Center Of Mass Diffusion Research Articles

Macromolecule and Particle Dynamics in Confined Media

Dynamic properties play an important role in designing functional polymer nanocomposites, impacting molecular transport and phase separation kinetics. When nanoparticle (NP) size is comparable to polymer chain size, segmental relaxations may be influenced by changes in chain conformations and packing at the polymer/NP interface. Following the reptation model, these changes can perturb the longest relaxation time, in particular, the center-of-mass (COM) dynamics of polymer chains in entangled melts. This Perspective focuses on unsolved issues in polymer COM diffusion and local dynamics and segmental motions in the presence of NPs. The article introduces the effect of NP size, shape, surface modification, and enthalpic interactions on polymer diffusion and further relates dynamic studies in PNCs to macromolecular transport in bio-related systems and nanopores. Studies of local dynamics also provide insights into how entanglement density, monomeric friction, and chain conformation are influenced by NPs and h...

Transport of acetylene adsorbed in CuBTC metal organic framework

Metal organic frameworks (MOFs) are an important class of material which has a potential to be used for variety of applications such as in storage materials, pollution control, etc. Here we report a molecular dynamics simulation study investigating dynamical behaviour of the smallest and linear hydrocarbon, acetylene, adsorbed in CuBTC MOF. CuBTC has complex network structure consisting of large pores and tetrahedral pockets connected by windows. Calculated mean squared displacements of the acetylene molecules adsorbed in CuBTC showed anomalous behaviour with change in concentration. This has been understood by studying the evolution of the trajectories and free energy map. There are two pathways for an acetylene molecule to diffuse inside CuBTC. One is through tetrahedral pockets and other is through large pores. It is found that tetrahedral pockets are potential minima sites and most of the molecules reside there at low concentration. Free energy map also showed that there exists a higher energy barrier if diffusion occurs through tetrahedral pockets rather than large pores. Relative population of acetylene molecules in large pores is found to increase with the concentration and since energy barrier is less while diffusing through large pores, it leads to increase in the average diffusivity at higher concentration. It is found that relative population of acetylene molecules diffusing through different pathways and collision between the molecules decide the average diffusivity of the molecules inside CuBTC. Analysis of intermediate scattering function indicated that there exist three time scales associated with the centre of mass diffusion of the acetylene molecules in CuBTC framework.

Anomalous chain diffusion in unentangled model polymer nanocomposites

We studied unentangled poly(ethylene-alt-propylene) (PEP) in a composite with hydrophobic silica particles as a function of the filler concentration. Our neutron spin echo (NSE) experiments cover both the internal dynamics as well as the center of mass diffusion beyond the Rouse time. The key experimental results are (i) all of the chains are equally mobile, (ii) the basic segmental (Rouse) relaxation rate is unaffected even at highest filler concentrations, and (iii) apparently the obstacles reduce significantly the translational center of mass motion. This happens, even in the case when the particles do not significantly confine the polymer. (iv) A transition from regular to anomalous diffusion in the Rouse regime at the highest particle fractions is clearly evidenced. In order to understand the microscopic mechanisms underlying the experimental observations, we performed coarse grained simulations. We demonstrate that the geometrical confinement only affects the dynamics at a long time scale outside the experimental window and therefore it is not able to explain the results found in the NSE experiments. The consideration of inter-chain interactions, however, results in a significant influence even at shorter times and a quantitative agreement between the experiments and simulations was found. The simulations clearly demonstrate that the interfaces cause a deceleration of the chains in their close vicinity. Then the inter-chain interactions carry this slowing down to the other chains at a time-scale of the Rouse relaxation time. Hence, in the experimental datasets an overall slowing down is observed.

