Reply to the 'Comment on "Simulations of ionization equilibria in weak polyelectrolyte solutions and gels"' by J. Landsgesell, L. Nová, O. Rud, F. Uhlík, D. Sean, P. Hebbeker, C. Holm and P. Kosovan, Soft Matter, 2019, 15, 1155-1185.

Levin and Bakhshandeh suggested in their comment that (1), we stated in our recent review that pH-pKA is a universal parameter for titrating systems, that (2), we omitted to mention in our review the broken symmetry of the constant pH algorithm, and that (3), a constant pH simulation must include a grand-canonical exchange of ions with the reservoir. As a reply to (1), we point out that Levin and Bakhshandeh misquoted and hence invalidated our original statement. We therefore explain in detail under which circumstances pH-pKA can be a universal parameter, and also demonstrate why their numerical example is not in contradiction to our statement. Moreover, the fact that pH-pKA is not a universal parameter for titrating systems is well known in the pertinent literature. Regarding (2), we admit that the symmetry-breaking feature of the constant pH algorithm has escaped our attention at the time of writing the review. We added some clarifying remarks to this behavior. Concerning (3), we point out that the grand-canonical coupling and the resultant Donnan potential are not features of single-phase systems, but are essential for two-phase systems, as was shown in a recent paper by some of us, see J. Landsgesell et al., Macromolecules, 2020, 53, 3007-3020.

Modeling the Phase Transition in Hydrophobic Weak Polyelectrolyte Gels under Compression.

One of the emerging water desalination techniques relies on the compression of a polyelectrolyte gel. The pressures needed reach tens of bars, which are too high for many applications, damage the gel and prevent its reuse. Here, we study the process by means of coarse-grained simulations of hydrophobic weak polyelectrolyte gels and show that the necessary pressures can be lowered to only a few bars. We show that the dependence of applied pressure on the gel density contains a plateau indicating a phase separation. The phase separation was also confirmed by an analytical mean-field theory. The results of our study show that changes in the pH or salinity can induce the phase transition in the gel. We also found that ionization of the gel enhances its ion capacity, whereas increasing the gel hydrophobicity lowers the pressure required for gel compression. Therefore, combining both strategies enables the optimization of polyelectrolyte gel compression for water desalination purposes.

Hairy Gels: A Computational Study.

We present results of MD and MC simulations of the equilibrium properties of swelling gels with comb-like or bottlebrush subchains and compare them to scaling-theory predictions. In accordance with theory, the simulation results demonstrate that swelling coefficient of the gel increases as a function of the polymerization degree of the main chains and exhibits a very weak maximum (or is virtually constant) as a function of the polymerization degree and grafting density of side chains. The bulk osmotic modulus passes through a shallow minimum as the polymerization degree of the side chains increases. This minimum is attributed to the onset of overlap of side chains belonging to different bottlebrush strands in the swollen gel.

Ho2C2 Cluster with Flexible Configurations inside a Large C2(61)-C92 Cage.

Carbide clusterfullerenes (CCFs) have been of great concern due to their potential applications in materials science, in which the internal carbide cluster plays vital roles in the stability and properties of CCF. However, there still remains a debate about what configuration is ideal for the internal carbide cluster. In this work, we isolated two isomers (I and II) of Ho2C94 and studied them by means of mass spectrometry, UV-vis-NIR spectroscopy, and cyclic/differential pulse voltammetry. A combined study of single-crystal X-ray diffraction (SC-XRD) and density functional theory (DFT) computation ascertains isomer-I as Ho2C2@C2(61)-C92, in which the Ho2C2 cluster displays variable configurations from planar zigzag to folded butterfly with very small distortion energy (∼10 kJ/mol). This study hence confirms that the internal carbide cluster is intrinsically flexible over a broad geometrical range in a relatively large fullerene cage, where the nanoscale compression effect is almost negligible.

Computer modeling of polymer stars in variable solvent conditions: a comparison of MD simulations, self-consistent field (SCF) modeling and novel hybrid Monte Carlo SCF approach.

