Thermodynamics of deformation of an isolated polymer chain

Summary Deformation-dependent change in internal energy of a polymer chain affects also conformational entropy as a result of dependence of statistical characteristics upon the distribution of rotational isomers in the chain. Formulas describing deformation-dependent internal energy (distribution of rotational isomers), free energy and length of statistical segment have been derived using a model of rotational isomers, and assuming non-Gaussian conformational statistics. Example computations have been performed for polyethylene. The computations show decrease in the fraction of gauche isomers with increasing deformation, and the decrease is stronger for shorter chains, especially for the chains composed of less than 10³ C-C bonds. Corrections related to the non-Gaussian statistics and finite molecular weight lead to lower fraction of the gauche component in the chain. Fraction of gauche isomers in a deformed polyethylene chain has been calculated numerically byAllegra andAvitabile (10) using a method of matrices proposed byFlory (11). Although the authors (10) received qualitatively comparable results with our results, they discussed the subject for Gaussian chains in terms of different measure of chain deformation, 1, which does not show clearly the effect of the chain length. Calculations presented in this paper provide analytical formulas for the deformation-dependent thermodynamic and statistical characteristics of a deformed chain macromolecule with non-Gaussian statistics and finite molecular weight. As a result of the decrease of gauche isomers the length of statistical segment increases with increasing chain deformation, and it increases stronger for shorter chains. Temperature effect on the behaviour of a deformed chain macromolecule is also discussed. General formula for the elastic force and local stress tensor have been derived.With 4 figures     

Vibrational spectra and assignments of 2-phenylethanol and 2-phenoxyethanol

The structural stability of 2-phenyl- and 2-phenoxyethanols were investigated at the DFT-B3LYP/6-311G**, MP2 and MP4(SDQ) levels of theory. From the calculations at the three levels of theory 2-phenylethanol and 2-phenoxyethanol were predicted to exist predominantly in non-planar gauche conformations. For 2-phenylethanol the lowest energy Gg1 structure was predicted to be stabilized by an interaction between the hydroxyl H atom and the phenyl ring. For 2-phenoxyethanol the Ggg1 structure was predicted to be strongly stabilized by dipolar interactions between the hydroxyl H atom and the phenoxy O atom of the alcohol. For both alcohols the planar trans structure with minimum steric interactions between the CH₂ groups was predicted to be significantly higher in energy than the ground state gauche structure of the alcohols. The dipolar interactions are reported to play more important role than steric ones in stabilizing the molecules. The vibrational frequencies of each of the two alcohols in its lowest energy gauche structure were computed at the B3LYP level and tentative vibrational assignments were made for their normal modes on the basis of the calculated and experimental data.     

Influence of Side Chain Conformation on the Activity of Glycosidase Inhibitors

Substrate side chain conformation impacts reactivity during glycosylation and glycoside hydrolysis and is restricted by many glycosidases and glycosyltransferases during catalysis. We show that the side chains of gluco and manno iminosugars can be restricted to predominant conformations by strategic installation of a methyl group. Glycosidase inhibition studies reveal that iminosugars with the gauche,gauche side chain conformations are 6- to 10-fold more potent than isosteric compounds with the gauche,trans conformation; a manno-configured iminosugar with the gauche,gauche conformation is a 27-fold better inhibitor than 1-deoxymannojirimycin. The results are discussed in terms of the energetic benefits of preorganization, particularly when in synergy with favorable hydrophobic interactions. The demonstration that inhibitor side chain preorganization can favorably impact glycosidase inhibition paves the way for improved inhibitor design through conformational preorganization.     

