Molecular dynamics and neutron scattering study of the dependence of polyelectrolyte dendrimer conformation on counterion behavior

Atomistic molecular dynamics (MD) simulations and contrast variation small angle neutron scattering (SANS) have been combined to investigate the Generation-5 polyelectrolyte polyamidoamine starburst dendrimer. This work reveals the dendrimer conformational dependence on counterion association at different levels of molecular charge. The accuracy of the simulations is verified through satisfactory comparison between modeled results, such as excess intra-dendrimer scattering length density distribution and hydration level, and their experimental counterparts. While the counterion distributions are not directly measureable with SANS, the spatial distribution of the counterions and their dendrimer association are extracted from the validated MD equilibrium trajectories. It is found that the conformation of the charged dendrimer is strongly dependent on the counterion association. Sensitivity of the distribution of counterions around charged amines to the counterion valency is qualitatively explained by adopting Langmuir adsorption theory. Moreover, via extending the concept of electrical double layer for compact charged colloids, we define an effective radius of a charged dendrimer including the spatial distribution of counterions in its vicinity. Within the same framework, the correlation between the strength of intra-dendrimer electrostatic repulsion and the counterion valency and dynamics is also addressed.     

Comparison of equilibrium ion density distribution and trapping force in penning, Paul, and combined ion traps

Starting from the classical Boltzmann distribution, we obtain the ion density distribution in the limit of either high temperature/low density (Coulomb interaction energy much less than ion kinetic energy) or low temperature/high density (kinetic energy much less than Coulomb interaction energy), and the trapping force for an ion cloud in Penning ion cyclotron resonance, Paul (quadrupole), and combined (Paul trap in a uniform axial static magnetic field) traps. At equilibrium (total angular momentum conserved), the ion cloud rotates at a constant frequency in Penning and combined traps. In a Penning trap, the maximum ion density is proportional to B ²/m (B is magnetic field and m is the mass of ions), whereas the maximum ion density in a Paul trap is proportional to (V _rf ² /mΩ² r ₀ ⁴ ), with Mathieu equation axial q value <0.4 to satisfy the pseudopotential approximation. Ion maximum densities in both Penning and Paul ion traps depend on the trapping field (magnetic or electric) and ion mass, but not on ion charge. In a Penning trap at maximum ion density (zero pressure), the radial (but not the axial) trapping potential is mass dependent, whereas both radial and axial potentials in a Paul trap at maximum ion density are mass dependent.     

关于聚电解质单链抗衡离子浓度径向分布的研究

采用单分子荧光显微统计光谱技术,通过将pH响应型荧光探针分子精确标记于聚苯乙烯磺酸钠分子链末端,并通过不同长度的多肽链调节分子链与探针分子间的距离,有效测量了聚苯乙烯磺酸钠单分子链的抗衡离子浓度的空间分布.实验结果清晰展示了聚电解质分子链的抗衡离子云结构,并确定了抗衡离子浓度随着距离分子链末端长度的不同而发生变化的规律,为描述聚电解质抗衡离子浓度的径向分布特征提供了实验信息.     

Behaviour of cationic polyelectrolytes upon binding of electrolytes: effects of polycation structure, counterions and nature of the solvent

 The effects of polycation structure, counterions and the nature of the solvent on the interaction between low-molecular-weight salts with some cationic polyelectrolytes in water and methanol were investigated. The polyelectrolytes used in this study were cationic polymers with quaternary nitrogen atoms in the backbone with or without a nonpolar side chain (polymer type PCA₅H₁, PCA₅D₁ and PCA₅) or tertiary amine nitrogen atoms in the main chain (polymer type PEGA). LiCl, NaCl, KCl, NaBr, NaI and Na₂SO₄ were used as low-molecular-weight salts. The interaction between polycations and salts was followed by viscometric and conductometric measurements. The study of the interaction of monovalent counterions with cationic polyelectrolytes emphasized an increase in the interaction with the decrease in the radius of the hydrated counterion, both for strong polycations and for weak polycations, suggesting that counterion binding is nonspecific. In the case of SO²⁻ ₄ anions, the Λ_m−c ^1/2 curve passes through a minimum at c _p values between 1 × 10⁻³ and 3 × 10⁻³ unit mol/l; this phenomenon can be explained by the maximum counterion interaction owing to the capacity of the polyvalent counterion to bind two charged groups by intra- or interchain bridges. The investigation of the influence of the polycation structure on the counterion binding indicated an increase in charged group–counterion interactions with a decrease in the nonpolar chain length and an increase in the quaternary ammonium salt group content (charge density) in the chain. The polyelectrolyte with tertiary amine groups in the chain, PEGA, showed, on one hand, a cation adsorption order as K⁺>Na⁺>Li⁺ and, on the other hand, a stronger association between ions and PEGA chains in methanol than in water owing to the poorer solvating effect of methanol on the cations. Received: 20 February 2001 Accepted: 29 June 2001     

