Molecular dynamic studies of the compatibility of some cellulose derivatives with selected ionic liquids

Molecular dynamics techniques were used to study oligomers that mimic cellulose and various derivatives in the amorphous phase, including cellulose (C), methyl cellulose (MC), hydroxypropyl cellulose (HPC), and carboxymethyl cellulose (CMC). Densities and solubility parameters were determined for a series of oligomers with increasing chain length. Both properties were found to change linearly with the degree of polymerization (from monomers to dodecamers). Extrapolated predictions of the densities (g/cm³) for long chain polymers are: C, 1.42; MC, 1.33; HPC, 1.30; and CMC, 1.42. Computed values for the solubility parameter (MPa^1/2) are: C, 25.39; MC, 21.43; HPC, 21.70; and CMC, 24.35. We also evaluated the sensitivity of the solubility parameter to changes in the calculated density and found the dependence to be significant. The calculated solubility parameters were evaluated against experimental and other theoretical values as well as against selected ionic liquids comprised of cations in the imidazolium family and the chloride and trifluoroacetate anions.     

Determination of solubility parameters for poly(3-hydroxyalkanoates).

The three dimensional solubility parameters defined by Hansen are based on dispersion forces between structural units, interaction between polar groups and hydrogen bonding. For polar polymers such as poly(3-hydroxyalkanoates), P(3HA), this approach was used to obtain the three coordinates of a solubility parameter in terms of: a dispersion part, a polar part and a hydrogen bonding part. Thirty-eight different solvents for poly(3-hydroxybutyrate), PHB, which are mentioned in the literature are examined by this method and the theoretical predictions are compared with the experimental reports. Another overall comparison between PHA polymers provides their Hansen and Hildebrand parameters for side chain lengths up to C13. In this series a linear progression in calculated solubility parameters with side chain length was found. An Appendix provides information and data on calculation of the solubility parameters. While the solubility information is limited and only covers homopolymers, it should help to highlight some of the contradictions regarding PHB solubility. This semi-empirical approach is only valid for amorphous polymers hence crystallinity effects, which are important with PHB, as well as molecular weight effects still require analysis.     

Experimental and theoretical estimation of the Hansen solubility parameters of paramylon esters based on the degrees of substitution and chain lengths of their acyl groups

Paramylon is a natural hydrophilic polysaccharide produced in the pyrenoids of euglenoids, and esterification may render paramylon hydrophobic. Esterification imparts not only thermoplasticity, but also potential compatibilities with other polymer resins and fillers. However, the dependence of the compatibility on the structure of the polymer ester has not yet been systematically studied. To estimate the affinities between paramylon esters and hydrophobic organic solvents/resins, the dependences of their Hansen solubility parameters, which are association indices, on the degrees of substitution and chain lengths of the ester groups were investigated. Experimental and theoretical investigations were conducted using the dissolution and Fedors methods, respectively. Esterification decreased the solubility parameter from 49 (paramylon) to approximately 18 MPa^1/2 (paramylon esters), indicating that the potential affinities of paramylon esters for hydrophobic organic solvents/polymers increased. A multiple regression analysis was also performed to investigate the effects of acyl chain length and degree of substitution with acyl groups on the solubility parameter. The solubility parameters of the paramylon derivatives were continuously variable from hydrophilic to -phobic. Hence, esterification with various acyl groups may control the hydrophobicities of paramylon esters, enhancing their miscibilities with various hydrophobic organic solvents and resins.     

The Calculation of 3D Solubility Parameters Using Molecular Models

Abstract

In this paper we describe the use of molecular mechanics models to examine detailed intermolecular interactions within the liquid state of a common nonionic surfactant system, nonyl phenol ethoxylate (NPE). Using constant energy molecular dynamics simulations we have studied the relative strengths of dispersive interactions versus polar interactions and have estimated three dimensional solubility parameters for NPE systems as a function of temperature and ethylene oxide content. The predictions at 300 K are in good agreement with three dimensional solubility parameters predicted using group contribution tables. Models of the amorphous liquid state were represented by single molecular structures of NPE in a periodic cell. The solubility parameters predicted with these models were in good agreement with those values derived from models having eight NPE molecules packed into a cell with the exception of the electrostatic interactions, which are the most sensitive to system size effects.     

