Effects of Sodium and Magnesium Cations on the Aggregation of

Subscriber access provided by Iowa State University | Library

B: Fluid Interfaces, Colloids, Polymers, Soft Matter, Surfactants, and Glassy Materials

Effects of Sodium and Magnesium Cations on the Aggregation of Chromonic Solutions Using Molecular Dynamics Oscar M. Matus Rivas, and Alejandro D. Rey J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b12130 • Publication Date (Web): 23 Jan 2019 Downloaded from http://pubs.acs.org on January 29, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Effects of Sodium and Magnesium Cations on the Aggregation of Chromonic Solutions using Molecular Dynamics Oscar M. Matus Rivas and Alejandro D. Rey∗ Department of Chemical Engineering, McGill University, Montreal, Quebec, H3A OC5, Canada E-mail: [email protected]

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Lyotropic chromonic liquid crystals (LCLC) constitute a unique variety of watersoluble mesogens that spontaneously assemble into elongated aggregates, thereby resulting in the formation of liquid crystal phases depending on the temperature and concentration. The influence of ionic additives on the aggregation of LCLC has been extensively studied, but the molecular mechanisms governing these effects remain unclear. In this investigation, we perform atomistic molecular dynamics simulations of dilute sunset yellow (SSY) LCLC solutions doped with NaCl and MgCl2 salts. Structural and dynamical properties of SSY hydration shells are considerably modified by the partial substitution of their H-bonds with sodium/magnesium-sulfonate ion-pairs. Although the intermolecular distance of ∼ 3.4 Å between SSY mesogens is preserved regardless of the ionic content, the growing number of ion-pairs favors the reduction of the electrostatic repulsion between mesogens, increasing the length of SSY stacks. Moreover, magnesium cations exert the strongest electrostatic effects due to their higher hydration capabilities and acute electrostatic binding to SSY. For these reasons, experimental observations of dilute SSY solutions doped with Mg2+ exhibit higher nematic-to-isotropic transition temperatures than Na+ . This work provides a fundamental understanding of the influence of ionic additives on the self-assembly of diluted LCLC solutions derived from the synergistic molecular mechanisms between mesogens, the solvent, and cations.

Introduction Lyotropic chromonic liquid crystals (LCLC) are a unique class of amphiphilic mesogens that have been the subject of considerable interest in recent years 1–6 . Chromonic mesogens’ (CM) structure is composed of rigid plank-like polyaromatic cores decorated with peripheral ionic solubilizing groups. When they are dissolved in a solvent, commonly water, CM self-assemble into aggregates by weak non-covalent interactions followed by their subsequent growth and alignment, forming liquid crystalline phases depending on concentration and temperature 6 .

2


Page 2 of 43

Page 3 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Chromonics stacking occurs even in highly diluted concentrations, as opposed to other lyotropic systems, such as surfactants, where aggregation starts at the critical micelle concentration 1–4 . The average size of chromonic aggregates increases with concentration, eventually forming nematic (N) phases, where columnar aggregates align to a preferred direction. Coexistence between isotropic (I) and N phases are typically observed for an ample range of concentrations and temperatures. Further concentration increments could lead to the emergence of hexagonal columnar (C) phases with both positional and orientational order 1–4 . LCLC phases are typically observed in dyes 7–10 , drugs 11,12 , and nucleic acids 13,14 . Moreover, chromonics have shown a growing number of potential applications, such as biosensing 15,16 , development of organic electronics 17 , micro-pattering 18,19 , preparation of highly ordered dried films 20 , fabrication of vertically aligned graphene layers 21 , and active matter manipulation 22 . The aggregation model of CMs could also be useful for expanding the understanding of the spontaneous aggregation of aromatic compounds decorated with polar substituents in solution. Some examples include B-DNA bases and chromonic mixtures 23 , benzene-1,3,5-tricarboxamide (BTA) aggregates and its derivates 24,25 , amphiphilic peptidebased supramolecular polymers 26,27 , surfactant nematics 28 , and supramolecular biopolymers such as amyloid fibrils 29 , collagen films and biological liquid crystals 30–35 . The influence of ionic additives, in particular mono- and divalent salts, on the aggregation of LCLC have generated considerable interest in recent years. These studies have been performed mostly on sunset yellow (SSY) 36–39 and disodium cromoglycate (DSCG) 40,41 chromonic mesogens utilizing a variety of experimental techniques. Other ionic additives also investigated include monovalent pH changing agents (such as NaOH and HCl) and multivalent agents (such as tetravalent spermine) 37 , urea and formamide 42 . The effect of ionic salts on LCLC phase diagrams was initially investigated for DSCG solutions doped with NaCl 40 . This monovalent salt increased the transition temperature from the homogeneous N phase to the biphasic N+I phase, TN→N+I , as well as the biphasic N+I to I phase transition temperature, TN+I→I . Another investigation confirmed TN→N+I and

3



TN+I→I increment trends for DSCG solutions doped with several monovalent salts including Na+ and K+ cations 41 . SSY solutions in the I phase doped with mono- (Na+ ) and divalent (Mg2+ ) salts exhibited a similar temperature expansion on the I phase to I+N coexistence region, TI→N+I 37 . In this case, TI→N+I increments were more pronounced for divalent than monovalent salts. However, an apparent contradictory N phase destabilization effect was reported for higher concentrated SSY solution with NaCl where both TN→N+I and TN+I→I temperatures decreased 38 . To clarify this, Park et al. 39 explored the electrostatic influence of NaCl on both high and low SSY concentrations. At low SSY concentration ( ∼ 32 wt%), NaCl induced the reduction of both transition temperatures, suggesting the suppression of orientational order in chromonic aggregates. For even more concentrated SSY solutions in the C phase, they observed the suppression of both orientational and positional order directing SSY solution to the N phase. Based on these observations, the authors proposed that NaCl reduce the electrostatic repulsion between SSY mesogens and aggregates inducing the transition temperature shifts mentioned above. They suggested that SSY charges screened by NaCl could produce two contrasting trends, namely, the increase of stacks physical length (enhancing orientational order), and the reduction of their persistence length (lowering both positional and orientational order). Although significant progress has been made on the fundamental understanding of the aggregation of LCLC with ionic salts, some of its important molecular mechanisms remain unexplored. Atomistic molecular dynamics (MD) simulations have been proved to be a reliable and powerful tool for the understanding of LCLC aggregation by characterizing their structural, dynamical and thermodynamic properties 43–46 . In the present work, we perform all-atom MD simulations to identify the key molecular interactions responsible of the selfassembly of diluted SSY solutions doped with mono- and divalent ionic salts, namely NaCl

4


Page 4 of 43

Page 5 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


and MgCl2 , respectively. We evaluate the polarizing effects induced by sodium/magnesium cations on the structural and dynamical properties of chromonic aggregates (in the low concentration regime) and their corresponding hydrogen bonding (H-bonding) interactions. SSY mesogens are modeled using the NH hydrazone tautomeric form which has been shown to be the most abundant in aqueous solution 47,48 . Ionic salts are simulated utilizing appropriate Na+ , Mg2+ and Cl− ions models. This choice provides the simplest representation available of the most important mono- and divalent cations experimentally tested on chromonic solutions. Two different NaCl and MgCl2 salt concentrations are selected to evaluate their particular polarizing effects on an I phase SSY solution at neutral pH where only SSY sulfonate oxygens are ionized. Ionic salts concentration range is selected following Park et al. 37 experiments to quantify the unique non-covalent mechanisms between mesogens, solvent, and Na+ /Mg2+ responsible of modifying TI→N+I temperatures in salt-doped diluted SSY solutions. The present investigation provides a detailed description of the equilibrium structure of SSY aggregates in I phase as a function of doping salt type and concentration. The influence of cations on the modification of SSY aggregates size, as well as the intramolecular structure between SSY mesogens are evaluated. The effect of ionic salts on the electrostatic screening of SSY repulsive forces is assessed by measuring the structural (pair or radial distribution functions), dynamics (residence times) and affinity (desolvation energy barriers) properties of cations bound to SSY stacks. Finally, the impact of the added ionic content to the hydration state of SSY stacks is examined by characterizing the H-bonding density of SSY aggregates as well as their solvation dynamics employing H-bonding lifetimes. The understanding gained from this study provides insight on the synergistic molecular mechanisms between SSY mesogens, the solvent, and cations leading to the particular phase behavior and spontaneous aggregation of diluted CMs doped with mono- and divalent ionic salts. Concentrated solution of CMs are beyond the scope of this paper.

5



Computational details and methods Initial geometry optimization of an SSY monomer was carried out utilizing ab initio density functional theory (DFT) using the van der Waals (VDW) exchange-correlation functional with LMKLL reparametrization 49 . These calculations were performed employing normconserving Troullier-Martins pseudopotentials 50 and double-ζ polarized (DZP) basis set with a force tolerance of 0.005 eV/Å and energy cutoff of 300 Ry using the SIESTA code 51 . The resulting relaxed SSY monomer structure was utilized as input to the subsequent partial electronic charges and forcefield parameters assignation. SSY molecular interactions were described with the general amber forcefield (GAFF v2.1) 52 whose parameters were assigned to optimized SSY molecules using AmberTools16 with restrained electrostatic potential (RESP) HF/6-31G*//HF/6-31G* charges 53 calculated from the PyRED server 54 using Gaussian 09 (Rev. A.02). TIP3P-Ew model was utilized for water molecules 55 . Sodium cations and chloride anions were modeled after Joung and Cheatham, III parameters 56 while magnesium cations using Li-Mertz parameters 57 . A complete reference of SSY forcefield parameters used in this work is provided in the Supporting Information (SI) Figure S1 and Tables S1-S5. Molecular dynamics simulations were run with LAMMPS code 58 using a 2 fs integration time step. Equilibration was assured by performing a 25 ns run in the canonical ensemble (NVT) followed by a 200 ns run in the isobaric-isothermal ensemble (NPT) for each simulated system. Additional 100 ns runs in the NPT ensemble were treated as production for data collection and analysis. Production trajectories were collected every 2 ps given a total of 50, 000 frames. The temperature was kept constant at 300 K using a 5 element long NoseHoover thermostat chain with a damping parameter of 0.1 ps while pressure was controlled at 1 atm using a Nose-Hoover barostat chain of length 5 with a damping parameter of 1.0 ps 59 . The bonds and angles of water were constrained with the SHAKE algorithm with a 10−4 tolerance 60 . Particle-particle-particle mesh (PPPM) solver was employed to simulate long-range Coulombic interactions 61 with a relative force tolerance of 10−4 . A single cutoff of 10.0 Å was utilized for Coulombic interactions. An inner cutoff of 8.0 Å, and an outer cutoff 6


