Modeling mass transport in dense polymer membranes: cooperative synergy among multiple scale approaches

The modeling description of basic transport phenomena of either liquid, gas or vapor molecules in dense polymeric membranes is of tremendous impact for the separation industry, which relies on solid models for the design of optimal process conditions, for the selection of the most suitable membrane materials as well as for the development of novel ones. Such models need to deal with several physical aspects and phenomena, spanning over broad time and length scales, thus requiring multiple approaches. The solid frameworks now available mainly rely on the solution–diffusion theory, in which equation of state models and free volume theories are applied for the description of thermodynamic and kinetic properties, to be coupled in appropriate transport schemes

How to describe and predict plasticization in glassy polymeric membranes for gas separations

In glassy polymeric membranes, gas permeability shows different trends as upstream pressure increases, including the monotonous decline, a monotonous increase, as well as an initial decline followed by a subsequent increase after a minimum permeability value is reached. The minimum value, whenever present, occurs at a pressure conventionally indicated as the plasticization pressure. It is currently accepted that permeability behavior can be conveniently well described by a transport model only below plasticization pressure, while above that value the onset of additional phenomena at higher pressures are responsible of the observed increase in permeability and decrease in selectivity. On the other hand, the plasticization phenomenon has not been further inspected thus far, in terms of material property variations. With the aim to reach to a deeper understanding of the phenomenon, we have experimentally inspected the behavior of Matrimid polyimide membranes, by analyzing both transport and mechanical properties. The permeability behavior and the “plasticization” effects induced by CO2 have been studied by increasing the upstream pressure at different fixed values of downstream pressure. The mechanical properties studied include elastic modulus and viscoelastic response of samples saturated at different CO2 pressures up to and above plasticization pressure. The trends obtained are rather interesting and actually not fully in line with what expected based on the current qualitative interpretation. We also show that the observed gas permeability behavior can be described by considering only a solution-diffusion model in which the penetrant mobility varies with its concentration in the polymer matrix through an exponential law, with two adjustable parameters only. Diffusivity is thus taken as the product of molecular mobility and a thermodynamic factor, calculated by using the NELF model for thermodynamic properties of the glassy phase. It is observed that by fitting the only two adjustable parameters to the initial branch of the permeability isotherm, the above solubility diffusivity model allows the prediction of the plasticization pressure, at all values of downstream pressures used, without introducing any additional physical phenomenon. The agreement observed between model calculations and experimental data of CO2 permeability in Matrimid, as well as in various glassy polymers, is very satisfactory. That allows us to offer a deeper insight on the so-called plasticization phenomenon. The analysis of the permeability and the solubility isotherms, and the evaluation of concentration and swelling profiles in the membrane, show that in some cases the plasticization phenomena take place after part of the membrane has turned into rubbery phase. However, in other relevant cases as in Matrimid, the minimum in permeability is observed when the entire membrane is still glassy (and characterized by mechanical behavior comparable to the pure “dry” material), but with a polymer swelling sufficient for a permeability increase. Finally, it is observed that all parameters used have a defined independent physical meaning, which might lead to the development of general correlations with both polymer and penetrant properties, based on which permeability predictions can be obtained

Measurement of the CKM angle γ from a combination of B±→Dh± analyses

A combination of three LHCb measurements of the CKM angle γ is presented. The decays B±→D K± and B±→Dπ± are used, where D denotes an admixture of D0 and D0 mesons, decaying into K+K−, π+π−, K±π∓, K±π∓π±π∓, K0Sπ+π−, or K0S K+K− final states. All measurements use a dataset corresponding to 1.0 fb−1 of integrated luminosity. Combining results from B±→D K± decays alone a best-fit value of γ =72.0◦ is found, and confidence intervals are set γ ∈ [56.4,86.7]◦ at 68% CL, γ ∈ [42.6,99.6]◦ at 95% CL. The best-fit value of γ found from a combination of results from B±→Dπ± decays alone, is γ =18.9◦, and the confidence intervals γ ∈ [7.4,99.2]◦ ∪ [167.9,176.4]◦ at 68% CL are set, without constraint at 95% CL. The combination of results from B± → D K± and B± → Dπ± decays gives a best-fit value of γ =72.6◦ and the confidence intervals γ ∈ [55.4,82.3]◦ at 68% CL, γ ∈ [40.2,92.7]◦ at 95% CL are set. All values are expressed modulo 180◦, and are obtained taking into account the effect of D0–D0 mixing

