Counterion Size Research Articles

Electrokinetic and dielectric response of a concentrated salt-free colloid: Different approaches to counterion finite-size effects.

In the present work, a general model is developed for the electrokinetics and dielectric response of a concentrated salt-free colloid that takes into account the finite size of the counterions released by the particles to the solution. The effects associated with the counterion finite size have been addressed using a hard-sphere model approach elaborated by Carnahan and Starling [N. F. Carnahan and K. E. Starling, Equationof state for nonattracting rigid spheres, J. Chem. Phys. 51, 635 (1969)0021-960610.1063/1.1672048]. A more simple description of the finite size of the counterions based on that by Bikerman has also been considered for comparison. The studies carried out in this work include predictions on the effect of the finite counterion size on the equilibrium properties of the colloid and its electrokinetic and dielectric response when it is subjected to constant or alternating electric fields. The results show how important the counterion finite-size effects are for most of the electrokinetic and dielectric properties of highly charged and concentrated colloids, mainly for the static and dynamic electrophoretic mobilities. Furthermore, new insights are provided on the counterion condensation effect when counterions are allowed to have finite size. Focus is placed on the changes undergone by their concentration in the condensation layer for low-salt and highly charged colloids.

Effects of Counter Anion Type on Melt Rheological Properties of Hyperbranched Polyethylene Ionomers Containing Covalently Bound Quaternary Ammonium Cations

AbstractThe paper investigates the effects of counter anions of varying sizes including BF4–, PF6–, SbF6–, and Tf2N– on the rheological properties of a range of hyperbranched polyethylene ionomers containing covalently bound quaternary ammonium cations. While the choice of counter anions has no significant effect on thermal properties, distinct effects on rheological properties have been demonstrated. With the increase of counter anion size in the order from BF4– to PF6–, SbF6–, and Tf2N–, the ionic interactions of the counter anion with the quaternary ammonium ion weaken, leading to reduced terminal relaxation time, zero‐shear viscosity, and flow activation energy. The differences in these properties are most pronounced with the ionomer having Tf2N– counter anion since it is significantly larger than the others.

Ultrananoporous supercapacitor with ionic liquid comprised of two-site cation: an Ising model study (II)

A four-state one-dimension discrete spin model with the nearest neighbor and partial next nearest neighbor lattice interactions is proposed for describing electrical double layer formed by ionic liquid in cylindrical pore that can accommodate only one row of particles. The model, in which cation is modeled as a dimer formed by two hard spheres (HSs): one is positively charged with diameter , while the other is neutral with diameter , and anion is modeled by charged HS with diameter , is designed to investigate effects of pore diameter , ion transfer free energy, ion size and electrical valence on behaviors of specific differential capacitance and specific energy storage and its saturation value . Relevant Kramers–Wannier transfer matrix is , which gives system partition function by numerically solving maximum real root of the relevant characteristic equation. Main findings are briefly described below. (i) The ion valence has little effect on the value, but does reduce the threshold voltage strength , beyond which the energy storage reaches . However, the ion valence (whether co- or counter-ion) raises both the and values as the relevant ion size decreases enough. (ii) Decreasing of the value weakly reduces the value, but raises the peak height and the value obviously; correlation between the value and value becomes stronger with the ions getting more pore hostile. (iii) With the counter-ion or co-ion charged site size decreasing, both the value and value rise. However, the effect of the co-ion charged site size is weakened as the co-ion gets more pore hostile, and the cation neutral site size influences on the value less than the cation charged site size does. (iv) Pore friendly co-ion or pore hostile counter-ion always helps in raising the value; the two have significant synergistic effect with the co-ion pore friendliness playing more important role than the counter-ion pore hostility.

Evidence of Counterion Size Effect on the Stability of Columnar Phase of Ionic Liquid Crystals Based on Pyridinium Salts Derived from N-3,4,5-Tri(alkyloxy)-benzyl-4-pyridones

The synthesis and characterization of novel ionic liquid crystals based on pyridinium salts with Br− and PF6− counterions are described in this work. These pyridinium salts were derived from 4-hydroxypyridine, both by N- and O-alkylation. The 3,4,5-tri(alkyloxy)-benzyl mesogenic unit was attached to the nitrogen atom of the pyridinium ring. Alkyl chains with a different number of carbon atoms (6, 8, 10, 12 and 14) were employed in order to show the effect on the stability of mesophase. The POM (polarizing optical microscopy) and XRD (powder X-ray diffraction) studies indicated that bromide salts with shorter chains C6, C8 and C10 do not show mesomorphic properties, while longer chain analogues with C12 and C14 exhibit two enantiotropic columnar phases. Surprisingly, the pyridinium salts with the larger size PF6− counterion do not exhibit liquid crystal properties.

