Diffusivity and Viscosity of Concentrated Hydrogenated Polybutadiene Solutions

Simulating Stress–Strain Behavior by Using Individual Chains: Uniaxial Deformation of Amorphous Cis- and Trans-1,4-Polybutadiene

This work develops a probability-based numerical method for quantifying mechanical properties of non-Gaussian chains subject to uniaxial deformation, with the intention of being able to incorporate polymer–polymer and polymer–filler interactions. The numerical method arises from a probabilistic approach for evaluating the elastic free energy change of chain end-to-end vectors under deformation. The elastic free energy change, force, and stress computed by applying the numerical method to uniaxial deformation of an ensemble of Gaussian chains were in excellent agreement with analytical solutions that were obtained with a Gaussian chain model. Next, the method was applied to configurations of cis- and trans-1,4-polybutadiene chains of various molecular weights that were generated under unperturbed conditions over a range of temperatures with a Rotational Isomeric State (RIS) approach in previous work (Polymer 2015, 62, 129–138). Forces and stresses increased with deformation, and further dependences on chain molecular weight and temperature were confirmed. Compression forces normal to the imposed deformation were much larger than tension forces on chains. Smaller molecular weight chains represent the equivalent of a much more tightly cross-linked network, resulting in greater moduli than larger chains. Young’s moduli computed from the coarse-grained numerical model were in good agreement with experimental results.

Injectable chitosan/collagen hydrogels nano-engineered with functionalized single wall carbon nanotubes for minimally invasive applications in bone

Mechanical robustness is an essential consideration in the development of hydrogel platforms for bone regeneration, and despite significant advances in the field of injectable hydrogels, many fail in this regard. Inspired by the mechanical properties of carboxylated single wall carbon nanotubes (COOH-SWCNTs) and the biological advantages of natural polymers, COOH-SWCNTs were integrated into chitosan and collagen to formulate mechanically robust, injectable and thermoresponsive hydrogels with interconnected molecular structure for load-bearing applications. This study presents a complete characterisation of the structural and biological properties, and mechanism of gelation of these novel formulated hydrogels. Results demonstrate that β-glycerophosphate (β-GP) and temperature play important roles in attaining gelation at physiological conditions, and the integration with COOH-SWCNTs significantly changed the structural morphology of the hydrogels to a more porous and aligned network. This led to a crystalline structure and significantly increased the mechanical strength of the hydrogels from kPa to MPa, which is closer to the mechanical strength of the bone. Moreover, increased osteoblast proliferation and rapid adsorption of hydroxyapatite on the surface of the hydrogels indicates increased bioactivity with addition of COOH-SWCNTs. Therefore, these nano-engineered hydrogels are expected to have wide utility in the area of bone tissue engineering and regenerative medicine.

Concepts of Nucleation in Polymer Crystallization

Nucleation plays a vital role in polymer crystallization, in which chain connectivity and thus the multiple length and time scales make crystal nucleation of polymer chains an interesting but complex subject. Though the topic has been intensively studied in the past decades, there are still many open questions to answer. The final properties of semicrystalline polymer materials are affected by all of the following: the starting melt, paths of nucleation, organization of lamellar crystals and evolution of the final crystalline structures. In this viewpoint, we attempt to discuss some of the remaining open questions and corresponding concepts: non-equilibrated polymers, self-induced nucleation, microscopic kinetics of different processes, metastability of polymer lamellar crystals, hierarchical order and cooperativity involved in nucleation, etc. Addressing these open questions through a combination of novel concepts, new theories and advanced approaches provides a deeper understanding of the multifaceted process of crystal nucleation of polymers.

Modeling of Entangled Polymer Diffusion in Melts and Nanocomposites: A Review

This review concerns modeling studies of the fundamental problem of entangled (reptational) homopolymer diffusion in melts and nanocomposite materials in comparison to experiments. In polymer melts, the developed united atom and multibead spring models predict an exponent of the molecular weight dependence to the polymer diffusion very similar to experiments and the tube reptation model. There are rather unexplored parameters that can influence polymer diffusion such as polymer semiflexibility or polydispersity, leading to a different exponent. Models with soft potentials or slip-springs can estimate accurately the tube model predictions in polymer melts enabling us to reach larger length scales and simulate well entangled polymers. However, in polymer nanocomposites, reptational polymer diffusion is more complicated due to nanoparticle fillers size, loading, geometry and polymer-nanoparticle interactions.

