Dielectric relaxation spectra of block polymers containing sequential type-A dipoles are considered. Spectra of a specific set of block copolymers can be combined to isolate the dynamic cross-correlation between the motions of two distinct parts of the same polymer chain. Unlike past treatments of this problem, no model is assumed for the underlying polymer dynamics.
Using molecular dynamics simulations we examine the dynamics of a family of model polymers with varying chain length and torsional potential barriers. We focus on features of the dynamics of polymers that are seen experimentally but absent in simulations of freely rotating and freely jointed chains. The reduced effect of volume on the segmental dynamics with increasing chain length, a capacity for pressure densification, and the deviation from constant Johari-Goldstein relaxation time at constant segmental relaxation time all have a common origin - torsional rigidity, and these effects become …
We adapt Fluorescence Correlation spectroscopy (FCS) formalism to the studies of the dynamics of semi-flexible polymers and derive expressions relating FCS correlation function to the longitudinal and transverse mean square displacements of polymer segments. We use the derived expressions to measure the dynamics of actin filaments in two experimental situations: filaments labeled at distinct positions and homogeneously labeled filaments. Both approaches give consistent results and allow to measure the temporal dependence of the segmental mean-square displacement (MSD) over almost five decades …
Glassy polymers show strain hardening: at constant extensional load, their flow first accelerates, then arrests. Recent experiments have found this to be accompanied by a striking and unexplained dip in the segmental relaxation time. Here we explain such behavior by combining a minimal model of flow-induced liquefaction of a glass, with a description of the stress carried by strained polymers, creating a non-factorable interplay between aging and strain-induced rejuvenation. Under constant load, liquefaction of segmental motion permits strong flow that creates polymer-borne stress. This slows …
We study the segmental dynamics of poly(ethylene oxide) (PEO) from microscopic simulations in the neat polymer and a polymer electrolyte (PEO/LiBF$_4$) by analyzing the normal modes. We verify the applicability of the Rouse theory, specifically for the polymer electrolyte where dynamic heterogeneities, arising from cation-polymer interactions, alter the mobility non-uniformly along the chains. We find that the Rouse modes for both the systems are orthogonal despite the presence of non-exponential relaxation of the modes and violation of the Gaussian self-similarity of the chains. The slowdown …
Amphiphilic block copolymer solutions form various micellar structures including micelles and vesicles. We applied the density functional theory for block copolymers which we have proposed to amphiphilic block copolymer systems. The 3 dimensional simulation for AB diblock copolymer solutions and AB diblock copolymer / A homopolymer blends has been done and it is shown that the spherical micelles, cylindrical micelles and spherical vesicles are formed. It is also shown that the phase diagram for AB diblock copolymer / A homopolymer blends qualitatively agrees with the phase diagram obtained by …
Published dielectric relaxation measurements on polypropylene glycol and 1,4-polyisoprene are analyzed to determine the relative effect that thermal energy and volume have on the temperature dependence of the normal mode relaxation times, and compare this to their effect on the temperature dependence of the local segmental relaxation times. We find that for both polymers at temperatures well above Tg, both relaxation modes are governed more by thermal energy than by volume, although the latter's contribution is not negligible. Such a result is consistent with an assumption underlying models fo…
Presenting theoretical arguments and numerical results we demonstrate long-range intrachain correlations in concentrated solutions and melts of long flexible polymers which cause a systematic swelling of short chain segments. They can be traced back to the incompressibility of the melt leading to an effective repulsion $u(s) \approx s/ρR^3(s) \approx ce/\sqrt{s}$ when connecting two segments together where $s$ denotes the curvilinear length of a segment, $R(s)$ its typical size, $ce \approx 1/ρbe^3$ the ``swelling coefficient", $be$ the effective bond length and $ρ$ the monomer density. The re…
A novel type of hybrid colloids is presented, based on the association of several polymeric systems and ferrofluids. On the one hand, we use inorganic nanoparticles made of magnetic iron oxide prepared at the LI2C, which response to a magnetic field of low intensity. On the other hand the organic part is made either of long linear polyacrylamide chains or of mesoscopic structures (vesicles and micelles) self-assembled from amphiphile polybutadiene-b-poly(glutamic acid) di-block copolymers, which conformation is pH-sensitive.
