Entropic phase separation in polymer-microemulsion networks

Designing Superselectivity in Linker-Mediated Multivalent Nanoparticle Adsorption

Using a statistical mechanical model and numerical simulations, we provide the design principle for the bridging strength (ξ) and linker density (ρ) dependent superselectivity in linker-mediated multivalent nanoparticle adsorption. When the bridges are insufficient, the formation of multiple bridges leads to both ξ- and ρ-dependent superselectivity. When the bridges are excessive, the system becomes insensitive to bridging strength due to entropy-induced self-saturation and shows a superselective desorption with respect to the linker density. Counterintuitively, lower linker density or stronger bridging strength enhances the superselectivity. These findings help the understanding of relevant biological processes and open up opportunities for applications in biosensing, drug delivery, and programmable self-assembly.

Affinity and Valence Impact the Extent and Symmetry of Phase Separation of Multivalent Proteins

Biomolecular self-assembly spatially segregates proteins with a limited number of binding sites (valence) into condensates that coexist with a dilute phase. We develop a many-body lattice model for a three-component system of proteins with fixed valence in a solvent. We compare the predictions of the model to experimental phase diagrams that we measure in vivo, which allows us to vary specifically a binding site's affinity and valency. We find that the extent of phase separation varies exponentially with affinity and increases with valency. Valency alone determines the symmetry of the phase diagram.

Designing Enhanced Entropy Binding in Single-Chain Nanoparticles

Single-chain nanoparticles (SCNPs) are a new class of bio- and soft-matter polymeric objects in which a fraction of the monomers are able to form equivalently intra- or interpolymer bonds. Here we numerically show that a fully entropic gas-liquid phase separation can take place in SCNP systems. Control over the discontinuous (first-order) change-from a phase of independent diluted (fully-bonded) polymers to a phase in which polymers entropically bind to each other to form a (fully-bonded) polymer network-can be achieved by a judicious design of the patterns of reactive monomers along the polymer chain. Such a sensitivity arises from a delicate balance between the distinct entropic contributions controlling the binding.

Rigidity-Tuned Full-Color Emission: Uncommon Luminescence Change from Polymer Free-Volume Variations

Probing the rigidity change of microenvironments via tracking embedded molecular fluorophore emissions represents a robust approach to monitor various polymer microstructural evolutions and biomolecular events with a high spatiotemporal resolution. However, reported fluorophores exclusively blueshift their emissions (termed as "rigidochromism") or merely alter intensities upon rigidification, suffering from inferior sensitivities, low-contrast outputs, and attenuated biocompatibilities. Here, phenanthridine-fused triazatruxene fluorophores (PTFs) with pronounced bathochromic emission (up to 135 nm) toward rigidifying media at a low loading of 5 ppm without sacrificing the quantum yields and lifetime are developed. PTFs effectively interact with polymeric matrixes through polar-π interactions and form charge-transfer complexes, resulting to a remarkable fluorescent color change from blue to red-orange over matrix rigidifying. Such a unique anti-rigidochromism enables a highly sensitive rigidity detection (i.e., a subtle polymer molecular-weight change (as low as 1000 Da vs up to 10 kDa for conventional probes) can result to obvious emission color changes). PTFs are able to noninvasively detect polymerization kinetics and in situ optically report polymer degradations. The broadly (nearly full-spectrum) tunable emission and the efficient coupling between anti-rigidochromism and polymer hierarchical structures/topologies render fluorescence with controlled wavelength and chirality, leading to an unprecedented free-volume-based data encryption and anti-counterfeiting technology with a superhigh security level.

