Unperturbed chain dimensions of isotactic polypropylene in theta solvents

The unperturbed mean-square end-to-end distance 〈R₀²〉 and its temperature variation d In 〈R₀²〉/dT for isotactic polypropylene have been estimated from intrinsic viscosity data in three theta solvents, i.e., diphenyl, diphenyl ether, and dibenzyl ether, measured at their θ temperatures as determined by precipitation temperature measurements. The characteristic ratios, 〈R₀²〉/nl², where n is the number of bonds of length l in the main chain, evaluated by assuming Φ = 2.87 × 10²¹, are 5.80 in diphenyl (at θ = 125.1°C.), 5.41 in diphenyl ether (at θ = 142.8°C.), and 4.56 in dibenzyl ether (at θ = 183.2°C.). These values lead to the temperature coefficient d In 〈R₀²〉/dT = ?4.09 × 10^?3 deg.^?1 Results are compared with the data previously reported on polyethylene.     

Melt‐state polymer chain dimensions as a function of temperature

The 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, M_e = ρN_anp³ (g mol^?1), where n_t denotes the number (～21) of entanglement strands in a cube with the dimensions of the reptation tube diameter (d_t) and ρ is the chain density. The product np³ is the displaced volume (V_e) 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     

Thermodynamic parameters of polymer-solvent systems from light-scattering measurements below the theta temperature

As is well known, the chemical potentials of polymer and solvent in solution and, hence, the Flory-Huggins interaction parameter χ can be determined from scattered light intensities from dilute and concentrated solutions of the polymer in the solvent concerned. Preferably, measurements should be performed at temperatures as low as possible, provided the temperature exceeds the cloudpoint for the concentration used. It is shown that the lower the temperature and, consequently the higher the scattered light intensity, the better is the accuracy of the parameters obtained. At each temperature the scattered light intensity shows a maximum at some concentration. Below the theta temperature the ratio of scattered light intensity and concentrations also shows a maximum at some concentration. The values and the concentrations of these maxima for various temperatures enable the maximum of the spinodal to be determined. The spinodal itself can be determined by an extrapolation procedure of the reciprocal scattered light intensities. Measurements have been performed with three narrow-distribution polystyrene samples in cyclohexane. On the basis of the results, χ, and its dependence on concentration, temperature, and molecular weight can be determined to high accuracy.     

Neutron scattering in polymer gels at the theta temperature

Small angle elastic neutron scattering was performed on three polystyrene networks swollen to equilibrium in cyclohexane at the theta temperature. Comparison of the SANS spectra with similar measurements in uncross-linked solutions reveals that in the intermediate Q region the gels behave like solutions of lower concentration than the equivalent solutions. We assume that the gel spectra are composed of a static component plus a dynamic, or solution-like part. By a suitable fitting procedure, the former can be estimated, yielding the mean square static concentration fluctuation <Δφ²> generated by cross-linking contraints in the gel. Independent measurement of the swelling pressure of these gels permits an estimate to be made of the scattering intensity I(Q=0) of the dynamic part of the spectrum. Plausible agreement is found between the macroscopic and microscopic estimations of the osmotic compressibility if allowance is made for the concentration polydispersity in the gels.     

The dimensions of a polymer chain at the coil-to-globule transition

Simple models of the star-branched and linear polymers were studied by means of a Monte Carlo method. The chains were confined on a simple cubic lattice. Star-branched polymers consisted of f=3 arms of equal length. The total number of beads in both types of polymers was varied from N=49 to N=799. The simulations were performed in different solvent qualities—from a good solvent to a collapsed globule regime. The static properties of the chains under consideration were measured as functions of the temperature of the system. It appeared that the ratio of the radius of gyration to the mean end-to-end vector is very sensitive to solvent quality. It shows that the coil-to-globule transition is a complicated phenomenon. The possible explanation of the phenomenon is discussed.     

Static structure factor and chain dimensions in polymer blends with non-local mixing entropy

It is suggested that the non-locality of the entropy part of the interaction parameter in partially miscible blends can be measured directly by scattering experiments. The structure factor computed in the random phase approximation is compared with experiments on weakly crosslinked polystyrene (PS) polyvinylmethylether (PVME) blends. These polymers have significantly different monomer units to form ‘smooth’ (PVME) and ‘rough’ (PS) polymers. An excess scattering is observed and related to the non-locality. It is further shown that these effects are significant near the glass transition of the blend. In particular, the influence of the non-local mixing entropy on the single chain behaviour close to the onset of the microphase separation is studied quantitatively.     

