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102-479: Gels are mostly liquid by mass , yet they behave like solids because of a three-dimensional cross-linked network within the liquid. It is the cross-linking within the fluid that gives a gel its structure (hardness) and contributes to the adhesive stick ( tack ). In this way, gels are a dispersion of molecules of a liquid within a solid medium. The word gel was coined by 19th-century Scottish chemist Thomas Graham by clipping from gelatine . The process of forming

204-543: A degree of flexibility very similar to natural tissue, due to their significant water content. As responsive " smart materials ," hydrogels can encapsulate chemical systems which upon stimulation by external factors such as a change of pH may cause specific compounds such as glucose to be liberated to the environment, in most cases by a gel-sol transition to the liquid state. Chemomechanical polymers are mostly also hydrogels, which upon stimulation change their volume and can serve as actuators or sensors . The first appearance of

306-547: A drug release matrix. A hydrogel is a network of polymer chains that are hydrophilic, sometimes found as a colloidal gel in which water is the dispersion medium. A three-dimensional solid results from the hydrophilic polymer chains being held together by cross-links. Because of the inherent cross-links, the structural integrity of the hydrogel network does not dissolve from the high concentration of water. Hydrogels are highly absorbent (they can contain over 90% water) natural or synthetic polymeric networks. Hydrogels also possess

408-698: A final volume of 100   mL of solution would be labeled as "1%" or "1% m/v" (mass/volume). This is incorrect because the unit "%" can only be used for dimensionless quantities. Instead, the concentration should simply be given in units of g/mL. Percent solution or percentage solution are thus terms best reserved for mass percent solutions (m/m, m%, or mass solute/mass total solution after mixing), or volume percent solutions (v/v, v%, or volume solute per volume of total solution after mixing). The very ambiguous terms percent solution and percentage solutions with no other qualifiers continue to occasionally be encountered. In thermal engineering , vapor quality

510-408: A free energy difference density. The form of f gel ( λ 1 , λ 2 , λ 3 ) {\displaystyle f_{\text{gel}}(\lambda _{1},\lambda _{2},\lambda _{3})} naturally assumes two contributions of radically different physical origins, one associated with the elastic deformation of the polymer network, and

612-460: A gel is called gelation . Gels consist of a solid three-dimensional network that spans the volume of a liquid medium and ensnares it through surface tension effects. This internal network structure may result from physical bonds such as polymer chain entanglements (see polymers ) (physical gels) or chemical bonds such as disulfide bonds (see thiomers ) (chemical gels), as well as crystallites or other junctions that remain intact within

714-421: A given compound may increase or decrease with temperature. The van 't Hoff equation relates the change of solubility equilibrium constant ( K sp ) to temperature change and to reaction enthalpy change. For most solids and liquids, their solubility increases with temperature because their dissolution reaction is endothermic (Δ H  > 0). In liquid water at high temperatures, (e.g. that approaching

816-447: A large increase in solubility with temperature (Δ H  > 0). Some solutes (e.g. sodium chloride in water) exhibit solubility that is fairly independent of temperature (Δ H  ≈ 0). A few, such as calcium sulfate ( gypsum ) and cerium(III) sulfate , become less soluble in water as temperature increases (Δ H  < 0). This is also the case for calcium hydroxide ( portlandite ), whose solubility at 70 °C

918-422: A lesser extent, solubility will depend on the ionic strength of solutions. The last two effects can be quantified using the equation for solubility equilibrium . For a solid that dissolves in a redox reaction, solubility is expected to depend on the potential (within the range of potentials under which the solid remains the thermodynamically stable phase). For example, solubility of gold in high-temperature water

1020-501: A long time to establish (hours, days, months, or many years; depending on the nature of the solute and other factors). The rate of dissolution can be often expressed by the Noyes–Whitney equation or the Nernst and Brunner equation of the form: where: For dissolution limited by diffusion (or mass transfer if mixing is present), C s {\displaystyle C_{s}}

1122-411: A minimum, which is below 120 °C for most permanent gases ), but more soluble in organic solvents (endothermic dissolution reaction related to their solvation). The chart shows solubility curves for some typical solid inorganic salts in liquid water (temperature is in degrees Celsius , i.e. kelvins minus 273.15). Many salts behave like barium nitrate and disodium hydrogen arsenate , and show

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1224-517: A more complex pattern is observed, as with sodium sulfate , where the less soluble deca hydrate crystal ( mirabilite ) loses water of crystallization at 32 °C to form a more soluble anhydrous phase ( thenardite ) with a smaller change in Gibbs free energy (Δ G ) in the dissolution reaction. The solubility of organic compounds nearly always increases with temperature. The technique of recrystallization , used for purification of solids, depends on