Using Microemulsions: Formulation Based on Knowledge of Their Mesostructure

Microemulsions, as thermodynamically stable mixtures of oil, water, and surfactant, are known and have been studied for more than 70 years. However, even today there are still quite a number of unclear aspects, and more recent research work has modified and extended our picture. This review gives a short overview of how the understanding of microemulsions has developed, the current view on their properties and structural features, and in particular, how they are related to applications. We also discuss more recent developments regarding nonclassical microemulsions such as surfactant-free (ultraflexible) microemulsions or ones containing uncommon solvents or amphiphiles (like antagonistic salts). These new findings challenge to some extent our previous understanding of microemulsions, which therefore has to be extended to look at the different types of microemulsions in a unified way. In particular, the flexibility of the amphiphilic film is the key property to classify different microemulsion types and their properties in this review. Such a classification of microemulsions requires a thorough determination of their structural properties, and therefore, the experimental methods to determine microemulsion structure and dynamics are reviewed briefly, with a particular emphasis on recent developments in the field of direct imaging by means of electron microscopy. Based on this classification of microemulsions, we then discuss their applications, where the application demands have to be met by the properties of the microemulsion, which in turn are controlled by the flexibility of their amphiphilic interface. Another frequently important aspect for applications is the control of the rheological properties. Normally, microemulsions are low viscous and therefore enhancing viscosity has to be achieved by either having high concentrations (often not wished for) or additives, which do not significantly interfere with the microemulsion. Accordingly, this review gives a comprehensive account of the properties of microemulsions, including most recent developments and bringing them together from a united viewpoint, with an emphasis on how this affects the way of formulating microemulsions for a given application with desired properties.

Ensemble fluctuations matter for variances of macroscopic variables

Extending recent work on stress fluctuations in complex fluids and amorphous solids we describe in general terms the ensemble average [Formula: see text] and the standard deviation [Formula: see text] of the variance [Formula: see text] of time series [Formula: see text] of a stochastic process x(t) measured over a finite sampling time [Formula: see text]. Assuming a stationary, Gaussian and ergodic process, [Formula: see text] is given by a functional [Formula: see text] of the autocorrelation function h(t). [Formula: see text] is shown to become large and similar to [Formula: see text] if [Formula: see text] corresponds to a fast relaxation process. Albeit [Formula: see text] does not hold in general for non-ergodic systems, the deviations for common systems with many microstates are merely finite-size corrections. Various issues are illustrated for shear-stress fluctuations in simple coarse-grained model systems.

Equilibrium size distribution and phase separation of multivalent, molecular assemblies in dilute solution

Multivalent molecules can bind a limited number of multiple neighbors via specific interactions. In this paper, we investigate theoretically the self-assembly and phase separation of such molecules in dilute solution. We show that the equilibrium size (n) distributions of linear or branched assemblies qualitatively differ; the former decays exponentially with the relative size n/N[combining macron] (N[combining macron] = n), while the latter decays as a power law, with an exponential cutoff only for n ⪆ N[combining macron]2 ≫ N[combining macron]. In some cases, finite, branched assemblies are unstable and show a sol-gel transition at a critical concentration. In dilute solutions, non-specific interactions result in phase separation, whose critical point is described by an effective Flory Huggins theory that is sensitive to the nature of these distributions.

Combinatorial-Entropy-Driven Aggregation in DNA-Grafted Nanoparticles

We use computer simulations and experiments to study the interactions between nanoparticles (NPs) grafted with self-complementary DNA strands. Each strand ends with a sticky palindromic single-stranded sequence, allowing it to associate equally favorably with strands grafted on the same particle or on different NPs. Surprisingly we find an attractive interaction between a pair of NPs, and we demonstrate that at low temperature it arises purely from a combinatorial-entropy contribution. We evaluate theoretically and verify numerically this entropic contribution originating from the number of distinct bonding patterns associated with intra- and interparticle binding. This entropic attraction becomes more favorable with decreasing inter-NP distance because more sticky ends can participate in making this choice.

Surface-triggered cascade reactions between DNA linkers direct the self-assembly of colloidal crystals of controllable thickness