Page 6 of 43

Page 7 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


of 10.0 Å were used for Lennard-Jones (LJ) interactions using a force switching function 62,63 to smoothly shift the LJ force values to zero between the inner and outer cutoff radii. SSY systems were modeled in the isotropic phase at a concentration of 6.5 wt%, and 300 K. Excess salt concentration was calculated using molality units, m (moles of salt in 1 kg of water) 37 . A set of five simulations comprised of 20 SSY mesogens were run, corresponding to a control system with no added ionic additives (system A), two systems doped with 0.5 m and 1.0 m excess NaCl salt (system B and C, respectively) and two more systems doped with 0.5 m and 1.0 m MgCl2 salt (systems D and E, respectively). The total number of excess cations included in each solution modeled (Na+ for systems B-C; Mg2+ for systems D-E) were 65 for 0.5 m models (systems B and D) and 130 for 1.0 m models (systems C and E ). The total number of Cl- anions were determined accordingly to its doping salt stoichiometry. A summary of the number of particles in each modeled system is presented in the SI Table S6. All molecular simulations included two Na+ counterions per SSY mesogen which are intrinsic to SSY crystal structure (40 sodium counterions in total). Once systems B and C were equilibrated, the origin of sodium atoms, i.e., Na+ counterions and excess Na+ cation, was indistinguishable during the analysis phase. The initial configuration of each simulation box was prepared by placing 7, 224 water molecules with 20 SSY molecules 3

and their corresponding number of ions in a 61.0 × 61.0 × 61.0 Å cubic box. The atomic positions of all particles were placed randomly in the simulation box using the Packmol code 64 using different random seeds for each system. LAMMPS input files were prepared using Moltemplate software 65 by assigning forcefield and partial charges parameters to the random atomic coordinates previously generated. The analysis of production trajectories was carried out using MDAnalysis library 66,67 (MDA) unless otherwise stated. The visualization of molecular trajectories was performed using VMD software 68 . The local atomic structure of SSY solutions was characterized with the help of radial distribution functions (RDFs), gij (r), which quantify the probability of finding particle type j at a radial separation r from a reference particle type i at any given time 69 .

7



Page 8 of 43

RDFs were averaged over production trajectories with a bin size of 0.03 Å. The radial integral of gij (r), or cumulative coordination number nij (r), was computed to measure the number Rr of neighboring particles j around a central particle i, i.e., nij (r) = 4πρj 0 gij (r0 ) r02 dr0 , where ρj is the number density of particle type j. The coordination number of particles was found by integrating nij (r) up to the first minimum of gij (r), which corresponds to the first spherical shell. Hydrogen bonds (H-bonds) between selected donor and acceptor pairs were registered using the Hydrogen Bond analysis module from MDA package 66,67 . Typical values for donor-hydrogen-acceptor angle θD−H···A ≥ 150◦ and acceptor-hydrogen length rA···H ≤ 3.0 Å were used to detect H-bonds 70 . For intramolecular H-bonds, where both donor and acceptor atoms are located within the same molecule, deviation from linear geometry is more pronounced compared to intermolecular H-bonds due to inherent conformational restrictions. Thus, θD−H···A ≥ 120◦ was chosen to accurately capture these interactions 71 . H-bond densities were computed by dividing the total number of H-bonds observed by the total volume of the simulation box. This quantity was averaged over time for the whole production trajectories. H-bonding dynamics were characterized employing the average H-bond lifetimes employing MDA hydrogen bond autocorrelation module 72 . H-bond lifetimes were estimated from the time autocorrelation function 73 *P Cx (t) =

hij (t0 ) hij (t0 + t) P hij (t0 )2

+ (1)

where hij monitored the presence or absence of a particular H-bond pair ij, i.e., hij = 1 if pair ij satisfies the corresponding H-bond geometric criteria, or hij = 0 otherwise. Angular brackets h· · · i denote time average over a series of starting times in the production trajectories. Two different definitions of H-bond lifetimes were used where subscript x in Equation (1) could refer to either continuous (CC (t)) or intermittent (CI (t)) functions. For continuous H-bond lifetime definition, τC , function hij measured the average time a particular H-bond interaction remained paired. If a given H-bond were broken, it would

8


Page 9 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


be considered unattached for the remaining time. Thus, CC (t) measured the mean H-bond lifetime. On the contrary, intermittent H-bond lifetime definition, τI , allowed H-bonds to break and eventually reestablish letting function hij to register them again at a subsequent time. Hence, this definition evaluated the time that a specific H-bond pair remains in the same local area allowing water molecule to rotate and translate around a specific vicinity. H-bond lifetimes were obtained by integrating each time autocorrelation function definition as follows Z τx =

∞

Cx (t0 ) dt0

(2)

0

where Cx (t) is fitted to a multi-exponential function accordingly, i.e., for continuous lifetime definition, CC (t) = A1 e−t/τ1 + (1 − A1 ) e−t/τ2 , while for intermittent lifetime definition, CI (t) = A1 e−t/τ1 + A2 e−t/τ2 + (1 − A1 − A2 ) e−t/τ3 . For intermittent H-bond lifetimes, an additional set of production trajectories were carried out in the NPT ensemble at 300 K and 1 atm starting from the last frame of standard production runs. Trajectory frames were recorder every 0.005 ps for a total of 2.5 ns simulation time. Self-diffusion coefficients were estimated from the mean square displacement (MSD) of

particles using the Einstein relation 74 , [r (t0 − t) − r (t0 )]2 = 6Dt, where [r (t0 − t) − r (t0 )]2 is the MSD of a diffusing particle, D is the self-diffusion coefficient, and t is the observation time. MSD calculations were computed using VMD diffusion coefficient tool 75 . Binding affinity of ion-pairs were studied estimating their potential of mean force (PMF) or free energy radial profile, unless otherwise discussed. PMF profiles were obtained using the relationship 76 UP M F (r) = −kB T ln gij (r)

(3)

where UP M F (r) is the PMF as a function of radial separation r, kB is Boltzmann constant, T is the average simulation temperature, and gij (r) are the corresponding RDF defined above.

9



Results and Discussion Sunset Yellow aggregation structure The aggregation of SSY molecules is characterized by the pair distribution functions, gN −N (r), between intermolecular −N−N− bonds from SSY NH hydrazone groups (−NH−N−C−), presented in Figure 1(a). The sharp gN −N (r) peaks, which progressively decrease their intensity with r, are approximately evenly spaced by ∼ 3 Å followed by shallow minima. The first set of peaks, shown approximately at r = 3.5 Å, represent the intermolecular distance between adjacent SSY molecules. The second maxima seen around r = 6.9 Å depict the average distance between two SSY molecules separated apart by one SSY mesogen. These values are in excellent agreement with X-ray diffraction results showing that the separation distance between adjacent SSY molecules is ∼ 3.4 Å 7,47 and their two molecular thicknesses distance is ∼ 6.8 Å 47 . gN −N (r) satisfactorily captures the discrete structural order between SSY molecules forming columnar-like aggregates along a stacking direction and confirms that SSY face-on aggregation pattern is not disrupted with the addition of excess salt. A: No added salt B: 0.5 m NaCl C: 1.0 m NaCl D: 0.5 m MgCl2 E: 1.0 m MgCl2

(a)

120 90

20.0

(b)

17.5 15.0 12.5

nN − N (r)

150

gN − N (r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 43

10.0

60

7.5 5.0

30

2.5 0

0.0 0.0

2.5

5.0

7.5

10.0 r(Å)

12.5

15.0

17.5

20.0

0

3

6

9

12

15

r(Å)

Figure 1. (a) Pair distribution function gN −N (r) and (b) cumulative coordination number nN −N (r) between intermolecular −N−N− atoms from NH hydrazone group. The effect of ionic salts is more evident from the cumulative coordination number, nN −N (r), as shown in Figure 1(b). nN −N (r) is described as a strictly increasing stepwise curve as a function of distance r. Each step or semi-plateau region is correlated to a RDF 10


18

Page 11 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


shell from Figure 1(a). The growth of nN −N (r) is more pronounced in systems B-E compared to the salt-free system A. It infers that the excess number of available cations allows SSY molecules to stack more efficiently by increasing the number of mesogens per stacking column, i.e., raising the columnar length of individual SSY aggregates. A cluster analysis was performed to count the total number of aggregated columns per system including the total number of SSY monomers per stack using aggregate/atom compute in LAMMPS. A cutoff distance of 6.1 Å, which corresponds to the first minima observed in Figure 1(a), was used to replicate gN −N (r) first radial shell. Size distribution results for SSY solutions are presented in Table 1 while their final self-assembled structures are visualized in Figure 2. These analyses confirm that SSY aggregate size increases in salt-doped systems. The maximum stacking extension is observed for systems C and D with a single 20-molecule long SSY stack, which is characterized by the fastest nN −N (r) slope growth. Systems B and E selfassemble into two stacking columns of different sizes; an almost even number of molecules per column is observed in system E (9- and 11-molecule long stacks) while system B favors a 16-mesogens long column with a smaller SSY tetramer stack. While the extension of SSY aggregates is directly proportional to NaCl concentration, systems doped with MgCl2 show a contrary effect. System E (1.0 m MgCl2 ) exhibits a smaller nN −N (r) magnitude compared to the less concentrated system D (0.5 m MgCl2 ). This suggests that Mg2+ exerts stronger screening polarization effect on SSY mesogens than Na+ . Table 1. Aggregation size distribution of simulated SSY systems Systems

No. of SSY aggregates

No. of SSY molecules per aggregate

A: No added salt

3

7, 5, 8

B: 0.5 m NaCl

2

4, 16

C: 1.0 m NaCl

1

20

D: 0.5 m MgCl2

1

20

E: 1.0 m MgCl2

2

9, 11

The intermolecular −N−N− coordination number calculated for the salt-free system is 11



Page 12 of 43

∼ 3 while for salt-doped systems this value is raised to ∼ 4. It proves that SSY aggregates are not perfectly aligned along the stacking direction forming vertical columnar stacks. Instead, their stacking columns are semi-flexible and this appears to be enhanced by the incorporation of salt additives 39 . Otherwise, these coordination numbers would be expected to be approximately 2. However, a detailed understanding and characterization of SSY stacks’ flexibility is out of the scope of this study.

