Chains In Dilute Solution Research Articles

Estimating Poly(N-isopropylacrylamide) size in solution below the LCST using fluorescence correlation spectroscopy with non-covalent bound fluorophores

Accurate size measurements of nanosized polymer chains in dilute solutions is important for understanding polymer behavior, however, these measurements can be challenging to implement accurately, and are technique dependent. Here we explore the use of Fluorescence Correlation Spectroscopy (FCS) to determine the size of single polymer chains in dilute solutions (<2 wt%). FCS, a technique with single molecule sensitivity, generally requires the use of covalently labelled polymers which can distort physicochemical behavior. Here, FCS based size measurements were based on the non-covalent interaction of fluorophores (Alexa 405, Atto 390, and Atto 425) with PNIPAm in water at 25 °C (below the Lower Critical Solution Temperature).FCS estimated size (hydrodynamic radius) of three different MW PNIPAm samples in water were: 5.0 ± 1.0 nm (28.5 kDa), 5.0 ± 1.0 nm (38 kDa), 3.3 ± 0.5 nm (55.5 kDa), in reasonable agreement with theoretical calculations. Accuracy was directly related to the fraction of PNIPAm-bound fluorophore, which were, for 1 wt% PNIPAm solutions in water: ∼11.5 % (Atto 390), ∼8.1 % (Atto 425), and 4 % (Alexa 405). This method has several advantages in that it does not require a covalent labelling of PNIPAm, it can be implemented on very small sample volumes, and allows for in-situ measurements.

Reaction kinetics of chitosan nanogels crosslinked by genipin

Crosslinking of chitosan chains in dilute solution by natural crosslinker genipin leads to biocompatible nanogels. Here we investigated the reaction kinetics between chitosan and genipin in a 200 mM acetate buffer at 37 °C, and the structural and conformational evolutions of the nanogels during the crosslinking reaction by multi detection asymmetric flow field-flow fractionation (AF4). Upon crosslinking by genipin, the z-average hydrodynamic radius Rhz of the chitosan chains increased from 26 nm to 130 nm, while the weight average molar mass Mw increased from 2.0 × 105 g/mol to 1.8 × 107 g/mol. The crosslinking reaction appeared to be first-order and size-dependent. In particular, the intrachain crosslinking reaction was preferentially for nanogels having the larger size, leading to formation of branched chains/nanogels having a wide range of molar masses between 106 and 108 g/mol but a similar radius of gyration Rg ∼ 40 nm. For the largest nanogel fractions with M > 2.0 × 108 g/mol, both Rg and Rh showed a scaling relation with exponent 1/3 and a structure parameter Rg/Rh = 0.74, as expected for the hard sphere particle. The reaction was accompanied by a reduction of charge density and an increase in hydrophobicity of chitosan nanogels, which plays a key role in the formation of uniform size nanogels with chain density ρ(Rh) up to 0.45 g/cm3.

Conformation of a Comb-like Chain in Solution: Effect of Backbone Rigidity.

We study the effect of backbone rigidity on the conformation of comb-like chains in dilute solution by using Brownian dynamics simulations. Our results demonstrate that the backbone rigidity can control the effect of side chains on the conformation of comb-like chains; that is, the relative strength of the excluded-volume interactions from backbone monomer-graft and graft-graft to backbone monomer-monomer gradually weakens with the increase of backbone rigidity. Only when the rigidity of the backbone tends to be flexible and the grafting density is high is the effect of excluded volume of graft-graft on the conformation of comb-like chains significant enough, and other cases can be ignored. Our results show that the radius of gyration of comb-like chains and the persistence length of the backbone are exponentially related to the stretching factor, where the power exponent exhibits an increase with the increase of the strength of bending energy. These finds provide new insights for characterizing the structure properties of comb-like chains.

Quantifying Exciton Transport in Singlet Fission Diblock Copolymers.

