Stick Boundary Conditions Research Articles

How Does the Alkyl Chain Length of an Ionic Liquid Influence Solute Rotation in the Presence of an Electrolyte?

Fluorescence anisotropies of a nonpolar solute, 9-phenylanthracene (9-PA), have been measured in 1-alkyl-3-methylimidazolium (alkyl = methyl, butyl, octyl, and dodecyl) bis(trifluoromethylsulfonyl)imides ([RMIM][Tf2N]) with varying amounts (0-0.3 mole fraction) of lithium bis(trifluoromethylsulfonyl)imide (LiTf2N). This study has been carried out to understand how the length of the alkyl chain and the concentration of the electrolyte influence the rotational diffusion of a nonpolar solute. It has been observed that the addition of an electrolyte to the ionic liquid increases the bulk viscosity of the system significantly, as the Li+ cations strongly coordinate with the [Tf2N] anions in the polar domains. The reorientation times of 9-PA have been analyzed with the aid of Stokes-Einstein-Debye hydrodynamic (SED) theory, and they fall within the broad limits set by the hydrodynamic slip and stick boundary conditions. However, deviations from the SED theory have been noticed upon addition of LiTf2N, and the influence of the electrolyte is more pronounced in the case of ionic liquids with shorter alkyl chains. The observed trends have been rationalized in terms of electrolyte-induced structural changes in these ionic liquids.

Effect of Hydrogen Bonds on the Vibrational Relaxation and Orientational Relaxation Dynamics of HN3 and N3(-) in Solutions.

Hydrogen bonds (H-bonds) play an important role in determining the structures and dynamics of molecular systems. In this work, we investigated the effect of H-bonds on the vibrational population relaxation and orientational relaxation dynamics of HN3 and N3(-) in methanol (CH3OH) and N,N-dimethyl sulfoxide (DMSO) using polarization-controlled infrared pump-probe spectroscopy and quantum chemical calculations. Our detailed analysis of experimental and computational results reveals that both vibrational population relaxation and orientational relaxation dynamics of HN3 and N3(-) in CH3OH and DMSO are substantially dependent on the strength of the H-bonds between the probing solute and its surrounding solvent. Especially in the case of N3(-) in CH3OH, the vibrational population relaxation of N3(-) is found to occur by a direct intermolecular vibrational energy transfer to CH3OH due to large vibrational coupling strength. The orientational relaxation dynamics of HN3 and N3(-), which are well fit by a biexponential function, are analyzed by the wobbling-in-a-cone model and extended Debye-Stokes-Einstein equation. Depending on the intermolecular interactions, the slow overall orientational relaxation occurs under slip, stick, and superstick boundary conditions. For HN3 and N3(-) in CH3OH and DMSO, the vibrational population relaxation becomes faster but the orientational relaxation becomes slower as the H-bond strength is increased. Our current results imply that H-bonds have significant effects on the vibrational population relaxation and orientational relaxation dynamics of a small solute whose size is comparable to the size of the solvent.

Comparison of different coupling schemes between counterions and charged nanoparticles in multiparticle collision dynamics.

We applied the multiparticle collision dynamics (MPC) simulation technique to highly asymmetric electrolytes in solution, i.e., charged nanoparticles and their counterions in a solvent. These systems belong to a domain of solute size which ranges between the electrolyte and the colloidal domains, where most analytical theories are expected to fail, and efficient simulation techniques are still missing. MPC is a mesoscopic simulation method which mimics hydrodynamics properties of a fluid, includes thermal fluctuations, and can be coupled to a molecular dynamics of solutes. We took advantage of the size asymmetry between nanoparticles and counterions to treat the coupling between solutes and the solvent bath within the MPC method. Counterions were coupled to the solvent bath during the collision step and nanoparticles either through a direct interaction force or with stochastic rotation rules which mimic stick boundary conditions. Moreover, we adapted the simulation procedure to address the issue of the strong electrostatic interactions between solutes of opposite charges. We show that the short-ranged repulsion between counterions and nanoparticles can be modeled by stochastic reflection rules. This simulation scheme is very efficient from a computational point of view. We have also computed the transport coefficients for various densities. The diffusion of counterions was found in one case to increase slightly with the volume fraction of nanoparticles. The deviation of the electric conductivity from the ideal behavior (solutes at infinite dilution without any direct interactions) is found to be strong.