Figure 2. Final aggregation structures observed for SSY systems: (a) salt-free, (b) 0.5 m NaCl, (c) 1.0 m NaCl, (d) 0.5 m MgCl2 , and (e) 1.0 m MgCl2 ; water molecules are omitted for clarity, while Na+ and Mg2+ are represented as green and orange spheres, respectively. (f) H-bonds example around a single SSY mesogen. (g) Na+ and Mg2+ ion-pairs representation. (h) SSY NH hydrazone molecular structure.

Chromonic - Solvent interactions Figure 3(a) displays the RDFs between sulfonate and water oxygens, gOSO− −Ow (r). The 3

first set of peaks centered at r = 2.7 Å corresponds to the formation of H-bonds between SSY sulfonate oxygens (acceptors) and water (donors). The second set of peaks located at

12


Page 13 of 43

r = 5.0 Å are significantly less sharp than the previous one. Both sets of peaks indicate the formation of two well-differentiated hydration shells around chromonic stacks. This confirms the formation of a H-bonding network around SSY aggregates (see Figure 2(f)). The coordination number of OSO−3 −Ow H-bonds is ∼ 2 for all systems suggesting that each sulfonate oxygen formed a bifurcated or three-center H-bonds by directly interacting with two water molecules simultaneously. The location of RDFs peaks remains invariant regardless of the excess salt content. The magnitude of gOSO− −Ow (r) first peak shows the following order 3

for the simulated systems: E > D > A > B > C. This suggests that the influence of Mg2+ increases the probability of finding OSO−3 −Ow H–bonds by possibly augmenting their relative strength. On the other hand, Na+ systems appear to decrease gOSO− −Ow (r) probability with 3

concentration. 1.75

(r)

1.50 1.25

A: No added salt B: 0.5 m NaCl C: 1.0 m NaCl D: 0.5 m MgCl2 E: 1.0 m MgCl2

(b)

1.75 1.50

1.00

3

−

− OW

2.00


(a)

gOC = O − OW (r)

2.00

gOSO

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.75

1.25 1.00 0.75

0.50

0.50

0.25

0.25

0.00

0.00 0

2

4

6

8 r(Å)

10

12

14

16

0

2

4

6

8 r(Å)

10

12

14

Figure 3. (a) Sulfonate-water oxygens and (b) carbonyl-water oxygens radial distribution functions. Subtle differences in gOSO− −Ow (r) minima are also seen. For systems where only Na+ 3

are present (A, B and C), minima are located at r = 3.3 Å and r = 5.5 Å, respectively. For systems with both Na+ counterions and excess Mg+2 (D and E), minima are located at r = 3.2 Å and r = 5.6 Å, respectively. This demonstrates that water molecules are slightly tighter packed with MgCl2 and suggests that their mobility could be constrained around OSO−3 atoms. Additionally, the length of the second hydration shell appears to be somewhat expanded towards the solvent bulk in MgCl2 models. This minimal expansion 13


16


in Mg2+ systems could be triggered by the presence of a small peak or bump between the two hydration shells at approximately r = 4.0 Å. This feature has been previously observed in other supramolecular self-assembly simulations involving interactions between surfactants and divalent cations 77,78 . The small middle peak is originated by the polarization that Mg2+ cations exert on the solvent resulting in the ordering of water molecules around the divalent cations. Hence, the structure of the H-bonding network of systems D and E are modified to a greater extent compared to the other simulated systems. H-bonding network formation around carbonyl sites, OC=O − OW , was also verified by gOC=O −OW (r) RDFs in Figure 3(b) (see Figure 2(f)). A single predominant peak is seen again at r = 2.7 Å followed by a very diffuse and weak second hydration shell around r = 5.2 Å. First hydration shell minima are located approximately at r = 3.4 Å with a coordination number close to 2.0. It confirms that carbonyl oxygens form three-center H-bonds as well. H-bonding changes caused by ionic salts appear to be less sensible in carbonyl sites compared to sulfonate ones since gOC=O −OW (r) intensities are barely altered (except for system E which shows a sharper value). Additionally, the magnitude of the first set of gOC=O −OW (r) peaks is less pronounced than the previous case. This behavior is expected since ionized sulfonate groups (negatively charged OSO−3 ) are more effectively screened by the solvent and cations. 3.0

H-bond density (No. /nm 3 )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 43

1e 2

1e 1

6

1.2

5

1.0

2.0

4

0.8

1.5

3

0.6

1.0

2

0.4

1

0.2

0

0.0

2.5

0.5 0.0

(a)

O SO3 -O W O C = O -O W −

1e 1

(b)

N NH -O C = O

A: No B: 0.5 m C: 1.0 m D: 0.5 m E: 1.0 m NaCl MgCl2 MgCl2 added salt NaCl

A: No B: 0.5 m C: 1.0 m D: 0.5 m E: 1.0 m NaCl MgCl2 MgCl2 added salt NaCl

Figure 4. H-bond densities for SSY oxygens: (a) sulfonate-solvent (circles), and carbonylsolvent (triangles). (b) Intramolecular nitrogen-carbonyl oxygen (diamonds). Error bars are smaller than symbols used. The calculated H-bond densities observed between sulfonate/carbonyl oxygens (accep14


Page 15 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


tors) with water oxygens (donors), OSO−3 −OW and OC=O −OW , respectively, are provided in Figure 4(a). OSO−3 −OW H-bond densities are roughly ten times more abundant than OC=O −OW ones, as anticipated from the previous results. The salt-free system exhibits the highest H-bond densities compared to salt-doped systems. It indicates that when excess salt is added to SSY solutions, a fraction of H-bonds previously formed is replaced by cation–anion (in sulfonate groups) and cation-dipole (in carbonyl sites) interactions. These interactions lower the overall H-bond density around SSY stacks. Systems doped with NaCl show a progressively decrease of H-bond density with salt concentration increments (systems B and C). In systems doped with MgCl2 , the H-bond density reduction is less noticeable since it progressively recovers as excess salt concentration increases; although system D shows an initial decrement in H-bond density, doubling MgCl2 concentration in system E barely alters the H-bond density of SSY stacks compared to the salt-free reference system. These observations support RDF results discussed above by quantitatively demonstrating that SSY H-bonding is more abundant in systems doped with MgCl2 than with NaCl ones. Figure 4(b) shows the intramolecular H-bond densities between hydrazone nitrogens (donors) and carbonyl oxygens (acceptors), NNH −OC=O . These H-bond densities remain practically constant, except for system E, which decreased ∼ 40% compared to the other systems. Intramolecular NNH −OC=O H-bonds provide structural stability within each SSY molecule by linking the hydrazone group to the naphthyl ring through the carbonyl oxygen. Since there is only one possible NNH −OC=O H-bond per SSY molecule, its average number provides a rough estimation of the amount of SSY mesogens forming this interaction. It was found that ∼ 85% of SSY mesogens exhibit intramolecular H-bonds. This suggests that SSY rigid cores conformations are somewhat not heavily influenced by the added ionic content (except for 1.0 m MgCl2 model which showed a 50% intramolecular H-bond formation). The average acceptor-hydrogen lengths, rA···H , and donor-hydrogen-acceptor angles, θD−H···A , were determined for the H-bond pairs discussed above (Table S7). Average rA···H values for OSO−3 and OC=O acceptors are 1.88 Å and 1.90 Å, respectively in systems A-C. For systems 15



Page 16 of 43

D and E, however, these distances average 1.84 and 1.88 Å, respectively. It is well known that stronger H-bonds are correlated with shorter rA···H distances. Consequently, these results imply that sulfonate oxygens H-bonds are relatively stronger than carbonyl ones, and also, the overall H-bonding strength is enhanced when Mg2+ cations are available in the solution. rA···H distances for intramolecular NNH −OC=O H-bonds are approximately 2.0 Å. This category is the weakest H-bonding interaction seen in all simulated SSY systems. Moreover, H-bonds ranging from 180◦ < θ < 140◦ and 1.70 Å < rA···H < 2.00 Å are commonly regarded as moderate or normal H-bonds 71 . Moderate H-bond absolute enthalpies can typically extend from 5 to 10 kcal mol−1 and are commonly found in water and proteins 71,79 . OSO−3 and OC=O acceptors fall in this category with an average H-bonds angle of 163◦ . Intramolecular H-bond angles vary from 120◦ < θ < 140◦ with a mean of 128◦ . This proves that the chosen geometric criteria were appropriated since it correctly characterizes NNH −OC=O geometrical constraints within each SSY mesogen.

Chromonic-Cations interactions The interactions between SSY oxygen atoms and the different cations in solution were investigated by computing their respective RDFs (see Figure 2(g)). In Figure 5(a), RDFs between sulfonate oxygens and sodium cations, gOSO− −Na+ (r), are presented for all system 3

studied. Two well-defined sets of gOSO− −Na+ (r) peaks, or radial shells, are shown. The 3

first set, represented as sharp peaks around r = 2.3 Å, evidence the formation of relatively strong OSO−3 −Na+ ion-pairs around SSY stacks, whose magnitude is undoubtedly larger than OSO−3 −OW interactions previously discussed. This confirms the electrostatic, or more specifically, charge–charge nature of OSO−3 −Na+ pairs. The second gOSO− −Na+ (r) peak set 3

seen around r = 4.6 Å is significantly less pronounced than the preceding one. Both peaks are separated by a deep gap caused by the inherent repulsion of sodium cations sitting on the first and second radial shells, respectively. This gap is approximately occupied with water molecules which are either interacting with SSY via H-bonding or being polarized by 16


Page 17 of 43

the cations (Na+ for systems A-C, and both Na+ /Mg2+ for systems D and E). Moreover, the intensity of gOSO− −Na+ (r) first peaks varies depending the concentration and type of 3

ions in the solution. RDFs intensity decreases as follows for each system: A > B > C > D ≈ E. In systems A-C, the probability of contact between OSO−3 −Na+ pairs decreases as NaCl concentration is doubled. This suggests that most of the added Na+ cations are polarized by the solvent in the bulk, and only a minor fraction of them interact directly with SSY. On the other hand, when MgCl2 salt is present (systems D and E), the probability of OSO−3 −Na+ contacts remains invariably low regardless the dopant salt concentration. It points out that OSO−3 −Na+ pairs are partially replaced with OSO−3 −Mg2+ ones, resulting in a uniform reduction of gOSO− −Na+ (r) intensity. 3

30

40 30

gOSO

3

3

−

−

− Na +

(r)

40

D: 0.5 m MgCl2 E: 1.0 m MgCl2

(b)

50

(r)

50

60


(a)

− Mg 2 +

60

gOSO

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


20 10

20 10

0

0 0

1

2

3

4 r(Å)

5

6

7

8

0

1

2

3

4 r(Å)