Computer-aided modeling is a systematic approach to grasp the physics of macromolecules, but it remains essential to know when to trust the results and when not. For a polymer star, we consider three approaches: (i) Molecular Dynamics (MD) simulations and implementing a coarse-grained model, (ii) the self-consistent field approach based on a mean-field approximation and implementing the lattice model due to Scheutjens and Fleer (SF-SCF) and (iii) novel hybrid Monte Carlo self-consistent field (MC-SCF) method, which combines a coarse-grained model driven by a Monte Carlo method and a mean-field representation driven by SF-SCF. We compare the performance of these approaches under a wide range of solvent qualities. The MD approach is formally the most exact but suffers from reasonable convergence. The mean-field approach works similarly in all solvent qualities but is quantitatively least accurate. The MC-SCF hybrid allows us to combine the benefits of the simulation route and the effective performance of SCF. We consider the center-to-end distance Rce, the radius of gyration Rg2 of the star and the polymer density profiles φ(r) of polymer-segments in it. All three methods show a good qualitative agreement one to another. The MC-SCF method is in good agreement with the scaling predictions in the whole range of solvent quality values showing that it grasps the essential physics while remaining computationally in bounds.

Zeolite (In)Stability under Aqueous or Steaming Conditions.

Zeolites are among the most environmentally friendly materials produced industrially at the Megaton scale. They find numerous commercial applications, particularly in catalysis, adsorption, and separation. Under ambient conditions aluminosilicate zeolites are stable when exposed to water or water vapor. However, at extreme conditions as high temperature, high water vapor pressure or increased acidity/basicity, their crystalline framework can be destroyed. The stability of the zeolite framework under aqueous conditions also depends on the concentration and character of heteroatoms (other than Al) and the topology of the zeolite. The factors critical for zeolite (in)stability in the presence of water under various conditions are reviewed from the experimental as well as computational sides. Nonreactive and reactive interactions of water with zeolites are addressed. The goal of this review is to provide a comparative overview of all-silica zeolites, aluminosilicates and zeolites with other heteroatoms (Ti, Sn, and Ge) when contacted with water. Due attention is also devoted to the situation when partial zeolite hydrolysis is used beneficially, such as the formation of hierarchical zeolites, synthesis of new zeolites or fine-tuning catalytic or adsorption characteristics of zeolites.

Ho2O@D3(85)-C92: Highly Stretched Cluster Dictated by a Giant Cage and Unexplored Isomerization.

For endohedral metallofullerenes (EMFs), it has been well established that the cage shape and size should match those of the endohedral cluster. As a result, sufficient cluster-cage interaction can be achieved, which is essential for mutual stabilization. Nevertheless, how a small endohedral cluster nests in a giant fullerene has been less explored. Herein, we report a pair of large oxide-cluster fullerene (OCF) isomers, denoted as Ho2O@C92-I and -II. Crystallographic studies reveal that major isomer-I possesses a D3(85)-C92 cage with a highly stretched Ho2O cluster inside, which contributes to achieving regular metal-cage contacts. Density functional theory (DFT) computations also reveal the predominant abundance of the D3(85) isomer relative to the other two possible minor species including C1(67) and C2(64) isomers. Moreover, electrochemical (EC) studies verify that the isomers exhibit almost identical redox behaviors, indicating their similar cage structures. On the basis of the remarkable topological similarity of D3(85) and C1(67) isomers, isomer-II is likely to be Ho2O@C1(67)-C92, though it remains to be confirmed. Our studies thus provide new insights into the cage-cluster interplay and cage isomerization, both contributing to a better understanding of large EMFs.

Intramolecular micellization and nanopatterning in pH- and thermo-responsive molecular brushes.