We present an extensive molecular dynamics (MD) simulation study of the lithium ion transport in ternary polymer electrolytes consisting of poly(ethylene oxide) (PEO), lithium-bis(trifluoromethane)sulfonimide (LiTFSI) and the ionic liquid N-methyl-N-propylpyrrolidinium bis(trifluoromethane)sulfonimide (PYR13TFSI). In particular, we focus on two different strategies by which the ternary electrolytes can be devised, namely by (a) adding the ionic liquid to PEO20LiTFSI, and (b) substituting the PEO chains in PEO20LiTFSI by the ionic liquid. In order to grasp the changes of the overall lithium tra…
The polymer dynamics of homogeneous C$_{60}$-polystyrene mixtures in the molten state are studied via molecular simulations using two interconnected levels of representation for polystyrene nanocomposites: (a) A coarse-grained representation, in which each polystyrene repeat unit is mapped into a single "superatom" and each fullerene is viewed as a spherical shell. Equilibration of coarse-grained polymer-nanoparticle systems at all length scales is achieved via connectivity-altering Monte Carlo simulations. (b) An atomistic representation, where both nanoparticles and polymer chains are repres…
Designing Multivalent Copolymers for Selective Targeting of Multicomponent Surfaces
Faculty of Chemistry and Chemical Engineering, University of Maribor（马里博尔大学化学与化工学院）；The Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska（沿海大学数学、自然科学与信息技术学院）；Institute for Environmental Protection and Sensors（环境保护与传感器研究所）；Department of Materials Science and Engineering, Johns Hopkins University（约翰斯·霍普金斯大学材料科学与工程系）
Using different segmental dynamics and relaxation, characteristics of the interface growth is examined in an electrophoretic deposition of polymer chains on a three (2+1) dimensional discrete lattice with a Monte Carlo simulation. Incorporation of faster modes such as crankshaft and reptation movements along with the relatively slow kink-jump dynamics seems crucial in relaxing the interface width. As the continuously released polymer chains are driven (via segmental movements) and deposited, the interface width $W$ grows with the number of time steps $t$, $W \propto t^β,$ ($β\sim 0.4$--$0.8)$,…
Physically confining polymers into nanoscale pores induces significant changes in their dynamics. Although different results on the effect of confinement on the dynamics of polymers have been reported, changes in the segmental mobility of polymers typically are correlated with changes in their chain mobility due to increased monomeric relaxation times. In this study, we show that translational and segmental dynamics of polymers confined in disordered packings of nanoparticles can exhibit completely opposite behavior. We monitor the capillary rise dynamics of entangled polystyrene (PS) in disor…
The effect of confinement in the segmental relaxation of polymers is considered. On the basis of a thermodynamic model we discuss the emerging relevance of the fast degrees of freedom in stimulating the much slower segmental relaxation, as an effect of the constraints at the walls of the amorphous regions. In the case that confinement is due to the presence of crystalline domains, a quasi-poissonian distribution of local constraining conditions is derived as a result of thermodynamic equilibrium. This implies that the average free energy barrier $ΔF$ for conformational rearrangement is of the …
Dielectric spectroscopy measurements over a broad range of temperature and pressure were carried out on poly(oxybutylene) (POB), a type-A polymer (dielectrically-active normal mode). There are three dynamic processes appearing at lower frequency, the normal and segmental relaxation modes, and a conductivity arising from ionic impurities. In combination with pressure-volume-temperature measurements, the dielectric data were used to assess the respective roles of thermal energy and density in controlling the relaxation times and their variation with T and P. We find that the local segmental and …
We consider star polymers, consisting of two different polymer species, in a solvent subject to quenched correlated structural obstacles. We assume that the disorder is correlated with a power-law decay of the pair correlation function g(x)\sim x^{-a}. Applying the field-theoretical renormalization group approach in d dimensions, we analyze different scenarios of scaling behavior working to first order of a double ε=4-d, δ=4-a expansion. We discuss the influence of the correlated disorder on the resulting scaling laws and possible manifestations such as diffusion controlled reactions in the vi…
