Correction: Dobrovskiy et al. The Transport Properties of Semi-Crystalline Polyetherimide BPDA-P3 in Amorphous and Ordered States: Computer Simulations. Membranes 2022, 12, 856.

The authors wish to make a change to the published paper [...].

Size matters: asphaltenes with enlarged aromatic cores promote heat transfer in organic phase-change materials.

Recent experiments and atomistic computer simulations have shown that asphaltene byproducts of oil refineries can serve as thermal conductivity enhancers for organic phase-change materials such as paraffin and therefore have the potential to improve the performance of paraffin-based heat storage devices. In this work, we explore how the size of the polycyclic aromatic cores of asphaltenes affects the properties of paraffin-asphaltene systems by means of atomistic molecular dynamics simulations. We show that increasing the size of the asphaltene core from 7-8 aromatic rings to ∼20 rings drastically changes the aggregation behavior of asphaltenes. Instead of relatively small, compact aggregates formed by small-core asphaltene molecules, enlarged cores promote the formation of extended single-column structures stabilized in paraffin by asphaltene's aliphatic periphery. Chemical modification of the asphaltenes by removing the periphery leads to the formation of bundles of columns. In contrast to small-core molecules, asphaltenes with enlarged cores do not suppress paraffin crystallization even at high filler concentrations. Remarkably, asphaltenes with enlarged aromatic cores are able to increase the thermal conductivity of liquid paraffin to a greater extent compared to their small-core counterparts. This effect becomes even more pronounced for modified asphaltenes without the aliphatic side groups. Overall, our computational findings suggest that asphaltenes with enlarged aromatic cores can significantly improve the performance of heat storage devices based on organic phase change materials.

The Effect of Mechanical Elongation on the Thermal Conductivity of Amorphous and Semicrystalline Thermoplastic Polyimides: Atomistic Simulations.

Over the past few decades, the enhancement of polymer thermal conductivity has attracted considerable attention in the scientific community due to its potential for the development of new thermal interface materials (TIM) for both electronic and electrical devices. The mechanical elongation of polymers may be considered as an appropriate tool for the improvement of heat transport through polymers without the necessary addition of nanofillers. Polyimides (PIs) in particular have some of the best thermal, dielectric, and mechanical properties, as well as radiation and chemical resistance. They can therefore be used as polymer binders in TIM without compromising their dielectric properties. In the present study, the effects of uniaxial deformation on the thermal conductivity of thermoplastic PIs were examined for the first time using atomistic computer simulations. We believe that this approach will be important for the development of thermal interface materials based on thermoplastic PIs with improved thermal conductivity properties. Current research has focused on the analysis of three thermoplastic PIs: two semicrystalline, namely BPDA-P3 and R-BAPB; and one amorphous, ULTEMTM. To evaluate the impact of uniaxial deformation on the thermal conductivity, samples of these PIs were deformed up to 200% at a temperature of 600 K, slightly above the melting temperatures of BPDA-P3 and R-BAPB. The thermal conductivity coefficients of these PIs increased in the glassy state and above the glass transition point. Notably, some improvement in the thermal conductivity of the amorphous polyimide ULTEMTM was achieved. Our study demonstrates that the thermal conductivity coefficient is anisotropic in different directions with respect to the deformation axis and shows a significant increase in both semicrystalline and amorphous PIs in the direction parallel to the deformation. Both types of structural ordering (self-ordering of semicrystalline PI and mechanical elongation) led to the same significant increase in thermal conductivity coefficient.

Mesoscale computer modeling of asphaltene aggregation in liquid paraffin.