Conformational transitions and nanoscale self-organization triggered in double pH- and thermo-responsive molecular brushes by varying environmental conditions are studied by means of analytical mean-field theory and numerical Scheutjens-Fleer self-consistent field modelling. Such molecular brushes are composed of multiple thermo-responsive side chains end-grafted onto the main chain (backbone) and are capable of acquiring ionic charges via reversible (de)protonation of the monomer units. Competition of long-range Coulomb repulsion with short-range solvophobic interactions leads to complex patterns in the intramolecular self-organization of molecular brushes. In particular, we observed formation of pearl necklace-like structures with multiple dense nanodomains formed by weakly ionized collapsed side chains and stabilized by a fraction protruding into the solution and strongly ionized ones. Such structures are thermodynamically stable in a certain parameter range and can be termed as intramolecular micelles. The stimuli-induced intramolecular nanopatterning occurs via a sequence of quasi-first order phase transitions corresponding to splitting/fusion of collapsed domains accompanied by jumps in the average degree of ionization and macromolecular dimensions. A re-entrant sequence of transitions is observed when the salt concentration is used as a control parameter. These theoretical predictions provide guidelines for design of smart unimolecular devices, for example multicompartment nanocarriers of active substances or nanosensors.

Multivalent counterions accumulate in star-like polyelectrolytes and collapse the polymer in spite of increasing its ionization.

We used computer simulations to explore the dissociative and conformational behaviour of branched weak polyelectrolytes with multivalent counterions. We compared simulated titration curves and chain sizes in the presence of added salt of various valencies, keeping the total charge of salt constant. We showed that multivalent counterions enhance ionization of the weak polyelectrolytes, in spite of collapsing of the chains. We provided evidence that such an effect is absent in systems with only monovalent counterions at the same ionic strength, and thus cannot be attributed to electrostatic screening. We attributed it to strong ion-ion correlations that we quantified by comparing potentials of mean force with the mean electrostatic potentials. Finally, we used the partition coefficient to quantify the ability of star-like polyelectrolytes to capture multivalent ions, that is important for water-treatment applications. Our work provides fundamental understanding of the mechanism of polyelectrolyte collapse and ionization response upon addition of multivalent ions.

Antimony(i) → Pd(ii) complexes with the (µ-Sb)Pd2 coordination framework.

The reaction of the antimony(i) compound ArSb (1) (where Ar = C6H3-2,6-(CH[double bond, length as m-dash]NtBu)2) with various dimeric allyl palladium(ii) complexes [Pd(η3-allyl)(µ-X)]2 (where allyl = C3H5 or C3H4Me; X = Cl or CF3CO2) in a 1 : 1 stoichiometric ratio gave unique complexes with the µ-ArSb moiety bridging two palladium fragments, i.e. [{Pd(η3-C3H5)Cl}2(µ-ArSb)] (2), [{Pd(η3-C3H4Me)Cl}2(µ-ArSb)] (3) and [{Pd(η3-C3H5)(CF3CO2)}2(µ-ArSb)] (4). Compound 1 serves formally as a 4e donor in 2-4. The treatment of 2 with another equivalent of ArSb led to the formation of the [Pd(η3-C3H5)(Cl)(µ-ArSb)] complex (5), proving that 1 is able to function as a 2e donor in target complexes as well. The structures of 2-5 were described in detail both in solution (NMR and mass spectrometry) and in the solid state (single crystal X-ray diffraction analysis). DFT methods were used to compare bonding in the 1 : 1 (5) and 1 : 2 (2) complexes. Furthermore, a comprehensive 121Sb Mössbauer spectroscopic investigation of complexes 2 and 5 along with parent ArSbCl2 (6) and 1 was performed. For comparison, complexes [Fe(CO)4(ArSb)] (7) and [Mo(CO)5(ArSb)] (8) were also included in this study.

Ho2O@C84: Crystallographic Evidence Showing Linear Metallic Oxide Cluster Encapsulated in IPR Fullerene Cage of D2d(51591)-C84.

