Kuhn Length Research Articles

Physical aging and glass transition of hairy nanoparticle assemblies

ABSTRACTMatrix free assemblies of polymer‐grafted, “hairy” nanoparticles (aHNP) exhibit novel morphology, dielectric, and mechanical properties, as well as providing means to overcome dispersion challenges ubiquitous to conventional polymer‐inorganic nanocomposite blends. Physical aging of the amorphous polymer glass between the close‐packed nanoparticles (NPs) will dominate long‐term stability; however, the energetics of volume recovery within the aHNPs is unknown. Herein, we compare glass transition temperature (Tg) and enthalpy recovery of aHNPs to NP‐polymer blends, across different nano‐silica loadings (0–50 v/v%) and canopy architecture of polystyrene (PS) grafted silica. For aHNPs, the grafting of PS to silica imposes an additional design constraint between silica volume fraction, graft density, and graft molecular weight. At low and intermediate silica volume fraction, the Tg of blended nanocomposites is independent of silica content, reflecting a neutral polymer‐NP interface. For aHNPs, the Tg decreases with silica content, implying that chain tethering decreases local segment density more than the effect of molecular weight or polymer‐NP interactions. Additionally, the Tg of the aHNPs is higher than a linear matrix of comparable molecular weight, implying a complementary effect to local segment density that constrains cooperativity. In contrast, enthalpy recovery rate in the blend or aHNP glass is retarded comparably. In addition, a cross‐over temperature, Tx, emerges deep within the glass where the enthalpy recovery process of all nanocomposites becomes similar to linear unfilled matrices. Differences between structural recovery in aHNP and blended nanocomposites occur only at the highest silica loadings (∼ 50 v/v%), where enthalpy recovery for aHNPs is substantially suppressed relative to the blended counterparts. The absence of physical aging at these loadings is independent of brush architecture (graft density or molecular weight of tethered chains) and indicates that the impact of chain tethering on effective bulk structural relaxation starts to appear at particle‐particle surface separations on the order of the Kuhn length. Overall, these observations can be understood within the context of how three separate structural characteristics impact local segment density and relaxation processes: the dimension and architecture of the tethered polymer chains, the separation between NP surfaces, and the confinement imposed by chain tethering and space filling within the aHNP. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 319–330

Effect of chain stiffness on the competition between crystallization and glass-formation in model unentangled polymers.

We map out the solid-state morphologies formed by model soft-pearl-necklace polymers as a function of chain stiffness, spanning the range from fully flexible to rodlike chains. The ratio of Kuhn length to bead diameter (lK/r0) increases monotonically with increasing bending stiffness kb and yields a one-parameter model that relates chain shape to bulk morphology. In the flexible limit, monomers occupy the sites of close-packed crystallites while chains retain random-walk-like order. In the rodlike limit, nematic chain ordering typical of lamellar precursors coexists with close-packing. At intermediate values of bending stiffness, the competition between random-walk-like and nematic chain ordering produces glass-formation; the range of kb over which this occurs increases with the thermal cooling rate |Ṫ| implemented in our molecular dynamics simulations. Finally, values of kb between the glass-forming and rodlike ranges produce complex ordered phases such as close-packed spirals. Our results should provide a useful initial step in a coarse-grained modeling approach to systematically determining the effect of chain stiffness on the crystallization-vs-glass-formation competition in both synthetic and colloidal polymers.

Computer Simulations of Bottle Brushes: From Melts to Soft Networks

Using a combination of molecular dynamics simulations and analytical calculations, we study dense bottle- brush systems in a melt and network state. Analysis of our simulation results shows that bottle-brush macromolecules in melt behave as ideal chains with effective Kuhn length bK. Simulations show that the bottle-brush-induced bending rigidity is due to an entropy decrease caused by redistribution of the side chains upon backbone bending. The Kuhn length of the bottle brushes increases with increasing the side-chain degree of polymerization nsc as bK ∝ nsc 0.46 . This model of bottle-brush macromolecules is extended to describe mechanical properties of bottle-brush networks in linear and nonlinear deformation regimes. In the linear deformation regime, the network shear modulus scales with the degree of polymerization of the side chains as G0 ∝ (nsc +1 ) −1 as long as the ratio of the Kuhn length, bK, to the size of the fully extended bottle-brush backbone between cross-links, Rmax, is smaller than unity, bK/Rmax ≪ 1. Bottle-brush networks with bK/Rmax ∝ 1 demonstrate behavior similar to that of networks of semiflexible chains with G0 ∝ nsc −0.5 . In the nonlinear network deformation regime, the deformation-dependent shear modulus is a universal function of the first strain invariant I1 and bottle-brush backbone deformation ratio β describing stretching ability of the bottle-brush backbone between cross-links.

