A Molecular Thermodynamic Model of Coacervation in Solutions of Polycations and Oppositely Charged Micelles.

To guide the rational design of personal care formulations, we formulate a molecular thermodynamic model that predicts coacervation from cationic polymers and mixed micelles containing neutral and anionic surfactants and added salt. These coacervates, which form as a result of dilution of conditioning shampoos during use, deposit conditioning agents and other actives to the scalp or skin and also provide lubrication benefits. Our model accounts for mixing entropy, hydrophobic interactions of polycation with water, free energies of bindings of oppositely charged groups to micelles and polycations, and electrostatic interactions that capture connectivity of charged groups on the polycation chain and the micelle. The model outputs are the compositions of surfactants, polycation, salt, and water in the coacervate and in its coexisting dilute phase, along with the binding fractions and coacervate volume fraction. We study the effects of overall composition (of surfactant, polycation, and added salt), charge fractions on micelles and polycations, and binding free energies on the phase diagram of coacervates. Then, we perform coacervation experiments for three systems: sodium dodecyl sulfate (SDS)-JR30M, sodium methyl cocoyl taurate (Taurate)-JR30M, and sodium lauryl alaninate (Alaninate)-JR30M, where JR30M is a cationic derivative of hydroxyethylcellulose (cat-HEC), and rationalize their coacervation data using our model. For comparison with experiment, we also develop a parametrization scheme to obtain the requisite binding energies and Flory-Huggins χ parameter. We find that our model predictions agree reasonably well with the experimental data, and that the sulfate-free surfactants of Taurate and Alaninate display much larger 2-phase regions compared to SDS with JR30M.

Brownian dynamics simulations of telechelic polymer - latex suspensions under steady shear.

We carry out coarse-grained Brownian dynamics simulations of shearing flow of a colloidal suspension bridged by telechelic polymers with "sticky" end groups and vary sticker strength ε over a range from 3 to 12 in units of kBT, motivated by an interest in simulating the rheology of latex paints. The most extensive results are obtained for dumbbells, but the trends are confirmed for 3-bead trumbbells and chains of up to 11 beads. The numbers of colloids and of polymers are also varied over a wide range to confirm trends established for smaller, more computationally affordable, systems. The dynamics are the result of an interplay of the shear rate and three different times scales: the time τBridge for a sticker on a bridging chain to be released from a particle surface, which scales as exp(0.77ε), the time for the polymer chain to relax, τR, which scales as the square of polymer chain length, and the time τD for a colloid to diffuse a distance comparable to its own radius, R, which scales as R3. The scalings of the bridge-to-loop and loop-to-bridge times namely τBL ∝ exp (0.75ε) and τLB ∝ exp (0.71ε), are similar to those of τBridge, for ε values above around 5 kBT, because of the relatively short chains considered here (i.e., 60 Kuhn steps). However, τR becomes more dominant for longer chains, as shown by Travitz and Larson. The zero-shear viscosity η0 is estimated from the Green-Kubo relation, and found to scale as exp (0.69ε), similar to that of τBridge. A weak influence of η0 on τD is observed, with the influence expected to become stronger when τD becomes larger, as shown previously by Wang and Larson. At shear rates in the nonlinear regime, shear-thinning is found with exponents ≈ -0.10 to -0.60, and the first normal stress difference is positive, consistent with some of the experimental data of Chatterjee et al. on model latex paint formulations. The weakness of the shear thinning, relative to that of hydrophobically modified ethoxylated urethane (HEUR) solutions without colloids, is likely due to the observed insensitivity of the loop-to-bridge and bridge-to-loop transition times to the imposed shear rate. This preliminary study provides the first mesoscale simulations of these suspensions, useful for assessing and improving both more accurate multi-scale models and eventually constitutive equations for these complex suspensions.

Extracting free energies of counterion binding to polyelectrolytes by molecular dynamics simulations.