Singlet fission (SF) is a mechanism of exciton multiplication in organic chromophores, which has potential to drive highly efficient optoelectronic devices. Creating effective device architectures that operate by SF critically depends on electronic interactions across multiple length scales─from individual molecules to interchromophore interactions that facilitate multiexciton dephasing and exciton diffusion toward donor-acceptor interfaces. Therefore, it is imperative to understand the underpinnings of multiexciton transport and interfacial energy transfer in multichromophore systems. Interestingly, block copolymers (BCPs) can be designed to control multiscale interactions by tailoring the nature of the building blocks, yet SF dynamics are not well understood in these macromolecules. Here, we designed diblock copolymers comprising an inherent energy cleft at the interface between a block with pendent pentacene chromophores and an additional block with pendent tetracene chromophores. The singlet and triplet energy offset between the two blocks creates a driving force for exciton transport along the BCP chain in dilute solution. Using time-resolved optical spectroscopy, we have quantified the yields of key energy transfer steps, including both singlet and triplet energy transfer processes across the pentacene-tetracene interface. From this modular BCP architecture, we correlate the energy transfer time scales and relative yields with the length of each block. The ability to quantify these energy transfer processes provides valuable insights into exciton transport at critical length scales between bulk crystalline systems and small-molecule dimers─an area that has been underexplored.

Dilute solution properties of some star poly(ether urethane)s-based on erythromycin propionate core

Solution behaviour of new star poly(ether urethane)s based on erythromycin propionate core at different concentrations and temperatures in N,N-dimethyl formamide was studied by viscometry. The impact of the star polyurethanes chemical structures and molecular weights, solvent, temperature and of the interactions from the system on the viscosities and dimensions of the polymer chain in dilute solution was investigated. The model of Qian and Rudin was used to predict the hydrodynamic properties of the solvated star polyurethanes in solution. The variations of the hydrodynamic parameters expressed by intrinsic viscosity, expansion factor, second virial coefficient, unperturbed dimension parameters, hydrodynamic volume as well as of the dimensions of the polymer chain namely radius of gyration and density were studied, justifying that the conformational changes from the system occur as result of the interactions generated by hard segments, polyether arm and the solvent. MDI star polyurethanes evidence less expanded conformation in comparison with TDI star polyurethanes as attested by GPC results, intrinsic viscosity and parameter for unperturbed dimensions. The solubility parameter is found higher for TDI star polyurethanes and higher content of urethane groups.

Unraveling the conformational properties of comb-like Poly(propargyl acrylate)-graft-poly(2-ethyl-2-oxazoline) chains in dilute solutions

We report the preparation and conformational property in solution of a library of comb-like poly(propargyl acrylate)-graft-poly(2-ethyl-2-oxazoline) (PPANb-g-PEtOx47-σg) samples with varied grafting densities (σg) ranging from 0 to 0.68. An azido end-functionalized linear poly(2-ethyl-2-oxazoline) (PEtOx-N3) as grafting side chain with a molar mass of 4700 g mol−1 was synthesized by the living cationic ring opening polymerization (CROP) of 2-ethyl-2-oxazoline (EtOx), followed by the sequential post-polymerization azidation modification at the living chain end of PEtOx. Poly(propargyl acrylate) (PPA) as the backbone was prepared by the chemical transformation from the ATRP-made poly(tert-butyl acrylate) (PtBA). Comb-like PPANb-g-PEtOx47-σg samples with different σg were eventually obtained by grafting PEtOx-N3 onto PPA backbone via the copper(I)-catalyzed alkyne-azide cycloaddition (CuAAC) reaction under varied [PEtOx-N3]0/[alkyne]0 ratios. Quadruple-detection size-exclusion chromatography (QD-SEC) system was used to extract the molecular parameters of the obtained comb-like polymers, including molar mass (M), viscometric radius (Rη), and intrinsic viscosity ([η]), etc. The comb-like chain showing a scaling-law of Rη ∼ σg0.34 was confirmed in the shortest backbone, which is fairly accordant with our previous results in polystyrene system. In addition, a transition of polymer shape from star-like to comb-like, and further to branched comb-like structure was observed as the backbone length increases. The transition from star-like to comb-like could be attributed to the continuous increase of length-diameter ratio, which would lead to that the comb-like chain changes its molecular feature from isotropic to anisotropic. On the other hand, the transition from comb-like to branched comb-like should be due to the presence of the intermolecular Glasser-Hay coupling side reactions in comb-like polymers.

Conformational transitions and helical structures of a dipolar chain in external electric fields.