NMR Studies of Solvent Effect on Internal Rotation in Some Non-Symmetrical 1,2-Disubstituted Ethanes

The A₂B₂ system of PMR spectra of 3-bromopropionic acid, 3-chloropropionic acid, 3-bromopropionitrile, and 3-chloropropionitrile exhibit appreciable solvent effect at room temperature. NMR spectroscopic parameters of A₂B₂ spectrum as well as physical parameters related to internal rotation, i. e. the highest energy barrier and the energy difference between rotamers, were determined for these compounds in the medium of various solvents. It was found that in the case of 3-bromopropionic acid, the trans rotamer is more stable than the gauche rotamers, and the energy difference decreases with increasing dielectric constant of solvent. While in the case of 3-bromopropionitrile, the gauche rotamers were found to be more stable than the trans rotamer and the energy difference increases with increasing dielectric constant of solvent. In the remaining two compounds, 3-chloropropionic acid and 3-chloropropionitrile, both trans and gauche rotamers are equally stable in a solvent of low dielectric constant, however in a solvent of higher dielectric constant, the gauche rotamers become more stable than the trans rotamer and the energy difference becomes more pronounced with increasing dielectric constant of solvent.     

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.     

Configurational entropy of polyethylene and other linear polymers

The configurational entropy of the polyethylene chain at the melting points calculated in two ways. In both calculations, tetrahedral angles and discrete trans and gauche arrangements of all bonds are assumed, and trans bonds are assumed more stable than gauche by energy U₁. First, calculations are made on chains of up to N = 18 bonds, disallowing all configurations having overlapping atoms, and the result is extrapolated to large N. Second, a calculation is made directly for long chains, with overlaps excluded only over every short chain segment. The results are in almost exact agreement, suggesting that the second method can be safely used with other molecules. The calculated configurational entropy is in line with that suggested by the entropy of fusion, assuming the chains to acquire a configurational freedom in the melt which approaches that of independent chains.     

Elastic behavior of bimodal poly(dimethylsiloxane) networks

The rubberlike elastic behavior of bimodal poly(dimethylsiloxane) (PDMS) networks was investigated by the Monte Carlo simulation method and enumeration calculation method on the basis of the rotational‐isomeric‐state (RIS) model. These bimodal PDMS networks consist of short chains (chain length from 10 to 20) as well as long chains (chain length equal to 150). For long PDMS chains, through generating many PDMS conformations in the equilibrium state using the Monte Carlo simulation method we can obtain the average Helmholtz free energy and the average energy. For short PDMS chains with chain lengths from 10 to 20, as the total number of conformations is only from 6.56 × 10³ to 3.87 × 10⁸, we adopt the enumeration calculation method. The deformation is partitioned nonaffinely between the long and short chains, and this partitioning can be determined by requiring the free energy of the deformed network to be minimized. Chain dimensions and thermodynamic statistical properties of bimodal PDMS networks at various elongation ratios are discussed. We find that elastic force f increases with elongation ratio λ; the energy contribution f_u to elastic force is significant, and the ratio of ranges from 0.15 to 0.36 at T = 343 K. In the meantime, elastic force f increases with the average energy 〈U〉. The energy change in the process of tensile elongation is taken over, which has been ignored in previous theories. Our calculations may provide some insights into the phenomena of rubberlike elasticity of bimodal networks. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 105–114, 2002     

Monte Carlo simulation of tetrahedral chains, 5. The pivot-algorithm for non-athermal linear and star-branched polymers

By use of the pivot algorithm, star-branched chains with F = 3–12 arms of length n, nF = 480, and linear chains (F = 2) are generated on a tetrahedral lattice. In order to simulate different qualities of the solvent, specific short-range interactions are taken into account. Whereas in athermal systems a new configuration — which is obtained by rotating that part of an arm which contains the chain end around a randomly selected bond by ± 120° — is accepted if it is self-avoiding, for non-athermal systems the Metropolis-Rosenbluth criterion with respect to energy must be satisfied in addition. Calculating the energy of the configuration, nearest-neighbour interactions (each contact contributes an energy Φ·kT, Φ < 0 characterizing endothermal solutions and Φ > 0 exothermal ones) are considered only; no energy is introduced to distinguish between trans and gauche bonds. A rather quick response of chain properties to the variation of thermodynamic conditions is demonstrated. The average acceptance fraction f̄ has its maximum value for athermal conditions, slightly decreases for exothermal conditions and strongly decreases with increasingly negative Φ-values. However, for Φ = −0,5 — representing a solution near theta-conditions — still 25% of attempted moves are accepted for all F-values examined. The dependence of global properties (characterized by the mean-square radius of gyration) on Φ and F is in full accordance with most Monte Carlo results.     

