The possibility of prescribing local interactions between nano- and microscopic components that direct them to assemble in a predictable fashion is a central goal of nanotechnology research. In this article we advance a new paradigm in which self-assembly of DNA-functionalized colloidal particles is programmed using linker oligonucleotides dispersed in solution. We find a phase diagram that is surprisingly rich compared to phase diagrams typical of other DNA-functionalized colloidal particles that interact by direct hybridization, including a re-entrant melting transition upon increasing linker concentration, and show that multiple linker species can be combined together to prescribe many interactions simultaneously. A new theory predicts the observed phase behavior quantitatively without any fitting parameters. Taken together, these experiments and model lay the groundwork for future research in programmable self-assembly, enabling the possibility of programming the hundreds of specific interactions needed to assemble fully-addressable, mesoscopic structures, while also expanding our fundamental understanding of the unique phase behavior possible in colloidal suspensions.
Developing construction methods of materials tailored for given applications with absolute control over building block placement poses an immense challenge. DNA-coated colloids offer the possibility of realising programmable self-assembly, which, in principle, can assemble almost any structure in equilibrium, but remains challenging experimentally. Here, we propose an innovative system of linker-mediated mobile DNA-coated colloids (mDNACCs), in which mDNACCs are bridged by the free DNA linkers in solution, whose two single-stranded DNA tails can bind with specific single-stranded DNA receptors…
Colloidal nanocrystal gels can be assembled using a difunctional "linker" molecule to mediate bonding between nanocrystals. The conditions for gelation and the structure of the gel are controlled macroscopically by the linker concentration and microscopically by the linker's molecular characteristics. Here, we demonstrate using a toy model for a colloid-linker mixture that linker flexibility plays a key role in determining both phase behavior and structure of the mixture. We fix the linker length and systematically vary its bending stiffness to span the flexible, semiflexible, and rigid regime…
We extend Wertheim's thermodynamic perturbation theory to derive the association free energy of a multicomponent mixture for which double bonds can form between any two pairs of the molecules' arbitrary number of bonding sites. This generalization reduces in limiting cases to prior theories that restrict double bonding to at most one pair of sites per molecule. We apply the new theory to an associating mixture of colloidal particles ("colloids") and flexible chain molecules ("linkers"). The linkers have two functional end groups, each of which may bond to one of several sites on the colloids. …
Colloids coated with single-stranded DNA (ssDNA) can bind selectively to other colloids coated with complementary ssDNA. The fact that DNA-coated colloids (DNACCs) can bind to specific partners opens the prospect of making colloidal `molecules'. However, in order to design DNACC-based molecules, we must be able to control the valency of the colloids, i.e. the number of partners to which a given DNACC can bind. One obvious, but not very simple approach is to decorate the colloidal surface with patches of single-stranded DNA that selectively bind those on other colloids. Here we propose a design…
Much work has studied effective interactions between micron-sized particles carrying linkers forming reversible, inter-particle linkages. These studies allowed understanding the equilibrium properties of colloids interacting through ligand-receptor interactions. Nevertheless, understanding the kinetics of multivalent interactions remains an open problem. Here, we study how molecular details of the linkers, such as the reaction rates at which inter-particle linkages form/break, affect the relative dynamics of pairs of cross-linked colloids. Using a simulation method tracking single binding/unbi…
We characterize the self-assembly of colloidal particles with surface mobile DNA linkers under kinetically limited valence conditions. For this, we put forward a computer simulation model that captures quantitatively the interplay between the main dynamic processes governing these systems and allows the simulation of the long time scales reached in experiments. The model is validated by direct comparison with available experimental results, showing an overall good agreement that includes measurements of the average effective valence and its probability distribution as a function of the density…
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, 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 self-assembly of crystals with a controllable number of layers. Specifically, we consider colloidal particles funct…