We use all-atom molecular dynamics simulations to extract ΔGeff, the free energy of binding of potassium ions K+ to the partially charged polyelectrolyte poly(acrylic acid), or PAA, in dilute regimes. Upon increasing the charge fraction of PAA, the chains adopt more extended conformations, and simultaneously, potassium ions bind more strongly (i.e., with more negative ΔGeff) to the highly charged chains to relieve electrostatic repulsions between charged monomers along the chains. We compare the simulation results with the predictions of a model that describes potassium binding to PAA chains as a reversible reaction whose binding free energy (ΔGeff) is adjusted from its intrinsic value (ΔG) by electrostatic correlations, captured by a random phase approximation. The bare or intrinsic binding free energy ΔG, which is an input in the model, depends on the binding species and is obtained from the radial distribution function of K+ around the charged monomer of a singly charged, short PAA chain in dilute solutions. We find that the model yields semi-quantitative predictions for ΔGeff and the degree of potassium binding to PAA chains, α, as a function of PAA charge fraction without using fitting parameters.

Overcharging of polyelectrolyte complexes: an entropic phenomenon.

Overcharging in complex coacervation, in which a polyelectrolyte complex coacervate (PEC) initially containing equal moles of the cationic and anionic monomers absorbs a large excess of one type of polyelectrolyte species, is predicted using a recently developed thermodynamic model describing complexation through a combination of reversible ion binding on the chains and long-range electrostatic correlations. We show that overcharging is favored roughly equally by the translational entropy of released counterions and the binding entropy of polyelectrolytes in the polyelectrolyte complex, thus helping resolve competing explanations for overcharging in the literature. We find that the extent of overcharging is non-monotonic in the concentration of added salt and increases with both strength of ion-pairing between polyions and chain hydrophobicity. The predicted extent of overcharging of the PEC is directly compared with that of multilayers made of poly(diallyldimethylammonium), PDADMA, and poly(styrene-sulfonate), PSS, overcompensated by the polycation in two different salts: KBr and NaCl. Accounting for the specificity of salt ion interactions with the polyelectrolytes, we find good qualitative agreement between theory and experiment.

Correction: Time-dependent shear rate inhomogeneities and shear bands in a thixotropic yield-stress fluid under transient shear.

Correction for 'Time-dependent shear rate inhomogeneities and shear bands in a thixotropic yield-stress fluid under transient shear' by Yufei Wei et al., Soft Matter, 2019, 15, 7956-7967, DOI: 10.1039/C9SM00902G.

Search for the Source of an Apparent Interfacial Resistance To Mass Transfer of CnEm Surfactants To the Water/Oil Interface.

Experiments have shown that relaxation of oil/water interfacial tension by adsorption of alkyl ethoxylate surfactants from water onto an oil droplet is delayed relative to diffusion-controlled adsorption. We examine possible causes of this delay, and we show that several are implausible. We find that redissolution of the surfactant in the oil droplet cannot explain the apparent interfacial resistance at short times because the interface will preferentially fill before any such redissolution occurs. We also perform umbrella sampling with molecular dynamics simulation and do not find any evidence of a free-energy barrier or low-diffusivity zone near the interface. Nor do we find evidence from the simulation that premicellar aggregation slows diffusion enough to cause the observed resistance to interfacial adsorption. We are therefore unable to pinpoint the cause of the resistance, but we suggest that "dead time" associated with the experimental method could be responsible-specifically a local depletion of surfactant by the ejected droplet when creating the fresh interface between the oil and water.

Salt- and pH-induced swelling of a poly(acrylic acid) brush via quartz crystal microbalance w/dissipation (QCM-D).