5

6

Figure 5. Radial distribution functions between (a) sulfonate oxygens-sodium cations; and (b) sulfonate oxygens-magnesium cations. The RDFs between SSY sulfonate oxygens and magnesium cations, gOSO− −M g2+ (r), are 3

+

displayed in Figure 5(b). They show similar trends to OSO−3 −Na ion-pairs, but some notable differences are evident. Although two ionic shells are clearly defined, their intensity is substantially increased when compared to their sodium equivalents. Very high initial maxima set at r = 2.0 Å is followed by a less sharp one at r = 4.2 Å. Using system D as reference, gOSO− −M g2+ (r) first peak intensity is approximately 4 times larger than its gOSO− −Na+ (r) 3

3

counterpart. This supports that magnesium cations are strongly bound to SSY sulfonates. Moreover, both peaks sets are separated by a very deep and wide well where both RDFs 17


7

8


practically vanished. It points out that the mutual repulsion between Mg2+ from the first and second hydration shells is stronger than Na+ . Thus, a slightly larger number of water molecules are potentially allocated between gOSO− −M g2+ (r) peaks, as suggested in Figure 3. 3

Similarly to gOSO− −Na+ (r) trends, the intensity of gOSO− −M g2+ (r) peaks is lowered as MgCl2 3

3

concentration is doubled. It confirms that most Mg2+ are located in the bulk of the solvent, and only a minor fraction of them bound to OSO−3 . Evident distinctions between Na+ and Mg2+ cations interacting with SSY sulfonate oxygens arise from their polarization strength differences. Due to the higher charge density of magnesium cations, they appear more tightly packed around sulfonate oxygens than sodium ones. It has been reported that average ion-water oxygen distances are approximately 2.13 Å for Mg2+ −OW 80 and 2.34 Å for Na+ −OW 81 . These measurements were obtained from quantum mechanical and neutron diffraction methods, respectively. The equivalent Mg2+ −OSO−3 and Na+ −OSO−3 distances extracted from Figure 5 are in good agreement with these reported values. From an experimental perspective, the smaller size of Mg2+ could also facilitate shorter OSO−3 −Mg2+ bound distances, since the estimated ionic radius for Mg2+ is 0.65 Å, while for Na+ is 0.95 Å 82 .

10

12


(a)

8 6 4 2

D: 0.5 m MgCl2 E: 1.0 m MgCl2

(b)

10

gOC = O − Mg 2 + (r)

12

gOC = O − Na + (r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 43

8 6 4 2

0

0 0

2

4

6

8

10 r(Å)

12

14

16

18

20

0

2

4

6

8

10

12

14

16

r(Å)

Figure 6. Radial distribution functions between (a) carbonyl oxygens-sodium cations; and (b) carbonyl oxygens-magnesium cations. The RDFs between carbonyl oxygens and Na+ /Mg2+ cations, which form ion-dipole interactions (Figure 6), were also computed to assess their structural differences against sulfonate 18


18

20

Page 19 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ion-pairs previously discussed. The general trends observed for sulfonate oxygens-cations RDFs remain somewhat intact for ion-carbonyl oxygens RDFs, gOC=O −Na+ /Mg2+ (r), such as the location of both first and second spherical shells. Nevertheless, some significant differences are noticeable. First, the intensity of gOC=O −Na+ /Mg2+ (r) peaks decreases considerably. This observation suggests that the actual average number of ion-carbonyl contacts should be very limited compared to ion-sulfonate ones. Also, the emergence of a third wide radial shell, located approximately around r = 10 Å , is evident in gOC=O −Na+ /Mg2+ (r) curves. This nonsharp peak set corresponds to Na+ /Mg2+ directly interacting with sulfonate sites (around their respective radial shells) that are detected by gOC=O −Na+ /Mg2+ (r) functions. These results, together with H-bonding density evidence, demonstrate that sulfonate groups are far more polarizable than dipole-ion carbonyl ones. The average number of ion-oxygen contacts in SSY molecules, presented in Table 2, were estimated by directly averaging OSO−3 −Na+ /Mg2+ ion-pairs and OC=O −Na+ /Mg2+ contacts over the whole production trajectory for each system. The percentage of cations bound to SSY polar oxygens was also estimated. The number in parentheses is the average uncertainty (as standard error). Ion-sulfonate contacts dominate not only H-bonding but also ion contact interactions, as expected. For Na+ , the number of ionic contacts around sulfonate sites is ∼ 10 times larger than those seen around carbonyl oxygens. For Mg2+ pairs, which are also predominantly bound to sulfonate oxygens, their interaction with carbonyl oxygens is practically inexistent, with only a single OC=O −Mg2+ pair registered for system E. For this reason, the remaining analysis of cation-oxygen interaction will focus on sulfonate sites only. As ionic salt concentration is increased, the percentage of Na+ and Mg2+ bound to SSY sulfonate oxygen decreases. This confirms that the vast majority of cations remain unbound to SSY aggregates. Instead, cations are hydrated by the solvent in the bulk. Nonetheless, the actual number of ion-sulfonate contacts in SSY stacks increases with concentration. Average OSO−3 −Na+ contacts increase from 9.2 in system A to 15.4, and 20.5 in systems B and C, respectively. This significant increment in system C could explain the pronounced drop in

19



Page 20 of 43

H-bond density seen in Figure 4(a). For systems D and E, average OSO−3 −Na+ ion-pairs number remain fixed around 4. However, for OSO−3 −Mg2+ pairs, contacts number increases from 13 in system D to 19 in system E. These values quantitatively corroborate that Mg2+ cations dominate SSY interactions over Na+ ones, as initially suggested by RDFs trends discussed above. Although the increment of magnesium-sulfonate contacts from systems D to E is large, the overall H-bond density drop in system E is minimal. For this reason, Mg2+ must also contribute to the enhancement of H-bonding density when compared to NaCl doped systems. Table 2. Average ion contacts with sulfonate and carbonyl oxygens System


Mg2+ · · · OSO− 3

Na+ · · · OSO− 3

Na+ · · · OC=O

Mg2+ · · · OC=O

Contact number

Bound Na+ %

Contact number

Bound Mg2+ %

Contact number

Bound Na+ %

Contact number

Bound Mg2+ %

9.2(1) 15.4(1) 20.5(2) 3.9(1) 3.8(1)

23.0 14.6 12.1 9.7 9.6

− − − 13.0(0) 19.0(0)

− − − 20.0 14.6

0.7(0) 1.3(1) 2.1(1) 0.4(0) 0.3(0)

1.9 1.2 1.2 0.9 0.8

− − − 0.0 1.0(0)

− − − 0.0 0.8

H-bonds and ion-pairs dynamics The dynamic behavior of SSY H-bonds was analyzed by estimating their individual average lifetimes, where both continuous, τC , and intermittent, τI , lifetime definitions (Equation 2) were fitted from the autocorrelation function presented in Equation (1). The estimated fit for the continuous, CC (t), and intermittent, CI (t), time autocorrelation functions for OSO−3 −OW and OC=O −OW H-bonds (acceptor-donor) are depicted in Figure 7 while their corresponding H-bond lifetimes, τC and τI , are shown in Table 3. As seen in Figures 7(a)-(b), the continuous relaxation of H-bonds is somewhat similar for all systems. For sulfonate sites, two CC (t) decay trends are easily differentiated between mono- (systems A-C) and divalent (systems D-E) models. Slower CC (t) decays are directly correlated to the presence of Mg2+ in the solution since τC lifetimes slightly increase from 0.30 20


1.0

(a)

No added salt 0.5 m NaCl 1.0 m NaCl 0.5 m MgCl2 1.0 m MgCl2

CC (t)

0.8 0.6 0.4

OSO3

−

0.2

1.0

(b)


0.8

− OW

0.6 0.4

OC = O − OW

0.2

0.0

0.0 0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.00

0.25

0.50

Time (ps) 1.0

(c)

1.0

0.4

OSO3

−

0.2

1.00

1.25

− OW

0.0

(d)

1.50

1.75

2.00


0.8

CI (t)

0.6

0.75

Time (ps) No added salt 0.5 m NaCl 1.0 m NaCl 0.5 m MgCl2 1.0 m MgCl2

0.8

CI (t)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


CC (t)

Page 21 of 43

0.6 0.4

OC = O − OW

0.2 0.0

0

15

30

45

60

75

90

105 120 135 150

0

Time (ps)

15

30

45

60

75

90

105 120 135 150

Time (ps)

Figure 7. Estimated continuous time autocorrelation functions (HBAC) CC (t) for (a) sulfonate-water oxygens and (b) carbonyl-water oxygens H-bonds. Intermittent HBAC CI (t) for (c) sulfonate-water oxygens and (d) carbonyl-water oxygens H-bonds.

21



ps (in systems A-C) up to 0.34-0.35 ps (in systems D and E, respectively). This represents a ∼ 13% and ∼ 17% τC increment in systems D and E, respectively, when compared to the reference system A. For carbonyl H-bonds, CC (t) relaxation curves almost overlap with each other following an apparent single decay trend, as seen in Figure 7(b). However, very subtle and gradual increments of τC are distinguishable as both NaCl and MgCl2 concentrations are increased. Again, the highest τC magnitudes are found for systems doped with MgCl2 (D and E) with τC = 0.27 ps. This value represents a ∼ 12.5% increment from salt-free system A. The magnitudes of τC for sulfonate sites are relatively larger compared to carbonyl ones. These results are in a good agreement with the H-bond strength relative to H-bonds equilibrium distances, rA···H , as discussed above. Consequently, τC predictions dynamically verify that SSY H-bonds between water and the negatively charged sulfonate groups are stronger, and therefore, dominate the hydration of SSY aggregates. Figures 7(c)-(d) show the intermittent time autocorrelation relaxation, CI (t), for sulfonate and carbonyl H-bonds, respectively. While τC evaluates the mean lifetime that a specific H-bond pair remains attached, intermittent lifetime definition, τI provides an estimate of the time a given water molecule remains close to a particular SSY polar site vicinity. It is worth noting that τI allows the breakage and reformation of specific H-bonding pairs. Thus, τI could be interpreted as the average residence time of water around sulfonate or carbonyl sites. The relaxation of CI (t) is similar to their continuous lifetime counterparts but takes place over a more extended period, resulting in larger τI , as expected. Also, intermittent H-bond lifetimes increase as doping salt concentration is raised according to the following simulated system’s order: A < B < C < D < E. Systems D and E, present the slowest intermittent lifetime dynamics for both H-bonding sites studied. This suggests that Mg2+ cations increase the average strength of H-bonds around SSY polar sites, and also, that water mobility around SSY molecules is reduced by ionic salts. This polarization effect is stronger around sulfonates sites where practically most Mg2+ ion-pairs occur. The different H-bonding dynamics exerted by mono- and divalent salts can be explained