General method for calculating helical parameters of polymer chains from bond lengths,bond angles,and internal-rotation angles

Helical conformations of infinite polymer chains may be described by the helical parameters, d and θ (the translation along the helix axis and the angle of rotation about the axis per repeat unit), _pi (the distance of the ith atom from the axis), d_ij, and d_ij (the translation along the axis and the angle of rotation, respectively, on passing from the ith atom to the jth). A general method has been worked out for calculating all those helical parameters from the bond lengths, bond angles, and internal-rotation angles. The positions of the main chain and side chain atoms with respect to the axis may also be calculated. All the equations are applicable to any helical polymer chain and are readily programmed for electronic computers. A method is also presented for calculating the partial derivatives of helical parameters with respect to molecular parameters.     

Conformational Disorder Enhances Solubility and Photovoltaic Performance of a Thiophene–Quinoxaline Copolymer

The side‐chain architecture of alternating copolymers based on thiophene and quinoxaline (TQ) is found to strongly influence the solubility and photovoltaic performance. In particular, TQ polymers with different linear or branched alkyloxy‐phenyl side chains on the quinoxaline unit are compared. Attaching the linear alkyloxy side‐chain segment at the meta‐ instead of the para‐position of the phenyl ring reduces the planarity of the backbone as well as the ability to order. However, the delocalisation across the backbone is not affected, which permits the design of high‐performance TQ polymers that do not aggregate in solution. The use of branched meta‐(2‐ethylhexyl)oxy‐phenyl side‐chains results in a TQ polymer with an intermediate degree of order. The reduced tendency for aggregation of TQ polymers with linear meta‐alkyloxy‐phenyl persists in the solid state. As a result, it is possible to avoid the decrease in charge‐transfer state energy that is observed for bulk‐heterojunction blends of more ordered TQ polymers and fullerenes. The associated gain in open‐circuit voltage of disordered TQ:fullerene solar cells, accompanied by a higher short‐circuit current density, leads to a higher power conversion efficiency overall. Thus, in contrast to other donor polymers, for TQ polymers there is no need to compromise between solubility and photovoltaic performance.     

Molecular Mechanics Studies of Molybdenum Disulphide Catalysts Parameterisation of Molybdenum and Sulphur

Abstract

A method for the parameterisation of molybdenum disulphide is presented which reproduces the crystal structure accurately. The method involves calculating parameters such that there is no net force contribution from any individual term of the potential on any atom. Ideal bond lengths and bond angles are taken from the X-ray crystal structure; stretching and bending force constants are calculated from a combination of spectroscopic data and quantum mechanics calculations, whereby the energy function with bond length or bond angle is calculated and fitted with an harmonic potential. For the non-bonded Lennard-Jones parameters, the dispersion coefficient C was calculated by an interpolation of existing published parameters using a multiple regression and then the crystal energy was minimised with respect to the van der Waals radius r₀ using a fixed crystal fragment.

These parameters were tested for various models of the hexagonal and rhombohedral forms of MoS₂. RMS fits between structures minimised with molecular mechanics and experimental models ranged from 0.006 Å to 0.012 Å.     

Variance of Writhe for Wormlike DNA Rings with Excluded Volume

Abstract

We have calculated the variance of the equilibrium distribution of a circular wormlike polymer chain over the writhing number, <((Wr)² )>, with allowance for the excluded volume effects. Within this model the <((Wr)² )> value is a function of the number of Kuhn statistical segments, n, and the chain diameter, d measured in Kuhn statistical lengths, b. Simulated DNA chains varied from 200 to 10,000 base pairs and the d value varied from 0.02 to 0.2. Theory predicts a considerable ionic strength dependence of the DNA superhelix energy as a consequence of the change in the DNA diameter. A comparison with the available experimental data has yielded an estimate of the DNA torsional rigidity, the Kuhn statistical length, and the effective diameter of the double helix under conditions of the complete screening of the DNA electrostatic potential.     

