Unperturbed Dimensions Research Articles

The use of molecular dynamics for the study of solution properties of guar gum

Size exclusion chromatography with dual detection, i.e., employing a refractive index, concentration sensitive, detector together with a multiangle light scattering detector which is sensitive to molecular size, has been applied to study the solution properties of guar gum in water with different concentrations of K2SO4 at 25 °C. The analysis of a single highly polydisperse sample is enough for obtaining calibration curves for molecular weight and radius of gyration and the scaling law coefficients. The influence of the ionic strength on the conformational properties of the polymer can also be analyzed. Moreover, unperturbed dimensions can be obtained by extrapolation of the values measured in a good solvent. The value of the characteristic ratio of the unperturbed dimensions thus obtained is Cn=〈r2〉0/nl2≈19±1. A theoretical analysis is also included. Thus, molecular dynamics procedures were employed to analyze the conformational properties of an oligomer of guar gum under different conditions; namely, standing alone in vacuo, in bulk solid state and in water solution, both with and without salt. These conformational properties were then employed to compute molecular dimensions of Monte Carlo generated chains with different lengths according to standard procedures of the matrix multiplication scheme, thus allowing the evaluation of both perturbed and unperturbed dimensions which are in very good agreement with the experimental values. Moreover our result permits the explanation of the discrepancies among experimental and theoretical values reported in the literature.

Combination of SEC/MALS experimental procedures and theoretical analysis for studying the solution properties of macromolecules

Size-exclusion chromatography (SEC) with dual detection, i.e., employing refractive index (RI) and multiangle light-scattering (MALS) detectors, has been applied to study the solution properties of two very different polymer–solvent systems at 25 °C: poly( N-vinylcarbazole) (PVCz) in an organic solvent THF that is a very good solvent and a system under θ conditions that is formed by polyvinylpyrrolidone (PVP) in water containing a 0.1 M concentration of NaNO 3. In both cases, the analysis of a single highly polydisperse sample obtained by free radical polymerization is enough for obtaining molecular weight and radius of gyration calibration curves, molecular weight distributions (MWD) (and thus, molecular weight averages), molecular dimensions, scaling laws coefficients and unperturbed dimensions. Extrapolation to θ conditions produces values of the characteristic ratio of the unperturbed dimensions C n =〈 r 2〉 o/ nl 2=15.9 and 14, respectively, for PVCz and PVP. Unperturbed dimensions are also theoretically calculated with different models such as Kuhn equivalent chain, worm-like chain and rotational isomeric states model. Conformational parameters required for this last model were taken from the literature in the case of PVCz; however, they are calculated by molecular dynamics simulations in the case of PVP. Theoretical values obtained with the RIS model are in good agreement with the experimental results.

RIS Models and Unperturbed Chain Properties of Polyesters Containing 1,3‐Cyclobutylene and 1,4‐Cyclohexylene Linkages

AbstractPolyesters containing 1,3‐cyclobutylene and 1,4‐cyclohexylene linkages in the main chain are investigated using conformational energy calculations. Rotational isomeric state (RIS) models are developed for poly(1,4‐cyclohexylenedimethylene terephthalate) (PCT), poly(1,4‐cyclohexylenedimethylene 2,5‐dimethylterephthalate) (DMPCT), poly(1,4‐cyclohexylenedimethylene 1,4‐cyclohexylenedicarboxylate) (PCC), and poly(2,2,4,4‐tetramethyl‐1,3‐cyclobutylene terephthalate) (CBDO). In DMPCT, the ester linkage prefers skewed conformations with respect to the phenyl group to relieve the steric strain caused by the methyl groups. The methyl groups on the cyclobutanediol moiety in CBDO restrict the rotational freedom about the oxycyclobutylene linkage. The unperturbed dimensions as described by characteristic ratio and persistence length are calculated for the trans and cis configurations of these polyesters. CBDO shows highly extended chain conformations among these polyesters indicating relative chain rigidity of the backbone. For DMPCT and PCC, in their trans configuration, the chain dimensions decrease with an increase in temperature while for their cis configurations, the chain dimensions increase with temperature, arising from basic differences in the fragment structures that control the competition of the relative populations as affected by temperature. Temperature has negligible influence on the unperturbed dimensions of both isomeric linkages of CBDO, while this is true for the trans configuration of PCT. The study shows that induction of cyclobutylene groups in the main chain results in a greater rigidity for homopolyesters than for chains with cyclohexylene groups. Structure of the repeat units of polyesters in the planar trans configuration and the schematic of the RIS models with definition of geometrical parameters.imageStructure of the repeat units of polyesters in the planar trans configuration and the schematic of the RIS models with definition of geometrical parameters.

