Adrian R. Rennie
Uppsala University
Uppsala, Sweden
This glossary of terms is intended to provide a brief guide to the technical expressions used in the description of the properties of colloids, polymers and interfaces. By necessity, the account of each topic is brief. In some cases an equation is quoted or a quantity is defined mathematically but the description cannot replace a full textbook account of the subject!
The terms are arranged alphabetically but many links are provided within this Guide so that further clarification of the topic can be found. The explanation is at an introductory level. The experienced reader will have to excuse a few simplifications.
Note. In order to use notation that is standard, equations have been set using the symbol definitions for HTML 4. If this is not available to your browser, the equations may be confusing. As most browsers can display these symbols, this method was chosen in place of using large numbers of graphic elements for equations. A previous version used the FONT FACE tag but this is deprecated in HTML 4 and is not supported by all browsers.
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This is a polymerisation reaction that occurs by addition of a monomer to a double bond between two carbon atoms. The reaction will remove the double bond. A typical example is the polymerisation of ethylene (ethene) as follows:
RCH2=CH2 + CH2=CH2 -> RCH2-CH2-CH2=CH2
Repeated addition of ethylene in this way will give rise to a long chain polymer. The product in this example is polyethylene (polyethene or polythene). However many other common polymers are based on olefinic and other monomers that react like this such as styrene, vinyl chloride, butadiene etc.
Adsorption is the property of binding to a surface or interface. It is characterised by a surface excess of one species, Γ, in molecules or moles per unit area at the interface. Surfactants and polymers are both liable to bind to interfaces of solutions. This property may be of crucial importance in imparting colloidal stability to dispersions and in other applications of surfactants such as their use in detergency and as wetting aids. Gases can also adsorb to substrates.
An isotherm is the description of the variation of adsorbed amount at an interface with temperature. Different assumptions about the adsorption process lead to quite different variations of the adsorbed amount (surface excess) with temperature. Some simple models include the Gibbs adsorption equation for solutions and the Langmuir isotherm for adsorption to solid substrates.
The determination of a contact angle of a liquid on a solid is not always a simple equilibrium measurement. Some hysteresis is often displayed when a drop moves on a surface. The angle at the surface that has not been wetted by the liquid (advancing contact angle) may be significantly different to that on the other side of the drop where a previously wetted surface is losing contact (receding contact angle) with the solid.
An aerosol is defined in colloid science as a dispersion of liquid drops in a gas. In some other disciplines such as environmental it may be used more broadly to describe also other fine particles in a gas. This should not be confused with the popular name of a specific anionic surfactant, Aerosol-OT.
Aerosol-OT (abbreviated AOT) is the popular name of a specific anionic surfactant, sodium bis (2-ethylhexyl) sulfosuccinate. This should not be confused with the general term aerosol used for dispersions of a liquid in a gas.
This is the number of molecules that are associated together to form a micelle (or other association colloid). It may depend on the concentration of surfactant. For normal, spherical micelles this may be about ~100 but values can vary from a few molecules to many thousand.
An alternating copolymer is a polymer formed from two monomers in a regular alternating sequence such as that of A and B monomers:
ABABABABAB......
This contrasts with random and block copolymers.
A polymer with no crystalline structure. It could be solid and glassy, liquid like or an elastomer depending on the molecular structure.
Molecules that have parts (hydrophilic) that like aqueous media and other parts that like organic (hydrophobic) phases.
The term anionic polymerisation is used to describe a polymer that is prepared using an anionic initiator. These reactions can be used to produce highly monodisperse polymers.
A surfactant with a head group that has a negative charge when ionised.
Antioxidants are additives for materials such as polymers that inhibit the oxidative degradation of the product. They are usually based on molecules that will react with, and remove radicals as they are formed.
See Aerosol-OT, AOT.
This is a simple measure of the anisotropy of, for example, anisotropic colloidal particles. The precise definition will depend on the shape of the particles. For rods it is useful to use the ratio of length to diameter, for plate-like particles the ratio of diameter to thickness can be used. For ellipsoids of revolution the ratio of the longest to shortest diameter is a convenient measure of anisotropy.
Colloidal dispersions that forms from self-assembly of small molecules such as surfactants to form a stable dispersion are known as association colloids. These can, for example, be micelles, reverse micelles, or microemulsion phases. In contrast to many other colloidal dispersions, these are often thermodynamically stable rather than metastable.
A material is described as 'atactic' if there is no regularity as regards the stereochemistry of substituent groups on successive monomers of a polymer molecule. Tacticity of polymers can influence crystallinity and physical properties. An atactic polymer is random as regards the structure and this contrasts with isotactic and syndiotactic polymers.
See Brunauer-Emmett-Teller Isotherm.
A polymer that occurs naturally, some examples are proteins and carbohydrates. Many materials including DNA, muscle tissue and some components of foods are polymers. These contrast with synthetic polymers that are prepared industrially or in a laboratory.
Birefringence is the property of a material that has a different refractive index in different directions in the sample. Such materials will rotate the plane of polarised light (as the light in one direction will travel faster than another). This is commonly observed in aligned polymers and in some liquid crystal phases that have a preferred direction of alignment. Birefringence can be observed by looking at a sample between crossed-polarisers or with a polarising microscope.
A copolymer in which the different components are separated in to discrete regions of each individual polymer molecule. This can be compared with random copolymers. A di-block copolymer of monomers A and B would have a sequence of the type AAAAAAABBBBBBB.
This is a polymer with branch points in the backbone of the molecule. The physical properties such as viscosity and crystallinity may depend on the extent of branching (as well as the molecular mass).
This is a process of flocculation that occurs when a long polymer is able to adsorb to the surface of more than one colloidal particle. This binds the particle together as a floc.
The random motion of small (colloidal) particles that arises from the collisions with molecules and other particles undergoing thermal motion is known as Brownian motion. This gives rise to diffusion of the particles. This motion was first observed, under a microscope, for pollen grains on the surface of water but is common to all small objects.
This model of adsorption incorporates the possibility of multilayer adsorption of molecules to substrates. It assumes that there is an attractive energy of adsorption for the molecules with a substrate and that there is a different binding energy for further molecules to adsorb to the first layer (i.e. the molecule substrate interaction is not the same as the interaction between the adsorbing molecules. The equation for this adsorption isotherm is:
θ = Z p / [(po - p){ 1 + (Z - 1)(p/po}]
where Z is related to the energy of adsorption:
Z = exp {(E1 - Ev)/ RT }.
The BET isotherm has often been used to model adsorption of inert gases to solid surfaces where it can be used to determine the specific surface area if the area per gas molecule is known.
A narrow bore tube (capillary) through which a known volume of liquid is timed as it flows. This allows the viscosity of the liquid to be determined. This method is convenient for dilute solutions and liquids of low viscosity. It is often used to characterise the molecular mass of polymers using the Mark-Houwink equation.
It is common for the liquids to flow under gravity. In consequence, the levels of liquids in the viscometers have to be carefully maintained. It is also common to perform dilution experiments to measure a series of concentrations. These require elaboration on the simple design. As viscosity is usually dependent sensitively on temperature, the viscometers are normally placed in water baths for measurements.
As there is a profile of flow rates across the diameter of a capillary, this measurement does not correspond to a definite strain rate. However the flow is often chosen to be sufficiently slow that the measurement is effectively made of the zero shear viscosity.
A surfactant with a head group that has a positive charge when ionised.
This is the Flory-Huggins parameter that describes the enthalpy of interaction of a polymer with a solvent or of interaction between two polymers.
This describes the orientation of side groups about, for example, a double bond. If groups are found on opposite sides there is a 'trans' conformation shown schematically as:
/=/ or \=\
The alternative arrangement with both groups on the same side would be shown as:
\=/ or /=\.
Some non-ionic surfactants dissolve less readily in water with increasing temperature. This occurs with, for example, head groups made from ethylene oxide -(CH2CH2O)- . The surfactant therefore comes out of solution on raising the temperature above the Cloud Point. This contrasts with the Krafft boundary seen with ionic surfactants.
See critical micelle concentration.
These are finely divided dispersions of one material in a second continuous phase. The size of colloidal particles is between that of individual small molecules and macroscopic objects. It is convenient to take a limit as at least one dimension should be less than or of the order of a micrometre (10-6 m). The colloid consists of a dispersed phase in a continuous dispersion medium. A wide variety of combinations can exist and some are shown in the following table:
| Name | Dispersed Phase | Dispersion Medium |
|---|---|---|
| Foam | Gas | Liquid |
| Solid Foam | Gas | Solid |
| Sol, paste, latex | Solid | Liquid |
| Smoke | Solid | Gas |
| Emulsions, microemulsions | Liquid | Liquid |
Other association colloids may be formed by self-assembly of small molecules in solutions.