The conformational behavior of a single dipolar chain in a uniform electric field is investigated by molecular dynamics simulations. The dipolar chain is modeled as a backbone bead-on-spring chain of equally charged beads, each connected by a rigid spring with an oppositely charged side bead that can freely rotate around the backbone bead. In the strong coupling regime, when the dipolar chain is in the globular state due to a strong electrostatic correlational attraction, the application of an electric field causes the chain swelling and elongation along the field direction. In the weak coupling regime, a qualitatively new regime is found when the swollen dipolar chain shrinks along the field direction adopting flattened conformations due to the field-induced anisotropy of the chain rigidity and the head-to-tail attraction of the dipoles orienting along the field lines. A novel helical conformation is detected for low-polar media and strong electric fields. An increasing rigidity of the backbone chain leads to some stabilization of the helical conformation and the formation of double and triple helices as well as flat spread springs. Fine tuning of the interplay between dipolar and volume interactions by external electric fields induces re-orientation of rod-like dipolar chains in dilute solutions. The obtained results can provide new ways to control dipolar polymer conformations and design materials with responsive properties.

Insensitivity of Sterically Defined Helical Chain Conformations to Solvent Quality in Dilute Solution.

The interplay between polymer-polymer and polymer-solvent interactions as well as interactions that impose secondary structures determines the conformation of polymer chains in dilute solution. Polypeptoids-poly(N-substituted glycines) have been shown to form helical secondary structures primarily driven by steric interactions from chiral, bulky side chains, while polypeptoids with a racemic mixture of the same side chains lead to unstructured coil chains with a shorter Kuhn length. Small-angle neutron scattering (SANS) of the polypeptoids in dilute solution reveals that the helical polypeptoids are only locally stiffer than the coil chains formed from the racemic analogue, but exhibit overall flexibility. We show that chain conformations of both helical and coil polypeptoids (in terms of radius of gyration, Rg) are insensitive to solvent quality (parametrized by the second virial coefficient, A2). Potential effects from the bulky, chiral/racemic side chains dominating chain conformations are excluded by comparison with an achiral polypeptoid lacking side chain chirality. The specific interactions between polypeptoid segments are likely dominating the chain conformations in this type of polypeptoids as opposed to polymer-solvent interactions or energetic contributions from the helical secondary structure.

Relaxation Time Spectrum and Dynamics of Stretched Polymer Chain in Dilute θ Solution: Implicit Solvent Model versus Explicit Solvent Model

AbstractRelaxation dynamics of a single stretched polymer chain after releasing the two fixed ends in dilute solutions are investigated by using implicit solvent and explicit solvent molecular dynamic simulations. The phase diagram of polymer in explicit solvent solution is determined, and the θ point is estimated by the form factor of the polymer chain. The relaxation time spectrum is obtained by the inverse Laplace transform of length–time decay curves of the relaxation process. The dependencies of the longest relaxation time in the spectrum on the chain length are compared with the scaling prediction of the Rouse model and the Zimm model of flexible chains. In this paper, it is confirmed that the dynamical scaling analysis of theoretical models are in good agreement with the simulation models in all range of polymerization degree of chain studied. The coarse‐grained explicit solvent simulation model of polymer chain in dilute solution developed in this paper can be a good numerical model for the future study of the dynamics process of macromolecules with hydrodynamic interactions in solutions.

Light Scattering Study of Internal Motions of Ultralong Comb-like Chains in Dilute Solutions under Good Solvent Conditions

Internal dynamics of polymer chains is one of the most important fundamental problems in polymer physics. This work reports the first example of a dynamic light scattering (DLS) study of internal m...

Solvation and diffusion of poly(vinyl alcohol) chains in a hydrated inorganic ionic liquid.

While the behavior of polyelectrolyte chains in aqueous salt solutions has been extensively studied, little is known about polar polymer chains in solvents with extremely high concentrations of inorganic ions, such as those found in ionic liquids (ILs). Here, we report on expansion, solvation and diffusion of poly(vinyl alcohol), PVA, chains in dilute solutions of a hydrated inorganic IL phase change material (PCM), lithium nitrate trihydrate (LNH). This solvent has an extremely high concentration of inorganic ions (≈18 M) with a low concentration of water molecules largely forming solvation shells of Li+ and NO3- ions, as shown using ATR-FTIR spectroscopy. Diffusion and hydrodynamic size of PVA chains of different molecular weights in this unusual solvent were studied using fluorescence correlation spectroscopy (FCS). A higher scaling exponent obtained from the molecular weight dependences of the diffusion coefficients of PVA chains as well as a lower overlap concentration (c*) of PVA in LNH solutions as measured by FCS suggest an expansion of the polymer coils in this solvent. We argue that enhanced solubility of PVA in LNH solutions is likely a result of increased rigidification of polymer chains due to the binding of solvated Li+ ions, which is demonstrated using 7Li NMR spectroscopy. We believe that an understanding of solvation and ion-binding capability can offer crucial insight into designing polymer-based shape stabilization matrices for inorganic PCMs.