Construction of chiral polyesters from polycondensation of multifunctional monomer containing both flexible amino acid and rigid pendant groups with aromatic diols

A number of chiral wholly aromatic polyesters (PEs) with phthalimido and flexible chiral unit in the backbone were prepared from a chiral synthesized diacid monomer, 5-(3-methyl-2-phthalimidylpentanoylamino)isophthalic acid (1), and various aromatic diols via the polyesterification reaction. The tosyl chloride/pyridine/N,N-dimethylformamide (DMF) system was used as a condensing agent. All of the these polymers having bulky phthalimido and amino acid functionalities in the side chain showed excellent solubility and readily dissolved in various solvents such as N-methyl-2-pyrrolidinone, N,N-dimethylacetamide and DMF. Since, these chiral polymers have natural amino acids in the polymer architecture, they are expected to be biodegradable and therefore may be classified under eco-friendly polymers. They had useful levels of thermal stability associated with excellent solubility. Thermogravimetric analysis (TGA) showed that the obtained PEs are rather thermally stable, 10% weight loss temperatures in excess of 317°C, and char yields at 700°C in the nitrogen atmosphere higher than 24%. The resulting polymers were obtained in good yields with inherent viscosities ranging between 0.22 and 0.56 dL/g and were characterized with FT-IR, ¹H-NMR, elemental and TGA techniques.     

Energetics of hydrophobic matching in lipid-protein interactions

Lipid chain length modulates the activity of transmembrane proteins by mismatch between the hydrophobic span of the protein and that of the lipid membrane. Relative binding affinities of lipids with different chain lengths are used to estimate the excess free energy of lipid-protein interaction that arises from hydrophobic mismatch. For a wide range of integral proteins and peptides, the energy cost is much less than the elastic penalty of fully stretching or compressing the lipid chains to achieve complete hydrophobic matching. The chain length dependences of the free energies of lipid association are described by a model that combines elastic chain extension with a free energy term that depends linearly on the extent of residual mismatch. The excess free energy densities involved lie in the region of 0.5-2.0 k_BT.nm⁻². Values of this size could arise from exposure of hydrophobic groups to polar portions of the lipid or protein, but not directly to water, or alternatively from changes in tilt of the transmembrane helices that are energetically comparable to those activating mechanosensitive channels. The influence of hydrophobic mismatch on dimerization of transmembrane helices and their transfer between lipid vesicles, and on shifts in chain-melting transitions of lipid bilayers by incorporated proteins, is analyzed by using the same thermodynamic model. Segmental order parameters confirm that elastic lipid chain distortions are insufficient to compensate fully for the mismatch, but the dependence on chain length with tryptophan-anchored peptides requires that the free energy density of hydrophobic mismatch should increase with increasing extent of mismatch.     

Agreement between Single Crystal X-Ray and Molecular Mechanical Sugar Ring Conformations

Abstract

We have calculated the deoxyribose sugar energy for a wide range of puckering parameters, (q, W), using different force fields. The intra-ring bond lengths, bond angles, and dihedral angles are calculated for every energy minimized structure and compared with 224 sugar ring structures available from DNA single crystal x-ray data. A modified Weiner's force field yields an excellent agreement with x-ray data.

The calculated energy surface shows a variable amplitude repuckering path, with an average distortion of 0.42 Å. Most of the experimental values of (q, W) fall within 1.0 Kcal/mol from the calculated minimum.     

Molecular dynamics simulations of the interaction of phospholipid bilayers with polycaprolactone

The molecular interaction between common polymer chains and the cell membrane is unknown. Molecular dynamics simulations offer an emerging tool to characterise the nature of the interaction between common degradable polymer chains used in biomedical applications, such as polycaprolactone, and model cell membranes. Herein we characterise with all-atomistic and coarse-grained molecular dynamics simulations the interaction between single polycaprolactone chains of varying chain lengths with a phospholipid membrane. We find that the length of the polymer chain greatly affects the nature of interaction with the membrane, as well as the membrane properties. Furthermore, we next utilise advanced sampling techniques in molecular dynamics to characterise the two-dimensional free energy surface for the interaction of varying polymer chain lengths (short, intermediate, and long) with model cell membranes. We find that the free energy minimum shifts from the membrane-water interface to the hydrophobic core of the phospholipid membrane as a function of chain length. Finally, we perform coarse-grained molecular dynamics simulations of slightly larger membranes with polymers of the same length and characterise the results as compared with all-atomistic molecular dynamics simulations. These results can be used to design polymer chain lengths and chemistries to optimise their interaction with cell membranes at the molecular level.     

