Polymers In Poor Solvents Research Articles

Enhanced diffusion and universal Rouse-like scaling of an active polymer in poor solvent

Enhanced diffusion and universal Rouse-like scaling of an active polymer in poor solvent

Solvent effect on equilibrium organization of confined polymers.

The equilibrium organization of two polymers in strong confinement has been extensively investigated in the scope of simple models in the recent past, after it was suggested that the entropic repulsion between polymers could be a mechanism for chromosome separation in living cells. Despite many efforts, how solvent quality can manipulate separation or compaction for the formation of domains in a two-polymer model system within symmetric or asymmetric confinement still remains elusive. This paper presents some important findings for a two-polymer system within box-like (symmetric) and triangle-like (asymmetric) confinement with equal areas, in terms of structural transitions such as from a single globule to individual globules, non-monotonic change in polymer size, variation in the free-energy barrier with separation, etc. By using the exact enumeration method on a two-dimensional self-avoiding walk model of polymers, our results reveal that the polymers have a greater preference to form individual globules rather than a 'micelle'-like single globule in triangular confinement compared to box-like confinement. Additionally, our results suggest that asymmetric confinement can act as an ideal tool to trap polymers in poor solvents due to the large free-energy barrier.

Theory of polymers in poor solvents: Inter-chain interaction, second virial coefficient, and Θ point

Quantifying inter-chain interaction and determining Θ point is of fundamental importance in polymer science and engineering. Here, we apply a constrained self-consistent field theory which can fully capture the coupling between the position-dependent interaction and chain conformation. By tracking the density profile and free energy as a function of center-of-mass separation distance, we analyze the kinetic process of fission/fusion and calculate the potential of mean force as well as the second virial coefficient B 2 thereby in poor solvents. We show that the fission of the two-chain associate exhibits a necking behavior and a discontinuous breaking point, which shares the similarity with the tensile process of typical macroscopic bulk materials. The Θ point is determined by extrapolating the χ -dependence of B 2 plot to the vanishing point for very long chains. Our theory predicts a linear relationship between χ Θ ( N ) and N −1/2 , with a positive slope. The intercept yields χ Θ (∞) = 0.5, which coincides with the prediction from Flory-Huggins theory and verifies the consistency of the Θ point defined by different criteria in the limit of infinitely long chain. Furthermore, the slope of χ Θ ( N ) versus N −1/2 becomes larger as chain stiffness increases. χ Θ ( N ) = 0.5 for infinitely flexible polymers. Our theoretical predictions are in good agreement with the results obtained by off-lattice Monte Carlo simulation. • A constrained SCFT is applied to capture the coupling between the position-dependent interaction and chain conformation. • Potential of mean force (PMF) is quantified and kinetic process during fission/fusion of two polymer chains is analyzed. • Θ point χ Θ is determined by extrapolating the χ -dependent second virial coefficient curve. • χ Θ ( N ) is found to linearly depend on N −1/2 with a positive slope and the intercept χ Θ (∞) = 0.5. • The slope of χ Θ ( N ) versus N −1/2 increases with chain stiffness. For infinitely flexible polymers, χ Θ ( N ) = 0.5.

Sequence effects on internal structure of droplets of associative polymers

Intrinsically disordered proteins (IDPs) can form liquid-like membraneless organelles, gels, and fibers in cells and in vitro. In this study, we propose a simple model of IDPs as associative polymers in poor solvent and explore the formation of transient liquid droplets and their transformation into solid-like aggregates. We use Langevin dynamics simulations of short polymers with two stickers placed symmetrically along their contour to study the effect of the primary sequence of these polymers on their organization inside condensed droplets. We observe that the shape, size, and number of sticker clusters inside the droplet change from a long cylindrical fiber to many compact clusters as one varies the location of stickers along the chain contour. Aging caused by the conversion of intramoleclular to intermolecular associations is observed in droplets of telechelic polymers but not for other sequences of associating polymers. The relevance of our results to condensates of IDPs is discussed.