The effects of the length of each hydrophobic end block N_{st} and polymer concentration \barϕ_{P} on the transition broadness in amphiphilic ABA symmetric triblock copolymer solutions are studied using the self-consistent field lattice model. When the system is cooled, micelles are observed, i.e.,the homogenous solution (unimer)-micelle transition occurs. When N_{st} is increased, at fixed \barϕ_{P}, micelles occur at higher temperature, and the temperature-dependent range of micellar aggregation and half-width of specific heat peak for unimer-micelle transition increase monotonously. Compare…
Polymer properties are inherently multi-scale in nature, where delicate local interaction details play a key role in describing their global conformational behavior. In this context, deriving coarse-grained (CG) multi-scale models for polymeric liquids is a non-trivial task. Further complexities arise when dealing with copolymer systems with varying microscopic sequences, especially when they are of an amphiphilic nature. In this work, we derive a segment-based generic CG model for amphiphilic copolymers consisting of repeat units of hydrophobic (methylene) and hydrophilic (ethylene oxide) mon…
Using the self-consistent field lattice model, polymer concentration $\barϕ_{P}$ and chain length $N$ (keeping the length ratio of hydrophobic to hydrophilic blocks constant) the effects on temperature-dependent behavior of micelles are studied, in amphiphilic symmetric ABA triblock copolymer solutions. When chain length is increased, at fixed $\barϕ_{P}$, micelles occur at higher temperature. The variations of average volume fraction of stickers $\barϕ_\textrm{co}^\textrm{s}$ and the lattice site numbers $N_\textrm{co}^\textrm{ls}$ at the micellar cores with temperature are dependent on $N$ a…
Simulating soft matter systems such as the cytoskeleton can enable deep understanding of experimentally observed phenomena. One challenge of modeling such systems is realistic description of the steric repulsion between nearby polymers. Previous models of the polymeric excluded volume interaction have the deficit of being non-analytic, being computationally expensive, or allowing polymers to erroneously cross each other. A recent solution to these issues, implemented in the MEDYAN simulation platform, uses analytical expressions obtained from integrating an interaction kernel along the lengths…
Physico-chemical study of polymer mixtures formed by a polycation and a zwitterionic copolymer in aqueous solution and upon adsorption onto negatively charged surfaces
A coarse-graining strategy for dilute and semi-dilute solutions of interacting polymers, and of colloid polymer mixtures is briefly described. Monomer degrees of freedom are traced out to derive an effective, state dependent pair potential between the polymer centres of mass. The cross-over between good and poor solvent conditions is discussed within a scaling analysis. The method is extended to block copolymers represented as "necklaces" of soft "blobs", and its success is illustrated here in the case of a symmetric diblock copolymer which exhibits microphase separation.
During the past years we have investigated the complexation between nanocolloids and oppositely charged polymers. The nanocolloids examined were ionic surfactant micelles and inorganic oxide nanoparticles. For the polymers, we used homopolyelectrolytes and block copolymers with linear and comb architectures. In general, the attractive interactions between oppositely charged species are strong and as such, the simple mixing of solutions containing dispersed constituents yield to a precipitation, or to a phase separation. We have developed means to control the electrostatically-driven attraction…
A versatile and transferable coarse-grained (CG) model was developed to investigate the self-assembly of two ubiquitous methacrylate-based copolymers: poly(ethylene oxide-b-methylmethacrylate) (PEO-b-PMMA) and poly(ethylene oxide-b-butylmethacrylate) (PEO-b-PBMA). We derive effective CG potentials that can reproduce their behaviour in aqueous and organic polymer solutions, pure copolymer systems, and at the air-water interface following a hybrid structural-thermodynamic approach, which incorporates macroscopic and atomistic-level information. The parameterization of the intramolecular CG poten…
We study the conformational properties of complex polymer macromolecules, consisting in general of $n$ subsequently connected chains (blocks) of different lengths and distinct chemical structure. Depending on the solvent conditions, the inter- or intrachain interactions of some blocks may vanish, causing the rich conformational behavior. Our main attention is focused on the universal conformational properties of such molecules. Applying the direct polymer renormalization group approach, we derive the analytical expressions for the scaling exponent $γ(n)$, governing the number of possible confo…