A columnar phase is a liquid crystal in which the molecules or particles are stacked in columns. There is some regular arrangement of the columns (for example hexagonal packing) but there is no spatial correlation between individual particles/molecules in the different columns.
A comb copolymer is a polymer formed side chains that consist of a different monomer. This contrasts with other copolymers where there are two or more different monomers in the main polymer chain.
The term complex fluid is used to describe materials that have deformation properties that are non-Newtonian. The mechanical properties may vary with shear history or strain rate. There are also likely to be changes in viscosity with concentration. Often this term is used as a general expression for colloidal dispersions or the melts and concentrated solutions of polymer.
This is a polymer solution above the overlap concentration. The polymers are entangled with each other. Diffusion is highly hindered and the viscosity will be large as the molecules are constrained to move by reptation.
This is a polymerisation reaction in which a small molecule (such as water) is released (or 'condensed'). Examples would include polyesters (e.g. PET). The chemical formula for such an esterification reaction is:
RCOOH + HOR' -> RCOOR' + H2O
and a molecule of water (H2O) is produced as each pair of monomers reacts. In order to make a polymer it is necessary that each monomer has two functional groups. In the case of a polyester, there are in principle two possibilities. Either each monomer could have both an acid (-COOH) and alcohol (-OH) group or there can be two different monomers, one a difunctional acid and the other a difunctional alcohol.
This is a geometry design for a rheometer with a flat horizontal plate above which is placed a shallow cone (with the point usually flattened). The angle is chosen so that the thickness of the sample increases uniformly with radius. As the relative velocity also increases with radius when one element rotates against the other, the angle can be chosen so that shear gradient is effectively constant across the entire sample.
The particular way that a polymer molecule is arranged is described as its conformation. A polymer with free rotation about some bonds will many different possible conformations. The balance of free energy including both entropy and internal energy of polymer-polymer and polymer-solvent interactions will determine the probability of different conformations. For example, it will be unlikely that a polymer at equilibrium, would be oriented so that all segments were in a line however they cannot overlap each other and bunch closely. The quality of a solvent (see good solvent) will cause a polymer to expand or contract.
This is a polymer with alternating single and double bonds between carbon atoms in the polymer chain. In such a polymer, the electrons can be delocalised. Such materials can form conductors or semiconductors if appropriately doped.
Depending on the surface tension of different materials, a well-defined angle is obtained for the contact of a liquid on a solid. The contact angle is defined as the angle between the tangent to solid-vapour interface and the line of the solid-liquid interface. The angle is chosen to be that containing the liquid. The angle can be zero if the liquid wets the solid surface. The value of the contact angle is related to the different interfacial tensions by Young's equation. The advancing and receding contact angles of a liquid on a surface are often different.
Rheometers can be constructed in two distinct ways. In a controlled strain rheometer, a defined strain is applied to the sample at a controlled frequency or in a particular time sequence. The stress required to deform the sample is then measured. This contrasts with a controlled stress rheometer.
Rheometers can be constructed in two distinct ways. In a controlled stress rheometer, a defined stress is applied to the sample at a controlled frequency or in a particular time sequence. The response of the sample (strain) is then measured. This contrasts with a controlled strain rheometer.
These are polymers that are formed from one or more monomers so that the molecule consists of chemically heterogeneous components. These can be arranged in different ways: see e.g. block copolymers and random copolymers. These molecules contrast with homopolymers.
This geometry of rheological measurement has concentric cylinders with the liquid under test between them. The outer cylinder rotates. Provided that the height of the cylinders (and the liquid) is adequately high there is only a small effect of the liquid between the bases of the cylinders. The gap between the two cylinders should be small compared with the radius to obtain a uniform shear gradient.
In mixed solutions of surfactants and polymers there is often association at a surfactant concentration below the normal critical micelle concentration, (c.m.c.). This is usually caused by binding of surfactant to the polymer molecules. There will be a discontinuity in the slope of a plot of surface tension versus concentration at this concentration.
When salt is added to a charge-stabilised colloid, the screening length is reduced and at a particular concentration the dispersion is no longer stable (such that there is no secondary minimum in the DLVO potential). The concentration of salt at which the particles are no longer stable and begin to aggregate is the critical coagulation concentration (CCC).
This is the concentration above which surfactants form micelles in solution. The change in properties that occur as micelles form is marked by sharp transitions in many physical quantities such as the surface tension of the solution, conductivity, turbidity and nuclear magnetic resonance chemical shifts.
A cross-link joins two polymer molecules together. If there are many cross-links in a material, it will form a continuous network such as a gel or an elastomer. Entanglements may act as temporary or transient cross-links but it is normal to use chemical reactions to produce covalent bonds in order to make elastomers.
This method uses transmission electron microscopy to investigate samples that have been frozen rapidly so as to preserve structure in liquid samples. The cooling of thin films by rapid immersion in refrigerant is designed to form glassy states of a liquid structure so as to avoid artefacts produced by crystallisation. It can be used to observe micelles, vesicles and other structures.
A polymer with regular crystalline structure in some regions. Almost no polymers crystallise perfectly - they are usually semi-crystalline. The overall structure will consist of crystalline regions (often chain folded lamellae) surrounded by amorphous regions of lower density. This structure contrast with that of completely amorphous polymers.
This is an abbreviation for the cationic surfactant, cetyl trimethyl ammonium bromide. It has the molecular formula C16H33N(CH3)3+ Br-. This is a common synthetic surfactant used, for example, in mineral processing.
A cubatic structure is a liquid crystalline arangement of plate-like particles (discs), which has short stacks that are approximately equiaxial. The height (or length) of the stack of particles thus corresponds to the diameter. The short columns tend to pack with neighbours almost orthogonal to each other such that there is no overall preferential orientation. The number of particles in a stack will depend on the axial ratio (thickness to diameter) of the particles.
The Deborah number, De is the ratio of a structural relaxation time, τ, in a sample to the time involved in a rheological measurement, t:
D = τ / t .
This is the number of monomers that combine together to form a polymer molecule. The molecular mass of the polymer, M, is related to the degree of polymerisation, N, and the molecular mass of the monomer, m, by M = N m.
This is a means to measure the surface tension of a liquid by determining the maximal force to pull a ring through the surface. Although the force on a circular line contact can be estimated easily, the actual force is depend on details of the radius of the ring, R and radius of the wire, r, that actually forms the ring as well as the density. The mass of liquid in the meniscus can be significant. The formula relating the surface tension γ with these parameters is:
γ= F / 4 π R
where F is the force additional to the weight of the ring, and R is the radius of the ring. This formula applies if the the thickness of the ring, r, is negligible compared to the radius of the ring. f(r,R) are a set of empirical corrections described by Harkins and Jordan that account for the weight of the liquid in the meniscus.
This is a particular case of a polymer with multiple branches. It is made by successive growth of polyfunctional monomers onto an initiator with multiple functionality. This gives rise to a tree-like structure with the number of branches increasing away from the centre. After a certain number of growth steps, that depends on the functionality of the branch points, growth will be limited by reason of congestion.
This is a force that arises from the osmotic pressure of a second component in a dispersion of colloidal particles. As particles or polymers cannot penetrate gaps smaller than their size. This gives rise to a non-uniform osmotic pressure and attractive interaction when particles approach each other.
Dialysis is the equilibration of a solution with pure solvent or a solution with a different solute or different concentration. If the two solutions are separated by a semi-permeable membrane, solvent molecules and small ions may pass freely while other, larger species in solution such as polymers and colloids are retained in their original concentration in each solution.
Dialysis is a convenient means of preparing solutions with particular counter-ions or at a particular ionic strength as dispersion media for colloids. This process is used in medicine to remove salt in the case of renal failure.
The differential scanning calorimeter (DSC) is an instrument that can make calorimetric measurements of heat capacity and energies of phase transitions by comparing the energy required to heat two different containers (e.g. one empty, one with sample) at the same rate. The ratio of electrical power input to heating rate gives the heat capacity. The areas of peaks observed gives the energy associated with a phase transition.
The importance of DSC measurements for polymers is that a glass transition can be observed as a discontinuity in the heat capacity. The degree of crystallinity of semi-crystalline polymers can be determined from the heat of melting. Melting temperatures can easily be measured and these are often found to depend on heating rates.
This is a dynamic light scattering experiment performed on optically dense (opaque or multiply scattering) samples. Despite the complications of multiple scattering the light that is scattered back from the sample can be interpreted in simple ways to provide information about the motion and hence size of particles in a dispersion.