The impact of steric repulsion on the total free energy of electric double layer capacitors

We present an analysis of the total free energy of a supercapacitor modelled with a composite diffuse layer (CDL) formed by a steric repulsive potential. The steric potential is modelled with a simple approximation to the Bikerman steric potential, enabling derivation of an analytical expression for the total free energy of the supercapacitor in terms of the size and valency of the electrolyte counterions and electrode potentials. The analytical expression for the total free energy of the supercapacitor matches the exact numerical Bikerman calculation at high potential with relative error close to 1%. This provides an upper bound over the more accurate Carnahan-Starling model. A maximum upper bound for the energy is also provided in the limit where bulk concentrations approach the ion concentration cap. We analyze the relative contribution of the steric interaction to the total free energy. At large voltages, the steric free energy is comparable in magnitude to that of the electrostatic free energy, and introduces ion-size effects in the energy of the supercapacitor. Consequently at high potentials the total free energy exceeds (doubles) the classical energy 12CV2, indicating that this formula does not correctly describe the available stored energy from the experimentally measured capacitance.

Electrostatic free energies carry structural information on nucleic acid molecules in solution.

Over the last several decades, a range of experimental techniques from x-ray crystallography and atomic force microscopy to nuclear magnetic resonance and small angle x-ray scattering have probed nucleic acid structure and conformation with high resolution both in the condensed state and in solution. We present a computational study that examines the prospect of using electrostatic free energy measurements to detect 3D conformational properties of nucleic acid molecules in solution. As an example, we consider the conformational difference between A- and B-form double helices whose structures differ in the values of two key parameters-the helical radius and rise per basepair. Mapping the double helix onto a smooth charged cylinder reveals that electrostatic free energies for molecular helices can, indeed, be described by two parameters: the axial charge spacing and the radius of a corresponding equivalent cylinder. We show that electrostatic free energies are also sensitive to the local structure of the molecular interface with the surrounding electrolyte. A free energy measurement accuracy of 1%, achievable using the escape time electrometry (ETe) technique, could be expected to offer a measurement precision on the radius of the double helix of approximately 1 Å. Electrostatic free energy measurements may, therefore, not only provide information on the structure and conformation of biomolecules but could also shed light on the interfacial hydration layer and the size and arrangement of counterions at the molecular interface in solution.

Effect of counter-ion on rheological properties of mixed surfactant solutions

The effects of the charge, size and concentration of counter-ions (Na+, NH4+, K+, Mg2+, Ca2+ and Al3+) on the rheological properties of 300 mM SLES+CAPB surfactant solutions are studied and compared with results available in the literature for the effects of Na+ and K+ on SLES solution. The results show that all counter-ions studied are able to induce formation of wormlike micelles in a certain concentration range – as a consequence, the solution viscosity passes through a high maximum as a function of salt concentration. The salt concentration leading to maximum in the solution viscosity decreases with increasing the charge density of the counter-ion, defined as the ratio of the charge of the counterion and its hydrated radius, Z/R. The maximum viscosity in the salt curve decreases with increasing the hydrated radius of the counter-ion. The addition of CAPB to SLES leads to about 10-fold higher viscosity and to higher maximum viscosity in the presence of K+ as compared to Na+, whereas the opposite trend was observed for SLES alone. These effects are attributed to the interplay between the anionic and zwitterionic surfactants, and the electrolyte in the mixed SLES+CAPB system.