Molecular dynamics simulations of end‐grafted polymers with charged side chains

We report molecular dynamics simulations on bottle‐brush polyelectrolytes end‐grafted to a planar surface. For each bottle‐brush polyelectrolyte, flexible charged side chains are anchored to one neutral main chain. The effects of the counterion valence and the grafting density on the density profiles and the structural characteristics of the brush were studied in this work. It is found that the electrostatic repulsion between charged monomers in the side chains leads an extended conformation of the brush in a solution containing monovalent counterions, while strong electrostatic binding of multivalent counterions to the side chains has a significant contribution to the collapse of the brush. For the trivalent case, the distribution of end monomers in the main chains becomes broader upon decreasing the grafting density, as compared with the monovalent case. However, the position of the distribution for the monovalent case is relatively insensitive to the change of the grafting density. Additionally, with increased counterion valence, enhanced electrostatic correlation between counterions and charged side chains also weakens the diffusive ability of counterions. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Low density spectrum of transverse NMR in molecular gases. Application to hydrogen

The low density behaviour of the spectral lineshape function associated with the relaxation of the transverse components of the nuclear magnetization of a homonuclear diatomic gas of spin $\text{1}\text{2}$ nuclei is studied from the point of view of a recent kinetic theory approach to NMR in molecular gases. It is shown that as a critical density is approached (from above), the relaxation (in time-domain) passes over from exponential to non-exponential behaviour. For the special case in which the spin—rotation relaxation mechanism predominates, an analytic solution to the problem has been given, while for molecular hydrogen which has, in addition to the aforementioned mechanism, dipolar relaxation, the behaviour of the lineshape function has been obtained numerically. The critical density at which the relaxation passes from exponential to nonexponential in H₂ is found to be of the order of 3 × 10^?3 amagats which lies, at present, still outside experimental accessibility. One important consequence of this result is that the traditional Abragam formula for the transverse relaxation time T₂ is clearly seen to be invalid below ≈ 5 × 10^?3 amagats.     

抗衡离子对硫酸盐表面活性剂气/液界面性质影响的分子动力学模拟

采用全原子分子动力学方法研究了抗衡离子为第一主族离子(Li⁺、Na⁺、K⁺、Rb⁺和Cs⁺)的十二烷基硫酸盐表面活性剂的气/液界面性质. 通过分析体系中各组分的密度分布曲线, 考察表面活性剂单分子层在界面的聚集形态, 并利用径向分布函数分析了表面活性剂极性头基与抗衡离子间的相互作用. 研究结果表明: 随着抗衡离子半径的增大, 不同体系的界面水层厚度依次增加, 表面活性剂极性头基与抗衡离子形成的Stern和扩散层厚度也相应增加. 但表面活性剂吸附层的抗衡离子缔合度以及体系表面张力却随抗衡离子半径的增大而减小. 研究表明抗衡离子的差异对十二烷基硫酸盐表面活性剂气/液界面性质有很大影响.     

Behavior of Two Almost Identical Spins during the CPMG Pulse Sequence

Multiple‐spin‐echo experiments have found wide use in nuclear magnetic resonance spectroscopy. In particular, the Carr–Purcell–Meiboom–Gill (CPMG) pulse sequence is used to determine transverse relaxation times T₂. Herein it is demonstrated, both theoretically and experimentally, that for a pair of almost identical spins‐1/2 the experimental setup can have a profound effect on the observed spin dynamics. It is shown that, in the case of dipolar relaxation, the measured T₂ values can roughly vary between the limits of identical and unlike spins, just depending on the repetition rate of π pulses with respect to chemical shift separation. Such an effect can, in the extreme narrowing regime, amount to a 50 % difference.     

