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Gaussian effective interaction between flexible dendrimers of fourth generation: A theoretical and experimental study
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We propose a theory for the effective interaction between soft dendritic molecules that is based on the shape of the monomer density profile of the macromolecules at infinite dilutions. By applying Flory-type arguments and making use of the experimentally measured density profiles, we derive a Gaussian effective interaction whose parameters are determined by the size and monomer number of the dendrimers that are derived from small-angle neutron scattering (SANS) measurements. By applying this theory to concentrated dendrimer solutions we calculate theoretical structure factors and compare them with experimental ones, derived from a detailed analysis of SANS-data. We find very good agreement between theory and experiment below the overlap concentration, where drastic shape deformations of the dendrimers are absent. © 2002 American Institute of Physics.
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... Ultrasoft colloids, such as dendrimers and star polymers, are featured by extraordinary molecular flexibility [1][2][3][4][5][6]. The amount of elastic energy stored by such a particle that undergoes a large strain can be just hundreds of or even tens of the thermal energy [7][8][9][10], which distinguishes it from emulsions, most microgels, or other common deformable particles [10][11][12][13][14][15][16][17]. Consequently, ultrasoft colloids exhibit significant thermal-activated molecular fluctuations. ...
... Many SAS analyses deteriorate at volume fractions higher than about 10%. For example, the calculated SAS curve may not match the position or height of the main peak [7,9] or underestimate the intensity at small Q (Q is the scattering vector) [39,40]. Thus, it is possible that the fluctuation effect is important in interpreting the SAS data of ultrasoft colloids and can be extracted by reasonable modeling. ...
... Thus, the fluctuation effect is expected to be more considerable in dendrimers. Their ultrasoftness can be characterized by a Gaussian-like interparticle pair potential with an amplitude tens times the thermal energy [9]. Deuterium oxide (D 2 O) was acquired from Cambridge Isotope Laboratories, Inc., Andover, MA, USA. ...
An ultrasoft colloidal particle fluctuates due to its flexibility. Such fluctuation is essential for colloidal structure and dynamics, but is challenging to quantify experimentally. We use dendrimers as a model system to study the fluctuation of ultrasoft colloids. By considering the dynamic polydispersity in the small-angle neutron scattering (SANS) model and introducing the fluctuation of invasive water into the contrast in SANS, we reveal the fluctuating amplitudes of the size and shape of the dendrimer of generation 6 at finite concentrations. The size fluctuation is suppressed while the shape fluctuation increases as the weight fraction of dendrimers passes 11%. With neutron spin echo data, we suggest that such a crossover originates from the competition between the inter- and intraparticle dynamics. Further investigation on lower-generation samples shows a contrary result, which suggests a structural basis for these dynamic phenomena.
... Ultrasoft colloids, such as dendrimers and star polymers, are featured by extraordinary molecular flexibility [1][2][3][4][5][6]. The elastic energy stored by such a particle that undergoes a large strain can be just hundreds of or even tens of the thermal energy [7][8][9][10], which distinguishes them from emulsions, most microgels, or other common deformable particles [10][11][12][13][14][15][16][17]. Consequently, ultrasoft colloids exhibit significant molecular fluctuations. ...
... Many SAS analyses deteriorate at volume fractions higher than about 10%. For example, the calculated SAS curve may not well match the position or height of the main peak [7,9], or underestimate the intensity at small Q (Q is the scattering vector) [35]. Thus, it is possible that the fluctuation effect is important in interpreting the SAS data of ultrasoft colloids, and can be extracted by reasonable modelling. ...
... where n p is the number density of dendrimer molecules, A denotes the contrast of the scattering length between solute particle and solvent, P (Q) is the average form factor normalized at Q = 0, and S (Q) is the apparent structure factor given by S (Q) = 1 + β(Q)[S(Q) − 1], where β(Q) is the polydispersity factor [37] that incor-porates the size and shape fluctuations into the analysis, and S(Q) is the inter-particle structure factor. S(Q) is calculated by the Percus-Yevick closure of the Ornstein-Zernike equation [38] with a Gaussian pair potential [9]. We first explore the size fluctuation by modeling the fluctuating dendrimers as a collection of polydisperse spheres. ...
Ultrasoft colloidal particle fluctuates due to its flexibility. Such fluctuation is essential for colloidal structure and dynamics, but is challenging to quantify experimentally. We use dendrimers as a model system to study the fluctuation of ultrasoft colloids. By considering the dynamic polydispersity in the small-angle neutron scattering (SANS) model, and introducing the fluctuation of invasive water into the contrast in SANS, we reveal the fluctuating amplitudes of the size and shape of the dendrimer of generation 6 at finite concentrations. The size fluctuation is suppressed while the shape fluctuation increases as the weight fraction of dendrimers passes 11%. With neutron spin echo data, we suggest that such crossover originates from the competition between the inter- and intra-particle dynamics. Further investigation on lower-generation samples shows a contrary result, which suggests a structural basis for these dynamic phenomena.