Theoretical Insight into Dispersion of Silica Nanoparticles in Polymer Melts.

Silica nanoparticles dispersed in polystyrene, poly(methyl methacrylate), and poly(ethylene oxide) melts have been investigated using a density functional approach. The polymers are regarded as coarse-grained semiflexible chains, and the segment sizes are represented by their Kuhn lengths. The particle-particle and particle-polymer interactions are calculated with the Hamaker theory to reflect the relationship between particles and polymer melts. The effects of particle volume fraction and size on the particle dispersion have been quantitatively determined to evaluate their dispersion/aggregation behavior in these polymer melts. It is shown that theoretical predictions are generally in good agreement with the corresponding experimental results, providing the reasonable verification of particle dispersion/agglomeration and polymer depletion.

All Polymer Diffusion Regimes Covered by Combining Field-Cycling and Field-Gradient1H NMR

Field-cycling and field-gradient 1H NMR experiments were combined to reveal the segmental mean-square displacement as a function of time for polydimethylsiloxane (PDMS) and polybutadiene (PB). Together, more than 10 decades in time are covered, and all four power-law regimes of the tube-reptation (TR) model are identified with exponents rather close to the predicted ones. Characteristic polymer properties like the tube diameter a0, the Kuhn length b, the mean-square end-to-end distance ⟨R02⟩, the segmental correlation time τs(T), the entanglement time τe(T), and the disengagement time τd(T) are estimated from the measurements and compared to results from literature. Concerning τd(T), fair agreement is found. In the case of τe, agreement with rheological data is achieved when the time constant is extracted from the minimum in the shear modulus G″(ω). Concerning the TR predictions the molar mass (M) dependence of τd is essentially reproduced. Yet, calculating τe from τd for PDMS yields agreement with experi...

Molecular structure of self-healing polyampholyte hydrogels analyzed from tensile behaviors.

Recently, charge balanced polyampholytes (PA) have been found to form tough and self-healing hydrogels. This class of physical hydrogels have a very high equilibrated polymer concentration in water (ca. 40-50 wt%), and are strongly viscoelastic. They are synthesized by random copolymerization of equal amounts of oppositely charged monomers at a high concentration, followed by a dialysis process of the small counter-ions and co-ions in water. The randomly distributed, opposite charges of the polymer form multiple ionic bonds of intra- and inter-chains with strength distribution. The strong inter-chain bonds, stabilized by topological entanglement, serve as quasi-permanent crosslinks, imparting the elasticity, while the weak bonds, both inter- and intra-chains, reversibly break and re-form to dissipate energy to toughen the materials. In this work, we intend to clarify the structure of the physical PA hydrogels from the tensile behaviors of the PA hydrogels. To clarify the structure and its formation mechanism, we analysed the tensile behaviors of the samples before and after the dialysis. We separated the quasi-permanent crosslinking of strong inter-chain bonds and the dynamic crosslinking of weak inter-chain bonds by using a combined model that consists of the Upper Convected Maxwell model and the Gent strain hardening model. The model fitting of the tensile behaviors extracts quantitative structural parameters, including the densities of weak and strong inter-chain bonds and the theoretical finite extensibility of polymer chains. Based on the fitting results of the combined model, the structural parameters of partial chains at a fixed observation time, including the Kuhn number, Kuhn length, and chain conformation, are determined using the scaling theory. The effects of monomer concentration at preparation, the effect of dialysis and the initial strain rate on the dynamic structure of PA gels, are discussed based on these analyses.