Asphaltenes represent a novel class of carbon nanofillers that are of potential interest for many applications, including polymer nanocomposites, solar cells, and domestic heat storage devices. In this work, we developed a realistic coarse-grained Martini model that was refined against the thermodynamic data extracted from atomistic simulations. This allowed us to explore the aggregation behavior of thousands of asphaltene molecules in liquid paraffin on a microsecond time scale. Our computational findings show that native asphaltenes with aliphatic side groups form small clusters that are uniformly distributed in paraffin. The chemical modification of asphaltenes via cutting off their aliphatic periphery changes their aggregation behavior: modified asphaltenes form extended stacks whose size increases with asphaltene concentration. At a certain large concentration (44 mol. %), the stacks of modified asphaltenes partly overlap, leading to the formation of large, disordered super-aggregates. Importantly, the size of such super-aggregates increases with the simulation box due to phase separation in the paraffin-asphaltene system. The mobility of native asphaltenes is systematically lower than that of their modified counterparts since the aliphatic side groups mix with paraffin chains, slowing down the diffusion of native asphaltenes. We also show that diffusion coefficients of asphaltenes are not very sensitive to the system size: enlarging the simulation box results in some increase in diffusion coefficients, with the effect being less pronounced at high asphaltene concentrations. Overall, our findings provide valuable insight into the aggregation behavior of asphaltenes on spatial and time scales that are normally beyond the scales accessible for atomistic simulations.

Cooling-Rate Computer Simulations for the Description of Crystallization of Organic Phase-Change Materials.

A molecular-level insight into phase transformations is in great demand for many molecular systems. It can be gained through computer simulations in which cooling is applied to a system at a constant rate. However, the impact of the cooling rate on the crystallization process is largely unknown. To this end, here we performed atomic-scale molecular dynamics simulations of organic phase-change materials (paraffins), in which the cooling rate was varied over four orders of magnitude. Our computational results clearly show that a certain threshold (1.2 × 1011 K/min) in the values of cooling rates exists. When cooling is slower than the threshold, the simulations qualitatively reproduce an experimentally observed abrupt change in the temperature dependence of the density, enthalpy, and thermal conductivity of paraffins upon crystallization. Beyond this threshold, when cooling is too fast, the paraffin's properties in simulations start to deviate considerably from experimental data: the faster the cooling, the larger part of the system is trapped in the supercooled liquid state. Thus, a proper choice of a cooling rate is of tremendous importance in computer simulations of organic phase-change materials, which are of great promise for use in domestic heat storage devices.

Machine Learning with Enormous "Synthetic" Data Sets: Predicting Glass Transition Temperature of Polyimides Using Graph Convolutional Neural Networks.

In the present work, we address the problem of utilizing machine learning (ML) methods to predict the thermal properties of polymers by establishing "structure-property" relationships. Having focused on a particular class of heterocyclic polymers, namely polyimides (PIs), we developed a graph convolutional neural network (GCNN), being one of the most promising tools for working with big data, to predict the PI glass transition temperature T g as an example of the fundamental property of polymers. To train the GCNN, we propose an original methodology based on using a "transfer learning" approach with an enormous "synthetic" data set for pretraining and a small experimental data set for its fine-tuning. The "synthetic" data set contains more than 6 million combinatorically generated repeating units of PIs and theoretical values of their T g values calculated using the well-established Askadskii's quantitative structure-property relationship (QSPR) computational scheme. Additionally, an experimental data set for 214 PIs was also collected from the literature for training, fine-tuning, and validation of the GCNN. Both "synthetic" and experimental data sets are included into a PolyAskInG database (Polymer Askadskii's Intelligent Gateway). By using the PolyAskInG database, we developed GCNN which allows estimation of T g of PI with a mean absolute error (MAE) of about 20 K, which is 1.5 times lower than in the case of Askadskii QSPR analysis (33 K). To prove the efficiency and usability of the proposed GCNN architecture and training methodology for predicting polymer properties, we also employed "transfer learning" to develop alternative GCNN pretrained on proxy-characteristics taken from the popular quantum-chemical QM9 database for small compounds and fine-tuned on an experimental T g values data set from PolyAskInG database. The obtained results indicate that pretraining of GCNN on the "synthetic" polymer data set provides MAE which is almost twice as low as that in the case of using the QM9 data set in the pretraining stage (∼41 K). Furthermore, we address the questions associated with the influence of the differences in the size of the experimental and "synthetic" data sets (so-called "reality gap" problem), as well as their chemical composition on the training quality. Our results state the overall priority of using polymer data sets for developing deep neural networks, and GCNN in particular, for efficient prediction of polymer properties. Moreover, our work opens up a challenge for the theoretically supported generation of large "synthetic" data sets of polymer properties for the training of the complex ML models. The proposed methodology is rather versatile and may be generalized for predicting other properties of different polymers and copolymers synthesized through the polycondensation reaction.