Role of Chain Length in the Formation of Frank-Kasper Phases in Diblock Copolymers

The phase behavior of poly(styrene)-b-poly(1,4-butadiene) diblock copolymers with a polymer block invariant degree of polymerization N[over ¯]_{b}≈800 shows no evidence of Frank-Kasper phases, in contrast to low molar mass diblock copolymers (N[over ¯]_{b}<100) with the same conformational asymmetry. A universal self-concentration crossover parameter N[over ¯]_{x}≈400 is identified, directly related to the crossover to entanglement dynamics in polymer melts. Mean-field behavior is recovered when N[over ¯]_{b}>N[over ¯]_{x}, while complex low symmetry phase formation is attributed to fluctuations and space-filling constraints, which dominate when N[over ¯]_{b}<N[over ¯]_{x}.

Solvent Effect on the Diffusion of Unentangled Linear Polymer Melts

We conducted molecular dynamics (MD) simulations to study how solvent chains affect the diffusion of linear polymers in the unentangled regime. For monodisperse solvent chains, the self-diffusivity of a tagged chain scales with its chain length. The solvent chain length affects both the prefactor and the exponent, the latter of which ranges from -0.79 to -0.85. The scaling exponent here deviates from -1 as predicted by the Rouse model, which may suggest that the friction coefficient increases with the solvent chain length. In addition, we carried out diffusion simulations on two polydisperse melts, one with the Flory-Schulz distribution and the other with the Gaussian distribution. The measured diffusivity as a function of the tagged chain length agrees with a simple proposed model accounting for the heterogeneous medium.

A new insight into the conformation and melt dynamics of hydrogenated polybutadiene as revealed by computer simulations

Extensive molecular dynamics simulations of the macromolecular conformation and the melt dynamics for model polymers of different molecular weights have been carried out. The selected models are hydrogenated polybutadienes with a 2% content of ethyl branches and linear polyethylene. It will be shown that the density and chain stiffness are clearly affected by both the molecular weight and the presence of ethyl branches. Furthermore, the results obtained from the simulations on the molecular size and, more remarkably, chain dynamics, perfectly match the neutron scattering experiments performed by Zamponi et al. in hydrogenated polybutadienes. We observe a clear chain contraction and a slow dynamics for the hydrogenated polybutadiene with respect to the linear chain of the same molecular length. Using the Likhtman-McLeish definitions, the obtained values of the entanglement relaxation time (τe) and the tube diameter (a) are found to be in agreement with the available experimental data (by rheology and neutron spin echo) as well as with those obtained by the simulations. Finally, a very good agreement of diffusion coefficients as a function of the molecular weight between simulations and experiments is observed. Therefore, there exists a clear difference between the results obtained for branched and linear polyethylene, accounting for a definitive effect of the short chain branching on the conformational properties and the melt dynamics of polyolefins.

Effect of 7S/11S ratio on the network structure of heat-induced soy protein gels: a study of probe release

The effect of 7S/11S ratio on the soy gel network will be uncovered by probe diffusion kinetics.

Crossover between activated reptation and arm retraction mechanisms in entangled rod-coil block copolymers

Using a coarse-grained slip-spring model, the dynamics of rod-coil block copolymers is explored over a wide parameter space to fully capture the crossover between the short rod (activated reptation) and long rod (arm retraction) limits. An analytical, closed-form expression for curvilinear diffusion by activated reptation was derived by separating the drag into individual components for the rod and coil block. Curvilinear diffusion in the intermediate rod regime, where both mechanisms are important, was then found to be faster than predicted when both mechanisms are independently combined. The discrepancy in the crossover regime arises because the rod-coil copolymer's exploration of space is not accurately described by either a coil homopolymer (assumed by activated reptation) or a rod homopolymer (assumed by arm retraction). This effect is explored by tracking the rod orientation as the polymer reptates, confirming that the polymer reptates along a path that becomes more rodlike as the rod fraction is increased. Thus, activated reptation under-predicts diffusion because the rod can choose reptation paths that are more extended than the coil homopolymer by renewal of the entanglement tube from the ends. Arm retraction under-predicts diffusion because minor rotations of the rod allow some motion before full retractions of the coil block. Finally, more familiar 3-dimensional center-of-mass diffusion measurements are related to the curvilinear diffusion analysis because the ratio of these two quantities varies smoothly between the coil and rod homopolymer limits as the reptation path becomes more extended.