Solvatochromism and conformational changes in fully dissolved poly(3-alkylthiophene)s.

Absorption spectroscopy is commonly utilized to probe optical properties that can be related, among other things, to the conformation of single, isolated conjugated polymer chains in solution. It is frequently suggested that changes in peak positions of optical spectra result from variations in the stiffness of polymer chains in solution because this modifies the conjugation length. In this work we utilize ultraviolet-visible (UV-vis) spectroscopy, small angle neutron scattering (SANS), and all atom molecular dynamic (AA-MD) simulations to closely probe the relationship between the conformation of single-chains of poly(3-alkylthiophene)s (P3ATs) and their optical properties. SANS results show variations in the radius of gyration and Kuhn length as a function of alkyl chain length, and structure, as well as the solvent environment. Furthermore, both SANS and MD simulations show that dissolved P3HT chains are more rigid in solvents where self-assembly and crystallization are possible. Shifts in P3AT optical properties were also observed for different solvent environments. However, these changes were not correlated to the changes in polymer conformation. Furthermore, changes in optical properties could not be perfectly described by generalized solvent-solute interactions. AA-MD simulations provide new insights into specific polymer-solvent interactions not accounted for in generalized solvatochromic theory. This work highlights the need for experiments and molecular simulations that further inform the specific role of solvent molecules on local polymer conformation and on optical properties.

Loop formation and stability of self-avoiding polymer chains

Using 3-dimensional Langevin dynamics simulations, we investigated the dynamics of loop formation of chains with excluded volume interactions, and the stability of the formed loop. The mean looping time τl scales with chain length N and corresponding scaling exponent α increases linearly with the capture radius scaled by the Kuhn length a/l due to the effect of finite chain length. We also showed that the probability density function of the looping time is well fitted by a single exponential. Finally, we found that the mean unlooping time τu hardly depends on chain length N for a given a/l and that the stability of a formed loop is enhanced with increasing a/l.

A new entropy model for RNA: part III. Is the folding free energy landscape of RNA funnel shaped?

The concept of a free energy (FE) landscape, in which the conformations of a polymer progressively take on the structure of the native state while spiraling down a FE surface that resembles the shape of a funnel, has long been viewed as the reason why a complex protein structure forms so rapidly compared to the number of conformations available to it. On the other hand, this landscape picture is less clear with RNA due to the multiplicity of conformations and the uncertainties in the current thermodynamics. It is therefore sometimes proposed that within the ensemble of suboptimal states of the RNA molecule, the vast majority of those states all closely resemble the native state and therefore simply overwhelm the few states that represent the global minimum FE. However, calculations of the free energy of observed structures often suggest that the most frequently observed cluster of structures are far from the minimum FE, particularly in the case of long sequences. If so, then such a FE surface is unlikely to be funnel shaped. We have been developing a version of <em>vsfold</em> that can evaluate the suboptimal structures of the FE surface (through a modified version called <em>vs_subopt</em>). Here we show that the ensemble of suboptimal structures for a number of known RNA structures can actually be both close to the minimum FE and also be the dominant observed structure when a proper Kuhn length is selected. Two state aptamers known as riboswitches can show neighboring FE states in the suboptimal structures that match the observed structures and their relative difference in FE is well within the range of the binding free energy of the metabolite. For the riboswitches and other short RNA sequences (less than 250 nt), the flow of the suboptimal structures (including pseudoknots) tended to resemble a rock rolling down a hill along the reaction coordinate axis. An important insight yielded by the cross-linking entropy (CLE) model is that the global entropy limits the size of domains. Hence, based on the CLE model, Levinthal’s paradox is overcome by the funnel shape in the FE, by a reduction in the number of degrees of freedom due to Kuhn length, and by limits on the size of the domains that can form. These concepts are also applicable to calculating transition rates between different suboptimal structures.