We construct a theoretical model for the dynamics of a microscale colloidal particle, modeled as an interval, moving horizontally on a DNA-coated surface, modelled as a line coated with springs that can stick to the interval. Averaging over the fast DNA dynamics leads to an evolution equation for the particle in isolation, which contains both friction and diffusion. The DNA-induced friction coefficient depends on the physical properties of the DNA, and substituting parameter values typical of a 1$μ$m colloid coated densely with weakly interacting DNA gives a coefficient about 100 times larger …
Kinetic Criticality in Linker-Mediated Colloidal Aggregation
Center for Functional Nanomaterials, Brookhaven National Laboratory（布鲁克海文国家实验室功能纳米材料中心）；Department of Chemical Engineering, Columbia University（哥伦比亚大学化学工程系）；Avram and Stella Goldstein-Goren Department of Biotechnology, Ben-Gurion University of the Negev（内盖夫本-古里安大学阿夫拉姆和斯特拉·戈德斯坦-戈尔恩生物技术系）；Department of Applied Physics and Applied Mathematics, Columbia University（哥伦比亚大学应用物理与应用数学系）；Center for Nanomedicine, Institute for Basic Science（基础科学研究所纳米医学中心）；Department of Nano Biomedical Engineering, Yonsei University（延世大学纳米生物工程系）
Low-density "equilibrium" gels that consist of a percolated, kinetically arrested network of colloidal particles and are resilient to aging can be fabricated by restricting the number of effective bonds that form between the colloids. Valence-restricted patchy particles have long served as one archetypal example of such materials, but equilibrium gels can also be realized through a synthetically simpler and scalable strategy that introduces a secondary linker, such as a small ditopic molecule, to mediate the bonds between the colloids. Here, we consider the case where the ditopic linker molecu…
In this paper, we theoretically study the electrostatic interaction between a pair of identical colloids with constant surface potentials sitting in close vicinity of each other at a fluid interface. By employing a simplified yet reasonable model system, the problem is solved within the framework of classical density functional theory and linearized as well as nonlinear Poisson-Boltzmann (PB) theory. Apart from providing a sound theoretical framework generally applicable to any such problem, our novel findings, all of which contradict common beliefs, include the following: first, quantitative …
The miniaturization of machines towards the micron and nanoscales requires the development of joint-like elements that enable and constrain motion. We present a facile method to create colloidal joints, that is, anisotropic colloidal particles containing surface mobile DNA linkers that control the motion range of bonded particles. We demonstrate quantitatively that we can control the flexibility of these colloidal joints by tuning the DNA linker concentration in the bond area. We show that the colloidal shape controls the range of motion that these colloidal joints enable, due to the finite-si…
The physical mechanism of elasticity of liquid surfaces coated with colloidal particles is proposed. It is suggested that particles are separated by water clearings and the capillary interaction between them is negligible. The case is treated when the colloidal layer is deformed normally to its surface. The elasticity arises as an interfacial effect. The effective Young modulus of a surface depends on the interfacial tension, equilibrium contact angle, radius of colloidal particles and their surface density. For the nanometrically scaled particles the line tension becomes essential and has an …
One of the challenges of self-assembling finite-sized colloidal aggregates with a sought morphology is the necessity of precisely sorting the position of the colloids at the microscopic scale to avoid the formation of off-target structures. Microfluidic platforms address this problem by loading into single droplets the exact amount of colloids entering the targeted aggregate. Using theory and simulations, in this paper, we validate a more versatile design allowing us to fabricate different types of finite-sized aggregates, including colloidal molecules or core-shell clusters, starting from fin…
Colloids that attractively bond to only a few neighbors (e.g., patchy particles) can form equilibrium gels with distinctive dynamic properties that are stable in time. Here, we use a coarse-grained model to explore the dynamics of linked networks of patchy colloids whose average valence is macroscopically, rather than microscopically, constrained. Simulation results for the model show dynamic hallmarks of equilibrium gel formation and establish that the colloid-colloid bond persistence time controls the characteristic slow relaxation of the self-intermediate scattering function. The model feat…
Just like atoms combine into molecules, colloids can self-organize into predetermined structures according to a set of design principles. Controlling valence -- the number of inter-particle bonds -- is a prerequisite for the assembly of complex architectures. The assembly can be directed via solid `patchy' particles with prescribed geometries to make, for example, a colloidal diamond. We demonstrate here that the nanoscale ordering of individual molecular linkers can combine to program the structure of microscopic assemblies. Specifically, we experimentally show that covering initially isotrop…
