Conformational Properties of Comb-shaped Polyelectrolytes with Negatively Charged Backbone and Neutral Side Chains Studied by a Generic Coarse-grained Bead-and-Spring Model

A generic coarse-grained bead-and-spring model,mapped onto comb-shaped polycarboxylate-based(PCE)superplasticizers,is developed and studied by Langevin molecular dynamics simulations with implicit solvent and explicit counterions.The agreement on the radius of gyration of the PCEs with experiments shows that our model can be useful in studying the equilibrium sizes of PCEs in solution.The effects of ionic strength,side-chain number,and side-chain length on the conformational behavior of PCEs in solution are explored.Single-chain equilibrium properties,including the radius of gyration,end-to-end distance and persistenee length of the polymer backbone,shape-asphericity parameter,and the mean span dimension,are determined.It is found that with the increase of ionic strength,the equilibrium sizes of the polymers decrease only slightly,and a linear dependenew of the persistence length of backbone on the Debye screening length is found,in good agreement with the theory developed by Dobrynin.Increasing side-chain numbers and/or side-chain lengths increases not only the equilibrium sizes(radius of gyration and mean span)of the polymer as a whole,but also the persistence length of the backbone due to excluded volume interactions.     

Simulation analysis of the temperature dependence of lignin structure and dynamics

Lignins are hydrophobic, branched polymers that regulate water conduction and provide protection against chemical and biological degradation in plant cell walls. Lignins also form a residual barrier to effective hydrolysis of plant biomass pretreated at elevated temperatures in cellulosic ethanol production. Here, the temperature-dependent structure and dynamics of individual softwood lignin polymers in aqueous solution are examined using extensive (17 μs) molecular dynamics simulations. With decreasing temperature the lignins are found to transition from mobile, extended to glassy, compact states. The polymers are composed of blobs, inside which the radius of gyration of a polymer segment is a power-law function of the number of monomers comprising it. In the low temperature states the blobs are interpermeable, the polymer does not conform to Zimm/Stockmayer theory, and branching does not lead to reduction of the polymer size, the radius of gyration being instead determined by shape anisotropy. At high temperatures the blobs become spatially separated leading to a fractal crumpled globule form. The low-temperature collapse is thermodynamically driven by the increase of the translational entropy and density fluctuations of water molecules removed from the hydration shell, thus distinguishing lignin collapse from enthalpically driven coil-globule polymer transitions and providing a thermodynamic role of hydration water density fluctuations in driving hydrophobic polymer collapse. Although hydrophobic, lignin is wetted, leading to locally enhanced chain dynamics of solvent-exposed monomers. The detailed characterization obtained here provides insight at atomic detail into processes relevant to biomass pretreatment for cellulosic ethanol production and general polymer coil-globule transition phenomena.     

Structure and dynamic properties of colloidal asphaltene aggregates

The abundant literature involving asphaltene often contrasts dynamic measurements of asphaltene solutions, highlighting the presence of small particle sizes between 1 and 3 nm, with static scattering measurements, revealing larger aggregates with a radius of gyration around 7 nm. This work demonstrates the complementary use of the two techniques: a homemade dynamic light scattering setup adapted to dark and fluorescent solutions, and small-angle X-ray and neutron scattering. Asphaltene solutions in toluene are prepared by a centrifugation separation to investigate asphaltene polydispersity. These experiments demonstrate that asphaltene solutions are made of Brownian colloidal aggregates. The hydrodynamic radii of asphaltene aggregates are between 5 and 10 nm, while their radii of gyration are roughly comparable, between 3.7 and 7.7 nm. A small fraction of asphaltenes with hydrodynamic and gyration radii around 40 nm is found in the pellet of the centrifugation tube. The fractal character of the largest clusters is observed from small angle scattering nearly on a decade length scale. Previous results on aggregation mechanisms are confirmed ( Eyssautier, J., et al. J. Phys. Chem. B 2011 , 115 , 6827 ): nanoaggregates of 3 nm radius, and with hydrodynamic properties also frequently illustrated in the literature, aggregate to form fractal clusters with a dispersity of aggregation number.     