Influence of temperature on molecular regroupings and chain rupture under stretching deformation of high‐oriented linear polyethylene

Conformational regrouping and rupture of macromolecular chains at different stretching deformation temperatures of highly oriented linear polyethylene samples (monofilaments) were studied. Measurements of the relative concentration of rotational isomers and chain rupture were determined by IR spectroscopy. Regroupings occur in the highly oriented polymer when elastic stretching of the sample exceeds a threshold value, irrespective of deformation temperature; this is assumed to be due to steric conditions that influence the cooperative transition of coiled‐chain isomers in the extended isomeric conformational state. Polymer stretching at elevated temperatures, in comparison with room temperature, occurred at considerably lower loads and showed increases in elastic deformation, extent of conformational regroupings of molecular segments and reduction in the number of macromolecular ruptures. Deformation at identical values was accompanied by a smaller decrease in concentration of coiled‐chain rotational isomers. The number of molecular chain ruptures, which is proportional to stress load, appeared to be unaffected by temperature. It is proposed that the small decreases observed in the content of coiled‐chain isomers and of chain rupture with deformation are facilitated by macromolecular slippage processes that occur through polymer crystallites.     

An ab initio structural and vibrational analysis of gauche,trans,trans- and gauche,cis,trans-hexa-1,3,5-trienes

The results of complete geometry optimizations of the high energy stable gauche,Trans,trans- and gauche,Cis,trans- rotamers of hexa-1,3,5-trienes are reported at the RHF/6-31G//RHF/B-31G level. The angles of rotation around one of the single C-C bonds are found to be 33.7° and 45.5°, respectively. The corresponding harmonic force fields of these molecules are also reported at this level and corrected using scale factors transferred from buta 1,3-diene. Aspecial scale factor was used for the central C=C double bond stretching coordinate to take into account vibronic coupling. The theoretical vibrational frequencies, calculated with the scaled quantum mechanical (SQM) force fields, allow a complete interpretation of the experimental vibrational spectra of these molecules.Preliminary results were reported at the Austin XII Symposium on Molecular Structure, Austin, TX, February 28 through March 3, 1988, S 18, p. 111 (USA) and at the XIXth European Congress on Molecular Spectroscopy, Dresden, September 4 through September 8, 1989, p. 226 (GDR).     

Vibrational spectra and conformations of chloromethyldimethyl- and tris(chloromethyl)phosphine oxides

A study was carried out on the IR spectra of (CH₃)₂P(O)CH₂Cl and (CH₂Cl)₂PO. The frequencies and forms of the normal modes were calculated. The molecular mechanics method was used to calculate the energy of the various conformations of these molecules. (CH₃)₂P(O)CH₂Cl in the liquid and solution is a mixture of trans and gauche conformations, while (CH₂Cl)₃PO is a mixture of trans,gauche,gauche, trans,gauche,gauche, and gauche,gauche,gauche conformations.S. M. Kirov Kazan Chemical Engineering Institute and A. E. Arbuzov Institute of Organic and Physical Chemistry, Kazan Branch, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 30, No. 6, pp. 38–46, November–December, 1989.     

Modulation of ionization and structural properties of weak polyelectrolytes due to 1D, 2D,and 3D confinement

What is the impact of reducing the space available to molecules onto their properties is a fundamental question for capillary systems, molecular biology and transport, protein and material sciences. Possibly influenced by space restriction, ionization degree has rarely been studied for confined polyelectrolytes; Monte Carlo titrations and coarse‐grained models are thus used to investigate structural and ionization changes induced on a single polyelectrolyte chain by confinement into slit (1D), cylindrical (2D), or spherical (3D) cavities. Four polyelectrolyte models differing in chain stiffness and the possible formation of charged hydrogen bonds (c? H? bonds) are studied. Low pH effective ionization constants (pK_a ) of confined chains are lower than for the free species if c? H? bonds can be formed. This is especially evident for 3D‐confined stiff chains, a finding rationalized by the impact of global compression onto chain conformations. If no c? H? bonds are allowed, chain ionization is largely unaffected by 1D or 2D confinement, while it is depressed by 3D. Chain confinement Helmholtz energy (ΔA _conf) was computed as a function of both pH and confining width (W) to gauge the impact of ionization‐induced stiffening onto ΔA _conf versus W behavior, the partition coefficient governing absorption, and the average number of c? H? bond formed. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55 , 1088–1102     