22


Page 22 of 43

Page 23 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


by examining their hydration capabilities with the solvent, which are accurately reproduced by the selected ion parameters 56,57 . Magnesium cations coordinate ∼ 6 water molecules while sodium cations exhibit a first coordination shell of ∼ 5 83 . Therefore, the dynamics of water molecules, either in bulk or directly interacting with the chromonic stacks, are suppressed due to the increment of available cations in each doped system. Moreover, the slower H-bonding dynamics seen in systems doped with MgCl2 is caused by the larger hydration capabilities of magnesium cations. It implies that Mg2+ directly forming OSO−3 −Mg2+ pairs are also able to polarize neighboring water molecules at some extent. For this reason, the H-bond densities of solutions doped with MgCl2 , particularly system E, are less compromised than those systems doped with NaCl (see Figure 4). This observation is also supported by experimental findings where is acknowledged that water molecules being polarized by magnesium cations are acidic and therefore, increase their H-bond donating potential 82 . Table 3. Continuous (τC ) and intermittent (τI ) H-bond residence time averages Ow −H · · · OSO− 3

Ow −H · · · OC=O

τC (ps)

τI (ps)

τC (ps)

τI (ps)

A: No added salt

0.30

7.09

0.24

9.75

B: 0.5 m NaCl

0.30

7.87

0.25

10.54

C: 1.0 m NaCl

0.30

8.54

0.26

11.92

D: 0.5 m MgCl2

0.35

17.18

0.27

15.08

E: 1.0 m MgCl2

0.34

20.25

0.27

19.19

System

Average residence time of sodium (τNa+ ) and magnesium (τMg2+ ) cations interacting with SSY sulfonate oxygens were investigated utilizing an analogous time autocorrelation function to Equation (1), CNa+ (t) and CMg2+ (t), respectively, with a continuous multi-exponential fitting definition. In this case, a new binary function h0ij was defined to register the formation of unique Na+ −OSO−3 and Mg2+ −OSO−3 ion-pairs. The separation distance r between cations and sulfonate oxygens was used as the only geometrical criterion to register ion-pairs formation with r ≤ 3.1 Å for Na+ and r ≤ 2.4 Å for Mg2+ . These values were taken from their corresponding gij (r) first minimum in Figure 5. The intermittent multi-exponential fitting 23



definition (equivalent to CI (t) in H-bonds) was discarded to described cations dynamics to avoid an overestimation of Na+ ion-pairs lifetimes. Due to their limited number of cations in solution, Na+ recrossing from the bulk to the first hydration shell (and vice versa), could bind recursively to the same sulfonate oxygen site previously occupied, and thus, experience a deficient sampling. This was not an issue when measuring intermittent H-bond lifetimes (τI ) given that the more significant number of solvent molecules available, together with the dynamic nature of the H-bonding network, reduced the probability of finding repeated H-bond pairs over long periods of simulation time. No added salt 0.5 m NaCl 1.0 m NaCl 0.5 m MgCl2 1.0 m MgCl2

(a)

0.8 0.6 0.4 0.2

1.0

(b)

0.9

CMg 2 + (t)

1.0

CNa + (t)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 43

0.8 0.7 0.6

0.0

0.5 m MgCl2 1.0 m MgCl2

0.5 0

25

50

75

100

125

150

0

Time (ps)

25

50

75

100

125

Time (ps)

Figure 8. Estimated time autocorrelation function decay profiles for (a) sodium and (b) magnesium cations bound to SSY sulfonate oxygens. The relaxation profiles of ion-pairs as a function of time are presented in Figure 8. Both ion-pairs exhibit much slower dynamics than H-bonds proving that ion-contacts are strongly bound to SSY stacks. A very slow CMg2+ (t) relaxation can be seen compared to the relatively faster decay of CNa+ (t). It suggests that once Mg2+ are bound to OSO−3 atoms they potentially remain attached for the rest of the simulation time. As a result, τMg2+ estimates are not possible to be extracted from CMg2+ (t) profiles but τM g2+ τN a+ is qualitatively assumed. τN a+ values estimated for systems A-E are: 22.36, 21.71, 20.89, 38.88 and 34.01 ps, respectively. On summary, the average time a particular Na+ −OSO−3 pair remains bound are approximately 2–3 times larger compared to intermittent H-bonds lifetimes (τI ). It is implied that residence times for Mg2+ −OSO−3 contacts would be more persistent than 24


150

Page 25 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Na+ −OSO−3 ones.

Solvent and cations self-diffusivities Global self-diffusivities of water oxygens, sodium and magnesium cations for each system are summarized in Table 4, while their corresponding MSD as a function of lag time plots are presented in Figure S2. Although TIP3P-Ew water model overestimates pure water self-diffusivity, i.e., D = 4.30 × 10−9 m 2s−1 at 298 K and 1 atm 55,84 , the evaluation of water self-diffusion coefficients for each system provides solid evidence of ions hydration, as discussed above. As NaCl or MgCl2 concentration is increased, the mobility of water molecules decreases, as expected. Taking system A as reference, where only Na+ counterions are present, water self-diffusivity is reduced by 7% and 14% for systems B and C, respectively. Similarly, for systems D and E, where both Na+ and Mg2+ cations polarized water synergistically, DWater is reduced by 15% and 25%, respectively. Thus, the decrease of water mobility is strongly seen in systems doped with MgCl2 . This observation is also congruent with H-bonding lifetimes and Mg2+ average solvation number previously discussed. The overall mobility of Na+ and Mg2+ is constrained as NaCl and MgCl2 concentration increases. The decrease in DN a+ and DM g2+ coefficients is originated mainly by the increasing number of cations being hydrated by the solvent, in addition to the increasing number of ion-pairs around SSY aggregates compromising cations mobility. The magnitude of DM g2+ coefficients is smaller than DN a+ ones, as suggested by their hydration numbers discussed above. These trends are also congruent with reported experimental self-diffusion coefficients, i.e., DN a+ = 1.334 × 10−9 m 2s−1 and DM g2+ = 0.706 × 10−9 m 2s−1 at 298.15 K 85,86 . For Na+ , the increase in DN a+ from system A to B is attributed to the greater number of sodium cations available in the bulk, compared to the salt-free system where only Na+ counterions are available. In system D and E, where the lowest DN a+ values are seen, the mobility of Na+ counterions are restrained by the strong polarizing effects of Mg2+ in the whole system.

25



Table 4. Estimated water, sodium and magnesium self-diffusion coefficients D (×10−9 m 2s−1 )

System

W ater

N a+

M g 2+

A: No added salt

4.008

1.169

-

B: 0.5 m NaCl

3.717

1.386

-

C: 1.0 m NaCl

3.434

1.272

-

D: 0.5 m MgCl2

3.398

1.271

0.638

E: 1.0 m MgCl2

2.999

1.067

0.552

Potential of mean force (a)

2 DB

1

10


0 1 SSM

2

3 2 1 0 1 2 3

(c)

8

UPMF (kcal mol −1 )

3

UPMF (kcal mol −1 )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 43

6 4

(b)

0

2

2

4

3

8

10

0 0.5 m MgCl2 1.0 m MgCl2

2

CM

6

4 0

2

4

6

8

10 r(Å)

12

14

16

18

20

0

2

4

6

8

10

12

14

16

r(Å)

Figure 9. Potential of mean force (PMF) derived from Equation (3) between (a) sulfonate oxygens and sodium cations; and (b) sulfonate oxygens and magnesium cations. (c) PMF computed from ABF simulations for magnesium-sulfonate ion-pairs.

The binding affinity between cations and SSY sulfonate oxygens was estimated by their PMF profiles through Equation 3. Na+ − OSO−3 and Mg2+ − OSO−3 PMF are presented in Figure 9(a)-(b). Taking Na+ − OSO−3 ion-pair as example (Figure 9(a)), three distinct extrema are identified 77,78,87,88 . The first minima observed at r = 2.3 Å corresponds to the equilibrium separation distance or direct contact between Na+ − OSO−3 (first gOSO− −Na+ (r) 3

peak in Figure 5(a)). This contact is regarded as the contact minimum (CM). The second minimum observed approximately at r = 4.6 Å corresponds to the solvent-separated-minima (SSM) (or the gOSO− −Na+ (r) second maximum in Figure 5(a)). Both minima, the CM and 3

the SSM, are separated by the desolvation barrier (DB) which must be overcome to observe 26


18

20

Page 27 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


transitions from the bound to the unbound state, and vice-versa. For Mg2+ − OSO−3 ionpairs (Figure 9(b)) only CM and SSM are clearly seen since PMF profiles diverge around the expected DB point. This trend indicates that the short-range repulsion between Mg2+ in the CM and the SSM is very strong compared to Na+ . Thus, Mg2+ mobility across the solvation shells is compromised (see Figure 8(b)). For this reason, Equation (3) does not accurately sample Mg2+ − OSO−3 DBs. To overcome this limitation, we utilized the adaptive biasing force (ABF) free energy technique using the collective variables (colvars) module 89,90 in LAMMPS. In this free energy method, an external force hF i is applied to the system to sample the configurational space along a given reaction coordinate, or collective variable (CV). This force is averaged over a specified number of samples. Moreover, the ABF method exerts an external biasing average force hFABF i which is opposite to hF i to ensure a uniform configurational space sampling. We defined the OSO−3 −Mg2+ separation distance r as the CV. To alleviate the computational burden, two equivalent simulation models with only 10 SSY mesogens were constructed using the same MgCl2 concentration as in systems D (0.5 m MgCl2 ) and E (1.0 m MgCl2 ). The starting configurations for ABF models were equilibrated in the NPT ensemble for 200 ns to make sure SSY aggregation took placed (in both models a single 10-SSY long column was achieved). A unique Mg2+ −OSO−3 pair was randomly selected as CV for each simulated system. The whole CV distance was divided into four non-overlapping windows of length 5.0 Å each (1.75 Å − 21.75 Å) with bins of 0.1 Å. Each window was equilibrated initially for 5 ns using steered molecular dynamics (SMD) simulations with a force constant of 0.05 kcal/(mol Å) to set CV initial separation distances. The ABF was applied after 1, 000 samples in each bin. Every window was run for 300 ns where convergence was satisfied. The Mg2+ −OSO−3 PMF profiles estimated from ABF are presented in Figure 9(c). These PMF profiles accurately reproduce the minima positions and general trends from those seen in Figure 9(b). Additionally, DBs are characterized for both SSY systems (D and E). For this reason, the free energy barriers defined next, are evaluated using ABF-calculated Mg2+ −OSO−3 extrema 27



