Polymer solutions and entropic-based systems for double-stranded DNA capillary electrophoresis and microchip electrophoresis

We give an overview of recent development of low-viscosity polymer solutions and entropic trapping networks for double-stranded DNA (dsDNA) separations by conventional capillary electrophoresis and microchip electrophoresis. Theoretical models for describing separation mechanisms, commonly used noncross-linked polymer solutions, thermoresponsive (viscosity-adjustable) polymer solutions, and novel entropic trapping networks are included. The thermoresponsive polymer solutions can be loaded at one temperature into microchannels at lower viscosities, and used in separation at another temperature at entanglement threshold concentrations and higher viscosities. The entropic-based separations use only arrays of regular obstacles acting as size-separations and do not need viscous polymer solutions. These progresses have potential in integration to automated capillary and microfluidic chip systems, enabling better reusability of separation microchannels, much shorter DNA separation times, and higher reproducibility due to less matrix degradation.     

Dual entropic and enthalpic processes in the lower critical solution temperature phase separation of poly(vinyl methyl ether) aqueous solutions

In the lower critical solution temperature phase separation of poly(vinyl methyl ether) aqueous solutions, the process corresponding to the weakening of the hydrogen bond interaction with increasing temperature is dominant and occurs over the entire concentration region of solutions and over a broad temperature range from 30 to 41°C, giving rise to the energetic enthalpic effect during phase separation, while the conformational change, that is, collapse of the swollen polymer coils, occurs only in the swelling polymer solution when the water concentration is above 38.3 wt %, giving rise to the entropic effect during phase separation. In addition, the entropic process corresponding to the collapse of the polymer coils occurs in a much narrow theta temperature range from 35.5 to 37°C. If the solution is held at a constant temperature for a sufficiently long time, 90% collapse of the polymer coils occurs in only the 0.5 °C temperature region between 35.5 and 36°C. Accordingly, in the enthalpic process, the most dramatic blueshift of the νC‐O bond peak occurs in the temperature range between 35 and 41°C, while this blueshift is only approximately 2 cm^?1 in the temperature range from 30 to 35°C, prior to the collapse of the polymer coils due to the entropic effect. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 323–330     

Continuum theory of polymer crystallization

We present a kinetic model of crystal growth of polymers of finite molecular weight. Experiments help to classify polymer crystallization broadly into two kinetic regimes. One is observed in melts or in high molar mass polymer solutions and is dominated by nucleation control with G approximately exp(1/TDeltaT), where G is the growth rate and DeltaT is the supercooling. The other is observed in low molar mass solutions (as well as for small molecules) and is diffusion controlled with G approximately DeltaT, for small DeltaT. Our model unifies these two regimes in a single formalism. The model accounts for the accumulation of polymer chains near the growth front and invokes an entropic barrier theory to recover both limits of nucleation and diffusion control. The basic theory applies to both melts and solutions, and we numerically calculate the growth details of a single crystal in a dilute solution. The effects of molecular weight and concentration are also determined considering conventional polymer dynamics. Our theory shows that entropic considerations, in addition to the traditional energetic arguments, can capture general trends of a vast range of phenomenology. Unifying ideas on crystallization from small molecules and from flexible polymer chains emerge from our theory.     

The interaction parameter of crosslinked networks and star polymers

Recent results on blends containing star polymers have revived the interest on the interaction parameters of structures that contain junctions between chains, a matter which can be connected with the earlier studies on the influence of crosslinks on the interaction parameters of polymer networks and gels. Here, we review results on crosslinked networks and star polymer solutions together with the more recent work on star polymer blends. The review covers swelling and elastic deformation of gels, differential vapour sorption between crosslinked and uncrosslinked polymers, osmotic equilibrium of gels and of star polymer solutions, and neutron scattering of polymer blends containing star polymers. In the systems reviewed, the interaction parameters of stars and networks differ from those of linear chains, and the difference is attributed mainly to entropic effects.     