Functionalizing colloids with reactive DNA linkers is a versatile way of programming self-assembly. DNA selectivity provides direct control over colloid-colloid interactions allowing the engineering of structures such as complex crystals or gels. However, the self-assembly of localized and finite structures remains an open problem with many potential applications. In this work, we present a system in which functionalized surfaces initiate a cascade reaction between linkers leading to the self-assembly of crystals with a controllable number of layers. Specifically, we consider colloidal particles functionalized by two families of complementary DNA linkers with mobile anchoring points, as found in experiments using emulsions or lipid bilayers. In bulk, intra-particle linkages formed by pairs of complementary linkers prevent the formation of inter-particle bridges and therefore colloid-colloid aggregation. However, colloids interact strongly with the surface given that the latter can destabilize intra-particle linkages. When in direct contact with the surface, colloids are activated, meaning that they feature more unpaired DNA linkers ready to react. Activated colloids can then capture and activate other colloids from the bulk through the formation of inter-particle linkages. Using simulations and theory, validated by existing experiments, we clarify the thermodynamics of the activation and binding process and explain how particle-particle interactions, within the adsorbed phase, weaken as a function of the distance from the surface. The latter observation underlies the possibility of self-assembling finite aggregates with controllable thickness and flat solid-gas interfaces. Our design suggests a new avenue to fabricate heterogeneous and finite structures.

Gels Obtained by Colloidal Self-Assembly of Amphiphilic Molecules

Gelation in water-based systems can be achieved in many different ways. This review focusses on ways that are based on self-assembly, i.e., a bottom-up approach. Self-assembly naturally requires amphiphilic molecules and accordingly the systems described here are based on surfactants and to some extent also on amphiphilic copolymers. In this review we are interested in cases of low and moderate concentrations of amphiphilic material employed to form hydrogels. Self-assembly allows for various approaches to achieve gelation. One of them is via increasing the effective volume fraction by encapsulating solvent, as in vesicles. Vesicles can be constructed in various morphologies and the different cases are discussed here. However, also the formation of very elongated worm-like micelles can lead to gelation, provided the structural relaxation times of these systems is long enough. Alternatively, one may employ amphiphilic copolymers of hydrophobically modified water soluble polymers that allow for network formation in solution by self-assembly due to having several hydrophobic modifications per polymer. Finally, one may combine such polymers with surfactant self-assemblies and thereby produce interconnected hybrid network systems with corresponding gel-like properties. As seen here there is a number of conceptually different approaches to achieve gelation by self-assembly and they may even become combined for further variation of the properties. These different approaches are described in this review to yield a comprehensive overview regarding the options for achieving gel formation by self-assembly.

Shear-stress fluctuations in self-assembled transient elastic networks

Focusing on shear-stress fluctuations, we investigate numerically a simple generic model for self-assembled transient networks formed by repulsive beads reversibly bridged by ideal springs. With Δt being the sampling time and t_{☆}(f)∼1/f the Maxwell relaxation time (set by the spring recombination frequency f), the dimensionless parameter Δx=Δt/t_{☆}(f) is systematically scanned from the liquid limit (Δx≫1) to the solid limit (Δx≪1) where the network topology is quenched and an ensemble average over m-independent configurations is required. Generalizing previous work on permanent networks, it is shown that the shear-stress relaxation modulus G(t) may be efficiently determined for all Δx using the simple-average expression G(t)=μ_{A}-h(t) with μ_{A}=G(0) characterizing the canonical-affine shear transformation of the system at t=0 and h(t) the (rescaled) mean-square displacement of the instantaneous shear stress as a function of time t. This relation is compared to the standard expression G(t)=c[over ̃](t) using the (rescaled) shear-stress autocorrelation function c[over ̃](t). Lower bounds for the m configurations required by both relations are given.

Microdynamics and arrest of coarsening during spinodal decomposition in thermoreversible colloidal gels

Coarsening and kinetic arrest of colloidal systems undergoing spinodal decomposition (SD) is a conserved motif for forming hierarchical, bicontinuous structures. Although the thermodynamic origins of SD in colloids are widely known, the microstructural processes responsible for its coarsening and associated dynamics en route to arrest remain elusive. To better elucidate the underlying large-scale microdynamical processes, we study a colloidal system with moderate-range attractions which displays characteristic features of arrested SD, and study its dynamics during coarsening through a combination of differential dynamic microscopy and real-space tracking. Using these recently developed imaging techniques, we reveal directly that the coarsening arises from collective dynamics of dense domains, which undergo slow, intermittent, and ballistic motion. These collective motions indicate interfacial effects to be the driving force of coarsening. The nature of the gelation enables control of the arrested length scale of coarsening by the depths of quenching into the spinodal regime, which we demonstrate to provide an effective means to control the elasticity of colloidal gels.