... Furthermore, the dendrimer conformation can be influenced by the solvent [239][240][241][242]. However, in general, limited conformational changes are observed in neutral, high-generation dendrimers thanks to their dense core, as demonstrated by their use as model nanoparticles with tunable stiffness [237,241,243,244]. ...
... The choice of the Gaussian pair potential represents a good approximation of the effective interaction between the centers of mass of ultrasoft colloids such as linear polymers chains and dendrimers. 37,[43][44][45][46][47][48] The equilibrium properties of soft Gaussian particles described by Eq. 28 are well represented by a weakly correlated mean-field fluid over a surprisingly wide density and temperature range, being more accurate for increasing particle densities. 37 In addition, the accuracy of mean-field DFT approach for bistable systems has been recently probed comparing the theoretical predictions for (active) two-state switching Gaussian colloids to reactive Brownian Dynamics simulation, finding good quantitative agreement. ...
Macromolecular crowding typically applies to biomolecular and polymer-based systems in which the individual particles often feature a two-state folded/unfolded or coil-to-globule transition, such as found for proteins and peptides, DNA and RNA, or supramolecular polymers. Here, we employ a mean-field density functional theory (DFT) of a model of soft and bistable responsive colloids (RCs) in which the size of the macromolecule is explicitly resolved as a degree of freedom living in a bimodal 'Landau' energy landscape (exhibiting big and small states), thus directly responding to the crowding environment. Using this RC-DFT we study the effects of self-crowding on the liquid bulk structure and thermodynamics for different energy barriers and softnesses of the bimodal energy landscape, in conditions close to the coil-to-globule transition. We find substantial crowding effects on the internal distributions, a complex polydispersity behavior, and quasi-universal compression curves for increasing (generalized) packing fractions. Moreover, we uncover distinct signatures of bimodal versus unimodal behavior in the particle compression. Finally, the analysis of the pair structure - derived from the test particle route - reveals that the microstructure of the liquid is quite inhomogeneous due to local depletion effects, tuneable by particle softness.
... Diffusion of particles in suspensions is widely encountered in nature and science, for example the silica nanoparticles in polyethylene glycol [1], polymer coils in solution [2], dendrimer solutions [3][4][5][6] and protein solution [7,8], polystyrene nanoparticles [9]. The investigation of diffusion of particles in suspensions must take into account both hydrodynamic and Brownian effects. ...
The diffusion of particles in suspension is investigated by a thermostat based on fluctuating hydrodynamics for dynamic simulations of implicit-solvent coarse-grained model which can take into account both hydrodynamic and Brownian effects. Particles with cut-and-shifted Lennard-Jones and Gaussian-core potential are studied. The results show that their diffusion process can be characterized by three regimes: ballistic motion, short-time diffusion and long-time diffusion. We observe that the mean square displacement (MSD) of regime I, ballistic motion, is proportional to t2. For the other two regimes, its MSD is proportional to t with different slopes. Furthermore, we study the diffusion coefficients of spherical particles from MSD at different volume fractions. For the cut-and-shifted Lennard-Jones potential model, we observe the diffusion coefficients decrease monotonously with the increase of volume fraction (0.02–0.3), consistent with the results of the experiment. However, for the Gauss-core potential model, the curve of long-time self-diffusion coefficient as a function of dimensional density (0.001 to 1) appears to be nonmonotonic. It shows that the long-time self-diffusion coefficient decreases monotonically when the dimensional density is below 0.3, and then increases anomalously when the dimensionless density passes through 0.3.
A combined experimental and theoretical study of the structural correlations in moderately concentrated suspensions of all‐DNA dendrimers of the second generation (G2) with controlled scaffold rigidity is reported here. Small‐angle X‐ray scattering experiments in concentrated aqueous saline solutions of stiff all‐DNA G2 dendritic constructs reveal a novel anomalous liquid‐like phase behavior which is reflected in the calculated structure factors as a two‐step increase at low scattering wave vectors. By developing a new design strategy for adjusting the particle's internal flexibility based on site‐selective incorporation of single‐stranded DNA linkers into the dendritic scaffold, it is shown that this unconventional type of self‐organization is strongly contingent on the dendrimer's stiffness. A comprehensive computer simulation study employing dendritic models with different levels of coarse‐graining, and two theoretical approaches based on effective, pair‐potential interactions, remarkably confirmed the origin of this unusual liquid‐like behavior. The results demonstrate that the precise control of the internal structure of the dendritic scaffold conferred by the DNA can be potentially used to engineer a rich palette of novel ultrasoft interaction potentials that could offer a route for directed self‐assembly of intriguing soft matter phases and experimental realizations of a host of unusual phenomena theoretically predicted for ultrasoft interacting systems.
