Relaxation Spectra Research Articles

Quantitative measurement of mammographic density in breast-tissue explants using portable NMR: Precision and accuracy.

Single-sided portable NMR (pNMR) has previously been demonstrated to be suitable for quantification of mammographic density (MD) in excised breast tissue samples. Here we investigate the precision and accuracy of pNMR measurements of MD ex vivo as compared with the gold standards. Forty-five breast-tissue explants from 9 prophylactic mastectomy patients were measured. The relative tissue water content was taken as the MD-equivalent quantity. In each sample, the water content was measured using some combination of three pNMR techniques (apparent T2, diffusion, and T1 measurements) and two gold-standard techniques (computed microtomography [μCT] and hematoxylin and eosin [H&E] histology). Pairwise correlation plots and Bland-Altman analysis were used to quantify the degree of agreement between pNMR techniques and the gold standards. Relative water content measured from both apparent T2 relaxation spectra, and diffusion decays exhibited strong correlation with the H&E and μCT results. Bland-Altman analysis yielded average bias values of -0.4, -2.6, 2.6, and 2.8 water percentage points (pp) and 95% confidence intervals of 13.1, 7.5, 11.2, and 11.8 pp for the H&E - T2, μCT - T2, H&E - diffusion, and μCT - diffusion comparison pairs, respectively. T1-based measurements were found to be less reliable, with the Bland-Altman confidence intervals of 27.7 and 33.0 pp when compared with H&E and μCT, respectively. Apparent T2-based and diffusion-based pNMR measurements enable quantification of MD in breast-tissue explants with the precision of approximately 10 pp and accuracy of approximately 3 pp or better, making pNMR a promising measurement modality for radiation-free quantification of MD.

Glass spectrum, excess wing phenomenon, and master curves in molecular glass formers: A multi-method approach.

The relaxation spectra of glass formers solely displaying an α-peak and excess wing contribution collected by various methods are reanalyzed to pin down their different spectral evolution. We show that master curve construction encompassing both α-peak and emerging excess wing works for depolarized light scattering (DLS) and nuclear magnetic resonance (NMR) relaxometry. It reveals the self-part of the slow dynamics' spectrum. Master curves are to be understood as a result of a more extensive scaling covering all temperatures instead of strict frequency-temperature superposition. DLS and NMR display identical relaxation spectra; yet, comparing different systems, we do not find a generic structural relaxation at variance with recent claims. Dielectric spectroscopy (DS) spectra show particularities, which render master curve construction obsolete. The DS α-peak is enhanced or suppressed with respect to that of DLS or NMR, yet, not correlated to the polarity of the liquid. Attempting to single out the excess wing from the overall spectrum discloses a stronger exponential temperature dependence of its amplitude compared to that below Tg and a link between its exponent and that of the fast dynamics' spectrum. Yet, such a decomposition of α-peak and excess wing appears to be unphysical. Among many different glasses, the amplitude of the excess wing power-law spectrum is found to be identical at Tg, interpreted as a relaxation analog to the Lindemann criterion.

Modeling linear and nonlinear rheology of industrial incompatible polymer blends

The ability to accurately predict the rheological behavior of the blends of two incompatible polymers is critical to the polymer industry. The constitutive modeling of incompatible polymer blends requires understanding the structure and dynamics of the blends across different length scales. The polydispersity of chain length at the molecular level and nonuniformity of flow field due to dispersed domains at the mesoscopic level present significant challenges to this industrially relevant problem. This work proposes a modeling framework for linear and nonlinear rheology of industrial incompatible polymer blends with sea-island morphology. For the individual components, we adopt the Rolie-Double-Poly model and generate the relaxation spectrum from an optimized molecular weight distribution. We derive a new mixing rule without empirical parameters from the flow field analysis inside and outside the droplets. The phase interface, modeled by an ellipsoidal model, contributes to the apparent rheology only at low shear rates. Our modeling approach is verified by the shear and extensional rheology of eight polymer blends with a broad range of viscosity ratios (0.01–100). We also show that the model has the ability to predict the nonlinear rheological behaviors of incompatible polymer blends with known molecular weight distributions and phase morphology.