An extension of cubic equations of state to vapor-liquid equilibria in polymer-solvent mixtures

Cubic equations of state (EOS) are extended to describe polymer-solvent vapor-liquid equilibria (VLE). The solvents are described the conventional way using critical parameters. To describe the pure polymers, only the weight-average molecular weight is necessary, though number-average molecular weight, polydispersity and melt density can be incorporated if desired. To extend the model to mixtures, a mixing rule that combines EOS with excess energy models is used. In this formulation, the excess Gibbs energy term is considered in two parts: the classical Flory term for the entropic contributions and a residual term that takes care of specific interactions between the solvent and the polymer. For athermal mixtures that exhibit no such interactions, the residual term drops out and the model becomes completely predictive. Otherwise, for residual contributions, depending upon the complexity of specific molecular interactions anticipated in the mixture, either a single parameter Flory expression or a two-parameter NRTL equation can be used. We conclude that the simple cubic EOS approach presented here is easy to use, yet competes successfully with more sophisticated EOS models developed particularly for polymer solutions. Moreover, it offers more flexibility if one or more parameters are to be tuned to the process data.     

(Liquid + liquid) equilibria of binary polymer solutions using a free-volume UNIQUAC-NRF model

In this work, a modified free-volume (FV) model based on the UNIQUAC-Nonrandom factor (UNIQUAC-NRF) model developed by Haghtalab and Asadollahi was proposed. While the combinatorial part of the proposed model for activity coefficient takes the same form as that of the entropic free-volume (entropic-FV) model, the residual part is similar to that of the UNIQUAC-NRF model. The proposed model, i.e., the FV-UNIQUAC-NRF model overcomes the main shortcoming of the original UNIQUAC-NRF model in predicting the lower critical solution temperature (LCST) for polymer solutions. The appearance of the LCST is believed to be attributed to the existence of the free volume differences between polymer and solvent molecules. Thus, the models without considering such differences fail to predict the LCST behavior of polymer solutions. The proposed model was applied to correlate the experimental data of (liquid + liquid) equilibria (LLE) for a number of binary polymer solutions at various temperatures. The values for the binary characteristic energy parameters for the proposed model and the FV-UNIQUAC model along with their average relative deviations from the experimental data were reported. It should be stated that the binary polymer solutions studied in this work were considered as monodisperse. The results obtained from the FV-UNIQUAC-NRF model were compared with those obtained from the FV-UNIQUAC model. The results of the proposed model show that the FV-UNIQUAC-NRF model can accurately correlate the experimental data for LLE of polymer solutions studied in this work. Also the error produced from the FV-UNIQUAC-NRF model show the slightly better accuracy in comparison with that from the FV-UNIQUAC model. The clear advantage of the proposed model, contrary to the original UNIQUAC-NRF model, is its capability in predicting the LCST for binary polymer solutions.     

Construction of approximate entropic forces for finitely extensible nonlinear elastic (FENE) polymers

When the stress applied to a Rouse-like polymer chain is large enough, one must use anharmonic entropic spring forces in order to keep the chain contour length from increasing to unphysical values. Although one can derive “exact” equations relating the spring extension to the entropic force produced by a finitely extensible non-linear elastic (FENE) random-walk polymer, such expressions are usually of little interest because their complexity would entail large evaluation times in numerical studies by computer. Moreover, these expressions can rarely be used directly in analytical studies. In this article, we describe a systematic method to construct analytically simple yet numerically accurate expressions to relate the entropic force to the extension of an entropic spring for a random-walk polymer chain in arbitrary dimension d ≥ 2. These expressions are modified Pade approximants which yield the correct asymptotic behaviours in both the small and large extension limits. It is shown that the well-known Warner empirical approximation is but a limiting case (for infinite dimensions).     

Nanoscience of single polymer chains revealed by nanofishing

The invention of atomic force microscopy (AFM) enabled us to study the statistical properties of single polymer chains by a method called "nanofishing," which stretches a single polymer chain adsorbed on a substrate with its one end by picking it at the other end. A force-extension curve obtained for a single polystyrene chain in a Theta solvent (cyclohexane) shows good agreement with a worm-like chain model and, therefore, gives microscopic information about entropic elasticity. Furthermore, the nanofishing technique can be used for dynamic viscoelastic measurement of single polymer chains. An AFM cantilever is mechanically oscillated at its resonant frequency during the stretching process. This technique enables the estimation of quantitative and simultaneous elongation-dependent changes of stiffness and viscosity of a single chain with the use of a phenomenological model. In this study, the effect of solvent on viscosity in low extension regions reveals that the viscosity is attributed to monomer-solvent friction. Thus, static and dynamic nanofishing techniques are shown to give powerful experimental proofs for several basic questions in polymer physics. The techniques are expected to reveal hidden properties of polymer chains or polymer solutions by any types of macroscopic measurements in the future.     