Conformational Characteristics of Poly(d-β-hydroxybutyrate)

We present characteristic ratios of the unperturbed dimensions Cr = 〈r2〉o/n〈l2〉, where 〈r2〉o is the mean-square unperturbed end-to-end distance and n is the number and 〈l2〉 is the mean-square lengt...

Effect of Side Groups on the Conformation of a Series of Polysiloxanes in Solution

The molecular conformation has been obtained for polysiloxane chains in which the pairs of substituents bonded at the silicon atom are CH3, CH3; C2H5, C2H5; CH3, C6H13; CH3, C16H33; and CH3, C6H5. Polysiloxanes dissolved in toluene and benzene were studied using a coupled system: Gel Permeation Chromatography/Light Scattering (GPC/LS). Attention was focused on the influence in the molecular conformation of the quality of the solvent and the type of substituent on the main chain. The results obtained were strongly dependent on the side group size and flexibility. Poly(dimethylsiloxane) samples of 273,400 and 97,600 daltons showed a semi-flexible conformation, but the sample of relatively low molecular weight (36×103 daltons) exhibited a slope of 0.6 in good solvents; i.e., demonstrated the behavior of dilute (non-overlapping) coils in a good solvent. With respect to the poly(diethylsiloxane), the source of the coil's expansion is the high mobility of the side chains. Poly(methylphenylsiloxane) exhibits a rigid rod conformation in both solvents. The orientation of the phenyl groups and the attractive interaction between these groups dominate the polysiloxane chain behavior in good solvents. For these polysiloxanes, the expansion factor value is analyzed and the influence of solvent on the polymer's unperturbed dimensions is discussed. Poly(methylhexylsiloxane) and poly(methylhexadecylsiloxane) show a spherical conformation in both solvents. This conformation may arise from strong interactions between the bulky side groups and the main chain.

Prediction of Melt State Poly(α-olefin) Rheological Properties: The Unsuspected Role of the Average Molecular Weight per Backbone Bond

It has previously been shown that the entanglement molecular weight (Me) and the plateau modulus ( ) of flexible polymers can be correlated to the unperturbed chain dimension, 〈R2〉0/M, chain density (ρ) via the use of the packing length (p), which is defined as the volume of a chain divided by its mean square end to end distance. For polyolefins and co-polyolefins where 〈R2〉0/M remains unmeasured a method is presented herein where knowledge of the average molecular weight per backbone bond (mb) allows and thus Meto be estimated. This is particularly valuable for the case of polyolefin copolymers where the melt chain dimensions (and thus the packing length) are unknown.

Conformational Analysis of Model Poly(ether urethane) Chains in the Unperturbed State and under External Forces

Conformational features of model poly(ether urethane) (PEU) single chains are investigated in the unperturbed state and under external force. Model PEUs consisting of symmetrical, aromatic, 1,4-phenylene diisocyanate (PDI) hard segments and poly(tetramethylene oxide) (PTMO) soft segments with varying lengths are considered. Rotational potential maps are calculated quantum mechanically using the AM1 parametrization with Gaussian98. Configurations of the chains are generated by the Monte Carlo technique, using the rotational isomeric state formalism and successive matrix multiplication scheme. Unperturbed dimensions, the change in dimensions when a force acts along the end-to-end vector, the stiffness, and toughness of the chain and orientability of segments under external force are characterized and compared with properties of polyethylene. The characteristic ratio of a long PEU chain is 5.0, and the Kuhn length for a single block is 9.2 A, both of which are smaller than the corresponding polyethylene values. The model chains are significantly more ductile and tougher than polyethylene. The orientability of the backbones exhibits a strong even-odd effect, with strongly orientable bonds neighbored by weakly orienting ones. The degree of rigidity of the phenyl group does not propagate far along the chain. The projection of the bond vectors on the phenyl axis decay rapidly with increasing distance of the bond along the chain.

