Isotopic Blends Research Articles

Closure to the PRISM equation derived from nonlinear response theory.

Nonlinear response theory is employed to derive a closure to the polymer reference interaction site model equation. The closure applies to a liquid of neutral polymers at melt densities. It can be considered a molecular generalization of the mean spherical approximation (MSA) closure of Lebowitz and Percus to the atomic Ornstein-Zernike (OZ) equation and is similar in some aspects to the reference "molecular" MSA (R-MMSA) closure of Schweizer and Yethiraj to PRISM. For a model binary blend of freely-jointed chains, the new closure predicts an unmixing critical temperature, Tc, via the susceptibility route that scales linearly with molecular weight, N, in agreement with Flory theory. Predictions for Tc of the new closure differ greatest from those of the R-MMSA at intermediate N, the latter being about 40% higher than the former there, but at large N, both theories give about the same values. For an isotopic blend of polyethylene, the new and R-MMSA closures predict a Tc about 25% higher than the experimental value, which is only moderately less accurate than the prediction of atomic OZ-MSA theory for Tc of methane. In this way, the derivation and its consequences help to identify the ingredients in a theory needed to properly model the equilibrium properties of a polymeric liquid at both short and long lengthscales.

Molecular Weight Dependence of Deuterium Exchange on Polyethylene: Direct Measurement and SANS Model

Following a hydrogen–deuterium exchange reaction, size-exclusion chromatography with infrared detection (SEC-IR) was used to measure the distribution of deuterium with respect to molecular weight on a polyethylene resin. The SEC-IR method reveals significant heterogeneity in the distribution of deuterium across molecular weight, including a fraction of high molecular weight chains that are nearly or completely unlabeled. Small-angle neutron scattering (SANS) was performed on the labeled polymer and an isotopic blend; the random phase approximation model prediction for the scattering from an n-component blend was successfully used to model the measured SANS data. Additionally, a Monte Carlo algorithm was used to fit the measured SANS data to a deuterium distribution, yielding a measurement consistent with that obtained from SEC-IR. The methods are compared to literature approaches for describing nonideal deuterium labeling. These results demonstrate the value of including detailed information about the distribution of deuterium in a scattering model and provide methods for probing the structure and interactions of complex polyolefin resins that have been labeled via heterogeneous catalysis.

Characterization of the Flory-Huggins interaction parameter of polymer thermodynamics

Flory-Huggins theory is the main basis of polymer solution and blend thermodynamics. A key piece of this theory is a parameter quantifying the enthalpic interactions between the components; however, experiments have revealed that this parameter is not composition independent, as originally assumed. This composition dependence has been attributed by some theorists to experimental error; others have tried to explain it based on several competing hypotheses. Here, we use atomistic simulations of isotopic blends based on realistic potentials to study this parameter without making any prior hypotheses. Simulations reveal a composition dependence of this parameter that compares well with experimental data, and serve to verify theoretical relationships between the various forms of this parameter.

Reduction of measurement uncertainty by experimental design in high-order (double, triple, and quadruple) isotope dilution mass spectrometry: application to GC-MS measurement of bromide

Since its introduction a century ago, isotope dilution analysis has played a central role in developments of analytical chemistry. This method has witnessed many elaborations and developments over the years. To date, we have single, double, and even triple isotope dilution methods. In this manuscript, we summarize the conceptual aspects of isotope dilution methods and introduce the quadruple dilution and the concept of exact matching triple and quadruple dilutions. The comparison of isotope dilution methods is performed by determination of bromide ions in groundwater using novel ethyl-derivatization chemistry in conjunction with GC/MS. We show that the benefits of higher-order isotope dilution methods are countered with a greater need for careful experimental design of the isotopic blends. Just as for ID(2)MS, ID(3)MS and ID(4)MS perform best when the isotope ratio of one sample/spike blend is matched with that of a standard/spike blend (exact matching).