Anisotropy of local relaxation properties of macromolecules. Spin-lattice relaxation of 13C nuclei,the nuclear overhauser effect and the estimation of parameters of an equivalent ellipsoid for kinetic segments of polymer chains

The expressions for the functions of spectral density at different orientations of the components of the internuclear vector with respect to the chain backbone, the frequency dependences of the spin-lattice relaxation time of ¹³C nuclei (T_1C) and the values of the nuclear Overhauser effect (NOE) were obtained for the tetrahedral lattice model of a polymer chain with three-unit kinetic elements. It was shown that peculiar features of the behavior of T_1C and NOE reflect the characteristic properties of the spectra of relaxation (correlation) times for “longitudinal” and “transverse” components of the internuclear vector. It was established that in the range of relatively short times of the relaxation spectrum the dynamics of an anisotropic kinetic segment of the chain may be described with the aid of a simple model of an elongated ellipsoid of rotation with an axial ratio of about 10. It is shown that the equivalent-ellipsoid model leads to significant differences from a more specific model of chain dynamics when a broad frequency range is considered.     

Studies on crude oil‐water biphasic mixtures by low‐field NMR

Low‐field ¹H NMR was used in this work for the analysis of mixtures involving crude oils and water. CPMG experiments were performed to determine the transverse relaxation time (T₂) distribution curves, which were computed by the inverse Laplace transform of the echo decay data. The instrument's ability of quantifying water and petroleum in biphasic mixtures following different methodologies was tested. For mixtures between deionized water and petroleum, one achieved excellent results, with root mean squared error of cross‐validation (RMSECV) of 0.8% for a regression between the water content (wt %) and the relative area of the water peak in the T₂ distribution curve, or a standard deviation of 0.9% for the relationship between the water content and the relative water peak area, corrected by the relative hydrogen index of the crude. In the case of biphasic mixtures of Mn²⁺‐doped water and crude oils, the best result of RMSECV = 1.6% was achieved by using the raw magnetization decay data for a partial least squares regression. Copyright © 2012 John Wiley & Sons, Ltd.     

Correlations and Fluctuations of Charged Colloids as Determined by Anomalous Small‐Angle X‐Ray Scattering

Summary: We performed molecular dynamics simulation of a charged colloidal particle with explicit counterions. Our work provides a direct comparison between simulations and ASAXS‐experiments, offering insight into the counterion distribution of charged colloidal suspensions. We give a detailed constitution of the appearing scattering terms with their physical meaning. It is shown that the cross‐correlation between a macroion and its counterions gives the meanfield approximation of the counterion density even if the counterion system is highly fluctuating. Furthermore, it is shown that cross‐correlations can be negative due to oscillations of the density amplitudes of the macroion and counterions and, therefore, must be distinguished from other scattering contributions. These oscillations become more pronounced if the counterions exhibit a fixed shape and if the size of the macroion and that of the counterion system are different.

Simulation sanpshot of a charged colloid (big central sphere) with counterions (small spheres).     

Analysis of a stacked-triangular platinum carbonyl cluster dianion, [Pt3(CO)6] 3 2− by252Cf-Plasma Desorption Mass Spectrometry

²⁵²Cf-Plasma Desorption Mass Spectrometry (²⁵²Cf-PDMS) has been used to investigate the [(Ph₃PCH₂C₅H₄)Fe(C₅H₅)]⁺ salt of the prototype dianionic, platinum carbonyl cluster, [Pt₃(CO)₃(₂-CO)₃] ₃ ^2– . An envelope of singly charged [Pt₉(CO) _x ]^– ions with the principal peak centered atx=8 was observed in the negative ion mass spectrum as a result of successive losses of the carbonyl ligands from the intact platinum core. Another feature of the negative ion spectrum was the prominent occurrence of other envelopes of multiple peaks which conform to Pt₁₂, Pt₁₅, Pt₁₈, Pt₂₁, and Pt₂₄ singly charged metal cores. An unexpected observation was the presence of singly charged positive ions of the dianionic cluster which were formed without incorporation of the counterion. A similar but, largely unresolvable, broad envelope of singly charged ions containing the Pt₉ core resulted with a peak maximum corresponding closely to the completely carbonylated cluster. The peak distribution extended from the fully decarbonylated cluster to well beyond the mass of the fully carbonylated cluster. Analogous peaks attributable to singly charged positive ions of the Pt₁₂, Pt₁₅, and Pt₁₈ clusters were also evident. Very little fragmentation was observed below the molecular ion in either the positive or negative ion mass spectra except for ions associated with the counterion. A detailed analysis of the mass spectra, including the types of ions observed and correlations with the molecular architecture are described.     