Oscillatory response of charged droplets in hydrogels

Characterization of droplet-hydrogel interfaces is of crucial importance to engineer droplet-hydrogel composites for a variety of applications. In order to develop electrokinetic diagnostic tools for probing droplet-hydrogel interfaces, the displacement of a charged droplet embedded in a polyelectrolyte hydrogel exposed to an oscillating electric field is determined theoretically. The polyelectrolyte hydrogel is modeled as an incompressible, charged, porous, and elastic solid saturated with a salted Newtonian fluid. The droplet is considered an incompressible Newtonian fluid with no charges within the droplet. The droplet-hydrogel interface is modeled as a surface with the thickness of zero and the electrostatic potential ζ. The polymer is allowed to slide past the surface of the droplet, with the extent of the sliding quantified with the kinetic friction law, for which the tangential stress of the polymer is proportional to the relative velocity of the polymer and the droplet fluid. The standard regular perturbation method is used to obtain a leading-order solution in ζ-potential for the droplet harmonic displacement, neglecting inertial and temporal ion-concentration effects. It is found that the electrical response is modulated significantly by the polymer boundary condition at the droplet surface. At frequencies higher than a transitional frequency, the impact of the polymer boundary condition vanishes, and the response asymptotes to that with stick boundary condition for the polymer at the droplet surface. In addition, the oscillatory susceptibility of the droplet, defined as the ratio of the droplet displacement to the strength of an applied oscillatory non-electrical force, is determined theoretically; this theoretical study helps to evaluate the validity of the linear response theory used in interpretation of microrheological experiments done with droplets. It is observed that at frequencies less than the transitional frequency, the oscillatory susceptibility would indicate only slip boundary condition for the polymer at the inclusion surface unless the inclusion viscosity is infinity.

Does addition of an electrolyte influence the rotational diffusion of nondipolar solutes in a protic ionic liquid?

Rotational diffusion of two structurally similar nondipolar solutes, 2,5-dimethyl-1,4-dioxo-3,6-diphenylpyrrolo[3,4-c]pyrrole (DMDPP) and 1,4-dioxo-3,6-diphenylpyrrolo[3,4-c]pyrrole (DPP), has been examined in ethylammonium nitrate-lithium nitrate (EAN-LiNO3) mixtures to understand the influence of added electrolyte on the local environment experienced by the solute molecules. The measured reorientation times of both DMDPP and DPP in EAN-LiNO3 mixtures fall within the broad limits set by the hydrodynamic slip and stick boundary conditions. The hydrogen bond accepting DMDPP and the hydrogen bond donating DPP experience specific interactions with the cation and anion of the ionic liquid, respectively. Addition of LiNO3 (0.1 and 0.2 mole fraction) to EAN induces only viscosity related effects on the rotational diffusion of the two nondipolar solutes. These observations suggest that the local environment experienced by DMDPP and DPP in EAN is not altered upon the addition of LiNO3. Our results are consistent with the structural details available in the literature for EAN-LiNO3 mixtures.

Peculiarities of shear flow in microchannels with superhydrophobic wall

203 Liquid flow in microscopic channels with hydro philic or hydrophobic walls is characterized by signifi cant hydrodynamic resistance. It can be reduced by using superhydrophobic coatings, which became known, first of all, for their record large contact angles [1]. This effect is due to small scale roughness of supe rhydrophobic surfaces, owing to which the liquid rests on the tops of surface asperities without entering troughs between them (Cassie–Baxter state). The absence of contacts with the solid walls in troughs also influences the liquid flow. At the interface with regions filled with gas bubbles, the shear components of the stress tensor are close to zero and virtually correspond to the conditions on a free surface. As a result, on the gas bubbles, the liquid flows freely (slips), whereas on the solid asperities the flow velocity is zero (stick boundary condition). The alternation of the slip and no slip regions reduces losses in comparison with the flow on a smooth surface and, as a consequence, gives rise to effective slip, which is characterized by effective slip length b*. This parameter is the extrapolated dis tance from the wall to an imaginary point at which the velocity is zero [2–4] (Fig. 1). The slip intensity increases with increasing surface fraction of gas bubble zones, because of which the effective slip length b* can reach several tens of microns [5, 6].