This is the random thermal motion of molecules or colloidal particles that gives rise to intermixing and collisions. The process is characterised by a random walk that represents a solution of a differential equation known as the diffusion equation. The mean square displacement x2 rather than the displacement, x increases linearly with time, t. The diffusion constant, D is given by:
D = x2 / t
This behaviour is known as Fick's law. The diffusion constant will typically depend on temperature by means of an activated process. If the diffusion involves mixing of two different species such as the swelling of a polymer by a solvent, D may be a function of concentration and more complicated behaviour such as that known as case II diffusion is observed.
The diffusive motion in polymer melts is well predicted by the reptation model.
This is a polymer solution below the overlap concentration. There is little interaction between the polymers that are not entangled with each other. The viscosity will vary linearly with concentration. The term dilute may also be applied to dispersions of colloidal particles that are not interacting with each other.
Measured physical quantities have units such as those of mass, length, time and energy. Some combinations of physical quantities have units that cancel completely. These dimensionless groups, such as Deborah number, Peclet number, Reynolds number etc. are convenient as a means to compare data for different physical systems. In order to determine the dimensions of a quantity, it is convenient to express it in base units. For example the base unit of length is a metre (m) and has dimensions of length (L). Area has dimensions L2 and volume has dimensions L3. Other dimensions are time (T), mass (M). Energy therefore has dimensions M L2 T-2.
DLVO theory accounts for the interaction between charged colloidal particles. It is based on the sum of a van der Waals attractive potential and a screened electrostatic potential arising from the "double layer" potential screened by ions in solution. The name DLVO comes from the two groups who separately developed this model: Deryagin and Landau, and Verwey and Overbeek.
Ionised particles in aqueous solution interact with each other by electrostatic forces. The simple charged interactions are moderated by two effects: counter-ions will tend to associate at least loosely with opposite charges. A further effect is the screening of these electrostatic forces by the bulk concentration of ions in solution. These forces can be calculated by solving the Poisson-Boltzmann equation to determine the distribution of charged species given a thermal distribution of energies.
See Differential Scanning Calorimeter
.Dynamic light scattering (in contrast to static light scattering is sometimes also called photon correlation spectroscopy (PCS). The correlation of scattered photons is measured. This can be used to determine the dynamic behaviour of particles or polymer molecules at length scales determined by the reciprocal of the scattering vector, Q = (4π/λ) sin(θ/2) and if there is a simple exponential decay characterised by a relaxation time, τ, the diffusion coefficient, D and hence hydrodynamic radius, can be determined as follows:
D = 1 / τ Q2
This contrasts with kinematic viscosity. For a definition see Viscosity.
The Einstein relation describes the variation in the viscosity η of a dilute dispersion with the volume fraction, φ, of dispersed material as:
η = η0 (1 + 2.5 φ)
where η0 is the viscosity of the pure solvent.
The elastic modulus is the ratio of stress to strain when a sample undergoes elastic deformation. It will depend on the type of strain. See, for example, shear modulus and Young's modulus.
This is a polymeric material that displays rubber-like elasticity. It is often formed by cross-linking polymers together but similar physical properties can be found in entangled networks and gels. In some materials the 'cross-links' can be formed by association between particular blocks of copolymers.
Electrophoresis is a term to describe the motion of a charged colloidal particle or polymer under the influence of an electric field. The particle will move at a velocity such that the electric force balances the viscous drag on the particle. The drag force will be determined by the hydrodynamic radius and the viscosity of the medium. The electric force will be given by a hydrodynamic potential such as the zeta potential. Electrophoresis is used as a means to separate different colloids and polyelectrolytes, as a means of analysis and to determine potentials. It can also be used to separate species with different charges (such as different proteins). The medium in which the polymers or particles move can be either a liquid or a gel (gel electrophoresis).
An electrorheological (ER) fluid is a material with rheological properties such as viscosity that change when an electric potential is applied.
Ellipsometry involves determining the change in polarization of light that is reflected from an interface so as to determine the properties of an interfacial layer. The change in polarization depends on the thickness and refractive index of the layers of material at an interface and so the experiment can be used to study the thickness of layers at solid interfaces or the amount of adsorption at a surface.
A colloidal dispersion of one liquid in another liquid (usually an oil and water). It is often 'stabilised' with a surfactant or with polymers. Emulsions are not usually truly stable but may be metastable. This contrasts with microemulsions.
A polymer that is prepared by polymerisation of a dispersion of monomer in a liquid. It is often stabilised with a surfactant or with polymers. This preparation involves an emulsion but the product is a colloidal dispersion of a polymer that is usually solid in the liquid. The product is known as a latex. Typically many vinyl polymers are prepared with radical initiators in this way.
In melts or in concentrated solutions above the overlap concentration, polymers will interpenetrate each other. This causes entanglements and restricts the motion (reptation) of the molecules to movement along a 'virtual tube' that surrounds each molecule and is defined by the entanglements with its neighbours.
ESEM is an acronym for environmental scanning electron microscope. This modification of a scanning electron microscope (SEM) allows samples to be observed at relatively high ambient pressures. The microscope is equipped with a differential pumping system so that the area around the sample is not at the same pressure as that of the rest of the electron microscope. Imaging and electron detection is distinctly different to that of a conventional SEM working in vacuum as the gas around the sample effectively forms part of the detector for electrons.
Expanded polystyrene is the solid foam that is formed by creating many small bubbles of gas in polystyrene that is normally a glassy, solid polymer. The expanded polystyrene is a very light material that can readily absorb energy on impact. It is widely used as a packaging material with trade names such as 'Styrofoam'.
Fillers are often added to polymers to improve the physical properties of the material. Typically carbon black particles are added to compounds of natural rubber as a reinforcing component that increases the elastic modulus and hardness. Other fillers include glass fibres that are added to increase the strength of plastics and a variety of minerals that may change the colour and mechanical properties. Some fillers such as graphite or metals may be added to increase the conductivity of polymers.
Colloids are described as flocculated when the individual particles have aggregated together to form clusters. This occurs when the repulsive potential that provides stability in a dispersion becomes less than the attraction.
The Flory-Huggins parameter describes the energy of interaction of a polymer segment with other polymers or with solvent molecules. It is normally designated by the Greek letter chi ( χ ). The energy is normally expressed in units of kBT where T is the absolute temperature and kB is Boltzmann's constant. A negative value indicates favourable interactions (tends to solution or miscibility) and a positive value indicates an unfavourable interaction.
A fractal aggregate is an assembly that appears to have similiar structure when viewed at different length scales. Simple examples would consist of clusters of particles that when examined would have a sub-structure that consists also of particles with the same geometry but a smaller size. This property of self-similarity gives rise to scaling laws for the variation of quantities such as the density, surface area and number of basic components with radius from the centre.
By way of example, the scaling of the number of particles, n, in an assembly within a radius R of the centre of mass is written as:
n(R) = k Rα
where k is a geometrical constant and the exponent α depends on the fractal structure. For an infinite uniform medium, α equals 3. In contrast an infinitely long polymer with a conformation that corresponds to a random walk will have this exponent α equal to 2.The idea of fractal structures is often applied to aggregates of particles such as colloids.
A gel is a network of either entangled or cross-linked polymers swollen by solvent. The term is also used to describe an aggregated system of colloidal particles that forms a continuous network.
This chromatography process involves pumping a dilute solution of polymer through a column with a porous packing. The small molecules are retained for longer on the column and are eluted and detected after the large molecules. This is a common analytical technique for determination of the molecular mass and polydispersity of a polymer sample. The polymers can be detected as they are eluted by measuring changes in the refractive index or infra-red absorption. In this case a calibration with secondary standards is required. In some modern instruments viscosity or light scattering detectors are directly connected to the output stream and give a direct measure of the absolute molecular mass. The technique is sometimes known by the alternative name of size exclusion chromatography from the mechanism of operation that is to exclude large molecules from pores. The method can be used as a preparative technique to fractionate polymers but is unsuited to very large volumes on an industrial scale.
This is a surfactant that has two parts: each has a head group and a tail group. The two parts are joined together covalently with a 'spacer' group.
The surface excess, Γ, which is the amount of a material adsorbed at an interface is related to the change in surface tension, γ, and with the activity, a, by:
Γ = -(1/RT) dγ/d ln(a)
where R is the Gas Constant and T is the absolute temperature. The activity is related to the concentration and for dilute solutions of non-ionic materials will be equal to the concentration, c. For ionic surfactants that are completely dissociated, the equation becomes:
Γ = -(1/2RT) dγ/d ln(c)
where the factor 2 accounts for the two ionic species. The equations only apply below the critical micelle concentration of surfactant solutions as the activity of the surfactant reaches a constant level and does not increase with concentration above this point.
