{"title":"Random Branching and Cross-linking of Polymer Chains, Analytical Functions for the Bivariate Molecular Weight Distributions","authors":"Rolf Bachmann, Marcel Klinger, Jan Meyer","doi":"10.1002/mats.202200062","DOIUrl":"10.1002/mats.202200062","url":null,"abstract":"<p>Cross-linking and branching of primary polymer molecules are investigated using the Galton–Watson (GW) process. Starting with the probability generating function (pgf) of the primary molecular weight distribution (MWD), analytical expressions are derived for the bivariate pgfs <i>g</i>(<i>n</i><sub>br</sub>, <i>s</i>) of branched polymers which depend also on the number of branch points <i>n</i><sub>br</sub>. The bivariate MWDs <i>n</i>(<i>n</i><sub>br</sub>, <i>i</i>) (<i>i</i>: number of molecular units) are then derived as Taylor expansions in s. All three cases of random branching: X-shaped (cross-linking), T-shaped (only one end takes part in the branching process), and H-shaped (both ends can take part in the branching process) are treated. An extension of the formalism does not require the construction of the pgf and allows the direct use of the MWD of the primary chains. However, using pgfs allows to go past the gel point and to determine the MWD and content of the sol. Explicit expressions are given for special distributions: the mono modal, the most probable, the Schulz-Zimm, the Poisson, and the Catalan distribution for the cases of X-shaped and T-shaped branching.</p>","PeriodicalId":18157,"journal":{"name":"Macromolecular Theory and Simulations","volume":"32 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44506970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Polyimide/Silica Nanocomposites with Enhanced Tensile Strength: Size Effects and Covalently Bonded Interface","authors":"Yu Wang, Wenlong Yang, Jiaqi Lin, Xinmei Liu, Yuhang Zuo, Hongguo Sun, Ying Yang","doi":"10.1002/mats.202200066","DOIUrl":"10.1002/mats.202200066","url":null,"abstract":"<p>In this work, the tensile strength of polyimide/silica composites with the covalently bonded interface (bonded PI/SiO<sub>2</sub>) is investigated by molecular dynamic simulation. It is found that the nanofiller with smaller size can bring out a larger number of hydrogen bonds and interfacial non-bond energy in the composites, resulting in higher tensile strength. As the immobilization of the PI chains in the vicinity of SiO<sub>2</sub>, the covalently bonded interface is found to offer a greater reinforcing effect than the unbonded interface that is confirmed by the self-diffusion coefficient. The tensile strength of 9 wt.% bonded PI/SiO<sub>2</sub> composites is 11.34% higher than that of the unbounded composites. The tensile strength of PI/SiO<sub>2</sub> composites is enhanced with the increase of SiO<sub>2</sub> concentration up to critical mass percent (<i>X<sub>c</sub></i>), beyond which it will be decreased. To quantitatively predict <i>X<sub>c</sub></i> of PI/SiO<sub>2</sub> composites, an empirical equation based on the non-bond energy of the composites is proposed. The empirical equation showed that the <i>X<sub>c</sub></i> of PI/SiO<sub>2</sub> composites ranged from 8.03 to 10.36 wt.%, which is consistent with experimental values. These results provided the understanding of size-dependent covalently bonded interface structure, which would be beneficial to the design of nanocomposites with excellent mechanical performances.</p>","PeriodicalId":18157,"journal":{"name":"Macromolecular Theory and Simulations","volume":"32 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45908224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Processing Properties and Thermal Stability of Poly(vinyl chloride-co-vinyl acetate) by Experiments and Molecular Dynamics Simulations","authors":"Runyue Li, Daolei Lin, Shiqin Xu, Xingzheng Chen, Guofeng Tian, Dezhen Wu","doi":"10.1002/mats.202200054","DOIUrl":"https://doi.org/10.1002/mats.202200054","url":null,"abstract":"<p>The effects of copolymerized monomer vinyl acetate (VAc) on processing properties and thermal stability of poly(vinyl chloride-co-vinyl acetate) (PVCA) are investigated via experiment and molecular dynamics simulation. Experimental results showed that PVCA with higher VAc content has larger loss tangent (tan<i>δ</i>), lower complex viscosity (<i>η</i>*), and glass transition temperature (Tg), which improved the processing properties of PVCA. A series of PVCA models are constructed to study the microstructure on the processing properties of PVCA, and the results showed the PVCA with higher VAc content exhibits larger molecular chain mobility and free volume fraction (FFV), smaller intermolecular interactions, and the mean square end-to-end distance (<Ree<sup>2</sup>>). Furthermore, the IR spectra of gas products indicated that thermal degradation of PVCA mainly generated hydrogen chloride (HCl), carboxylic acid, and aliphatic hydrocarbons between 200 and 500 °C, and the removal of HCl and carboxylic acid is almost simultaneous. The degradation models of PVCA chains demonstrated the C<span></span>Cl bond in vinyl chloride (VC) and C<span></span>O bond in VAc have similar thermal stability, which corresponded to the experimental results. In a word, the work provides a promising technique to study the structure and property of PVCA at molecular dynamic level.