Electrostatic-Mediated Intramolecular Cross-Linking Polymers in Concentrated Solutions

Since Kuhn in 1956 first proposed intramolecular cross-linking of isolated single-polymer chains in dilute solutions, the method has been extensively employed to achieve single-chain colloids and t...

Investigating the Dynamic Viscoelasticity of Single Polymer Chains using Atomic Force Microscopy

ABSTRACTIn single‐molecule force spectroscopy (SMFS), many studies have focused on the elasticity and conformation of polymer chains, but little attention has been devoted to the dynamic properties of single polymer chains. In this study, we measured the energy dissipation and elastic properties of single polystyrene (PS) chains in toluene, methanol, and N,N‐dimethylformamide using a homemade piezo‐control and data acquisition system externally coupled to a commercial atomic force microscope (AFM), which provided more accurate information regarding the dynamic properties of the PS chains. We quantitatively measured the chain length‐dependent changes in the stiffness and viscosity of a single chain using a phenomenological model consistent with the theory of viscoelasticity for polymer chains in dilute solution. The effective viscosity of a polymer chain can be determined using the Kirkwood model, which is independent of the intrinsic viscosity of the solvent and dependent on the interaction between the polymer and solvent. The results indicated that the viscosity of a single PS chain is dominated by the interaction between the polymer and solvent. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1736–1743

Evolution of Single Chain Conformation for Model Comb-Like Chains with Grafting Density Ranging from 0 to ∼100% in Dilute Solution.

This work aims to experimentally clarify how the single chain conformation evolves as a function of grafting density for model comb-like chains in dilute solution in the whole density regime. Via a combination of rational design, precise synthesis and accurate characterization, we obtained four sets of PPANb-g-PS30-σ comb-like samples with well-defined architectures and accurately extracted their molecular parameters by triple detection size exclusion chromatography (TD-SEC). With these samples in hand, we quantified how the excluded volume interaction and chain conformation evolve with the grafting density (σ) in the whole density regime. Three main findings are reported: (i) the graft-graft excluded volume interaction is not ignorable even in the low σ-regime; (ii) contrary to theoretical predictions, both the excluded volume interaction and the chain conformation are found to be Nb-dependent; (iii) both Rg ∼ σ1/3 and [η] ∼ σ0 are experimentally confirmed for comb-like chains from different σ and Nb, signifying a unique 3D mass-size growth pattern and a quasi-3D fractal feature. The obtained results help clarify some long-existed controversial issues in the field.

Scaling Laws for Polymer Chains Grafted onto Nanoparticles

AbstractAn experimental approach is presented for identifying the scaling laws for polymer chains grafted onto gold nanoparticles. Poly(ethylene oxide) of various molecular weights are grafted onto gold nanoparticles via thiol end‐functional groups. The polymer‐grafted nanoparticles are self‐assembled into monolayers from solvents of different quality. Over a significant range of graft densities, nanoparticle monolayers deposited from good (athermal) solvent exhibit particle spacing that scales according to theoretical predictions for chains in dilute solution. This unexpected result for ordered nanoparticle monolayers is discussed in the context of the deposition process. In monolayers deposited from theta solvent, molecular weight scaling of particle spacing breaks down, possibly due to chain length dependence of solvent quality. In poor solvent, the structure of nanoparticle assemblies is not sufficiently ordered to obtain reliable measurements, possibly due to loss of nanoparticle dispersion. This approach opens up the possibility for accurate measurement of the effect of solvent on grafted chain scaling in nanoparticle assemblies.

A comprehensive molecular dynamics study of a single polystyrene chain in a good solvent

In this study, molecular characteristics of polystyrene (PS) was calculated measuring its dilute-solution properties in toluene at 288.15 K via molecular dynamics (MD) simulations. The solution models consisted of PS chains with different number of repeating units all of which were in a dilute regime. In order to investigate the compatibility between the polymer and the solvent molecules, interaction energy and Flory-Huggins (FH) interaction parameter were estimated. The simulation results indicate that increasing the chain repeating units enhanced the interaction between the solute and the solvent. Additionally, the chain dimensions were evaluated calculating the radius of gyration (Rg) and end-to-end distance, r0. To determine the dynamic behavior of the chains in the solutions, mean square displacement (MSD) and diffusivity coefficient were calculated. The simulation results indicated that the chain rigidity at low molecular weight and chain flexibility with increasing the molecular weight influenced chains dynamic behavior and diffusivity. Moreover, radial distribution function (RDF) illustrated the effect of steric hindrance of the chains in dilute solution on capturing the solvent molecules. In addition, solution viscosity was calculated by performing non-equilibrium molecular dynamics simulation (NEMD). The obtained results of chain characteristics and viscosity showed a good agreement with experimental results published previously. This agreement confirms the accuracy of the applied simulation method to characterize the dilute solutions and the chains characteristics.