This is the temperature, Tg at which an amorphous polymer changes from a solid to a liquid state. Above this temperature large scale, diffusive motion of the polymer molecules becomes possible. This is not a first-order phase transition but can be characterised using a differential scanning calorimeter (DSC) to observe changes in the heat capacity It can also be observed in a variety of mechanical and dielectric measurements.
A good solvent for a polymer is one in which the interactions with the solvent molecules are energetically favoured over interactions with other segments of the polymer in solution. This leads to expanded conformation of the polymer chain and a radius of gyration that is larger than that in a polymer melt. In general, the size of the polymer will depend on the concentration of the solution as this determines the number of the polymer/polymer and polymer/solvent interactions. The variation in size with concentration is often described by the virial coefficients in a virial expansion.
In a good solvent the size of a polymer molecule (radius of gyration), Rg, varies with the degree of polymerisation, N, as Rg ~ N0.6 rather than Rg ~ N0.5 found in polymer melts and in theta solutions.
A grafted layer is chemically attached by bonds to an interface rather than adsorbed. This provides distinction between chemisorbed and physisorbed species.
A grafted copolymer is made by linking a polymer or polymers of one type to a another polymer molecule of a different composition.
A way of plotting scattering data (static light scattering, small-angle neutron scattering or small-angle X-ray scattering) for particles and polymers. Data is plotted as:
ln I(Q) vs. Q2
where Q is the scattering vector given by:
Q = (4π/λ) sin(θ/2)
and λ and θ are the wavelength and the scattering angle respectively.
The data should lie on a straight line for QRg less than 1 and the gradient is -Rg2/3. The intercept is proportional to the particle or molecular mass if an extrapolation of the data to zero concentration is made. This can be compared with a Zimm plot. The radius determined from this plot is the radius of gyration, Rg and for a spherical particle of radius R this is related by:
R2 = (5/3) Rg2
Rg is sometimes described as a Guinier radius.
Polyethylene, (PE) may not form as perfectly linear polymer chains with CH2 repeat units. The extent and type of branching will depend on the method of preparation. The most linear polyethylene will crystallise better than branched polymers and so has a higher density. It is therefore known as High Density Polyethylene (or HDPE).
The head group of a surfactant is the hydrophilic part that likes to be in contact with an aqueous phase. This contrasts with the tail.
The shear stress, σ of a fluid in the Herschel-Bulkley model is described by a yield stress, σ0 and a term that depends on the shear strain rate, γ.. It can be expressed as:
σ = σ0 + c γ.b
where c and b depend on the material. The exponent b is usually in the range 0.3 to 0.5.
Surfactants in aqueous solution form a variety of mesophases (some liquid crystal phases) as the concentration is increased. A hexagonal phase usually forms when elongated cylindrical aggregates (micelles or reverse micelles) are sufficiently concentrated that they have to pack in an array that is locally regular with hexagonal symmetry.
The HLB or hydrophilic-lipophilic balance of a surfactant is a measure of how much a surfactant partitions in to co-existing aqueous and oil phases. It is based on an empirical scale from about 1 to 20. Surfactants with a low HLB number are not dispersible in water. Those with a high value are soluble (and good dispersants) in water. An HLB value for a mixture is obtained by simply averaging the HLB values of the components in proportion to the composition.
These are polymers that are formed from one type of monomer so that the molecule consists of chemically uniform components. These molecules contrast with copolymers.
This is the radius of a particle or polymer molecule in solution that is determined from a measurement of mobility or diffusion, for example in viscosity or dynamic light scattering experiments. The diffusion coefficient, D is related to the viscosity η and the hydrodynamic radius, RH by:
D = kBT / 6 πη RH
where kB is the Boltzmann constant and T is the absolute temperature.
A hydrogel is a polymer gel that has the capacity to absorb a large fraction of water.
A molecule or a part of a molecule that likes to be in contact with water or an aqueous phase.
A molecule or a part of a molecule that does NOT like to be in contact with water or an aqueous phase.
This is sometimes more loosely called surface tension. It corresponds to the force per unit length on a line bounding the contact region between two fluids or a fluid and a solid. Generally it is directly equivalent to the energy per unit area associated with an interface. The term interfacial tension is sometimes used to distinguish between the energy per unit area for contacts between two bulk phases in contrast to surface tension that refers to a liquid or a solid in contact with a gas or vapour.
IEP is an abbreviation that is sometimes used for isoelectric point.
Ion exchange resins are porous solids with many ionisable groups that can be exchanged with ions in a solution. Depending on the material, either cations or anions may be exchanged. The usual procedure is to treat the resin with, for example, acid to protonate sites. The resin is then rinsed with pure water and can then be used to exchange the protons H+ with other ions in another solution or dispersion. Other resins would be used with bases to exchange OH- ions. Mixed bed ion exchange resins contain multiple species to exchange simultaneously both cations and anions. In this way dispersions of low ionic strength can be obtained.
A surfactant with a head group that is ionisable. These may be anionic, cationic or zwitterionic.
An ionomer is a polymer with a few groups that are ionisable. In contrast to a polyelectrolyte there are only a few groups, the molecules may not be soluble in water. However the polymers may act as associative thickeners in either aqueous or non-aqueous environments through hydrophobic or ionic associations respectively.
The phenomenon of iridescence (dispersion of light into different colours) is seen with some concentrated colloidal dispersions. The interaction between particles gives rise to regular separations such as those in crystalline materials. The distances are larger than those in conventional atomic or molecular solids and so Bragg diffraction can be seen with optical wavelengths.
The ionisation of many colloidal particles and biopolymers depends on the pH of the solvent. Different functional groups will dissociate at different pH. If there are mixtures of acidic and basic groups there will be a pH at which there will be an average charge of zero. This is the isoelectric point.
A polymer is described as 'isotactic' if the substituent groups on successive monomers have identical stereochemistry. Tacticity of polymers can have major influence on crystallinity and physical properties. An isotactic polymer has a single type of stereochemical structure and this contrasts with atactic and syndiotactic polymers.
This is often used in interface science as a (jargon) abbreviation for adsorption isotherm. In other fields it is used with a more general meaning. See adsorption isotherm.
The kinematic viscosity, μ, is equal to the dynamic viscosity, η, divided by the density of the fluid, ρ:
μ = η / ρ.
If not explicitly stated, the term viscosity is usually taken to mean the dynamic viscosity.
The Krafft boundary is a limit in solubility of a surfactant as temperature is decreased. In general, both the critical micelle concentration (CMC) and the solubility of 'monomeric' surfactant decrease with temperature. If the solubility of the isolated surfactant molecules falls below the CMC, all the surfactant present as micelles will precipitate at that temperature as micelles are only stable in equilibrium with 'monomeric' or individually dissolved molecules.
The viscosity, η, of a colloidal dispersion at high concentrations does not obey the linear Einstein formula but varies more rapidly with volume fraction, φ, in the following way:
η = η0 (1 - φ/φ0)2.5φ0
where φ0 is the maximum packing fraction of the particles and η0 is the viscosity of the pure solvent.
The various structures formed in solutions of surfactants are given names that relate to the structure but are not always straightforward to interpret. The term Lα is used to describe lamellar phases where the tails of the surfactant molecules assemble together to form two-dimensional bilayer aggregates separated by regions of solvent.
A structure found in many concentrated surfactant solutions. This is a liquid crystal in which there are regions of surfactant bilayers formed as the tails of surfactant molecules assemble together.
A Langmuir-Blodgett film is a monolayer or multilayer film that is prepared by transfer of a surface film from a Langmuir trough to a solid substrate. A single layer can be prepared by pulling or pushing a solid through the surface layer on the trough. Multilayers are prepared by repeating this process. The choice of orientation of the layer (heads or tails towards the substrate) can be chosen by selecting the direction of transfer (up or down through the Langmuir Film).
The Langmuir adsorption isotherm is a simple model used to describe the variation of amount of gas adsorbed on a solid surface with the partial pressure of the gas. The fraction of sites that are occupied, θ is related to the partial pressure of the adsorbate px by:
θ = px / (px + K)
where K is the ratio the rate constant of desorption to the rate constant of adsorption:
K = kdes / kads.
The model is based on the assumptions that there is only monolayer coverage with a fixed number of adsorption sites and that the rate of adsorption depends on the pressure of gas and that the rate of desorption at a given temperature depends on the number of occupied sites.