Les droits disciplinaires des fonctions publiques : « unification », « harmonisation » ou « distanciation ». A propos de la loi du 26 avril 2016 relative à la déontologie et aux droits et obligations des fonctionnaires

The production of tt‾ , W+bb‾ and W+cc‾ is studied in the forward region of proton–proton collisions collected at a centre-of-mass energy of 8 TeV by the LHCb experiment, corresponding to an integrated luminosity of 1.98±0.02 fb−1 . The W bosons are reconstructed in the decays W→ℓν , where ℓ denotes muon or electron, while the b and c quarks are reconstructed as jets. All measured cross-sections are in agreement with next-to-leading-order Standard Model predictions.The production of $t\overline{t}$, $W+b\overline{b}$ and $W+c\overline{c}$ is studied in the forward region of proton-proton collisions collected at a centre-of-mass energy of 8 TeV by the LHCb experiment, corresponding to an integrated luminosity of 1.98 $\pm$ 0.02 \mbox{fb}^{-1}. The $W$ bosons are reconstructed in the decays $W\rightarrow\ell\nu$, where $\ell$ denotes muon or electron, while the $b$ and $c$ quarks are reconstructed as jets. All measured cross-sections are in agreement with next-to-leading-order Standard Model predictions

Measurement of the J/ψ pair production cross-section in pp collisions at s=13 \sqrt{s}=13 TeV

The production cross-section of J/ψ pairs is measured using a data sample of pp collisions collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=13$ TeV, corresponding to an integrated luminosity of 279 ±11 pb$^{−1}$. The measurement is performed for J/ψ mesons with a transverse momentum of less than 10 GeV/c in the rapidity range 2.0 < y < 4.5. The production cross-section is measured to be 15.2 ± 1.0 ± 0.9 nb. The first uncertainty is statistical, and the second is systematic. The differential cross-sections as functions of several kinematic variables of the J/ψ pair are measured and compared to theoretical predictions.The production cross-section of $J/\psi$ pairs is measured using a data sample of $pp$ collisions collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s} = 13 \,{\mathrm{TeV}}$, corresponding to an integrated luminosity of $279 \pm 11 \,{\mathrm{pb^{-1}}}$. The measurement is performed for $J/\psi$ mesons with a transverse momentum of less than $10 \,{\mathrm{GeV}}/c$ in the rapidity range $2.0<y<4.5$. The production cross-section is measured to be $15.2 \pm 1.0 \pm 0.9 \,{\mathrm{nb}}$. The first uncertainty is statistical, and the second is systematic. The differential cross-sections as functions of several kinematic variables of the $J/\psi$ pair are measured and compared to theoretical predictions

Measurement of forward W→eνW\to e\nu production in pppp collisions at s=8 \sqrt{s}=8\,TeV