A new entropy model for RNA: part V, Incorporating the Flory-Huggins model in structure prediction and folding

The effect of solvent-biopolymer interactions is hardly negligible. Whereas the ideal (non-interacting) polymer consisting of N monomers in an ideal solvent is expected to have the terminal ends of its chain with a root-mean-squared (rms) end-to-end separation distance (<em>rms</em>) proportional to the square root of <em>N</em>, real interactions of a <em>rms</em> polymer both with itself and with the solvent often tend to strongly perturb <em>rms</em>. In <em>rms</em> poor solvent, the biopolymer can collapse into a small globule much smaller than the ideal <em>rms</em> due to excluding solvent. In good solvent, the biopolymer can swell to a size much larger than the ideal r due to favoring solvent. These effects require rms corrections to an ideal polymer equation. We have been developing the cross linking entropy (CLE) model in this series. The model attempts find the maximum entropy of a folded polymer by taking into account the correlation caused by bonding and other interactions of the structure. In RNA, this mostly occurs in the stems. Here we adapt CLE model to handle polymer swelling and collapse for RNA molecules both in good and in poor solvent. This work is intended to introduce this type of study and to allow its systematic application in problems of RNA folding and structure prediction. The current study suggests that there may be some tendency for RNA to behave as a polymer in poor solvent and that this collapse may happen in sequences longer than 50 nt.

Influence of shear on globule formation in dilute solutions of flexible polymers.

Polyelectrolytes, polymers in poor solvents, polymers mixed with particles, and other systems with attractions and repulsions show formation of globules/structures in equilibrium or in flow. To study the flow behavior of such systems, we developed a simple coarse-grained model with short ranged attractions and repulsions. Polymers are represented as charged bead-spring chains and they interact with oppositely charged colloids. Neglecting hydrodynamic interactions, we study the formation of compact polymer structures called globules. Under certain conditions, increase in shear rate decreases the mean first passage time to form a globule. At other conditions, shear flow causes the globules to breakup, similar to the globule-stretch transition of polymers in poor solvents.

Crumpled globule formation during collapse of a long flexible and semiflexible polymer in poor solvent.

By introducing explicit solvent particles and hydrodynamic interactions we demonstrate that crumpled globules are formed after the collapse of long polymer chains (N = 10(4)) in a poor solvent. During the collapse crumples of all sizes form sequentially, but small crumples are not stable and convert to blobs with Gaussian statistics. The observed effective mean squared distance R(2)(n) ∼ n(0.38) at n > Ne and contact probability index p(n) ∼ n(-0.5) at n ≫ Ne, which is not following either the model of a fractal globule, or the predictions for an equilibrium globule. Polymer chain stiffness pushes the system to form globular crystallite, and this freezes crumpled structure with R(2)(n) ∼ n(0.33) at n > Ne as a stable state. We note that there is some similarity to crumple globule formation and crystallization of polymer melt.

Theory of Polymer Chains in Poor Solvent: Single-Chain Structure, Solution Thermodynamics, and Θ Point

Using the language of the Flory chi parameter, we develop a theory that unifies the treatment of the single-chain structure and the solution thermodynamics of polymers in poor solvents. The structure of a globule and its melting thermodynamics is examined using the self-consistent filed theory. Our results show that the chain conformation involves three states prior to the globule-to-coil transition: the fully-collapsed globule, the swollen globule and the molten globule, which are distinguished by the core density and the interfacial thickness. By examining the chain-length dependence of the melting of the swollen globule, we find universal scaling behavior in the chain properties near the Theta point. The information of density profile and free energy of the globule is used in the dilute solution thermodynamics to study the phase equilibrium of polymer solution. Our results show different scaling behavior of the solubility of polymers in the dilute solution compared to the F-H theory, both in the chi dependence and the chain-length dependence. From the perspectives of single chain structure and solution thermodynamics, our results verifies the consistency of the Theta point defined by different criteria in the limit of infinite chain length: the disappearance of the second viral coefficient, the abrupt change in chain size and the critical point in the phase diagram of the polymer solution. Our results show the value of chi at the Theta point is 0.5 (for the case of equal monomer and solvent volume), which coincides with the value predicted from the F-H theory.