A variant of deposition using a Langmuir trough in which a layer is deposited by displacing the substrate through the spread monolayer with substrate surface parallel to the surface of the liquid. This contrasts with Langmuir-Blodgett deposition when the substrate moves perpendicular to the surface with the spread film. This method is sometimes used to transfer a final layer to a substrate after a sequence of Langmuir-Blodgett depositions.
A Langmuir trough is a device for studying surfaces of liquids with spread layers of insoluble, surface active materials. The sub-phase has a meniscus proud of the container. Movable barriers can be used to constrain a layer of molecules to a certain region of the surface. The monolayer can be compressed and isotherm measurements of surface pressure or surface tension against area per molecule made.
A colloidal dispersion of a polymer in a liquid (usually water). Natural rubber occurs as a latex (plural latices) but many other polymers can be prepared in that form by emulsion polymerisation.
Polyethylene (PE) may not form as perfectly linear polymer chains with CH2 repeat units. The extent and type of branching will depend on the method of preparation. Branched polyethylene will crystallise worse than linear polymers and so has a lower density and softening temperature. PE with long branches such as that made by the high-pressure process is therefore known as Low Density Polyethylene (or LDPE). This contrasts with LLDPE that has only short branches.
Light scattering is used as an experimental technique to determine the size and/or mobility of colloids and polymers. It can be divided in to two different techniques: static light scattering in which the angular distribution of scattered intensity is measured to determine the size of scattering objects and dynamic light scattering in which a correlation function of scattered photons is measured and is often used to determine mobility and to deduce a hydrodynamic size.
This is a polymer without branch points in the molecule. The physical properties such as viscosity and crystallinity may depend on the extent of branching (as well as the molecular mass).
This term means oil-loving or readily soluble in a non-polar medium. This contrasts with the term hydrophilic and would describe a hydrophobic group (tail) in a surfactant.
A liquid crystal is a state that is intermediate between a crystal with positional and orientational order in three dimensions and liquids with no long-range order. The different types of order can be found in nematic, smectic, columnar and cholesteric phases. Liquid crystals can be formed from a variety of small molecules that assemble due to specific molecular shapes or interactions, as well as from polymers with rigid backbones or side chains, by anisotropic particles, and by assemblies of surfactants.
Polyethylene (PE) may not form as perfectly linear polymer chains with CH2 repeat units. The extent and type of branching will depend on the method of preparation. Branched polyethylene will crystallise worse than linear polymers and so has a lower density and softening temperature. PE that is linear but has some short branches (methyl, ethyl etc.) is known as Linear Low Density Polyethylene (or LLDPE). This contrasts with LDPE that has long branches.
The structure in semi-crystalline polymers often consists of regions of crystalline and amorphous material with a uniform separation. This regular periodicity in the structure can be observed in electron microscopy or small-angle scattering experiments as a consequence of the difference in density of the two regions. The mean separation of crystalline regions is known as the long period.
Viscoelastic fluids display both elastic (solid) and liquid like properties. If measurements of mechanical response are made at a specific frequency, then the component of stress out of phase with the strain is the loss modulus. This can be compared with the storage modulus, which is a measure of the elastic response.
Ludox is a trade name of the Du Pont company for dispersions of silica (SiO2). These are available in a range of grades with different sizes and surface functionality.
This term means liquid-loving or readily soluble and so in an aqueous medium would correspond to 'hydrophilic'.
This term means liquid-hating or insoluble and so in an aqueous medium would correspond to 'hydrophobic'.
This is a liquid crystal that is formed by addition of an appropriate solvent to a material. The change in concentration that results in a mesophase contrasts with the behaviour of thermotropic liquid crystals. A typical example of a lyotropic liquid crystal is the lamellar phase of a surfactant.
This is a semi empirical relationship for the viscosity of dilute polymer solutions. The reduced viscosity is calculated as follows:
[η] = {η - η0} / η0 c
where η0 is the viscosity of the pure solvent, η is the viscosity of the solution at concentration c. The Mark-Houwink equation is
[η] = k Mα
where k and α are tabulated constants. These are generally specific to each polymer/solvent pair. α will usually be in the range 0.4 to 1.0. The form of this equation can be derived from the Einstein equation for dilute dispersions and the expression for the radius of gyration of polymers in good solvents.
Micelles are aggregates of small molecules such as surfactants that assemble together in a solution. These aggregates only form at concentrations above the critical micelle concentration. Micelles can have a wide range of size and shapes that will depend on the molecular structure of the constituent molecules as well as the concentration. The term reverse micelles is used to describe aggregates of amphiphiles in solvents where the hydrophobic chain is on the outside and the polar or hydrophilic part head is in the middle.
A colloidal dispersion of a liquid in another liquid (usually an oil and water) typically with a droplet size of a few nm. It is stabilised with surfactants and cosurfactants. In contrast to emulsions, microemulsions can be truly stable in a thermodynamic sense.
The molecular mass of a polymer is defined as for other compounds as the mass in grams of a mole (Avogadro's number) of molecules. It is of particular importance in polymers as many properties depend on the length or degree of polymerisation and thus the molecular mass of the molecules. Most synthetic polymers will have a distribution of molecular mass and it is often important to characterise this. It is common to distinguish various different averages of the molecular mass such as the number average molecular mass and the weight average molecular mass.
A monodisperse sample consists of colloidal particles or polymer molecules that all have identical size or mass. (For polymers this corresponds to MW/MN = 1). In practice perfectly monodisperse particles or polymers are difficult to achieve by chemical synthesis. However, in nature some materials, such as DNA and proteins can be made with perfect uniformity.
A monolayer is a single molecular layer of molecules at an interface. These can be adsorbed physically (Physisorbed) or grafted (Chemisorbed) to the surface. At some interfaces, boundary layers are restricted to a single layer (by binding to specific sites) or other processes. This contrast with the formation of bilayers or multilayers at other interfaces.
See Number average molecular mass.
The repeating chemical units that combine to form a polymer are known as monomers.
See Weight average molecular mass.
Natural rubber is a polymer produced in the sap of rubber trees (Hevea Brasiliensis) and some other plants. As a natural product, it is formed as a latex that can be collected and dried. The polymer is cis-polyisoprene. It is not cross-linked in the natural state and only becomes a durable solid when it is cross-linked, by for example, vulcanisation.
Nematic phases are liquid crystalline states in which there is a direction of preferred orientation but no long-range positional order.
These are materials in which there are links between all molecules or particles to provide a structure that spans the entire sample. There can be no large-scale motion or diffusion in these materials but they will often display rubber elasticity. Entanglements may act like to produce a transient network but after a long time or at sufficient stress, the material will undergo deformation.
These are liquids that have a constant viscosity that is independent of the shear rate or shear history of the sample. This contrasts with a non-Newtonian fluid.
A surfactant with a head group that is not ionisable.
These are liquids that have viscosity that changes with the shear rate or the shear history of the sample. For example the liquid may show shear thinning or shear thickening as the shear or flow rate changes. This contrasts with a Newtonian fluid.
The distribution of polymer sizes in most synthetic materials (polydispersity of molecular mass) implies that different averages will give different values. The number average is defined as the sum of niMi divided by the sum of ni where ni is the number of molecules in the distribution with mass Mi. The number average molecular mass is the quantity measured by determination of colligative properties such as osmotic pressure.
MN = Σ niMi / Σ ni
The Greek prefix 'oligo' means few. An oligomer is therefore a molecule made from a few monomers and contrasts with a polymer that has many monomers. There is no precise, formal definition of oligomer or where the transition to a polymer occurs as the degree of polymerisation increases. However it is often useful to think of polymers as being long enough to form entanglements or as being longer than a persistence length.
In systems such as liquid crystals that display partial order, for example only in orientation but not in position, it is useful to use a measure of the extent of ordering. Physicists define order parameters to describe these states. A simple example would be a description of the orientational order in a nematic phase that is described by an average of the angle which the particles or molecules make with the director, which is the overall orientation direction. Several different averages can be taken to provide an indication of the width of the distribution of orientations about this direction. The first order parameter is known as P2 and is defined as:
P2 = < (1/2 (3 - cos2θ) >
where θ is the angle that each particle or molecule makes to the director and < > indicates an average over all particles. Other order parameters would take averages over higher powers of cos θ. (These are other even Legendre polynomials.). The order parameters are chosen so that perfect order would give a value of 1 and no orientation would give an order parameter of zero.