Mn(III) complexes with nitro-substituted ligands—Spin states with a twist

Structural, magnetic, and computational data on two new Mn(III) complex cations in lattices with five different counterions and varying levels of solvation are compared to investigate the influence of the position of the electron-withdrawing ligand nitro-substituent on the thermal spin crossover profile. The [MnL1]+ (a) and [MnL2]+ (b) complex cations were prepared by complexation of Mn(III) to the Schiff base chelates formed from condensation of 3-nitrosalicylaldehyde or 5-nitrosalicylaldehyde, respectively, with 1,2-bis(3-aminopropylamino)ethane and were crystallized with NO3−, (1a/b), ClO4−, (2a/b), PF6−, (3a/b), CF3SO3− (4a/b), and BPh4− (5a/b) counterions. Magnetostructural analysis reveals a minor trend in the spin state preference depending on the position of the nitro substituent where the orientation is dependent on crystal packing. Compounds using the 3-NO2-sal2-323 ligand, H2L1, where the nitro group is bent out-of-plane to the benzene ring of the Schiff base, tend to stabilize the triplet state, S = 1, while those with the 5-NO2-sal2-323 Schiff base, H2L2, where the nitro group is almost perfectly aligned in-plane with the benzene ring, mostly stabilize the spin-quintet form, S = 2. Density functional theory calculations correctly describe the energetics of intermediate spin/high spin transitions in the complexes. The intrinsic molecular magnetic properties are only marginally dependent on the position of the nitro groups; the out-of-plane orientation for the 3-NO2 is stabilized by an intramolecular hydrogen bonding interaction between the nitro group and the equatorial sal ligand. This demonstrates that the control of magnetic behavior in the solid state is mainly a cooperative effect from the size and distribution of counterions, crystal packing, and intermolecular interactions. Three potential structural phase transitions were identified, in complexes 3a, 4a, and 5a · 2MeCN including one which is not coupled to a spin state change. Finally, a break in the pattern of Jahn-Teller distortion typical for [Mn(R-Sal2-323)]+ complexes was observed in two of the complexes with the 5-NO2 ligand, where elongation of the Mn–O bond lengths on warming replaced the usual pattern of elongation of only Mn–N distances.

Influence of finite ion size and dielectric decrement on the ion current rectification in a single conical nanopore

The ion current rectification (ICR) arising due to the transport of ionized liquids within a geometrically asymmetric nanopore is of great significance for the development of smart nanogadgets with unique working capabilities. Though the theoretical framework for the ICR is well developed, the influence of the finite size of ions on the ICR phenomena had not been addressed before. The ion steric repulsion due to finite ion size and dielectric decrement of the medium creates a counterion saturation. In this study, a modified electrokinetic model is adopted to describe the ICR phenomena of a single conical nanopore by considering the hydrated ions as finite-sized dielectric charged spheres. The Nernst–Planck equations for ion transport are modified to incorporate the short-range ion steric interactions modeled by the Boublik–Mansoori–Carnahan–Starling–Leland equation as well as Born force and dielectrophoretic force acting on the hydrated ions engender by the ion–solvent interactions. The counterion saturation attenuates the shielding effect of the surface charge of the nanopore leading to a larger ζ-potential and hence, a larger volume flux and reduced conduction. We find that the ion steric interactions and the dielectric decrement significantly influence the ICR phenomena as well as the ion selectivity of a conical nanopore, especially for moderate to high range of surface charge density, bulk concentration, and applied bias. We find that ICR varies linearly with temperature; however, the variation is found to be marginal. Our results show that the volume flux and the rectification factor of the conical nanopore can be suitably tuned by adding salt of larger counterion size or multivalent ions.

Ion transport and relaxation in phosphonium poly(ionic liquid) homo‐ and co‐polymers

AbstractIn the present work, a poly(ionic liquid) (PIL), poly(triphenyl‐4‐vinylbenzylphosphonium chloride) and a series of its random copolymers with nonionic hydrophobic poly(methyl methacrylate) (PMMA) are synthesized by conventional free radical polymerization (CFRP) and reversible addition‐fragmentation chain‐transfer (RAFT) polymerization. The understanding of some fundamental aspects about ion transport and relaxation mechanism in PIL and PIL copolymers are investigated using dielectric spectroscopy via several theoretical models. The influence of copolymer compositions, physical blending of neat PIL and PMMA, size of counter anions (Cl− and TFSI−) and variation of molecular weights on thermal stability, moisture sensitivity, ionic transport and relaxation properties are also studied. An enhancement of thermal stability and ionic transport property of the PIL copolymer is observed compared to those of the physically mixed blend of two homopolymers with same compositions. The incorporation of hydrophobic PMMA segment definitely decreases the moisture content in PIL copolymers than the PIL itself. In all these PIL‐ based systems, the temperature dependence of ionic conductivity, relaxation time and ion diffusivity are well described by Vogel‐Tammann‐Fulcher model. The studies of some fundamental properties of these new PIL copolymers with less moisture sensitivity may help in using them as potential polymer electrolytes in energy storage devices.