Grafting linkers with open ends of complementary single-stranded DNA makes a flexible tool to tune interactions between colloids,which facilitates the design of complex self-assembly structures. Recently, it has been proposed to coat colloids with mobile DNA linkers, which alleviates kinetic barriers without high-density grafting, and also allows the design of valency without patches.However, the self-assembly mechanism of this novel system is poorly understood.Using a combination of theory and simulation, we obtain phase diagrams forthe system in both two and three dimensional spaces, and fin…
The self-assembly of DNA-coated colloids into highly-ordered structures offers great promise for advanced optical materials. However, control of disorder, defects, melting, and crystal growth is hindered by the lack of a microscopic understanding of DNA-mediated colloidal interactions. Here we use total internal reflection microscopy to measure in situ the interaction potential between DNA-coated colloids with nanometer resolution and the macroscopic melting behavior. The range and strength of the interaction are measured and linked to key material design parameters, including DNA sequence, po…
We present a quantitative, multi-scale coarse-grained model of DNA coated colloids. The parameters of this model are transferable and are solely based on experimental data. As a test case, we focus on nano-sized colloids carrying single-stranded DNA strands of length comparable to the colloids' size. We show that in this regime, the common theoretical approach of assuming pairwise additivity of the colloidal pair interactions leads to quantitatively and sometimes even qualitatively wrong predictions of the phase behaviour of DNA-grafted colloids. Comparing to experimental data, we find that ou…
Colloidal structure, energy extensivity and Monte Carlo sampling properties of improved short-range interaction models for surfactant-coated magnetic nanoparticles
Self-assembly is traditionally described as the process through which an initially disordered system relaxes towards an equilibrium ordered phase only driven by local interactions between its building blocks. However, This definition is too restrictive. Nature itself provides examples of amorphous, yet functional, materials assembled upon kinetically arresting the pathway towards the ground state. Kinetic self-assembly is intrinsically more flexible and reliable than its equilibrium counterpart, allowing control over the morphology of the final phase by tuning both the interactions and the the…
Reliably distinguishing between cells based on minute differences in receptor density is crucial for cell-cell or virus-cell recognition, the initiation of signal transduction and selective targeting in directed drug delivery. Such sharp differentiation between different surfaces based on their receptor density can only be achieved by multivalent interactions. Several theoretical and experimental works have contributed to our understanding of this "superselectivity", however a versatile, controlled experimental model system that allows quantitative measurements on the ligand-receptor level is …
In order to study linker-mediated aggregation of colloidal particles with limited valence, we combine kinetic Monte Carlo simulations and an approximate theory based on the Smoluchowski equations. We found that aggregation depends strongly on two parameters, the ratio of the number of linkers and particles and the ratio of their diffusion coefficients. These control parameters are absent in single-species aggregation and provide a much greater variety and control of the resulting structures. We show that aggregation is non-trivial when two time scales of aggregation are present. Our aggregatio…
Colloidal particles partially coated with platinum and dispersed in H2O2 solution are often used as model self-propelled colloids. Most current data suggest that neutral self-diffusiophoresis propels these particles. However, several studies have shown strong ionic effects in this and related systems, such as a reduction of propulsion speed by salt. We investigate these ionic effects in Pt-coated polystyrene colloids, and find here that the direction of propulsion can be reversed by addition of an ionic surfactant, and that although adding pH neutral salts reduces the propulsion speed, adding …
By exploiting the exquisite selectivity of DNA hybridization, DNA-Coated Colloids (DNACCs) can be made to self-assemble in a wide variety of structures. The beauty of this system stems largely from its exceptional versatility and from the fact that a proper choice of the grafted DNA sequences yields fine control over the colloidal interactions. Theory and simulations have an important role to play in the optimal design of self- assembling DNACCs. At present, the powerful model-based design tools are not widely used, because the theoretical literature is fragmented and the connection between di…
At the heart of the structured architecture and complex dynamics of biological systems are specific and timely interactions operated by biomolecules. In many instances, biomolecular agents are spatially confined to flexible lipid membranes where, among other functions, they control cell adhesion, motility and tissue formation. Besides being central to several biological processes, \emph{multivalent interactions} mediated by reactive linkers confined to deformable substrates underpin the design of synthetic-biological platforms and advanced biomimetic materials. Here we review recent advances o…