1326-426: A percentage in this case, and the abbreviation "w/w" may be used to indicate "weight per weight". (The values in g/L and g/kg are similar for water, but that may not be the case for other solvents.) Alternatively, the solubility of a solute can be expressed in moles instead of mass. For example, if the quantity of solvent is given in kilograms , the value is the molality of the solution (mol/kg). The solubility of

1428-406: A percentage, and the abbreviation "v/v" for "volume per volume" may be used to indicate this choice. Conversion between these various ways of measuring solubility may not be trivial, since it may require knowing the density of the solution — which is often not measured, and cannot be predicted. While the total mass is conserved by dissolution, the final volume may be different from both the volume of

1530-442: A polymer solution of concentration ϕ 0 {\displaystyle \phi _{0}} and volume V 0 {\displaystyle V_{0}} is mixed with a pure solvent of volume ( λ 1 λ 2 λ 3 − 1 ) V 0 {\displaystyle (\lambda _{1}\lambda _{2}\lambda _{3}-1)V_{0}} to become

1632-470: A relatively high concentration of H + {\displaystyle {\text{H}}^{+}} and salt cations inside the gel. But because the concentration of H + {\displaystyle {\text{H}}^{+}} is locally higher, it suppresses the further ionization of the acid sites. This phenomenon is the prediction of the classical Donnan theory. However, with electrostatic interactions, there are further complications to

1734-471: A simple ionic compound (with positive and negative ions) such as sodium chloride (common salt) is easily soluble in a highly polar solvent (with some separation of positive (δ+) and negative (δ-) charges in the covalent molecule) such as water , as thus the sea is salty as it accumulates dissolved salts since early geological ages. The solubility is favored by entropy of mixing (Δ S ) and depends on enthalpy of dissolution (Δ H ) and

1836-463: A solute's different solubilities in hot and cold solvent. A few exceptions exist, such as certain cyclodextrins . For condensed phases (solids and liquids), the pressure dependence of solubility is typically weak and usually neglected in practice. Assuming an ideal solution , the dependence can be quantified as: where the index i {\displaystyle i} iterates the components, N i {\displaystyle N_{i}}

1938-490: A solution with polymer concentration ϕ {\displaystyle \phi } and volume λ 1 λ 2 λ 3 V 0 {\displaystyle \lambda _{1}\lambda _{2}\lambda _{3}V_{0}} . The free energy density change in this mixing step is given as where on the right-hand side, the first term is the Flory–Huggins energy density of

2040-449: A solvent depends primarily on its polarity . For example, a very polar ( hydrophilic ) solute such as urea is very soluble in highly polar water, less soluble in fairly polar methanol , and practically insoluble in non-polar solvents such as benzene . In contrast, a non-polar or lipophilic solute such as naphthalene is insoluble in water, fairly soluble in methanol, and highly soluble in non-polar benzene. In even more simple terms

2142-427: A substance in a liquid may also be expressed as the quantity of solute per quantity of solution , rather than of solvent. For example, following the common practice in titration , it may be expressed as moles of solute per litre of solution (mol/L), the molarity of the latter. In more specialized contexts the solubility may be given by the mole fraction (moles of solute per total moles of solute plus solvent) or by

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2244-469: Is a solid formed from a gel by drying with unhindered shrinkage. Xerogels usually retain high porosity (15–50%) and enormous surface area (150–900 m/g), along with very small pore size (1–10 nm). When solvent removal occurs under supercritical conditions, the network does not shrink and a highly porous, low-density material known as an aerogel is produced. Heat treatment of a xerogel at elevated temperature produces viscous sintering (shrinkage of

2346-432: Is about half of its value at 25 °C. The dissolution of calcium hydroxide in water is also an exothermic process (Δ H  < 0). As dictated by the van 't Hoff equation and Le Chatelier's principle , lowe temperatures favorsf dissolution of Ca(OH) 2 . Portlandite solubility increases at low temperature. This temperature dependence is sometimes referred to as "retrograde" or "inverse" solubility. Occasionally,

2448-410: Is an irreversible chemical reaction between the two substances, such as the reaction of calcium hydroxide with hydrochloric acid ; even though one might say, informally, that one "dissolved" the other. The solubility is also not the same as the rate of solution , which is how fast a solid solute dissolves in a liquid solvent. This property depends on many other variables, such as the physical form of

2550-399: Is defined for specific phases . For example, the solubility of aragonite and calcite in water are expected to differ, even though they are both polymorphs of calcium carbonate and have the same chemical formula . The solubility of one substance in another is determined by the balance of intermolecular forces between the solvent and solute, and the entropy change that accompanies