Dendrimers represent an entirely new class of macromolecules. They are ideal for water remediation by chemisorption as well as absorption because they have dense terminal functionality and internal cavities. In this research, as raw material, we used 1,3-bis(4,6-dichloro-1,3,5-triazine-2-yl)urea, triazine trichloride, and diethanolamine to develop nanoscale hydroxyl-terminated triazine-based dendrimer up to generations three. FT-IR, 1H NMR, 13C NMR and TEM measurements were used to characterize the structure of the dendrimer. In a series of experiments, full generation dendrimers G1, G2, and G3 were evaluated for Cu+2 and Cd+2 ions uptake from water. Copper and cadmium ion uptake capacity was studied over a variety of dendrimer generation, time and pH conditions. The overall results indicate an increase in generation, time, and pH, Cu+2 and Cd+2 ions uptake augmenting. FT-IR analyses of dendrimer-metal complexes confirmed the presence of metal in the dendrimer.
Using concepts from classical density functional theory, we investigate the freezing of a two-dimensional system of ultrasoft particles in a one-dimensional external potential, a phenomenon often called laser-induced freezing (LIF). In the first part of the paper, we present numerical results from free minimization of a mean-field density functional for a system of particles interacting via the GEM-4 potential. We show that the system does indeed display a LIF transition, although the interaction potential is markedly different from the cases studied before. We also introduce a suitably defined effective density within the potential wells ρ¯eff as a control parameter of LIF, rather than the amplitude of the external potential as in the common LIF scenario. In the second part, we suggest a theoretical description of the onset of LIF which is based on the pressure-balance equation relating the pressure tensor and the external potential. Evaluating this equation for the modulated liquid phase at effective density ρ¯eff and combining it with the (known) stability threshold of the corresponding bulk fluid, we can predict the critical effective density or, equivalently, the potential amplitude related to the onset of LIF. Our approach yields very good results for the model at hand and it is transferable, in principle, to other model systems.
We investigate the magnitude of density jumps across phase transitions
in soft-matter systems composed of macromolecular particles, like star
polymers or colloidal suspensions. The standard route to predict phase
transformations is to start from an effective interaction potential
between these macroparticles and map the phase diagram onto that of the
corresponding effective one-component system. Using density-functional
perturbation theory, we demonstrate that this procedure leads to wrong
density jumps if the number of microscopic degrees of freedom is coupled
to the number of macroparticles. In particular, the microscopic degrees
of freedom can drive a macroparticle phase transition to be isochoric,
i.e., to occur without any jump in the macroparticle density.
The analysis of dendrimers of fourth (G4) and fifth generation (G5) by small-angle Neutron scattering (SANS) in solution is presented. The contrast of the solute towards the solvent is changed systematically in order to elucidate the radial scattering length density (contrast variation). Contrast variation allows to determine the molecular weight of the dendrimers without additional assumptions. The data obtained here demonstrate that the dendrimer of fourth generation is a perfect structure whereas G5 has defects. Moreover, the analysis demonstrates that both dendrimer under consideration here have a compact structure where the density has its maximum at the center of the molecule.
Combining statistical-mechanical theories and neutron-scattering techniques, we show that the effective pair potential between star polymers is exponentially decaying for large distances and crosses over, at a density-dependent corona diameter, to an ultrasoft logarithmic repulsion for small distances. We also make the theoretical prediction that in concentrated star polymer solutions, this ultrasoft interaction induces an anomalous fluid structure factor which exhibits an unusually pronounced second peak.
The progression of the intramolecular organizations within dilute PAMAM
dendrimers are examined by use of small angle x-ray scattering (SAXS)
combined with comparisons to various electron density models. The SAXS
from dilute solutions of generation 3 (G3) PAMAM dendrimers is shown to
have scattering features simular to those of star molecules. This
contrasts with the SAXS from much larger G10 PAMAM dendrimers which
exhibits at least four clearly resolvable secondary maxima. These
features are successfully modeled by a system of constant density
spheres with a small amount of polydispersity. Scattering from
intermediate sized G4, G5, and G6 dendrimers maintain a consistent
evolution of internal structure progressing from ``star like'' to ``hard
sphere'' behavior.