Phase Behavior of Nonionic Microemulsions with Multi-end-capped Polymers and Its Relation to the Mesoscopic Structure

The polymer architecture of telechelic or associative polymers has a large impact on the bridging of self-assembled structures. This work presents the phase behavior, small angle neutron scattering (SANS), dynamic light scattering (DLS), and fluorescence correlation spectroscopy (FCS) of a nonionic oil-in-water (O/W) microemulsion with hydrophobically end-capped multiarm polymers with functionalities f = 2, 3, and 4. For high polymer concentrations and large average interdroplet distance relative to the end-to-end distance of the polymer, d/R(ee), the system phase separates into a dense, highly connected droplet network phase, in equilibrium with a dilute phase. The extent of the two-phase region is larger for polymers with similar length but higher f. The interaction potential between the droplets in the presence of polymer has both a repulsive and an attractive contribution as a result of the counterbalancing effects of the exclusion by polymer chains and bridging between droplets. This study experimentally demonstrates that higher polymer functionalities induce a stronger attractive force between droplets, which is responsible for a more extended phase separation region, and correlate with lower collective droplet diffusivities and higher amplitude of the second relaxation time in DLS. The viscosity and the droplet self-diffusion obtained from FCS, however, are dominated by the end-capped chain concentration.

Shear-stress relaxation and ensemble transformation of shear-stress autocorrelation functions

We revisit the relation between the shear-stress relaxation modulus G(t), computed at finite shear strain 0<γ≪1, and the shear-stress autocorrelation functions C(t)|(γ) and C(t)|(τ) computed, respectively, at imposed strain γ and mean stress τ. Focusing on permanent isotropic spring networks it is shown theoretically and computationally that in general G(t)=C(t)|(τ)=C(t)|(γ)+G(eq) for t>0 with G(eq) being the static equilibrium shear modulus. G(t) and C(t)|(γ) thus must become different for solids and it is impossible to obtain G(eq) alone from C(t)|(γ) as often assumed. We comment briefly on self-assembled transient networks where G(eq)(f) must vanish for a finite scission-recombination frequency f. We argue that G(t)=C(t)|(τ)=C(t)|(γ) should reveal an intermediate plateau set by the shear modulus G(eq)(f=0) of the quenched network.

Interactions between microemulsion droplets decorated with hydrophobically modified polymers: a small-angle neutron scattering study

The shape and interactions between microemulsion droplets (R = 8.2 nm, polydispersity 20%) either decorated with PEO modified with a single hydrophobic end function (PEO-m: C12H25 - (EO)n, M(PEO) = 5.2 kg/mol), or with telechelic polymers of twice the mass (PEO-2m: C12H25 - (EO)2n - C12H25, M(PEO) = 10.4 kg/mol) have been studied by small-angle neutron scattering (SANS). The results as a function of droplet and polymer concentration have been compared to the reference case of the bare microemulsion which was shown to be unchanged using Porod representations. The interactions between bare and decorated droplets have been analyzed using the structure factor S(q), at first in a model-free way based on its low-q limit S(q → 0). This analysis provides clear evidence on the concentration-dependent repulsive or attractive nature of the contributions to the pair droplet-droplet pair potential of the polymers. Model pair potentials describing the steric repulsions and attractions by copolymer bridging are used to describe the low-q behavior of the structure factor based on an integral equation approach, giving an estimate of the range and amplitude of the potentials. Moreover, they provide an explanation for the observed transient clustering in terms of a shallow minimum of the total potential, as they establish the respective repulsive and attractive contributions of the polymer molecules.