Chemical relaxation of co-operative conformational transitions of linear biopolymers

The kinetics and chemical relaxation of co-operative conformational changes of linear (bio)polymers (e.g. helix-coil transitions of polypeptides) are discussed on the basis of the linear ISING model. Chemical relaxation is in general shown to be described by 4N−5 relaxation times if the polymer chain consists of N elementary reaction sites. It is pointed out that nevertheless substantial simplifications of the theory can be achieved in many special cases of practical interest. Sufficiently short chains exhibit first-order kinetics resulting in a single relaxation time whereas for certain medium chain lengths zero-order kinetics plays a principal role in the relaxation process. For the particularly interesting case of very long chains a set of four relaxation equations is derived. The corresponding relaxation times are calculated assuming strong co-operativity and slow nucleation rates. However, it is almost exclusively the largest one of these relaxation times which actually controls the conformational change as turns out by means of a new approach to compute amplitude factors.     

Osmotic properties of poly(ethylene glycols): quantitative features of brush and bulk scaling laws

From glycosylated cell surfaces to sterically stabilized liposomes, polymers attached to membranes attract biological and therapeutic interest. Can the scaling laws of polymer "brushes" describe the physical properties of these coats? We delineate conditions where the Alexander-de Gennes theory of polymer brushes successfully fits the intermembrane distance versus applied osmotic stress data of Kenworthy et al. for poly(ethylene glycol)-grafted multilamellar liposomes. We establish that the polymer density and size in the brush must be high enough that, in a bulk solution of equivalent monomer density, the polymer osmotic pressure is independent of polymer molecular weight (the des Cloizeaux semidilute regime of bulk polymer solutions). The condition that attached polymers behave as semidilute bulk solutions offers a rigorous criterion for brush scaling-law behavior. There is a deep connection between the behaviors of semidilute polymer solutions in bulk and polymers grafted to a surface at a density such that neighbors pack to form a uniform brush. In this regime, two-parameter unconstrained fits of the Alexander-de Gennes brush scaling laws to the Kenworthy et al. data yield effective monomer lengths of 3.3-3.6 A, which agree with structural predictions. The fitted distances between grafting sites are larger than expected from the nominal mole fraction of poly(ethylene glycol)-lipids; the chains apparently saturate the surface. Osmotic stress measurements can be used to estimate the actual densities of membrane-grafted polymers.     

The growth of sickle hemoglobin polymers

The measurement of polymer growth is an essential element in characterization of assembly. We have developed a precise method of measuring the growth of sickle hemoglobin polymers by observing the time required for polymers to traverse a photolytically produced channel between a region in which polymers are created and a detection region. The presence of the polymer is functionally detected by observing its ability to create new polymers through the well-established process of heterogeneous nucleation. Using this method, we have determined the rate constants for monomer addition to and release from polymer ends, as well as their temperature dependences. At 25°C we find k₊ = 84 ± 2 mM⁻¹ s⁻¹ and k₋ = 790 ± 80 molecules/s from each end. These numbers are in accord with differential interference contrast measurements, and their ratio gives a solubility measured on individual fibers. The single-fiber solubility agrees with that measured in sedimentation experiments. The concentration dependence of the monomer addition rate is consistent with monomer addition, but not oligomer addition, to growing polymers. The concentration dependence suggests the presence of an activation enthalpy barrier, and the rate of monomer addition is not diffusion-limited. Analysis of the temperature dependence of the monomer addition rate reveals an apparent activation energy of 9.1 ± 0.6 kcal/mol.     