Fullerene C84 is the third-most-abundant species after C60 and C70. In the past decade, a variety of C84-based clusterfullerenes have been well-studied experimentally, which otherwise do not include oxide clusterfullerenes (OCFs). In this work, we report a comprehensive inspection of Ho2O@C84, including its mass, spectroscopic, crystallographic, electrochemical (EC), and density functional theory (DFT) studies. Importantly, crystallographic data reveal an IPR cage of D2d(51591)-C84 with a linear endohedral Ho-O-Ho cluster, indicating that the compression effect of the C84 cage is less pronounced compared to that of a smaller cage. The experimentally observed structure is confirmed by DFT computations, which also verify its superior stability. Further studies suggest that Ho2O@C84 has reduced EC and HOMO-LUMO gaps compared to those of empty species, again demonstrating the effect of cluster encapsulation.

Interactions of star-like polyelectrolyte micelles with hydrophobic counterions.

Hydrophobicity of a counterion has a profound effect on the interaction with polyelectrolytes similar to that of multivalency. Specifically, understanding this interaction in weak polyelectrolyte micelles might assist in developing nanocarriers for pH-controlled encapsulation and release. We used star-like weak polyelectrolyte micelles of polystyrene-block-poly(2-vinyl pyridine) (PS-P2VP) with fixed aggregation number as a model polyelectrolyte, and cobalt bis(1,2-dicarbollide) (COSAN) as a model hydrophobic anion. We used NMR to assess the mobility of the polymer segments in the presence of varying amounts of COSAN, and at varying protonation degrees of the polyelectrolyte. Same experiments with indifferent electrolyte (NaCl) were used as a control. Furthermore, we used coarse-grained simulations to obtain a detailed picture of the effect of hydrophobic counterions on the conformation of the micelles. A small amount of hydrophobic counterions causes morphological changes within the micelles, whereas a bigger amount causes precipitation. This was confirmed both in simulations and in experiments. Furthermore, adsorption of the counterions induces ionization of the collapsed segments of the polyelectrolyte. Although the COSAN/P2VP system is rather specific, the generic model used in the coarse-grained simulations shows that the observed behavior is a consequence of synergy of hydrophobic and electrostatic attraction between polyelectrolytes and hydrophobic counterions. Our study provides general insights into the molecular mechanisms of these interactions.

Ho2O@C74: Ho2O Cluster Expands within a Small Non-IPR Fullerene Cage of C2(13333)-C74.

Steering the cluster configuration inside a fullerene cage has been one of most interesting topics in the field of fullerenes, since the physical property of a cluster fullerene may be modified accordingly. It has been well-recognized that the cluster configuration can be tuned via altering the cage size. Typically, the carbide cluster and the oxide cluster are experimentally seen to be curled up within a small fullerene cage whereas they are expanded in a large cage. In this work, a new oxide cluster fullerene Ho2O@ C2(13333)-C74 is prepared and isolated. The single-crystal X-ray diffraction (XRD) study reveals that the Ho2O cluster, however, expands within the small non-IPR cage of C2(13333)-C74 with a Ho-O-Ho angle of >170°, indicating that cluster configuration is highly related to the cage shape and cage structure as well. The DFT computation demonstrates that the cluster-to-cage electron-transfer obviously enhances the aromaticity of the motif containing the fused-pentagon pair and hence stabilizes the non-IPR cage of C2(13333)-C74. In addition, the electrochemical and magnetic properties of Ho2O@ C2(13333)-C74 are studied to further investigate the effect of endohedral Ho2O cluster.

Simulations of ionization equilibria in weak polyelectrolyte solutions and gels.