In Situ Analysis of Bacterial Extracellular Polymeric Substances from a Pseudomonas fluorescens Biofilm by Combined Vibrational and Single Molecule Force Spectroscopies

Extracellular polymeric substances (EPS) play an important role in biofilm cohesion and adhesion to surfaces. EPS of a P. fluorescens biofilm were characterized through their vibrational spectra (infrared and Raman) and their conformational properties using single molecule force spectroscopy with specific probes for glucose, galactose, and N-acetyl glucosamine-rich EPS. Vibrational spectra evidenced the overproduction of glycogen and other carbohydrates in the biofilm. The conformational analysis was performed from both the freely jointed chain (FJC) and worm like chain (WLC) models. The results of the FJC fittings showed highly ramified and/or folded structures for all the detected EPS with molecular elongations up to 1000-2500 nm, and typical Kuhn lengths of glycogen macromolecules. The characteristics of galactose-rich EPS have been found to be significantly different from those of glucose- and N-acetyl glucosamine-rich EPS. On the basis of the theoretical fittings with the WLC model, our results suggested that carbohydrates may be associated with peptide domains.

Crosslink-induced shrinkage of grafted Gaussian chains.

The statistical mechanics of polymers grafted on surfaces has been the subject of intense research activity because of many potential applications. In this paper, we analytically investigate the conformational changes caused by a single crosslink on two ideal (Gaussian) chains grafted onto a rigid planar surface. Both the crosslink and the surface reduce the number of allowed configurations. In the absence of the hard substrate, the sole effect of the crosslink is a reduction in the effective Kuhn length of a tethered chain. The crosslink-induced shrinkage (collapse) of the grafted chains (mushrooms) turns out to be a reduction in the variance of the distribution of the height of the chain rather than a reduction of the height itself.

Wireframe and Tensegrity DNA Nanostructures

CONSPECTUS: Not only can triangulated wireframe network and tensegrity design be found in architecture, but it is also essential for the stability and organization of biological matter. Whether the scaffolding material is metal as in Buckminster Fuller's geodesic domes and Kenneth Snelson's floating compression sculptures or proteins like actin or spectrin making up the cytoskeleton of biological cells, wireframe and tensegrity construction can provide great stability while minimizing the material required. Given the mechanical properties of single- and double-stranded DNA, it is not surprising to find many variants of wireframe and tensegrity constructions in the emerging field of DNA nanotechnology, in which structures of almost arbitrary shape can be built with nanometer precision. The success of DNA self-assembly relies on the well-controlled hybridization of complementary DNA strands. Consequently, understanding the fundamental physical properties of these molecules is essential. Many experiments have shown that double-stranded DNA (in its most commonly occurring helical form, the B-form) behaves in a first approximation like a relatively stiff cylindrical beam with a persistence length of many times the length of its building blocks, the base pairs. However, it is harder to assign a persistence length to single-stranded DNA. Here, normally the Kuhn length is given, a measure that describes the length of individual rigid segments in a freely jointed chain. This length is on the order of a few nucleotides. Two immediate and important consequences arise from this high flexibility: single-stranded DNA is almost always present in a coiled conformation, and it behaves, just like all flexible polymers in solution, as an entropic spring. In this Account, we review the relation between the mechanical properties of DNA and design considerations for wireframe and tensegrity structures built from DNA. We illustrate various aspects of the successful evolution of DNA nanotechnology starting with the construction of four-way junctions and then allude to simple geometric objects such as the wireframe cube presented by Nadrian Seeman along with a variety of triangulated wireframe constructions. We examine DNA tensegrity triangles that self-assemble into crystals with sizes of several hundred micrometers as well as prestressed DNA origami tensegrity architecture, which uses single-stranded DNA with its entropic spring behavior as tension bearing components to organize stiff multihelix bundles in three dimensions. Finally, we discuss emerging applications of the aforementioned design principles in diverse fields such as diagnostics, drug delivery, or crystallography. Despite great advances in related research fields like protein and RNA engineering, DNA self-assembly is currently the most accessible technique to organize matter on the nanoscale, and we expect many more exciting applications to emerge.