We infer the swelling/de-swelling behavior of weakly ionizable poly(acrylic acid) (PAA) brushes of 2-39 kDa molar mass in the presence of KCl concentrations from 0.1-1000 mM, pH = 3, 7, and 9, and grafting densities σ = 0.12-2.15 chains per nm2 using a Quartz Crystal Microbalance with Dissipation (QCM-D), confirming and extending the work of Wu et al. to multiple chain lengths. At pH 7 and 9 (above the pKa ∼ 5), the brush initially swells at low KCl ionic strength (<10 mM) in the "osmotic brush" regime, and de-swells at higher salt concentrations, in the "salted brush" regime, and is relatively unaffected at pH 3, below the pKa, as expected. At pH 7, at low and moderate grafting densities, our results in the high-salt "salted brush" regime (Cs > 10 mM salt) agree with the predicted scaling H ∼ Nσ+1/3Cs-1/3 of brush height H, while in the low-salt "osmotic brush" regime (Cs < 10 mM salt), we find H ∼ Nσ+1/3Cs+0.28-0.38, whose dependence on Cs agrees with scaling theory for this regime, but the dependence on σ strongly disagrees with it. The predicted linearity in the degree of polymerization N is confirmed. The new results partially confirm scaling theory and clarify where improved theories and additional data are needed.

Time-dependent shear rate inhomogeneities and shear bands in a thixotropic yield-stress fluid under transient shear.

We study the rheological responses and shear-rate inhomogeneities and shear banding behaviors of a thixotropic fumed silica suspension in shear startup tests and flow reversal tests. We find that this suspension under transient shear exhibits not only viscoelasticity, yielding, kinematic hardening, and thixotropy, but also time-dependent shear inhomogeneities including bands when the apparent shear rate is below a critical value between 0.1 and 0.25 s-1. Through multiple shear startup tests and flow reversal tests, we find that thixotropy promotes flow heterogeneity while kinematic hardening suppresses it. We propose a simple thixo-plastic constitutive equation that can qualitatively predict the important features of the rheological response and banding dynamics in shear startup tests and flow reversal tests.

Computational self-assembly of colloidal crystals from Platonic polyhedral sphere clusters.

We explore a rich phase space of crystals self-assembled from colloidal "polyhedral sphere clusters (PSCs)," each of which consists of equal-sized "halo" spheres placed at the vertices of a polyhedron such that they just touch along each edge. Such clusters, created experimentally by fusing spheres, can facilitate assembly of useful colloidal crystal symmetries not attainable by unclustered spheres. While not crucial for their self-assembly, the center of the PSC can contain a "core" particle that can be used as a scaffold to build the PSC. Using Brownian dynamics simulations, we show the self-assembly of eight distinct crystalline phases from PSCs that correspond to the five Platonic polyhedra, and that are made of spheres with purely repulsive interactions. Strong crystalline order is seen in the centers of mass of the PSCs, or equivalently the core particles. The halo particles also may organize into crystal structures, usually with weaker crystalline order than the core particles. Notably, however, in crystals assembled from the octahedral and icosahedral PSCs, the halo particles are also well ordered, nesting within the crystals formed by the cores. Interestingly, despite the rounded nature of the PSCs, in some cases we obtain structures similar to those of the corresponding faceted polyhedra interacting only via excluded volume. Only the tetrahedral PSCs fail to self-assemble into a crystal, but we demonstrate that a pre-assembled crystal - whose halo particles sit on a close-packed face-centered cubic lattice, and whose core particles form a diamond structure - is stable at high density and melts into a hexagonal phase at lower density.

From well-entangled to partially-entangled wormlike micelles.