Application of Post–Widder inversion formula to the calculation of relaxation spectrum from relaxation modulus

Application of Post–Widder inversion formula to the calculation of relaxation spectrum from relaxation modulus

Viscoelastic materials are most energy efficient when loaded and unloaded at equal rates.

Biological springs can be used in nature for energy conservation and ultra-fast motion. The loading and unloading rates of elastic materials can play an important role in determining how the properties of these springs affect movements. We investigate the mechanical energy efficiency of biological springs (American bullfrog plantaris tendons and guinea fowl lateral gastrocnemius tendons) and synthetic elastomers. We measure these materials under symmetric rates (equal loading and unloading durations) and asymmetric rates (unequal loading and unloading durations) using novel dynamic mechanical analysis measurements. We find that mechanical efficiency is highest at symmetric rates and significantly decreases with a larger degree of asymmetry. A generalized one-dimensional Maxwell model with no fitting parameters captures the experimental results based on the independently characterized linear viscoelastic properties of the materials. The model further shows that a broader viscoelastic relaxation spectrum enhances the effect of rate-asymmetry on efficiency. Overall, our study provides valuable insights into the interplay between material properties and unloading dynamics in both biological and synthetic elastic systems.

Laun's rule for predicting the first normal stress coefficient in complex fluids: A comprehensive investigation using fractional calculus

Laun's rule [H. M. Laun, “Prediction of elastic strains of polymer melts in shear and elongation,” J. Rheol. 30, 459–501 (1986).] is commonly used for evaluating the rate-dependent first normal stress coefficient from the frequency dependence of the complex modulus. We investigate the mathematical conditions underlying the validity of Laun's relationship by employing the time-strain–separable Wagner constitutive formulation to develop an integral expression for the first normal stress coefficient of a complex fluid in steady shear flow. We utilize the fractional Maxwell liquid model to describe the linear relaxation dynamics compactly and accurately and incorporate material nonlinearities using a generalized damping function of Soskey–Winter form. We evaluate this integral representation of the first normal stress coefficient numerically and compare the predictions with Laun's empirical expression. For materials with a broad relaxation spectrum and sufficiently strong strain softening, Laun's relationship enables measurements of linear viscoelastic data to predict the general functional form of the first normal stress coefficient but often with a noticeable quantitative offset. Its predictive power can be enhanced by augmenting the original expression with an adjustable power-law index that is based on the linear viscoelastic characteristics of the specific material being considered. We develop an analytical expression enabling the calculation of the optimal power-law index from the frequency dependence of the viscoelastic spectrum and the strain-softening characteristics of the material. To illustrate this new framework, we analyze published data for an entangled polymer melt and for a semiflexible polymer solution; in both cases our new approach shows significantly improved prediction of the experimentally measured first normal stress coefficient.

Study on the Damage Characteristics and Internal Variable Modeling of Single-Fracture Sandstone under the Coupling Effect of Freeze–Thaw and Fatigue Load

The fractured rock mass in the western cold region is affected by freezing and thawing disasters and is prone to local damage and fracture along the fissures’ ends. The fatigue damage induced by repeated frost heave and traffic loads seriously endangers the stability of cold region roadbed. This paper selects sandstone as the research object. Firstly, 20 freeze–thaw cycles were performed on fractured sandstone samples with different inclination angles of 30°, 45°, 60°, and 90°. Subsequently, triaxial compression and triaxial fatigue loading tests were conducted to explore the mechanical properties and fracture morphology evolution mechanism during the compression process of freeze–thaw fractured sandstone. Nuclear magnetic resonance technology (NMR) was used to measure the H-containing fluid inside rock pores. The microscopic damage characteristics inside the rock were analyzed from the NMR T2 relaxation spectrum signal and pore size distribution characteristics. Based on the internal variable theory of continuum mechanics, a fatigue model of freeze–thaw fractured sandstone with different inclination angles was established. The results show that sandstone strength was negatively correlated with the fracture dip angle, and the axial deformation and shear failure angle were positively correlated with the fracture dip angle. The mechanical properties of the sandstone were deteriorated by fatigue loading. When the crack angle was 90°, the fatigue failure strength of the rock sample was the lowest. The T2 spectrum distribution of the fractured sandstone mainly had three peaks and the pore size was mainly medium and small pores. There was a small leftward shift after freeze–thaw cycles and fatigue loading. The T2 spectrum area was significantly affected by fatigue loading, with the highest rate of change at a crack angle of 30°. Through the fine correspondence between the axial residual deformation and the deformation modulus, a fatigue model with different crack inclination angles was established using the axial residual deformation as the internal variable, and the rationality of the model was verified by fatigue loading tests.