An osmometer is a device used to measure the osmotic pressure of a solution. Several types are produced. They can measure directly a pressure difference across a semi-permeable membrane. Alternatively, the vapour pressure above a solution can be measured. This information is used for determination of the molecular mass of polymers or the extent of association in solutions (effects such as the formation of micelles).
A pure solvent and a solution when separated by a semi-permeable membrane (which is impermeable to the solute) will try to reach equilibrium. In the absence of the membrane, the liquids would mix to form a solution of uniform concentration. In the presence of the membrane the only way to reach this state would be by pure solvent passing through the membrane so that the volume on each side changes. The volume of the solution will tend to increase and the volume of pure solvent will decrease. This flow can be inhibited by the application of a pressure difference to the system. The pressure that is required to inhibit flow in to a solution is the osmotic pressure.
The osmotic pressure, Π, can be related to the concentration, c, (in moles per unit volume) by:
Π V = n R T
where V is the volume of a dilute solution, n is the number of moles of the solute, T is the absolute temperature and R is the ideal gas constant. The concentration is simply given by:
c = n / V
and so the osmotic pressure can also be expressed as:
Π = c R T.
The measurement of osmotic pressure provides a means for determination of the molecular mass of a solute provided that the mass concentration and Π can be determined. This is a useful means of determining the number average molecular mass for polymers. The expression as follows relates Π to the molecular mass, M:
Π = (m / M V) R T
where m is the mass of the solute. As the osmotic pressure depends on the number of molecules or particles dissolved it also provides evidence for the formation of micelles in solutions of surfactants.
The concentration of a polymer in a solution at which the molecules begin to interpenetrate each other and become entangled. At this concentration there may be significant changes in properties such as sharp increases of viscosity and the mechanism of motion becomes reptation. The overlap concentration, Co may be crudely estimated as being given by the molecular mass, M and the radius of gyration, Rg by Co ~ M / Rg3.
The Peclet number, Pe, is a ratio in a fluid of the shear strain energy to the thermal energy taken over the volume of a particle or a typical structural dimension in the sample. If the Peclet number is large, shear flow dominates. When the Peclet number is small the random thermal (Brownian) motion is dominant. The Peclet number is defined as:
Pe = 6 π η a3 γ. / kBT
where η is the viscosity, a is the appropriate structural dimension, γ. is the strain rate, kB is Boltzmann's constant and T is the absolute temperature.
When Pe >> 1 it is easy for shear induced structural change or alignment to occur. In practice it is often found that concentrated particulate dispersions show shear thinning when the Peclet number is equal or greater than 1.
The persistence length is a measure of the 'stiffness' of a polymer molecule. It describes the length scale for which the chain can be thought to be rigid. This determines the step size that is appropriate to use to model the chain as a series of freely jointed links.
The persistence length will determine the radius of gyration of a polymer as well as the extent of entanglement that it experiences. The actual persistence length depends on the chemistry of the polymer (local rigidity and steric constraints). For polyelectrolytes it depends on the extent of dissociation and screening of ionic interactions along the polymer. It is therefore dependent on pH and ionic strength of the solution.
A trade name for polymethyl methacrylate (PMMA).
PET is the abbreviation for polyethylene terephthalate. This is a polymer (polyester) that is widely used both as fibres and to make other plastic products, for example bottles.
Theoretical models of polymers often make simplifying assumptions to make mathematical treatment straightforward. A model with a 'phantom' chain is one in which polymer molecules would be free to pass through each other rather than be constrained by physical entanglements or cross-links. This is sometimes a useful approximation in considering the conformation of polymers in melts or networks but is less useful in treating dynamic properties when entanglements may be crucial in determining the behaviour.
A phase diagram shows regions of composition for which particular equilibrium structures (or phases) are observed. The simplest diagram for a pure, single component system would indicate where, as a function of pressure and temperature, the gas liquid and solid phases are observed. In some materials there can be more structures such as liquid crystalline order or a variety of crystal structures. The concept can be extended further in several ways. If there are two or more components there can be regions of separation in to phases that are enriched in a particular component. Such diagrams will require extra axes to show each component. There are clear rules based on thermodynamics, which indicate that three phases can only co-exist at a point (triple point). Phase boundaries are lines or surfaces that separate two co-exiting phases. There can be regions in a phase diagram that do not correspond to stable structures or compositions but rather separate in to different phases with either different densities or compositions. The amounts of the separated phases are described by the lever rule.
In the area of soft matter some 'phase diagrams' have been presented and discussed more loosely. True thermodynamic equilibrium is sometimes difficult to establish and phase diagrams that include metastable states are sometimes shown. Diagrams are sometimes reported for variables such as shear rate that are not thermodynamic state functions. In other cases quasi-one component diagrams are shown for more complex systems such as colloidal dispersions. For all these cases, some care in interpreting the phase behaviour is required as the usual 'phase rules' are not always appropriate.
pI is an abbreviation that is sometimes used for the isoelectric point of a dispersion or polymer solution.
A Pickering emulsion is an emulsion that is stabilised by small particles bound to the surface of the drops of fluid rather than by a conventional, molecular surfactant.
Plastic materials are those which undergo permanent deformation (or yield) when subjected to stress. It is frequent to use the term plastic to describe polymeric materials, particularly those that are thermoplastic.
A plasticiser is a low molecular mass liquid that is added to a polymer that would normally be rigid or glassy so that it becomes plastic.
A trade name for polymethyl methacrylate (PMMA).
The distribution of molecular mass of polymers or colloidal particles is described as the polydispersity. The details of the shape of the distribution will depend on the preparation and any fractionation but, particularly for polymers, a simple measure of the distribution is often quoted as MW/MN where MW is the weight average molecular mass and MN is the number average molecular mass.
A polymer that has ionisable groups that can dissociate in aqueous solution. These polymers are usually water-soluble and can be anionic or cationic. Many biopolymers are polyelectrolytes. As the polyelectrolyte can be charged its properties will change with pH and ionic strength of the solution. A highly charged polymer may resemble a rigid rod. Polymers that have only a few ionisable groups are called ionomers.
Polyethylene is a polymer with CH2 as the repeating unit. It is usually made by an addition reaction of ethylene: CH2=CH2. The catalysts and methods of synthesis give rise, in practice, to polymers with some branching or other defects from the ideal molecular structure. These vary with the catalyst and reaction conditions. Different grades of this polymer are known as HDPE, LDPE, and LLDPE depending on the type of branching. The polymer is transparent and used for packaging, electrical insulation and a wide variety of fabricated components.
A molecule that is made by linking many small units (monomers) together to form a large molecule. The polymer can be made of a single species (homopolymers) or of several different monomers (copolymers). Polymers occur naturally (biopolymers) but are also made synthetically in large amounts. Apart from the chemical composition, polymers may also be categorised by physical properties such as crystallinity or linearity / branching.
The term polymerisation describes chemical reactions that produce polymers by repeated combination of monomers to make long or large molecules. The different types of reaction are numerous and several distinctly different ways of categorising the reactions are used. These include the physical state of reagents (e.g. emulsion polymerisation, suspension polymerisation), nature of the reaction (e.g. condensation, addition) or type of initiator or catalyst (e.g. anionic polymerisation).
This is a transparent, amorphous thermoplastic that is sold under the trade names 'Perspex' and 'Plexiglas'. The monomer methyl methacrylate has the following chemical formula:
CH2=C(CH3)(COOCH3).
The polymer is formed by addition reactions on the double bond. The bulky side group and the irregular tacticity in commercial preparations inhibits crystallisation.
The pair-potential distance curve for colloidal particles may have more than one minimum. The lowest energy state with the particles almost in contact is termed the primary minimum in contrast to other local minima (secondary minimum) that may provide a metastable dispersed state. The primary minimum is usually dominated by van der Waals attractions. For charge-stabilised dispersions, the potentials are described by the DLVO theory.
PTFE is the abbreviation for polytetrafluoroethylene. This is a polymer that is used for its low friction coefficient, chemical resistance and good electrical insulation. The chemical formula is -(CF2CF2)-n. It is widely known by the trade name 'Teflon'TM which is a product of the Du Pont Company.
This name is used in distinctly different ways. In chemistry, a urethane linkage corresponds to the following group:
-(NH)-(C=O)-O-
and is typically made by the reaction of a diisocyanate (OCNRCNO) and a glycol (HOR'OH) where R and R' different polymers or organic groups. This provides a route to block copolymers of various types. Polyurethane elastomers are formed in this way from a combination of soft segments (often polyesters or polyethers terminated with hydroxyl (OH) groups) that are flexible and hard segments (diisocynates) that associate or crystalise to form effective cross-links in a network that may be thermally reversible. Such thermally reversible elastomers are also sometimes known simply as polyurethanes. If polyfunctional rather than difunctional monomers or linking agents are chosen, chemically cross-linked networks are formed such as those in polyurethane foams.
