, K. F. & Shan, J. Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides. Nat. Photon. 10, 216–226 (2016).

Schaibley, J. R. et al. Valleytronics in 2D materials. Nat. Rev. Mater. 1, 16055 (2016).

Hong, J. et al. Layer-dependent anisotropic electronic structure of freestanding quasi-two-dimensional MoS2. Phys. Rev. B 93, 075440 (2016).

Gong, C. et al. Electronic and optoelectronic applications based on 2D novel anisotropic transition metal dichalcogenides. Adv. Sci. 4, 1700231 (2017).

Jung, Y., Zhou, Y. & Cha, J. J. Intercalation in two-dimensional transition metal chalcogenides. Inorg. Chem. Front. 3, 452–463 (2016).

Voiry, D., Mohite, A. & Chhowalla, M. Phase engineering of transition metal dichalcogenides. Chem. Soc. Rev. 44, 2702–2712 (2015).

Wang, L., Xu, Z., Wang, W. & Bai, X. Atomic mechanism of dynamic electrochemical lithiation processes of MoS2 nanosheets. J. Am. Chem. Soc. 136, 6693–6697 (2014).

Chhowalla, M. et al. The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets. Nat. Chem. 5, 263–275 (2013).

Sun, X., Wang, Z., Li, Z. & Fu, Y. Q. Origin of structural transformation in mono- and bi-layered molybdenum disulfide. Sci. Rep. 6, 26666 (2016).

Kappera, R. et al. Phase-engineered low-resistance contacts for ultrathin MoS2 transistors. Nat. Mater. 13, 1128–1134 (2014).

Cho, S. et al. Phase patterning for ohmic homojunction contact in MoTe2. Science 349, 625–628 (2015).

Lin, Y.-C., Dumcenco, D. O., Huang, Y.-S. & Suenaga, K. Atomic mechanism of the semiconducting-to-metallic phase transition in single-layered MoS2. Nat. Nanotech. 9, 391–396 (2014).

Yang, H., Kim, S. W., Chhowalla, M. & Lee, Y. H. Structural and quantum-state phase transitions in van der Waals layered materials. Nat. Phys. 13, 931–937 (2017).

Choe, D.-H., Sung, H.-J. & Chang, K. J. Understanding topological phase transition in monolayer transition metal dichalcogenides. Phys. Rev. B 93, 125109 (2016).

Wang, Y. et al. Structural phase transition in monolayer MoTe2 driven by electrostatic doping. Nature 550, 487–491 (2017).

Ma, Y. et al. Reversible semiconducting-to-metallic phase transition in chemical vapor deposition grown monolayer WSe2 and applications for devices. ACS Nano 9, 7383–7391 (2015).

Stephenson, T., Li, Z., Olsen, B. & Mitlin, D. Lithium ion battery applications of molybdenum disulfide (MoS2) nanocomposites. Energy Environ. Sci. 7, 209–231 (2014).

Xu, X., Liu, W., Kim, Y. & Cho, J. Nanostructured transition metal sulfides for lithium ion batteries: progress and challenges. Nano Today 9, 604–630 (2014).

Li, Y., Wu, D., Zhou, Z., Cabrera, C. R. & Chen, Z. Enhanced Li adsorption and diffusion on MoS2 zigzag nanoribbons by edge effects: a computational study. J. Phys. Chem. Lett. 3, 2221–2227 (2012).

Wang, H. et al. Electrochemical tuning of vertically aligned MoS2 nanofilms and its application in improving hydrogen evolution reaction. Proc. Natl Acad. Sci. USA 110, 19701–19706 (2013).

Xia, J. et al. Phase evolution of lithium intercalation dynamics in 2H-MoS2. Nanoscale 9, 7533–7540 (2017).

Xiong, F. et al. Li Intercalation in MoS2: in situ observation of its dynamics and tuning optical and electrical properties. Nano Lett. 15, 6777–6784 (2015).

Leng, K. et al. Phase restructuring in transition metal dichalcogenides for highly stable energy storage. ACS Nano 10, 9208–9215 (2016).

Jo, S. H. et al. Nanoscale memristor device as synapse in neuromorphic systems. Nano Lett. 10, 1297–1301 (2010).

Du, G. et al. Superior stability and high capacity of restacked molybdenum disulfide as anode material for lithium ion batteries. Chem. Commun. 46, 1106–1108 (2010).

Melitz, W., Shen, J., Kummel, A. C. & Lee, S. Kelvin probe force microscopy and its application. Surf. Sci. Rep. 66, 1–27 (2011).