We carry out numerical simulations of vesicle formation based on the density functional theory for block copolymer solutions. It is shown by solving the time evolution equations for concentrations that a polymer vesicle is spontaneously formed from the homogeneous state. The vesicle formation mechanism obtained by our simulation agree with the results of other simulations based on the particle models as well as experiments. By changing parameters such as the volume fraction of polymers or the Flory-Huggins interaction parameter between the hydrophobic subchains and solvents, we can obtain the …
Structure, Dynamics and Hydrogen Transport in Amorphous Polymers: An Analysis of the Interplay Between Free Volume Element Distribution and Local Segmental Dynamics from Molecular Dynamics Simulations
A series of amphiphilic LC block copolymers, in which the hydrophobic block is a smectic polymer poly(4-methoxyphenyl 4-(6-acryloyloxy-hexyloxy)-benzoate) (PA6ester1) and the hydrophilic block is polyethyleneglycol (PEG), were synthesized and characterized. The self-assembly of one of them in both the pure state and the dilute aqueous solution was investigated in detail. Nano-structures in the pure state were studied by SAXS and WAXS on samples aligned by a magnetic field. A hexagonal cylindrical micro-segregation phase was observed with a lattice distance of 11.2 nm. The PEG blocks are in the…
We report on the formation of colloidal complexes resulting from the electrostatic self-assembly of polyelectrolyte-neutral block copolymers and oppositely charged surfactants. The copolymers investigated are asymmetric and characterized by a large neutral block. Using light, neutron and x-ray scattering experiments, we have shown that the colloidal complexes exhibit a core-shell microstructure. The core is described as a dense and disordered micro-phase of micelles connected by the polyelectrolyte blocks, whereas the shell is a diffuse brush made from the neutral chains. Colloidal complexes w…
Glassy polymers show strain hardening: at constant extensional load, their flow first accelerates, then arrests. Recent experiments under such loading have found this to be accompanied by a striking dip in the segmental relaxation time. This can be explained by a minimal nonfactorable model combining flow-induced melting of a glass with the buildup of stress carried by strained polymers. Within this model, liquefaction of segmental motion permits strong flow that creates polymer-borne stress, slowing the deformation enough for the segmental (or solvent) modes to then re-vitrify. Here we presen…
The presence of nanoparticles in a diblock copolymer leads to changes in the morphology and properties of the matrix and can produce highly organized hybrid materials. The resulting material properties depend not only on the polymer composition but also on the size, shape, and surface properties of the colloids. The dynamics of this kind of systems using a hybrid mesoscopic approach has been studied in this work. A continuum description for the polymer is used, while colloids are individually resolved. The method allows for a variable preference of the colloids, which can have different sizes,…
The presence of a viscoelastic mechanism distinctly different from the segmental a-relaxation and the Rouse modes within the glass-rubber transition zone of polymers had been justified by theoretical considerations, and subsequently experimentally verified in different bulk polymers by various techniques, and in several laboratories. Referred to in the literature as the sub-Rouse modes, they were also found in polymer thin films by the creep compliance measurements of McKenna and co-workers Established by experiment and theoretical considerations is the enhanced mobility of sub-Rouse modes in …
Using fast off-lattice Monte Carlo simulations with experimentally accessible fluctuations, we report the first systematic study unambiguously quantifying the shift of the order-disorder transition (ODT) $χ^*$ of symmetric diblock copolymers from the mean-field prediction $χ^*_{\rm MF}$. Our simulations are performed in a canonical ensemble with variable box lengths to eliminate the restriction of periodic boundary conditions on the lamellar period. Exactly the same model system (Hamiltonian) is used in both our simulations and mean-field theory; the ODT shift is therefore due to the fluctuati…
We introduce a mesoscale technique for simulating the structure and rheology of block copolymer melts and blends in hydrodynamic flows. The technique couples dynamic self consistent field theory (DSCFT) with continuum hydrodynamics and flow penalization to simulate polymeric fluid flows in channels of arbitrary geometry. We demonstrate the method by studying phase separation of an ABC triblock copolymer melt in a sub-micron channel with neutral wall wetting conditions. We find that surface wetting effects and shear effects compete, producing wall-perpendicular lamellae in the absence of flow, …
