On the Thermodynamical Admissibility of the Triphasic Theory of Charged Hydrated Tissues

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
J. M. Huyghe ◽  
W. Wilson ◽  
K. Malakpoor
Keyword(s):  
Free Energy ◽  
Articular Cartilage ◽  
Second Law Of Thermodynamics ◽  
Volume Effect ◽  
Closed Cycle ◽  
Chemical Expansion ◽  
Deformation Behaviors ◽  
Triphasic Theory ◽  
Loading And Unloading ◽  
Stress Term

The triphasic theory on soft charged hydrated tissues (Lai, W. M., Hou, J. S., and Mow, V. C., 1991, “A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage,” ASME J. Biomech. Eng., 113, pp. 245–258) attributes the swelling propensity of articular cartilage to three different mechanisms: Donnan osmosis, excluded volume effect, and chemical expansion stress. The aim of this study is to evaluate the thermodynamic plausibility of the triphasic theory. The free energy of a sample of articular cartilage subjected to a closed cycle of mechanical and chemical loading is calculated using the triphasic theory. It is shown that the chemical expansion stress term induces an unphysiological generation of free energy during each closed cycle of loading and unloading. As the cycle of loading and unloading can be repeated an indefinite number of times, any amount of free energy can be drawn from a sample of articular cartilage, if the triphasic theory were true. The formulation for the chemical expansion stress as used in the triphasic theory conflicts with the second law of thermodynamics.

A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage

1991 ◽  
Vol 113 (3) ◽  
pp. 245-258 ◽  
Author(s):  
W. M. Lai ◽  
J. S. Hou ◽  
V. C. Mow
Keyword(s):  
Articular Cartilage ◽  
Charge Density ◽  
Fixed Charge ◽  
Solid Matrix ◽  
Confined Compression ◽  
Fixed Charge Density ◽  
Chemical Expansion ◽  
Chemical Potentials ◽  
Free Swelling ◽  
Triphasic Theory

Swelling of articular cartilage depends on its fixed charge density and distribution, the stiffness of its collagen-proteoglycan matrix, and the ion concentrations in the interstitium. A theory for a tertiary mixture has been developed, including the two fluid-solid phases (biphasic), and an ion phase, representing cation and anion of a single salt, to describe the deformation and stress fields for cartilage under chemical and/or mechanical loads. This triphasic theory combines the physico-chemical theory for ionic and polyionic (proteoglycan) solutions with the biphasic theory for cartilage. The present model assumes the fixed charge groups to remain unchanged, and that the counter-ions are the cations of a single salt of the bathing solution. The momentum equation for the neutral salt and for the intersitial water are expressed in terms of their chemical potentials whose gradients are the driving forces for their movements. These chemical potentials depend on fluid pressure p, salt concentration c, solid matrix dilatation e and fixed charge density cF. For a uni-uni valent salt such as NaCl, they are given by μi = μoi + (RT/Mi)ln[γ±2c (c + c F)] and μW = μow + [p − RTφ(2c + cF) + Bwe]/ρTw, where R, T, Mi, γ±, φ, ρTw and Bw are universal gas constant, absolute temperature, molecular weight, mean activity coefficient of salt, osmotic coefficient, true density of water, and a coupling material coefficient, respectively. For infinitesimal strains and material isotropy, the stress-strain relationship for the total mixture stress is σ = − pI − TcI + λs(trE)I + 2μsE, where E is the strain tensor and (λs,μs) are the Lame´ constants of the elastic solid matrix. The chemical-expansion stress (− Tc) derives from the charge-to-charge repulsive forces within the solid matrix. This theory can be applied to both equilibrium and non-equilibrium problems. For equilibrium free swelling problems, the theory yields the well known Donnan equilibrium ion distribution and osmotic pressure equations, along with an analytical expression for the “pre-stress” in the solid matrix. For the confined-compression swelling problem, it predicts that the applied compressive stress is shared by three load support mechanisms: 1) the Donnan osmotic pressure; 2) the chemical-expansion stress; and 3) the solid matrix elastic stress. Numerical calculations have been made, based on a set of equilibrium free-swelling and confined-compression data, to assess the relative contribution of each mechanism to load support. Our results show that all three mechanisms are important in determining the overall compressive stiffness of cartilage.