良溶剂中环形高分子单链的结构与动力学性质的模拟研究

本文采用多粒子碰撞动力学与分子动力学耦合的模拟方法研究了环形高分子单链在良溶剂中的静态与动态性质,并与线形分子进行了对比.研究发现,环形高分子链内粒子之间的平均距离小于线形链,即粒子排列得更加紧密;相应的均方回转半径也小于线形链,线形链与环形链的均方回转半径的比值为1.77;同时,环形链扩散的速度也比线形链快,两者比值为1.10.模拟结果揭示了扩散行为是排斥体积作用和流体力学相互作用耦合的结果,在扩散过程中,流体力学相互作用消减了排斥体积作用对扩散行为的贡献.此外,通过对有和没有流体力学相互作用的多粒子碰撞动力学得到的结果作对比,研究了流体力学相互作用对高分子静态和动态行为的影响,结果表明,流体力学相互作用使高分子链在极稀溶液中的扩散速度变快.     

Estimation of the dynamic size of fractal aggregates

A model is presented for an aggregation act occurring between two aggregates of any mass and fractal dimension. The kinetics of aggregation is also analyzed, as well as some previous works concerning the structure of fractal aggregates. As a result, a generalized curve is derived describing the normalized dynamic radius of clusters of spherical character as dependent on both the aggregate fractal dimension and the space dimension. It is shown how the curve may be utilized to determine the dynamic size of anisotropic aggregates. The obtained dependence can be used to estimate the dynamic size of fractal aggregates, to evaluate the prefactor in mass–radius relation and to model the aggregation kinetics.     

线形、梳形和星形高分子静态和动态性质的模拟

以梳形高分子为纽带,基于粗粒化分子动力学模拟方法,研究了线形、梳形和星形拓扑结构高分子的静态和动态性质,以揭示稀溶液中高分子链行为与链拓扑结构依赖关系的一般性规律.研究结果表明,随着线形-梳形-星形的链拓扑结构转变,回转半径的标度关系由仅依赖分子聚合度转变为同时依赖链聚合度与臂数或侧链数.分析了星形高分子和梳形高分子的静态和动态性质的特征规律.星形高分子的臂数增加使其尺寸迅速减小,形状则由长椭球形转变为类球形,且扩散系数也随之增加;其均方回转半径(〈R_g〉)和扩散系数(D)与分子聚合度(N)及臂数(f)的标度规律为〈R_g〉~N~(0.581)f~(-0.402),D~N~(-0.763)f~(0.227).梳形高分子的静态与动态性质与分子聚合度及侧链数的依赖关系为〈R_g〉~N~(0.597)f~(-0.212)(每个支化点只有一条侧链)和〈R_g〉~N~(0.599)f~(-0.316)(每个支化点有多条侧链).     

Multiparticle sintering dynamics: from fractal-like aggregates to compact structures

Multiparticle sintering is encountered in almost all high temperature processes for material synthesis (titania, silica, and nickel) and energy generation (e.g., fly ash formation) resulting in aggregates of primary particles (hard- or sinter-bonded agglomerates). This mechanism of particle growth is investigated quantitatively by mass and energy balances during viscous sintering of amorphous aerosol materials (e.g., SiO(2) and polymers) that typically have a distribution of sizes and complex morphology. This model is validated at limited cases of sintering between two (equally or unequally sized) particles, and chains of particles. The evolution of morphology, surface area and radii of gyration of multiparticle aggregates are elucidated for various sizes and initial fractal dimension. For each of these structures that had been generated by diffusion limited (DLA), cluster-cluster (DLCA), and ballistic particle-cluster agglomeration (BPCA) the surface area evolution is monitored and found to scale differently than that of the radius of gyration (moment of inertia). Expressions are proposed for the evolution of fractal dimension and the surface area of aggregates undergoing viscous sintering. These expressions are important in design of aerosol processes with population balance equations (PBE) and/or fluid dynamic simulations for material synthesis or minimization and even suppression of particle formation.     

Light-scattering study of the aggregation of syndiotactic poly(methyl methacrylate) in solution.