Wang, F. et al. Chemical distribution and bonding of lithium in intercalated graphite: identification with optimized electron energy loss spectroscopy. ACS Nano 5, 1190–1197 (2011).

Rasamani, K. D., Alimohammadi, F. & Sun, Y. Interlayer-expanded MoS2. Mater. Today 20, 83–91 (2017).

Valov, I. et al. Nanobatteries in redox-based resistive switches require extension of memristor theory. Nat. Commun. 4, 1771 (2013).

Park, G.-S. et al. In situ observation of filamentary conducting channels in an asymmetric Ta2O5−x/TaO2−x bilayer structure. Nat. Commun. 4, 2382 (2013).

Yang, Y. et al. Observation of conducting filament growth in nanoscale resistive memories. Nat. Commun. 3, 732 (2012).

Fonseca, R. in Synaptic Tagging and Capture (ed. Sajikumar, S.) 29–44 (Springer, New York, 2015).

Muller, D., Hefft, S. & Figurov, A. Heterosynaptic interactions between UP and LTD in CA1 hippocampal slices. Neuron 14, 599–605 (1995).

Nishiyama, M., Hong, K., Mikoshiba, K., Poo, M.-M. & Kato, K. Calcium stores regulate the polarity and input specificity of synaptic modification. Nature 408, 584–588 (2000).

Royer, S. & Paré, D. Conservation of total synaptic weight through balanced synaptic depression and potentiation. Nature 422, 518–522 (2003).

Bailey, C. H., Giustetto, M., Huang, Y.-Y., Hawkins, R. D. & Kandel, E. R. Is heterosynaptic modulation essential for stabilizing hebbian plasticity and memory. Nat. Rev. Neurosci. 1, 11–20 (2000).

Sheridan, P. M. et al. Sparse coding with memristor networks. Nat. Nanotech. 12, 784–789 (2017).

Borghetti, J. et al. ‘Memristive’ switches enable ‘stateful’ logic operations via material implication. Nature 464, 873–876 (2010).

Yu, Y. et al. Gate-tunable phase transitions in thin flakes of 1T-TaS2. Nat. Nanotech. 10, 270–276 (2015).

Zhu, J. et al. Ion gated synaptic transistors based on 2D van der Waals crystals with tunable diffusive dynamics. Adv. Mater. 30, 1800195 (2018).

He, K., Poole, C., Mak, K. F. & Shan, J. Experimental demonstration of continuous electronic structure tuning via strain in atomically thin MoS2. Nano Lett. 13, 2931–2936 (2013).

Conley, H. J. et al. Bandgap engineering of strained monolayer and bilayer MoS2. Nano Lett. 13, 3626–3630 (2013).

Sangwan, V. K. et al. Multi-terminal memtransistors from polycrystalline monolayer molybdenum disulfide. Nature 554, 500 (2018).

Zhu, L. Q., Wan, C. J., Guo, L. Q., Shi, Y. & Wan, Q. Artificial synapse network on inorganic proton conductor for neuromorphic systems. Nat. Commun. 5, 3158 (2014).

Yang, Y., Chen, B. & Lu, D. W. Memristive physically evolving networks enabling the emulation of heterosynaptic plasticity. Adv. Mater. 27, 7720–7727 (2015).

Wang, Z. et al. Memristors with diffusive dynamics as synaptic emulators for neuromorphic computing. Nat. Mater. 16, 101–108 (2016).

Zhu, X., Lee, J. & Lu, D. W. Iodine vacancy redistribution in organic–inorganic halide perovskite films and resistive switching effects. Adv. Mater. 29, 1700527 (2017).

Zhu, X., Du, C., Jeong, Y. & Lu, D. W. Emulation of synaptic metaplasticity in memristors. Nanoscale 9, 45–51 (2017).