Lattice treatment of thermodynamic properties of ring and linear polymer mixtures

Expressions for the entropy and free energy of mixing a solvent with a mixture of linear and cyclic polymer molecules are derived. The entropy of mixing is deduced from the number of ways of arranging on a honeycomb lattice a mixture of totally flexible molecules made up of N_R rings and N_C chains. An equation is obtained through the combination of two independent expressions for the number of ways of arranging rings and chains. The free energy of mixing is deduced from the entropy and the enthalpy of mixing, using two distinct interaction parameters for ring and for chain molecules. The chemical potentials for solvent, ring polymer, and linear polymer are derived from the free energy of mixing. These quantities are found to be functions of the mole fraction of rings in the polymer mixture. © 1993 John Wiley & Sons, Inc.     

Protein side chain modeling with orientation-dependent atomic force fields derived by series expansions

We describe the development of new force fields for protein side chain modeling called optimized side chain atomic energy (OSCAR). The distance‐dependent energy functions (OSCAR‐d) and side‐chain dihedral angle potential energy functions were represented as power and Fourier series, respectively. The resulting 802 adjustable parameters were optimized by discriminating the native side chain conformations from non‐native conformations, using a training set of 12,000 side chains for each residue type. In the course of optimization, for every residue, its side chain was replaced by varying rotamers, whereas conformations for all other residues were kept as they appeared in the crystal structure. Then, the OSCAR‐d were multiplied by an orientation‐dependent function to yield OSCAR‐o. A total of 1087 parameters of the orientation‐dependent energy functions (OSCAR‐o) were optimized by maximizing the energy gap between the native conformation and subrotamers calculated as low energy by OSCAR‐d. When OSCAR‐o with optimized parameters were used to model side chain conformations simultaneously for 218 recently released protein structures, the prediction accuracies were 88.8% for χ₁, 79.7% for χ_{1 + 2}, 1.24 Å overall root mean square deviation (RMSD), and 0.62 Å RMSD for core residues, respectively, compared with the next‐best performing side‐chain modeling program which achieved 86.6% for χ₁, 75.7% for χ_{1 + 2}, 1.40 Å overall RMSD, and 0.86 Å RMSD for core residues, respectively. The continuous energy functions obtained in this study are suitable for gradient‐based optimization techniques for protein structure refinement. A program with built‐in OSCAR for protein side chain prediction is available for download at http://sysimm.ifrec.osaka‐u.ac.jp/OSCAR/ . © 2011 Wiley Periodicals, Inc. J Comput Chem 2011     

CORRELATION BETWEEN GLASS TRANSITION OF POLYMERS AND ENERGY OF ROTATIONAL ISOMERIZATION OF MOLECULAR CHAINS

It has been shown that the free volume fraction at T_g is not a universal parameter for linear polymers of different molecular structure. The reason is that the volume expansion at T_g is partially contributed from the change of the numbers of conformations of isolated molecular chains due to internal rotation. In this paper, glassy transformation was connected with internal rotation of isolated molecular chains, and the relationship between free volume fraction of polymers at T_g and energy e of rotational isomerization of isolated molecular chains was formulated, e=-k·T_g·In (△α·T_g/1-△α. T_g). The values of calculated from the above formula are in good agreement with those published in the literatures. Thus, the method described in this paper can be used to estimate a parameter for the flexibility of isolated molecular chains.7     

Structural study of oxalamide compounds: H, C, and DFT calculations

The conformational properties of some N-alkyl, N,N′-dialky, and tetraalkyloxalamides have been investigated, in vacuo and in solvent using DFT methods at the B3LYP/6-31G^∗∗ computational level. Special emphasis has been given on oxalamides with substituents of the type -CH₂CH₂OH. In oxalamides with the N-H group (N-alkyl and N,N′-dialky), the most stable conformations are those in which the oxalamide moiety adopts a planar s-trans arrangement and the amide bonds are trans. A different situation appears in the case of tetraalkyloxalamides, in which the oxalamide moiety always adopts a skewed arrangement and there are conformations with similar energy. A careful study of ¹³C and ¹H NMR spectra together with theoretical calculations (GIAO method) allowed the assignment of the signals of these conformers. The presence of the -CH₂CH₂OH chain produces numerous rotamers. The most stable rotamers, in vacuo, are those with strong intramolecular hydrogen bonds, however in solvent, hydrogen bonds are not crucial to establish the most stable specie and depend on the solvent used.     