Spin relaxation and structure of light-induced spin-correlated PCBM−/P3HT+ radical pairs

The electron spin echo (ESE) technique is applied to determine the spin relaxation times of long-lived light-induced radicals and short-term spin-correlated radical pairs (SCRPs) formed by the laser flash of a composite consisting of [6,6]-phenyl-C₆₁-butyric acid methyl ether (PCBM) and poly-(3-hexylthiophene) (P3HT) at 80 K. The ESE signal dependences recorded to measure the longitudinal relaxation times of P3HT⁺/PCBM^? SCRPs and the free P3HT⁺ radical are fitted by the exp(-(t/T ₁)^0.6) dependence with T ₁ values lying in the microsecond time scale. The difference in the transverse spin relaxation times of the P3HT⁺/PCBM^? radical paira appeared after selective and non-selective echo-detected EPR spectrum excitation is explained by the instantaneous diffusion model. Based on the model, the magnetic interaction energy between the electron spins in P3HT⁺/PCBM^? SCRPs is estimated; E/? ～ 10⁶ s^?1.     

Enrichment and distribution of counterions in spherical polyelectrolyte brushes probed by SAXS

The spatial correlation of counterions [Li⁺, Na⁺, Rb⁺, Cs⁺, NH₄⁺, (CH₃)₄N⁺] with spherical polyelectrolyte brushes (SPBs), which consist of a PS core and chemically grafted PSS chains, was comprehensively studied through a combination of SAXS, DLS, and Zeta potential. Results show that the SAXS intensity profiles of the brush appears to be “insensitive” to the concentration of Na⁺. By contrast, introducing salt ions with a density lower than sodium [NH₄⁺, (CH₃)₄N⁺ and Li⁺] into the brush layer will cause a decrease in the scattering intensity while introducing those with a higher density than sodium (Rb⁺ and Cs⁺) will cause the opposite result. As verified by the combined results of SAXS, DLS, and Zeta potential, the collapse of the brush and the enrichment of the counterions in the brush layer occur simultaneously. It was further demonstrated that the concentration of counterions enriched in the innermost layer of the brush shell can be enhanced up to hundreds of times compared with the bulk concentration, and the counterion distribution in SPB shell follows a radial attenuation distribution. SAXS is confirmed to be powerful in probing the enrichment and distribution of counterions within SPB. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 738–747     

Interaction between Na+ and polymer in aqueous solution of sodium salts of poly(2-hydroxyethyl methacrylate-co-methacrylic acid) studied by 23Na-NMR

The interaction between Na⁺ and polymer was studied by ²³Na-NMR for the aqueous solution of P(HEMA-co-MAANa), sodium salt of poly(2-hydroxyethyl methacrylate-co-methacrylic acid), as a function of the polymer concentration, charge density of the polymer chain, and temperature. The NMR line width of ²³Na-NMR in 1% (w/v) aqueous solution of the P(HEMA-co-MAANa) narrowed with increasing temperature due to the rapid exchange of Na⁺ between free and polymer-bound states with a rate of exchange exceeding the quadrupolar relaxation rate in the latter state. At high concentrations of the polymer above 1.0% (w/v) at 298 K, the ²³Na-NMR relaxation fits for a single Lorentzian due to the rapid exchange between two Na⁺ states. However, it follows a biexponential decay of magnetization in dilute solutions of polymer. The biexponential decay character of relaxation increased with the increase of the fraction of the MAANa monomer unit on the polymer chain. This feature of ²³Na-NMR relaxation was used to deduce the correlation time (τ_c), the degree of binding (p_B), and the quadrupole coupling constants (X) of the polymer-bound counterion. The χ and τ_c values show that the mobilities of the polymer chain are correlated with the motion of Na⁺ in aqueous solution of the polymer and there is a small degree of the specific binding between COO^? and Na⁺. No evidence in support of the intramolecular conformational change by the charge density variation in P(HEMA-co-MAANa) was obtained. © 1993 John Wiley & Sons, Inc.     