This article recapitulates the state of the art regarding simulations of ionization equilibria of weak polyelectrolyte solutions and gels. We start out by reviewing the essential thermodynamics of ionization and show how the weak polyelectrolyte ionization differs from the ionization of simple weak acids and bases. Next, we describe simulation methods for ionization reactions, focusing on two methods: the constant-pH ensemble and the reaction ensemble. After discussing the advantages and limitations of both methods, we review the existing simulation literature. We discuss coarse-grained simulations of weak polyelectrolytes with respect to ionization equilibria, conformational properties, and the effects of salt, both in good and poor solvent conditions. This is followed by a discussion of branched star-like weak polyelectrolytes and weak polyelectrolyte gels. At the end we touch upon the interactions of weak polyelectrolytes with other polymers, surfaces, nanoparticles and proteins. Although proteins are an important class of weak polyelectrolytes, we explicitly exclude simulations of protein ionization equilibria, unless they involve protein-polyelectrolyte interactions. Finally, we try to identify gaps and open problems in the existing simulation literature, and propose challenges for future development.

Isolation and Structural Characterization of Er@ C2 v(9)-C82 and Er@ C s(6)-C82: Regioselective Dimerization of a Pristine Endohedral Metallofullerene Induced by Cage Symmetry.

Two Er@C82 isomers have been isolated and unambiguously characterized as Er@ C2 v(9)-C82 and Er@ C s(6)-C82, respectively, by single-crystal X-ray diffraction. Er@ C s(6)-C82 is identified as a dimeric structure in the crystalline state, but dimerization does not occur for Er@ C2 v(9)-C82 under identical crystallization conditions, indicating a cage-symmetry-induced dimerization process. Density functional theory calculations reveal that the major unpaired spin resides on a special C atom of Er@ C s(6)-C82, which leads to regioselective dimerization. Calculations also found that the dimeric structure of Er@ C s(6)-C82·Ni(OEP) is much more stable than the two monomers, suggesting a thermodynamically favorable dimerization process. Vis-near-IR spectrometric and electrochemical results demonstrate that the electronic structure of Er@C82 isomers is Er3+@C823-, instead of the theoretically proposed Er2+@C822-.

Comparing the reactivity of isomeric phosphinoferrocene nitrile and isocyanide in Pd(ii) complexes: synthesis of simple coordination compounds vs. preparation of P-chelated insertion products and Fischer-type carbenes.

Isomeric phosphinoferrocene ligands, viz. 1'-(diphenylphosphino)-1-cyanoferrocene (1) and 1'-(diphenylphosphino)-1-isocyanoferrocene (2), show markedly different coordination behaviours. For instance, the reactions of 1 with [PdCl2(MeCN)2] and [(LNC)Pd(µ-Cl)]2 (LNC = [2-(dimethylamino-κN)methyl]phenyl-κC1) produced the "phosphine" complexes [PdCl2(1-κP)2] (7) and [(LNC)PdCl(1-κP)] (8), and the latter was converted into the coordination polymer [(LNC)Pd(µ(P,N)-1)][SbF6] (9). Conversely, the reaction of 2 with [(LNC)Pd(µ-Cl)]2 involved coordination of the phosphine moiety and simultaneous insertion of the isocyanide group into the Pd-C bond, giving rise to the P,η1-imidoyl complex [PdCl(Ph2PfcN[double bond, length as m-dash]CC6H4CH2NMe2-κ3C,N,P)] (10; fc = ferrocene-1,1'-diyl). Compound 10 was further transformed into the Fischer carbene [PdCl(Ph2PfcN(Me)CC6H4CH2NMe2-κ3P,C,N)][BF4] (11) by methylation with [Me3O][BF4]. The reactions of 2 with Pd-Me and Pd(η3-allyl) precursors also led to imidoyl complexes [Pd(µ-Cl)(Ph2PfcN[double bond, length as m-dash]CR-κ2C,P)]2 (R = Me: 12, R = allyl: 15), which were cleaved with PPh3 into the corresponding monopalladium complexes [PdCl(PPh3)(Ph2PfcN[double bond, length as m-dash]CR-κ2C,P)] (R = Me: 13, R = allyl: 16). The treatment of 12 and 15 with thallium(i) acetylacetonate (acac) produced [Pd(acac-O,O')(Ph2PfcN[double bond, length as m-dash]CR-κ2C,P)] (R = Me: 17, R = allyl: 18). Through proton transfer, these complexes reacted with Ph2PCH2CO2H, ultimately producing bis-chelate complexes [Pd(Ph2PCH2CO2-κ2O,P)(Ph2PfcN[double bond, length as m-dash]CR)] (R = Me: 19, R = prop-1-enyl (sic!): 20). In addition, compound 13 was converted into the P-chelated carbene [PdCl(PPh3)(Ph2PfcN(Me)CMe-κ2C,P)][BF4] (14). Compounds 10, 11, 13 and 14 were studied by cyclic voltammetry and by DFT computations.