</p>","PeriodicalId":18157,"journal":{"name":"Macromolecular Theory and Simulations","volume":"32 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50154334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Copolymerization Reactivity Ratio Inference: Determining Confidence Contours in Parameter Space via a Bayesian Hierarchical Approach","authors":"Robert Reischke","doi":"10.1002/mats.202200063","DOIUrl":"10.1002/mats.202200063","url":null,"abstract":"<p>Confidence contours in parameter space are a helpful tool to compare and classify determined estimators. For more intricate parameter estimations of nonlinear nature or complex error structures, the procedure of determining confidence contours is a statistically complex task. For polymer chemists, such particular cases are encountered in determination of reactivity ratios in copolymerization. Hereby, determination of reactivity ratios in copolymerization requires nonlinear parameter estimation. Additionally, data may possess (possibly correlated) errors in both dependent and independent variables. A common approach for such nonlinear estimations is the error-in-variables model yielding statistically unbiased estimators. Regarding reactivity ratios, to date published procedures neglect the non-Gaussian structure of the error estimates that is a consequence of the nonlinearity of the model. In this publication, this issue is addressed by employing a Bayesian hierarchical model, which correctly propagates the errors of all variables. The statistical procedure is discussed in chemist friendly language to encourage confident usage of the tool. The approach is based on a <span>Python</span> program requiring minimal installation effort. A detailed manual of the code is included in the appendix of this work, in an effort to make this procedure available to all interested polymer chemists.</p>","PeriodicalId":18157,"journal":{"name":"Macromolecular Theory and Simulations","volume":"32 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mats.202200063","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47639267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Masthead: Macromol. Theory Simul. 6/2022","authors":"","doi":"10.1002/mats.202270012","DOIUrl":"https://doi.org/10.1002/mats.202270012","url":null,"abstract":"","PeriodicalId":18157,"journal":{"name":"Macromolecular Theory and Simulations","volume":"31 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mats.202270012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137537529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Effects of Primary Structure of Reactive Polymers on Network Structure and Mechanical Properties of Gels","authors":"Tsutomu Furuya, Tsuyoshi Koga","doi":"10.1002/mats.202270011","DOIUrl":"https://doi.org/10.1002/mats.202270011","url":null,"abstract":"<p><b>Front Cover</b>: The effects of the primary structure of reactive polymers on the structure and mechanical properties of gels are studied by a molecular dynamics simulation. The figure illustrates the improvement of structure uniformity by changing the arrangement of functional groups from a random one (top) to a periodic one (bottom), where red surfaces show low crosslinking density regions. This is reported by Tsutomu Furuya and Tsuyoshi Koga in article number 2200044.\u0000\u0000 <figure>\u0000 <div><picture>\u0000 <source></source></picture><p></p>\u0000 </div>\u0000 </figure></p>","PeriodicalId":18157,"journal":{"name":"Macromolecular Theory and Simulations","volume":"31 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mats.202270011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137537530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Atomistic Modeling of Mechanical Properties and Creep Behavior of Graphene Oxide Reinforced Natural Rubber Composites","authors":"Aviral Srivastava, Sumit Sharma, Pramod Rakt Patel","doi":"10.1002/mats.202200053","DOIUrl":"https://doi.org/10.1002/mats.202200053","url":null,"abstract":"<p>In the realm of polymer composites, the research of nanoparticles has risen in prominence. Graphene oxide (GO) is one of the best nanofillers in natural rubber (NR). In this work, GO nanosheets are utilized as reinforcement in an NR composite to anticipate mechanical characteristics. The researchers project the effect of GO sheets in NR with varied volume percentages and defective GO sheet reinforcement in NR composites. When the volume percentage of GO sheet in the NR nanocomposite is 4.6% and 7.2%, respectively, the value of Young's modulus rose by 68.8% and 166.2%. GO/NR with a 7.2% volume fraction has the highest ultimate tensile strength as compared with lower volume fractions of GO/NR nanocomposites. An increase of 63.49% in ultimate tensile strength in GO/NR nanocomposites (7.2% vol fraction) is seen as compared with pristine NR. Creep characteristics of NR nanocomposites are also investigated. The results reveal that the addition of GO sheets considerably increases the creep resistance strength of NR nanocomposites. The zone of secondary creep grows narrower as the continuous stress level increases.