Study on conformational transition of EVA random copolymer in selective solvent mixtures

The dilute solution property of ethylene-vinyl acetate (EVA) random copolymer in 1,2-dichloroethane/cyclohexane (DCE/CYH) selective solvent mixture has been studied by viscometry, light scattering, differential refractomertry and UV spectrophotometry. It was found that both ethylene- and viny1 acetate sequence associations of EVA random copolymer displayed in both DCE and CYH solvents respectively, especially in DCE. Disassociation appeared when the volume fraction of CYH in the DCE/CYH solvent mixture φ c was from 0.6 to 0.8. However, in this region, the extreme values of the intrinsic viscosity [ η], Huggins constant k ′, unperturbed dimension K θ , refractive index increment d n/d c occurred, and a discontinuity behavior of the preferential adsorption coefficient λ ′ and UV spectra demonstrated. These phenomena were attributed to conformational transition of the EVA molecule in solution, which was caused by DCE and CYH selective solvents, respectively.

Elastic Properties of Well-Defined, High-Density Poly(methyl methacrylate) Brushes Studied by Electromechanical Interferometry

We have investigated the elastic properties of dry polymer brushes comprising low-polydispersity poly(methyl methacrylate) (PMMA) chains with high graft densities over 0.4 chains/nm2 by means of electromechanical interferometry. End-grafting on a glass plate by living radical polymerization yielded high-density brushes composed of the highly stretched graft chains, and the layer thickness of the brushes is 4−5 times as large as the unperturbed dimension of the graft chains. The layer thickness change induced by an applied electric field (electrostriction) is measured by a Nomarski optical interferometer as a function of temperature. The analysis of the electromechanical and dielectric data yields the plate compressibility (κp) of the brushes in the glassy and molten states. Comparison of the results for the high-density PMMA brushes and a reference spin-coated PMMA layer reveals the differences in the elastic and dielectric properties between a brush composed of highly stretched graft chains and a layer f...

Solution Properties of Poly(N-vinylcarbazole) and Its Copolymers with Methyl Methacrylate

Solution properties of poly(N-vinylcarbazole) (PVCz) and copolymers of N-vinylcarbazole with methyl methacrylate are investigated by using SEC coupled with differential refractive index (RI), multiangle light scattering (MALS), and UV detectors. The technique affords information on molecular weight, molecular weight distributions, and the chemical composition of copolymers. Moreover, the polymer dimensions are investigated in two different solvents, tetrahydrofuran (THF) and toluene, which are good and poor solvents, respectively, for poly(N-vinylcarbazole). The collapse of the polymer chain, the scaling laws, unperturbed dimensions, and characteristic ratios are determined by employing only a broad polydisperse polymer sample. The results are in good agreement with those obtained by much more complex procedures for the homopolymer PVCz. The influence of the methyl methacrylate content in the dimensions of the copolymer chains is analyzed. Unperturbed dimensions are also calculated employing a simple two-state RIS model. Agreement between calculated and measured values of Cn is excellent for homopolymers and copolymers with contents of MMA units up to ca. 80%.

Melt‐state polymer chain dimensions as a function of temperature

AbstractThe unperturbed chain dimensions (〈R2〉o/M) of cis/trans‐1,4‐polyisoprene, a near‐atactic poly(methyl methacrylate), and atactic polyolefins were measured as a function of temperature in the melt state via small‐angle neutron scattering (SANS). The polyolefinic materials were derived from polydienes or polystyrene via hydrogenation or deuteration and represent structures not encountered commercially. The parent polymers were prepared via lithium‐based anionic polymerizations in cyclohexane with, in some cases, a polymer microstructure modifier present. The polyolefins retained the near‐monodisperse molecular weight distributions exhibited by the precursor materials. The melt SANS‐based chain dimension data allowed the evaluation of the temperature coefficients [dln 〈R2〉o/dT(κ)] for these polymers. The evaluated polymers obeyed the packing length (p)‐based expressions of the plateau modulus, G = kT/np3 (MPa), and the entanglement molecular weight, Me = ρNanp3 (g mol−1), where nt denotes the number (∼21) of entanglement strands in a cube with the dimensions of the reptation tube diameter (dt) and ρ is the chain density. The product np3 is the displaced volume (Ve) of an entanglement that is also expressible as pd or kT/G. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1768–1776, 2002

Universal aspects of macromolecules in polymer blends, solutions, and supercritical mixtures.

