Polymer 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.

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.

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.

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

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.

Structural characterization of aqueous solution poly(oligo(ethylene oxide) monomethyl methacrylate)-grafted silica nanoparticles.

The structure of aqueous dispersions of poly(oligo(ethylene oxide) monomethyl methacrylate)-grafted silica nanoparticles was characterized using contrast variation small-angle neutron scattering studies. Modeling the low hybrid concentration dispersion scattering data using a fuzzy sphere and a polydisperse core-shell model, demonstrated that the polymer chains are highly swollen in the dispersions as compared to the dimensions of the free polymer chains in dilute solution. At higher hybrid concentrations, the dispersions were well described using a Percus-Yevick approximation to describe the structure factor. These structural characterization tools are excellent starting points for effective molecular level descriptors of dewetting and macroscopic phase transitions for polymer tethered hybrid nanoparticle systems.

Samuel Frederick Edwards: Founder of modern polymer and soft matter theory

This year marks the 50th anniversary of the seminal paper by Sam Edwards on the statistical mechanics of a single polymer chain in dilute solution, a paper that in one stroke founded the modern quantitative understanding of polymer matter, and vaulted soft condensed matter on to the stage of theoretical physics (1). Sir Samuel Frederick Edwards, universally known as “Sam,” was a giant of theoretical physics; he passed away in Cambridge, England on May 7, 2015. The problem solved in his 1965 paper (1) addresses the simplest question that one can ask at a fundamental level about polymeric matter: given the number of monomers in a chain, how big is the polymer itself in 3D space? It is also an extraordinarily difficult problem: a polymer chain is almost a random configuration in space, yet it has to respect the constraint that atoms cannot overlap, restricting the positions of the monomers in a nonlocal way and generally resulting in a polymer chain that is somewhat expanded compared with a random walk. Paul Flory, the great polymer chemist, had provided an ingenious heuristic solution to the problem of one chain, but a detailed and systematic understanding remained out of reach. Edwards formulated the problem in terms of path integrals, and solved it in an excellent approximation using self-consistent field theory. Edwards’ method would, in time, become the basis for a complete attack on all phases of polymeric matter, not only single chains but dilute and concentrated solutions, disordered phases such as rubber and gels, charged phases such as polyelectrolytes, and even dynamical properties. A decade after Edwards’ work, Pierre-Gilles de Gennes would show that Edwards’ ideas could be extended to take into account critical fluctuations using renormalization group ideas (2). This approach would be refined in great detail by subsequent studies, allowing accurate computation of universal scaling functions governing the physical chemistry of all polymers in solution and providing excellent agreement with experiment. de Gennes would be awarded the 1991 Nobel Prize in physics for his many contributions to soft matter, but many believed that Edwards’ contributions, so frequently linked with de Gennes’, deserved similar recognition.

Monte Carlo simulations of lattice models for single polymer systems.

Single linear polymer chains in dilute solutions under good solvent conditions are studied by Monte Carlo simulations with the pruned-enriched Rosenbluth method up to the chain length N~O(10(4)). Based on the standard simple cubic lattice model (SCLM) with fixed bond length and the bond fluctuation model (BFM) with bond lengths in a range between 2 and √10, we investigate the conformations of polymer chains described by self-avoiding walks on the simple cubic lattice, and by random walks and non-reversible random walks in the absence of excluded volume interactions. In addition to flexible chains, we also extend our study to semiflexible chains for different stiffness controlled by a bending potential. The persistence lengths of chains extracted from the orientational correlations are estimated for all cases. We show that chains based on the BFM are more flexible than those based on the SCLM for a fixed bending energy. The microscopic differences between these two lattice models are discussed and the theoretical predictions of scaling laws given in the literature are checked and verified. Our simulations clarify that a different mapping ratio between the coarse-grained models and the atomistically realistic description of polymers is required in a coarse-graining approach due to the different crossovers to the asymptotic behavior.