First and second laws of thermodynamics: relationship, “inconsistency”, hidden effects

2020 ◽  
pp. 63-73
Author(s):  
A. M. Savchenko ◽  
Yu. V. Konovalov ◽  
A. V. Laushkin
Keyword(s):  
Free Energy ◽  
Internal Energy ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Entropy Of Mixing ◽  
Ideal Mixing ◽  
Laws Of Thermodynamics ◽  
Relationship Of ◽  
The Relationship

The relationship of the first and second laws of thermodynamics based on their energy nature is considered. It is noted that the processes described by the second law of thermodynamics often take place hidden within the system, which makes it difficult to detect them. Nevertheless, even with ideal mixing, an increase in the internal energy of the system occurs, numerically equal to an increase in free energy. The largest contribution to the change in the value of free energy is made by the entropy of mixing, which has energy significance. The entropy of mixing can do the job, which is confirmed in particular by osmotic processes.

scholarly journals A thermodynamic approach to rate-type models in deformable ferroelectrics

2020 ◽  
Author(s):  
Claudio Giorgi ◽  
Angelo Morro
Keyword(s):  
Free Energy ◽  
Electric Field ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Energy Models ◽  
Polarization Electric Field ◽  
Field Plane ◽  
Vector Valued ◽  
Rate Type ◽  
Hysteretic Properties

AbstractThe purpose of the paper is to establish vector-valued rate-type models for the hysteretic properties in deformable ferroelectrics within the framework of continuum thermodynamics. Unlike electroelasticity and piezoelectricity, in ferroelectricity both the polarization and the electric field are simultaneously independent variables so that the constitutive functions depend on both. This viewpoint is naturally related to the fact that an hysteresis loop is a closed curve in the polarization–electric field plane. For the sake of generality, the deformation of the material and the dependence on the temperature are allowed to occur. The constitutive functions are required to be consistent with the principle of objectivity and the second law of thermodynamics. Objectivity implies that the constitutive equations are form invariant within the set of Euclidean frames. Among other results, the second law requires a general property on the relation between the polarization and the electric field via a differential equation. This equation shows a dependence fully characterized by two quantities: the free energy and a function which is related to the dissipative character of the hysteresis. As a consequence, different hysteresis models may have the same free energy. Models compatible with thermodynamics are then determined by appropriate selections of the free energy and of the dissipative part. Correspondingly, major and minor hysteretic loops are plotted.

scholarly journals The Effect of the Protein Synthesis Entropy Reduction on the Cell Size Regulation and Division Size of Unicellular Organisms

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 94
Author(s):  
Mohammad Razavi ◽  
Seyed Majid Saberi Fathi ◽  
Jack Adam Tuszynski
Keyword(s):  
Free Energy ◽  
Protein Synthesis ◽  
Cell Size ◽  
Cell Biology ◽  
Second Law Of Thermodynamics ◽  
Underlying Mechanism ◽  
Energy Balance Equation ◽  
Second Law ◽  
Entropy Reduction ◽  
Unicellular Organisms

The underlying mechanism determining the size of a particular cell is one of the fundamental unknowns in cell biology. Here, using a new approach that could be used for most of unicellular species, we show that the protein synthesis and cell size are interconnected biophysically and that protein synthesis may be the chief mechanism in establishing size limitations of unicellular organisms. This result is obtained based on the free energy balance equation of protein synthesis and the second law of thermodynamics. Our calculations show that protein synthesis involves a considerable amount of entropy reduction due to polymerization of amino acids depending on the cytoplasmic volume of the cell. The amount of entropy reduction will increase with cell growth and eventually makes the free energy variations of the protein synthesis positive (that is, forbidden thermodynamically). Within the limits of the second law of thermodynamics we propose a framework to estimate the optimal cell size at division.