Page 28 of 43

values. The binding energy barrier, ∆Ub+ = UDB − USSM , is defined as the energy barrier that cations in the SSM must overcome in order to bind with SSY solubilizing groups, i.e., displace the cations from the SSM to the CM. The energy barrier required to break cation-sulfonate contacts in the CM and move them back to the SSM is defined as the dissociation energy barrier, ∆Ud− = ∆UDB − ∆UCM . A summary of ∆Ub+ and ∆Ud− for the Na+ − OSO−3 and Mg2+ −OSO−3 ionic pairs are presented in Table (5) in kB T units. The magnitude of both ∆Ub+ and ∆Ud− are considerably larger for Mg2+ ion-pairs. In system D for example, the binding energy barrier for Na+ − OSO−3 is ∆Ub+ = 2.65kB T (1.58 kcal/mol) while for Mg2+ − OSO−3 ∆Ub+ = 21.67 kB T (12.92 kcal/mol). This represents a ∆Ub+ approximately 8 times larger for Mg2+ . An analogous trend is observed for ∆Ud− in system D which is almost 6 times larger for Mg2+ contacts. Hence, it is energetically more difficult for Mg2+ to penetrate to or escape from the first hydration shell around SSY sulfonate oxygens. On the contrary, Na+ cations can relatively easily enter the first hydration shell and associate or dissociate with OSO−3 atoms, due to their relatively smaller DB magnitudes. This confirms that Na+ polarizes weakly SSY sulfonate oxygens compared to Mg2+ ion-pairs. Table 5. Binding, ∆Ub+ , and dissociation, ∆Ud− , energy barriers derived from potential of mean force calculations Na+ − OSO− 3

System

Mg2+ − OSO− * 3

HW − OSO− 3

∆Ub+ /kB T

∆Ud− /kB T

∆Ub+ /kB T

∆Ud− /kB T

∆Ub+ /kB T

∆Ud− /kB T

A: No added salt

2.61

3.88

−

−

1.47

2.16

B: 0.5 m NaCl

2.57

3.84

−

−

1.43

2.08

C: 1.0 m NaCl

2.44

3.73

−

−

1.41

2.06

D: 0.5 m MgCl2

2.65

3.90

21.67

22.10

1.67

2.35

E: 1.0 m MgCl2

2.57

3.84

19.81

21.48

1.70

2.30

*Desolvation barriers were estimated from ABF simulations. PMF between hydrogens from the solvent and sulfonate oxygens, i.e., HW −OSO−3 , were also calculated from Equation 3 to roughly compare chromonic H-bonding affinity strength to Na+ /Mg2+ − OSO−3 ion-pairs (Figure S3). Both HW −OSO−3 binding and dissociation energy 28


Page 29 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


barriers are consistently smaller in magnitude than those reported for cations (see Table 5). As a result, SSY H-bonds broke and reform continuously allowing water molecules to rotate and move around sulfonate groups. Moreover, the magnitude differences between Na+ − OSO−3 and HW −OSO−3 DBs are not substantially dissimilar. This suggests that solvent thermal fluctuations could contribute to the disturbance of Na+ − OSO−3 ion-pairs. On the other hand, only the addition of MgCl2 to the chromonic solution increases HW −OSO−3 ∆Ub+ and ∆Ud− magnitudes compared to the salt-free reference model. It proves that stronger Hbonds around sulfonate sites are promoted in systems D and E, due to the stronger hydration effects of magnesium cations. H-bonding enhancement by Mg2+ is also supported by average H-bonding lengths and intermittent H-bonding lifetimes discussed above. Therefore, the substitution of H-bonds by Na+ /Mg2+ − OSO−3 contacts results in stronger enthalpic interactions along SSY stacks. This process enables the effective reduction of the electrostatic repulsion between SSY mesogens manifested as extended chromonic aggregates. In particular, two distinct binding modes between cations and sulfonates are discerned according to Na+ /Mg2+ DBs attributes. Additionally, the acute electrostatic affinity between Mg2+ and OSO−3 confirms that Mg2+ − OSO−3 ion-pairs remain attached during the whole production trajectories. This also indicates that the magnitude of DBs from Figure 9 are directly correlated to the ion-pairs residence times discussed in Figure 8.

Atomistic perspectives of electrostatic effects The spontaneous stacking of SSY LCLC is heavily dictated by the hydrophobic effect. In the absence of excess salt (system A), the aggregation of SSY molecules is driven by the minimization of unfavorable hydrophobic contacts between chromonic polyaromatic cores and the solvent. Consequently, face-on aggregation or π-π stacking between SSY mesogens is achieved to maximize the number of H-bonds, mostly around sulfonate sites. The release of water molecules and sodium counterions away from SSY hydrophobic cores also contributes to the aggregation process. Although the momentary immobilization of water molecules 29



around SSY stacks leads to an apparent local decrease of entropy, the dynamical nature of these H-bonds causes an overall entropic gain of the system due to their constant breaking and formation. When NaCl and MgCl2 salts are included (systems B-E), the extra number of cations alters the original H-bonding network balance by replacing H-bonds with ion-pairs. The H-bond density of SSY aggregates decreases accordingly as a function of salt type and concentration. Ionic contacts (Na+ − OSO−3 and Mg2+ − OSO−3 ) are highly energetic favorable compared to standard H-bonds due to their higher association/dissociation energy barriers (primarily for Mg2+ − OSO−3 contacts). Thus, the lack of H-bonds, or apparent entropic loss, is compensated by the increasing number of strong bound ion-pairs resulting in a favorable enthalpic gain for the columnar system. The inclusion of excess Na+ and Mg2+ does not alter the intra-molecular structure of SSY mesogens, i.e., the typical ∼ 3.4 Å separation distance observed between SSY polyaromatic cores. This basic structural feature is not exclusive of chromonics stacking (including stacked nucleic acids base pairs) since it has been typically observed between graphite layers 91 . Instead, the H-bonding network around chromonics is primarily modified by the addition of ionic salts 36 . We also confirm that the size of SSY aggregates increases when ionic salts are included in the simulated system. From a molecular perspective, the extension of chromonic stacks is caused by the reduction of the electrostatic repulsion between SSY mesogens/stacks due to the larger number of ion-pairs modifying the H-bonding environment. This suggests that SSY stacking free energy increases depending on the ionic salt type and its concentration. These results are congruent with experimental findings for low concentrations of SSY solutions doped with mono- and divalent ionic salts 37,39,41,92 . The extension of SSY stacks is particularly favored in system C (1.0 m NaCl) and system D (0.5 m MgCl2 ) by forming a single 20-molecule long SSY aggregate, i.e., the maximum number of stacked units possible for the current simulation conditions. However, only half of the number of cations are required in system D (65 Mg2+ ) compared to system C (130

30


Page 30 of 43

Page 31 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Na+ ) for screening SSY electrostatic repulsion. This is attributed to the stronger polarization capabilities of Mg2+ which are accounted for its higher hydration number, shorter CM distances, stronger binding affinity to SSY sulfonate sites, and finally its ability to increase H-bonding network strength. For these reasons, the increase of the isotropic to nematic transition temperatures TI→(I−N) , experimentally reported for SSY solutions, is higher for Mg2+ than Na+ 37 . Moreover, when MgCl2 concentration is doubled in system E (1.0 m MgCl2 ), the average size of SSY aggregates is also increased (compared to reference system A). However, two almost evenly-sized SSY stacks are formed instead. This behavior can be explained by the large number of Mg2+ forming ion-pairs with SSY mesogens in addition to the vast number of cations being hydrated by the solvent. Thus, this positively charged environment could limit SSY stacks to merge into a single one. A different trend is observed in system B (0.5 m NaCl) where a longer aggregate with 16 elements is promoted. This contrasts the distinct electrostatic impact that hydrated mono- and divalent cations exert on SSY aggregates and their surroundings. These findings demonstrate that chromonic self-assembly of dilute SSY solutions doped with ionic salts is essentially defined by how the H-bonds around SSY polarized groups are maximized as a consequence of the effective minimization of electrostatic repulsion between chromonic stacks. This process is dictated by the polarization strength of cations bound to SSY aggregates and their surroundings. The relationship between CMs solubilizing groups and their potential ability to establish solvation/desolvation interactions with water (including electrostatic interactions with counterions or doping ions) are crucial to understanding chromonic aggregation 93 . As noted by Dickinson, et al. 91 , aggregation patterns of LCLC appear to be dependent on the number of solubilizing groups and their locations around chromonic polyaromatic cores. Thus, understanding chromonics non-covalent interactions with the solvent and counter ions (or any additional ionic dopants) are decisive to explain complex chromonic self-assembly patterns not yet fully understood, such as in Acid Red 266 94 .

31



Conclusions We performed atomistic MD simulations to investigate the non-covalent interactions leading to the aggregation and phase behavior of SSY solutions doped with NaCl and MgCl2 salts. The formation of ion-pairs between Na+ /Mg2+ and sulfonate oxygens alters the structural and dynamical hydration properties of SSY aggregates compared to the salt-free solution. This analysis confirms that the polarization of sulfonate oxygens by mono- (Na+ ) and divalent (Mg2+ ) cations leads to the decrease of the H-bonding density around chromonic stacks. Simultaneously, H-bonding dynamics are slowed down by the influence of cations in SSY hydration shells resulting in the increase of H-bond lifetimes as a function of ionic salt concentration. PMF for Na+ − OSO−3 and Mg2+ − OSO−3 ion-pairs demonstrate two distinct binding mechanisms based on the polarization strength of each cation type. PMF profiles for Mg2+ show particularly high desolvation barriers supporting the formation of strong and long-lasting magnesium-oxygen contacts. Conversely, the moderate desolvation barriers for Na+ prove that weaker sodium-oxygen pairs are dynamically able to bind/unbind from SSY. Both ion-pairs are energetically favored over conventional solvent-chromonic H-bonds. Ionic salts promote the extension of SSY aggregates while preserving the characteristic intermolecular stacking distance of ∼ 3.4 Å between chromonic mesogens. The substitution of weak H-bonds with stronger Na+ /Mg2+ −OSO−3 pairs decreases the overall electrostatic repulsion among SSY structures. It implies that SSY stacking free energy is increased as a result of the strong binding between cations and sulfonate oxygens. Polarization effects exerted by Mg2+ on SSY solutions, i.e., on both chromonic stacks and their corresponding H-bonding network, were remarkably stronger than Na+ . For this reason, Mg2+ divalent salts exhibit experimentally larger nematic-to-isotropic transition temperature shifts than Na+ monovalent salts in moderately concentrated SSY solutions.