BOTTS: broadband optimized time-temperature superposition for vastly accelerated viscoelastic data acquisition.

Modern materials design strategies take advantage of the increasing amount of materials property data available and increasingly complex algorithms to take advantage of those data. However, viscoelastic materials resist this trend towards increased data rates due to their inherent time-dependent properties. Therefore, viscoelasticity measurements present a roadblock for data collection in an important aspect of material design. For thermorheologically simple (TRS) materials, time-temperature superposition (TTS) made relaxation spectrum measurements faster relative to, for example, very long creep experiments. However, TTS itself currently faces a speed limit originating in the common logarithmic discrete frequency sweep (DFS) mode of operation. In DFS, the measurement time is proportional (by a factor much greater than one) to the lowest frequency of measurement. This state of affairs has not improved for TTS for half a century or more. We utilize recent work in experimental rheometry on windowed chirps to collect three decades of complex modulus data simultaneously, resulting in a ∼500% increase in data collection. In BOTTS, we superpose several isothermal chirp responses to produce a master curve in a fraction of time required by the traditional DFS-TTS technique. The chirp responses have good, albeit nontrivial, signal-to-noise properties. We use linear error propagation and a noise-weighted least squares approach to automatically incorporate all the data into a reliable shifting method. Using model thermoset polymers, we show that DFS-TTS and BOTTS results are comparable, and therefore BOTTS data represent a first step towards a faster method for master curve generation from unmodified rheological measurement instruments.

Rehydration characteristics of dried icefish (Salangidae) with different drying methods by low‐field nuclear magnetic resonance and magnetic resonance imaging

AbstractIcefish (Salangidae) is a valuable aquatic product that is often dried for preservation. The purpose of this study was to investigate the effect of different drying methods on the rehydration quality of icefish. Low‐field nuclear magnetic resonance (LF‐NMR) was used to compare the rehydration rate, moisture migration and distribution of icefish dried by cold air (8, 10, 12°C) and hot air (40, 50, 60°C) The muscle fibers structure of dried icefish and magnetic resonance imaging (MRI) of icefish after rehydration were examined. The results showed that cold air drying resulted in higher values of these parameters than hot air drying. MRI analysis revealed that cold air dried icefish retained more water after rehydration than hot air dried icefish. The T2 transverse relaxation spectra of rehydrated icefish exhibited three peaks corresponding to bound water, immobilized water and free water. The proportion of immobilized water increased significantly and accounted for more than 92% after rehydration, while the proportion of free water was around 2%–3%. Cold air drying preserved the muscle fiber structure and protein network better than hot air drying, which improved the rehydration quality of icefish. The study provides theoretical and data support for using cold air drying technology in aquatic product processing.Practical applicationsThe focus of this study is to compare the effect of different drying methods on the rehydration rate of icefish. The results indicate that part of the bound water migrated to the immobilized water during the initial stage of rehydration, which increased the content of immobilized water and reduced the binding force of some bound water. The T2 value shifts to the right in all groups, indicating that the binding force between biological macromolecules (such as myofibrillar protein) and icefish water was weakened. Different drying methods have a significant impact on changes in the internal water status of rehydrated icefish samples. Our results suggest that cold air drying is a better method for drying icefish compared to hot air drying, as it improves its rehydration quality. The findings of this study can be useful for food industry personnel who are involved in fish processing, preservation, and nutrition.