The self-diffusion coefficients (SDCs) of Na + , Cs + , and Ba 2+ have been determined in Nafion-117 membrane having mixed cationic compositions. Membranes with different proportions of Na + –Cs + , Cs + –Ba 2+ , Na + –Ba 2+ , and Ag + –Ba 2+ cations have been prepared by equilibrating with solutions containing different ratios of these cations. The SDCs of the cations (DNa, DCs, DBa) and the ionic compositions of the membrane have been determined using a radiotracer method. For the Na–Cs and Cs–Ba systems, the SDCs of the cations have been found to be independent of the ionic compositions of the membrane. In the case of the Na–Ba system, DNa does not change with ionic composition, while DBa has been found to be strongly dependent on the ionic composition of the membrane and decreases continuously with increasing Na + content in the membrane. Similar results have also been obtained for DBa in the case of the Ag–Ba system. The specific conductivities (κimp) of the membrane in mixed cationic forms have also been obtained from ac impedance measurement and compared with that (κcal) calculated from the SDC data. For the Na–Ba system, the increment of κimp with increase in the Na + content of the membrane has been found to be parabolic, whereas for the Na–Cs system the increment is linear. The reason behind the different behaviors for different types of ionic systems has been qualitatively explained based on different transport pathways of the cations in the membrane.

Key Points

  • Important ions cannot pass through membranes by passive diffusion if they could, maintaining specific concentrations of ions would be impossible.
  • Osmotic pressure is directly proportional to the number of solute atoms or molecules ions exert more pressure per unit mass than do non- electrolytes.
  • Electrolyte ions require facilitated diffusion and active transport to cross the semi-permeable membranes.
  • Facilitated diffusion occurs through protein -based channels, which allow passage of the solute along a concentration gradient.
  • In active transport, energy from ATP changes the shape of membrane proteins that move ions against a concentration gradient.

Examples of Facilitated Diffusion

A number of important molecules undergo facilitated diffusion to move between cells and subcellular organelles.

Glucose Transporter

When food is digested, there is a high concentration of glucose within the small intestine. This is transported through the membranes of the cells of the alimentary canal, towards the endothelial cells lining blood capillaries. Thereafter, glucose is transported throughout the body by the circulatory system. When blood flows through tissues that need energy, glucose traverses the endothelial cell membranes again and enters cells with low glucose concentration. Occasionally, when blood sugar levels drop, the movement can occur in reverse – from body tissues into blood circulation. For instance, hepatic cells can generate glucose even from non-carbohydrate sources to maintain a basal blood sugar concentration and prevent hypoglycemia.

The glucose transporter that facilitates this movement is a carrier protein that has two major conformational structures. While the exact three-dimensional structure is not known, the binding of glucose probably causes a conformational change that makes the binding site face the interior of the cell. When glucose is released into the cell, the transporter returns to its original conformation.

Ion Channels

Ion channels have been extensively studied in excitatory cells like neurons and muscle fibers since the movement of ions across the membrane is an integral part of their function. These channel proteins form pores on the lipid bilayer that can be either in the open or closed conformation, depending on the electrical potential of the cell and the binding of ligands. In this sense, these proteins are called ‘gated’ channels.

The presence of ion pumps in most cells ensures that the ionic composition of the extracellular fluid is different from the cytosol. The resting potential of any cell is driven by this process, with an excess of sodium ions in the extracellular region and an excess of potassium ions within the cell. The electrical and concentration gradient generated in this manner is used for the propagation of action potentials along neurons and the contractility of muscle cells.

When a small change in the voltage of a cell occurs, sodium ion channels open and allow the rapid ingress of sodium ions into the cell. This, in turn, induces the opening of potassium ion channels, allowing these ions to move outward, demonstrating that the diffusion of one substance can occur independently of another. In a few milliseconds, a region in the cell membrane can undergo large changes in voltage – from -75 mV to +30 mV.

The binding of neurotransmitters like acetylcholine to receptors on muscle cells changes the permeability of ligand-gated ion channels. The transmembrane channel is made of multiple subunits arranged like a closed cylinder. The binding of the ligand (acetylcholine) alters the conformation of the hydrophobic side chains that block the central passage. This leads to the rapid influx of sodium ions into the muscle cell. The change in the electric potential of the cell further results in the opening of calcium ion channels, which then lead to the contraction of the muscle fiber.


Like other transmembrane proteins, aquaporins have not been fully characterized. However, it is known that there are many such channels for the rapid passage of water molecules in nearly every cell. These highly conserved proteins are present in bacteria, plants, fungi and animals. Mutations in the proteins forming aquaporins can lead to diseases like diabetes insipidus.

How is it that ionic diffusion is independent of other ions? - Biology

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The solubility of a solute is its maximum possible concentration at solubility equilibrium in a given amount of solvent. Solubility is affected by temperature and other physical conditions.

Substances that dissolve in water are called water-soluble. A simple water-soluble ionic compound like sodium chloride dissolves in water by breaking up into monatomic ions. Here, it is more favorable for the water molecules and ions to interact in solution than it is for the ions to remain in the ordered solid.