The effect of excluded volume on polymer dispersant action

1975 ◽  
Vol 343 (1635) ◽  
pp. 427-442 ◽  
Keyword(s):  
Free Energy ◽  
High Surface ◽  
Volume Effect ◽  
Polymer Chains ◽  
Excluded Volume ◽  
Density Distributions ◽  
Excluded Volume Effects ◽  
Adsorbed Polymer ◽  
Polymer Distribution ◽  
Dimensional Equation

Polymer-stabilized colloid particles are modelled theoretically by plane surfaces on to which polymer chains are adsorbed by one end only. Interactions between segments of the polymer are treated as an excluded volume effect. It is shown that for high surface densities the polymer distribution function exactly satisfies a one dimensional equation which is solved numerically for two values of excluded volume to give the polymer segment density distributions and the free energy of interaction for various separations of the plane surfaces. It is found that a positive value of excluded volume greatly increases the repulsive free energy compared with that for chains with zero excluded volume, particularly at large separation distances of the surfaces. Excluded volume effects must therefore play an important part in the stabilization of colloids by adsorbed polymer.

Direct Osmotic Pressure Measurements in Articular Cartilage Demonstrate Nonideal and Concentration-Dependent Phenomena

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Brandon K. Zimmerman ◽  
Robert J. Nims ◽  
Alex Chen ◽  
Clark T. Hung ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Osmotic Pressure ◽  
Electrostatic Interactions ◽  
Swelling Pressure ◽  
Confined Compression ◽  
Human Cartilage ◽  
Poisson Boltzmann ◽  
Triphasic Theory

Abstract The osmotic pressure in articular cartilage serves an important mechanical function in healthy tissue. Its magnitude is thought to play a role in advancing osteoarthritis. The aims of this study were to: (1) isolate and quantify the magnitude of cartilage swelling pressure in situ; and (2) identify the effect of salt concentration on material parameters. Confined compression stress-relaxation testing was performed on 18 immature bovine and six mature human cartilage samples in solutions of varying osmolarities. Direct measurements of osmotic pressure revealed nonideal and concentration-dependent osmotic behavior, with magnitudes approximately 1/3 those predicted by ideal Donnan law. A modified Donnan constitutive behavior was able to capture the aggregate behavior of all samples with a single adjustable parameter. Results of curve-fitting transient stress-relaxation data with triphasic theory in febio demonstrated concentration-dependent material properties. The aggregate modulus HA increased threefold as the external concentration decreased from hypertonic 2 M to hypotonic 0.001 M NaCl (bovine: HA=0.420±0.109 MPa to 1.266±0.438 MPa; human: HA=0.499±0.208 MPa to 1.597±0.455 MPa), within a triphasic theory inclusive of osmotic effects. This study provides a novel and simple analytical model for cartilage osmotic pressure which may be used in computational simulations, validated with direct in situ measurements. A key finding is the simultaneous existence of Donnan osmotic and Poisson–Boltzmann electrostatic interactions within cartilage.

Application of a Chemical Thermodynamic Model to the Gibbs Free Energy of Aqueous Electrolyte Solutions. New Equations for the Activity and Osmotic Coefficients

1991 ◽  
Vol 44 (9) ◽  
pp. 1195
Author(s):  
JV Leyendekkers
Keyword(s):  
Free Energy ◽  
Gibbs Free Energy ◽  
Short Range ◽  
Van Der Waals ◽  
Osmotic Coefficients ◽  
Electrolyte Solutions ◽  
Solute Concentration ◽  
Volume Effect ◽  
Chemical Thermodynamic ◽  
Short Range Repulsion