Spin-coating technique is very fast, cheap, reproducible, simple and needs less material to fabricate films of particulate systems/colloids. Their thickness and uniformity may be controlled by means of external fields. We apply magnetic fields during the spin-coating of a moderately concentrated superparamagnetic colloid (made of silica coated magnetite particles). We study the influence of different magnetic field configurations (homogeneous and inhomogeneous) on the resulting spin-coated deposits and compare experimental results under various conditions. Superparamagnetic colloids behave as,…
DNA-coated colloids can self-assemble into an incredible diversity of crystal structures, but applications of this technology are limited by poor understanding and control over the dynamical crystallization pathways. To address this challenge, we use microfluidics to quantify the self-assembly dynamics of DNA-programmed colloidal crystals, from thermally-activated nucleation through reaction-limited and diffusion-limited phases of crystal growth. Our detailed measurements of the temperature and concentration dependence of the kinetics at all stages along the crystallization pathway provide a s…
DNA plays a special role in polymer science not just because of the highly selective recognition of complementary single DNA strands but also because bacteria can express DNA chains that are very long yet perfectly monodisperse. The latter reason makes long DNA molecules widely used as model systems in polymer science. Here, we report the unusual self-assembly that takes place in systems of colloids coated with very long double-stranded DNA. In particular, we find that colloids coated with such long DNA can assemble into unique floating crystalline monolayers. Floating colloidal structures hav…
We report a study of reversible adsorption of DNA-coated colloids on complementary functionalized oil droplets. We show that it is possible to control the surface coverage of oil droplets by colloidal particles, by exploiting the fact that during slow adsorption, compositional arrest takes place well before structural arrest occurs. As a consequence, we can prepare colloid-coated oil droplets with a `frozen' degree of loading, but with fully ergodic colloidal dynamics on the droplets. We illustrate the equilibrium nature of the adsorbed colloidal phase by exploring the quasi two-dimensional (2…
Understanding multibody interactions between colloidal particles out of equilibrium has a profound impact on dynamical processes such as colloidal self assembly. However, traditional colloidal interactions are effectively quasi-static on colloidal timescales and cannot be modulated out of equilibrium. A mechanism to dynamically tune the interactions during colloidal contacts can provide new avenues for self assembly and material design. In this work, we develop a framework based on polymer-coated colloids and demonstrate that in-plane surface mobility and mechanical relaxation of polymers at c…
A heterogeneous and dilute suspension of catalytically active colloids is studied as a non-equilibrium analogue of ionic systems, which has the remarkable feature of action-reaction symmetry breaking. Symmetrically coated colloids are found to join up to form self-assembled molecules that could be inert or have spontaneous activity in the form of net translational velocity and spin depending on their symmetry properties and their constituents. The type of activity can be adjusted by changing the surface chemistry and ambient variables that control the surface reactions and the phoretic drift.
Phase Behavior and Selectivity of DNA-linked Nanoparticle Assemblies
我们提出了一个模型，可以解释实验观察到的DNA-纳米粒子组装体的相行为（R。Jin等人，JACS 125，1643（2003）; T. A. Taton等人，Science 289，1757（2000））。溶解的DNA连接体与DNA包覆的纳米颗粒的结合可以通过利用服从分数统计的量子颗粒的类比来描述。根据实验结果，我们预测的纳米胶体的相分离温度增加的DNA覆盖的胶体表面。加入盐后，分层温度随盐浓度的增加而增加。我们的分析提出了一种实验策略，将微观DNA序列映射到DNA纳米颗粒溶液的宏观相行为上。这种方法应该提高检测特定DNA序列中（单个）突变的方法的效率。
Virtually all clinical applications of magnetic nanoparticles (MNPs) require the formulation of biocompatible, water-based magnetic colloids. For magnetic hyperthermia, the requirements also include a high colloidal stability against precipitation and agglomeration of the constituent MNPs, in order to keep the heating efficiency of the ferrofluid in the long term. The specific power absorption (SPA) of single-domain MNPs depends critically on the average particle size and size distribution width, therefore first-rate reproducibility among different batches regarding these parameters are also n…
We study the non-equilibrium coarsening dynamics of a binary liquid solvent around a colloidal particle in a presence of a time-dependent temperature gradient that emerges after temperature quench of a suitably coated colloid surface. The solvent is maintained at its critical concentration and the colloid is fixed in space. The coarsening patterns near the surface are shown to be strongly dependent on the colloid surface adsorption properties and on the temperature evolution. The temperature gradient alters the morphology of a binary solvent near the surface of a colloid as compared to the coa…