A quartz crystal microbalance (QCM) is a crystal that will change its resonant response according to the mass of material at the surface. This can be sensitive to very small amounts of material. The crystals can also be used in solutions so as to measure the amount of material that is bound to the surface of the crystal. These instruments can thus be used to study adsorption and grafting of molecules to interfaces.
This is a measure of the size of a polymer molecule and can be defined in terms of the distribution of distances (in any direction) ri of each monomer in the molecule from the centre of gravity of the molecule:
Rg2 = Σi ri2
It can be shown that a freely jointed chain of N links of length a has the following, Rg:
Rg2 = N a2 / 6
In practice N may not be the number of monomers as there may be a finite persistence length or stiffness of a polymer chain and a may correspond to the length of several monomers that extend in one direction.
A copolymer in which the different components are arranged randomly or statistically in each individual polymer molecule. This can be compared with block copolymers. A sequence of monomers in a random copolymer of monomers A and B might be AABABBAAABBBBABABBAA. It is also possible to have alternating copolymers of the type ABABABABABAB. These are NOT random.
The determination of a contact angle of a liquid on a solid is not always a simple equilibrium measurement. Some hysteresis is often displayed when a drop moves on a surface. The angle at the surface that has not been wetted by the liquid (advancing contact angle) may be significantly different to that on the other side of the drop where a previously wetted surface is losing contact (receding contact angle) with the solid.
The reduced viscosity is defined as:
[η] = {η - η0} / η0 c
where η0 is the viscosity of the pure solvent, and η is the viscosity of a solution at concentration c. This quantity is useful as it can be used, by means of the Mark-Houwink equation to determine the molecular mass of polymers from measurements of viscosity of dilute solutions.
The mechanism by which polymers move through entanglements with other polymers in melts or concentrated solutions. An entangled polymer is constrained to move along a path (or 'tube' defined by the entanglements it has in its original position. The mechanism is named after the wriggling motion of reptiles such as snakes or worms. This process gives rise to a characteristic variation of the diffusion coefficient, D, as 1/N2 where N is the degree of polymerisation (proportional to the molecular weight). There are related predictions for the viscosity, which in the simplest theory is proportional to N3.
These are aggregates, as micelles, of small molecules such as surfactants that assemble to together in a non-aqueous solution. The hydrophilic parts of the molecules associate to form the centre of the aggregate in contrast to normal micelles in aqueous solution where the hydrophobic tails form the core.
This is a dimensionless number that determines when a fluid flow may become turbulent. The Reynolds number, Re, depends on the ratio of inertial forces to viscous forces in a fluid and is related to the flow velocity, v, density, ρ, and viscosity, η by:
Re = ρ v L / η
where L is a characteristic dimension of the flow field (e.g. diameter of pipe etc.). The expression is sometimes given it terms of the kinematic viscosity, μ (=η/ρ) as:
Re = v L / μ
Some expressions for Re may also include numerical constants (such as π) to account for particular flow geometries. Turbulence occurs at high Reynolds numbers.
Study of the flow properties of materials. It is often concerned with viscoelastic liquids.
This is a device to measure the rheological properties of a fluid. These usually investigate deformation of liquids under shear. The stress required to produce a certain rate of strain is determined. It is common to design instruments to make measurements over a range of frequencies. The stress may not be in phase with the strain and determination of the 'in-phase' and 'out-of-phase' components may be important.
The elastic response of polymers that are cross-linked to form a network or are dominated by entanglements is distinctly different to that shown by other materials. The change in free energy on deformation is dominated by reducing the conformational entropy and there is negligible change in the internal energy. This gives rise to an elastic modulus that increases with temperature and depends on the distance (number of monomers) between entanglements or cross-links. When cross-linked, natural rubber displays this type of elasticity.
See Small-Angle Neutron Scattering.
See Small-Angle X-ray Scattering.
A scaling law describes the way that a physical quantity varies with some other quantity. They are common in the study of polymers with examples arising from the reptation theory with a diffusion coefficient varying with the degree of polymerisation, N as D ~ 1/N2. Other examples of scaling laws are the expressions for the size of polymers.
This variation of electron microscopy raster scans a beam of electrons across a sample to form an image. Images can be formed from scattered electrons or by other techniques such as observation of fluorescence. The technique has lower spatial resolution than transmission electron microscopy but can be used to observe larger colloidal particles.
An electrolyte in solution provides screening of the interactions of charged particles. The screening length, 1/κ, is obtained from solutions of the Poisson-Boltzmann equation and is given by:
1 / κ = {(e2NA / ε kBT) Σi cizi}-1/2
where e is the electronic charge, NA is Avogadro's number, ε is the permittivity of the solution, kB is Boltzmann's constant, T is the absolute temperature, ci is the concentration of ionic species i with elementary charge zi. For a solution of a 1:1 electrolyte of concentration, c, this simplifies to:
1 / κ = {(2e2NA / ε kBT) c }-1/2
Size exclusion chromatography (SEC) is an alternative name for gel permeation chromatography, GPC. See the notes on GPC for a brief description of this technique for separation of polymers of different molecular mass.
SDS is an abbreviation for the anionic surfactant sodium dodecyl sulfate. It has the molecular formula C12H25SO4- Na+. This is a common synthetic surfactant frequently used in cleaning formulations and personal care products. It is sometimes known by the name sodium lauryl sulfate.
The pair-potential distance curve for colloidal particles may have more than one minimum. The lowest energy state with the particles almost in contact is termed the primary minimum in contrast to the secondary minimum that can provide a metastable dispersed state. For charge-stabilised dispersions, the potentials are described by the DLVO theory.
A Self-Assembled Monolayer (SAM) is a layer of material that is grafted at a surface or interface formed from a reagent that forms a single uniform layer. Typical reagents will use the reaction of a thiol with gold or a trichlorosilane with SiOH groups. A wide variety of groups can be attached in this way to modify the stability of colloidal particles or to change surface properties.
This is a trajectory that does not cross the same point in space. A real polymer molecule will have this property (as it occupies space) but some simple statistical models, such as random steps in any direction, of conformations may not have this property. However, given the large size of many polymers this distinction from a random walk may not always be important.
Most polymers that crystallise cannot order completely. There are crystalline regions separated by amorphous parts. Indeed a single molecule is likely, to form part of some crystalline and some amorphous regions. It is often useful to determine the extent of crystallisation in polymers by calorimetric or diffraction measurements.
A semi-permeable membrane is a barrier that can be passed by some species in a solution but not by others. The selection is often on the basis of molecular size. Pore sizes in a membrane can inhibit the passage of large molecules such as polymers. Such membranes can be used to measure directly the osmotic pressure in a solution. Membranes that retain particles or large molecules may also be used in dialysis so that a solution or dispersion medium that is concentrated in a salt is equilibrated with pure water. Such membranes are also used in dialysis.
Shear is the deformation of a material, either solid or liquid, that is caused by opposing forces that are applied in the plane of opposite faces of a sample. This causes layers of material to slide over one another in a direction parallel to the applied stress. This contrasts with deformation where the strain is elongational.
The shear modulus, G, is the elastic constant of a material that describes the relationship between shear stress, σg and shear strain, γ.
G = σe / γ.
A fluid is shear thickening if the viscosity increases with increasing shear strain rate. This occurs in some concentrated colloidal dispersions at high shear rates. This is one characteristic that occurs in a Non-Newtonian fluid.
A fluid is shear thinning if the viscosity reduces with increasing shear strain rate. This is characteristic of many concentrated colloidal dispersions over a wide range of shear rates. This is a typical characteristic of a Non-Newtonian fluid.
A silicone (or siloxane) polymer consists of a backbone formed with alternating silicon and oxygen atoms Si-O-Si-O-Si-O- etc. The Si atoms will normally be attached to two other groups. A common silicone is polydimethylsiloxane (PDMS) which has the repeat unit:
-(Si(CH3)2-O)-.
PDMS is fluid at room temperature and has a low variation of viscosity with temperature. It is a component of silicone oils and silicone greases. Other common silicone polymers and silicone fluids include phenyl groups in place of some of the methyl groups. Polymers with high molecular mass can also be formed and cross-linked to form an elastomer known as silicone rubber.