Thermodynamic and stereochemical aspects of the polymerizability of glycolide and lactide

The ring-opening polymerizations of the dilactones glycolide and the S,S- and S,R-stereoisomers of lactide were studied using quantum mechanical methods. The ring strain and the conformational distribution of these cyclic monomers and of the polymers were calculated, and the effect of the medium on the polymerization was predicted, for both bulk and solution. The polymerizability of the three monomers in the gas phase, that is, nonpolar medium, is much greater than that of δ-valerolactone or 1,4-dioxan-2-one. This difference vanishes in the polar medium chloroform, which is attributed to the fact that, while all of these monomers possess polar cis-lactone bonds, the three dilactones possess small dipole moments. The data are combined to give polymerization enthalpy and free energy values. The four stereoregular lactide polymers did not differ significantly in energy. Accordingly, the ability to synthesize any one of these rests on catalyst specificity (“polymer chain-end control”). Although introduction of sterically demanding methyl groups into glycolide is expected to favor coiled conformations and decrease polymerizability, this was not found to be the case. Good agreement of calculated values with experimental data from the literature was achieved.     

Steric and bridging interactions between two plates induced by grafted polyelectrolytes

If colloidal particles are grafted with a polymer, then the grafted chains can provide steric repulsion between them. If some of the grafted polymer chains are also adsorbed to a second particle, then a bridging force is generated as well. For uncharged plates and polymer, the following contributions to the free energy of the system have been taken into account in the calculation of the interaction force: (i) the Flory-Huggins expression for the mixing free energy of the grafted chains with the liquid; (ii) the entropy loss due to the connectivity of the polymeric segments; (iii) the van der Waals interactions between the segments and the plates; and (iv) the free energy of adsorption of the polymer segments of the grafted chains on the other plate. For charged plates, the electrostatic free energy as well as the free energy of the electrolyte are included in the total free energy of the system. By minimizing the free energy with respect to the segment concentration and, when it is the case, with respect to the electrical potential, equations for the segment number density distribution and for the electrical potential are obtained, on the basis of which the interactions between two plates grafted with polymer chains that can be also adsorbed on the other plate were calculated. The interaction thus obtained includes steric and bridging forces.     

Effect of double bond position on lipid bilayer properties: insight through atomistic simulations

Phosphatidylcholines (PCs) are among the most common phospholipids in plasma membranes. Their structural and dynamic properties are known to be strongly affected by unsaturation of lipid hydrocarbon chains, yet the role of the exact positions of the double bonds is poorly understood. In this work, we shed light on this matter through atomic-scale molecular dynamics simulations of eight different one-component lipid bilayers comprised of PCs with 18 carbons in their acyl chains. By introducing a single double bond in each acyl chain and varying its position in a systematic manner, we elucidate the effects of a double bond on various membrane properties. Studies in the fluid phase show that a number of membrane properties depend on the double bond position. In particular, when the double bond in an acyl chain is located close to the membrane-water interface, the area per lipid is considerably larger than that found for a saturated lipid. Further, when the double bond is shifted from the interfacial region toward membrane center, the area per lipid is observed to increase and have a maximum when the double bond is in the middle of the chain. Beyond this point, the surface area decreases systematically as the double bond approaches membrane center. These changes in area per lipid are accompanied by corresponding changes in membrane thickness and ordering of the chains. Further changes are observed in the tilt angles of the chains, membrane hydration together with changes in the number of gauche conformations, and direct head group interactions. All of these effects can be associated with changes in acyl chain conformations and local effects of the double bond on the packing of the surrounding atoms.