2652-656: Is equal to the solubility of the substance. When the dissolution rate of a pure substance is normalized to the surface area of the solid (which usually changes with time during the dissolution process), then it is expressed in kg/m s and referred to as "intrinsic dissolution rate". The intrinsic dissolution rate is defined by the United States Pharmacopeia . Dissolution rates vary by orders of magnitude between different systems. Typically, very low dissolution rates parallel low solubilities, and substances with high solubilities exhibit high dissolution rates, as suggested by

2754-480: Is extruded around it. Mass fraction (chemistry) In chemistry , the mass fraction of a substance within a mixture is the ratio w i {\displaystyle w_{i}} (alternatively denoted Y i {\displaystyle Y_{i}} ) of the mass m i {\displaystyle m_{i}} of that substance to the total mass m tot {\displaystyle m_{\text{tot}}} of

2856-399: Is high both elastically and electrostatically and hence suppress ionization. Even though this ionization suppression is qualitatively similar to that of Donnan prediction, it is absent without electrostatic consideration and present irrespective of ion partitioning. The combination of both effects as well as gel elasticity determines the volume of the gel at equilibrium. Due to the complexity of

2958-419: Is initially formed by the assembly of particles into a space-spanning network, leading to a phase arrest. In the aging phase, the particles slowly rearrange to form thicker strands, increasing the elasticity of the material. Gels can also be collapsed and separated by external fields such as gravity. Colloidal gels show linear response rheology at low amplitudes. These materials have been explored as candidates for

3060-436: Is just a polymer network, without solvent). This is so because the free energy penalty to stretch an ideal polymer segment N {\displaystyle N} monomers of size b {\displaystyle b} between crosslinks to an end-to-end distance R {\displaystyle R} is approximately given by This is the origin of both gel and rubber elasticity . But one key difference

3162-433: Is less than 0.1 g per 100 mL of solvent. Solubility occurs under dynamic equilibrium, which means that solubility results from the simultaneous and opposing processes of dissolution and phase joining (e.g. precipitation of solids ). A stable state of the solubility equilibrium occurs when the rates of dissolution and re-joining are equal, meaning the relative amounts of dissolved and non-dissolved materials are equal. If

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3264-513: Is like that from above substituting the relation between mass and molar concentration: where c i {\displaystyle c_{i}} is the molar concentration, and M i {\displaystyle M_{i}} is the molar mass of the component i {\displaystyle i} . Mass percentage is defined as the mass fraction multiplied by 100. The mole fraction x i {\displaystyle x_{i}} can be calculated using

3366-776: Is monomer volume, N {\displaystyle N} is polymer strand length and χ {\displaystyle \chi } is the Flory-Huggins energy parameter. Because in a network, the polymer length is effectively infinite, we can take the limit N → ∞ {\displaystyle N\to \infty } and f ( ϕ ) {\displaystyle f(\phi )} reduces to Substitution of this expression into f mix ( λ 1 , λ 2 , λ 3 ) {\displaystyle f_{\text{mix}}(\lambda _{1},\lambda _{2},\lambda _{3})} and addition of

3468-497: Is not an instantaneous process. The rate of solubilization (in kg/s) is related to the solubility product and the surface area of the material. The speed at which a solid dissolves may depend on its crystallinity or lack thereof in the case of amorphous solids and the surface area (crystallite size) and the presence of polymorphism . Many practical systems illustrate this effect, for example in designing methods for controlled drug delivery . In some cases, solubility equilibria can take

3570-408: Is observed to be almost an order of magnitude higher (i.e. about ten times higher) when the redox potential is controlled using a highly oxidizing Fe 3 O 4 -Fe 2 O 3 redox buffer than with a moderately oxidizing Ni - NiO buffer. Solubility (metastable, at concentrations approaching saturation) also depends on the physical size of the crystal or droplet of solute (or, strictly speaking, on

3672-399: Is one way of expressing the composition of a mixture in a dimensionless size ; mole fraction (percentage by moles , mol%) and volume fraction ( percentage by volume , vol%) are others. When the prevalences of interest are those of individual chemical elements , rather than of compounds or other substances, the term mass fraction can also refer to the ratio of the mass of an element to

3774-450: Is only partially by the classical Donnan theory. As a starting point we can neglect the electrostatic interactions among ions. Then at equilibrium, some of the weak acid sites in the gel would dissociate to form A − {\displaystyle {\text{A}}^{-}} that electrostatically attracts positive charged H + {\displaystyle {\text{H}}^{+}} and salt cations leading to

3876-441: Is polymer volume fraction. Suppose the initial gel has a polymer volume fraction of ϕ 0 {\displaystyle \phi _{0}} , the polymer volume fraction after swelling would be ϕ = ϕ 0 / λ 1 λ 2 λ 3 {\displaystyle \phi =\phi _{0}/\lambda _{1}\lambda _{2}\lambda _{3}} since