Syndiotactic poly(methyl methacrylate (s-PMMA) may undergo aggregation in n-butyl chloride (n-BuCl) at temperatures below the theta temperature. The aggregation behavior of the s-PMMA with weight-average molecular weight M(w) =6.06 x 10(5) g mol(-1) was studied by a combination of static and dynamic laser-light-scattering experiments. A solution of concentration 1.12 x 10(-4) g mL(-1) was quenched from 50 degrees C (above the theta temperature in n-BuCl, 35 degrees C to 12 degrees C, and the aggregation process was measured over 60 h. The time dependence of M(w) the root-mean-square z-average radius of gyration < R(g) >, and the average hydrodynamic radius were used to monitor the growth of the aggregates, with the result M(w) approximately < R(g) > d(f) (where d(f) = 1.98 +/- 0.02), which implies the formation of a fractal aggregate. The observed fractal dimension, d(f), is close to that expected for a reaction-limited cluster aggregation for which d(f) = 2.1. In addition, atomic force microscopy was used to image the aggregates.     

Deposition of spherical particles onto cylindrical solid surfaces. I. Numerical simulations

The permeability of fractal porous aggregates with realistic three-dimensional structure is investigated theoretically using model aggregates composed of identical spherical primary particles. Synthetic aggregates are generated by several techniques, including a lattice-based method, simulation of aggregation by differential settling and turbulent shear, and the specification of simple cubic structures, resulting in aggregates characterized by the number of primary particles, solid fraction, characteristic radius, and fractal dimension. Stokesian dynamics is used to determine the total hydrodynamic force on and the distribution of velocity within an aggregate exposed to a uniform flow. The aggregate permeability is calculated by comparing these values with the total force and velocity distribution calculated from the Brinkman equation applied locally and to the entire aggregate using permeability expressions from the literature. The relationship between the aggregate permeability and solid fraction is found to be best predicted by permeability expressions based on cylindrical rather than spherical geometrical elements, the latter tending to underestimate the aggregate permeability significantly. The permeability expressions of Jackson and James or Davies provide good estimates of the force on and flow through porous aggregates of known structure. These relationships are used to identify a number of general characteristics of fractal aggregates.     

Hydrodynamic forces and critical stresses in low-density aggregates under shear flow

The distribution of stresses in rigid colloidal aggregates under a shear flow was investigated numerically for particle-cluster and cluster-cluster aggregates with fractal dimensions ranging from 1.7 to 2.3. stokesian dynamics was used to calculate the hydrodynamic force on each monomer, while the internal intermonomer interactions were calculated by applying force and torque balances on each primary particle. Although the hydrodynamic forces act mainly on the periphery of the clusters, their filamentous structure propagates and accumulates internal stresses toward the inner region of the aggregates, where consequently the most loaded intermonomer bonds are located. The spatial stress distribution, when scaled by the proper power of the radius of gyration, is independent of aggregate size and fractal dimension. This feature has made it possible to identify the most probable locations of bond failure in the structure and to estimate the relationship between shear rate and particle size for the occurrence of restructuring and of breakage.     

Prediction of three-dimensional fractal dimensions using the two-dimensional properties of fractal aggregates