Rotational dynamics of imidazolium-based ionic liquids: do the nature of the anion and the length of the alkyl chain influence the dynamics?

The rotational dynamics of 1-alkyl-3-methylimidazolium-based ionic liquids has been investigated by monitoring their inherent fluorescence with the intent to unravel the characteristics of the emitting species. For this purpose, temperature-dependent fluorescence anisotropies of 1-alkyl-3-methylimidazolium (alkyl = ethyl and hexyl) ionic liquids with anions such as tris(pentafluoroethyl)trifluorophosphate ([FAP]), bis(trifluoromethylsulfonyl)imide ([Tf2N]), tetrafluoroborate ([BF4]), and hexafluorophosphate ([PF6]) have been measured. It has been observed that the reorientation times (τr) of the ionic liquids with an ethyl chain scale linearly with viscosity and were found to be independent of the nature of the anion. The experimentally measured τr values are a factor of 3 longer than the ones calculated for 1-ethyl-3-methylimidazolium cation using the Stokes-Einstein-Debye (SED) hydrodynamic theory with stick boundary condition, which suggests that the emitting species is not the imidazolium moiety but some kind of associated species. The reorientation times of ionic liquids with a hexyl chain, in contrast, follow the trend τr([FAP]) > τr([Tf2N]) = τr([BF4]) > τr([PF6]) at a given viscosity (η) and temperature (T). The ability of the ionic liquids with longer alkyl chains to form the organized structure appears to be responsible for the observed behavior considering the fact that significant deviations from linearity have been noticed in the τr versus η/T plots for strongly associating anions [BF4] and [PF6], especially at ambient temperatures.

Photophysics and rotational diffusion of hydrophilic molecule in polymer and polyols.

In this work we report the photophysics and rotational diffusion of a hydrophilic solute 7-(N,N'-diethylamino)coumarin-3-carboxylic acid (7-DCCA) in four protic solvents: poly(ethylene glycol), ethylene glycol, tetraethylene glycol, and glycerol, with variation of temperature. The cumulative effect of polarity, viscosity, and structural features of these solvents, as well as specific solute-solvent interaction on the photophysical properties of 7-DCCA was discussed. We observed significant differences in both steady-state and time-resolved emission properties. Estimation of activation energy of viscous flow and activation energy of nonradiative decay reinforce our assumption of a cumulative effect. It was observed that, in all solvents, H-bonding interactions are mainly responsible for changing the spectral properties. Study of rotational relaxation behavior demonstrates superstick boundary condition to be operative in ethylene glycol. It is due to the H-bonding interaction between 7-DCCA and ethylene glycol. Similarly, stick boundary condition is followed in case of tetraethylene glycol at 278 K and further from 293 K. Convergence to the stick boundary is observed in case of poly(ethylene glycol). These changes can be attributed to the change in structural organization in both poly(ethylene glycol) and tetraethylene glycol.

Rotational diffusion of nondipolar and charged solutes in alkyl-substituted imidazolium triflimides: effect of C2 methylation on solute rotation.

Rotational diffusion of a nondipolar solute 2,5-dimethyl-1,4-dioxo-3,6-diphenylpyrrolo[3,4-c]pyrrole (DMDPP) and a charged solute rhodamine 110 (R110) has been investigated in 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([BMIM][Tf2N]) and 1-butyl-2,3-dimethylimidazolium bis(trifluoromethylsulfonyl)imide ([BMMIM][Tf2N]) to understand the influence of the C2 methylation on solute rotation. The measured reorientation times of the nondipolar solute DMDPP are similar in both the ionic liquids and follow Stokes-Einstein-Debye hydrodynamic theory with slip hydrodynamics. In contrast, rotational diffusion of the charged solute R110 in [BMIM][Tf2N] obeys stick hydrodynamics due to specific interactions with the anion of the ionic liquid. Nevertheless, the intriguing result of this study is that the reorientation times of R110 in [BMMIM][Tf2N] deviate significantly from the predictions of stick hydrodynamics, especially at ambient temperatures. The solute-solvent boundary condition parameter Cobs, which is defined as the ratio of the measured reorientation time to the one calculated using the SED theory with stick boundary condition, for R110 is lower by a factor of 2 in [BMMIM][Tf2N] compared to [BMIM][Tf2N] at 298 K. Upon increasing the temperature, Cobs gradually increases and eventually matches with that obtained in [BMIM][Tf2N] at 348 K. It has been well established that methylation of the C2 position in [BMMIM][Tf2N] switches off the main hydrogen-bonding interaction between the anion and the cation, but increases the Coulombic interactions. As a consequence of the enhanced interionic interactions between the cation and anion of the ionic liquid, specific interactions between R110 and [Tf2N] diminish leading to the faster rotation of the solute. However, such an influence is not apparent in case of DMDPP as it does not experience specific interactions with either the cation or the anion of these ionic liquids.