Linear and Nonlinear Rheological Behavior of Fibrillar Methylcellulose Hydrogels

Cryogenic transmission electron microscopy and small-angle neutron scattering recently have revealed that the well-known thermoreversible gelation of methylcellulose (MC) in water is due to the formation of fibrils, with a diameter of 15 ± 2 nm. Here we report that both the linear and nonlinear viscoelastic response of MC solutions and gels can be described by a filament-based mechanical model. In particular, large-amplitude oscillatory shear experiments show that aqueous MC materials transition from shear thinning to shear thickening behavior at the gelation temperature. The critical stress at which MC gels depart from the linear viscoelastic regime and begin to stiffen is well predicted from the filament model over a concentration range of 0.18-2.0 wt %. These predictions are based on fibril densities and persistence lengths obtained experimentally from neutron scattering, combined with cross-link spacings inferred from the gel modulus via the same model.

Release behavior of non-network proteins and its relationship to the structure of heat-induced soy protein gels

Heat-induced soy protein gels were prepared by heating protein solutions at 12%, 15% ,or 18% for 0.5, 1.0, or 2.0 h. The release of non-network proteins from gel slices was conducted in 10 mM pH 7.0 sodium phosphate buffer. SDS-PAGE and diagonal electrophoresis demonstrated that the released proteins consisted of undenatured AB subunits and denatured proteins including monomers of A polypeptides, disulfide bond linked dimers, trimers, and polymers of A polypeptides, and an unidentified 15 kDa protein. SEC-HPLC analysis of non-network proteins revealed three major protein peaks, with molecular weights of approximately 253.9, 44.8, and 9.7 kDa. The experimental data showed that the time-dependent release of the three fractions from soy protein gels fit Fick's second law. An increasing protein concentration or heating time resulted in a decrease in diffusion coefficients of non-network proteins. A power law expression was used to describe the relationship between non-network protein diffusion coefficient and molecular weight, for which the exponent (α) shifted to higher value with an increase in protein concentration or heating time, indicating that a more compact gel structure was formed.

Tube Curvature Slows the Motion of Rod-Coil Block Copolymers through Activated Reptation

Understanding the dynamics of molecules with complex shapes is important as researchers develop advanced materials using hybrid molecules. This study applies a slip-spring model to visualize and quantify the entangled dynamics of rod-coil block copolymers. The parameters of the model are determined by matching with molecular dynamics simulation results. By monitoring the positions of polymers along the entanglement tube, rod-coil copolymers are shown to disfavor configurations where the rod occupies curved portions of the tube of randomly varying curvature created by the coil ends. This confirms that reptation of copolymers occurs by an activated mechanism and is the first demonstration of the activation barriers that have been previously inferred through diffusion measurements by simulation and experiment. The barriers to diffusion are further quantified by considering the curvilinear motion of ring polymers, and their effect on diffusion is quantitatively captured by considering one-dimensional motion along an entanglement tube with a rough free energy potential.

Molecular-scale simulation of cross-flow migration in polymer melts

The first ever molecular-scale simulation of cross-flow migration effects in dense polymer melts is presented; simulations for both unentangled and entangled chains are presented. At quiescence a small depletion next to the wall for the segmental densities of longer chains is present, a corresponding excess exists about one-half a radii of gyration away from the wall, and uniform values are observed further from the wall. In shear flow the melts exhibit similar behavior as the quiescent case; a constant shear rate across the gap does not induce chain length based migration. In contradistinction, parabolic flow (where gradients in shear rate are present) causes profound migration for both unentangled and entangled melts. Mapping onto polyethylene and calculating stress shows the system is far below the stress required to break chains. Accordingly, our findings are consistent with flow induced migration mechanisms predominating over competing chain degradation mechanisms thus resolving a 40 year old controversy.

Molecular scale simulation of homopolymer wall slip

The first molecular scale simulation of highly entangled polydisperse homopolymers that is capable of capturing all three regions--no slip, weak slip, and strong slip--of the hydrodynamic boundary condition is presented. An on-lattice dynamic Monte Carlo technique capable of correctly capturing both unentangled and entangled polymer dynamics is used to study the molecular details of wall slip phenomena for homopolymers and energetically neutral walls. For unentangled chains (those exhibiting Rouse dynamics) weak slip is not present but evidence of strong slip is manifest at very high shear rates. For entangled chains (of sufficient length to exhibit reptation dynamics), both weak and strong slip are observed. Consistent with numerous experimental studies, disentanglement and cohesive failure occur at high shear rates. Disentanglement is clearly evidenced in a nonlinear velocity profile that exhibits shear banding, in an excess of chain ends at the slip plane, and perhaps most importantly in a nonmonotonic stress versus shear rate response. The chain end density exhibits a pretransitional periodicity prior to disentanglement. Unentangled Rouse chains do not show this pretransitional response or a bifurcation in their stress versus shear rate response. Finally, it is shown that when polydispersity is introduced, slip phenomena are severely reduced and the inherent constitutive bifurcation is limited to a small region. Predictions are in post facto agreement with many experiments, are distinct from existing results obtained using molecular dynamics simulation techniques, and shed light on fundamental mechanisms of polymer wall slip.