Properties of star-branched and linear chains in confined space. A Monte-Carlo study

We have studied the properties of simple models of linear and star-branched polymer chains confined in a slit formed by two parallel impenetrable walls. The polymer chains consisted of identical united atoms (homopolymers) and were restricted to a simple cubic lattice. Two macromolecular architectures of the chain: linear and regular stars with three branches of equal length, were studied. The excluded volume was the only potential introduced into the model and thus the system was athermal. Monte-Carlo simulations with the sampling algorithm based on the chains local changes of conformation were carried out for chains with different lengths as well as for different distances between the confining surfaces. We found that the properties of model chains differ for both macromolecular architectures but a universal behavior for both kinds of chains was also found. Investigation of the frequency of chain-wall contacts shows that the ends of the chains are much more mobile than the rest of the chain, especially in the vicinity of the branching point in star polymers.Figure The scheme of a star-branched (left) and a linear (right) chain located between two parallel impenetrable surfaces.     

The Flexibility of Alternating dA—dT Sequences

Abstract

The flexibility of alternating poly (dA—dT) has been investigated by the technique of transient electric dichroism. Rotational relaxation times, which are very sensitive to changes in the end-to-end length of flexible polymers, are determined from the field free dichroism decay curves of four, well defined fragments of poly (dA—dT) ranging in size from 136 to 270 base pairs. Persistence lengths, calculated from the results of Hagerman and Zimm (Biopolymers (1981) 29, 1481–1502), are in the range 200–250 A. This makes alternating dA—dT sequences about twice as flexible as naturally occurring, “random” sequence DNA. Considering a bend around a nucleosome, for example, this difference in persistence length translates to an energy difference between poly (dA—dT) and random sequence DNA of 0. 17 kT/base pair or 1 kcal per 10 base pair stretch. This energy difference is sufficiently large to suggest that dA—dT sequences could serve as markers in DNA packaging, for example, at sites where DNA must tightly bend to accommodate structures.     

Simulation of Polymer Solutions by Dissipative Particle Dynamics

Abstract

Dissipative Particle Dynamics (DPD) is employed to model the dynamics and rheology of polymer solutions, and suspensions of spherical particles with adsorbed polymers. Static and dynamic scaling relationships for the variation of radius of gyration and relaxation time with polymer chain length are reviewed, demonstrating that the DPD polymer solution model correctly represents the effects of hydrodynamic interaction and excluded volume. Rheological simulations for both polymer solutions and polymer-sphere suspensions predict Newtonian viscosities at low shear rate followed by shear-thinning behavior as a reduced shear rate of unity is approached. Both the Newtonian viscosity and the extent of shear-thinning are greatly enhanced in the case of good solvents, compared to the viscosity curves for polymers and polymer-spheres structures dissolved in theta solvents and poor solvents.     

Dissipative particle dynamics simulation of the soft micro actuator using polymer chain displacement in electro-osmotic flow

ABSTRACT

In this research, the numerical simulation of a soft polymer micro actuator performance has been investigated using the dissipative particle dynamics method in electro-osmotic flow. Effective factors including electro-osmotic flow and polymer chain parameters have been studied. First of all, considering a wide range of electro-osmotic parameters, the validation of analytical results is carried out in a simple micro channel. The electric field and zeta potential changes are linearly related to the flow rate, and the kh parameter behaves nonlinearly to around the kh?=?10. In the following, a convergent–divergent channel is used for the soft micro actuator simulation in which a polymer chain as a heart of actuation is embedded in the middle. As the main control parameter, the direction of the electric field is changed every 4?s, and it leads to a reciprocating motion. The numerical results indicate that the displacement of the soft polymer chain will be increased by enhancing the electric field, the number of beads, decreasing the harmonic bond coefficient and also exposing more length of a polymer chain in front of fluid flow. The results of this study may be useful for some future applications such as artificial fibres and muscles.     

Predicting Liquid–Vapour Equilibria for Water Using an ab-initio Potential from Histogram Reweighting Monte Carlo Simulations

Abstract

The coexisting densities for an ab-initio model for water have been calculated using grand canonical Monte Carlo simulations with the histogram reweighting technique. Although good agreement with experimental data is found for the radial distribution function at room temperature, the predicted critical density and temperature are well below both the experimental value as well as predictions from semi-empirical potentials. Improvement in the repulsive part of the ab-initio potential is suggested as a way to obtain better agreement with experiment.