Poly(Pyridinium Salt)s Containing 2,7-Diamino-9,9'-Dioctylfluorene Moieties with Various Organic Counterions Exhibiting Both Lyotropic Liquid-Crystalline and Light-Emitting Properties.

A series of poly(pyridinium salt)s-fluorene main-chain ionic polymers with various organic counterions were synthesized by using ring-transmutation polymerization and metathesis reactions. Their chemical structures were characterized by Fourier Transform Infrared (FTIR), proton (1H), and fluorine 19 (19F) nuclear magnetic resonance (NMR) spectrometers. These polymers showed a number-average molecular weight (Mns) between 96.5 and 107.8 kg/mol and polydispersity index (PDI) in the range of 1.12–1.88. They exhibited fully-grown lyotropic phases in polar protic and aprotic solvents at different critical concentrations. Small-angle X-ray scattering for one polymer example indicates lyotropic structure formation for 60–80% solvent fraction. A lyotropic smectic phase contains 10 nm polymer platelets connected by tie molecules. The structure also incorporates a square packing motif within platelets. Thermal properties of polymers were affected by the size of counterions as determined by differential scanning calorimetry and thermogravimetric analysis measurements. Their ultraviolet-visible (UV-Vis) absorption spectra in different organic solvents were essentially identical, indicating that the closely spaced π-π* transitions occurred in their conjugated polymer structures. In contrast, the emission spectra of polymers exhibited a positive solvatochromism on changing the polarity of solvents. They emitted green lights in both polar and nonpolar organic solvents and showed blue light in the film-states, but their λem peaks were dependent on the size of the counterions. They formed aggregates in polar aprotic and protic solvents with the addition of water (v/v, 0–90%), and their λem peaks were blue shifted.

Regulating the species and the counter-ion size of proton acids to prepare novel poly(4-aminodiphenylamine) nanomaterials for supercapacitors

Poly(4-aminodiphenylamine) nanosheets have been prepared by using different proton acids as dopants and a cationic surfactant as the structure-directing agent, which exhibit intertwined nanosheet morphology and superior electrochemical properties.

Impact of finite ion size, Born energy difference and dielectric decrement on the electroosmosis of multivalent ionic mixtures in a nanotube

The electroosmotic flow (EOF) in a nanotube is analyzed by considering the finite ion size and dielectric decrement effects. The ion transport is governed by the modified Nernst-Planck equation, which takes into account the ion steric repulsion, Born energy difference, and dielectrophoretic force. The dielectric permittivity is considered to depend on the ionic concentration and ion size. The governing equations for fluid flow, ion transport, and electric field are solved numerically in their full form. The steric interaction is accounted, based on the Boublik–Mansoori–Carnahan–Starling–Leland (BMCSL) model, which considers the nonuniform ion size for monovalent as well as multivalent salts. We made a quantitative comparison with the standard PNP model for the lower range of charge density and highlighted the impact of ion size and dielectric decrement effects. For a highly charged surface, the impact due to finite ion size is non-negligible when the Debye length is in the order of the nanotube radius. However, the dielectric decrement is found to have a strong impact on a higher range of surface charge density or bulk ionic concentration. The EOF and the ion selectivity of the mixed electrolyte solution of different counterion size are considered in the present study. Present study provides an in-depth analysis of EOF through a cylindrical nanotube beyond the dilute solution and low charge density limits, which has not been addressed before.

The effect of counter-ion substitution on poly(phthalazinone ether ketone) amphoteric ion exchange membranes for vanadium redox flow battery

The study proposed a novel method to prepare poly(phthalazinone ether ketone) amphoteric ion exchange membranes (Q/S-M) with both increased efficiency and chemical stability for vanadium redox flow battery (VRB) applications. Q/S-M membranes were obtained after the successive amination and acidification process of blend base membranes prepared from brominated poly(phthalazinone ether ketone) (BPPEK) and sulfonated poly(phthalazinone ether ketone) substituted by counter-ions (SPPEK-M), where M was defined as counter-ions: Li+, Na+ and K+. The study analyzed the effect of counter-ion size on properties of Q/S-M membranes, which were compared with those for Q/S membrane obtained from BPPEK and SPPEK in acid form. Q/S and Q/S-M membranes maintained the same composition of ionic groups. The Q/S-M membranes induced by bigger counter-ion size showed the increasing of water content and ion diffusion rate, which was higher than that of Q/S membrane. Related to Q/S membrane, Q/S–K membrane possessed almost half area resistance (0.67 Ω cm2 vs 1.43 Ω cm2), and the value was close to that of Nafion115. Q/S-M membranes exhibited a 96.0–98.8% decrease in VO2+ permeability over Nafion115. Q/S–K membrane displayed a 6.5% increase in VE and correspondingly a 6.2% increase in EE over Q/S membrane, maintaining superior EE than Nafion115 (89.7% vs 86.5%). The ex-situ degradation test in VO2+ solutions indicated that despite close EE, Q/S–K membrane showed superior chemical stability over amphoteric ion exchange membranes (AIEMs) in our previous works. There was no obvious efficiency decay of Q/S–K membrane during 100-cycles test, indicating the good duration in operating VRB.