3978-421: Is stretch by a factor of λ {\displaystyle \lambda } in all three directions. Under the affine network approximation, the mean-square end-to-end distance in the gel increases from initial R 0 2 {\displaystyle R_{0}^{2}} to ( λ R 0 ) 2 {\displaystyle (\lambda R_{0})^{2}} and

4080-474: Is stretched by factors λ 1 {\displaystyle \lambda _{1}} , λ 2 {\displaystyle \lambda _{2}} and λ 3 {\displaystyle \lambda _{3}} in the three orthogonal directions during swelling after being immersed in a solvent phase of initial volume V s 0 {\displaystyle V_{s0}} . The final deformed volume of gel

4182-411: Is that gel contains an additional solvent phase and hence is capable of having significant volume changes under deformation by taking in and out solvent. For example, a gel could swell to several times its initial volume after being immersed in a solvent after equilibrium is reached. This is the phenomenon of gel swelling. On the contrary, if we take the swollen gel out and allow the solvent to evaporate,

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4284-434: Is the mole fraction of the i {\displaystyle i} -th component in the solution, P {\displaystyle P} is the pressure, the index T {\displaystyle T} refers to constant temperature, V i , a q {\displaystyle V_{i,aq}} is the partial molar volume of the i {\displaystyle i} -th component in

4386-421: Is the partial pressure (in atm), and c {\displaystyle c} is the concentration of the dissolved gas in the liquid (in mol/L). The solubility of gases is sometimes also quantified using Bunsen solubility coefficient . In the presence of small bubbles , the solubility of the gas does not depend on the bubble radius in any other way than through the effect of the radius on pressure (i.e.

4488-424: Is then λ 1 λ 2 λ 3 V 0 {\displaystyle \lambda _{1}\lambda _{2}\lambda _{3}V_{0}} and the total volume of the system is V 0 + V s 0 {\displaystyle V_{0}+V_{s0}} , that is assumed constant during the swelling process for simplicity of treatment. The swollen state of

4590-501: Is used for the mass fraction of vapor in the steam. In alloys, especially those of noble metals, the term fineness is used for the mass fraction of the noble metal in the alloy. The mass fraction is independent of temperature until phase change occurs. The mixing of two pure components can be expressed introducing the (mass) mixing ratio of them r m = m 2 m 1 {\displaystyle r_{m}={\frac {m_{2}}{m_{1}}}} . Then

4692-413: Is used to fill the plastic tubes containing the fibers. The main purpose of the gel is to prevent water intrusion if the buffer tube is breached, but the gel also buffers the fibers against mechanical damage when the tube is bent around corners during installation, or flexed. Additionally, the gel acts as a processing aid when the cable is being constructed, keeping the fibers central whilst the tube material

4794-480: Is used to quantify the solubility of gases in solvents. The solubility of a gas in a solvent is directly proportional to the partial pressure of that gas above the solvent. This relationship is similar to Raoult's law and can be written as: where k H {\displaystyle k_{\rm {H}}} is a temperature-dependent constant (for example, 769.2 L · atm / mol for dioxygen (O 2 ) in water at 298 K), p {\displaystyle p}

4896-520: Is usually solid or liquid. Both may be pure substances, or may themselves be solutions. Gases are always miscible in all proportions, except in very extreme situations, and a solid or liquid can be "dissolved" in a gas only by passing into the gaseous state first. The solubility mainly depends on the composition of solute and solvent (including their pH and the presence of other dissolved substances) as well as on temperature and pressure. The dependency can often be explained in terms of interactions between

4998-497: The critical temperature ), the solubility of ionic solutes tends to decrease due to the change of properties and structure of liquid water; the lower dielectric constant results in a less polar solvent and in a change of hydration energy affecting the Δ G of the dissolution reaction. Gaseous solutes exhibit more complex behavior with temperature. As the temperature is raised, gases usually become less soluble in water (exothermic dissolution reaction related to their hydration) (to

5100-441: The elastic properties and firmness of the organogel. Often, these systems are based on self-assembly of the structurant molecules. (An example of formation of an undesired thermoreversible network is the occurrence of wax crystallization in petroleum .) Organogels have potential for use in a number of applications, such as in pharmaceuticals , cosmetics, art conservation, and food. A xerogel / ˈ z ɪər oʊ ˌ dʒ ɛ l /

5202-485: The hydrophobic effect . The free energy of dissolution ( Gibbs energy ) depends on temperature and is given by the relationship: Δ G = Δ H – TΔ S . Smaller Δ G means greater solubility. Chemists often exploit differences in solubilities to separate and purify compounds from reaction mixtures, using the technique of liquid-liquid extraction . This applies in vast areas of chemistry from drug synthesis to spent nuclear fuel reprocessing. Dissolution