How to Make the Stress Relaxation Experiment for Polymers More Informative.

Different viscoelastic models and characteristics are commonly used to describe, analyze, compare and improve the mechanical properties of polymers. A time-dependent linear relaxation modulus next to frequency-domain storage and loss moduli are the basic rheological material functions of polymers. The exponential Maxwell model and the exponential stretched Kohlrausch-Williams-Watts model are, probably, the most known linear rheological models of polymers. There are different identification methods for such models, some of which are dedicated to specific models, while others are general in nature. However, the identification result, i.e., the best model, always depends on the specific experimental data on the basis of which it was determined. When the rheological stress relaxation test is performed, the data are composed of the sampling instants used in the test and on the measurements of the relaxation modulus of the real material. To build a relaxation modulus model that does not depend on sampling instants is a fundamental concern. The problem of weighted least-squares approximation of the real relaxation modulus is discussed when only the noise-corrupted time-measurements of the relaxation modulus are accessible for identification. A wide class of models, that are continuous, differentiable and Lipschitz with respect to parameters, is considered for the relaxation modulus approximation. The main results concern the models that are selected asymptotically as the number of measurements tends to infinity. It is shown that even when the true relaxation modulus description is completely unknown, the approximate optimal model parameters can be derived from the measurement data that are obtained for sampling instants that are selected randomly due to the appropriate randomization introduced whenever certain conditions regarding the adopted class of models are satisfied. It is shown that the most commonly used stress relaxation models, the Maxwell and Kohlrausch-Williams-Watts models, satisfy these conditions. Since the practical problems of the identification of relaxation modulus models are usually ill posed, Tikhonov regularization is applied to guarantee the stability of the regularized solutions. The approximate optimal model is a strongly consistent estimate of the regularized model that is optimal in the sense of the deterministic integral weighted square error. An identification algorithm leading to the best regularized model is presented. The stochastic-type convergence analysis is conducted for noise-corrupted relaxation modulus measurements, and the exponential convergence rate is proved. Numerical studies for different models of the relaxation modulus used in the polymer rheology are presented for the material described by a bimodal Gauss-like relaxation spectrum. Numerical studies have shown that if appropriate randomization is introduced in the selection of sampling instants, then optimal regularized models of the relaxation modulus being asymptotically independent of these time instants can be recovered from the stress relaxation experiment data. The robustness of the identification algorithm to measurement noises was demonstrated both by analytical and numerical analyses.

Investigation on the rheological behavior of PA6 film during biaxial stretching

In this work, the rheological behavior of polyamide 6 (PA6) film during biaxial stretching was investigated. Firstly, the cast film was subjected to different ratios of biaxial stretching, and the stress calculation expression of biaxial stretching was derived. Then the generalized Maxwell model was employed to fit the stress-time curves in the heat setting stage. It was found that the elastic-plastic deformation during biaxial stretching influenced the stress rebound or relaxation in the heat setting. Finally, the relaxation spectrum and activation energy spectrum were calculated according to the fitting curves. It was found that the stress relaxation process of PA6 film was divided into multiple stages, but the stress rebound process was relatively simple. According to the activation energy spectrum, we speculated that stress relaxation was a process of releasing energy, and stress rebound was a process of absorbing energy. With the increased stretching ratio, the peaks on the activation energy spectrum became sharper and the intensity increased. Indicating that more energy was released or absorbed under the larger stretching ratio. The obtained results would provide theoretical guidance for further understanding the biaxial stretching deformation mechanism of polymer films.