We derive an expression for the free energy of the blends of block copolymers expressed as a functional of the density distribution of the monomer of each block. The expression is a generalization of the Flory-Huggins-de Gennes theory for homo polymer blends, and also a generalization of the Ohta-Kawasaki theory for the melts of diblock copolymers. The expression can be used for any blends of homopolymers and block copolymers of any topological structure. The expression gives a fast and stable computational method to calculate the micro and macro phase separation of the blends of homopolymers …
Polymer vesicles are stable robust vesicles made from block copolymer amphiphiles. Recent progress in the chemical design of block copolymers opens up the exciting possibility of creating a wide variety of polymer vesicles with varying fine structure, functionality and geometry. Polymer vesicles not only constitute useful systems for drug delivery and micro/nano-reactors but also provide an invaluable arena for exploring the ordering of matter on curved surfaces embedded in three dimensions. By choosing suitable liquid-crystalline polymers for one of the copolymer components one can create ves…
Block copolymer melts self-assemble in the bulk into a variety of nanostructures, making them perfect candidates to template the position of nanoparticles. The morphological changes of block copolymers are studied in the presence of a considerable filling fraction of colloids. Furthermore, colloids can be found to assemble into ordered hexagonally close-packed structures in a defined number of layers when softly confined within the phase-separated block copolymer. A high concentration of interface-compatible nanoparticles leads to complex block copolymer morphologies depending on the polymeric…
We review recent simulation studies of interfaces between immiscible homopolymer phases. Special emphasis is given to the presentation of efficient simulation techniques and powerful methods of data analysis, such as the analysis of capillary wave spectra. Possible reasons for polymer incompatibility and ways to relate model dependent interaction parameters to an effective Flory Huggins parameter are discussed. Various interfaces are then considered and characterised with respect to their microscopic structure and thermodynamic properties. In particular, interfaces between homopolymers of equa…
Characteristics of relaxed density profile and conformation of polymer chains are studied by a Monte Carlo simulation on a discrete lattice in three dimensions using different segmental (kink-jump $K$, crank-shaft $C$, reptation $R$) dynamics. Three distinct density regimes, substrate, bulk, and interface, are identified. With the $KC$ segmental dynamics we find that the substrate coverage grows with a power-law, $d_s \propto t^γ$ with a field dependent nonuniversal exponent $γ= 0.23 + 0.7 E$. The bulk volume fraction $d_b$ and the substrate polymer density ($d_s$) increases exponentially with…
We have studied the phase behavior of the poly(n-butyl acrylate)-b-poly(acrylic acid) block copolymer in a mixture of two miscible solvents, water and tetrahydrofuran (THF). The techniques used to examine the different polymers, structures and phases formed in mixed solvents were static and dynamic light scattering, small-angle neutron scattering, nuclear magnetic resonance and fluorescence microscopy. By lowering the water/THF mixing ratio X, the sequence unimers, micron-sized droplets, polymeric micelles was observed. The transition between unimers and the micron-sized droplets occurred at X…
The reaction of $AB_m$ monomers (m=2,3) with a multifunctional B_f-type polymer chain ("hypergrafting") is studied by coarse-grained molecular dynamics simulations. The $AB_m$ monomers are hypergrafted using the slow monomer addition strategy. Fully dendronized, i.e., perfectly branched polymers are also simulated for comparison. The degree of branching DB of the molecules obtained with the "hypergrafting" process critically depends on the rate with which monomers attach to inner monomers compared to terminal monomers. This ratio is more favorable if the $AB_m$ monomers have lower reactivity, …
A mode-coupling theory for dense polymeric systems is developed which unifyingly incorporates the segmental cage effect relevant for structural slowing down and polymer chain conformational degrees of freedom. An ideal glass transition of polymer melts is predicted which becomes molecular-weight independent for large molecules. The theory provides a microscopic justification for the use of the Rouse theory in polymer melts, and the results for Rouse-mode correlators and mean-squared displacements are in good agreement with computer simulation results.