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5304-427: The mass fraction at equilibrium (mass of solute per mass of solute plus solvent). Both are dimensionless numbers between 0 and 1 which may be expressed as percentages (%). For solutions of liquids or gases in liquids, the quantities of both substances may be given volume rather than mass or mole amount; such as litre of solute per litre of solvent, or litre of solute per litre of solution. The value may be given as

5406-412: The reagents have been dissolved in a suitable solvent. Water is by far the most common such solvent. The term "soluble" is sometimes used for materials that can form colloidal suspensions of very fine solid particles in a liquid. The quantitative solubility of such substances is generally not well-defined, however. The solubility of a specific solute in a specific solvent is generally expressed as

5508-518: The specific surface area or molar surface area of the solute). For quantification, see the equation in the article on solubility equilibrium . For highly defective crystals, solubility may increase with the increasing degree of disorder. Both of these effects occur because of the dependence of solubility constant on the Gibbs energy of the crystal. The last two effects, although often difficult to measure, are of practical importance. For example, they provide

5610-491: The Earth orbit and its rotation axis progressively change and modify the solar irradiance at the Earth surface, temperature starts to increase. When a deglaciation period is initiated, the progressive warming of the oceans releases CO 2 into the atmosphere because of its lower solubility in warmer sea water. In turn, higher levels of CO 2 in the atmosphere increase the greenhouse effect and carbon dioxide acts as an amplifier of

5712-461: The Noyes-Whitney equation. Solubility constants are used to describe saturated solutions of ionic compounds of relatively low solubility (see solubility equilibrium ). The solubility constant is a special case of an equilibrium constant . Since it is a product of ion concentrations in equilibrium, it is also known as the solubility product . It describes the balance between dissolved ions from

5814-454: The charged nature of H + {\displaystyle {\text{H}}^{+}} and A − {\displaystyle {\text{A}}^{-}} , electrostatic interactions with other ions in the systems. This is effectively a reacting system governed by acid-base equilibrium modulated by electrostatic effects, and is relevant in drug delivery , sea water desalination and dialysis technologies. Due to

5916-791: The concentration of a saturated solution of the two. Any of the several ways of expressing concentration of solutions can be used, such as the mass , volume , or amount in moles of the solute for a specific mass, volume, or mole amount of the solvent or of the solution. In particular, chemical handbooks often express the solubility as grams of solute per 100 millilitres of solvent (g/(100 mL), often written as g/100 ml), or as grams of solute per decilitre of solvent (g/dL); or, less commonly, as grams of solute per litre of solvent (g/L). The quantity of solvent can instead be expressed in mass, as grams of solute per 100 grams of solvent (g/(100 g), often written as g/100 g), or as grams of solute per kilogram of solvent (g/kg). The number may be expressed as

6018-403: The coupled acid-base equilibrium, electrostatics and network elasticity, only recently has such system been correctly recreated in computer simulations . Some species secrete gels that are effective in parasite control. For example, the long-finned pilot whale secretes an enzymatic gel that rests on the outer surface of this animal and helps prevent other organisms from establishing colonies on

6120-402: The driving force for precipitate aging (the crystal size spontaneously increasing with time). The solubility of a given solute in a given solvent is function of temperature. Depending on the change in enthalpy (Δ H ) of the dissolution reaction, i.e. , on the endothermic (Δ H  > 0) or exothermic (Δ H  < 0) character of the dissolution reaction, the solubility of

6222-514: The elastic energy of one stand can be written as where R ref {\displaystyle R_{\text{ref}}} is the mean-square fluctuation in end-to-end distance of one strand. The modulus of the gel is then this single-strand elastic energy multiplied by strand number density ν = ϕ / N b 3 {\displaystyle \nu =\phi /Nb^{3}} to give This modulus can then be equated to osmotic pressure (through differentiation of

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6324-439: The elastic nature of the gel, the dispersion of A − {\displaystyle {\text{A}}^{-}} in the system is constrained and hence, there will be a partitioning of salts ions and H + {\displaystyle {\text{H}}^{+}} inside and outside the gel, which is intimately coupled to the polyelectrolyte degree of ionization. This ion partitioning inside and outside

6426-445: The extending fluid. Virtually any fluid can be used as an extender including water ( hydrogels ), oil, and air ( aerogel ). Both by weight and volume, gels are mostly fluid in composition and thus exhibit densities similar to those of their constituent liquids. Edible jelly is a common example of a hydrogel and has approximately the density of water. Polyionic polymers are polymers with an ionic functional group. The ionic charges prevent

