The phrase soft matterit is generally used to define materials which, although presenting in the condensed phase, are neither simple liquids nor crystalline solids. In fact, the ms occupies an intermediate position between the liquid state, in which the molecules are able to freely exchange their positions, and the crystalline solid state, in which they are arranged at the vertices of a lattice. In soft materials, molecules, even without occupying fixed positions, are in some way constrained and do not have the freedom to exchange among themselves. The ms is of great importance in daily life: in fact it is present, for example, in paints, adhesives and soaps and, also, in most of the foods. And its role is crucial in the life sciences sector. Other soft materials are found in important industrial processes,
The first large class of soft materials includes polymers made up of macromolecules in which a large number of hydrocarbon-type units are joined together to form flexible chains. A second large class is represented by colloids, where a phase finely divided into particles which can have dimensions between a few tens of nanometers and a few microns is dispersed in a continuous phase. There are different types of these dispersions, depending on the physical form of the dispersed phase: if it is solid, the dispersion is called sol ; if instead it is made up of droplets of an insoluble liquid in the liquid that makes up the continuous phase, an emulsion is present; finally, when the dispersed phase is made up of bubbles of gas, the dispersion is called foam . Another important category is represented by surfactant solutions, which are usually composed of amphiphilic molecules, containing a highly hydrophilic portion, which tends to dissolve in water, and another markedly hydrophobic, i.e. rejected by water. In an aqueous solution the hydrophobic parts of different surfactant molecules join together to generate particular structures called micelles . Liquid crystals are also very important from a scientific and application point of view, in which anisotropic molecular structures can generate states characterized by intermediate orders between those of a simple liquid and a crystalline solid.
The term softrefers to the macroscopic mechanical properties of this type of materials, which are able to flow under certain conditions. In general, they exhibit viscoelastic properties, that is, showing both the tendency to flow, moreover typical of viscous fluids, and the ability to deform when subjected to stress, typical of elastic fluids. There are therefore very clear differences with respect to the behavior of a crystalline solid, whose molecules appear tightly packed. If a crystalline solid is subjected to compression, its molecules are pushed towards each other causing an atomic excitation that requires energy in the order of a few electron volts per atom. Even minimal compressions are therefore associated with energies very close to those of bond between the atoms and consequently the solids are subject to brittle fracture. Soft materials, on the contrary, are able to withstand very high compressions without suffering any visible damage, despite the fact that their fracture energy is much less. Consider, for example, a polymeric gel, usually characterized by a high resilience, i.e. by a high ability to resist impacts which can be related to the poor connectivity at the molecular level of the material. The polymer molecules form a lattice that can be easily distorted the instant the gel is compressed. The individual macromolecules are flexible, and the molecular bonds inside them can rotate and therefore allow an elongation of the chains without the atomic distortions typical of crystalline solids occurring. The polymer gels also have rather low densities and this allows the polymer chains to have sufficient space to be able to distort freely without causing local molecular thickenings. It must also be taken into account that each polymer chain is not fixed in a single configuration, but fluctuates from one random configuration to another. Since the links in the chain have independent orientations, for certain characteristic dimensions the path described by a polymeric chain in space is random. Compression has the effect of reducing these dimensions by limiting the number of possible configurations. The distortion of the polymer thus causes a decrease in entropy, which requires that work be carried out on the system. In addition, a voltage is produced in the polymer molecule. In any case, the energies involved are far less than those required in the compressions of the crystalline solids, and are in the order ofkT ( k is Boltzmann’s constant and T is the absolute temperature), which represents the thermal energy and that, at ambient temperature, that is approximately 1 / 40 electron volts.