Copper(I) complexes with N-(2-quinolinylmethylene)-1, 5-dimethyl- 2-phenyl-1-pyrazole-3-(2H)-one and phosphine as ligands: Effective catalyst for Sonogashira cross-coupling reaction

A new series of copper(I) complexes of the type [Cu( L )(PPh 3 ) 2 ]X( 1a-c ) and [Cu( L )(dppe)]X ( 2a-c ) have been prepared by the reaction of Cu(MeCN) 4 ]X (Where X = ClO 4 - , BF 4 - and PF 6 - ) with N-(2-quinolinylmethylene)-1,5-dimethyl-2-phenyl-1-pyrazole-3-(2H)-one ( L ) in presence of triphenyl- phosphine (PPh 3 ) or 1,2-bis(diphenylphosphino)ethane (dppe) as an ancillary ligand. The UV–Visible spectra indicate that the ancillary phosphine ligands significantly perturb the MLCT state of copper(I) complexes. The thermally stable 1a-c and 2a-c complexes exhibit quasireversible redox behaviour corresponding to Cu(I)/Cu(II) couple. All complexes were tested as catalyst for Sonogashira cross-coupling of phenylacetylene with aryl iodide. The results showed that all complexes worked as an effective catalyst at low temperature yielded substituted aryl alkynes as a product. The nature of phosphine ligands and size of counter anions shows marked effect on their catalytic properties of all the complexes .

The effect of electro-neutrality violation inside a charged spherical cavity on the capacitance curve shape in DFT approach and interpretation of mean electrostatic potential

The effect of electro-neutrality deviation in small charged cavities on the shape of the capacitance curve is investigated in this study. The data required are obtained using the modified fundamental measure theory and two models; namely, the restricted primitive model (RPM) and the primitive model (PM). The results of RPM investigations show that the capacitance curve will take on a bell shape when electro-neutrality parameter decreases with increasing surface charge, but that it exhibits a camel shape when electro-neutrality parameter shows a maximum versus surface charge. This behavior is essentially governed by both curvature and bulk concentration as it is observed that electro-neutrality parameter declines at high enough bulk concentrations and large enough curvatures. The PM study results indicate that an increase in the ratio of anion size to that of cation gives rise to higher positive values of the electric potential at zero surface charge. Moreover, it is seen that an increase in counter ion size causes more deviations from the electro-neutral condition while an increase in co-ion size relative to that of counter ions leads to the minimum value of electro-neutrality parameter versus surface charge but to a maximum for larger counter ions. Finally, it is found that, at the saturation point, the value for electro-neutrality parameter and, thereby, that for capacitance both become dependent on the size of counter ions. Base on the concept of the work in the thermodynamics and definition of mean electrostatic potential we interpreted all the terms present in the mean electrostatic potential in spherical cavity.

Sky-Blue-Emissive Perovskite Light-Emitting Diodes: Crystal Growth and Interfacial Control Using Conjugated Polyelectrolytes as a Hole-Transporting Layer.