6528-493: The extent of solubility for a given application. For example, U.S. Pharmacopoeia gives the following terms, according to the mass m sv of solvent required to dissolve one unit of mass m su of solute: (The solubilities of the examples are approximate, for water at 20–25 °C.) The thresholds to describe something as insoluble, or similar terms, may depend on the application. For example, one source states that substances are described as "insoluble" when their solubility

6630-416: The final swollen gel, the second is associated with the initial gel and the third is of the pure solvent prior to mixing. Substitution of ϕ = ϕ 0 / λ 1 λ 2 λ 3 {\displaystyle \phi =\phi _{0}/\lambda _{1}\lambda _{2}\lambda _{3}} leads to Note that the second term is independent of

6732-627: The formation of tightly coiled polymer chains. This allows them to contribute more to viscosity in their stretched state, because the stretched-out polymer takes up more space. This is also the reason gel hardens. See polyelectrolyte for more information. A colloidal gel consists of a percolated network of particles in a fluid medium, providing mechanical properties , in particular the emergence of elastic behaviour. The particles can show attractive interactions through osmotic depletion or through polymeric links. Colloidal gels have three phases in their lifespan: gelation, aging and collapse. The gel

6834-430: The formula where M i {\displaystyle M_{i}} is the molar mass of the component i {\displaystyle i} , and M ¯ {\displaystyle {\bar {M}}} is the average molar mass of the mixture. Replacing the expression of the molar-mass products, In a spatially non-uniform mixture, the mass fraction gradient gives rise to

6936-404: The free energy) to give the same equation as we found above. Consider a hydrogel made of polyelectrolytes decorated with weak acid groups that can ionize according to the reaction is immersed in a salt solution of physiological concentration. The degree of ionization of the polyelectrolytes is then controlled by the pH {\displaystyle {\text{pH}}} and due to

7038-414: The gel is analogous to the partitioning of ions across a semipemerable membrane in classical Donnan theory, but a membrane is not needed here because the gel volume constraint imposed by network elasticity effectively acts its role, in preventing the macroions to pass through the fictitious membrane while allowing ions to pass. The coupling between the ion partitioning and polyelectrolyte ionization degree

7140-627: The gel is now completely characterized by stretch factors λ 1 {\displaystyle \lambda _{1}} , λ 2 {\displaystyle \lambda _{2}} and λ 3 {\displaystyle \lambda _{3}} and hence it is of interest to derive the deformation free energy as a function of them, denoted as f gel ( λ 1 , λ 2 , λ 3 ) {\displaystyle f_{\text{gel}}(\lambda _{1},\lambda _{2},\lambda _{3})} . For analogy to

7242-478: The gel would shrink to roughly its original size. This gel volume change can alternatively be introduced by applying external forces. If a uniaxial compressive stress is applied to a gel, some solvent contained in the gel would be squeezed out and the gel shrinks in the applied-stress direction. To study the gel mechanical state in equilibrium, a good starting point is to consider a cubic gel of volume V 0 {\displaystyle V_{0}} that

7344-479: The general warming. A popular aphorism used for predicting solubility is " like dissolves like " also expressed in the Latin language as " Similia similibus solventur ". This statement indicates that a solute will dissolve best in a solvent that has a similar chemical structure to itself, based on favorable entropy of mixing . This view is simplistic, but it is a useful rule of thumb. The overall solvation capacity of

7446-475: The historical treatment of rubber elasticity and mixing free energy, f gel ( λ 1 , λ 2 , λ 3 ) {\displaystyle f_{\text{gel}}(\lambda _{1},\lambda _{2},\lambda _{3})} is most often defined as the free energy difference after and before the swelling normalized by the initial gel volume V 0 {\displaystyle V_{0}} , that is,

7548-416: The hydrogel structure to obtain nanocomposites with tailored functionality. Nanocomposite hydrogels can be engineered to possess superior physical, chemical, electrical, thermal, and biological properties. Many gels display thixotropy – they become fluid when agitated, but resolidify when resting. In general, gels are apparently solid, jelly-like materials. It is a type of non-Newtonian fluid . By replacing

7650-488: The initial state. On the other hand, the mixing term f mix ( λ 1 , λ 2 , λ 3 ) {\displaystyle f_{\text{mix}}(\lambda _{1},\lambda _{2},\lambda _{3})} is usually treated by the Flory-Huggins free energy of concentrated polymer solutions f ( ϕ ) {\displaystyle f(\phi )} , where ϕ {\displaystyle \phi }

7752-485: The liquid with gas it is possible to prepare aerogels , materials with exceptional properties including very low density, high specific surface areas , and excellent thermal insulation properties. A gel is in essence the mixture of a polymer network and a solvent phase. Upon stretching, the network crosslinks are moved further apart from each other. Due to the polymer strands between crosslinks acting as entropic springs , gels demonstrate elasticity like rubber (which