The preparation and use of synthetic isotope mixtures for testing the accuracy of the PTIMS method for 10B/11B isotope ratio determination using boron mannitol complex and NaCl for the formation of Na2BO2+

The development of a method for determination of isotopic composition requires calibration of the method over a wide range of isotopic ratios. Further, validation of data obtained by the method requires isotopic reference materials spanning a wide range of ratios. In the present studies, gravimetric synthetic mixtures of boron with 10% 10B to 95% 10B were prepared by mixing solutions of enriched boron isotopes. The solutions of 10B and 11B enriched isotopes were calibrated using isotopic reference material NIST SRM-951 as a spike for isotope dilution. 10B/11B atom ratios in all the blends were determined by Positive Thermal Ionization Mass Spectrometry (PTIMS) using NaCl with mannitol for the formation of Na2BO2+. A measurement precision of about 0.03% was obtained from repetitive P-TIMS analyses of the mixtures with 10B content ranging from 10 to 70%. An instrument isotope fractionation factor (K-factor) of 0.99935 ± 0.00030 (1 s) was obtained for 10B/11B atom ratios of the different blends and this agreed with the K-factor determined from P-TIMS analysis of NIST SRM-951. The different isotopic blends prepared were also used in Inductively Coupled Plasma Quadrupole Mass Spectrometry, (ICP-QMS) employing NIST SRM-951 (10B/11B ratio of 0.2473) as a bracketing standard. An accuracy and precision of about 0.5% was obtained during ICP-QMS analyses of these mixtures. A novel and simple method for validation of analysis methodology with synthetic mixtures prepared using enriched isotopes is described in the present work.

Molecular changes on drawing isotopic blends of polyethylene and ethylene copolymers. Part 2. MCIRS studies

The technique of mixed crystal FTIR spectroscopy has been applied to uniaxially drawn isotopic blends of linear polyethylene and ethylene copolymers. Following the drawing of melt-quenched samples at 1mmmin−1, clamped samples were cooled with liquid nitrogen. Analysis of the CD2 bending vibration of the ‘guest’ perdeuterated species enabled the arrangement of crystal stems to be characterised. Changes in band components observed were identified with the processes of polymer crystallisation, the untwisting of lamellar ribbons perpendicular to the draw direction and coarse slip. For example, the appearance of new doublets or increased splittings is related to crystallisation, while an increase in singlet band area, at least at higher draw ratios, is indicative of coarse slip. Crystallisation appears to be complete at a draw ratio of 4 for a linear polyethylene sample with low guest molecular weight. For similar copolymer ‘guest’ molecular weights, the processes identified above are delayed to higher levels of deformation. This was attributed to copolymer branches hindering both crystallisation and chain translation through lamellae. Estimates of the crystallite block size present after drawing enable a quantitative description of coarse slip to be obtained. A progressive increase in width of the central singlet for two of these samples is tentatively ascribed to variations in molecular strain.

Reliably estimating bare chi from compressible blends in the grand canonical ensemble

The bare chi characterizing polymer blends plays a significant role in their macroscopic description. Therefore, its experimental determination, especially from small-angle-neutron-scattering experiments on isotopic blends, is of prime importance in thermodynamic investigations. Experimentally extracted quantity, commonly known as the effective chi is affected by thermodynamics, in particular by polymer connectivity, and composition and density fluctuations. The present work is primarily concerned with studying four possible effective chis, one of which is closely related to the conventionally defined effective chi, to see which one plays the role of a reliable estimator of the bare chi. We show that the conventionally extracted effective chi is not a good measure of the bare chi in most blends. A related quantity that does not contain any density fluctuations, and one which can be easily extracted, is a good estimator of the bare chi in all blends except weakly interacting asymmetric blends (see text for definition). The density fluctuation contribution is given by ( Δ v ¯ ) 2 / 2 TK T , where Δ v ¯ is the difference of the partial monomer volumes and K T is the compressibility. Our effective chis are theory-independent. From our calculations and by explicitly treating experimental data, we show that the effective chis, as defined here, have weak composition dependence and do not diverge in the composition wings. We elucidate the impact of compressibility and interactions on the behavior of the effective chis and their relationship with the bare chi.

Conformation of Cyclics and Linear Chain Polymers in Bulk by SANS

Small-angle neutron scattering (SANS) has been used to investigate the conformation of linear and cyclic poly(dimethylsiloxane)s (PDMS) in chemically identical, undiluted blends. SANS measurements have been carried out on (1) linear hydrogenous (H) mixed with linear deuterated (D) PDMS and (2) cyclic H mixed with cyclic D PDMS. The conformational behavior of the cyclic and linear polymers is studied over a wide range of molar mass and composition. Isotopic blends of linear PDMS are shown to adopt conformations that agree well with theoretical predictions for Gaussian random-coil polymers and confirm previous SANS studies. As expected for chains obeying Gaussian statistics, the mean radii of gyration, Rg, scale with the weight-average molar mass as Rg ∝ Mw0.5. A detailed study of H/D cyclic PDMS mixtures is presented, and we demonstrate that, since Rg ∝ Mw0.4, highly flexible cyclic polymers in the melt adopt an even more compact conformation than that of unperturbed rings. This behavior confirms previous ...