Linking Catalyst-Coated Isotropic Colloids into "Active" Flexible Chains Enhances Their Diffusivity.

Active colloids are not constrained by equilibrium: ballistic propulsion, superdiffusive behavior, or enhanced diffusivities have been reported for active Janus particles. At high concentrations, interactions between active colloids give rise to complex emergent behavior. Their collective dynamics result in the formation of several hundred particle-strong flocks or swarms. Here, we demonstrate significant diffusivity enhancement for colloidal objects that neither have a Janus architecture nor are at high concentrations. We employ uniformly catalyst-coated, viz. chemo-mechanically, isotropic colloids and link them into a chain to enforce proximity. Activity arises from hydrodynamic interactions between enchained colloidal beads due to reaction-induced phoretic flows catalyzed by platinum nanoparticles on the colloid surface. This results in diffusivity enhancements of up to 60% for individual chains in dilute solution. Chains with increasing flexibility exhibit higher diffusivities. Simulations accounting for hydrodynamic interactions between enchained colloids due to active phoretic flows accurately capture the experimental diffusivity. These simulations reveal that the enhancement in diffusivity can be attributed to the interplay between chain conformational fluctuations and activity. Our results show that activity can be used to systematically modulate the mobility of soft slender bodies.

Understanding looping kinetics of a long polymer molecule in solution. Exact solution for delta function sink model

A diffusion theory for intramolecular reactions of polymer chain in dilute solution is formulated. We give a detailed analytical expression for calculation of rate of polymer looping in solution. The physical problem of looping can be modeled mathematically with the use of a Smoluchowski-like equation with a Dirac delta function sink of finite strength. The solution of this equation is expressed in terms of Laplace Transform of the Green’s function for end-to-end motion of the polymer in absence of the sink. We have defined two different rate constants, the long term rate constant and the average rate constant. The average rate constant and long term rate constant varies with several parameters such as length of the polymer (N), bond length (b) and the relaxation time τR. The long term rate constant is independent of the initial probability distribution.

Hydrodynamic Interactions and Entanglements of Polymer Solutions in Many-Body Dissipative Particle Dynamics.

Using many-body dissipative particle dynamics (MDPD), polymer solutions with concentrations spanning dilute and semidilute regimes are modeled. The parameterization of MDPD interactions for systems with liquid–vapor coexistence is established by mapping to the mean-field Flory–Huggins theory. The characterization of static and dynamic properties of polymer chains is focused on the effects of hydrodynamic interactions and entanglements. The coil–globule transition of polymer chains in dilute solutions is probed by varying solvent quality and measuring the radius of gyration and end-to-end distance. Both static and dynamic scaling relations for polymer chains in poor, theta, and good solvents are in good agreement with the Zimm theory with hydrodynamic interactions considered. Semidilute solutions with polymer volume fractions up to 0.7 exhibit the screening of excluded volume interactions and subsequent shrinking of polymer coils. Furthermore, entanglements become dominant in the semidilute solutions, which inhibit diffusion and relaxation of chains. Quantitative analysis of topology violation confirms that entanglements are correctly captured in the MDPD simulations.

Control globular structure formation of a copolymer chain through inverse design.

A copolymer chain in dilute solution can exhibit various globular structures with characteristic morphologies, which makes it a potentially useful candidate for artificial materials design. However, the chain has a huge conformation space and may not naturally form the globular structure we desire. An ideal way to control globular structure formation should be inverse design, i.e., starting from the target structure and finding out what kind of polymers can effectively generate it. To accomplish this, we propose an inverse design procedure, which is combined with Wang-Landau Monte Carlo to fully and precisely explore the huge conformation space of the chain. Starting from a desired target structure, all the geometrically possible sequences are exactly enumerated. Interestingly, reasonable interaction strengths are obtained and found to be not specified for only one sequence. Instead, they can be combined with many other sequences and also achieve a relatively high yield for target structure, although these sequences may be rather different. These results confirm the possibility of controlling globular structure formation of a copolymer chain through inverse design and pave the way for targeted materials design.