Oil-in-water microemulsion droplets of TDMAO/decane interconnected by the telechelic C18-EO150-C18: clustering and network formation

The effect of a doubly hydrophobically end-capped water soluble polymer (C18-PEO150-C18) on the properties of an oil-in-water (O/W) droplet microemulsion (R ∼ 2.85 nm) has been studied as a function of the amount of added telechelic polymer. Macroscopically one observes a substantial increase of viscosity once a concentration of ∼5 hydrophobic stickers per droplet is surpassed and effective cross-linking of the droplets takes place. SANS measurements show that the size of the individual droplets is not affected by the polymer addition but it induces attractive interactions at low concentration and repulsive ones at high polymer content. Measurements of the diffusion coefficient by DLS and FCS show increasing sizes at low polymer addition that can be attributed to the formation of clusters of microemulsion droplets interconnected by the polymer. At higher polymer content the network formation leads to an additional slow relaxation mode in DLS that can be related to the rheological behaviour, while the self-diffusion observed in FCS attains a lower plateau value, i.e., the microemulsion droplets remain effectively fixed within the network. The combination of SANS, DLS, and FCS allows us to derive a self-consistent picture of the evolution of structure and dynamics of the mixed system microemulsion/telechelic polymer as a function of the polymer content, which is not only relevant for controlling the macroscopic rheological properties but also with respect to the internal dynamics as it is, for instance, relevant for the release and transport of active agents.

Structure and dynamics of networks in mixtures of hydrophobically modified telechelic multiarm polymers and oil in water microemulsions

The structural and dynamical properties of oil-in-water (O/W) microemulsions (MEs) modified with telechelic polymers of different functionality (e.g., number of hydrophobically modified arms, f) were studied by means of dynamic light scattering (DLS), small-angle neutron scattering (SANS), and high frequency rheology measurements as a function of the polymer architecture and the amount of added polymer. For this purpose, we employed tailor-made hydrophobically end-capped poly(N,N-dimethylacrylamide) star polymers of a variable number of endcaps, f, of different alkyl chain lengths, synthesized by the reversible addition-fragmentation chain transfer method. The addition of the different end-capped polymers to an uncharged ME of O/W droplets leads to a large enhancement of the viscosity of the systems. SANS experiments show that the O/W ME droplets are not changed upon the addition of the polymer, and its presence only changes the interdroplet interactions. The viscosity increases largely upon addition of a polymer, and this enhancement depends pronouncedly on the alkyl length of the hydrophobic sticker as it controls the residence time in a ME droplet. Similarly, the high frequency modulus G(0) depends on the amount of added polymer but not on the sticker length. G(0) was found to be directly proportional to f - 1. The onset of network formation is shifted to a lower number of stickers per ME droplet with increasing f, and the network formation becomes more effective. Thus, the dynamics of network formation are controlled by the polymer architecture. The effect on the dynamics seen by DLS is even more pronounced. Upon increasing the polymer concentration, slower relaxation modes appear that become especially pronounced with increasing number of arms. The relaxation dynamics are correlated to the rheological relaxation, and both are controlled by the polymer architecture.

Impulsive correction to the elastic moduli obtained using the stress-fluctuation formalism in systems with truncated pair potential

The truncation of a pair potential at a distance rc is well known to imply, in general, an impulsive correction to the pressure and other moments of the first derivatives of the potential. That, depending on rc, the truncation may also be of relevance to higher derivatives is shown theoretically for the Born contributions to the elastic moduli obtained using the stress-fluctuation formalism in d dimensions. Focusing on isotropic liquids for which the shear modulus G must vanish by construction, the predicted corrections are tested numerically for binary mixtures and polydisperse Lennard-Jones beads in, respectively, d=3 and 2 dimensions. Both models being glass formers, we comment briefly on the temperature (T) dependence of the (corrected) shear modulus G(T) around the glass transition temperature Tg.

Structure of microemulsion-ABA triblock copolymer networks

Structural equilibrium properties of transient networks formed by microemulsion droplets and ABA triblock copolymers in solution have been studied by Monte Carlo simulation. The droplets were represented by soft spheres, and the polymers were represented by junctions connected by harmonic bonds with an angular potential regulating the intrinsic chain stiffness. The interaction parameters were selected such that the end A-blocks were localized inside the droplets and the middle B-block in the continuous phase. The influence of (i) the polymer concentration, (ii) the polymer stiffness, and (iii) the contour length of the middle B-block on the formation and the structure of the microemulsion-polymer network were investigated using polymer end-to-end separation probability distribution functions, droplet radial distribution functions, droplet-droplet nearest-neighbor probability distribution functions, and network connectivity indicators. An increase of the polymer-droplet number ratio had a strong impact on the network formation. Under typical conditions and at an intermediate polymer-droplet number ratio, (i) the fraction of polymers forming bridges between droplets increased from essentially zero to unity and (ii) the fraction of polymers that were forming loops decreased as the ratio of the polymer end-to-end separation and the surface-to-surface separation between neighboring droplets for a hypothetical homogeneous droplet distribution was increased from 0.5 to 2. For long and flexible polymers, a mesoscopic segregation triggered by a depletion attraction between droplets appeared, and, furthermore, for sufficiently stiff chains, only bridge conformations occurred. The percolation probability could be represented as a function of the average droplet cluster size only, across all systems.