7854-485: The mass fractions of the components will be The mass ratio equals the ratio of mass fractions of components: due to division of both numerator and denominator by the sum of masses of components. The mass fraction of a component in a solution is the ratio of the mass concentration of that component ρ i (density of that component in the mixture) to the density of solution ρ {\displaystyle \rho } . The relation to molar concentration

7956-454: The mixture. Expressed as a formula, the mass fraction is: Because the individual masses of the ingredients of a mixture sum to m tot {\displaystyle m_{\text{tot}}} , their mass fractions sum to unity: Mass fraction can also be expressed, with a denominator of 100, as percentage by mass (in commercial contexts often called percentage by weight , abbreviated wt.% or % w/w ; see mass versus weight ). It

8058-429: The network contribution leads to This provides the starting point to examining the swelling equilibrium of a gel network immersed in solvent. It can be shown that gel swelling is the competition between two forces, one is the osmotic pressure of the polymer solution that favors the take in of solvent and expansion, the other is the restoring force of the polymer network elasticity that favors shrinkage. At equilibrium,

8160-427: The number of monomers remains the same while the gel volume has increased by a factor of λ 1 λ 2 λ 3 {\displaystyle \lambda _{1}\lambda _{2}\lambda _{3}} . As the polymer volume fraction decreases from ϕ 0 {\displaystyle \phi _{0}} to ϕ {\displaystyle \phi } ,

8262-447: The other with the mixing of the network with the solvent. Hence, we write We now consider the two contributions separately. The polymer elastic deformation term is independent of the solvent phase and has the same expression as a rubber, as derived in the Kuhn's theory of rubber elasticity : where G 0 {\displaystyle G_{0}} denotes the shear modulus of

8364-439: The particles ( atoms , molecules , or ions ) of the two substances, and of thermodynamic concepts such as enthalpy and entropy . Under certain conditions, the concentration of the solute can exceed its usual solubility limit. The result is a supersaturated solution , which is metastable and will rapidly exclude the excess solute if a suitable nucleation site appears. The concept of solubility does not apply when there

8466-401: The phenomenon of diffusion . Solubility In chemistry , solubility is the ability of a substance , the solute , to form a solution with another substance, the solvent . Insolubility is the opposite property, the inability of the solute to form such a solution. The extent of the solubility of a substance in a specific solvent is generally measured as the concentration of

8568-426: The picture. Consider the case of two adjacent, initially uncharged acid sites HA {\displaystyle {\text{HA}}} are both dissociated to form A − {\displaystyle {\text{A}}^{-}} . Since the two sites are both negatively charged, there will be a charge-charge repulsion along the backbone of the polymer than tends to stretch the chain. This energy cost

8670-405: The salt and undissolved salt. The solubility constant is also "applicable" (i.e. useful) to precipitation , the reverse of the dissolving reaction. As with other equilibrium constants, temperature can affect the numerical value of solubility constant. While the solubility constant is not as simple as solubility, the value of this constant is generally independent of the presence of other species in

8772-414: The solubility of gas in the liquid in contact with small bubbles is increased due to pressure increase by Δ p  = 2γ/ r ; see Young–Laplace equation ). Henry's law is valid for gases that do not undergo change of chemical speciation on dissolution. Sieverts' law shows a case when this assumption does not hold. The carbon dioxide solubility in seawater is also affected by temperature, pH of

8874-483: The solubility per mole of solution is usually computed and quoted as if the solute does not dissociate or form complexes—that is, by pretending that the mole amount of solution is the sum of the mole amounts of the two substances. The extent of solubility ranges widely, from infinitely soluble (without limit, i.e. miscible ) such as ethanol in water, to essentially insoluble, such as titanium dioxide in water. A number of other descriptive terms are also used to qualify

8976-401: The solute in a saturated solution, one in which no more solute can be dissolved. At this point, the two substances are said to be at the solubility equilibrium . For some solutes and solvents, there may be no such limit, in which case the two substances are said to be " miscible in all proportions" (or just "miscible"). The solute can be a solid , a liquid , or a gas , while the solvent

9078-453: The solute is not recovered upon evaporation of the solvent, the process is referred to as solvolysis. The thermodynamic concept of solubility does not apply straightforwardly to solvolysis. When a solute dissolves, it may form several species in the solution. For example, an aqueous solution of cobalt(II) chloride can afford [Co(H 2 O) 6 ] , [CoCl(H 2 O) 5 ] , CoCl 2 (H 2 O) 2 , each of which interconverts. Solubility

9180-587: The solution, V i , c r {\displaystyle V_{i,cr}} is the partial molar volume of the i {\displaystyle i} -th component in the dissolving solid, and R {\displaystyle R} is the universal gas constant . The pressure dependence of solubility does occasionally have practical significance. For example, precipitation fouling of oil fields and wells by calcium sulfate (which decreases its solubility with decreasing pressure) can result in decreased productivity with time. Henry's law