32


Page 32 of 43

Page 33 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Acknowledgement This investigation was supported by the Natural Science and Engineering Research Council of Canada (223086) (NSERC). OMR is grateful to Consejo Nacional de Ciencia y Tecnología (382822) (CONACyT) and McGill Engineering Doctoral Award (MEDA) scholarships for financial assistance. A. D. R is grateful to McGill University for financial support through the James McGill Professorship appointment. The authors are thankful to Compute Canada and Calcul Québec for access to their parallel computing facilities.

Supporting Information Available Interatomic potential parameter for SSY mesogens; simulated systems particles details; Hbonding average geometric parameters; MSD plots for sodium, magnesium and the solvent; and HW −OSO−3 PMF profiles are provided for reference.

References (1) Lydon, J. Chromonic mesophases. Curr. Opin. Colloid Interface Sci. 2004, 8, 480–490. (2) Tam-Chang, S.-W.; Huang, L. Chromonic liquid crystals: properties and applications as functional materials. Chem. Commun. 2008, 1957–1967. (3) Lydon, J. Chromonic review. J. Mater. Chem. 2010, 20, 10071–10099. (4) Lydon, J. Chromonic liquid crystalline phases. Liq. Cryst. 2011, 38, 1663–1681. (5) Park, H.-S.; Lavrentovich, O. D. Liquid crystals beyond displays: chemistry, physics, and applications; John Wiley & Sons: Hoboken, NJ, 2012. (6) Collings, P. J.; Goldstein, J. N.; Hamilton, E. J.; Mercado, B. R.; Nieser, K. J.; Re-

33



gan, M. H. The nature of the assembly process in chromonic liquid crystals. Liq. Cryst. Rev. 2015, 3, 1–27. (7) Horowitz, V. R.; Janowitz, L. A.; Modic, A. L.; Heiney, P. A.; Collings, P. J. Aggregation behavior and chromonic liquid crystal properties of an anionic monoazo dye. Phys. Rev. E 2005, 72, 041710. (8) Tomasik, M. R.; Collings, P. J. Aggregation behavior and chromonic liquid crystal phase of a dye derived from naphthalenecarboxylic acid. J. Phys. Chem. B 2008, 112, 9883–9889. (9) Neumann, B.; Huber, K.; Pollmann, P. A comparative experimental study of the aggregation of Acid Red 266 in aqueous solution by use of 19 F-NMR, UV/Vis spectroscopy and static light scattering. Phys. Chem. Chem. Phys. 2000, 2, 3687–3695. (10) Ruslim, C.; Matsunaga, D.; Hashimoto, M.; Tamaki, T.; Ichimura, K. Structural characteristics of the chromonic mesophases of CI Direct Blue 67. Langmuir 2003, 19, 3686–3691. (11) Cox, J.; Woodard, G.; McCrone, W. Solid-state chemistry of cromolyn sodium (disodium cromoglycate). J. Pharm. Sci. 1971, 60, 1458–1465. (12) Agra-Kooijman, D. M.; Singh, G.; Lorenz, A.; Collings, P. J.; Kitzerow, H.-S.; Kumar, S. Columnar molecular aggregation in the aqueous solutions of disodium cromoglycate. Phys. Rev. E 2014, 89, 062504. (13) Spindler, L.; Olenik, I. D.; Čopič, M.; Romih, R.; Cerar, J.; Škerjanc, J.; Mariani, P. Dynamic light scattering and 31 P NMR spectroscopy study of the self-assembly of deoxyguanosine 5’-monophosphate. Eur. Phys. J. E 2002, 7, 95–102. (14) Tone, C. M.; De Santo, M. P.; Ciuchi, F. The role of surface energy in guanosine nucleotide alignment: An intriguing scenario. Colloids Surf. B 2014, 119, 99–105. 34


Page 34 of 43

Page 35 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(15) Shiyanovskii, S.; Lavrentovich, O.; Schneider, T.; Ishikawa, T.; Smalyukh, I.; Woolverton, C.; Niehaus, G.; Doane, K. Lyotropic chromonic liquid crystals for biological sensing applications. Mol. Cryst. Liq. Cryst. 2005, 434, 259–587. (16) Shiyanovskii, S. V.; Schneider, T.; Smalyukh, I. I.; Ishikawa, T.; Niehaus, G.; Doane, K.; Woolverton, C. J.; Lavrentovich, O. Real-time microbe detection based on director distortions around growing immune complexes in lyotropic chromonic liquid crystals. Phys. Rev. E 2005, 71, 020702. (17) Nazarenko, V.; Boiko, O.; Anisimov, M.; Kadashchuk, A.; Nastishin, Y. A.; Golovin, A.; Lavrentovich, O. Lyotropic chromonic liquid crystal semiconductors for water-solution processable organic electronics. Appl. Phys. Lett. 2010, 97, 284. (18) Tam-Chang, S.-W.; Helbley, J.; Carson, T. D.; Seo, W.; Iverson, I. K. Template-guided organization of chromonic liquid crystals into micropatterned anisotropic organic solids. Chem. Commun. 2006, 503–505. (19) Kim, J. Y.; Nayani, K.; Jeong, H. S.; Jeon, H.-J.; Yoo, H.-W.; Lee, E. H.; Park, J. O.; Srinivasarao, M.; Jung, H.-T. Macroscopic alignment of chromonic liquid crystals using patterned substrates. Phys. Chem. Chem. Phys. 2016, 18, 10362–10366. (20) Sergan, T.; Kelly, J. Negative uniaxial films from lyotropic liquid crystalline material for liquid crystal display applications. Liq. Cryst. 2000, 27, 1481–1484. (21) Guo, F.; Mukhopadhyay, A.; Sheldon, B. W.; Hurt, R. H. Vertically aligned graphene layer arrays from chromonic liquid crystal precursors. Adv. Mater. 2011, 23, 508–513. (22) Peng, C.; Turiv, T.; Guo, Y.; Wei, Q.-H.; Lavrentovich, O. D. Command of active matter by topological defects and patterns. Science 2016, 354, 882–885. (23) Theis, J. G.; Smith, G. P.; Yi, Y.; Walba, D. M.; Clark, N. A. Liquid crystal phase

35



behavior of a DNA dodecamer and the chromonic dye Sunset Yellow. Phys. Rev. E 2018, 98, 042701. (24) Cantekin, S.; de Greef, T. F.; Palmans, A. R. Benzene-1, 3, 5-tricarboxamide: a versatile ordering moiety for supramolecular chemistry. Chem. Soc. Rev. 2012, 41, 6125–6137. (25) Bejagam, K. K.; Fiorin, G.; Klein, M. L.; Balasubramanian, S. Supramolecular polymerization of benzene-1, 3, 5-tricarboxamide: a molecular dynamics simulation study. J. Phys. Chem. B 2014, 118, 5218–5228. (26) Ghadiri, M. R.; Granja, J. R.; Milligan, R. A.; McRee, D. E.; Khazanovich, N. Selfassembling organic nanotubes based on a cyclic peptide architecture. Nature 1993, 366, 324. (27) Zhao, X.; Pan, F.; Xu, H.; Yaseen, M.; Shan, H.; Hauser, C. A.; Zhang, S.; Lu, J. R. Molecular self-assembly and applications of designer peptide amphiphiles. Chem. Soc. Rev. 2010, 39, 3480–3498. (28) Rey, A. D.; Herrera-Valencia, E. Self-assembled supramolecular architectures; John Wiley & Sons, 2012; Chapter 2, pp 21–77. (29) Fändrich, M. On the structural definition of amyloid fibrils and other polypeptide aggregates. Cell. Mol. Life Sci. 2007, 64, 2066–2078. (30) Rey, A. D. Liquid crystal models of biological materials and processes. Soft Matter 2010, 6, 3402–3429. (31) Rey, A. D.; Herrera-Valencia, E. E. Liquid crystal models of biological materials and silk spinning. Biopolymers 2012, 97, 374–396. (32) Rey, A. D.; Servio, P.; Herrera-Valencia, E. Bioinspired model of mechanical energy harvesting based on flexoelectric membranes. Phys. Rev. E 2013, 87, 022505.

36


Page 36 of 43

Page 37 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(33) Rey, A. D.; Herrera-Valencia, E.; Murugesan, Y. K. Structure and dynamics of biological liquid crystals. Liq. Cryst. 2014, 41, 430–451. (34) Gutierrez, O. F. A.; Rey, A. D. Biological plywood film formation from para-nematic liquid crystalline organization. Soft Matter 2017, 13, 8076–8088. (35) Rofouie, P.; Pasini, D.; Rey, A. D. Morphology of elastic nematic liquid crystal membranes. Soft Matter 2017, 13, 5366–5380. (36) Prasad, S. K.; Nair, G. G.; Hegde, G.; Jayalakshmi, V. Evidence of wormlike micellar behavior in chromonic liquid crystals: Rheological, X-ray, and dielectric studies. J. Phys. Chem. B 2007, 111, 9741–9746. (37) Park, H.-S.; Kang, S.-W.; Tortora, L.; Nastishin, Y.; Finotello, D.; Kumar, S.; Lavrentovich, O. D. Self-assembly of lyotropic chromonic liquid crystal sunset yellow and effects of ionic additives. J. Phys. Chem. B 2008, 112, 16307–16319. (38) Jones, J.; Lue, L.; Ormerod, A.; Tiddy, G. The influence of sodium chloride on the selfassociation and chromonic mesophase formation of Edicol Sunset Yellow. Liq. Cryst. 2010, 37, 711–722. (39) Park, H.-S.; Kang, S.-W.; Tortora, L.; Kumar, S.; Lavrentovich, O. D. Condensation of self-assembled lyotropic chromonic liquid crystal sunset yellow in aqueous solutions crowded with polyethylene glycol and doped with salt. Langmuir 2011, 27, 4164–4175. (40) Yu, L. J.; Saupe, A. Deuteron resonance of D2O of nematic disodium cromoglycatewater systems. Mol. Cryst. Liq. Cryst. 1982, 80, 129–134. (41) Kostko, A. F.; Cipriano, B. H.; Pinchuk, O. A.; Ziserman, L.; Anisimov, M. A.; Danino, D.; Raghavan, S. R. Salt effects on the phase behavior, structure, and rheology of chromonic liquid crystals. J. Phys. Chem. B 2005, 109, 19126–19133.