Experimental measurement of coil-rod-coil block copolymer tracer diffusion through entangled coil homopolymers

The diffusion of coil-rod-coil triblock copolymers in entangled coil homopolymers is experimentally measured and demonstrated to be significantly slower than rod or coil homopolymers of the same molecular weight. A model coil-rod-coil triblock was prepared by expressing rodlike alanine-rich α-helical polypeptides in E. coli and conjugating coillike poly(ethylene oxide) (PEO) to both ends to form coil-rod-coil triblock copolymers. Tracer diffusion through entangled PEO homopolymer melts was measured using forced Rayleigh scattering at various rod lengths, coil molecular weights, and coil homopolymer concentrations. For rod lengths, L, that are close to the entanglementh length, a, the ratio between triblock diffusivity and coil homopolymer diffusivity decreases monotonically and is only a function of L/a, in quantitative agreement with previous simulation results. For large rod lengths, diffusion follows an arm retraction scaling, which is also consistent with previous theoretical predictions. These experimental results support the key predictions of theory and simulation, suggesting that the mismatch in curvature between rod and coil entanglement tubes leads to the observed diffusional slowing.

An enhanced entangled polymer model for dissipative particle dynamics

We develop an alternative polymer model to capture entanglements within the dissipative particle dynamics (DPD) framework by using simplified bond-bond repulsive interactions to prevent bond crossings. We show that structural and thermodynamic properties can be improved by applying a segmental repulsive potential (SRP) that is a function of the distance between the midpoints of the segments, rather than the minimum distance between segments. The alternative approach, termed the modified segmental repulsive potential (mSRP), is shown to produce chain structures and thermodynamic properties that are similar to the softly repulsive, flexible chains of standard DPD. Parameters for the mSRP are determined from topological, structural, and thermodynamic considerations. The effectiveness of the mSRP in capturing entanglements is demonstrated by calculating the diffusion and mechanical properties of an entangled polymer melt.

Diffusion of Entangled Rod-Coil Block Copolymers

The diffusion of entangled rod-coil block copolymers is investigated by molecular dynamics (MD) simulations, and theories are introduced that describe the observed features and underlying physics. The reptation of rod-coil block copolymers is dominated by the mismatch between the curvature of the rod and coil entanglement tubes, which results in dramatically slower diffusion of rod-coils compared to the rod and coil homopolymers. For small rods, a local curvature-dependent free energy penalty results in a rough energy surface inside the entanglement tube, causing diffusivity to decrease with rod length. For large rods, rotational hindrances on the rod dominate, causing the coil block to relax by an arm retraction mechanism and diffusivity to decrease exponentially with coil size.

Diffusion in polymer solutions studied by fluorescence correlation spectroscopy

We employed fluorescence correlation spectroscopy (FCS) to study the diffusion of molecular and macromolecular tracers in polystyrene solutions over a broad range of concentrations (c) and molecular weights (M(w,m)) of the matrix polymer. Molecular tracer diffusion scales only with the matrix concentration and superimposes on a single, nonpolymer specific, curve. On the contrary, the diffusion of macromolecular tracers in solutions of matrix polymers with M(w,m) sufficiently larger than the tracer molecular weight scales with c/c(p)*, where c(p)* is the tracer overlap concentration. We further demonstrate that FCS can address local and global dynamics simultaneously.

Enhanced mobility of confined polymers

Non-classical behaviour, brought about by a confinement that imposes spatial constraints on molecules, is opening avenues to novel applications. For example, carbon nanotubes, which show rapid and selective transport of small molecules across the nanotubes, have significant potential as biological or chemical separation materials for organic solvents or gaseous molecules. With polymers, when the dimensions of a confining volume are much less than the radius of gyration, a quantitative understanding of perturbations to chain dynamics due to geometric constraints remains a challenge and, with the development of nanofabrication processes, the dynamics of confined polymers have significant technological implications. Here, we describe a weak molecular-weight-dependent mobility of polymers confined within nanoscopic cylindrical pores having diameters smaller than the dimension of the chains in the bulk. On the basis of the chain configuration along the pore axis, the measured mobility of polymers in the confined geometry is much higher than the mobility of the unconfined chain. With the emergence of nanofabrication processes based on polymer flow, the unexpected enhancement in flow and reduction in intermolecular entanglements are of significant importance in the design and execution of processing strategies.