Synthesis and non-conventional structure of square-planar Pd(ii) and Pt(ii) complexes with an N,C,N-chelated stibinidene ligand.

The N,C,N-chelated stibinidene, ArSb (Ar = C6H3-2,6-(CH[double bond, length as m-dash]NtBu)2), reacts with Pt(ii) compounds [PtCl2L2] resulting in the formation of 1 : 1 complexes, cis-[PtCl2L(ArSb)] (L = Me2S (1), dmso (2)). In contrast, attempts to synthesize similar Pd(ii) complexes failed, resulting only in the formation of elemental palladium. To increase the stability of the ArSb complexes, in particular those containing Pd(ii), the simple auxiliary ligands were replaced with C,N-chelating ones, which led to a set of four compounds of the type [RMCl(ArSb)], where R = C6H4-2-(CH2NMe2) or Fe(η5-C5H4)(η5-C5H3-2-(CH2NMe2)) and M = Pd (3, 5) or Pt (4, 6). Compounds 1-6 were characterized by 1H and 13C{1H} NMR spectroscopy and single-crystal X-ray diffraction analysis, and in the case of ferrocene derivatives 5 and 6, also by cyclic voltammetry. Compounds 2-6 were shown to form rotamers in solution due to the side-on coordination of the ArSb ligand and a hindered rotation around the Sb-Pd(Pt) bond. This process was investigated by 1H-VT-NMR spectroscopy and by DFT computations.

Local pH and Effective pK of a Polyelectrolyte Chain: Two Names for One Quantity?

In recent experiments, the "local pH" near polyelectrolyte chains was determined from the shift in the effective acidity constant of fluorescent pH indicators attached to the macromolecules. This indirect determination raises the question if the analyzed quantity was indeed the "local pH" and what this term actually means. In this study, we combined experiments and simulations to demonstrate that the shift in ionization constant is slightly lower than the difference between the pH and the "local pH". This offset is caused by correlations between fluctuations in chain conformation, small-ion distribution, and fluorophore ionization.

Eu@C72: Computed Comparable Populations of Two Non-IPR Isomers.

Relative concentrations of six isomeric Eu@C 72 -one based on the IPR C 72 cage (i.e., obeying the isolated-pentagon rule, IPR), two cages with a pentagon-pentagon junction (symmetries C 2 and C 2 v ), a cage with one heptagon, a cage with two heptagons, and a cage with two pentagon-pentagon fusions-are DFT computed using the Gibbs energy in a broad temperature interval. It is shown that the two non-IPR isomers with one pentagon-pentagon junction prevail at any relevant temperature and exhibit comparable populations. The IPR-satisfying structure is disfavored by both energy and entropy.

Local pH and effective pKA of weak polyelectrolytes - insights from computer simulations.

In this work we study the titration behavior of weak polyelectrolytes by computer simulations. We analyze the local pH near the chains at various conditions and provide molecular-level insight which complements the recent experimental determination of this quantity. Next, we analyze the non-ideal titration behaviour of weak polyelectrolytes in solution, calculate the effective ionization constant and compare the simulation results with theoretical predictions. In contrast with the universal behaviour with respect to chain length, we find non-universality and deviations from theory with respect to polymer concentration and permittivity of the solvent. The latter we explain in terms of counterion condensation and ion correlation effects, which lead to reversal of the non-ideal titration behaviour at very low permittivities. We discuss the impact of these findings on the interpretation of experimental results.