We combine mechanical rheometry, diffusing wave spectroscopy (DWS), and small angle neutron scattering (SANS) with a simulation model, the "pointer algorithm", to obtain characteristic lengths and time constants for wormlike micelle (WLM) solutions over a range of salt concentrations encompassing the transition from unentangled to entangled solutions. The solutions contain sodium lauryl ethylene glycol sulfate (SLE1S), cocamidopropyl betaine (CAPB), and NaCl. The pointer algorithm is extended to include relaxation of unentangled micelles, allowing micelle parameters to be extracted from the rheology of partially entangled solutions. DWS provides the data at high frequency needed to determine micelle persistence length accurately. From pointer algorithm fits to rheology, we observe a salt-induced rapid change in micellar length as the solution enters the well-entangled regime and a weaker growth with surfactant concentration consistent with mean-field theory. At a lower surfactant concentration, micelle length and persistence length from SANS are roughly consistent with values from rheology once the lower surfactant concentration used in SANS is accounted for. This is, to our knowledge, the first time that quantitative comparisons of structural features including micelle length are made between rheology and SANS. Finally, scaling laws for micelle diffusion and recombination times indicate that micelle kinetics are reaction controlled leading to mean-field recombination with surrounding micelles over the entire range of concentration of interest except at very low and very high surfactant concentrations where either short micelles or branched micelle clusters are dominant.

A metastable nematic precursor accelerates polyethylene oligomer crystallization as determined by atomistic simulations and self-consistent field theory.

Using PYS, TraPPE, OPLS-L, and Flexible-Williams (FW) force field models, atomistic simulations at temperatures ranging from 450 K to 600 K are performed to predict the melt density ρ, the persistence length Np, the nematic coupling constant α, and crystallization dynamics for pentacontane (C50). The coupling constant α arises from packing entropy of rodlike Kuhn segments and increases with increasing ρ and Np. Together with a self-consistent field theory, Np and α are then used to predict the isotropic-to-nematic (IN) transition temperature for polyethylene (PE) oligomers as a function of chain length. The nematic phase is found to be metastable since the IN transition temperature lies below the crystal melting temperatures for C50 in simulations using different force fields. Finally, isothermal simulations of crystallization for PE C50 oligomers and C1000 polymers show that crystal nucleation may be much accelerated by quenching below the IN transition temperature, where chains in the isotropic state first rapidly form nematic ordered domains, within which crystalline order then grows. We also find that the PYS, TraPPE, and FW models overpredict the melting temperature for C50 by around 50 K, while the most flexible OPLS-L model gives a melting temperature within around 10 K of the experimental value. Although giving a more accurate melting temperature, the slow crystallization kinetics of the OPLS-L model may limit its application in direct simulations of PE crystallization.

Nonmonotonic Scission and Branching Free Energies as Functions of Hydrotrope Concentration for Charged Micelles.

Using coarse-grained molecular dynamics simulations and an umbrella sampling method that uses local surfactant density as a reaction coordinate, we directly calculate, for the first time, both the scission and branching free energies of a model charged micelle [cationic cetyltrimethylammonium chloride (CTAC)] in the presence of inorganic and organic salts (hydrotropes). We find that while inorganic salt only weakly affects the micelle scission energy, organic hydrotropes produce a strong, nonmonotonic dependence of both scission energy and branching on salt concentration. The nonmonotonicity in scission energy is traced to a competition between electrostatic screening of the repulsions among the surfactant head groups and thinning of the micellar core, which result from attachment of the hydrotropes to the micelle surface. We are able to correlate the nonmonotonicity in the scission energy of CTAC micelles with the peak observed experimentally in viscosity versus hydrotrope concentration and the location of this peak in CTAC solutions.

Stretch and Breakage of Wormlike Micelles under Uniaxial Strain: A Simulation Study and Comparison with Experimental Results.

We use coarse-grained (CG) molecular dynamics simulations to determine the effect of uniaxial strain on the stress, scission stress, and scission energy of solutions of wormlike micelles of cetyltrimethylammonium chloride/sodium salicylate (NaSal). We find that the breaking stress, stretch modulus, and scission energy of the charged micelles are nonmonotonic functions of oppositely charged hydrotrope (NaSal) concentration. While the stretch modulus shows a peak at a value of surfactant-to-hydrotrope concentration ratio ( R) close to unity as expected due to neutralization of head-group charge at R = 1, the breaking stress and scission energy produce a peak at R < 1.0 because of thinning of the micelle diameter with increased R. The breaking stress from the simulations depends on the rate of deformation and roughly agrees with the experimental values of Rothstein ( J. Rheol. 2003 , 47 , 1227 ) after extrapolation to the much lower experimental rates. The method and results can be used to predict the effects of flow and mechanical stress on rates of micellar breakage, which is important in the rheology of wormlike micellar solutions.