Hydrogen-Bond Structure and Low-Frequency Dynamics of Electrolyte Solutions: Hydration Numbers from ab Initio Water Reorientation Dynamics and Dielectric Relaxation Spectroscopy

We present an atomistic simulation scheme for the determination of the hydration number (h) of aqueous electrolyte solutions based on the calculation of the water dipole reorientation dynamics. In this methodology, the time evolution of an aqueous electrolyte solution generated from ab initio molecular dynamics simulations is used to compute the reorientation time of different water subpopulations. The value of h is determined by considering whether the reorientation time of the water subpopulations is retarded with respect to bulk-like behavior. The application of this computational protocol to magnesium chloride (MgCl₂) solutions at different concentrations (0.6–2.8 mol kg⁻¹) gives h values in excellent agreement with experimental hydration numbers obtained using GHz-to-THz dielectric relaxation spectroscopy. This methodology is attractive because it is based on a well-defined criterion for the definition of hydration number and provides a link with the molecular-level processes responsible for affecting bulk solution behavior. Analysis of the ab initio molecular dynamics trajectories using radial distribution functions, hydrogen bonding statistics, vibrational density of states, water-water hydrogen bonding lifetimes, and water dipole reorientation reveals that MgCl₂ has a considerable influence on the hydrogen bond network compared with bulk water. These effects have been assigned to the specific strong Mg-water interaction rather than the Cl-water interaction.     

Dynamic behavior of chemical reactivity indices in density functional theory: A Bohn-Oppenheimer quantum molecular dynamics study

Dynamic behaviors of chemical concepts in density functional theory such as frontier orbitals (HOMO/LUMO), chemical potential, hardness, and electrophilicity index have been investigated in this work in the context of Bohn-Oppenheimer quantum molecular dynamics in association with molecular conformation changes. Exemplary molecular systems like CH ₅ ⁺ , Cl⁻ (H₂O)₃₀ and Ca²⁺ (H₂O)1₅ are studied at 300 K in the gas phase, demonstrating that HOMO is more dynamic than LUMO, chemical potential and hardness often fluctuate concurrently. It is argued that DFT concepts and indices may serve as a good framework to understand molecular conformation changes as well as other dynamic phenomena.     

Influence of mechanical properties of pectin films on charge density and charge density distribution in pectin macromolecule

The hydration and mechanical properties of citrus pectin films were examined in conditions relevant to those in the plant cell wall. The pectins used for this study varied in the degree of esterification (DE) (high or low) and charge distribution on the backbone (random or block). The hydration of the films was controlled in an osmotic pressure experiment using polyethylene glycol solutions (PEG 20000). Hysteresis tests at constant deformation rate (stress vs deformation) were used for investigating the mechanical behaviour of films. Mechanical and hydration properties of pectin films were examined as a function of charge density, charge density distribution and counterion environment—K⁺, Ca²⁺, Mg²⁺. Swelling decreased with increasing counterion concentration. The effect is stronger in the case of Ca²⁺ and Mg²⁺ for low esterified pectins and therefore crosslinks from divalent ions could be assumed. The crosslink effect is confirmed in mechanical experiments where an increase in the film tensile modulus is observed with increasing counterion concentration. It is shown for the first time that in case of highly concentrated pectin solutions Mg²⁺ cations also act as a crosslinker for pectin macromolecules.     

Stabilization of Linear C3 by Two Donor Ligands: A Theoretical Study of L-C3-L (L=PPh3, NHCMe,cAACMe)**

Quantum chemical studies using density functional theory and ab initio methods have been carried out for the molecules L-C₃-L with L=PPh₃ ( 1 ), NHC^Me ( 2 , NHC=N-heterocyclic carbene), and cAAC^Me ( 3 , cAAC=cyclic (alkyl)(amino) carbene). The calculations predict that 1 and 2 have equilibrium geometries where the ligands are bonded with rather acute bonding angles at the linear C₃ moiety. The phosphine adduct 1 has a synclinal (gauche) conformation whereas 2 exhibits a trans conformation of the ligands. In contrast, the compound 3 possesses a nearly linear arrangement of the carbene ligands at the C₃ fragment. The bond dissociation energies of the ligands have the order 1 < 2 < 3 . The bonding analysis using charge and energy decomposition methods suggests that 3 is best described as a cumulene with electron-sharing double bonds between neutral fragments (cAAC^Me)₂ and C₃ in the respective electronic quintet state yielding (cAAC^Me)=C₃=(cAAC^Me). In contrast, 1 and 2 possess electron-sharing and dative bonds between positively charged ligands [(PPh₃)₂]⁺ or [(NHC^Me)₂]⁺ and negatively charged [C₃]⁻ fragments in the respective doublet state.