9282-557: The solution, and by the carbonate buffer. The decrease of solubility of carbon dioxide in seawater when temperature increases is also an important retroaction factor (positive feedback) exacerbating past and future climate changes as observed in ice cores from the Vostok site in Antarctica . At the geological time scale, because of the Milankovich cycles , when the astronomical parameters of

9384-409: The solvation. Factors such as temperature and pressure will alter this balance, thus changing the solubility. Solubility may also strongly depend on the presence of other species dissolved in the solvent, for example, complex-forming anions ( ligands ) in liquids. Solubility will also depend on the excess or deficiency of a common ion in the solution , a phenomenon known as the common-ion effect . To

9486-415: The solvent and the sum of the two volumes. Moreover, many solids (such as acids and salts ) will dissociate in non-trivial ways when dissolved; conversely, the solvent may form coordination complexes with the molecules or ions of the solute. In those cases, the sum of the moles of molecules of solute and solvent is not really the total moles of independent particles solution. To sidestep that problem,

9588-441: The solvent is removed, all of the substance that had dissolved is recovered. The term solubility is also used in some fields where the solute is altered by solvolysis . For example, many metals and their oxides are said to be "soluble in hydrochloric acid", although in fact the aqueous acid irreversibly degrades the solid to give soluble products. Most ionic solids dissociate when dissolved in polar solvents. In those cases where

9690-466: The stretching factors λ 1 {\displaystyle \lambda _{1}} , λ 2 {\displaystyle \lambda _{2}} and λ 3 {\displaystyle \lambda _{3}} and hence can be dropped in subsequent analysis. Now we make use of the Flory-Huggins free energy for a polymer-solvent solution that reads where v c {\displaystyle v_{c}}

9792-423: The subject discusses the use of hydrogels for nucleus pulposus replacement, cartilage replacement, and synthetic tissue models. Many substances can form gels when a suitable thickener or gelling agent is added to their formula. This approach is common in the manufacture of a wide range of products, from foods to paints and adhesives. In fiber optic communications, a soft gel resembling hair gel in viscosity

9894-536: The surface of these whales' bodies. Hydrogels existing naturally in the body include mucus , the vitreous humor of the eye, cartilage , tendons and blood clots . Their viscoelastic nature results in the soft tissue component of the body, disparate from the mineral-based hard tissue of the skeletal system. Researchers are actively developing synthetically derived tissue replacement technologies derived from hydrogels, for both temporary implants (degradable) and permanent implants (non-degradable). A review article on

9996-435: The term 'hydrogel' in the literature was in 1894. An organogel is a non-crystalline , non-glassy thermoreversible ( thermoplastic ) solid material composed of a liquid organic phase entrapped in a three-dimensionally cross-linked network. The liquid can be, for example, an organic solvent , mineral oil , or vegetable oil . The solubility and particle dimensions of the structurant are important characteristics for

10098-528: The total mass of a sample. In these contexts an alternative term is mass percent composition . The mass fraction of an element in a compound can be calculated from the compound's empirical formula or its chemical formula . Percent concentration does not refer to this quantity. This improper name persists, especially in elementary textbooks. In biology, the unit "%" is sometimes (incorrectly) used to denote mass concentration, also called mass/volume percentage . A solution with 1   g of solute dissolved in

10200-493: The two effects exactly cancel each other in principle and the associated λ 1 {\displaystyle \lambda _{1}} , λ 2 {\displaystyle \lambda _{2}} and λ 3 {\displaystyle \lambda _{3}} define the equilibrium gel volume. In solving the force balance equation, graphical solutions are often preferred. In an alternative, scaling approach, suppose an isotropic gel

10302-458: The two substances and the manner and intensity of mixing. The concept and measure of solubility are extremely important in many sciences besides chemistry, such as geology , biology , physics , and oceanography , as well as in engineering , medicine , agriculture , and even in non-technical activities like painting , cleaning , cooking , and brewing . Most chemical reactions of scientific, industrial, or practical interest only happen after

10404-642: The xerogel due to a small amount of viscous flow) which results in a denser and more robust solid, the density and porosity achieved depend on the sintering conditions. Nanocomposite hydrogels or hybrid hydrogels, are highly hydrated polymeric networks, either physically or covalently crosslinked with each other and/or with nanoparticles or nanostructures. Nanocomposite hydrogels can mimic native tissue properties, structure and microenvironment due to their hydrated and interconnected porous structure. A wide range of nanoparticles, such as carbon-based, polymeric, ceramic, and metallic nanomaterials can be incorporated within

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