In this work, we present a review of recently achieved progress in the field of soft condensed matter physics, and in particular on the study of the static properties of solutions or suspensions of colloidal particles. The latter are macromolecular entities with typical sizes ranging from 1 nm to 1mum and their suspension typically contain, in addition to the solvent, smaller components such as salt ions or free polymer chains. The theoretical tool introduced is the effective Hamiltonian which formally results by a canonical trace over the smaller degrees of freedom for a fixed, ``frozen'' configuration of the large ones. After presenting the formal definitions of this effective Hamiltonian, we proceed with the applications to some common soft matter systems having a variable softness and ranging from free polymer chains to hard colloidal particles. We begin from the extreme case of nondiverging effective interactions between ultrasoft polymer chains and derive an exact criterion to determine the topology of the phase diagrams of such systems. We use star polymers with a variable arm number /f as a hybrid system in order to interpolate between these two extremes. By deriving an effective interaction between stars we can monitor the change in the phase behavior of a system as the steepness of the repulsion between its constituent particles increases. We also review recent results on the nature and the effects of short-range attractions on the phase diagrams of spherical, nonoverlapping colloidal particles.
Starburst dendrimers are three-dimensional, highly ordered oligomeric and polymeric compounds formed by reiterative reaction sequences starting from smaller molecules—“initiator cores” such as ammonia or pentaerythritol. Protecting group strategies are crucial in these syntheses, which proceed via discrete “Aufbau” stages referred to as generations. Critical molecular design parameters (CMDPs) such as size, shape, and surface chemistry may be controlled by the reactions and synthetic building blocks used. Starburst dendrimers can mimic certain properties of micelles and liposomes and even those of biomolecules and the still more complicated, but highly organized, building blocks of biological systems. Numerous applications of these compounds are conceivable, particularly in mimicking the functions of large biomolecules as drug carriers and immunogens. This new branch of “supramolecular chemistry” should spark new developments in both organic and macromolecular chemistry.
What have Apollo, Voyager, Magellan and Galileo told us about the solar system? In Our Worlds, eight planetary scientists explain what we know about their favourite world and why they find it fascinating to explore with space age techniques. Writing from a personal point of view, the distinguished researchers give a unique insight into planetary science during today's golden age of discovery. With passion and punch, the authors describe the most enticing discoveries about their subject. In this voyage of exploration you meet Mars, Venus, and the Moon, take a trip with Comet Halley, visit the moons Io, Titan, and Triton, and see asteroids close up. This is an insider's perspective written for a general readership by scientists at the cutting edge.
Urea-functionalized dendrimers are prepared which show very efficient phase transfer, in particular of the diagnostically relevant anions pertechnetate, perrhenate and ATP; the extractability rates are evaluated quantitatively by tracer methods; their pH dependancy allows controlled release of guest molecules from the dendrimer host.
Using small-angle neutron scattering and liquid integral equation theory, we relate the structure factor of flexible dendrimers of th generation to their average shape. The shape is measured as a radial density profile of monomers belonging to a single dendrimer. From that, we derive an effective interaction of Gaussian form between pairs of dendrimers and compute the structure factor using the hypernetted chain approximation. Excellent agreement with the corresponding experimental results is obtained, without the use of adjustable parameters. The present analysis thus strongly supports the previous finding that flexible dendrimers of low generation present fluctuating structures akin to star polymers.
Solutions of the poly(propylene imine) dendrimers DAB-dendr-(PA)32 and DAB-dendr-(PA)64 in methanol are investigated with small angle neutron scattering over the range of dendrimer mass fraction 0.01 ≤ x ≤ 0.80. The single particle scattering function, P(q), is used to calculate the structure factor, S(q), of the dendrimer solutions and to evaluate the radius of gyration of the dendrimers in dilute solution giving (DAB-dendr-(PA)32) = 12.4 ± 0.2 Å and (DAB-dendr-(PA)64) = (15.6 ± 0.2) Å. In each case the segment density in dilute solution is 0.35 ± 0.03 g cm-3, leaving a large fraction of the dendrimer volume accessible to solvent. We define the “dilute solution regime” for dendrimers to extend to a concentration where the swollen dendrimer volume fraction first equals the value 0.64, which comes at a dendrimer weight fraction of x = 0.25. At this concentration, the spatial arrangement of the dendrimers can be described as a random close packing. For higher concentrations, the experimental scattering functions appear to be self-similar up to a mass fraction of x ≈ 0.60. These observations are consistent with a model of concentrated dendrimer solutions which assumes that individual dendrimers collapse to maintain a volume fraction φ ≈ 0.64, which is the volume fraction of random close packing of hard spheres. Preliminary small X-ray scattering data give further evidence of the dendrimer collapse.