A more complex water-soluble ionic compound like sodium nitrate contains ions that are composed of multiple atoms covalently bound together, or polyatomic ions. When sodium nitrate dissolves, the polyatomic nitrate ions do not split into nitrogen and oxygen. Instead, the ions disperse in solution as intact units.

Substances that do not dissolve in water are water-insoluble. For example, silver chloride is a water-insoluble ionic compound. In this case, it is more favorable for the ions to remain in the ordered solid than to interact with water and disperse in the solution.

The solubility of an ionic compound in water depends on the ion pair that makes up the compound. Chemists have formulated a set of empirical guidelines to predict the solubility of ionic compounds in water. Exceptions to these guidelines are rare.

All nitrates and acetates are soluble. Similarly, all ammonium and non-lithium alkali metal compounds are soluble, as are nearly all lithium salts.

Sulfate compounds are soluble, with the exception of its salts with lead, mercury, and silver &ndash remember the acronym LMS or the phrase Let Me See &ndash and calcium, barium, and strontium &ndash remember the acronym CBS or the phrase Come By Soon.

All chloride, bromide, and iodide salts are soluble, with the exception of their salts with LMS &ndash lead, mercury, and silver &ndash as well as copper(I) and thallium.

Moving to insoluble compounds, sulfides and hydroxides are insoluble, with the exception of their salts with alkali metals and barium. In addition, ammonium sulfide is soluble, and strontium hydroxide is soluble when heated.

Similarly, carbonates and phosphates are insoluble, with the exception of their ammonium and non-lithium alkali metal salts.

4.7: Solubility of Ionic Compounds

Solubility is the measure of the maximum amount of solute that can be dissolved in a given quantity of solvent at a given temperature and pressure. Solubility is usually measured in molarity (M) or moles per liter (mol/L). A compound is termed soluble if it dissolves in water.

When soluble salts dissolve in water, the ions in the solid separate and disperse uniformly throughout the solution this process represents a physical change known as dissociation. Potassium chloride (KCl) is an example of a soluble salt. When solid KCl is added to water, the positive (hydrogen) end of the polar water molecules is attracted to the negative chloride ions, and the negative (oxygen) ends of water are attracted to the positive potassium ions. The water molecules surround individual K + and Cl &minus ions, reducing the strong forces that bind the ions together and letting them move off into solution as solvated ions.

Another example of a soluble salt is silver nitrate, AgNO3, which dissolves in water as Ag + and NO3 - ions. Nitrate, NO3 - , is a polyatomic ion, and in solution, it stays intact as a single whole unit. Unlike monatomic ions (K + , Cl - , Ag + ), which contain only one atom, polyatomic ions are a group of atoms that carry a charge (NO3 - , SO4 2- , NH4 + ). They remain such in solution and do not split into individual atoms.

A compound is termed insoluble if it does not dissolve in water. However, in reality, &ldquoinsoluble&rdquo compounds dissolve to some extent, that is, less than 0.01 M.

In the case of insoluble salts, the strong interionic forces that bind the ions in the solid are stronger than the ion-dipole forces between individual ions and water molecules. As a result, the ions stay intact and do not separate. Thus, most of the compound remains undissolved in water. Silver chloride (AgCl) is an example of an insoluble salt. The water molecules cannot overcome the strong interionic forces that bind the Ag + and Cl - ions together hence, the solid remains undissolved.

Solubility Rules

The solubility of ionic compounds in water depends on the type of ions (cation and anion) that form the compounds. For example, AgNO3 is water-soluble, but AgCl is water-insoluble. The solubility of a salt can be predicted by following a set of empirical rules (listed below), developed based on the observations on many ionic compounds.

i) Compounds containing ammonium ions (NH4 + ) and alkali metal cations are soluble
ii) All nitrates and acetates are always soluble.
iii) Chloride, bromide, and iodide compounds are soluble with the exception of those of silver, lead, and mercury(I)
iv) All sulfate salts are soluble except their salts with silver, lead, mercury(I), barium, strontium, and calcium
v) All carbonates, sulfites, and phosphates are insoluble except their salts with ammonium and alkali metal cations.
vi) Sulfides and hydroxides of all salts are insoluble, with the exception of their salts with alkali metal cations, ammonium ion, and calcium, strontium, and barium ions.
vii) All oxide-containing compounds are insoluble except their compounds with calcium, barium, and alkali metal cations.

Watch the video: 1. Ion Passive Diffusion in Solution (September 2022).


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