The various soft materials, although so different from each other, have some very significant characteristics in common. First of all, the length scales that define their structures, between the atomic and macroscopic dimensions, and which are called mesoscopic. Colloidal particles are typically smaller than one micron, the polymer chains have lengths in the order of a few tens of nanometers. The theoretical models used to describe these materials must take into account this variety of dimensions, emancipating themselves from the details relating to the atomic scale. It is interesting to note that a universal behavior common to various substances emerges: for example, many aspects of the behavior of polymers do not derive from the chemical characteristics of the individual units that compose them, but from the topological ones deriving from the fact that a polymer molecule is long, flexible and cannot be crossed by other chains. A typical example is represented by the viscosity of a polymer, which depends, according to a power law, on the molecular weight of the chains. The optical properties of a dispersion also depend on the average size of the particles that compose it according to a power law. Thermal fluctuations are also a very important factor in determining the characteristics of soft materials. In fact, despite being larger than the atomic dimensions, the structural units that make up the soft materials are generally small enough to suffer the effects of Brownian motion. Not only that, but also the typical energies associated with the formation of the structures present in a soft material are comparable, in order of magnitude, to thermal energy. They should therefore be visualized as subject to continuous motion: the polymer molecules in solution twist and turn continuously,
Finally, the materials are generally characterized by the ability to form structures on a mesoscopic level. Thanks to the importance of Brownian motion, soft materials are able to evolve towards equilibrium, which however must be conceived in a dynamic way. Furthermore, the subtle balances between enthalpic and entropic factors often generate a very varied phase behavior, in which even very complex structures can spontaneously form. At a higher level, supramolecular structures often form .
The types of structures that can occur in soft materials are very different. There are remarkable phenomena of intramolecular organization. A significant example is represented by the helical structure assumed by many polypeptides, due to the formation of hydrogen bonds between neighboring monometric units, with a mechanism not unlike that which governs the formation of the DNA double helix.
Among the most important rearrangement phenomena offered by systems consisting of molecules of a single type are those that can occur in molten copolymers. A copolymer is a polymer chain that is not chemically homogeneous, but has monometric units of two different types, A and B. The succession of the two types of units in the chain can be alternated, when a unit A is always followed by a chain B , or random. In block copolymers, the chains have two separate blocks, one composed entirely of type A units and the other of type B units. If the two portions of a block copolymer are not mutually soluble, in the molten state they tend to separate, but this it is prevented by the fact that the two parts belong to the same chain. Consequently in the fusion microdomains are created, each of which contains the portion A or the portion B of the different copolymer chains. By increasing the size of the domains, the interfacial area between the regions occupied by the portions A and those occupied by the portions B decreases, with a consequent decrease in free energy. At the same time, however, this causes the chains to lengthen, reducing their entropy. In the end, by balancing these two conflicting contributions,A occupied by the blocks A. If ϕ A is small, less than 0 , 2 , spherical domains of A are formed in a matrix of B, while if ϕ A is approximately equal to 0 , 3, the portion A shaped of the cylindrical domains . When, on the other hand, the volumetric fractions occupied by A and B are comparable, lamellar structures are generated.
As mentioned above, other rather well-known examples of organization are represented by the formation of micelles in aqueous surfactant solutions. This process is caused by the so-called hydrophobic effect, which justifies why water and hydrocarbon substances are not mutually miscible. This derives from a local rearrangement of water molecules in tetrahedral structures that is created every time hydrocarbon molecules come to find themselves in an aqueous environment giving rise to a decrease in entropy. The phase separation between water and hydrocarbons usually takes place on a macroscopic scale, but in the case of surfactants, which have an amphiphilic character, this hydrophobic effect causes mesoscopic formation of structures, the micelles, which generally have dimensions that do not exceed a few nanometers. It is the presence of groups with markedly different affinities towards water which endow the surfactants with amphiphilic properties. Often it is an ionic head attached to a hydrocarbon chain. The most common surfactants are salts of fatty acids. These molecules, placed in an aqueous solution, above a certain critical concentration have a propensity to assemble together to form structures that are usually spherical, but which can also take cylindrical or double-layer forms ( The most common surfactants are salts of fatty acids. These molecules, placed in an aqueous solution, above a certain critical concentration have a propensity to assemble together to form structures that are usually spherical, but which can also take cylindrical or double-layer forms ( The most common surfactants are salts of fatty acids. These molecules, placed in an aqueous solution, above a certain critical concentration have a propensity to assemble together to form structures that are usually spherical, but which can also take cylindrical or double-layer forms (Fig. 1 ). There are rather simple geometric criteria to predict the type of structure formed by the surfactant molecules, depending on the value assumed by the ratio v / l c to 0 , where v represents the volume occupied by the hydrocarbon tail, at 0 the area of the head group at the surface of the aggregate and l c the critical length of the chain, related to the length of the hydrocarbon chain, completely extended.