Polymer Dynamics in Nanochannels of Porous Silicon: A Neutron Spin Echo Study

Neutron spin echo spectra of poly(ethylene oxide) (PEO) melts confined in porous silicon (the mean pore diameter: 13 nm) were recorded at Q = 0.05, 0.08, and 0.11 Å−1 and successfully analyzed in terms of a two-state model, where chains adsorbed to the pore walls exhibit much slower internal dynamics than in the bulk and their centers-of-mass do not move, while free chains have bulklike internal dynamics and diffuse within an infinite cylinder in the center of the pore. The radius of this cylinder was found to be 1.4 nm for PEO 3 kg/mol (3k); this corresponds to the thickness of the adsorbed layer to be approximately equal to the Flory radius. As opposed to PEO 10k, for which details on the center of mass diffusion could not be discerned, for PEO 3k the diffusion rate along the pore was found to be smaller than that in the radial direction.

Self-Diffusion in Chitosan Networks: From a Gel−Gel Method to Fluorescence Recovery after Photobleaching by Fringe Pattern

The diffusion properties of caffeine and dextran within chitosan networks with controlled structure were investigated using a gel-gel method and fluorescence recovery after photobleaching (FRAP) by fringe pattern. The center of mass diffusion was studied by varying the molecular weight of dextran macromolecules labeled with fluorescein isothiocyanate (FITC). It was shown that the diffusion was drastically slowed down above a critical molecular weight around 10 5 g/mol.

Diffusive motions in liquid medium-chain n-alkanes as seen by quasielastic time-of-flight neutron spectroscopy

Different diffusive motions in liquid C(32)H(66) on a picosecond time scale could be disentangled by resolution resolved quasielastic time-of-flight neutron spectroscopy (QENS). It is demonstrated that at all observation times, the dominating motion causes a Q(2) proportionality of the QENS signal, which indicates a Fickian diffusion mechanism. The observed motions can be characterized by an observation time dependent apparent diffusion coefficient D(a)(t(o)), which is up to one order of magnitude larger than the molecular self-diffusion coefficient D(s). By comparison with molecular dynamics simulations, the identified motions are attributed to displacements of hydrogen atoms reflecting not only global but also local molecular trajectories. Despite the rodlike shape of the molecules, the center of mass diffusion was found to be essentially isotropic. A coherent picture of the diffusional processes ranging from the fast tumbling of CH(2) groups to the slow long range molecular diffusion is presented.

A Cell- Surface Polymer Reptation Mechanism for Tumor Transendothelial Transport of Macromolecules

Polymer reptation is a process by which flexible linear polymers can migrate around obstacles and through pores and around other polymer molecules. It has successfully described quantitative behavior of polymer melts and has been invoked in explaining DNA separation according to length in sequencing gels. This mechanism may therefore be useful in delivering contrast agents or therapeutic drugs to tumors as these must traverse from the intravascular space through the tumor endothelial junction gaps and into the tumor. In this work, we show that polymers capable of weak interactions with tumor endothelium can translocate into the tumor interstitium at up to 9 times the rate of polymers without such cell-surface interactions. We propose a new mechanism by which the polymers diffuse along the cell surface and through cell junction gaps that occur in the tumor endothelium. This process can be halted in a number of ways that demonstrate that the surface interaction is essential for the higher transport rate. Alternative transport mechanisms are ruled out by further tests of polymer length scaling dependence, and by comparison of transport rates to those for globular constructs. Polymers of Gd-DTPA-polylysine and related backbones were investigated in an animal model of breast cancer and prostate cancer. Polymer lengths ranged from 30 nm to 300 nm, (from 100 to 700 lysine residues) and the polymer constructs had a cross section of approximately 1.2 nm in radius. Polymer uptake rate into tumors for an equivalent hydrodynamic size globular macromolecule was some 135 times larger demonstrating the importance of this transport mechanism compared to free diffusion of globular macromolecules through the endothelium junction pores. The polymer length scaling, with monomer number N, on rate of tumor transport goes as N(-1), which rejects alternative transport processes such as pinocytosis, active transport, and particle like center of mass diffusion through pores. This N(-1) scaling implies a cell-surface assisted polymer reptation process. This new transport mechanism allows very strong discrimination of aggressive tumors from nonaggressive tumors in animal model studies.