Phase diagram for microphase separation transition in poor solvent polymer solutions

In the present paper, we consider the possibility of microphase separation transition in poor solvent polymer solutions. It is shown that this phenomenon can take place if the following two conditions are fulfilled: i) there is a large entropic contribution to the entropy of polymer/solvent mixing, i.e., solvent acts like a plastisizer; ii) this entropic contribution is nonlocal. Both conditions are met below the glass transition temperature for the pure polymer near the so-called Berghmans point when the glass transition curve intersects the liquid-liquid phase separation curve for polymer solutions. The phase diagram for the microphase separation transition is calculated within the framework of weak segregation approximation first proposed by Leibler for block-copolymer systems. The regions of stability of different microdomain structures (lamellar, triangular, body-centered-cubic) are obtained. It is shown that under certain conditions the phase diagram can have two critical points related to the macro- and microphase separation respectively.This paper is dedicated to Prof. E. W. Fischer on the occasion of his 65th Birthday.This work was done in the course of the Humboldt Research Award stay of A.R. Khokhlov at the Max-Planck-Institute for Polymer Research in Mainz. During this stay A.R.K. greatly benefited from numerous discussions with Professor E.W. Fischer who introduced him to the fascinating field of glass transition in polymer systems and formulated several new directions for future research.     

An improvement in the flory corresponding-states theory of polymer solutions

The original Flory corresponding-states theory of polymer solutions requires an entropic correction parameter Q₁₂, the sign and value of which seem to be arbitrary, and the physical meaning of which is obscure. Moreover, calculated excess volumes of mixing for many polymer solutions are often in significant disagreement with experimental data. In order to eliminate these problems, we have modified the kinetic part of the partition function, introduced an effective mass for the mixture segment, and adopted the nonlinearity of the number of degrees of freedom with respect to the composition for the mixture segment. In addition, the effect of nonrandom configurations of the segments in the mixture has been included. In the improved equations, derived in this work, the Flory interaction parameter χ can be considered to comprise three parts: (a) a kinetic part due to the contribution of the average number of degrees of freedom and the effective mass of the mixture; (b) a free volume part; and (c) an interaction part including the contributions due to the contact interaction and the nonrandom configuration of the segments in the mixture, caused by the interaction. The improved theory is in good agreement with literature data on polystyrene solutions and poly (dimethyl siloxane) solutions.     

Lattice cluster theory of associating polymers. II. Enthalpy and entropy of self-assembly and Flory-Huggins interaction parameter χ for solutions of telechelic molecules

The lattice cluster theory for solutions of telechelic polymer chains, developed in paper I, is applied to determine the enthalpy Δh(p) and entropy Δs(p) of self-assembly of linear telechelics and to evaluate the Flory-Huggins (FH) interaction parameter χ governing the phase behavior of these systems. Particular focus is placed on examining how these interaction variables depend on the composition of the solution, temperature, van der Waals and local "sticky" interaction energies, and the length of the individual telechelic chains. The FH interaction parameter χ is found to exhibit an entropy-enthalpy compensation effect between the "entropic" and "enthalpic" portions as either the composition or mass of the telechelic species is varied, providing unique theoretical insights into this commonly reported, yet, enigmatic phenomenon.     

Gel electrophoretic mobility of single-stranded DNA: the two reptation field-dependent factors

The reptation model is the dominant theory in understanding the electrophoretic separation of single-stranded DNA molecules in gels or entangled polymer solutions. Recently, we showed that the Ogston and reptation regimes are separated by an entropic trapping regime at low field intensities. Here, we report the first comparison of the field-dependent part of the DNA mobility for both small and long reptating molecules. We show that both mobilities increase linearly with field intensity, with the mobility of the longer (comigrating) fragments increasing faster than that of the smaller ones. We compare our results to the predictions of the biased reptation model.     