A measurement of the cross-section for $W \to e\nu$ production in $pp$ collisions is presented using data corresponding to an integrated luminosity of $2\,$fb$^{-1}$ collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=8\,$TeV. The electrons are required to have more than $20\,$GeV of transverse momentum and to lie between 2.00 and 4.25 in pseudorapidity. The inclusive $W$ production cross-sections, where the $W$ decays to $e\nu$, are measured to be \begin{align*} \begin{split} \sigma_{W^{+} \to e^{+}\nu_{e}}&=1124.4\pm 2.1\pm 21.5\pm 11.2\pm 13.0\,\mathrm{pb},\\ \sigma_{W^{-} \to e^{-}\bar{\nu}_{e}}&=\,\,\,809.0\pm 1.9\pm 18.1\pm\,\,\,7.0\pm \phantom{0}9.4\,\mathrm{pb}, \end{split} \end{align*} where the first uncertainties are statistical, the second are systematic, the third are due to the knowledge of the LHC beam energy and the fourth are due to the luminosity determination. Differential cross-sections as a function of the electron pseudorapidity are measured. The $W^{+}/W^{-}$ cross-section ratio and production charge asymmetry are also reported. Results are compared with theoretical predictions at next-to-next-to-leading order in perturbative quantum chromodynamics. Finally, in a precise test of lepton universality, the ratio of $W$ boson branching fractions is determined to be \begin{align*} \begin{split} \mathcal{B}(W \to e\nu)/\mathcal{B}(W \to \mu\nu)=1.020\pm 0.002\pm 0.019, \end{split} \end{align*} where the first uncertainty is statistical and the second is systematic.A measurement of the cross-section for $W \to e\nu$ production in $pp$ collisions is presented using data corresponding to an integrated luminosity of $2\,$fb$^{-1}$ collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=8\,$TeV. The electrons are required to have more than $20\,$GeV of transverse momentum and to lie between 2.00 and 4.25 in pseudorapidity. The inclusive $W$ production cross-sections, where the $W$ decays to $e\nu$, are measured to be \begin{equation*} \sigma_{W^{+} \to e^{+}\nu_{e}}=1124.4\pm 2.1\pm 21.5\pm 11.2\pm 13.0\,\mathrm{pb}, \end{equation*} \begin{equation*} \sigma_{W^{-} \to e^{-}\bar{\nu}_{e}}=\,\,\,809.0\pm 1.9\pm 18.1\pm\,\,\,7.0\pm \phantom{0}9.4\,\mathrm{pb}, \end{equation*} where the first uncertainties are statistical, the second are systematic, the third are due to the knowledge of the LHC beam energy and the fourth are due to the luminosity determination. Differential cross-sections as a function of the electron pseudorapidity are measured. The $W^{+}/W^{-}$ cross-section ratio and production charge asymmetry are also reported. Results are compared with theoretical predictions at next-to-next-to-leading order in perturbative quantum chromodynamics. Finally, in a precise test of lepton universality, the ratio of $W$ boson branching fractions is determined to be \begin{equation*} \mathcal{B}(W \to e\nu)/\mathcal{B}(W \to \mu\nu)=1.020\pm 0.002\pm 0.019, \end{equation*} where the first uncertainty is statistical and the second is systematic.A measurement of the cross-section for W → eν production in pp collisions is presented using data corresponding to an integrated luminosity of 2 fb$^{−1}$ collected by the LHCb experiment at a centre-of-mass energy of $\sqrt{s}=8$ TeV. The electrons are required to have more than 20 GeV of transverse momentum and to lie between 2.00 and 4.25 in pseudorapidity. The inclusive W production cross-sections, where the W decays to eν, are measured to be ${\sigma}_{W^{+}\to {e}^{+}{\nu}_e}=1124.4\pm 2.1\pm 21.5\pm 11.2\pm 13.0\kern0.5em \mathrm{p}\mathrm{b},$ ${\sigma}_{W^{-}\to {e}^{-}{\overline{\nu}}_e}=809.0\pm 1.9\pm 18.1\pm \kern0.5em 7.0\pm \kern0.5em 9.4\,\mathrm{p}\mathrm{b},$ where the first uncertainties are statistical, the second are systematic, the third are due to the knowledge of the LHC beam energy and the fourth are due to the luminosity determination

Permeability and solubility of carbon dioxide in different glassy polymer systems with and without plasticization

The description of permeability and solubility of CO 2 in different complex polymer matrices in the glassy state is analyzed by considering the diffusion coef\ufb01cient as the product of a kinetic factor, mobility, and a thermodynamic factor associated to the concentration dependence of the chemical potential of the diffusing species, according to what recently presented for different pure polymers [Minelli and Sarti, J. Membr. Sci. 435 (2013) 176\u2013185]. The thermodynamic factor is calculated in a predictive way by using the nonequilibrium lattice \ufb02uid model (NELF) or is obtained directly from experimental solubility isotherms, when pure component parameters for the NELF model are not available. The mobility factor is considered to depend exponentially from penetrant concentration, following the usual trend commonly found experimentally, and its expression contains only two adjustable parameters. The permeability model is used to describe steady state permeation of CO 2 in a series of complex glassy phases, formed by polysulfone (PSf) and polyphenylene oxide (PPO) with different plasticizers, glassy polymer blends, glassy random copolymers and crosslinked polyimides. The analysis shows that in all the cases examined, the model used is able to describe the experimental trends in a simple and effective way, accounting for all the different behaviors observed, in which permeability is either decreasing or increasing with upstream pressure and even when permeability is non-monotonous and presents a minimum value due to the so-called plasticization effect. A general correlation is also found for both model parameters: the in\ufb01nite dilution mobility correlates well with the reciprocal fractional free volume, according to the FFV theory, while the plasticization factor is associated to the swelling coef\ufb01cient of the polymer matrix