Chain expansion and chain localisation in the homogenous regime of blends of liquid low molar mass polysiloxanes as revealed by neutron scattering investigations

Abstract Using small angle neutron scattering and neutron spin echo spectroscopy, two isotopic blends of low molar mass polydimethylsiloxane (PDMS) and polyethylmethylsiloxane (PEMS), and the corresponding binary blends d-PDMS/ p-PEMS and p-PDMS/d-PEMS (d: deuterated, p: protonated) were studied at the critical composition in the homogeneous regime. From the scattering data it becomes evident that coil dimensions and collective dynamics of these both blend systems behave significantly different. Compared to the isotopic mixtures, which exhibit the expected unperturbed chain dimensions and the typical Rouse relaxation, in the binary blends, which differ by a large shift with respect to the critical temperature, considerable coil expansion and spatially restricted Rouse relaxation occur. Both these structural and dynamic effects are in agreement with the model of droplet formation and chain localization, resulting from the existence of microscopic heterogeneities within the spinodal boundaries of the phase diagram. In addition, the observation of Rouse relaxation, spatially restricted to microscopic length scales, provides a new access to the molecular understanding of the critical slowing down of the mutual diffusion process, observed by photon correlation spectroscopy.

Molecular changes on drawing isotopic blends of polyethylene and ethylene copolymers: 1. Static and time-resolved sans studies

Small angle neutron scattering (sans) has been used to observe changes in molecular orientation on deformation of isotopic, melt quenched blends of linear polyethylene and copolymers with butyl and hexyl branches, using uniaxial drawing. In no case was there evidence of significant isotopic fractionation either before or during deformation. Samples left clamped in the neutron beam following deformation showed no evidence of molecular relaxation, while significant changes in molecular orientation with time were observed for samples unclamped after deformation. This latter behaviour could be fitted adequately by a single exponential decay and the relaxation time was found to be of the order of tens of minutes. This relaxation time increased with both increasing molecular weight and the presence of branching. For samples drawn to draw ratios of up to 3.0, the anisotropy in the radius of gyration was compared with predictions for affine deformation. Only in the cases of linear labelled guest molecules in either a linear or copolymer host were significant departures from the affine model observed: no such departures were found for copolymer guest molecules. This is interpreted in terms of a delay in crystallite disruption until higher draw ratios for copolymer guest molecules with respect to linear guest.

Thermodynamic interaction parameter of star–star polybutadiene blends

AbstractThe value of the thermodynamic interaction parameter, χeff, for star–star polybutadiene blends was determined with small‐angle neutron scattering. Blends in which the stars have the same number of arms and blends in which the stars have different numbers of arms are investigated. For star–star isotopic blends with components having the same number of arms, the presence of the junction point of the star leads to a value of χeff that is larger than that for an analogous linear–linear isotopic blend. However, changes in the value of χeff resulting from small dissimilarities in the number of arms of the two components in the isotopic star–star blends were too small to resolve. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 247–257, 2003

The effect of short chain branching on local chain organisation in isotopically labelled blends of polyethylene

The complementary techniques of small angle neutron scattering (SANS) and infra-red spectroscopy have been used to determine features of molecular trajectory for isotopic blends incorporating linear polyethylene and copolymers containing butyl or hexyl branches. SANS data show both a more compact conformation for a copolymer guest molecule than for a linear guest and also a smaller molecular expansion with increasing molecular weight when both guest and host are copolymers. These blends also show the smallest proportion of [lcub ]110[rcub ] isolated guest stems, while wholly linear blends show the largest proportion, on the evidence of the infra-red CD 2 bending band profiles. Estimates are made of the sizes of ‘groups’ of adjacent stems, and these also show a corresponding dependence on the sample type, indicating a higher proportion of adjacent re-entry for copolymer blends than for linear blends.

Beyond Flory-Huggins theory: new classes of blend miscibility associated with monomer structural asymmetry.