Hydrodynamic simulations of self-phoretic microswimmers

A mesoscopic hydrodynamic model to simulate synthetic self-propelled Janus particles which is thermophoretically or diffusiophoretically driven is here developed. We first propose a model for a passive colloidal sphere which reproduces the correct rotational dynamics together with strong phoretic effect. This colloid solution model employs a multiparticle collision dynamics description of the solvent, and combines stick boundary conditions with colloid-solvent potential interactions. Asymmetric and specific colloidal surface is introduced to produce the properties of self-phoretic Janus particles. A comparative study of Janus and microdimer phoretic swimmers is performed in terms of their swimming velocities and induced flow behavior. Self-phoretic microdimers display long range hydrodynamic interactions with a decay of 1/r(2), which is similar to the decay of gradient fields generated by self-phoretic particle, and can be characterized as pullers or pushers. In contrast, Janus particles are characterized by short range hydrodynamic interactions with a decay of 1/r(3) and behave as neutral swimmers.

Influence of Solute Charge and Pyrrolidinium Ionic Liquid Alkyl Chain Length on Probe Rotational Reorientation Dynamics

In recent years, the effect of molecular charge on the rotational dynamics of probe solutes in room-temperature ionic liquids (RTILs) has been a subject of growing interest. For the purpose of extending our understanding of charged solute behavior within RTILs, we have studied the rotational dynamics of three illustrative xanthene fluorescent probes within a series of N-alkylpyrrolidinium bis(trifluoromethylsulfonyl)imide ([Cnmpyr][Tf2N]) RTILs with different n-alkyl chain lengths (n = 3, 4, 6, 8, or 10) using time-resolved fluorescence anisotropy decay. The rotational dynamics of the neutral probe rhodamine B (RhB) dye lies between the stick and slip boundary conditions due to the influence of specific hydrogen bonding interactions. The rotation of the negatively charged sulforhodamine 640 (SR640) is slower than that of its positively charged counterpart rhodamine 6G (R6G). An analysis based upon Stokes-Einstein-Debye hydrodynamics indicates that SR640 adheres to stick boundary conditions due to specific interactions, whereas the faster rotation of R6G is attributed to weaker electrostatic interactions. No significant dependence of the rotational dynamics on the solvent alkyl chain length was observed for any of the three dyes, suggesting that the specific interactions between dyes and RTILs are relatively independent of this solvent parameter.

A unifying mode-coupling theory for transport properties of electrolyte solutions. II. Results for equal-sized ions electrolytes

On the basis of a versatile mode-coupling theory (MCT) method developed in Paper I [C. Contreras Aburto and G. Nägele, J. Chem. Phys. 139, 134109 (2013)], we investigate the concentration dependence of conduction-diffusion linear transport properties for a symmetric binary electrolyte solution. The ions are treated in this method as charged Brownian spheres, and the solvent-mediated ion-ion hydrodynamic interactions are accounted for also in the ion atmosphere relaxation effect. By means of a simplified solution scheme, convenient semi-analytic MCT expressions are derived for the electrophoretic mobilities, and the molar conductivity, of an electrolyte mixture with equal-sized ions. These expressions reduce to the classical Debye-Falkenhagen-Onsager-Fuoss results in the limit of very low ion concentration. The MCT expressions are numerically evaluated for a binary electrolyte, and compared to experimental data and results by another theoretical method. Our analysis encloses, in addition, the electrolyte viscosity. To analyze the dynamic influence of the hydration shell, the significance of mixed slip-stick hydrodynamic surface boundary conditions, and the effect of solvent permeability are explored. For the stick boundary condition employed in the hydrodynamic diffusivity tensors, our theoretical results for the molar conductivity and viscosity of an aqueous 1:1 electrolyte are in good overall agreement with reported experimental data for aqueous NaCl solutions, for concentrations extending even up to two molar.