The chemical thermodynamic (CT) model, based on the extended Tait equation, has been applied to the Gibbs free energy of aqueous solutions of sodium chloride and potassium chloride at 25°C. Equations for the activity and osmotic coefficients were derived. These are made up of the Debye-Huckel limiting slope term, a van der Waals co-volume effect term covering short-range repulsion, a term covering the water compression by the solute and a short-range attractive term. The distance of closest approach derived from the model is the same as that expected for the van der Waals effect. The individual components of the partial molal free energy, that is, the effects of solute concentration on the water and solute respectively, have been calculated.

scholarly journals Structure for Energy Cycle: A unique status of Second Law of Thermodynamics for living systems

2018 ◽  
Author(s):  
Shu-Nong Bai ◽  
Hao Ge ◽  
Hong Qian
Keyword(s):  
Free Energy ◽  
Second Law Of Thermodynamics ◽  
Chemical Kinetic ◽  
Chemical Processes ◽  
Spontaneous Formation ◽  
Energy Cycle ◽  
Molecular Force ◽  
Living Organisms ◽  
Dynamic Formation ◽  
Unique Status

AbstractDistinguishing things from beings, or matters from lives, is a fundamental question. Extending E. Schrödinger’sneg-entropyand I. Prigogine’sdissipative structure, we propose a chemical kinetic view that the earliest “live” process is essentially a special interaction between a pair of specific components under a corresponding, particular environmental conditions. The interaction exists as an inter-molecular-force-bond complex (IMFBC) that couples two separate chemical processes: One is the spontaneous formation of an IMFBC driven by the decrease of Gibbs free energy as a dissipative process; while the other is the disassembly of the IMFBC driven thermodynamically by free energy input from the environment. The two processes that are coupled by the IMFBC were originated independently and considered non-living on Earth, but the IMFBC coupling of the two can be considered as the earliest form of metabolism: This forms the first landmark on the path from things to a being. The dynamic formation and dissemblance of the IMFBCs, as composite individuals, follows a principle designated as “… structure for energy for structure for energy…”, the cycle continues, shortly “structure for energy cycle”. With additional features derived from an IMFBC, such as multiple intermediates, autocatalytic ability of one individual upon the formation of another, aqueous medium, and mutual beneficial relationship between formation of polypeptides and nucleic acids, etc., the IMFBC-centered “live” process spontaneously evolved into more complex living organisms with the characteristics one currently knows.

scholarly journals Living models or life modelled? On the use of models in the free energy principle

2020 ◽  
pp. 105971232091867
Author(s):  
Thomas van Es
Keyword(s):  
Free Energy ◽  
Second Law Of Thermodynamics ◽  
Living Systems ◽  
Theoretic Approach ◽  
Energy Principle ◽  
Free Energy Principle ◽  
Information Theoretic ◽  
Conceptual Clarity ◽  
The Status ◽  
Information Theoretic Approach

The free energy principle (FEP) is an information-theoretic approach to living systems. FEP characterizes life by living systems’ resistance to the second law of thermodynamics: living systems do not randomly visit the possible states, but actively work to remain within a set of viable states. In FEP, this is modelled mathematically. Yet, the status of these models is typically unclear: are these models employed by organisms or strictly scientific tools of understanding? In this article, I argue for an instrumentalist take on models in FEP. I shall argue that models used as instruments for knowledge by scientists and models as implemented by organisms to navigate the world are being conflated, which leads to erroneous conclusions. I further argue that a realist position is unwarranted. First, it overgenerates models and thus trivializes the notion of modelling. Second, even when the mathematical mechanisms described by FEP are implemented in an organism, they do not constitute a model. They are covariational, not representational in nature, and precede the social practices that have shaped our scientific modelling practice. I finally argue that the above arguments do not affect the instrumentalist position. An instrumentalist approach can further add to conceptual clarity in the FEP literature.

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