Fractal dimension analysis using an optical imaging analysis technique is a powerful tool in obtaining morphological information of particulate aggregates formed in coagulation processes. However, as image analysis uses two-dimensional projected images of the aggregates, it is only applicable to one and two-dimensional fractal analyses. In this study, three-dimensional fractal dimensions are estimated from image analysis by characterizing relationships between three-dimensional fractal dimensions (D(3)) and one (D(1)) and two-dimensional fractal dimensions (D(2) and D(pf)). The characterization of these fractal dimensions were achieved by creating populations of aggregates based on the pre-defined radius of gyration while varying the number of primary particles in an aggregate and three-dimensional fractal dimensions. Approximately 2000 simulated aggregates were grouped into 33 populations based on the radius of gyration of each aggregate class. Each population included from 15 to 115 aggregates and the number of primary particles in an aggregate varied from 10 to 1000. Characterization of the fractal dimensions demonstrated that the one-dimensional fractal dimensions could not be used to estimate two- and three-dimensional fractal dimensions. However, two-dimensional fractal dimensions obtained statistically, well-characterized relationships with aggregates of a three-dimensional fractal characterization. Three-dimensional fractal dimensions obtained in this study were compared with previously published experimental values where both two-dimensional fractal and three-dimensional fractal data were given. In the case of inorganic aggregates, when experimentally obtained three-dimensional fractal dimensions were 1.75, 1.86, 1.83+/-0.07, 2.24+/-0.22, and 1.72+/-0.13, computed three-dimensional fractal dimensions using two-dimensional fractal dimensions were 1.75, 1.76, 1.77+/-0.04, 2.11+/-0.09, and 1.76+/-0.03, respectively. However, when primary particles were biological colloids, experimentally obtained three-dimensional fractal dimensions were 1.99+/-0.08 and 2.14+/-0.04, and computed values were both 1.79+/-0.08. Analysis of the three-dimensional fractal dimensions with the imaging analysis technique was comparable to the conventional methods of both light scattering and electrical sensing when primary particles are inorganic colloids.     

Development of knotting during the collapse transition of polymers

A dynamic Monte Carlo simulation of the collapse transition of polymer chains is presented. The chains are represented as self-avoiding walks on the simple cubic lattice with a nearest-neighbor contact potential to model the effect of solvent quality. The knot state of the chains is determined using the knot group procedure presented in the accompanying paper. The equilibrium knot spectrum and the equilibrium rms radius of gyration as functions of the chain length and the contact potential are reported. The collapse transition was studied following quenches from good-to poor-solvent conditions. Our results confirm the prediction that the newly formed globule is not yet at equilibrium, since it has not yet achieved its equilibrium knot spectrum. For our model system, the relaxation of the knot spectrum is about an order of magnitude slower than that of the radius of gyration. The collapse transition is also studied for a model in which both ends of the chain remain in good-solvent conditions. Over the time scale of these simulations, knot formation is frustrated in this inhomogeneous model, verifying that the mechanism of knotting is the tunneling of chain ends in and out of the globule.     

Polymer translocation through a nanopore: a two-dimensional Monte Carlo study

We investigate the problem of polymer translocation through a nanopore in the absence of an external driving force. To this end, we use the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. To overcome the entropic barrier without artificial restrictions, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau required for the polymer to completely exit the pore on either end. We find numerically that tau scales with the chain length N as tau approximately N(1+2nu), where nu is the Flory exponent. This is the same scaling as predicted for the translocation time of a polymer which passes through the nanopore in one direction only. We examine the interplay between the pore length L and the radius of gyration R(g). For LR(g), we find tau approximately N. In addition, we numerically find the scaling function describing crossover between short and long pores. We also show that tau has a minimum as a function of L for longer chains when the radius of gyration along the pore direction R( parallel) approximately L. Finally, we demonstrate that the stiffness of the polymer does not change the scaling behavior of translocation dynamics for single-segment dynamics.     

Mathematical modeling of polymer-induced flocculation by charge neutralization

A detailed mathematical model for flocculation of colloidal suspensions in presence of salts and polymers is described and validated. In former case, the classical DLVO theory, which accounts for relevant variables such as pH and salt concentration, is incorporated into a geometrically sectioned discrete population balance model. For processes involving polymers, flocculation via simple charge neutralization is modeled using a modified DLVO theory in which the effect of adsorbed polymer layers on van der Waals attraction is included. The fractal dimension of aggregates is obtained by dynamic scaling of experimental data for time evolution of mean aggregate size. The particle surface potential is assumed to be approximately equal to the zeta potential. The model predictions are in close agreement with experimental results for flocculation of colloidal hematite suspensions in the presence of KCl and polyacrylic acid at different concentrations. In particular, given values of model parameters, e.g., Hamaker constant, fractal dimension, surface potential, and thickness of adsorbed polymer layer, the model can realistically describe the kinetics of flocculation by a simple charge neutralization mechanism and track the evolution of floc size distribution. Representative examples of sensitivity of the flocculation model to perturbations in surface potential and fractal dimension and to modification in the DLVO theory for polymer-coated particles are included.     