Entropic stochastic resonance of a flexible polymer chain in a confined system

We have studied the dynamics of a flexible polymer chain in constrained dumb-bell-shape geometry subject to a periodic force and external noise along the longitudinal direction. It is found that the system exhibits a feature of entropic stochastic resonance (ESR), i.e., the temporal coherence of the polymer motion can reach a maximum level for an optimal noise intensity. We demonstrate that the occurrence of ESR is robust to the change of chain length, while the bottleneck width should be properly chosen. A gravity force in the vertical direction is not necessary for the ESR here, however, the elastic coupling between polymer beads is crucial.     

New polymer systems exhibiting microphase separation transition with the formation of nano-microstructures

The concept of microphase separation was up to now widely applied mainly to the conformational transitions in block-copolymer solutions and melts. However, recently it became obvious that this concept has a much more general meaning. It was shown that microphase separation transition can be observed in random copolymers, interpenetrating polymer networks, polyelectrolyte mixtures, poor solvent polyelectrolyte solutions, ionomer solutions and melts, polymer blends and solutions with nonlocal entropy of mixing. In all these examples the emerging microdomain structures correspond to the nanometer scale, therefore the study of these effects can lead to the new ways of obtaining polymer materials with controlled nano-microstructure. In this presentation the review of our recent findings on microphase separation in some of the above-mentioned systems will be presented. 1. The problem of microphase separation in the systems containing weakly charged polyelectrolytes (polyelectrolyte mixtures and poor solvent polyelectrolyte solutions) will be considered. From the methodic point of view, it will be shown that this problem can be solved by direct minimization of the free energy, without the use of “weak segregation” or “strong segregation” assumptions which are common in the theory of block-copolymers. The final phase diagrams exhibit wide macroscopic phase separation regions, which is their main difference from the corresponding phase diagrams for block-copolymer systems. The formation of microdomains is thus coupled with macroscopic phase separation: in most of the cases microdomain structure is formed in one of the coexisting phases after macroscopic phase separation takes place [1] - [2]. 2. The formation of the multiplet structure in ionomer melts and solutions can be also considered as the microphase separation in the random copolymer system with the formation of the “micelles” (or clusters) of ionic links. The parallels with micelle formation in block-copolymer systems can be established if one considers a new “superstrong segregation regime” for block-copolymer microstructures. This regime can be indeed observed for diblock copolymers with one ionomeric and one neutral block [3]. 3. The microphase separation transition in ordinary polymer blends and solutions is also possible. The conditions for this effect are: (i) significant entropic contribution to polymer/polymer or polymer/solvent miscibility, (ii) the nonlocal character of this contribution with a high value of the nonlocality radius. It is argued that one can expect that the entropy nonlocality radius increases in the vicinity of the glass transition for the blend or polymer solutions (in the latter case solvent molecules act like “poor solvent plasticisers”). Computer simulation data supporting the theoretical prediction of microphase separation transition in these systems will be presented [4] - [5].     

Interactions between colloidal particles induced by polymer brushes grafted onto the substrate

We investigate the interaction energy between two colloidal particles on or immersed in nonadsorbing polymer brushes grafted onto the substrate as a function of the separation of the particles by the use of a self-consistent-field theory calculation. Depending on the colloidal size and the penetration depth, we demonstrate the existence of a repulsive energy barrier of several kBT, which can be interpreted by separating the interaction energy into three parts: colloid-polymer interfacial energy, entropic contribution due to "depletion zone" overlap of colloidal particles, and entropic elastic energy of grafted chains by the compression of particles. The existence of a repulsive barrier which is of entirely entropic origin can lead to kinetic stabilization of the mixture rather than depletion flocculation or phase separation. Therefore, the present result may suggest an approach for controlling the self-assembling behavior of colloids for the formation of target structures, by tuning the colloidal interaction on the grafting substrate under appropriate selection of colloidal size, effective gravity (influencing the penetration depth), and brush coverage density.     