Polymer architecture dictates multiple relaxation processes in soft networks with two orthogonal dynamic bonds

Materials with tunable modulus, viscosity, and complex viscoelastic spectra are crucial in applications such as self-healing, additive manufacturing, and energy damping. It is still challenging to predictively design polymer networks with hierarchical relaxation processes, as many competing factors affect dynamics. Here, networks with both pendant and telechelic architecture are synthesized with mixed orthogonal dynamic bonds to understand how the network connectivity and bond exchange mechanisms govern the overall relaxation spectrum. A hydrogen-bonding group and a vitrimeric dynamic crosslinker are combined into the same network, and multimodal relaxation is observed in both pendant and telechelic networks. This is in stark contrast to similar networks where two dynamic bonds share the same exchange mechanism. With the incorporation of orthogonal dynamic bonds, the mixed network also demonstrates excellent damping and improved mechanical properties. In addition, two relaxation processes arise when only hydrogen-bond exchange is present, and both modes are retained in the mixed dynamic networks. This work provides molecular insights for the predictive design of hierarchical dynamics in soft materials.

Three-Dimensional Calcium Copper Titanate/Epoxy-Boron Nitride Nanosheets Dielectrics toward High Dielectric Constant and Low Loss

Epoxy dielectric materials with high permittivity and low loss were fabricated via inversely introducing epoxy-boron nitride nanosheets (EP-BNNS) mixtures into a continuous three-dimensional CaCu3Ti4O12 (3D CCTO) ceramic network constructed by template method. The obtained 3D CCTO/EP-1.0%BNNS composite exhibited an enhanced permittivity of 25.8 and suppressed low loss of 0.032 (@ 1 kHz), 170%, and 89% of conventional CCTO/EP system, respectively. In addition, the activation energy derived from the isothermal dielectric relaxation spectra increases with the addition of BNNS, indicating that the presence of BNNS restrains the dipolar polarization of EP composites.

Synergism between yellow mustard gum and κ-carrageenan studied by structural and rheological methods

Yellow mustard gum (YMG), a clean-label hydrocolloid with commercial potential, has been found to synergistically interact with κ-carrageenan to form a stronger gel. The primary gelation mechanism has been proposed but needs a thorough investigation and understanding from multiple techniques. In addition to the rheological methods of dynamic oscillation, this study used transient mechanical tests (stress relaxation), differential scanning calorimetry (DSC) and cryogenic scanning electron microscopy (cryo-SEM) to evaluate gel characteristics, thermal properties and microstructure of YMG-κ-carrageenan binary gels. The stress relaxation spectrum showed that the interactions between the two types of gums were mainly polymer associations. The DSC cooling and heating scans revealed that YMG did not disturb the coil-to-helix transition of κ-carrageenan but affected its helix aggregation during gel setting. The microstructure of the binary gel network captured by cryo-SEM showed a denser and more compact gel structure with smaller pores in comparison with the κ-carrageenan gel structure. All these results supported a refined gelation mechanism proposed in this study. This thorough investigation of the synergistic gelation between YMG and κ-carrageenan not only supports applications of the binary mixtures as texturizers, gelling aids and thickeners but also expands the application of YMG to promote its eventual commercialization.

Improved parameter acquisition of generalized Maxwell model in asphalt mixtures by continuous relaxation spectrum

The generalized Maxwell (GM) model is widely used to describe the viscoelastic behavior and predict performance of asphalt mixtures. However, the existing methods may not provide satisfactory accuracy because relaxation spectral distribution features are not considered. In this study, the methods (area equalization (AE) and peak equalization (PE) method) consider the distribution characteristics of the relaxation spectrum were proposed to obtain the Prony series parameters of the GM model. Two typical asphalt mixtures, HMA (hot mix asphalt mixture) and WMA (warm mix asphalt mixture), were used as case studies. The Prony series parameters of the GM model obtained by the proposed methods and existing methods (traditional fitting (TF) method and Limit equalization (LE) method) were discussed and analyzed. The derived Prony series parameters were also employed in finite element (FE) simulations to inversely predict dynamic modulus, and the simulated results were then compared with the experimental results. The results indicate that the spring stiffnesses of Maxwell elements in the Prony series parameters obtained by different methods have different distribution features. For the TF method, the Maxwell element with larger relaxation time has smaller spring stiffness. In the LE and PE method, the spring stiffness of the Maxwell element first increases and then decreases as the relaxation time increases. The spring stiffness is the same for the different Maxwell elements in the AE method. More importantly, the number of branches of the GM model is increased from 6 to 12, the relative error of the predicted dynamic modulus of HMA by the PE, AE, LE and TF method is reduced from 29.8% to 4.8%, from 49.9% to 25.9%, from 61.4% to 32.7%, from 159.1% to 133.9% respectively. The PE method has the best accuracy in FE analysis, even with a smaller number of branches of the GM model. The similar conclusion can also be summarized in the dynamic modulus prediction of WMA. Therefore, the PE method that considers the rate of change of the relaxation spectrum is preferentially recommended to obtain the Prony series parameters of the GM model.