Thermal restructuring of fractal clusters: the case of a strawberry-like core-shell polymer colloid

Thermal restructuring of fractal styrene-acrylate copolymer clusters dispersed in water has been investigated experimentally in the temperature range between 313 and 363 K. The particles constituting the clusters are of strawberry-like core-shell structure with a soft core and a rigid shell grafted on the core polymer chains. Due to the incomplete coverage of the core, the rather soft core may "flow out" through the open areas of the shell, leading to coalescence with the neighboring particles. The clusters were generated under diffusion-limited cluster aggregation conditions, and the restructuring kinetics was monitored by small-angle light scattering. Two sets of thermal restructuring experiments have been performed at various temperatures: (1) restructuring of growing clusters during aggregation and (2) restructuring of preformed clusters in the absence of aggregation. It is found that restructuring occurs only at temperature values above 323 K. In the absence of aggregation, restructuring leads to an increase of the fractal dimension and a decrease of the radius of gyration of the clusters. At sufficiently long times, both quantities reach a plateau value due to the presence of the grafted rigid shell, which constrains the coalescence of the soft core. A simple model, based on coalescence theory of liquid droplets and accounting for the incomplete coalescence and its dependence on temperature, has been developed to interpret the restructuring kinetics in the absence of aggregation. It is found that the proposed model can represent the measured experimental data well.     

Formation and structure of pachyman aggregates in dimethyl sulfoxide containing water

The aggregation of pachyman, β-(1 → 3)-D -glucan (M_w = 1.68 × 10⁵) from the Poria cocos mycelia, was investigated using static and dynamic laser light scattering (LLS) in dimethyl sulfoxide (DMSO) containing about 15% water, which leads to large aggregates. Both the time dependence of hydrodynamic radius and the angle dependence of the scattering intensity were used to calculate the fractal dimension (d_f) of the aggregates. The aggregation rate and average size of aggregates increase dramatically with increasing the polymer concentration from 1.7 × 10⁻⁴ g/mL to 8.6 × 10⁻⁴ g/mL, and with the decrease of the solvent quality, that is, water content from 13 to 15%. In the cases, the fractal dimensions change from 1.94 to 2.43 and from 1.92 to 2.54, respectively, suggesting that transforms of aggregation processes: a slow process called reaction-limited cluster aggregation (RLCA) to a fast process called diffusion-limited cluster aggregation (DLCA) in different polymer concentrations and water content. The fractal dimensions above 2 of the fast aggregation is larger than the 1.75 predicted for the ideal DLCA model, suggesting that the aggregation involves a restructuring process through the interchain hydrogen bonding interaction. There are no aggregates of pachyman in DMSO without water, but aggregates formed in the DMSO containing 15% water at 25°C as a compact structure. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3201–3207, 1999     

Modeling of polyethylene and poly (L-lactide) polymer blends and diblock copolymer: chain length and volume fraction effects on structural arrangement

Dissipative particle dynamics (DPD), a mesoscopic simulation approach, has been used to investigate the chain length effect on the structural property of the immiscible polyethylene (PE)/poly(L-lactide) (PLLA) polymer in a polymer blend and in a system with their diblock copolymer. In this work, the interaction parameter in DPD simulation, related to the Flory-Huggins interaction parameter chi, is estimated by the calculation of mixing energy for each pair of components in molecular dynamics simulation. The immiscibility property of PE and PLLA polymers induces the phase separation and exhibits different architectures at different volume fractions. In order to observe the structural property, the radius of gyration is used to observe the detailed arrangement of the polymer chains. It shows that the structure arrangement of a polymer chain is dependent on the phase structure and has a significantly different structural arrangement character for the very short chains in the homopolymer and copolymers. The chain length effect on the degree of stretching or extension of polymers has also been observed. As the chain length increases, the chain exhibits more stretching behavior at lamellae, perforated lamellae, and cylindrical configurations, whereas the chain exhibits a similar degree of stretching or extension at the cluster configuration.     