Unlike liquid-crystalline mesophases, liotropic ones are formed in solution, and their formation is controlled by the concentration of a species which usually has an amphiphilic character. The ability to form micelles has been emphasized for surfactants, but in reality they exhibit quite varied phase behavior with increasing concentration. At low concentrations the micelles do not show any type of order related to their positions, but at slightly higher concentrations they tend to manifest repulsive interactions, which can derive from steric effects and of excluded volume. Consequently, the micelles begin to occupy the space more efficiently, settling down, for example, at the vertices of cubes, the sides of which have lengths in theFig. 2 A ), therefore considerably larger than the atomic dimensions. The effect, as regards the macroscopic physical form and the behavior of the materials, is remarkable, given that in these conditions the surfactant solutions take on the appearance of a gel, with very high viscosities, and exhibit a certain flow limit, therefore it is necessary to subject the material to a minimum stress so that it begins to flow. By further increasing the concentration of the surfactant, the micelles take on a cylindrical shape and organize themselves on hexagonal structures, thus forming columnar liquid crystals ( fig. 2 B ). At even higher concentrations the micelles form flat bilayers, which constitute a smectic phase (Fig. 2 C ). In reality, the description given is rather simplified, because the phase behavior of the surfactants is very complicated and depends on the size of the hydrophilic head and the hydrophobic tail, on the ionic strength of the solution, on the possible presence of co-surfactants, etc.
Colloidal dispersions and polymers
The two main classes of soft materials, colloidal dispersions and polymers, can be considered as ways through which polyatomic aggregates can be obtained. In the first case, the dispersed form is often used to obtain materials with particular physical characteristics. For example, the carbon black dispersed in the ink, due to its colloidal nature, shows an efficient absorption of the incident light, or the dispersions in which granules of magnetite are encapsulated in polystyrene particles, in turn dispersed in water, allow to obtain polymer-coated ferrofluids. Sometimes, however, the dispersed form serves to impart particular chemical properties to materials, as in the case of photosensitive granules in photographic films,
Colloidal dispersions can be produced by chopping masses, more or less large, of materials by mechanical methods. The particles obtained in this way are subsequently dispersed in a continuous phase. However, it is not easy to provide sufficient mechanical stresses to obtain colloidal-sized particles, especially when the mass is in the solid state. Furthermore, the dispersions obtained in this way usually consist of particles with a large particle size distribution, and sometimes of irregular shapes. Therefore in general it is preferred to produce colloidal dispersions by resorting to methods by which, in some way, the molecules of a substance, dissolved in a continuous phase, are induced to join together to form the dispersion, such as, for example, through a nucleation process. By operating in such a way that nucleation is completed in a short time, it is possible to obtain dispersions in which the particle sizes are characterized by a rather narrow size distribution.
In any case, colloidal particles have a tendency to join together, under the effect of the attractive forces of van der Waals which become more and more consistent as the particles grow in size. The dispersed state is, in most cases, thermodynamically disadvantaged, since it involves, compared to the massive one, an energy expenditure linked to the formation of the interfacial surface. However, it is possible to stabilize the dispersion, creating a potential barrier between the particles which must be at least greater than kT , or of the energy associated with the molecular motions. It can be obtained through electrostatic or steric effects, or through the combination of the two, through electrosteric effects. Electrostatic stabilization is usually obtained by attaching electrically charged groups to the surface of the particles by chemical or physical adsorption. In this way, locally unbalanced charges are created which cause the onset of Coulombian repulsions between the particles.
The situation is actually a little more complex if the particles are dispersed in water, since ions are always present in the water, which shield electrostatic interactions. A charged surface particle attracts counterions, a part of which binds tightly to the surface of the particle itself forming the Stern layer, while the remaining part forms a diffuse concentration profile, creating an electrostatic potential which, under certain conditions, can be expressed with a function that exponentially decays with the gradual removal from the surface of the particle. By combining the attractive potential that derives from van der Waals forces with the electrostatic repulsive potential, it is possible to obtain the interaction potential between two particles ( fig. 3), as established by the DLVO theory (from the initials of B. Derjaguin, LD Landau, EJ Verwej and T. Overbeek). Since the rapidity with which the electrostatic potential decays when moving away from the surface of the particle increases as the ionic strength of the continuous phase increases, in an electrostatically stabilized dispersion it is possible to prevail the attractive forces and induce flocculation between the particles, adding sufficient quantities of salts.