Extended de Gennes Regime of DNA Confined in a Nanochannel

Scaling regimes for polymers confined to tubular channels are well established when the channel cross-sectional dimension is either very small (Odjik regime) or large (classic de Gennes regime) relative to the polymer Kuhn length. However, experiments of confined polymers using DNA as a model system are usually located in the intermediate region between these two regimes. In the literature, controversy exists regarding the existence of the extended de Gennes regime in this intermediate region. Here we use simulations and theory to reconcile conflicting theories and confirm the existence of extended de Gennes regime. We show that prior work did not support the notion of this regime because of the use of a wrong confinement free energy. In a broad sense, the extended de Gennes regime corresponds to the situation when excluded volume interaction is weaker than thermal energy. Such a situation also occurs in many other cases, such as semidilute polymer solutions and polymers under tension. This work should be...

Single-Molecule Force Measurements by Nano-Handling of Individual Dendronized Polymers

A nano-handling technique based on atomic force microscopy (AFM) is presented that allows reliable measuring of force-extension profiles of single-polymer molecules. The basis of the method is a properly functionalized solid substrate, to which a small amount of the polymers in question is adsorbed. The sample is first imaged in amplitude modulation mode in solution with a functionalized AFM cantilever, and a polymer chain is picked up with the AFM tip at one of the ends of the polymer molecule. Force curves are recorded by stretching the attached polymer molecule many times. After the force experiments, the molecule is imaged again. In this fashion, one can ascertain that the force experiments are truly carried out with one individual molecule. With this technique, the force response of amino-functionalized dendronized polymers was studied and it could be accurately described by the freely jointed chain model with chain elasticity. A monotonic dependence of the mechanical properties of these polymers up to generation 4 was found. The elastic constant was independent of the generation and solution composition. On the other hand, the effective Kuhn length increased with the generation at higher salt concentrations. The mechanical response of dendronized polymers can be tuned with solution composition.

Systematic Coarse-Graining of the Dynamics of Self-Attractive Semiflexible Polymers

We develop a coarse-graining procedure, using bead–rod chains with varying numbers of rods per Kuhn length (Nr,K), to model the conformational dynamics of polymer chains with bending stiffness and self-attraction. We find the conditions under which increased chain resolution leads to converged results for the effect of bending stiffness, attractive interaction strength (e), and shearing flow on the conformational dynamics. As chain stiffness increases, we find a collapse transition that becomes steeper as attractive strength increases. The collapsed state depends not only on the net dimensionless attractive strength e* = eNr,K between each Kuhn step of the chain but also on the ratio of bead diameter to Kuhn length (σ*). At high e* (>0.8/σ*), collapsed globules are produced at moderate chain diameter σ* = 1/4, while for fat chains with σ* = 1, helices are formed, and for thin ones with σ* = 1/16, tori, folded bundles, and finally globules are formed as e* increases.

Sequential Domain Realignment Driven by Conformational Asymmetry in Block Copolymer Thin Films

In this contribution, we use dissipative particle dynamics simulations to investigate the orientations of lamella-forming copolymers with two blocks of equal molecular weight confined in thin films. We employ neutral and symmetric interactions between the copolymer blocks and the walls, a situation for which contradicting observations have been made in experiments and previous theoretical studies. Our model takes into account a realistic degree of conformational asymmetry between the blocks, which stems from unequal Kuhn lengths of the constituent monomers. We perform a thorough scaling analysis to exclude finite size effects, and find, in agreement with experiments, a remarkable cascade of morphological transitions from parallel to perpendicular orientations when the film height is varied. We demonstrate that the emergence of a stable parallel configuration stems from entropic effects due to the conformational asymmetry and the confinement of the system.

Peptide Desorption Kinetics from Single Molecule Force Spectroscopy Studies

We use a combined experimental/theoretical approach to determine the intrinsic monomeric desorption rate k0 of polytyrosine and polylysine homopeptides from flat surfaces. To this end, single polypeptide molecules are covalently attached to an AFM cantilever tip and desorbed from hydrophobic self-assembled monolayers in two complementary experimental protocols. In the constant-pulling-velocity protocol, the cantilever is moved at finite velocity away from the surface and the distance at which the constant plateau force regime ends and the polymer detaches is recorded. In the waiting-time protocol, the cantilever is held at a fixed distance above the surface and the time until the polymer detaches is recorded. The desorption plateau force is varied between 10 and 90 pN, by systematically changing the aqueous solvent quality via the addition of ethanol or salt. A simultaneous fit of the experimental data from both protocols with simple two-state kinetic polymer theory allows to unambiguously disentangle and determine the model parameters corresponding to polymer contour length L, Kuhn length a, adsorption free energy λ, and intrinsic monomeric desorption rate k0. Crucial to our analysis is that a statistically significant number of single-polymer desorption experiments are done with one and the same single polymer molecule for different solvent qualities. The surprisingly low value of about k0 ≈ 10(5) Hz points to significant cooperativity in the desorption process of single polymers.