Contributions of short-range and excluded-volume interactions to unperturbed polymer chain dimensions

A Monte Carlo study is made of the mean-square radius of gyration for the freely rotating chain with such fictitious excluded-volume interactions that the Lennard-Jones 6-12 potentials at the Theta temperature act only between the fourth-through (3+Delta)th-neighbor beads (Delta > or = 1) along the chain. The behavior of the asymptotic value (/n)infinity of the ratio /n as a function of the number n of bonds in the chain in the limit of n --> infinity is examined as a function of Delta. It is shown that the approach of (/n)infinity to its value for the real unperturbed chain with Delta = infinity is so slow that the interactions between even up to about 100th-neighbor beads should be taken into account in order to reproduce nearly its dimension. The result implies that the unperturbed polymer chain dimension as experimentally observed at the Theta temperature depends not only on short-range interactions but also to a considerable extent on the long-range excluded-volume interactions, and that the asymptotic value Cinfinity of the characteristic ratio Cn for the rotational isomeric state model in the limit of n --> infinity, which is determined only by the very local conformational energy, cannot be directly compared with the corresponding experimental value.     

Force-length relations in deformed coils above and below the theta state. Possible bimodality in the chain distribution function

Stretching of flexible macromolecules by an external force, acting on the chain ends, in solvents of variable quality was simulated by the Monte Carlo method on a tetrahedral lattice. The forcelength relations and the stress-induced changes in the population of the gauche conformers were calculated for coils in theta and athermal solvents. In poor solvents, the stretching of a collapsed coil involves a rather abrupt upturn of the force-length curve explained as a transition of a globular coil into an extended coil. In conformity with this interpretation, a bimodal shape of the chain vector distribution function P(R) was found in the intermediate range of deformation of collapsed coils. The significance of the results to the stress-strain behavior of networks with pronounced interaction (such as collapsed gels) are discussed.     

Photoinduced intramolecular charge separation in a polymer solid below the glass transition temperature

Photoinduced intramolecular charge separation (CS) in a polar polymer glass, cyanoethylated pullulan (CN-PUL), was studied below the glass transition temperature (Tg=395 K). A series of three carbazole (Cz: donor)-cyclohexane (S: spacer)-acceptor (A: acceptor) molecules (Cz-S-A) was used as intramolecular donor-acceptor dyads. The photoinduced CS rate was evaluated by the fluorescence decay measurement at temperatures from 100 to 400 K. The CS rate (kCS) increased above 200 K even far below Tg where micro-Brownian motions of the whole polymer chain are frozen. Below 200 K, on the other hand, kCS showed weak dependence on temperature. The temperature dependence of kCS is discussed in terms of the dielectric relaxation time of the polymer matrix. Consequently, CS below Tg was well explained by a thermally nonequilibrium electron transfer (ET) formula above 200 K and by a two-mode quantum-mechanical ET formula below 200 K. The increase in kCS above 200 K is mainly caused by a thermally activated low-frequency matrix mode originating from the side-chain relaxation of polar cyano groups. The weak temperature dependence of kCS can be explained by a nuclear-tunneling effect caused by a high-frequency matrix mode (variant Planck's over 2piomegH=250 cm-1) and an intramolecular vibrational mode (variant Planck's over 2piomegaQ=1300 cm-1). The high-frequency mode of the polymer matrix was attributed to a vibrational or librational motion of polar groups in the CN-PUL glassy solid.     

Molecular-dynamics simulations of the transport properties of a single polymer chain in two dimensions

Molecular-dynamics simulations are conducted to elucidate the critical factors affecting the transport properties of isolated polymer chains in strictly two dimensions. The relevance of surface inhomogeneity is critically examined. We unequivocally find that surface inhomogeneity is critical in obtaining transport behavior consistent with the recent measurements of surface diffusion for polymers adsorbed at the solid-liquid interface. For a systematic investigation of this point, heterogeneity was introduced by decorating the surface with impenetrable elements and we find that chain diffusivity crossed over from Rouse-type behavior to reptationlike with increasing surface coverage of obstacles. This transition in behavior occurred when the mean distance between obstacles is approximately equal to the end-to-end distance, Re, of the two-dimensional chain. Our results underscore the importance of surface disorder (not only literal obstacles but by reasonable extension also to other types of disorder) in determining the transport behavior of chains adsorbed to solids.     

Effect of the reference chain dimensions in the molecular theory of viscoelastic behavior of polymer networks

Mooney's version of the molecular theory of polymer networks has been generalized to the case when the external strain applied in the isotropic state is different from that at network formation. As in the theory of equilibrium behavior of the polymer networks, this generalization allows inclusion in the viscoelastic functions of effects connected with the temperature dependence of internal energy of the chains and with the strain effect of the solvent. From viscoelastic functions thus generalized, it is possible to derive a relation for calculation of the monomeric friction coefficient. It also suggests the possibility of superposing data obtained at various temperatures, degrees of swelling, and condition of network formation.     

Nuclear reaction analysis: A study on the interface formation in polymer mixtures below the critical point

We describe a method for directly determining the composition profile of deuterated polymer chains in polymer mixtures. Our technique, nuclear reaction analysis, is based on the ²H(³He, ⁴He)¹H nuclear reaction. By detecting ⁴He in a forward geometry, we achieve a spatial resolution of 14 nm (FWHM). We use this technique to probe the broadening of the interface between two partially miscible polymers. We found that such a system attains a finite interfacial width in equilibrium. For short times, we monitor the dynamics of interface formation. We found that the interfacial width increases significantly slower than in the case of free diffusion.     