Nucleation in Polymers and Soft Matter

Nucleation is a ubiquitous phenomenon in many physical, chemical, and biological processes. In this review, we describe recent progress on the theoretical study of nucleation in polymeric fluids and soft matter, including binary mixtures (polymer blends, polymers in poor solvents, compressible polymer-small molecule mixtures), block copolymer melts, and lipid membranes. We discuss the methodological development for studying nucleation as well as novel insights and new physics obtained in the study of the nucleation behavior in these systems.

Oscillatory shear rheology of dilute solutions of flexible polymers interacting with oppositely charged particles

Fluids with both attractions and repulsions among its constituents can exist in multiple states depending on nature of the interactions. An external flow can induce such systems to transition between the different states, such as the globule‐stretch transition for polymers in poor solvents. Brownian dynamics simulations of a dilute solution of polymers and colloids interacting via short‐ranged potentials are presented. For some values of the strength and range of interactions, compact structures of polymers and colloids are formed. An external flow is capable of pulling these globules apart, causing the polymers to stretch at a critical shear rate. In oscillatory shear, the shear rate can cycle between being above and below this critical shear rate leading to interesting dynamics. These dynamics are quantified using the rheological response in large amplitude oscillatory shear. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1365–1371, 2014

Dynamics of a polyelectrolyte in simple shear flow

The configurational dynamics of a polyelectrolyte (PE), subjected to a simple shear flow, is studied using Brownian dynamics (BD) and Dissipative Particle Dynamics (DPD) simulations of a bead-spring model with explicit counterions. We explore the effect of counterion condensation on the tumbling and extension of PEs by varying the shear rates for a range of values of the electrostatic coupling parameter A (which is defined as the ratio of the Bjerrum length to the size of the monomer). In all cases, the power spectrum of Rs(t) (which characterizes the projected length of the PE in the flow direction as a function of time) exhibits a power law decay at high frequencies, similar to that for a dumbbell in shear flow. For lower values of A (A ~ 2), the tumbling of the PE is periodic and is always associated with folding and stretching, which is in contrast to the oscillatory transition between the extended and globular states seen at higher values of A (A ~ 15). We observe that for A ~ 2 the tumbling frequency decreases and the average tumbling time increases with hydrodynamic interaction (HI). For A > 15, we observe a critical shear rate γ[combining dot]c below which there is considerable counterion condensation and the PE remains in the globular state with a structure akin to that of a neutral polymer in poor solvent. The γ[combining dot]c and the behavior of the PE above the critical shear rate are dependent on the HI. For a given shear rate, when there is considerable condensed counterion fluctuation, the PE extends as a whole and then collapses by the formation of folds with no observable periodicity in tumbling. When the condensed counterion fluctuations are suppressed, the polymer exhibits periodic tumbling. Simulation artifacts resulting from the implicit nature of the solvent and that due to boundary conditions are discussed by comparing the BD results with that obtained from the DPD simulations incorporating Ewald summation for electrostatics.