Shear-Induced Alignment of Janus Particle Lamellar Structures.

Control over the alignment of colloidal structures plays a crucial role in advanced reconfigurable materials. In this work, we study the alignment of Janus particle lamellar structures under shear flow via Brownian dynamics simulations. Lamellar alignment (orientation relative to flow direction) is measured as a function of the Péclet number (Pe)-the ratio of the viscous shear to the Brownian forces-the particle volume fraction, and the strength of the anisotropic interaction potential made dimensionless with thermal energy. Under conditions where lamellar structures are formed, three orientation regimes are observed: (1) random orientation for very small Pe, (2) parallel orientation-lamellae with their normals parallel to the direction of the velocity gradient-for intermediate values of Pe, and (3) perpendicular orientation-lamellae with their normals parallel to the vorticity direction-for large Pe. To understand the alignment mechanism, we carry out a scaling analysis of competing torques between a pair of particles in the lamellar structure. Our results suggest that the change of parallel to perpendicular orientation is independent of the particle volume fraction and is caused by the hydrodynamic and Brownian torques on the particles overcoming the torques resulting from the interparticle interactions. This initial study of shear-induced alignment on lamellar structures formed by Janus colloidal particles also opens the door for future applications where a reversible actuator for structure orientation is required.

Scission Free Energies for Wormlike Surfactant Micelles: Development of a Simulation Protocol, Application, and Validation for Personal Care Formulations.

We present a scheme to calculate wormlike micelle scission free energies from a potential of mean force (PMF) derived from a weighted histogram analysis method (WHAM) applied to coarse grained dissipative particle dynamics (DPD) simulations. In contrast to previous related work, we use a specially chosen external potential based on a reaction coordinate that reversibly drives surfactants out of the nascent scission location. For the application to a model body wash formulation, we predict how addition of NaCl and small molecules such as perfume raw materials (PRMs) affect scission energies. The results show qualitative agreement and correct trends compared to recently determined scission energies for the same system; however, a more rigorous parametrization of the underlying DPD potential is required for quantitative agreement.

Prediction of striped cylindrical micelles (SCMs) formed by dodecyl-ß-d-maltoside (DDM) surfactants.

Using fully atomistic and coarse-grained (CG) molecular dynamics (MD) simulations, we report, for the first time, the self-assembly of initially randomly dispersed dodecyl-ß-d-maltoside (DDM) surfactants into a striped cylindrical micelle (SCM) with lamellae of surfactant heads and tails alternating along the cylindrical axis, with both heads and tails in contact with the water. By changing the interaction strength of the head group with water relative to itself, we find that such micelles are most likely for head groups with marginal solubility in the water solvent. Unlike the surfactants in a regular cylindrical micelle, whose tails are in the fluid micelle interior, the diffusion of DDM surfactants along the micelle body is blocked by the lamellar patterning. As a consequence, branches cannot slide along the micelle body and surfactant molecules cannot exchange between the micelle body and the branch, which should have a significant impact on the rheological properties of these micelles.

Inertio-capillary cross-streamline drift of droplets in Poiseuille flow using dissipative particle dynamics simulations.