Effect of Heat Treatment on Dilute Solution Properties of Sugar Beet Pectin

Beet Pectin (SBP) polysaccharide. Aqueous solution properties of these samples have been studied using Ubbelohde capillary viscometer in the dilute regime. Intrinsic viscosity [?] was estimated for different SBP solution samples prepared from heat-treated SBP powdered samples with different heating time. Results suggest that heat treatment has a significant effect on solution behavior of SBP samples. Intrinsic viscosities decreased with increasing heating time indicating that heat-treated SBP molecules are compact than the untreated one and the compactness increases with increasing heating time at 80°C. The intrinsic viscosities of these samples were plotted as a function of the corresponding molecular weight of the samples and can be expressed by a power law. The power law exponent was estimated as 1.4 indicating that pectin molecules takes the conformation of stiff polymer chains in dilute solution. Dhaka Univ. J. Sci. 61(1): 117-123, 2013 (January) DOI: http://dx.doi.org/10.3329/dujs.v61i1.15107

Translational diffusion coefficients of macromolecules

The calculation of the translational diffusion coefficient of a single flexible polymer chain in dilute solution can be basically addressed either a) within the Einstein theory (calculating the time autocorrelation function of the macromolecule center of mass), or b) within the Kirkwood and Riseman theory for irreversible processes of macromolecules in solution. The equations of the latter theory can be solved employing different approximations that give rise to different values of the diffusion coefficient. In general, the value of the diffusion coefficient obtained through the different theories and approaches varies slightly depending on polymer features like flexibility. In this paper, we evaluate the most common procedures to compute the diffusion coefficient of flexible macromolecules via computer simulation and the difference between the values obtained.

Role of Borderline Solvents to Induce Pronounced Extended-Chain Lamellar Order in π-Stackable Polymers

Thin films of poly[2,5-bis(3-tetradecylthiophen-2-yl)thieno[3,2-b]thiophene] (C14–PBTTT) exhibit a monolayer-terraced morphology that indicates a pronounced lamellar order with π-stacks of extended polymer chains. Previously this remarkable state of order was thought to be promoted by the interdigitation of alkyl side chains between the lamellae during cooling from the liquid-crystalline (LC) phase. Here we establish that the key to this ordering in fact is the formation of unentangled π-stacks of extended polymer chains in dilute solutions of chlorobenzene (CB) or 1,2-dichlorobenzene (o-DCB), which though routinely used as the “best” solvents are in fact borderline solvents. Film formation causes these π-stacks to deposit substantially oriented in the film plane, while the subsequent anneal and cool from LC phase accentuates this incipient order to develop the monolayer-terraced morphology. This mechanism is supported by the following lines of evidence. (i) Hydrodynamic and viscometry measurements respec...

Internal motions of linear chains and spherical microgels in dilute solution

It is well known that for a flexible polymer chain in dilute solution, two different types of motions mainly contribute: the translation motion of the centres of mass of individual polymer chains; and the internal modes generated from the motions of segments with respect to the centre of mass of the chain. During the past two decades, with the advances in light scattering instrumentation and sophisticated methods of data analysis, both types of motions can be distinguished in experiments and utilized for testing molecular theories of polymer chain dynamics in dilute solution. In this article, we first review some previous experiments, in particular the dynamical properties of polystyrene (PS) and polyisoprene (PIP) chains in good and theta (Θ) solvents, and then our own results, including a comparative study of the internal motions of poly(N-isopropylacryl-amide) (PNIPAM) linear chains and spherical microgels under good solvent conditions. The final part of this article deals with how the solvent quality (the solution temperature) affects the internal mobility of PNIPAM linear chains and microgels.

Hole mobility on isolated chains of poly(3-hexylthiophene) by microwave conductivity measurement

We demonstrate a facile method to investigate intrinsic charge mobility on isolated chains of conjugated polymers by use of microwave absorption method. Hole carriers are generated on conjugated polymer chains in dilute solution by doping with the p-type dopants NOSbF(6), instead of using excitation sources of pulsed laser and electron beam as reported in the literature. The number of hole carriers can be easily estimated by doping level. Measurements on poly(3-hexylthiophene) in benzene with various doping levels from 0.1% to 3% indicate that the hole mobility can be divided into two ranges. In the doping level 0.1%-0.3%, the hole mobility maintains at the constant level 0.03 cm(2)/V s, which can be regarded as that on an isolated chain since the average number of hole carriers per chain is only around one. As the doping level is higher than 0.3%, a presence of multiple hole carriers on a chain occurs, which results in a repulsion of hole carriers and leads to a reduced hole mobility.