Influence of the Organized Structure of 1-Alkyl-3-Methylimidazolium-Based Ionic Liquids on the Rotational Diffusion of an Ionic Solute

To understand the influence of organized structure of the ionic liquids on the rotational diffusion of a hydrogen bond donating ionic solute, reorientation times (τr) of rhodamine 110 (R110) have been measured in 1-alkyl-3-methylimidazolium ([Rmim+]) based ionic liquids with anions tetrafluoroborate ([BF4-]) and hexafluorophosphate ([PF6-]). The viscosity (η) was varied by changing the temperature (T) and also the alkyl chain length on the imidazolium cation (ethyl, butyl, hexyl, and octyl). It has been noticed that τr versus η/T plots contain two slopes corresponding to lower and higher values of η/T for ionic liquids with [BF4-] as well as [PF6-] anions. For lower values of η/T (<0.2 and <0.3 mPa s K(-1), respectively, for [Rmim+][BF4-] and [Rmim+][PF6-]), rotational diffusion of R110 follows Stokes-Einstein-Debye hydrodynamic theory with stick boundary condition due to specific interactions between the solute and the anions of the ionic liquids. In contrast, at higher η/T, the rotational diffusion of the solute is faster than the stick predictions and this trend could not be explained by the quasihydrodynamic theories of Gierer-Wirtz and Dote-Kivelson-Schwartz as well. Diminishing hydrogen bonding interactions between the solute and the anions, which transpire as a consequence of the organized structure of the ionic liquids, are responsible for the observed behavior.

Heat transfer in flow of nonlinear fluids with viscous dissipation

The rotational flow of viscoplastic fluids between concentric cylinders is examined while dissipation due to viscous effects through the energy balance. The viscosity of fluid is simultaneously dependent on shear rate and temperature. Exponential dependence of viscosity on temperature is modeled through Nahme law, and the shear dependency is modeled according to the Carreau equation. Hydrodynamically, stick boundary conditions are applied, and thermally, both constant temperature and constant heat flux on the exterior of cylinders are considered. The governing motion and energy balance equations are coupled adding complexity to the already highly correlated set of differential equations. Introduction of Nahme number has resulted in a nonlinear base flow between the cylinders. As well, the condition of constant heat flux has moved the point of maximum temperature toward the inner cylinder. Taking viscous heating into account, the effects of parameters such as Nahme and Brinkman numbers, material time and pseudoplasticity constant on the stability of the flow are investigated. Moreover, the study shows that the total entropy generation number decreases as the fluid elasticity increases. It, however, increases with increasing Nahme and Brinkman numbers.

Effect of the Alkyl Chain Length on the Rotational Dynamics of Nonpolar and Dipolar Solutes in a Series of N-Alkyl-N-Methylmorpholinium Ionic Liquids

Rotational dynamics of two dipolar solutes, 4-aminophthalimide (AP) and 6-propionyl-2-dimethylaminonaphthalene (PRODAN), and a nonpolar solute, anthracene, have been studied in N-alkyl-N-methylmorpholinium (alkyl = ethyl, butyl, hexyl, and octyl) bis(trifluoromethansulfonyl)imide (Tf2N) ionic liquids as a function of temperature and excitation wavelength to probe the microheterogeneous nature of these ionic liquids, which are recently reported to be more structured than the imidazolium ionic liquids (Khara and Samanta, J. Phys. Chem. B2012, 116, 13430-13438). Analysis of the measured rotational time constants of the solutes in terms of the Stokes-Einstein-Debye (SED) hydrodynamic theory reveals that with increase in the alkyl chain length attached to the cationic component of the ionic liquids, AP shows stick to superstick behavior, PRODAN rotation lies between stick and slip boundary conditions, whereas anthracene exhibits slip to sub slip behavior. The contrasting rotational dynamics of these probe molecules is a reflection of their location in distinct environments of the ionic liquids thus demonstrating the heterogeneity of these ionic liquids. The microheterogeneity of these media, in particular, those with the long alkyl chain, is further evidence from the excitation wavelength dependence study of the rotational diffusion of the dipolar probe molecules.