Flory-Huggins (FH) theory is restricted to polymer mixtures whose monomers are structurally identical, a situation limited to isotopic blends and computer simulations. We investigate the influence of monomer structure on blend miscibility and scattering properties using the lattice cluster theory generalization of the FH model. Monomer structural asymmetry is shown to profoundly affect blend miscibility (T(c),phi(c)), chain swelling (T(theta)), and the scale (xi) and intensity [S(0)] of composition fluctuations. Four distinct blend miscibility classes are identified and experimental evidence for these classes is discussed.

Strong isotopic labeling effects on the pressure dependent thermodynamics of polydimethylsiloxane/polyethylmethylsiloxane blends

Using photon correlation spectroscopy we show that isotopic labeling can strongly alter the pressure dependent thermodynamics of polydimethylsiloxane/polyethylmethylsiloxane blends, while each blend enhances its miscibility upon pressurization up to 2 kbar. The pressure dependence of the Flory interaction parameter, χ, changes by a factor of 4 when the deuteration of side groups is switched from one polymer to the other, but its pressure dependence is always negative. These results may be understood as being driven by the very different negative excess volumes of mixing for these different isotopic blends. We have attempted to unify our understanding of the role of pressure on blend thermodynamics into a single master plot by examining our data on volume changes on mixing vs the interaction parameter for the polysiloxane blends, and those from neutron scattering experiments on polyolefin blends and on a blend of a polyolefin and a polysiloxane. We find no universal trends when examined on this basis, and instead observe that variations in the chemical identity of the polymers in question and their chain lengths lead to very different plots. Further, since both neutron scattering and light scattering provide the same qualitative results, we argue that these results are not artefacts of either experimental technique. Our results strongly argue that the role of pressure on blend thermodynamics are much more complex than previously anticipated, and stress the need for improved theories for this important class of experiments.

Chain dimensions in polysilicate-filled poly(dimethyl siloxane)

We present experimental results on the single chain dimensions of isotopic blends (both mismatched and matched molecular masses) of poly(dimethyl siloxane) (PDMS) containing trimethylsilyl-treated polysilicate particles (fillers) and compare these results with Monte Carlo calculations. For polymer chains which are approximately the same size as the filler particle, a decrease in chain dimensions is observed relative to the unfilled chain dimensions at all filler concentrations. For larger chains, at low filler concentrations, an increase in chain dimensions relative to the unfilled chain dimensions is observed. Both results are in agreement with existing Monte Carlo predictions. However, at even higher filler contents, which are beyond the scope of the Monte Carlo predictions, the chain dimensions reach a maximum value before decreasing to values which are still larger than the unfilled chain dimensions. A simple excluded volume model is proposed which accounts for these observations at higher filler content.

An innovative method for extracting isotopic information from low-resolution gamma spectra

A method is described for the extraction of isotopic information from attenuated gamma-ray spectra using the gross-count material basis set (GC-MBS) model. This method solves for the isotopic composition of an unknown mixture of isotopes attenuated through an absorber of unknown material. For binary isotopic combinations the problem is nonlinear in only one variable and is easily solved using standard line optimization techniques. Results are presented for NaI spectrum analyses of various binary combinations of enriched uranium, depleted uranium, low burnup Pu, 137Cs, and 133Ba attenuated through a suite of absorbers ranging in Z from polyethylene through lead. The GC-MBS method results are compared to those computed using ordinary response function fitting and with a simple net peak area method. The GC-MBS method was found to be significantly more accurate than the other methods over the range of absorbers and isotopic blends studied.

Molecular Weight and Compositional Dependence of Isotopic Blends

The chain length and compositional dependence of the effective chi parameter, χs, in model isotopic polyethylene blends were determined at two different temperatures using our recently developed optimized cluster theory for polymer mixtures. χs was found to have a concave-up compositional dependence that decreased with increasing temperature and molecular weight, in agreement with neutron scattering measurements. A best fit to the chain length dependence of χs at constant temperature and composition had the form, χs = χs(∞) + D/N, where N is the number of segments comprising the polymers. In addition, the calculated compositional dependence of χs could be accurately described by a simple functional form that was previously proposed to fit experimental data on isotopic blends. However, the theory underestimates the breadth of the compositional dependence reported in the literature.

Deviation of early stage of spinodal decomposition from the Cahn-Hilliard-Cook theory observed in an isotopic polymer blend

The early stage of spinodal decomposition was studied by small-angle neutron scattering in the critical mixture of the isotopic blend deutero-polystyrene/polystyrene (d-PS/PS) of equal molecular volume of 1.42 × 10 6 cm 3/mol. The time evolution of this process is described by the dynamical structure factor. The observed time evolution of the fluctuation modes is a non-exponential. The analysis of the data has shown that the non-exponential behavior was attributed to a time-dependent increase of the “range” of the Onsager coefficient.