The steric stabilization of the dispersions is instead obtained by making adsorb polymer molecules on the surface of the particles. Bringing the particles closer together causes compression of the chains of these polymers, compression which induces an osmotic repulsion mechanism: by restricting the number of conformations accessible to each chain, an increase in entropy is caused. Also in this way it is therefore possible to create a potential barrier to flocculation, which unlike electrostatic stabilization is not sensitive to the concentration of salts in solution, but depends on the interactions between polymer and continuous phase, and on temperature. Block copolymers are generally the most efficient systems in imparting steric stabilization: one block must have affinity for the dispersed phase, the other for the continuous phase. Electrosteric stabilization is obtained by substances capable of combining the two electrostatic and steric mechanisms, and is typically obtained bypolyelectrolytes .
If a certain amount of electrolyte is added to an electrostatically stabilized dispersion, or if the temperature is changed to a dispersion that is sterically stabilized, it is possible to induce destabilization, causing the particles to flocculate. The particles, endowed with a certain thermal energy, move under the effect of their Brownian motions and collide, and since they are no longer equipped with any barrier that stabilizes them, each collision causes flocculation. At first doublets and triplets are formed, then larger and larger clusters which, at a certain point, being too large to be subject to Brownian motion, settle.
A flocculation process that has attracted particular attention and that has been widely studied is the so-called diffusive growth process, in which the cluster is built by adding the particles one by one to each other, in conditions of infinite dilution. It is assumed that flocculation occurs with a very high speed, at the infinite limit, and consequently the formation of the cluster is kinetically limited by the diffusion of the particles. In these clusters the particles follow one another following a random path, thus forming highly branched, open, apparently disordered structures typical of fractal systems. For these types of flakes applies a scaling law of the type at k/ In = k exp ( 1 / D f ), where a is the radius of the single particle, in k the radius of the floc, k the number of particles contained therein and D f a parameter called fractal dimension , which is worth 1 , 7 if this aggregation occurs in a two-dimensional space, and 2 , 5if instead it takes place in a three-dimensional space. Diffusional aggregation has many affinities with various growth processes, albeit very different physically, such as the growth of bacterial colonies.
Polymer synthesis can be conceived as another way of forming polyatomic structures by binding small molecules together in a flexible chain. The relative directions of subsequent bonds between the molecules are quite random. The directional correlation between the bonds becomes almost negligible after a few bond lengths, so that the statistical properties of a long polymer chain are those of a random path. However, it should be noted that the ‘random path’ model does not fully describe the conformation of a polymer in solution, and this is due to the fact that it does not take into consideration any impediment to the possibility that the path returns to a position already previously visited, while it is necessary to take into account the fact that the individual monometric segments repel each other and are mutually impenetrable. If the polymer chain is perfectly described by a random path, its dimensions, described e.g. from the turning radius, they are proportional to the power1 / 2 of the number N of monomer units contained in the chain, but if we take into account the fact that the monomer units repel each other it is estimated that the radius of gyration depends on the power 3 / 5 of N .
The size of a polymer molecule is consequently greater than that which would be calculated by the effect of the random path and the chain is arranged in a more open structure.
The type of symmetry that is observed in a polymer chain is similar to that which occurs in a cluster of particles, and is called a dilational order; its characteristic aspect is represented by the fact that the properties of the material do not vary when a change of scale is made. However, the flexibility of a polymer provides certain properties that particle aggregates do not possess. The latter are ‘frozen’ in fixed configurations, while the polymer chains are free to explore entire sets of random directions of the bonds. To the randomness of each chain configuration corresponds a certain entropy, which can be exploited as a reservoir of heat and work. A chain can undergo large deformations under the action of weak perturbations, no larger than the thermal energy kT, without however suffering permanent effects. The colloidal dispersions can be concentrated until reaching a dispersed phase content which is corresponding to the “maximum packing” conditions. These are essentially determined by geometric conditions and depend on the particle size distribution of the particles: for a monodisperse dispersion, in which the particles have all the same dimensions, the conditions of maximum packing correspond to a volumetric fraction of particles equal to 0 , 63. Polydisperse distributions make it possible to increase the volumetric fraction which corresponds to the maximum packaging. Polymers, on the other hand, can be concentrated up to volumetric fractions near the unit. In the total absence of solvent, the chains interpenetrate and twist, forming what, with the English term, are called entanglements, so that each chain interacts with hundreds of other chains. Any stress that is imparted on the system is transmitted and can produce large, but reversible deformations in each chain. It is precisely these deformations that produce the return forces that act in elastic materials. The melted polymers respond like elastic materials when the stresses are fast, if instead they are slow, the chains have enough time to free themselves from their entanglements, forgetting about their original distortions: in these conditions they tend to flow, showing at the same time a predominantly viscous rather than elastic behavior. The motion of a polymer chain, bound by the presence of all the other chains to which it is twisted, has been described by a mechanism called reptation. The use of this term, which indicates the movement of many reptiles, in particular of snakes, is explained by the fact that the motion of the polymer chain recalls precisely the movement of a snake that moves its long tail among the blades of grass, which in turn well represent the other chains to which the polymer is twisted and which it cannot cross. The difference between a molten polymer and an elastic material, i.e. a rubber, is represented by the fact that in the latter the entanglements are permanent, and are chemically created by cross-linking reactions.