Modeling the relaxation time of DNA confined in a nanochannel.

Using a mapping between a Rouse dumbbell model and fine-grained Monte Carlo simulations, we have computed the relaxation time of λ-DNA in a high ionic strength buffer confined in a nanochannel. The relaxation time thus obtained agrees quantitatively with experimental data [Reisner et al., Phys. Rev. Lett. 94, 196101 (2005)] using only a single O(1) fitting parameter to account for the uncertainty in model parameters. In addition to validating our mapping, this agreement supports our previous estimates of the friction coefficient of DNA confined in a nanochannel [Tree et al., Phys. Rev. Lett. 108, 228105 (2012)], which have been difficult to validate due to the lack of direct experimental data. Furthermore, the model calculation shows that as the channel size passes below approximately 100 nm (or roughly the Kuhn length of DNA) there is a dramatic drop in the relaxation time. Inasmuch as the chain friction rises with decreasing channel size, the reduction in the relaxation time can be solely attributed to the sharp decline in the fluctuations of the chain extension. Practically, the low variance in the observed DNA extension in such small channels has important implications for genome mapping.

Comparison of the Binding of Polyvinylpyrrolidone and Polyethylene Oxide to Ag Surfaces: Elements of a Successful Structure-Directing Agent

We investigate the origins of experimentally observed differences in the structure-directing capabilities of polyvinylpyrrolidone (PVP) and polyethylene oxide (PEO) for the shape-selective, colloidal synthesis of {100}-faceted Ag nanostructures. Using dispersion-corrected density-functional theory, we calculate the binding energies of polymer repeat units to Ag(100) and Ag(111). At the level of the repeat unit, the energetic preference for PEO to bind to {100} facets (∼40 meV) is half that of PVP. At the chain level, we use the Kuhn length to define the polymer binding unit and this is 9 (3) repeat units for PVP (PEO). A thermodynamic model predicts that the {100} binding selectivity of PVP is 107 times higher than that of PEO at synthesis temperatures. These results are consistent with experiment and demonstrate that a distinguishing characteristic of a successful polymer structure-directing agent is the pairing of facet-selective binding of the repeat unit with a sufficiently stiff chain.

A new entropy model for RNA: part II. Persistence-related entropic contributions to RNA secondary structure free energy calculations

In previous work, we have shown that the entropy of a folded RNA molecule can be divided into local and global contributions using the cross-linking entropy (CLE) model, where, in the case of RNA, the cross- links are the base-pair stacking interactions. The local contribution to the CLE is revealed in the Kuhn length (a measure of the stiffness of the RNA). The Kuhn length acts as a scaling parameter. When the size of the system is rescaled, the relationship between local and global free energy must be renormalized to reflect this rescaling. In this renormalization process, the Kuhn length increases, the local entropy also increases due to freezing out of the local conformational degrees of freedom. At the same time, as the number of degrees of freedom decrease, there is a significant reduction in the global entropy. Here we present a method, based on the concepts of renormalization theory, to quantitatively estimate the size of the contribution from the local entropy as a function of the Kuhn length. The local entropy correction is used to predict the current empirically derived constant in the Jacobson-Stockmayer equation. The variation in the Kuhn length is shown to be largely influenced by the length of the double-stranded RNA stems formed in the secondary structure of folded RNA. This result is used to test the resulting entropy under a variable Kuhn length in stem-loop structures. Comparisons between a variable Kuhn length and a static Kuhn length on a short stem-loop of RNA are also examined. The model is quite general and is also directly applicable to protein structure and folding problems.