Kinetic Monte Carlo method for rule-based modeling of biochemical networks

We present a kinetic Monte Carlo method for simulating chemical transformations specified by reaction rules, which can be viewed as generators of chemical reactions, or equivalently, definitions of reaction classes. A rule identifies the molecular components involved in a transformation, how these components change, conditions that affect whether a transformation occurs, and a rate law. The computational cost of the method, unlike conventional simulation approaches, is independent of the number of possible reactions, which need not be specified in advance or explicitly generated in a simulation. To demonstrate the method, we apply it to study the kinetics of multivalent ligand-receptor interactions. We expect the method will be useful for studying cellular signaling systems and other physical systems involving aggregation phenomena.

Influence of nanoparticle addition on the properties of wormlike micellar solutions

The addition of positively charged, 30 nm diameter silica nanoparticles to cationic wormlike micellar solutions of cetyltrimethylammonium bromide and sodium nitrate is studied using a combination of rheology, small angle neutron scattering, dynamic light scattering, and cryo-transmission electron microscopy. The mixtures are single phase up to particle volume fractions of 1%. The addition of like-charged particles significantly increases the wormlike micelle (WLM) solution's zero shear rate viscosity, longest relaxation time, and storage modulus. The changes are hypothesized to originate from a close association of the particles with the micellar mesh. Small angle neutron scattering measurements with contrast matching demonstrate associations between particles mitigated by the WLMs. The effective interparticle interactions measured by SANS can explain the observed phase behavior. Dynamic light scattering measurements confirm the dynamic coupling of the particles to the micellar mesh.

Liquid-vapor transition driven by bond disorder

We report grand-canonical Monte Carlo simulations of an equimolar mixture of hard colloids coated with long polymers that have a complementary functionalization. Such systems have the potential to function as self-healing materials. Under conditions where the complementary polymer ends are strongly associated, we observe a first-order vapor-liquid transition from a dilute gas of colloidal dimers to a dense, liquid-like phase. This transition is driven exclusively by the increase in entropy associated with bond disorder-an effect that was predicted theoretically by Zilman et al. [Phys. Rev. Lett. 91, 015901 (2003)10.1103/PhysRevLett.91.015901]. Our simulations rationalize experimental observations by Schmatko et al. [Soft Matter 03 (2007) 703.].

Hydrophilic alcohol ethoxylates as efficiency boosters for microemulsions

Highly amphiphilic polyalkane-PEO diblock copolymers drastically increase the solubilization capacity of surfactants in microemulsions if they are used in small quantities as additive to the surfactant. This effect goes along with an additional reduction of the already very low interfacial tension between water and oil. Lamellar phases, which usually develop when the surfactant becomes more efficient, are suppressed to a large extent. In this work we use another type of additive, namely hydrophilic alcohol ethoxylates. These amphiphiles are identical with the previously used block copolymers with respect to the hydrophilic moiety. However, they contain only small hydrocarbon groups ranging from C8 to C18. A typical example from the hydrophilic alcohol ethoxylates is C12E100. Both additive types increase surfactant efficiency equally with respect to mass fraction in the mixture. Because the alcohol ethoxylate additives decorate the surfactant film only on the aqueous side, they influence the curvature of the surfactant membrane or, in other words, the temperature behavior of the microemulsion. Together with nonionic surfactants, however, the shift of the one-phase region to higher temperatures is only a few degrees Celsius. Just as with the polyalkane-PEO block copolymers, the hydrophilic alcohol ethoxylates suppress lamellar phases. This behavior is especially pronounced if the hydrophobic groups are small or the PEO chains are long. We found that hydrophobic units as short as C 8 are sufficient to largely anchor the PEO chains at the interface. If C12 or C18 hydrocarbon unit are used instead, the PEO chains are fully interfacially active, even if the hydrophilic chain contains up to about 500 EO units. We applied the new additives in bicontinuous and in droplet microemulsions and used nonionic, as well as ionic, surfactants, namely C10E4 and AOT. In contrast to polyalkane-PEO blockcopolymers the new additives are easy to synthesize and are commercially available. Therefore, they might be interesting in applications.