We find using dissipative particle dynamics (DPD) simulations that a deformable droplet sheared in a narrow microchannel migrates to steady-state position that depends upon the dimensionless particle capillary number , which controls the droplet deformability (with Vmax the centerline velocity, µf the fluid viscosity, Γ the surface tension, R the droplet radius, and H the gap), the droplet (particle) Reynolds number , which controls inertia, where ρ is the fluid density, as well as on the viscosity ratio of the droplet to the suspending fluid κ = µd/µf. We find that when the Ohnesorge number is around 0.06, so that inertia is stronger than capillarity, at small capillary number Cap < 0.1, the droplet migrates to a position close to that observed for hard spheres by Segre and Silberberg, around 60% of the distance from the centerline to the wall, while for increasing Cap the droplet steady-state position moves smoothly towards the centerline, reaching around 20% of the distance from centerline to the wall when Cap reaches 0.5 or so. For higher Oh, the droplet position is much less sensitive to Cap, and remains at around 30% of the distance from centerline to the wall over the whole accessible range of Cap. The results are insensitive to viscosity ratios from unity to the highest value studied here, around 13, and the drift towards the centerline for increasing Cap is observed for ratios of droplet diameter to gap size ranging from 0.1 to 0.3. We also find consistency between our predictions and existing perturbation theory for small droplet or particle size, as well as with experimental data. Additionally, we assess the accuracy of the DPD method and conclude that with current computer resources and methods DPD is not readily able to predict cross-stream-line drift for small particle Reynolds number (much less than unity), or for droplets that are less than one tenth the gap size, owing to excessive noise and inadequate numbers of DPD particles per droplet.

A transport model and constitutive equation for oppositely charged polyelectrolyte mixtures with application to layer-by-layer assembly.

We develop a general framework for transport of polyions, solvent and salt, with intended application to Layer-by-Layer (LbL) assembly of polyelectrolyte monolayers (PEMs). The formulation for the first time includes electrostatics, chemical potential gradients, and mechanical stress gradients as driving forces for mass transport. The general model allows all species to be mobile throughout the process and avoids the assumptions of stepwise instantaneous equilibrium and/or immobilized structures typical of previous approaches, while reducing to these models in appropriate limits. A simple constitutive equation is derived for a mixture of oppositely charged polyelectrolytes that accounts for network strand dilution and cross-chain ion pairing by appending reactive terms to the Smoluchowski probability diffusion equation for network strand end-to-end vectors. The resulting general framework encompasses the Poisson equation describing the electrostatic potential distribution, an osmotic pressure balance, a stress constitutive equation, and a generalized flux law of polymer transport. The computational domain is split into a PEM phase and an external solution phase with an appropriate boundary condition derived for the interface between the two. The mobile species (water and small salt ions) are taken to be in a state of dynamic equilibrium with their distributions enslaved to the perturbations in the two polyion compositions. The proposed model captures the swelling response of PEM films to external solutions. For the first time, we studied the effects of the temporal evolution of electrostatic and stress distribution on the rate of chain loss and absorption during rinsing and dipping of an idealized and arbitrarily selected and rigid brush layer into external solutions. The temporal evolution provides a kinetic basis for the ability of LbL films to grow under conditions that thermodynamics alone suggests would cause them to be washed away and to account for partial desorption during washing. The proposed transport framework constitutes a solid basis for eventual quantitative modeling of LbL assembly and transport in polyion networks more generally.

Role of electrostatic correlations in polyelectrolyte charge association.

Reversible ion binding equilibria in polyelectrolyte solutions are strongly affected by interactions between dissociated ionic species. We examine how the structural correlations between ionic groups on polyelectrolytes impact the counterion binding. Treating the electrostatic correlation free energy using the classical Debye-Hückel expression leads to complete counterion dissociation in the concentrated regime. This unphysical behavior is shown to stem from improper regularization of the self-energy of dissociated ions and polyions and is mitigated by smearing point-like charges across a finite width. The influence of the self-energy on counterion binding is elaborated on by generalizing the Debye-Hückel free energy to polyelectrolytes with variable fractal dimension and stiffness. In the dilute regime, a greater propensity for binding is found for chains with more compact architectures, which in turn reduces the harsh self-repulsions of tightly packed arrangements of charge. In the concentrated regime, the effects of electrostatic correlations weaken due to screening and the extent of binding is governed by a balance of short-ranged interactions and the translational entropy of ions.