</p>","PeriodicalId":18157,"journal":{"name":"Macromolecular Theory and Simulations","volume":"32 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50136787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Molecular Dynamics Simulation for Separation Performance of PDMS/Fluorosilane Membrane with Different Mass Ratios in Acetone–Water Mixture","authors":"Yunrui Lan, Weijin Song, Jincheng Wang","doi":"10.1002/mats.202200057","DOIUrl":"10.1002/mats.202200057","url":null,"abstract":"<p>Polydimethylsiloxane (PDMS) membrane in suitable-fluorinated level have excellent pervaporation performance as well as antibiological contamination performance. The pervaporation membranes with different PDMS/fluorosilane mass ratios, the adsorption and dissolution behaviors of acetone molecules on the membrane surface, as well as the diffusion and permeation behaviors in the membranes are studied by all-atom molecular dynamics simulation (AAMDS). The results show that when the mass ratio of PDMS/fluorosilane is 100/20, the surface solubility of acetone is 11.711 (J cm<sup>−3</sup>)<sup>0.5</sup>, and the interfacial interaction is −16897.0415 kcal mol<sup>−1</sup>, both of which are the highest. The results of wide-angle X-ray diffraction (WAXD) showed that there are amorphous regions in the membranes suitable for acetone penetration. The maximum chain spacing of the PDMS/fluorosilane(100/20)_membranes is 10.8482 Å, and the free volume fraction (FFV) is 3.03%, both of which are the largest. The change rate of long-term mean square displacement (MSD) in PDMS/fluorosilane(100/20)_Membrane with time is 0.45269. The Young's modulus <i>E</i>, shear modulus <i>G</i>, volume modulus <i>K</i>, and Poisson's ratio <i>ν</i> of PDMS/fluorosilane(100/20)_Membrane are 0.3249, 0.4061, 0.0492 GPa and -0.5999, respectively. The elasticity of the membrane enhances the diffusion behavior of acetone molecules, and the self-diffusion coefficient of acetone in the membrane is 0.07545 Å<sup>2</sup> ps<sup>−1</sup>.</p>","PeriodicalId":18157,"journal":{"name":"Macromolecular Theory and Simulations","volume":"32 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44395789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Linear Relationship between Mean-Square Radius of Gyration and Graph Diameter, and Its Application to Network Polymers","authors":"Hidetaka Tobita","doi":"10.1002/mats.202200055","DOIUrl":"10.1002/mats.202200055","url":null,"abstract":"<p>Mean-square radius of gyration <i>Rg</i><sup>2</sup> and the graph diameter <i>D</i> of the random crosslinked network polymers are investigated to find a linear relationship, <i>Rg</i><sup>2</sup> = <i>a D</i>. The proportionality coefficient, <i>a</i> is dominated by the cycle (circuit) rank, or the number of intramolecular crosslinks <i>k</i><sub>c</sub>, and a convenient equation is proposed for the relationship between <i>a</i> and <i>k</i><sub>c</sub>. This relationship makes it possible to estimate <i>Rg</i><sup>2</sup> based on <i>D</i> and <i>k</i><sub>c</sub>, which can reduce the required computational time to determine the <i>Rg</i><sup>2</sup>-values greatly. This new method is applied to find that the contraction factor <i>g</i> decreases with <i>k</i><sub>c</sub>, and the differences in the primary chain length distribution that constitute the network polymers vanish for large <i>k</i><sub>c</sub>-values.</p>","PeriodicalId":18157,"journal":{"name":"Macromolecular Theory and Simulations","volume":"32 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48715660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Qi He, Zhao-Dong Xu, Yeshou Xu, Ying-Qing Guo, Xing-Huai Huang, Yao-Rong Dong, Abid Ali Shah
{"title":"Mechanical and Damping Properties Analyses of Small Molecular Modifiers/Nitrile-Butadiene Rubber Composite: Molecular Dynamics Simulation","authors":"Qi He, Zhao-Dong Xu, Yeshou Xu, Ying-Qing Guo, Xing-Huai Huang, Yao-Rong Dong, Abid Ali Shah","doi":"10.1002/mats.202200051","DOIUrl":"10.1002/mats.202200051","url":null,"abstract":"<p>Nitrile-butadiene rubber (NBR) has been wildly applied in vibration control technology, it is usually mixed with organic small molecular modifiers and well vulcanized, which can greatly enhance the mechanical and damping properties of the material. This work aims to design the optimum blending ratio of hindered phenol A/B/NBR composite with the best damping property by means of molecular dynamics (MD) simulation, and investigate the mechanical performance from the molecular level. The shear deformation simulation is conducted on pure NBR models to study the impact of rubber crosslink degree (CD) on elasticity and plasticity of NBR. To research the damping mechanism of the material, detailed analyses of the micro molecular structure and reciprocating shear simulation are carried out on NBR composite models with different hindered phenol A/B ratio. The simulation results indicate a strong positive correlation between intermolecular H-bonds and loss factor <i>η</i>, and the NBR composite with hindered phenol A/B per hundred rubber (phr) 30/30 shows the best damping performance.</p>","PeriodicalId":18157,"journal":{"name":"Macromolecular Theory and Simulations","volume":"32 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46761218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}