Stokesian dynamics of pill-shaped Janus particles with stick and slip boundary conditions

We study the forces and torques experienced by pill-shaped Janus particles of different aspect ratios where half of the surface obeys the no-slip boundary condition and the other half obeys the Navier slip condition of varying slip lengths. Using a recently developed boundary integral formulation whereby the traditional singular behavior of this approach is removed analytically, we quantify the strength of the forces and torques experienced by such particles in a uniform flow field in the Stokes regime. Depending on the aspect ratio and the slip length, the force transverse to the flow direction can change sign. This is a novel property unique to the Janus nature of the particles.

Rotational Dynamics of Metal Azide Ion Pairs in Dimethylsulfoxide Solutions

Azide ion is an excellent vibrational probe for studying ion-ion and ion-dipole interactions in solutions because its frequency is sensitively dependent on its local environments. When azide ion forms contact ion pairs with cations in dimethylsulfoxide (DMSO), free azide ion and contact ion pairs are spectrally well distinguished in FTIR spectra. Here, we investigated vibrational population relaxation, P(t), and orientational relaxation dynamics, r(t), of free azide ion and contact ion pairs (LiN3, NaN3, NH4N3, MgN3(+), and CaN3(+)) in DMSO by IR pump-probe spectroscopy. For metal azide ion pairs, the metal ion slowed down the vibrational relaxation of azide ion by acting like a thermal insulator. Biexponential behavior of r(t) was analyzed in the wobbling-in-a-cone model. The long time component of r(t) of free azide ion was found to be viscosity-dependent. The wobbling motion of azide ion within the frame of metal azide ion pairs was weakly dependent on the countercation. When the overall orientational relaxation of metal azide ion pairs was analyzed by the extended Debye-Stokes-Einstein equation, it was well described under stick or superstick boundary conditions due to a strong interaction between the metal ion and DMSO molecules. Our experimental results provide important insight in understanding the rotational dynamics of small ionic species in polar solvents when the size of the ionic species is smaller than or comparable to that of the solvent molecule.

Confinement-induced screening of hydrodynamic interactions and spinodal decomposition: Multiscale simulations of colloid-polymer mixtures

Phase separation kinetics of a colloid-polymer mixture confined between two planar repulsive walls is studied by a multiscale simulation approach. Colloids and polymers are described by particles interacting with continuous potentials suitable for molecular-dynamics simulation, while hydrodynamic interactions mediated by solvent particles are accounted for by the multiparticle collision dynamics method. Varying the distance D between the walls and the character of the boundary conditions, the interplay of structure formation parallel and perpendicular to the walls is studied, and the effect of hydrodynamics on the growth of domain size ℓd(t) with time t is elucidated. Only for slip boundary conditions a growth law ℓd(t)∝t2/3 is observed, but break-up of the percolating polymer-rich phase may “arrest” this growth. For stick boundary conditions hydrodynamic interactions are to a large extent screened and the diffusive Lifshitz-Slyozov growth law ℓd(t)∝t1/3 results.

Publisher's Note: “How to impose stick boundary conditions in coarse-grained hydrodynamics of Brownian colloids and semi-flexible fiber rheology” [J. Chem. Phys. 136, 064901 (2012)

First Page

How to impose stick boundary conditions in coarse-grained hydrodynamics of Brownian colloids and semi-flexible fiber rheology

Long-range hydrodynamics between colloidal particles or fibers is modelled by the fluid particle model. Two methods are considered to impose the fluid boundary conditions at colloidal surfaces. In the first method radial and transverse friction forces between particle and solvent are applied such that the correct friction and torque follows for moving or rotating particles. The force coefficients are calculated analytically and checked by numerical simulation. In the second method a collision rule is used between colloidal particle and solvent particle that imposes the stick boundary conditions exactly. The collision rule comprises a generalisation of the Lowe-Anderson thermostat to radial and transverse velocity differences.