The Transport Properties of Semi-Crystalline Polyetherimide BPDA-P3 in Amorphous and Ordered States: Computer Simulations.

The effect of polymer chain ordering on the transport properties of the polymer membrane was examined for the semi-crystalline heterocyclic polyetherimide (PEI) BPDA-P3 based on 3,3',4,4'-biphenyltetracarboxylic dianhydride (BPDA) and diamine 1,4-bis [4-(4-aminophenoxy)phenoxy]benzene (P3). All-atom Molecular Dynamics (MD) simulations were used to investigate the gas diffusion process carried through the pores of a free volume several nanometers in size. The long-term (~30 µs) MD simulations of BPDA-P3 were performed at T = 600 K, close to the experimental value of the melting temperature (Tm ≈ 577 K). It was found during the simulations that the transition of the PEI from an amorphous state to an ordered one occurred. We determined a decrease in solubility for both the gases examined (CO2 and CH4), caused by the redistribution of free volume elements occurring during the structural ordering of the polymer chains in glassy state (Tg ≈ 481 K). By analyzing the diffusion coefficients in the ordered state, the presence of gas diffusion anisotropy was found. However, the averaged values of the diffusion coefficients did not differ from each other in the amorphous and ordered states. Thus, permeability in the observed system is primarily determined by gas solubility, rather than by gas diffusion.

Rheological and Mechanical Properties of Thermoplastic Crystallizable Polyimide-Based Nanocomposites Filled with Carbon Nanotubes: Computer Simulations and Experiments.

Recently, a strong structural ordering of thermoplastic semi-crystalline polyimides near single-walled carbon nanotubes (SWCNTs) was found that can enhance their mechanical properties. In this study, a comparative analysis of the results of microsecond-scale all-atom computer simulations and experimental measurements of thermoplastic semi-crystalline polyimide R-BAPB synthesized on the basis of dianhydride R (1,3-bis-(3',4-dicarboxyphenoxy) benzene) and diamine BAPB (4,4'-bis-(4″-aminophenoxy) biphenyl) near the SWCNTs on the rheological properties of nanocomposites was performed. We observe the viscosity increase in the SWCNT-filled R-BAPB in the melt state both in computer simulations and experiments. For the first time, it is proven by computer simulation that this viscosity change is related to the structural ordering of the R-BAPB in the vicinity of SWCNT but not to the formation of interchain linkage. Additionally, strong anisotropy of the rheological properties of the R-BAPB near the SWCNT surface was detected due to the polyimide chain orientation. The increase in the viscosity of the polymer in the viscous-flow state and an increase in the values of the mechanical characteristics (Young's modulus and yield peak) of the SWCNT-R-BAPB nanocomposites in the glassy state are stronger in the directions along the ordering of polymer chains close to the carbon nanofiller surface. Thus, the new experimental data obtained on the R-BAPB-based nanocomposites filled with SWCNT, being extensively compared with simulation results, confirm the idea of the influence of macromolecular ordering near the carbon nanotube on the mechanical characteristics of the composite material.

Branched versus linear lactide chains for cellulose nanoparticle modification: an atomistic molecular dynamics study.

We studied the structure of brushes consisting of branched oligolactide (OLA) chains grafted onto the surface of cellulose nanoparticles (CNPs) in polylactide (PLA) and compared the outcomes to the case of grafting linear OLA chains using atomistic molecular dynamics simulations. The systems were considered in a melt state. The branched model OLA chains comprised one branching point and three branches, while the linear OLA chains examined had a molecular weight similar to the branched chains. It was shown that free branches of the branched OLA chains tend to fold back toward the CNPs due to dipole-dipole interactions within the grafted layer, in contrast to the well-established behavior of the grafted uncharged branched chains. This result, however, is in qualitative agreement with the conformational behavior known for linear OLA chains. At the same time, no significant difference in the effectiveness of covering the filler surface with grafted branched or linear OLA chains was found. In terms of the expelling ability of the grafted chains and the interaction between PLA and CNP or OLA, the linear chains were broadly similar (sparse grafting) or better (intermediate or dense grafting) compared to the branched ones. Thus, the grafted lactide chains with a linear architecture, rather than their branched counterpart, may be preferable for the covalent modification of cellulose nanoparticles.