We study experimentally and numerically a (quasi) two dimensional colloidal suspension of self-propelled spherical particles. The particles are carbon-coated Janus particles, which are propelled due to diffusiophoresis in a near-critical water-lutidine mixture. At low densities, we find that the driving stabilizes small clusters. At higher densities, the suspension undergoes a phase separation into large clusters and a dilute gas phase. The same qualitative behavior is observed in simulations of a minimal model for repulsive self-propelled particles lacking any alignment interactions. The obse…
Catalytically active colloids maintain non-equilibrium conditions in which they produce and deplete chemicals and hence effectively act as sources and sinks of molecules. While individual colloids that are symmetrically coated do not exhibit any form of dynamical activity, the concentration fields resulting from their chemical activity decay as $1/r$ and produce gradients that attract or repel other colloids depending on their surface chemistry and ambient variables. This results in a non-equilibrium analogue of ionic systems, but with the remarkable novel feature of action-reaction symmetry b…
Immediately before adsorption to a horizontal substrate, sinking polymer-coated colloids can undergo a complex sequence of landing, jumping, crawling and rolling events. Using video tracking we studied the soft adhesion to a horizontal flat plate of micron-size colloids coated by a controlled molar fraction $f$ of the polymer PLL-g-PNIPAM which is temperature sensitive. We ramp the temperature from below to above $T_c=32\pm 1^{\circ}$C, at which the PNIPAM polymer undergoes a transition triggering attractive interaction between microparticles and surface. The adsorption rate, the effective in-…
Recent surveys have shown that the number of nanoparticle-based formulations actually used at the clinical level is significantly lower than expected a decade ago. One reason for this is that the nanoparticle physicochemical properties fall short for handling the complexity of biological environments and for preventing nonspecific protein adsorption. In this study, we address the issue of the interactions of plasma proteins with polymer coated surfaces. To this aim, we use a non-covalent grafting-to method to functionalize iron oxide sub-10 nm nanoparticles and iron oxide flat substrates, and …
The connection between fundamental interactions acting in molecules in a fluid and macroscopically measured properties, such as the viscosity between colloidal particles coated with polymers, is studied here. The role that hydrodynamic and Brownian forces play in colloidal dispersions is also discussed. It is argued that many body systems in which all these interactions take place can be accurately solved using computational simulation tools. One of those modern tools is the technique known as dissipative particle dynamics, which incorporates Brownian and hydrodynamic forces, as well as basic …
Anisotropic particles oriented in a specific direction can act as artificial atoms and molecules, and their controlled assembly can result in a wide variety of ordered structures. Towards this, we demonstrate the orientation transitions of uncharged peanut-shaped polystyrene colloids, suspended in a non-ionic aprotic polar solvent, near a flat surface whose potential is static or time-varying. The charged surface is coated with an insulating dielectric layer to suppress electric currents. The transition between several orientation states such as random, normal or parallel orientation with resp…
DNA-coated colloids are a popular model system for self-assembly through tunable interactions. The DNA-encoded linkages between particles theoretically allow for very high specificity, but generally no directionality or long-range interactions. We introduce a two-dimensional lattice model for particles of many different types with short-range isotropic interactions that are pairwise specific. For this class of models, we address the fundamental question whether it is possible to reliably design the interactions so that the ground state is unique and corresponds to a given crystal structure. Fi…
Recently \1, we presented a general theory for calculat- ing the strength and properties of colloidal interactions mediated by ligand-receptor bonds (such as those that bind DNA-coated colloids). In this communication, we derive a surprisingly simple analytical form for the inter- action free energy, which was previously obtainable only via a costly numerical thermodynamic integration. As a result, the computational effort to obtain potentials of in- teraction is significantly reduced. Moreover, we can gain insight from this analytic expression for the free energy in limiting cases. In particu…
Nonlinear second-harmonic magnetic response (M2) was used to characterize an aqueous colloidal solution of dextran-coated magnetite (Fe3O4) nanoparticles. Data analysis with the formalism based on Gilbert-Landau-Lifshitz equation for stochastic dynamics of superparamagnetic (SP) particles ensured extensive quantifying of the system via a set of magnetic and magnetodynamic parameters, such as the mean magnetic moment, the damping constant, the longitudinal relaxation time, the magnetic anisotropy field and energy, and others. Combined with transmission electron microscopy and dynamic light scat…