Stress relaxation of PVC below the yield point

Stress relaxation of commercial poly(vinyl chloride) (PVC) is measured at strains below 3% and at different temperatures below the glass transition temperature. First it is shown that below the yield point the material follows a linear viscoelastic behavior. Then the data at a fixed deformation level (0.03) are fitted by considering a lognormal distribution function of relaxation times. Furthermore, from the measured stress-strain curves, the temperature dependence of the elastic tensile modulus is determined. The temperature dependence of the elastic modulus, the relaxation strength, and the parameters of the distribution: mean relaxation time, τ_m, and half-width, β, are given. Moreover, the distribution function and the temperature dependence of its characteristic parameters are discussed in terms of a cooperative model of the mechanisms involved in the mechanical relaxation of glassy polymers. Finally, the relationship proposed between the tensile modulus and the free volume helps explain the temperature dependence of the relaxation strength. © 1996 John Wiley & Sons, Inc.     

Confinement effect of chain dynamics in micrometer thick layers of a polymer melt below the critical molecular weight

Polymer melts confined in micrometer thick layers were examined with the aid of field-cycling NMR relaxometry. It is shown that chain dynamics under such moderate confinement conditions are perceptibly different from those observed in the bulk material. This is considered to be a consequence of the corset effect, which predicts a crossover between Rouse and reptationlike dynamics for molecular weights below the critical value at confinement length scales much larger than 10RF, where RF is the Flory radius of the bulk polymer coil [Fatkullin et al., New J. Phys. 6, 46 (2004)]. For the polymer species studied, a perfluoropolyether with a molecular weight of 11 000, the Flory radius is of the order 10 nm, so that the experiment refers to the far end of the predicted crossover region from confined to bulk chain dynamics. Remarkably the confinement effect is shown to reach polymer-wall distances of the order 100 Flory radii.     

The theta temperature of star polymers

We use equations derived from the blob theory to calculate the blob size and the theta temperature of star polymers. In contrast to the case of linear polymers these two parameters are calculated to depend on molecular mass for star polymers. For a given star polymer the theta temperature can be lower or higher than that of the corresponding linear polymer depending on the number and length of its branches. The results are compared with the blob model of Daoud and Cotton for star polymers. Experimental results obtained in the course of this study confirm our calculations.     

Lower critical solution temperature (LCST) and theta temperature of aqueous solutions of nonionic surface active agents of various polyoxyethylene chain lengths

Cloud points of aqueous solutions of homogeneous poly(oxyethylene)dodecyl ether derivatives (C₁₂(OE)_n: n=2–8) and the apparent theta temperatureT ^ap were determined from the abrupt changes in optical transmittance and the temperature dependence of the second virial coefficient obtained by light scattering measurements. It was found that the lower critical solution temperature (LCST) shifts to a lower temperature and lower concentration as the number of oxyethylene units in a molecule decreases. Because of this behavior of LCST, the modified Flory-Schultz plot of phase separation was applied to the present nonionic surfactant-water system, and its theta temperature obtained. The dependence ofT ^ap on the number of oxyethylene units suggests that the polyoxyethylene chain has different effects on the solubility of C₁₂(OE)_n in water forn less than or equal to 3 from those forn greater than or equal to 4.     

Adsorption systems at temperatures below the freezing point of the adsorptive

Isothermal adsorption studies and the measurement of dimensional changes below the bulk freezing point of the adsorbate indicate that substances adsorbed in porous solids are unable to freeze in situ. The difference between the vapour pressure or free energy of the unfrozen adsorbate and that of the bulk adsorptive outside of the porous system is resolved by a desorption process; the desorbed matter freezes outside of the system while the vapour pressure of the adsorbate remaining in the pores decreases through meniscus formation. Mechanical breakdown of the system occurs only then, when this process cannot be completed and an equilibrium state is not attained.This mechanism was found to be valid for porous silica glass, hydrated cement paste, bricks, and even for biological substances such as animal and plant tissue, and foodstuff. This understanding has led to the development of new methods for testing the durability of building materials, clarification of some problems of the BET surface area determination method and it suggests an explanation for the action of cryoprotective agents.     

Statistical rate theory determination of water properties below the triple point

We report a new method for determining the saturation vapor pressure, Ps(T), of water at conditions below its triple point. Ps(T) appears as a parameter in the statistical rate theory (SRT) expression for the net evaporation flux. We use measurements of the interfacial conditions during steady-state evaporation and condensation experiments and SRT to determine the values of Ps(T) from 50 different experiments over a range of interfacial conditions. From these values of Ps(T), we develop an analytical expression and from it calculate the liquid-vapor latent heat, Llv(T), and the constant pressure specific heat, cp(L)(T). The calculated values of these properties are compared with those obtained from independent measurements. This comparison indicates the SRT expressions for Llv(T) and cp(L)(T) are consistent with the measurements over a range of temperatures.