Do deviations from reptation scaling of entangled polymer melts result from single- or many-chain effects?

By studying the relaxation of small amounts of short entangled "probe" chains in a high molecular weight matrix, we show that the deviations from reptation scaling of the longest relaxation time are not as much dominated by single-chain effects (usually referred to as contour length fluctuations or CLF) as assumed by current mesoscopic models but also originate to a very significant extent from mutual chain relaxation effects. This result is in fact consistent with literature data on tracer and self-diffusion. Moreover, tube theories also overpredict the influence of CLF on the plateau modulus. Improved theories, simulations, and careful experiments are urgently needed to resolve this important question.

Pathways of Polymeric Vesicle Formation

Polymeric vesicle formation is dictated by the mutual diffusion of water into the bulk block copolymer and vice versa. The hydration of three poly(ethylene oxide)-co-poly(butylene oxide) copolymers with different molecular weights has been monitored both macroscopically (confocal laser scanning microscopy) and microscopically (small-angle X-ray scattering). Both methods have revealed that the amphiphilic block copolymers swell in water following two qualitatively different growth regimes. Initially, water and copolymer diffuse into each other following a subdiffusional growth as the result of a molecular-level arrangement of the amphiphilic membranes that comprise the swollen copolymer. After a critical time, which is exponential in polymer molecular weight, the amphiphilic membranes reach their equilibrium morphology and as a consequence the growth starts to follow Fickian diffusion. The complex hydration kinetics dictate the phases formed at the interface between the amphiphilic copolymer and water. Upon hydration of simple amphiphiles, the amphiphilic film swells and the concentration gradient at the interface with water gradually drops to zero. This strongly affects the complex driving forces that control vesicle formation. Indeed, to form vesicles, an energy barrier has to be overcome, and therefore a constant concentration gradient is required. We show, by enhancing the hydration kinetics via an ac field, how the interface concentration gradient is kept constant and the magnitude of this gradient dictates the final size of the vesicles.

Physical Gelation of Chitosan in the Presence of β-Glycerophosphate: The Effect of Temperature

When adding beta-glycerophosphate (beta-GP), a weak base, to chitosan aqueous solutions, the polymer remains in solution at neutral pH and room temperature, while homogeneous gelation of this system can be triggered upon heating. It is therefore one of the rare true physical chitosan hydrogels. In this study, physicochemical and rheological properties of chitosan solutions in the presence of acetic acid and beta-GP were investigated as a function of temperature in order to gain a better understanding of the gelation mechanisms. The gel structure formed at high temperature was only partially thermoreversible upon cooling to 5 degrees C because of the existence of remaining associations, confirmed by the spontaneous recovery of the gel after breakup at low temperature. Increasing temperature had no effect on the pH values of this system, while conductivity (and calculated ionic strength) increased. Values from the pH measurements were used to estimate the degree of protonation of each species as a function of temperature. The decreasing ratio of -NH3+ in chitosan and -OPO(O-)2 in beta-GP suggested reduced chitosan solubility along with a diminution of ionic interactions such as ionic bridging with increasing temperature. On the other hand, the increased ionic strength as a function of temperature, in the presence of beta-GP, enhanced screening of electrostatic repulsion and increased hydrophobic effect, resulting in favorable conditions for gel formation. Therefore, our study suggests that hydrophobic interactions and reduced solubility are the main driving force for chitosan gelation at high temperature in the presence of beta-GP.

Effect of bending and torsion rigidity on self-diffusion in polymer melts: A molecular-dynamics study

Extensive molecular-dynamics simulations have been performed to study the effect of chain conformational rigidity, controlled by bending and torsion potentials, on self-diffusion in polymer melts. The polymer model employs a novel torsion potential that avoids computational singularities without the need to impose rigid constraints on the bending angles. Two power laws are traditionally used to characterize the dependence of the self-diffusion coefficient on polymer length: D proportional to N(-nu) with nu=1 for N<Ne (Rouse regime) and with nu=2 for N>Ne (reptation regime), Ne being the entanglement length. Our simulations, at constant temperature and density, up to N=250 reveal that, as the chain rigidity increases, the exponent nu gradually increases towards nu=2.0 for N<Ne and nu=2.2 for N>Ne. The value of Ne is slightly increased from 70 for flexible chains, up to the point where the crossover becomes undefined. This behavior is confirmed also by an analysis of the bead mean-square displacement. Subsequent investigations of the Rouse modes, dynamical structure factor, and chain trajectories indicate that the pre-reptation regime, for short stiff chains, is a modified Rouse regime rather than reptation.