We demonstrate that macromolecules in miscible polymer blends may behave as good, Theta, and poor polymeric solvents for each other. We construct a conceptual phase diagram, delineating the range of validity of the random-phase approximation, outside of which polymers contract or expand beyond their unperturbed dimensions, contrary to common assumptions. Remarkably, the correlation length for polymer blends, solutions, and supercritical mixtures collapses onto a master curve, reflecting universal behavior for macromolecules in polymeric and small-molecule Theta solvents.

Effect of phenol derivatives on molecular dimensions of poly(N‐vinyl‐2‐pyrrolidone) in aqueous solution

AbstractThe unperturbed dimensions and thermodynamic parameters of poly(N‐vinyl‐2‐pyrrolidone) (PVP) were studied in aqueous solutions in the presence of certain phenolic cosolutes (phenol, catechol, hydroquinone, resorcinol, and phloroglucinol). The intrinsic viscosities at 25°C and the θ temperature, linear and thermodynamic expansions, and root mean square end to end distances were evaluated for the system that was employed. The sequence was obtained due to the effectiveness of the cosolutes in the order of phloroglucinol > resorcinol > hydroquinone > catechol > phenol. The effects of these cosolutes on the main thermodynamic parameters were reported to be due to the number and position of hydroxyl groups present. The thermodynamic interaction parameter was also evaluated and the enthalpic and entropic contributions were verified. The condition required for the θ temperature to correspond to a Flory interaction parameter of 0.5 was well provided, yielding a θ temperature of almost 0.5 for the system under study. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 473–477, 2002; DOI 10.1002/app.10047

Solution properties of poly(n-hexyl methacrylate) in homologous series of n-alkanes

Dilute solutions of poly(n-hexyl methacrylate) have been studied in the homologous series of alkanes at different temperatures using viscometry. Mark-Houwink relations in solvents widely differing in their thermodynamical quality were established together with the unperturbed dimensions and their temperature coefficient.

Behavior of γ-ray-irradiated pullulan in aqueous solutions of cationic (cetyltrimethylammonium hydroxide) and anionic (sodium dodecyl sulfate) surfactants

γ-ray-irradiated pullulan macromolecules acquire properties of an anionic polyelectrolyte and, upon aggregation with the oppositely charged surfactant cetyltrimethylammonium hydroxide, are found to precipitate according to their molecular weight. This provides a convenient means for obtaining polymer fractions with a narrower molecular-weight distribution than those of the original samples. The method can be employed to obtain fractions of radiation-modified pullulan required in the production of a blood-plasma substitute. Anionic properties of γ-ray-irradiated pullulan also manifest themselves in interactions with sodium dodecyl sulfate (SDS) in aqueous solution, which result in a significant change in the viscous behavior of the polysaccharide. Upon an increase in the concentration of γ-ray-irradiated pullulan in an SDS solution, the reduced viscosity of the polymer first increases and, upon reaching a certain concentration, C*, decreases. The C* values were found to be dependent on the molecular weight of the polymer. The phenomena observed are discussed in terms of the general theory of polymer solutions within which C* is treated as a critical concentration at which interpenetration of polymer molecules becomes important. Unperturbed dimensions of γ-ray-irradiated pullulan macromolecules were estimated on the basis of experimental viscosimetric data.

Incoherent neutron scattering and the dynamics of confined polycarbonate films.

Incoherent elastic neutron scattering measurements are performed on thin (75 to 1015 A) polycarbonate films supported on Si wafers. We find that the mean-square atomic displacement <u(2)> is diminished by thin film confinement. For film thicknesses comparable to the unperturbed dimensions of the macromolecule, we observe two characteristic crossover temperatures in <u(2)> as a function of temperature T, one above and the other below the bulk T(g). Furthermore, the harmonic force constant kappa, defined by the low temperature dependence of <u(2)> (i.e., kappa approximately k(B)T/<u(2)>), increases as the film thickness decreases. These observations suggest that the atoms are more strongly localized in the thin supported films.