Thermoresponsive core–shell microgels with silica nanoparticle cores: size, structure, and volume phase transition of the polymer shell

Core-shell microgels made of the thermoresponsive polymer poly(N-isopropylacrylamide) (PNIPAM) and silica nanoparticles as inorganic cores were investigated by dynamic light scattering (DLS) and small angle neutron scattering (SANS). In order to study the response of the particles upon changes of temperature, experiments were done in a temperature interval close to the volume phase transition temperature of the PNIPAM shell. While DLS probes the hydrodynamic dimensions of the particles, determining their centre of mass diffusion, SANS provides the correlation length xi of the PNIPAM network. Additionally, the composite particles were characterised by electron microscopy as well as atomic force microscopy to reveal the core-shell structure and at the same time the approximate dimensions and the shape of the microgels.

Internal dynamics in colloidal PNIPAM microgel particles immobilised in mesoscopic crystals

Abstract Internal dynamics of colloidal microgels based on N -isopropyl-acrylamide is investigated by means of neutron spin-echo spectroscopy. To avoid interference of the relaxation of interest with the centre of mass diffusion, the microgels were immobilised in a colloidal crystal. Due to the q -range used in these quasi-elastic neutron scattering experiments, it is possible to obtain nearly completely decaying ensemble averaged intermediate scattering functions 〈ISF〉 E . These can be fitted by single exponential forms, simplifying largely the data analysis compared with photon correlation spectroscopy. This is due to the fact that for light q 2 〈 ξ 2 〉→∞ can not be reached, whereas for neutrons this condition is approximately fulfilled. The obtained network diffusion coefficients decrease linearly with increasing cross-linker concentration. This is in contrast to previous results from photon correlation spectroscopy obtained for macroscopic poly( N -isopropyl-acrylamide) gels [Macromolecules, 29 (1996) 8746].

From Rouse dynamics to local relaxation: A neutron spin echo study on polyisobutylene melts

We investigated the single chain motions of monodisperse polyisobutylene chains in the melt by neutron spin echo spectroscopy. Thereby a wide range in momentum space over a large dynamic range was covered. Motional processes from the center of mass diffusion, the Rouse dynamics to the more local relaxation processes which limit the validity of the standard Rouse model, were elucidated. The observed dynamic structure factors were analyzed in terms of relevant theoretical approaches addressing the limiting factors of the Rouse model. We found that other than claimed in the literature effects of local chain stiffness—they were treated in terms of the all rotational states model and a bending force model—cannot account for the experimental observations. It appears that additional damping effects related to an internal viscosity of the chain have to be involved, in order to explain the experimental results.

Constant pressure simulations of lattice gas models

A method for constant pressure Monte Carlo simulations in lattice gas models is described. The simulation box is placed between two hard walls with fluctuating distance, and periodic boundary conditions are applied in the perpendicular directions. Continuous volume fluctuations in the bounded direction are made possible by introducing a generalized volume, which interpolates between the discrete values that correspond to the given lattice. This is achieved by using a surface potential variable which makes the lattice surface layer next to the hard wall gradually less accessible to particle occupation. The method is applied to the equation of state of noninteracting lattice gas models, where exact results are available for comparison, and also to less trivial models of interacting point-particles and athermal lattice chains, for which the quasichemical approximation (QCA) provides reliable results to compare with. For the chain simulations the method can be used in conjunction with the configuration biased Monte Carlo procedure in order to enhance its performance. However, since the Monte Carlo moves can be chosen to fit any desired kinetic model, our method can be used not only to generate constant pressure equilibrium ensembles, but also in the context of dynamic Monte Carlo studies. The center of mass diffusion in dense systems of athermal chains is investigated as an example. In all our static applications the method performs very well in comparison with exact or with QCA results, provided that the system size is large enough in the bounded direction. For small systems finite size effects are observed and analyzed, suggesting potential applications in the study of confined systems.