The rheological behavior of colloidal dispersions is, if possible, more complex than that of polymers, so there is a lack of general models capable of describing it. A. Einstein in 1906 calculated the viscous dissipation produced by the flow around a single sphere, and derived an equation for calculating the viscosity of a dispersion, linear in the volumetric fraction φ of the particles. This equation, however, applies in the case of very dilute systems, for values of φ lower than 3%. Furthermore, in these conditions, the dispersions behave like Newtonian fluids, since their viscosity does not depend on the cutting speed to which they are subjected, nor on the time in which these stresses are applied. As the volumetric fraction of the particles increases, things become more complicated, in the sense that the dispersions begin to show non-Newtonian behaviors and nonlinear dependencies emerge from φ. Viscosity grows exponentially as φ approaches the maximum packing fraction.
With the same volumetric fraction, the flocculated dispersions have higher viscosities than the stable dispersions, because the aggregates shield the flow, which tends to surround them rather than to cross them. However, the flocs, if reversible, tend to break under the action of the stresses and the viscosity therefore tends to return to the value that would compete with the stable dispersion. When the particle clusters take on such dimensions as to pervade the entire dispersion, this has elastic properties, in addition to showing a certain resistance to sliding, associated with the stress necessary to break this diffuse structure.
Interestingly, if the ionic strength of the continuous phase is very low, electrostatically stabilized dispersions can also take on a pseudocrystalline order due to the repulsive forces that tend to block particles on fixed positions: these structures are called colloidal crystals , and they manifest a rather high elastic modulus. When a colloidal crystal is made to flow, imposing a stress greater than its sliding resistance, its structure rearranges itself in order to accommodate a continuous deformation.
Colloidal dispersions often behave like dilating fluids, whose viscosity increases as the cutting speed increases, at fairly high cutting speeds. This type of phenomenon is associated with the formation of layered two-dimensional structures, which are however rather unstable and easily tend to be destroyed.
There are many aspects and phenomena related to the rheology of MS that have not yet been fully understood. Among these it is worth mentioning the reduction of viscous friction, so that few parts per million of polymer added to a liquid are able to significantly alter the way it flows in a tube, delaying the dissipation that occurs near the walls in turbulent flow conditions. Although this effect is widely exploited in practice, it has not yet been fully understood, and is the subject of intense study in the literature.
The importance of MS in life sciences has already been underlined. Traditionally the study of the ms was mainly concerned with systems of biological origin. Most of the glues and paints derived from products of natural origin, as well as most of the fibers. From the second half of the 20th° sec. onwards, the path of science of colloids and polymers and that of biology have progressively separated. On the one hand, in fact, we have witnessed the invention of synthetic polymers and the massive development of the plastic industry; on the other, the discovery of the genetic code and the development of protein crystallography have paved the way for the birth of molecular biology, which has achieved extraordinary success over the past few decades. However, molecular biology and the study of MS still have many themes in common. Suffice it to note that some of the key components of molecular biology, such as e.g. nucleic acids, proteins and polysaccharides are polymers. Furthermore, many of the most important biomembranes, such as e.g. phospholipids, are formed by assembly of amphiphilic molecules, in which two hydrocarbon chains attach to a single polar head group. This type of structure favors the formation of bilayers, even if the biomembranes are actually made up of complex mixtures of phospholipids and other amphiphilic molecules, as you can see inFig. 4 , which shows a schematic diagram of the membrane of a eukaryotic cell. It is now recognized that biomembranes formed by lipids synthesized by abiotic way played a very important role at the origin of life, since they allowed to compartmentalize the first biochemical reactions, thus constituting the prototypes of the cells. Biomembranes have evolved to a much greater degree of sophistication, but their behavior is subject to the same physical principles that allowed the formation of their very important progenitors.