Structure and rheological properties of model microemulsion networks filled with nanoparticles

Model microemulsion networks of oil droplets stabilized by non-ionic surfactant and telechelic polymer C18 -PEO(10k)- C18 have been studied for two droplet-to-polymer size ratios. The rheological properties of the networks have been measured as a function of network connectivity and can be described in terms of simple percolation laws. The network structure has been characterised by Small Angle Neutron Scattering (SANS). A Reverse Monte Carlo (RMC) approach is used to demonstrate the interplay of attraction and repulsion induced by the copolymer. These model networks are then used as matrix for the incorporation of silica nanoparticles (R = 10 nm), individual dispersion being checked by scattering. A strong impact on the rheological properties is found for silica volume fractions up to 9%. q(A-1).

Polymer-induced transient networks in water-in-oil microemulsions studied by small-angle x-ray and dynamic light scattering

We study water-in-oil microemulsions, in particular dispersions of water droplets coated with a monolayer of the anionic surfactant AOT in a continuous phase of n -decane. Upon addition of the amphiphilic triblock copolymer PEO(polyethylenoxide)-PI(polyisoprene)-PEO, a transient network is formed. At constant droplet size we vary the polymer concentration and there is clear evidence for an increasing crosslinking of the droplets from structural investigations with small-angle x-ray scattering. The dynamics of concentration fluctuations consisting of the translational diffusion of the droplets and the relaxation of the network are monitored with photon correlation spectroscopy. We mainly focus on the variation of the dynamic behavior as a function of the number of polymer molecules per droplet and the droplet volume fraction, which may be taken as a measure for the interdroplet distance. With increasing polymer content the dynamics of the system slows down and three different relaxation processes may be distinguished. We discuss the origin of the different relaxation modes. In particular, it turns out that the intermediate relaxation mode may be suppressed by index matching the oil matrix and the PI block and that it is effectively slowed down by an additional loading of the emulsion droplets with polyethylene glycol of increasing molecular weight.

SANS study of polymer-linked droplets

We report experimental results obtained from SANS on microemulsion droplets connected by a telechelic polymer. Thanks to its ability to anchor droplets through its short stickers, the addition of this polymer leads to the formation of transient aggregates. Measurements were performed on samples at low surfactant content in such a way that the droplets appear to be isolated with a separation distance longer than the end-to-end distance of the polymer. The locally spherical structure of the micelles is unchanged in size upon polymer addition whereas the large rise in scattered intensity at low Q is due to the induced effective attractive interaction between droplets. The fitting model that we propose allows a quantitative description of the bridging effect.

Heterogeneous diffusion in a reversible gel

We introduce a microscopically realistic model of a physical gel and use computer simulations to study its static and dynamic properties at thermal equilibrium. The phase diagram comprises a sol phase, a coexistence region ending at a critical point, a gelation line determined by geometric percolation, and an equilibrium gel phase unrelated to phase separation. The global structure of the gel is homogeneous, but the stress is only supported by a fractal network. The gel dynamics is highly heterogeneous and we propose a theoretical model to quantitatively describe dynamic heterogeneity in gels. We elucidate several differences between the dynamics of gels and that of glass formers.