Smooth deconvolution of low-field NMR signals

BackgroundLow resolution nuclear magnetic resonance (LR-NMR) is a common technique to identify the constituents of complex materials (such as food and biological samples). The output of LR-NMR experiments is a relaxation signal which can be modelled as a type of convolution of an unknown density of relaxation times with decaying exponential functions, plus random Gaussian noise. The challenge is to estimate that density, a severely ill-posed problem. A complication is that non-negativity constraints need to be imposed in order to obtain valid results. Significance and noveltyWe present a smooth deconvolution model for solution of the inverse estimation problem in LR-NMR relaxometry experiments. We model the logarithm of the relaxation time density as a smooth function using (adaptive) P-splines while matching the expected residual magnetisations with the observed ones. The roughness penalty removes the singularity of the deconvolution problem, and the estimated density is positive by design (since we model its logarithm). The model is non-linear, but it can be linearized easily. The penalty has to be tuned for each given sample. We describe an efficient EM-type algorithm to optimize the smoothing parameter(s). ResultsWe analyze a set of food samples (potato tubers). The relaxation spectra extracted using our method are similar to the ones described in the previous experiments but present sharper peaks. Using penalized signal regression we are able to accurately predict dry matter content of the samples using the estimated spectra as covariates.

Experimental Study on Spontaneous Imbibition of Coal Samples of Different Ranks Based on the NMR Relaxation Spectrum.

The comprehension of the mechanisms governing spontaneous water imbibition in gas-water systems plays a significant role in the operation of hydraulic fracturing and the development of coalbed methane (CBM). In this study, nuclear magnetic resonance (NMR) techniques were used to investigate the pore structure and fluid behavior of different rank coal samples during spontaneous imbibition. Analyses were conducted on the 1D NMR T2 spectrum, 2D NMR T1-T2 spectrum, and layer division T2 spectra to achieve accurate and detailed information about the internal pore structure of coal and the characteristics of fluid transport during spontaneous imbibition. Low-rank coal exhibits good pore connectivity and favorable pore sorting characteristics, indicating favorable reservoir conditions. High-rank coal has larger pore spaces and highly developed micropores, which are highly beneficial for gas adsorption. However, its poor pore sorting characteristics and connectivity limit the migration and diffusion of fluids within the reservoir. The imbibition capacity follows a specific order of contribution, with small pores (10-50 nm) having the most significant role, followed by micropores (2-10 nm), ultramicropores (r < 2 nm), mesopores (50-1000 nm), macropores (1000-10,000 nm), and microfractures (r ≥ 10,000 nm). Low-rank coal stands out due to the restricted development of ultramicropores and small pores, leading to a different contribution of imbibition capacity compared to other samples, where macropores and microfractures dominate over all pore types. The coal reservoirs with favorable pore sorting characteristics and pore connectivity tend to exhibit a tendency toward rapid saturation and attainment of a prompt stable state during the hydraulic fracturing process. Finally, the mechanism of the late retreat effect of imbibition and the laws governing different coal ranks, pore structures, and fluid transport were discussed. This study offers comprehensive analyses of the mechanism of coal spontaneous imbibition and the characteristic laws of fluid seepage, providing insights into the optimization of CBM recovery and reservoir management.