Correction: Toward realistic computer modeling of paraffin-based composite materials: critical assessment of atomic-scale models of paraffins.

[This corrects the article DOI: 10.1039/C9RA07325F.].

Toward Predictive Molecular Dynamics Simulations of Asphaltenes in Toluene and Heptane.

The conventional definition of asphaltenes is based on their solubility in toluene and their insolubility in heptane. We have utilized this definition to study the influence of partial charge parametrization on the aggregation behavior of asphaltenes using classical atomistic molecular dynamics simulations performed on the microsecond time scale. Under consideration here are toluene- and heptane-based systems with different partial charges parametrized using the general AMBER force field (GAFF). Systems with standard GAFF partial charges calculated by the AM1-BCC and HF/6-31G*(RESP) methods were simulated alongside systems without partial charges. The partial charges implemented differ in terms of the resulting electrical negativity of the asphaltene polyaromatic core, with the AM1-BCC method giving the greatest magnitude of the total core charge. Based on our analysis of the molecular relaxation and orientation, and on the aggregation behavior of asphaltenes in toluene and heptane, we proposed to use the partial charges obtained by the AM1-BCC method for the study of asphaltene aggregates. A good agreement with available experimental data was observed on the sizes of the aggregates, their fractal dimensions, and the solvent entrainment for the model asphaltenes in toluene and heptane. From the results obtained, we conclude that for a better predictive ability, simulation parameters must be carefully chosen, with particular attention paid to the partial charges owing to their influence on the electrical negativity of the asphaltene core and on the asphaltenes aggregation.

Toward realistic computer modeling of paraffin-based composite materials: critical assessment of atomic-scale models of paraffins.

Paraffin-based composites represent a promising class of materials with numerous practical applications such as e.g. heat storage. Computer modeling of these complex multicomponent systems requires a proper theoretical description of both the n-alkane matrix and the non-alkane filler molecules. The latter can be modeled with the use of a state-of-the-art general-purpose force field such as GAFF, CHARMM, OPLS-AA and GROMOS, while the paraffin matrix is traditionally described in the frame of relatively old, alkane-specific force fields (TraPPE, NERD, and PYS). In this paper we link these two types of models and evaluate the performance of several general-purpose force fields in computer modeling of paraffin by their systematic comparison with earlier alkane-specific models as well as with experimental data. To this end, we have performed molecular dynamics simulations of n-eicosane bulk samples with the use of 10 different force fields: TraPPE, NERD, PYS, OPLS-UA, GROMOS, GAFF, GAFF2, OPLS-AA, L-OPLS-AA, and CHARMM36. For each force field we calculated several thermal, structural and dynamic characteristics of n-eicosane over a wide temperature range. Overall, our findings show that the general-purpose force fields such as CHARMM36, L-OPLS-AA and GAFF/GAFF2 are able to provide a realistic description of n-eicosane samples. While alkane-specific models outperform most general-purpose force fields as far as the temperature dependence of mass density, the coefficient of volumetric thermal expansion in the liquid state, and the crystallization temperature are concerned, L-OPLS-AA, CHARMM36 and GAFF2 force fields provide a better match with experiment for the shear viscosity and the diffusion coefficient in melt. Furthermore, we show that most general-purpose force fields are able to reproduce qualitatively the experimental triclinic crystal structure of n-eicosane at low temperatures.

Structural Ordering in SWCNT-Polyimide Nanocomposites and Its Influence on Their Mechanical Properties.