Effect of molecular weight and its distribution on the spinodal for polydisperse polymer solutions

The Flory–Huggins interaction parameter χ(r_i) is considered as dependent on the chain length of a polymer. Therefore, a modified free energy expression of Flory–Huggins theory is obtained for the polydisperse polymer solutions. Based on this modified free energy expression and the thermodynamics of Gibbs, the expression of spinodal for polydisperse polymer solutions is obtained. For a given χ(r_i) according to de Gennes, the spinodals are calculated for polydisperse polymer solutions at different molecular weights and their distributions. It is found that all the interested variables r_n, r_w, r_z and molecular weight distribution have an effect on the spinodal for polydisperse polymer solutions, where the effect of changing r_w is much greater than that of changing r_n, r_z and molecular weight distribution.     

Reaction of polyamine polymer with molecular iodine via charge-transfer complex formation

The reaction of a Mannich base type-polyamine polymer with iodine (I₂) was studied kinetically and thermodynamically in order to clarify the polymer effects in the formation of triiodide ions (I₃^?). N,N-Dimethyl-p-(4-methylpiperazinomethyl) aniline and 1,4-dimethylpiperazine were used as low molecular weight donor model compounds. Triiodide ions are produced from the polyamine–I₂ system immediately after mixing the two-component solutions, while in the systems with I₂ and N,N-dimethyl-p-(4-methyl-piperazinomethyl)aniline and 1,4-dimethylpiperazine they are obtained only when relatively high concentrations of both donor and acceptor solutions were mixed. This is explained by the entropic contributions of the polymer chain such as the stacking effect of donor nitrogen atoms, i.e., the increment of local donor concentration around I₂ in the reaction field. The relation between the solution behavior of the reaction systems and the rate of formation of I₃^? ions also supports this kind of polymer effect. The effects of neighboring groups and dielectric constant on the reaction are also discussed.     

Single polymer chains as specific transducers of molecular recognition in scanning probe microscopy

A new approach for the specific detection and mapping of single molecule recognition is presented, based on the nonlinear elastic behavior of a single polymer chain. The process of molecular recognition between a ligand and a receptor is inherently accompanied by a decrease in the translational and rotational degrees of freedom of the two molecules. We show that a polymeric tether linked to the ligand can effectively transduce the configurational constraint imposed by molecular recognition into a measurable force, which is dominated by the entropic elasticity of the polymer. This force is specifically characterized by a strong nonlinearity when the extension of the polymer approaches its contour length. Thus, a polymer chain tethering the ligand to an oscillating cantilevered tip gives rise to a highly anharmonic motion upon ligand-receptor binding. Higher-harmonics atomic force microscopy allows us to detect this phenomenon in real time as a specific signature for the probing and mapping of single-molecule recognition.     

An incremental mean first passage analysis for a quasistatic model of polymer translocation through a nanopore

For the translocation of a polymer through a nanopore, a quasistatic assumption for the dynamics yields a tractable form for the entropic barrier. Although this is a much simplified model, interesting features such as robust scaling emerge from its application. To explore these details, we present a method of mapping the translocation process as an incremental mean first passage problem. In this approach, the quantity of interest is the average first time t(0) at which the polymer achieves a displacement of Δs in the translocation coordinate s. Constructing scenarios with different initial conditions and boundary conditions, analytic and exact numerical approaches are used to resolve the dynamics of translocation in detail and generate new insight into the nature of the entropic barrier.     

Free energy of mixing of cross-linked polymer blends

Free energy of mixing of cross-linked polymer blends is derived, as a modification to the Flory-Huggins-de Gennes free energy functional for linear polymer blends. The latter arrives from the assumption of mean-field, short-range thermal interactions among ideal Gaussian chains. However, upon cross-linking a linear chain, the chain no longer remains Gaussian; new chain architectures belying the threadlike image of linear chains emerge. Fractal dimensions of these nonlinear chain clusters convene and command new entropic interactions. Topological constraints by cross-links introduce long-range nonequilibrium elastic forces. Relatively shorter range steric repulsions between fractal network surfaces may arrive if cross-linking is carried out inside the blend's thermodynamically unstable region. Modified free energy has been used to highlight experiments on phase instability of cross-linked polymer blends.