Chemical reactions in poly(acrylonitrile-co-itaconic acid) during stabilization as revealed by solid-state NMR spectroscopy and 13C isotope labeling

Understanding and controlling chemical reactions of atactic-Poly(acrylonitrile) (PAN) and its copolymer during thermal heat-treatment under air are critical subjects to produce PAN-based carbon-fibers. Copolymerization of PAN with itaconic acid (IA) monomers effectively lowers initial chemical reaction temperature and thus promote chemical reactions during stabilization. In this work, detailed chemical structure of PAN and poly(acrylonitrile-co-itaconic acid) (PAI) stabilized under air atmosphere were studied by combined use of solid-state (ss) NMR spectroscopy and 13C isotope labeling. By applying 13C–13C INADEQUATE and fully relaxed 13C DPMAS NMR spectra, it was elucidated that 2% cyclized structure can be initially formed in PAI during stabilization. Moreover, five elemental reactions including cyclization, aromatization, oxidization, dehydrogenation, and intermolecular cross-linking were identified and corresponding structures were quantitatively analyzed in both PAN and PAI as a function of stabilization temperature. It was revealed that all the reactions concertedly occur in PAN in the narrow temperature range (290–340 °C). For PAI, it was demonstrated that cyclization and aromatization are dominant in the low temperature range (180–270 °C, regime I), dehydrogenation and intermolecular cross linking are promoted in the high temperature range (270–340 °C, regime II), and oxidization occurs across two regimes. The sensitivity enhanced ssNMR study not only provides fundamental understanding of the chemical reactions in PAN and PAI during stabilization but also guide ones to potentially control the stabilized structures from one dimensional structure to two dimensional one for PAI by choosing a proper temperature and time.

Effectiveness of DPD Simulations to Predict the Dynamics of Polymer Chains in Solutions at Equilibrium and Steady Shear Flows

AbstractThe suitability of dissipative particle dynamics simulations is investigated to predict the dynamics of polymer chains in dilute polymer solutions. The authors find that the predictions depend on the value of the repulsive parameter for bead‐bead pairwise interactions used in the DPD simulations (aij). For all systems, the chain sizes and the relaxation time spectrum are analyzed. For aij = 0, theta solvent behaviour is obtained, whereas the dynamics at equilibrium agrees well with the predictions of the Zimm model. For higher values of aij, the static properties of the chain show good solvent behaviour. However, the scaling laws for the chain dynamics at equilibrium show wide variations, with consistent results obtained only at an intermediate value of aij = 25. At higher values of the repulsive parameter (aij ⩾ 25), the simulations are also able to predict the abrupt cut‐off in the relaxation spectrum, which has been observed earlier in experiments of dilute solutions. To verify further, the chain dynamics in shear flow using DPD simulations is studied. Specifically, the variation of the chain is analysed stretch and end‐over‐end tumbling with shear rates. Overall, the trends obtained from DPD simulations agree well with those observed in earlier BD simulations.

On thermodynamics and relaxation properties of eukaryotic cells

Mechanical properties of eukaryotic cells play an important role in the development of pathological processes. Currently, there are no complete models reflecting the full phenomenology of the mechanical behavior of the cell. Statistical thermodynamics methods have the potential to provide a framework for understanding the influence of structural properties on the stress-strain state of cells under external loading. In this paper, we develop a statistically based thermodynamic description of the eukaryotic cell to simulate the processes of cell contraction or extension as well as stress relaxation. In addition, it is proposed to use an order parameter to describe the orientation properties of the cell cytoskeleton and obtained a form of free energy, depending on this parameter, temperature and external stress. An orientation-viscoelastic body as a model of a representative cell volume has been proposed in this paper. Following the linear thermodynamics, the evolution equations describing the mechanical behavior of the representative cell volume have been derived. It was shown that the power law for the relaxation times conventionally introduced by the usage of the fractional derivatives in generalized Maxwell-Kelvin viscoelasticity of the cell cytoskeleton mechanical behavior follows from the orientation kinetics of the ensemble of actin filaments revealing the orientation ordering with the signs of the first kind criticality. The introduction of a relaxation spectrum is discussed, allowing one to improve the consistency of simulation results with atomic force microscopy data of living cells.