High Intrachain Hole Mobility on Molecular Wires of Ladder-Type Poly(p-Phenylenes)

We have studied the high-frequency (34 GHz) mobility of positive charge carriers on isolated ladder-type polymer chains in dilute solution. We find that the high-frequency mobility is limited by the chain ends on chains as long as 35 monomers. The intrachain motion of charge carriers can be described by one-dimensional diffusion between infinitely high reflecting barriers, representing the chain ends. Our data indicate that the intrachain mobility for ladder-type polymer chains is close to 600 cm(2)/V s. With this high mobility the ladder-type polymer is a promising candidate for future use as an interconnecting wire in molecular electronics.

Effect of intermolecular disorder on the intrachain charge transport in ladder-type poly(p-phenylenes)

We have studied the real and imaginary parts of the complex intrachain mobility of charge carriers on solid samples of ladder-type polymers using time-resolved microwave conductivity measurements. Experiments on samples with a different average polymer chain length show that the motion of charge carriers is limited by the chain ends. The experimental results can be described by one-dimensional diffusive motion along the polymer backbone. The intrachain mobility deduced for an infinitely long ladder-type polymer chain (with no barriers to charge transport such as defects or conjugation breaks) subject to interchain interactions is $30\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}∕\mathrm{V}\phantom{\rule{0.2em}{0ex}}\mathrm{s}$. This value is 20 times lower than the intrachain mobility found for charges along infinitely long isolated ladder-type polymer chains in dilute solution. Thus we find that interchain interactions in solid samples severely decrease the intrachain charge carrier mobility. However, the intrachain mobility of $30\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}∕\mathrm{V}\phantom{\rule{0.2em}{0ex}}\mathrm{s}$ is more than four orders of magnitude higher than mobility values obtained from time of flight measurements reported in the literature. Hence, the performance of ladder-type polymers in optoelectronic devices can be significantly improved.

Dissipative Particle Dynamics Simulations of Polymer Chains: Scaling Laws and Shearing Response Compared to DNA Experiments

Dissipative particle dynamics simulations of several bead-spring representations of polymer chains in dilute solution are used to demonstrate the correct static scaling laws for the radius of gyration. Shear flow results for the wormlike chain simulating single DNA molecules compare well with average extensions from experiments, irrespective of the number of beads. However, coarse graining with more than a few beads degrades the agreement of the autocorrelation of the extension.

Triplet build in and decay of isolated polyspirobifluorene chains in dilute solution

The triplet kinetics of a conjugated polymer, polyspirobifluorene, have been studied using time resolved photoinduced absorption spectroscopy and gated emission delayed fluorescence. Working on isolated polymer chains in dilute solution, we pay particular attention to the buildup and decay of the triplet states following intersystem crossing from the excited singlet state. Confirmation of intersystem crossing as a monomolecular cold process has been made. At high excitation powers an initial fast decay of the triplet has been observed; this is attributed to intrachain triplet-triplet annihilation. From this observation we estimate the lower bound of the intersystem crossing yield as 1.2%. We also calculate the intrachain annihilation constant to be (2.9+/-0.1)x 10(8) cm(3) s(-1).

Ultrafast photogeneration of charged polarons on conjugated polymer chains in dilute solution

Ultrafast photoinduced absorption by infrared-active vibrational modes is used to study the photogeneration of polarons on semiconducting polymer chains in dilute solutions and in solid films of a soluble derivative of poly(para-phenylene vinylene). In dilute solutions, polaron pairs are photogenerated on the conjugated polymer within less than $250\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ with quantum efficiencies ${\ensuremath{\phi}}_{\mathrm{ch}}\ensuremath{\sim}3%$, about one-third of that for solid films of the same polymer. The excitation spectra of ${\ensuremath{\phi}}_{\mathrm{ch}}$ for both solutions and films show that ${\ensuremath{\phi}}_{\mathrm{ch}}$ is weakly dependent on photon energy between $2.2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ (the onset of absorption) and $4.7\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The recombination dynamics of polarons is very fast and highly dependent on the excitation density for polymer films, but it is significantly slower and less sensitive to pump intensity for the semiconducting polymer in dilute solution. We conclude that the positive and negative polarons on a single chain in solution are typically separated by hundreds of monomer repeat units and that their one-dimensional diffusion along the chain is inhibited by the intervening excitons. This, together with the suppression of interchain recombination, explains the surprisingly slower polaron recombination in isolated chains.