Using fully-atomistic models, tens-microseconds-long molecular-dynamic modelling was carried out for the first time to simulate the kinetics of polyimides ordering induced by the presence of single-walled carbon nanotube (SWCNT) nanofillers. Three polyimides (PI) were considered with different dianhydride fragments, namely 3,3',4,4'-biphenyltetracarboxylic dianhydride (BPDA), 2,3',3,4'-biphenyltetracarboxylic dianhydride (aBPDA), and 3,3',4,4'-oxidiphthalic dianhydride (ODPA) and same diamine 1,4-bis[4-(4-aminophenoxy)phenoxy]benzene (diamine P3). Both crystallizable PI BPDA-P3 and two amorphous polyimides ODPA-P3 and aBPDA-P3 reinforced by SWCNTs were studied. The structural properties of the nanocomposites at temperature close to the bulk polymer melting point were studied. The mechanical properties were determined for the nanocomposites cooled down to the glassy state. It was found that the SWCNT nanofiller initiates' structural ordering not only in the crystallizable BPDA-P3 but also in the amorphous ODPA-P3 samples were in agreement with previously obtained experimental results. Two stages of the structural ordering were detected in the presence of SWCNTs, namely the orientation of the planar moieties followed by the elongation of whole polymer chains. The first type of local ordering was observed on the microsecond time scale and did not lead to the change of the mechanical properties of a polymer binder in considered nanocomposites. At the end of the second stage, both BPDA-P3 and ODPA-P3 PI chains extended completely along the SWCNT surface, which in turn led to enhanced mechanical characteristics in their glassy state.

Atomistic Molecular Dynamics Simulations of the Initial Crystallization Stage in an SWCNT-Polyetherimide Nanocomposite.

Crystallization of all-aromatic heterocyclic polymers typically results in an improvement of their thermo-mechanical properties. Nucleation agents may be used to promote crystallization, and it is well known that the incorporation of nanoparticles, and in particular carbon-based nanofillers, may induce or accelerate crystallization through nucleation. The present study addresses the structural properties of polyetherimide-based nanocomposites and the initial stages of polyetherimide crystallization as a result of single-walled carbon nanotube (SWCNT) incorporation. We selected two amorphous thermoplastic polyetherimides ODPA-P3 and aBPDA-P3 based on 3,3',4,4'-oxydiphthalic dianhydride (ODPA), 2,3',3,4'-biphenyltetracarboxylic dianhydride (aBPDA) and diamine 1,4-bis[4-(4-aminophenoxy)phenoxy]benzene (P3) and simulated the onset of crystallization in the presence of SWCNTs using atomistic molecular dynamics. For ODPA-P3, we found that the planar phthalimide and phenylene moieties show pronounced ordering near the CNT (carbon nanotube) surface, which can be regarded as the initial stage of crystallization. We will discuss two possible mechanisms for ODPA-P3 crystallization in the presence of SWCNTs: the spatial confinement caused by the CNTs and π⁻π interactions at the CNT-polymer matrix interface. Based on our simulation results, we propose that ODPA-P3 crystallization is most likely initiated by favorable π⁻π interactions between the carbon nanofiller surface and the planar ODPA-P3 phthalimide and phenylene moieties.

Thermal properties of bulk polyimides: insights from computer modeling versus experiment.

Due to the great importance for many industrial applications it is crucial from the point of view of theoretical description to reproduce thermal properties of thermoplastic polyimides as accurate as possible in order to establish "chemical structure-physical properties" relationships of new materials. In this paper we employ differential scanning calorimetry, dilatometry, and atomistic molecular dynamics (MD) simulations to explore whether the state-of-the-art computer modeling can serve as a precise tool for probing thermal properties of polyimides with highly polar groups. For this purpose the polyimide R-BAPS based on dianhydride 1,3-bis(3',4-dicarboxyphenoxy)benzene (dianhydride R) and diamine 4,4'-bis(4''-aminophenoxy)biphenyl sulphone) (diamine BAPS) was synthesized and extensively studied. Overall, our findings show that the widely used glass-transition temperature Tg evaluated from MD simulations should be employed with great caution for verification of the polyimide computational models against experimental data: in addition to the well-known impact of the cooling rate on the glass-transition temperature, correct definition of Tg requires cooling that starts from very high temperatures (no less than 800 K for considered polyimides) and accurate evaluation of the appropriate cooling rate, otherwise the errors in the measured values of Tg become undefined. In contrast to the glass-transition temperature, the volumetric coefficient of thermal expansion (CTE) does not depend on the cooling rate in the low-temperature domain (T < Tg) so that comparison of computational and experimental values of CTE provides a much safer way for proper validation of the theoretical model when electrostatic interactions are taken into account explicitly. Remarkably, this conclusion is most likely of generic nature: we show that it also holds for the commercial polyimide EXTEM, another polyimide with a similar chemical structure.