37



(42) Ormerod, A. P.; Jones, J. W.; Wheatcroft, H.; Alfutimie, A.; Tiddy, G. J. The influence of polar additives on chromonic mesophase formation of Edicol Sunset Yellow. Liq. Cryst. 2015, 42, 772–782. (43) Chami, F.; Wilson, M. R. Molecular order in a chromonic liquid crystal: a molecular simulation study of the anionic azo dye sunset yellow. J. Am. Chem. Soc. 2010, 132, 7794–7802. (44) Akinshina, A.; Walker, M.; Wilson, M. R.; Tiddy, G. J.; Masters, A. J.; Carbone, P. Thermodynamics of the self-assembly of non-ionic chromonic molecules using atomistic simulations. The case of TP6EO2M in aqueous solution. Soft Matter 2015, 11, 680–691. (45) Matus Rivas, O. M.; Rey, A. D. Molecular dynamics on the self-assembly of mesogenic graphene precursors. Carbon 2016, 110, 189–199. (46) Matus Rivas, O. M.; Rey, A. D. Molecular dynamics of dilute binary chromonic liquid crystal mixtures. Mol. Syst. Des. Eng. 2017, 2, 223–234. (47) Edwards, D.; Jones, J.; Lozman, O.; Ormerod, A.; Sintyureva, M.; Tiddy, G. Chromonic liquid crystal formation by Edicol Sunset Yellow. J. Phys. Chem. B 2008, 112, 14628– 14636. (48) Yao, X.; Nayani, K.; Park, J. O.; Srinivasarao, M. Orientational order of a lyotropic chromonic liquid crystal measured by polarized Raman spectroscopy. J. Phys. Chem. B 2016, 120, 4508–4512. (49) Lee, K.; Murray, É. D.; Kong, L.; Lundqvist, B. I.; Langreth, D. C. Higher-accuracy van der Waals density functional. Phys. Rev. B 2010, 82, 081101. (50) Troullier, N.; Martins, J. L. Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B 1991, 43, 1993.

38


Page 38 of 43

Page 39 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(51) Soler, J. M.; Artacho, E.; Gale, J. D.; García, A.; Junquera, J.; Ordejón, P.; SánchezPortal, D. The SIESTA method for ab initio order-N materials simulation. J. Phys. Condens. Matter 2002, 14, 2745. (52) Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and testing of a general amber force field. J. Comput. Chem. 2004, 25, 1157–1174. (53) Bayly, C. I.; Cieplak, P.; Cornell, W.; Kollman, P. A. A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges: the RESP model. J. Phys. Chem. 1993, 97, 10269–10280. (54) Vanquelef, E.; Simon, S.; Marquant, G.; Garcia, E.; Klimerak, G.; Delepine, J. C.; Cieplak, P.; Dupradeau, F.-Y. RED Server: a web service for deriving RESP and ESP charges and building force field libraries for new molecules and molecular fragments. Nucleic Acids Res. 2011, 39, W511–W517. (55) Price, D. J.; Brooks III, C. L. A modified TIP3P water potential for simulation with Ewald summation. J. Chem. Phys. 2004, 121, 10096–10103. (56) Joung, I. S.; Cheatham III, T. E. Determination of alkali and halide monovalent ion parameters for use in explicitly solvated biomolecular simulations. J. Phys. Chem. B 2008, 112, 9020–9041. (57) Li, P.; Roberts, B. P.; Chakravorty, D. K.; Merz Jr, K. M. Rational design of particle mesh Ewald compatible Lennard-Jones parameters for+ 2 metal cations in explicit solvent. J. Chem. Theory Comput. 2013, 9, 2733–2748. (58) Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 1995, 117, 1–19. (59) Shinoda, W.; Shiga, M.; Mikami, M. Rapid estimation of elastic constants by molecular dynamics simulation under constant stress. Phys. Rev. B 2004, 69, 134103. 39



(60) Ryckaert, J.-P.; Ciccotti, G.; Berendsen, H. J. Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes. J. Comput. Phys. 1977, 23, 327–341. (61) Hockney, R. W.; Eastwood, J. W. Computer simulation using particles; crc Press, 1988. (62) Steinbach, P. J.; Brooks, B. R. New spherical-cutoff methods for long-range forces in macromolecular simulation. J. Comput. Chem. 1994, 15, 667–683. (63) Brooks, B. R.; Brooks III, C. L.; Mackerell Jr, A. D.; Nilsson, L.; Petrella, R. J.; Roux, B.; Won, Y.; Archontis, G.; Bartels, C.; Boresch, S. et al. CHARMM: the biomolecular simulation program. J. Comput. Chem. 2009, 30, 1545–1614. (64) Martínez, L.; Andrade, R.; Birgin, E. G.; Martínez, J. M. PACKMOL: a package for building initial configurations for molecular dynamics simulations. J. Comput. Chem. 2009, 30, 2157–2164. (65) Jewett, A. I.; Zhuang, Z.; Shea, J.-E. Moltemplate a coarse-grained model assembly tool. Biophys. J. 2013, 104, 169a. (66) Gowers, R. J.; Linke, M.; Barnoud, J.; Reddy, T. J.; Melo, M. N.; Seyler, S. L.; Dotson, D. L.; Domanski, J.; Buchoux, S.; Kenney, I. M. et al. MDAnalysis: a Python package for the rapid analysis of molecular dynamics simulations. Proceedings of the 15th Python in Science Conference. 2016; pp 98–105. (67) Michaud-Agrawal, N.; Denning, E. J.; Woolf, T. B.; Beckstein, O. MDAnalysis: a toolkit for the analysis of molecular dynamics simulations. J. Comput. Chem. 2011, 32, 2319–2327. (68) Humphrey, W.; Dalke, A.; Schulten, K. VMD: visual molecular dynamics. J. Mol. Graphics 1996, 14, 33–38.

40


Page 40 of 43

Page 41 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(69) Allen, M. P.; Tildesley, D. J. Computer simulation of liquids; Oxford university press, 2017. (70) Luzar, A.; Chandler, D. Effect of environment on hydrogen bond dynamics in liquid water. Phys. Rev. Lett. 1996, 76, 928. (71) Karshikoff, A. Non-covalent interactions in proteins; World Scientific, 2006. (72) Gowers, R. J.; Carbone, P. A multiscale approach to model hydrogen bonding: The case of polyamide. J. Chem. Phys. 2015, 142, 224907. (73) Rapaport, D. Hydrogen bonds in water: Network organization and lifetimes. Mol. Phys. 1983, 50, 1151–1162. (74) Rapaport, D. C. The art of molecular dynamics simulation; Cambridge university press, 2004. (75) Giorgino, T. Computing diffusion coefficients in macromolecular simulations: the Diffusion Coefficient Tool for VMD. Available from Github, 2015. (76) Chandler, D. Introduction to modern statistical mechanics; Oxford University Press, 1987. (77) Yan, H.; Yuan, S.-L.; Xu, G.-Y.; Liu, C.-B. Effect of Ca2+ and Mg2+ ions on surfactant solutions investigated by molecular dynamics simulation. Langmuir 2010, 26, 10448– 10459. (78) Yan, H.; Guo, X.-L.; Yuan, S.-L.; Liu, C.-B. Molecular dynamics study of the effect of calcium ions on the monolayer of SDC and SDSn surfactants at the vapor/liquid interface. Langmuir 2011, 27, 5762–5771. (79) Marechal, Y. The hydrogen bond and the water molecule; Elsevier, 2007.

41



(80) Lightstone, F. C.; Schwegler, E.; Hood, R. Q.; Gygi, F.; Galli, G. A first principles molecular dynamics simulation of the hydrated magnesium ion. Chem. Phys. Lett. 2001, 343, 549–555. (81) Mancinelli, R.; Botti, A.; Bruni, F.; Ricci, M.; Soper, A. Hydration of sodium, potassium, and chloride ions in solution and the concept of structure maker/breaker. J. Phys. Chem. B 2007, 111, 13570–13577. (82) Bowman, J. C.; Lenz, T. K.; Hud, N. V.; Williams, L. D. Cations in charge: magnesium ions in RNA folding and catalysis. Curr. Opin. Struct. Biol. 2012, 22, 262. (83) Marcus, Y. Effect of ions on the structure of water: structure making and breaking. Chem. Rev. 2009, 109, 1346–1370. (84) Orsi, M. Comparative assessment of the ELBA coarse-grained model for water. Mol. Phys. 2014, 112, 1566–1576. (85) Marcus, Y. Ion Properties; New York: Marcel Dekker, 1997, 1997. (86) Marcus, Y. Ions in water and biophysical implications: from chaos to cosmos; Springer Science & Business Media, 2012. (87) Ghosh, T.; García, A. E.; Garde, S. Molecular dynamics simulations of pressure effects on hydrophobic interactions. J. Am. Chem. Soc. 2001, 123, 10997–11003. (88) Ghosh, T.; García, A. E.; Garde, S. Water-mediated three-particle interactions between hydrophobic solutes: size, pressure, and salt effects. J. Phys. Chem. B 2003, 107, 612– 617. (89) Darve, E.; Rodríguez-Gómez, D.; Pohorille, A. Adaptive biasing force method for scalar and vector free energy calculations. J. Chem. Phys. 2008, 128, 144120. (90) Fiorin, G.; Klein, M. L.; Hénin, J. Using collective variables to drive molecular dynamics simulations. Mol. Phys. 2013, 111, 3345–3362. 42


Page 42 of 43

Page 43 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(91) Dickinson, A. J.; LaRacuente, N. D.; McKitterick, C. B.; Collings, P. J. Aggregate structure and free energy changes in chromonic liquid crystals. Mol. Cryst. Liq. Cryst. 2009, 509, 9–751. (92) Zhou, S. Lyotropic Chromonic Liquid Crystals; Springer, 2017; pp 33–49. (93) Martinez, C. R.; Iverson, B. L. Rethinking the term "pi-stacking”. Chem. Sci. 2012, 3, 2191–2201. (94) Alfutimie, A.; Ormerod, A.; Jones, J.; Wheatcroft, H.; Edwards, D. J.; Tiddy, G. Chromonic liquid crystals formed by CI Acid Red 266 and related structures. Liq. Cryst. 2015, 42, 1169–1178.

TOC Graphic

Na+ — SSY

Water — SSY

Dilute SSY solutions + Na+ and Mg2+

Mg2+ — SSY

43


Effects of Sodium and Magnesium Cations on the Aggregation of

Recommend Documents