A series of poly(fluorene-co-phenylene)-based anionic conjugated polyelectrolytes (CPEs) are prepared with varying sizes of counterions (tetramethylammonium, tetraethylammonium, and tetrabutylammonium (TBA+)) and studied as a hole-transporting layer (HTL) for sky-blue-emissive perovskite light-emitting diodes (PeLEDs). Ionic CPE HTLs improve the wettability, compatibility, and nucleation of perovskite crystals at interfaces, enabling highly crystalline perovskite crystal growth with enhanced light-emitting properties. By incorporating the CPE HTLs containing bulky TBA+ counterions (MPS2-TBA) in place of PEDOT:PSS, the decreased phonon-electron coupling and increased exciton binding energy in perovskites are measured by temperature-dependent photoluminescence (PL) measurements. By increasing the size of counterions in CPE interlayers, the PL intensities and lifetimes of perovskite films increase. Through space-charge-limited current measurements, the lowest trap density is measured in the perovskite film on MPS2-TBA, emphasizing a critical role of larger counterions. Using density functional theory, MPS2-TBA is calculated to show the strongest adsorption affinity toward the interstitial defect of lead ions, explaining its pronounced interfacial defect passivation. The counterion size in CPE interlayers is interpreted as a main factor to determine the adsorption affinity onto perovskite, which determines the interacted area as noncovalent adsorption occurs. Finally, the sky-blue-emissive quasi-2D PeLED with MPS2-TBA shows the highest luminance efficiency (a peak EQE of 2.6% at 489 nm) and significantly improved spectral stability.

Inter-surface effective electrostatic interactions in the presence of surface charge discreteness and solvent granularity

Effects of relative arrangement of discrete surface charges and solvent granularity on the effective potential of mean force (EPMF) are studied. Main conclusions are summarized as follows: (i) With consideration of the solvent granularity the EPMF always becomes more attractive, and one like charge attraction always appears even if the counter-ion is univalent. Moreover, with transition from asymmetrical to symmetrical surface charge distributions of similar surface charge compactness, attraction strength of the EPMF always rises; with increase of the counter-ion valence the EPMF attraction strength rises unless the surface charge configuration is asymmetrical and less compact and the counter-ion high-valence. (ii) Whether the surface charge distribution is asymmetrical or symmetrical, the EPMF tends to become more attractive in the compactness charge configuration than in the non-compactness charge configuration. (iii) The correlation between the EPMF attraction strength and bulk mole concentration can be positive or negative depending on the counter-ion valence, compactness of surface charge distribution, and average surface charge strength. Highly taking value of each of the three quantities helps in inducing one negative correlation and vice versa. (iv) Co-ion size has almost no influence on the EPMF, increasing or decreasing the counter-ion size inhibits or enhances the solvent granularity effect.

Porphyrin‐Based Conducting Polymer Hydrogel for Supercapacitor Application

Herein, the electrochemical properties and energy storage capability of a flexible, all‐solid‐state supercapacitor based on the supramolecular assembly of polypyrrole (PPy) and the anion of 5,10,15,20‐tetrakis(4‐sulfonatophenyl)‐21H,23H‐porphine manganese(III) chloride (MnTSPP) are reported. The electrode material consists of a conductive polymer hydrogel formed through the gelation initiated by cross‐linking of the dopant MnTSPP anion in the PPy chains. The morphology of the cross‐linked polymer hydrogel is that of a particle‐decorated nanofiber, which can perform as a flexible supercapacitor electrode material with a specific capacitance of 300 Fg−1 and capacitance retention of 78% up to 10 000 cycles. The anion of MnTSPP plays a pivotal role in enhancing the charge storage capability by facilitating the electron transfer between the polymer interchains. In addition, the steric hindrance due to the large size of the dopant counter ions of MnTSPP reduces the counterion drain effect and structural pulverization of PPy, thereby improving the capacitive retention.

The size and affinity effect of counterions on self-assembly of charged block copolymers.

The effect of counterions' size and affinity on the microphase separated morphologies of neutral-charged diblock copolymers is investigated systematically using a random phase approximation (RPA) and self-consistent field theory (SCFT). The phase diagrams as a function of χAB and fA at different counterion sizes and different affinities to neutral blocks are constructed, respectively. Stability limits calculated using the RPA are in good agreement with the disorder-body-centered cubic phase boundaries from SCFT calculations. It was found that increasing the size of counterions causes the phase diagram to shift upward and leftward, which is attributed to electrostatic interactions and the intrinsic volume of counterions. The domain size of the ordered phase shows an unexpected tendency that it decreases with increasing counterions' size. The counterions' distributions in H and G phases demonstrate that it is electrostatic interaction, instead of packing frustration, that plays a leading role in such systems. For finite size counterions, with the increase in affinity between counterions and neutral blocks, the phase diagram shifts upward, indicating the improved compatibility between different blocks. Furthermore, the affinity effect between counterions and neutral blocks can be mapped into an effective Flory parameter χAB ' = χAB + 0.27χBC.