Theory of Polymers in Poor Solvent: Phase Equilibrium and Nucleation Behavior

We study the phase equilibrium and nucleation behavior of polymers in poor solvent by accounting for the large, localized fluctuations in the form of single-chain globules and multichain clusters. The density profile and free energy of the single-chain globule and multichain clusters are obtained by self-consistent-field theory. This information is then used in the dilute solution thermodynamics to investigate the equilibrium cluster size distribution, solubility limit, and nucleation in the supersaturated state. Our results show that the solubility of the polymer in the dilute side of the solution is enhanced by several orders of magnitude relative to the prediction of the Flory–Huggins (F–H) theory, which scales with the chain length to the 2/3 power rather than a linear power as predicted from the F–H theory. Our results also suggest a higher critical value of χ, consistent with computer simulation and experiment results. In the supersaturated state, we work out an effective spinodal where the nucleation barrier to phase separation via growth of the clusters becomes comparable to the thermal energy kBT. For a given supersaturation, we find that the nucleation barrier is quadratic in the chain length, suggesting a much slower precipitation rate for longer polymer chains.

Macromolecular dynamics in crowded environments

The structural and dynamical properties of macromolecules in confining or crowded environments are different from those in simple bulk liquids. In this paper, both the conformational and diffusional dynamics of globular polymers are studied in solutions containing fixed spherical obstacles. These properties are studied as a function of obstacle volume fraction and size, as well as polymer chain length. The results are obtained using a hybrid scheme that combines multiparticle collision dynamics of the solvent with molecular dynamics that includes the interactions among the polymer monomers and between the polymer beads and obstacles and solvent molecules. The dynamics accounts for hydrodynamic interactions among the polymer beads and intermolecular forces with the solvent molecules. We consider polymers in poor solvents where the polymer chain adopts a compact globular structure in solution. Our results show that the collapse of the polymer chain to a compact globular state is strongly influenced by the obstacle array. A nonmonotonic variation in the radius of gyration with time is observed and the collapse time scale is much longer than that in simple solutions without obstacles. Hydrodynamic interactions are important at low obstacle volume fractions but are screened at high volume fractions. The diffusion of the globular polymer chain among the obstacles is subdiffusive in character on intermediate time scales where the dynamics explores the local structure of the heterogeneous environment. For large polymer chains in systems with high obstacle volume fractions, the chain adopts bloblike conformations that arise from trapping of portions of the chain in voids among the obstacles.

Effects of molecular crowding on stretching of polymers in poor solvent

We consider a linear polymer chain in a disordered environment modeled by percolation clusters on a square lattice. The disordered environment is meant to roughly represent molecular crowding as seen in cells. The model may be viewed as the simplest representation of biopolymers in a cell. We show the existence of intermediate states during stretching arising as a consequence of molecular crowding. In the constant distance ensemble the force-extension curves exhibit oscillations. We observe the emergence of two or more peaks in the probability distribution curves signaling the coexistence of different states and indicating that the transition is discontinuous unlike what is observed in the absence of molecular crowding.

The photochemistry of some main chain liquid crystalline 4,4′-stilbene dicarboxylate polyesters

Several aspects of the photochemistry and photophysics of four main chain liquid crystalline polyesters with a rigid trans-stilbene 4,4'-dicarboxylate mesogen as chromophore and flexible spacer groups are reported. The three polymers with the longest 'spacer' groups are liquid crystalline at room temperature, two have smectic phases. Chromophore aggregation has a dramatic effect on the photophysics and photochemistry of these polymers. Each of the polymers in poor solvents or as films has greatly perturbed UV-Vis absorption and fluorescence spectra due to aggregation of the stilbene chromophore. These effects are more pronounced upon annealing above the glass transition temperature, T(g), and in the mesophase. Film fluorescence is excitation wavelength dependent and is suppressed at elevated temperatures. The stilbene 'environment' in both films and solution is clearly heterogeneous and energy transfer processes relatively slow. The dominant photochemical reaction upon direct excitation above 300 nm is 2 + 2 photocycloaddition rendering polymer films insoluble. No significant trans-to-cis photoisomerization can be detected upon initial irradiation of the polymer films. There is evidence for the formation of aldehyde and carboxylate functionality upon irradiation in the presence of air. Loss of the aggregate UV-Vis absorption and fluorescence occurs during irradiation. Difference UV-Vis spectra of irradiated films suggest preferential initial consumption of dimeric aggregates. Loss of stilbene UV-Vis absorption upon irradiation above 300 nm can be partly photoreversed upon subsequent 254 nm irradiation. The rate of stilbene chromophore loss from films increased significantly above Tg and in the smectic phase above room temperature.