Influence of natural organic matter and ionic composition on the kinetics and structure of hematite colloid aggregation: implications to iron depletion in estuaries

The stability and aggregation behavior of iron oxide colloids in natural waters play an important role in controlling the fate, transport, and bioavailability of trace metals. Time-resolved dynamic light scattering experiments were carried out in a study of the aggregation kinetics and aggregate structure of natural organic matter (NOM) coated hematite colloids and bare hematite colloids. The aggregation behavior was examined over a range of solution chemistries, by adjusting the concentration of the supporting electrolyte-NaCl, CaCl2, or simulated seawater. With the solution pH adjusted so that NOM-coated and bare hematite colloids were at the same zeta potential, we observed a significant difference in colloid stability which results from the stability imparted to the colloids by the adsorbed NOM macromolecules. This enhanced stability of NOM-coated hematite colloids was not observed with CaCl2. Aggregate form expressed as fractal dimension was determined for both NOM-coated and bare hematite aggregates in both NaCl and CaCl2. The fractal dimensions of aggregates formed in the diffusion-limited regime indicate slightly more loosely packed aggregates for bare hematite than theory predicts. For NOM-coated hematite, a small decrease in fractal dimension was observed when the solution composition changed from NaCl to CaCl2. For systems in the reaction-limited regime, the measured fractal dimensions agreed with those in the literature. Colloid aggregation was also studied in synthetic seawater, a mixed cation system to simulate estuarine mixing. Those results describe the important phenomena of iron oxide aggregation and sedimentation in estuaries. When compared to field data from the Mullica Estuary, U.S.A., it is shown that collision efficiency is a good predictor of the iron removal in this natural system.     

Effects of hydrophobic substituents and salt on core-shell aggregates of hydrophobically modified chitosan: light scattering study

In this study we examine two methods of enhancement of aggregation of hydrophobically modified chitosan in dilute aqueous solutions: by increasing the content of n-dodecyl substituents, favoring hydrophobic association, and by increasing the amount of added low molecular weight salt, screening the electrostatic repulsion between similarly charged aggregating chains. By static and dynamic light scattering it was demonstrated that at the growth of the content of hydrophobic groups in the polymer (2-4 mol %) and of the amount of salt in solution (0.025-0.1 M) the weight fraction of aggregates increases, but the aggregation number remains unchanged. This behavior was attributed to the core-shell structure of the aggregates, which provides a low surface energy and strong attraction of associating groups inside the core. At the same time, the effects of the content of hydrophobic groups in the polymer and the ionic strength of the solution on the radii of the aggregates are quite different. Increasing the content of hydrophobic groups induces growth of the gyration radii of the aggregates, but does not affect their hydrodynamic radii. These data suggest the expansion of the hydrophobic core of the aggregates and the contraction of their highly swollen shell. On the other hand, increasing the salt concentration leads to a decrease of both the gyration and hydrodynamic radii of the aggregates, which is due to partial screening of electrostatic repulsion between similarly charged units and lowering of the osmotic pressure of counterions confined inside the aggregates.     

聚羧酸系高性能减水剂分子在稀溶液中尺寸及其在体积排除色谱表征中表观分子量的模型研究

针对被称为"第一代聚羧酸高性能减水剂"(以下简称为MPEG-type PCE)的甲基丙烯酸(MAA)/烯酸甲酯(MAA-MPEG)梳状共聚物分子,从高分子物理基础理论出发,构建等效自由连接链模型,结合前人的理论结果和实验数据,得到了MPEG-type PCE分子的回转半径、流体力学半径及其相应的支化参数的数学表达式.在此基础上,报道了以下三方面的工作:首先,将计算结果与文献中的实验结果进行比较,检验模型的合理性;其次,利用所建立的数学模型考察主链分子量、侧链分子量和侧链接枝密度对PCE分子的回转半径和流体力学半径的影响;最后,结合近年来发展的体积排除色谱分离理论,对PCE分子的真实分子量与其常规体积排除色谱"表观分子量"(又被称为GPC分子量)两者之间的差异进行了分析.本文所提出的计算模型和数学表达式没有不确定的指前因子,可用来估算MPEG-type PCE分子在稀水溶液中的尺寸以及根据其GPC分子量估算真实分子量.