Thin film confinement effects on the thermal properties of model photoresist polymers

The demand to print increasingly smaller microelectronic device features means that the thickness of the polymer films used in the lithographic processes must decrease. The thickness of these films is rapidly approaching the unperturbed dimensions of the polymer, length scales at which confinement deviations and dewetting are a significant concern. We combine specular x-ray reflectivity (SXR) and incoherent neutron scattering (INS) to probe the thermal stability and dynamical effects of thin film confinement in poly(hydroxy styrene) (PHS), a polymer used in a majority of the 248 nm deep UV photoresists. PHS forms stable thin films (down to 5 nm) that do not dewet over a wide temperature range on Si surfaces ranging from hydrophilic to hydrophobic. The surface energy has a profound influence on the magnitude of the thin film expansion coefficient, especially above the glass transition, in films as thick as 100 nm. Confinement also appears to suppress the mean-square atomic displacements and the level of anharmonicity in the dynamics, primarily above the bulk glass transition.

The Single Chain Properties of the Bisphenol A Polycarbonate by the Rotational-Isomeric-State Monte Carlo Method

The conformational properties of the bisphenol A polycarbonate (PC) were studied using the Rotational-Isomeric-State (RIS) Monte Carlo (MC) simulation. The conformations of a single PC chain were generated at theta condition in a wide range of molar mass and temperature. The mean square end-to-end distance ( ) converged to the limiting unperturbed dimension obtained from the conventional RIS method, at least over 1×104 conformations. The molecular dimension in terms of /M (M is molecular weight) by the RIS MC method using the published statistical weights of the PC is 1.09 A2 mol g-1. Both the dimensions were within the ranges of calculated or empirical data published previously. The chain rigidity of the PC chain is three times higher than that of the PS chain at 600 K. The intrinsic viscosity was predicted from the calculated radius of gyration (s). It was found out that the gyration or the conformation generated at theta state were closer to those of dilute solutions in p-dioxane at 303 K than in tetrahydrofuran (THF) solution at 297 K. In the future study, the conformation obtained from this study will be used as an initial structure to perform the molecular dynamics calculation in order to investigate interfacial properties of the PC bulk.

Molecular dimension and interaction parameters of polyacrylamide in water–dimethylsulphoxide mixtures: effect of temperature

The intrinsic viscosities [ η] of polyacrylamides having different molecular sizes are measured at 30–50°C temperature in various mixtures of water (good solvent) and dimethylsulphoxide (DMSO, poor solvent). The observed result and the Huggins constant values show a significant variation of cosolvency as a function of solvent composition ( ϕ) and temperature. The nature of plots of [ η] vs. ϕ DMSO indicates relative importance of entropy factors over energetic factors in determining molecular configuration at high temperature. The unperturbed dimensions ( K θ ) of the polymer are determined by various methods, which agree well with each other and exhibit a minimum at ϕ=0.5. The temperature coefficients of the unperturbed dimension ( K ′) gives both positive and negative values depending on the solvent composition, which indicates the variation of compactness and the presence of low and high energy configurations as a function of solvent composition. Molecular extension factor ( α n) and the chain rigidity ( σ) values are evaluated and the influence of temperature is discussed.

Chain dimensions and transport coefficients of sodium poly(isoprenesulfonate) in aqueous sodium chloride

AbstractSodium poly(isoprenesulfonate) (NaPIS) fractions consisting of 1,4‐ and 3,4‐isomeric units (0.44:0.56) and ranging in molecular weight from 4.9 × 103 to 2.0 × 105 were studied by static and dynamic light scattering, sedimentation equilibrium, and viscometry in aqueous NaCl of a salt concentration (Cs) of 0.5‐M at 25 °C. Viscosity data were also obtained at Cs = 0.05, 0.1, and 1 M. The measured z‐average radii of gyration 〈S2〉z1/2, intrinsic viscosities [η], and translational diffusion coefficients D at Cs = 0.5‐M showed that high molecular weight NaPIS in the aqueous salt behaves like a flexible chain in the good solvent limit. On the assumption that the distribution of 1,4‐ and 3,4‐isomeric units in the NaPIS chain is completely random, the [η] data for high molecular weights at Cs = 0.5 and 1 M were analyzed first in the conventional two‐parameter scheme to estimate the unperturbed dimension at infinite molecular weight and the mean binary cluster integral. By further invoking a coarse‐graining of the NaPIS molecule, all the [η] and D data in the entire molecular weight range were then analyzed on the basis of the current theories for the unperturbed wormlike chain combined with the quasi‐two‐parameter theory. It is shown that the experimental 〈S2〉z, [η], and D are explained by the theories with a degree of accuracy similar to that known for uncharged linear flexible homopolymers. © 2001 John Wiley &amp; Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2071–2080, 2001