Surface and bulk dissolution properties, and selectivity of DNA-linked nanoparticle assemblies

Using a simple mean-field model, we analyze the surface and bulk dissolution properties of DNA-linked nanoparticle assemblies. We find that the dissolution temperature and the sharpness of the dissolution profiles increase with the grafting density of the single-stranded DNA "probes" on the surface of colloids. The surface grafting density is controlled by the linker occupation number, in analogy with quantum particles obeying fractional statistics. The dissolution temperature increases logarithmically with the salt concentration. This is in agreement with the experimental findings [R. Jin, G. Wu, Z. Li, C. A. Mirkin, and G. C. Schatz, J. Am. Chem. Soc. 125, 1643 (2003)]. By exploiting the unique phase behavior of DNA-coated colloids, it should be possible to detect multiple "targets" in a single experiment by essentially mapping the DNA base-pair sequence onto the phase behavior of DNA-linked nanoparticle solution.

Loose Complexation of Weakly Charged Microemulsion Droplets and a Polyelectrolyte

The effect of polyelectrolyte addition on the properties of an oil-in-water (O/W) microemulsion of weakly charged spherical micelles is studied. The 81 A radius O/W droplets in this system can be charged by the partial substitution of the nonionic surfactant by a cationic surfactant. The effect of the addition of poly(acrylic acid) (PAA), which is a charged pH-dependent polyelectrolyte, on the interactions between charged or noncharged droplets has been investigated using SANS. We have characterized the phase behavior of this pH-smart system as a function of the microemulsion and the polyelectrolyte concentration and the number of charges per droplet at three pH values: pH = 2, 4.5, and 12. In particular, an associative phase separation due to the bridging of the droplets by the neutral PAA chains through H-bonds is observed with extremely low PAA addition at low pH. At the opposite, an addition of PAA at pH = 4.5 generates a strong repulsive contribution between neutral droplets. Electrostatic bonds between charged droplets and PAA, controlled by the number of charges per droplet, are responsible for a pH drift and then for an associative phase separation similar to that observed at low pH. Finally, at high pH, the creation of electrostatic bonds between fully charged PAA and charged droplets liberates sufficiently counterions in solution at high droplet charge density to screen the electrostatic interactions and to allow an associative phase separation.

The immunity of polymer-microemulsion networks

The concept of network immunity, i.e., the robustness of the network connectivity after a random deletion of edges or vertices, has been investigated in biological or communication networks. We apply this concept to a self-assembling, physical network of microemulsion droplets connected by telechelic polymers, where more than one polymer can connect a pair of droplets. The gel phase of this system has higher immunity if it is more likely to survive (i.e., maintain a macroscopic, connected component) when some of the polymers are randomly degraded. We consider the distribution p(sigma) of the number of polymers between a pair of droplets, and show that gel immunity decreases as the variance of p(sigma) increases. Repulsive interactions between the polymers decrease the variance, while attractive interactions increase the variance, and may result in a bimodal p(sigma).

Disorder in DNA-linked gold nanoparticle assemblies

We report experimental observations on the effect of disorder on the phase behavior of DNA-linked nanoparticle assemblies. Variation in DNA linker lengths results in different melting temperatures of the DNA-linked nanoparticle assemblies. We observed an unusual trend of a nonmonotonic "zigzag" pattern in the melting temperature as a function of DNA linker length. Linker DNA resulting in unequal DNA duplex lengths introduces disorder and lowers the melting temperature of the nanoparticle system. Comparison with free DNA thermodynamics shows that such an anomalous zigzag pattern does not exist for free DNA duplex melting, which suggests that the disorder introduced by unequal DNA duplex lengths results in this unusual collective behavior of DNA-linked nanoparticle assemblies.

Phase behavior and selectivity of DNA-linked nanoparticle assemblies

We propose a model that can account for the experimentally observed phase behavior of DNA-nanoparticle assemblies [J. Am. Chem. Soc. 125, 1643 (2003)]; Science 289, 1757 (2000)]]. The binding of DNA-coated nanoparticles by dissolved DNA linkers can be described by exploiting an analogy with quantum particles obeying fractional statistics. In accordance with experimental findings, we predict that the phase-separation temperature of the nanocolloids increases with the DNA coverage of the colloidal surface. Upon the addition of salt, the demixing temperature increases logarithmically with the salt concentration. Our analysis suggests an experimental strategy to map microscopic DNA sequences onto the macroscopic phase behavior of the DNA-nanoparticle solutions. Such an approach should enhance the efficiency of methods to detect (single) mutations in specific DNA sequences.