Nonproliferation and safeguards aspects of the IFR

The National Academy of Sciences (NAS) has declared that the large and growing stocks of plutonium from weapons dismantlement in the U.S. and the former Soviet Union FSU are a “clear and present danger” to peace and security. Moreover, the opinion of some experts that plutonium of any isotopic blend is a proliferation threat (Mark, 1993) has been well publicized, heightening the concern that plutonium produced in the civilian fuel cycle is itself a proliferation threat. Assuring that separated plutonium, from dismantled warheads as well as from civilian power programs, is under effective control has (again) become a high priority of U.S. diplomacy. One pole of the debate on how to manage this material is to declare it to be a waste, and to search for some way to dispose of it safely, securely, and permanently. The other pole is to view it as an energy resource and to safeguard it against diversion, putting it into active use in the civilian power program. The ultimate choice cannot be separated from the long-term strategy for use of peaceful nuclear power. Continued use of a once-through fuel cycle will lead to an ever-increasing quantity of excess plutonium—requiring safeguarding. Alternatively, recycling the worl's stocks of plutonium in fast reactors, contrary to common misconception, will cap the world supply of plutonium and hold it in working inventories for generating power. Transition from the current-generation light water cooled reactors (LWRs) to a future fast-reactor-based nuclear energy supply under international safeguards would, henceforth, limit world plutonium inventories to the amount necessary and useful for power generation, with no further excess production. The IFR offers complete recycle of plutonium, and indeed, of all transuranics, with essentially no transuranics sent to waste, so the need for perpetual safeguards of Integral Fast Reactor (IFR) waste is eliminated. The pyro-recycle process is more proliferation resistant than the current plutonium-uranium extraction process (PUREX) because at every step of the IFR recycle process the materials meet the “spent-fuel standard”. The scale of IFR recycle equipment is compatible with colocation of power reactors and their recycle facility, eliminating off-site transportation and storage of plutonium-bearing materials. Self-protecting radiation levels are unavoidable at all steps of the IFR cycle, and the resulting limitation of access contributes to making covert diversion of material from an IFR very difficult to accomplish and easy to detect. Material diverted either covertly or overtly from the IFR fuel cycle would be difficult (relative to material available by other means, such as LWR spent fuel) to process into weapons feedstock.

Effect of the Onsager coefficient and internal relaxation modes on spinodal decomposition in the high molecular isotopic blend polystyrene/deutero-polystyrene studied with small angle neutron scattering

The early state of spinodal decomposition was studied by small angle neutron scattering in the critical mixture of the isotopic blend deutero-polystyrene/polystyrene (d-PS/PS) of equal molecular volume of 1.42×106 cm3/mol in a temperature range 12 K≤‖Tc−T‖≤82 K. This process can be described by the relaxation between two static structure factors, S(Q) representing the equilibrium values of the system in the mixed state and at the temperature where phase separation occurs. The time evolution of the relaxation process is described by the dynamical structure factor, L(Q,t) which depends on the dynamic properties of the mixture. It will be shown that the static structure factor of a mixed system can also be determined in the unstable two-phase region during the early state of spinodal decomposition. Consistent values for the Flory–Huggins parameter were found in comparison with a lower molecular d-PS/PS sample and, therefore, a lower critical temperature which was even smaller than the phase separation temperatures of the present system. The observed time evolution of the fluctuation modes is nonexponential. Therefore, it was originally supposed that internal modes of the coil come into play. The analysis of the data with an ansatz by Akcasu, which takes internal modes into account showed, however, that the phase separation in the experimental range of wave number and time is dominated by the centre of mass diffusion as in the C–H–C case and the nonexponential behavior was attributed to a time dependent increase of the ‘‘range’’ of the Onsager coefficient. A range of the Onsager coefficient larger than the radius of gyration of a single coil is predicted in case of entangled polymers. However, no time dependence was predicted so far. The evaluated diffusion constants follow an Arrhenius behavior and are consistent with earlier studies. They show a D0∝N−2 scaling consistent with reptation. A further result is the observation of a second order peak in the structure factor already in the early times of spinodal decomposition. So far, this was only attributed to the late state of spinodal decomposition.