Shape instabilities in adsorbed polymer condensates

AbstractA polymer chain in a poor solvent collapses to a spherical globule. If this globule is subsequently deformed, either by stretching it or if it has some non‐zero net electric charge, it will become unstable to sinusoidal perturbations leading to novel final states. When such globules are imaged by direct methods such as atomic force microscopy the substrate on which they adsorb can affect the final morphological state. We therefore investigate strongly adsorbed polymers in poor solvents. We demonstrate that the real‐space, Self‐Consistent Field method is an ideal numerical tool in predicting equilibrium morphologies. New structures are predicted, which support previous explicit free energy calculations. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3327–3337, 2007

Chain organization and photophysics of conjugated polymer in poor solvents: Aggregates, agglomerates and collapsed coils

UV/vis absorption, excitation, and emission spectroscopies are utilized to explore the association behavior of conjugated polymer, poly[2-methoxy, 5-(2′-ethylhexyloxy)- p-phenylenevinylene] (MEH-PPV), in a homologous series of linear alcohols and solvent–nonsolvent systems. We demonstrate that the aggregation, agglomeration, and collapse of isolated chains, which all take place in the poor solvents, exhibit different optical signatures. The aggregate, in which chromophores interact electronically, causes a red shift of absorption and emission spectra while the weak interaction of chromophores in the agglomerates leaves electronic properties unaltered. The collapse of isolated chain is accompanied by a blue shift of the spectra. Energy transfer from excited chromophores of non-aggregated chains to the lower energy aggregates is significantly diminished in the system of alcohol solvents, allowing separate emissions from various chromophores to occur. The optical signatures and extent of energy transfer are used as tools to elucidate the association mechanism and chain organization of isolated chains into large particles upon decreasing solvent quality. The extreme collapse of isolated chains in the very poor solvents is found to inhibit the chain organization into aggregates.

Nano-pattern formation via grafted polymers in poor solvents

Abstract Patterned substrates and films are important in a variety of applications from microelectronics, bimemetic material fabrications and smart or switchable surfaces. Here we investigate the morphological structures that can form from a grafted polymer system immersed in a poor solvent. Novel morphological structures such as hexagonally ordered fused micelles, elongated cylindrical micelles and inverted solvent filled micelles are formed.

Shape of Micelles Formed From Strongly Adsorbed Grafted Polymers in Poor Solvents

AbstractSummary: We consider the shape of strongly adsorbed polymer chains in poor solvents. Using both SCF theory and Monte Carlo simulations, we find these chains undergo an instability which is driven, surprisingly, by polymer entropy. This instability occurs above some critical grafting separation and the intermediate segregation regime. An analytical calculation also suggests that this instability occurs for strongly adsorbed polymer chains. We proceed to study multi‐chain systems and observe a number of novel morphological structures including circular polymer droplets, lamellae and a polymer layer with a solvent‐filled hole.Shape of strongly adsorbed multi‐chain polymer globules.magnified imageShape of strongly adsorbed multi‐chain polymer globules.

Semiflexible grafted polymers in poor solvents: Toroidal, archway, and tower micelles

We study a system of grafted semiflexible polymers in a poor solvent which form toroidal or rodlike conformations in the bulk. However, because of the physical constraint of surface grafting, macrophase separation is inhibited and a number of different polymer aggregates (or micelles) form which can be related to the chains' stiffness and their affinity for each other. In contrast to the fully flexible Gaussian case, we observe a number of novel micelle structures, including tower micelles, archway micelles, and spider micelles. We also attempt to develop a phase diagram for the occurrence of these structures with respect to the variables of chain length, chain stiffness, and polymer grafting density.