Thermodynamic basis for vapor permeability in Ethyl Cellulose

The vapor permeability in glassy Ethyl Cellulose may show rather different behaviors versus upstream pressure, depending on the penetrant considered, including a monotonous decrease as well as a monotonous increase with increasing pressure. Such a spectrum of behaviors, experimentally well known, is still needing a unifying interpretation and a mathematical description, which we are now proposing in the present work. For each solute, at all different temperatures, the permeability in Ethyl Cellulose is described by means of a simple model with a solid thermodynamic basis. The thermo- dynamic behavior of the polymer/penetrant mixture is given by the nonequilibrium lattice \ufb02uid model (NELF), which provides the vapor solubility at different values of T and p. The penetrant permeability is described considering the diffusion coef\ufb01cient as the product of a purely kinetic factor, the mobility, and a thermodynamic factor related to the dependence of the chemical potential of the diffusing species on its concentration in the polymer. The thermodynamic factor is readily calculated from the NELF model, while the mobility factor is endowed with an exponential dependence on penetrant concentration, as often suggested by experimental data; its expression utilizes only two adjustable parameters: the in\ufb01nite dilution mobility coef\ufb01cient and the plasticization factor. The analysis indicates that this simple mathematical theory is able to describe accurately all the different behaviors observed experimentally, for all the penetrants inspected, at all temperatures. In addition, the two model parameters for mobility follow clear and simple correlations: the in\ufb01nite dilution mobility coef\ufb01cient scales with the penetrant size, and the plasticization factor is related to the ability of the penetrant to swell Ethyl Cellulose, as quanti\ufb01ed by the volume swelling coef\ufb01cient, which is available from independent information

Permeability and diffusivity of CO2 in glassy polymers with and without plasticization

The description of permeability and diffusivity in glassy polymers has been revisited by considering the diffusion coef\ufb01cient as the product of a kinetic factor, mobility, and a thermodynamic factor associated to the concentration dependence of the chemical potential of the diffusing species. The latter term does not contain any adjustable parameter since it is obtained directly from solubility isotherm data or can be even calculated in a predictive way by using well established predictive procedures as the Non Equilibrium Thermodynamics for Glassy Polymers (NET-GP) models. The mobility factor considered is endowed with an exponential dependence on penetrant concentration, following the usual trend commonly found experimentally, thus containing only two adjustable parameters. The resulting expressions for diffusivity and for permeability describe rather carefully the pressure dependence observed in glassy polymers, both in steady state permeation and in transient mass uptake, in all the cases inspected, even in the presence of the so called plasticization effects

Gas transport in glassy polymers: Prediction of diffusional time lag

The transport of gases in glassy polymeric membranes has been analyzed by means of a fundamental approach based on the nonequilibrium thermodynamic model for glassy polymers (NET-GP) that considers the penetrant chemical potential gradient as the actual driving force of the diffusional process. The diffusivity of a penetrant is thus described as the product of a purely kinetic quantity, the penetrant mobility, and a thermodynamic factor, accounting for the chemical potential dependence on its concentration in the polymer. The NET-GP approach, and the nonequilibrium lattice fluid (NELF) model in particular, describes the thermodynamic behavior of penetrant/polymer mixtures in the glassy state, at each pressure or composition. Moreover, the mobility is considered to follow a simple exponential dependence on penetrant concentration, as typically observed experimentally, using only two adjustable parameters, the infinite dilution penetrant mobility L10and the plasticization factor \uce\ub2, both determined from the analysis of the dependence of steady state permeability on upstream pressure. The available literature data of diffusional time lag as a function of penetrant upstream pressure has been reviewed and compared with model predictions, obtained after the values of the two model parameters (L10and \uce\ub2), have been conveniently determined from steady state permeability data. The model is shown to be able to describe very accurately the experimental time lag behaviors for all penetrant/polymer pairs inspected, including those presenting an increasing permeability with increasing upstream pressure. The model is thus more appropriate than the one based on Dual Mode Sorption, which usually provides an unsatisfactory description of time lag and required an ad hoc modification