Properties and Entanglements of Amorphous Polymer Interfaces

When two similar polymers contact in the melt to form a polymer-polymer interface, interdiffusion of random-coil chains occurs. For this case, we determine a set of properties, H, as a function of time, t, and molecular weight, M. They in clude the number of chains, n, number of bridges, p, average monomer inter penetration depth, X, the total monomer depth, Xo, the center of mass diffusion, χcm, the average contour interpenetration length, l, the total contour length, Lo, and the average bridge length, l p. The time dependent, H(t), and equilibrium solutions, H∞ , can be summarized as

Quasi-elastic neutron scattering study of the dynamics of 18-CROWN-6 in the liquid state

The internal and external dynamics of the 18-CROWN-6 molecule in the liquid state have been investigated by quasi-elastic neutron scattering in large energy and momentum transfer ranges. When Q increases, i.e. when smaller and smaller distances are tested in reciprocal space, different contributions are successively evidenced: Centre of mass diffusion for distances larger than the molecular size, then whole molecule rotations and finally internal dynamics resulting from fast conformational changes. This latter process is predominant at high Q. It is characterized by a cross-over at Q = 1·7 A between a smooth to a fast increase of the quasielastic width, in agreement with the predictions of various models of restricted jump or diffusion motions. Some characteristic parameters for these three dynamical processes are deduced and in particular a mean jump frequency of 1·5 × 1012 s-1 is associated with the conformational changes.

Studies of cyclic and linear poly(dimethyl siloxanes): 12. Observation of diffusion behaviour by quasielastic neutron scattering

High resolution neutron scattering experiments have been used to observe the diffusive motion of low molecular weight linear and cyclic poly(dimethyl siloxane) molecules in dilute solution in deuterated benzene. Diffusion coefficients ( D) and hydrodynamic radii ( R H) have been compared with values obtained by light scattering for higher molecular weight samples and with radii of gyration ( R g) obtained by small-angle neutron scattering. While the ratio D ring D chain is close to the predicted value of 0.85, the ratio R g R H falls below the theoretical value for both ring and chain molecules. The scattering curves show effects arising from both centre of mass diffusion and internal molecular motion, and the observed inverse correlation times are compared with calculated behaviour as a function of scattering vector, Q.

A theory of measurement error and its implications for spatial and temporal gradient sensing during chemotaxis.

In order that cells respond to environmental cues, they must be able to measure ambient ligand concentration. Concentrations fluctuate, however, because of thermal noise, and one can readily show that estimates based on concentration values at a particular moment will be subject to substantial error. Cells are therefore expected to average their estimates over some limited time period. In this paper we assume that a cell uses fractional receptor occupancy as a measure of ambient ligand concentration and develop general expressions for the error a cell makes because the length of the averaging period is necessarily limited. Our analysis is general, relieving many of the assumptions underlying the seminal work of Berg and Purcell. The most important formal difference is our inclusion of occupancy-dependent dissociation--a phenomenon that has been well-documented for many systems. In addition, our formulation permits signal averaging to begin before chemical equilibrium has been established and it allows binding kinetics to be nonlinear (i.e., biomolecular rather than pseudo-first-order). The results are applied to spatial and temporal concentration gradients. In particular we estimate the minimum averaging times required for cells to detect such gradients under typical in vitro conditions. These estimates involve assigning numerical values to receptor ligand rate constants. If the rate constants are at their maximum possible values (limited only by center of mass diffusion), then either temporal or spatial gradients can be detected in minutes or less. If, however, as suggested by experiments, the rate constants are several orders of magnitude below their diffusion-limited values, then under typical constant gradient conditions the time required to detect a spatial gradient is prohibitively long, whereas temporal gradients can still be detected in reasonable lengths of time. This result was obtained for large cells such as lymphocytes, as well as for the smaller, bacterial cells. The ratio of averaging times for the two mechanisms--amounting to several orders of magnitude--is well beyond what could be reconciled by limitations of the calculation, and strongly suggests heavy reliance on temporal sensing mechanisms under typical in vitro conditions with constant spatial gradients.