This technique that is often known as SANS is used to study structure in bulk polymers, polymer solutions and in colloidal dispersions. The principles are similar to elastic or static light scattering but relies on scattering contrast from nuclei. Different isotopes can scatter quite differently. SANS can be used to investigate blends of chemically identical but differently labelled materials such as the size of polymers in the bulk. SANS is also important as a tool to study opaque and multi-component systems. Typically experiments are performed with 'cold' neutrons with a wavelength of 0.5 to 1.2 nm. The small angles of measurement are needed to probe the large dimensions in polymers and colloids.
The interpretation of SANS data often relies on the simple formulae such as those of Zimm and Guinier to determine the size of colloids and polymers.
A technique that is often known as SAXS is used to study structure in bulk polymers, polymer solutions and in colloidal dispersions. The principles are similar to elastic or static light scattering or small-angle neutron scattering. Typically experiments are performed with a wavelength of 0.1 to 0.2 nm. Small angles of measurement are needed to probe the large dimensions in polymers and colloids.
A smectic material is a mesophase with a structure that has layers but no correlation between the position of particles or molecules within different layers. These are liquid crystals and there are various different smectic phases that may have for example tilt in the layers or other orientational order.
This is a particular class of surfactant that is a salt of a carboxylic acid. These are usually sodium salts. Commercial products that are sold as 'soap' may contain these materials but are likely to have a range of other components.
This is name given to materials that have a low or zero yield stress. It has been used to describe collectively materials such as polymers, gels, concentrated solutions and colloidal dispersions. It is often used to contrast with conventional or 'hard' condensed matter that consists of crystalline and glassy solids.
The energy associated with interfaces and the properties of surface layers can be very important in determining the properties of colloids and other finally divided materials. It is often useful to think about the amount of surface or interface per unit mass or per unit volume of material. This is known as the specific surface area. It can be measured by determining the gas adsorption (e.g. BET isotherm) or by making scattering measurements.
A spectroscopic ellipsometer uses a range of wavelengths rather than a fixed, single wavelength to probe the structure of interfaces. If the variation of refractive index with wavelength for materials at the interface is known, this may allow unique identification of the thickness and composition of surface layers when this would be ambiguous from just a measurement with a single wavelength.
This is a technique to produce thin, uniform films of polymers on solid substrates. A dilute solution is put on surface and the sample is then accelerated to a speed of a few thousand r.p.m. The solution is spun off the surface but leaves a residual film of solute. The thickness depends on the viscosity (which in turn varies with both the concentration and the molecular mass of the polymer) as well as the spin speed. Typically films of 10 to a few hundred nm thickness can be formed. The procedure is used to make devices from optoelectronic polymers and to put resists on the surface of conventional semiconductors in fabrication processes.
The colloid stability factor, W is usually defined as the inverse of the probability, P that a collision between two particles will result in them sticking together:
W = 1 / P.
Thus W is infinity when the probability is zero and the colloidal particles are stable. This idea is often used when discussing aggregation or flocculation.
A star polymer is a molecule that is multiply branched from a single point. It is characterised by the number of arms as well as the length (or degree of polymerisation) of the arms. Formally, a linear molecule could be considered as branched at the midpoint with a number of arms equal to 2. However true star polymers would have a number of arms equal to three or more.
A light scattering technique to measure the size (radius of gyration) and molecular mass of polymers, micelles and colloidal particles. The total scattered intensity I is measured as a function of angle <θ. For polymers the data is often interpreted by means of a Zimm plot. For solid objects, such as colloidal particles, it is more usual to use a Guinier plot.
Colloids can be stabilised with adsorbed or grafted polymers. The layers of polymer on particles will repel each other if they are in a good solvent and this will overcome the van der Waals attraction so that the particles will not aggregate.
Viscoelastic fluids display both elastic (solid) and liquid like properties. If measurements of mechanical response are made at a specific frequency, then the component of stress in phase with the strain is the storage modulus. This can be compared with the loss modulus, which is a measure of viscous response. The storage modulus corresponds to elastic strain and so energy can be recovered from this component of the stress.
Strain is a dimensionless measure of the deformation of a sample. The definition will depend on the type of deformation (e.g. elongation or shear). For elongation the strain, γ, would be given by:
γ = (lf / li) - 1
where li is the initial length and lf is the final length after deformation. Sometimes strain is given as a percentage and then it is calculated as:
% Strain = ({lf - li) / li} x 100
.If the deformation is a shear, the calculation corresponds to the ratio of the displacement to the distance in the perpendicular direction.
When a material is aligned by means of deformation or strain, there may be induced birefringence. This phenomenon of strain birefringence can be a useful tool to measure the molecular orientation in samples such as polymers. Sometimes the effect can be calibrated and used to measure the stress in a sample. Apart from molecular solids that align under deformation, some fluid phases can also show birefringence when subject to shear.
Strain rate is the rate of change of strain with time. It is often written as γ., and would be defined as
γ. = dγ/dt
where γ is the strain and t is time.
As with strain, strain rate will depend on the mode of deformation (e.g. elongation or shear).
Stress is the force per unit area that gives rise to deformation or flow of a sample. If the material is elastic, the deformation, or strain, will vary with the stress. For a Newtonian liquid, the viscosity is the ratio of stress to strain rate.
The surface excess, Γ, is the amount of material at a surface or interface present due to adsorption in excess of that due to the average concentration in the materials forming the interface. This quantity will have units of moles per unit area or molecules per unit area. In general this could depend on what region is defined as forming the interface. Surfactants are typical of materials that adsorb to interfaces and it is conventional to define the surface excess such that there is no excess or deficit of solvent at the interface.
The surfaces of most materials are different in composition or structure to that of the bulk. If there is a particular arrangement of either charged or polar species at an interface, there can be a difference between the electric potential at the surface and the bulk. This is known as the surface potential.
This is defined as the difference between the surface tension of a pure solvent and the surface tension of a liquid with a surface-active species at the surface. If the surface tension of the pure liquid is γ0 and the surface tension of the solution or in the presence of the surface-active layer is γ then the surface pressure, Π is given by:
Π = γ0 - γ
As the surface tension of a solution is usually reduced by a surfactant, the surface pressure will increase as the concentration increases.
The surface tension is the force per unit length exerted by a liquid in contact with a solid or another liquid. It can also be considered as a measure of the free energy per unit area associated with a surface or an interface. For example, a value for the surface tension of the water/vapour interface at 25 C is about 72 mN m-1 or 72 mJ m-2.
This is a SURFace ACTive AgeNT or, in other words, a molecule that tends to adsorb at surfaces or interfaces. Surfactants are usually amphiphilic molecules with water-soluble head groups and hydrophobic tails. The hydrophilic head group may be ionic or non-ionic. Surfactants generally lower the surface tension of water.
A polymer is described as 'syndiotactic' if the substituent groups on successive monomers have alternating stereochemistry. Tacticity of polymers can have major influence on crystallinity and physical properties. An isotactic polymer has a regular, alternating stereochemical structure and this contrasts with atactic and isotactic polymers.
A polymer that is made in the laboratory or made industrially. This is in contrast to biopolymers that occur naturally.
Tacticity describes the stereochemistry of a polymer with substituent groups on each monomer. As the polymer backbone or chain is long, a carbon atom in the chain with two different substituent groups X and Y will have a stereochemical centre (each of the bonds is to a different group or length of molecule). The relative orientation of the groups on successive monomers is described by the tacticity. If the substituents are all on the same side, the polymer is isotactic. If the substituents alternate, the polymer is syndiotactic. If there is no regular pattern of the substituent, the polymer is described as atactic.
Some common examples of polymers that can display a variety of tacticity are vinyl polymers such as polystyrene: the vinyl substituents can be arranged in a regular way (e.g. isotactic) or randomly (atactic). Sometimes the physical properties of a polymer are altered hugely by the tacticity. Atactic polypropylene softens at a low temperature and has poor mechanical properties. It is normal to produce isotactic polypropylene, which is a semi-crystalline polymer.
The tail group of a surfactant is the hydrophobic part that likes to be out of contact with an aqueous phase or in contact with oil. This contrasts with the head.
A tensiometer is a device to measure the surface tension of a liquid. It can be based on any of several different physical phenomena associated with surface tension. These include measurement of the force on a Wilhelmy plate in the liquid surface, the maximal force on pulling a ring through the surface of a liquid, the pressure inside a bubble or the shape of a spinning drop of one fluid in another liquid.
This is the temperature at which the glass transition occurs.
Thermogravimetric analysis (TGA) is a measurement of the change in mass of a sample as it is heated. It is used to study decomposition processes such as loss of solvent (e.g. dehydration) and oxidation.
Thermoplastic materials are those that become processable (flow) on heating either by melting of crystallites or by softening of a glass at the glass transition. This contrasts with thermoset materials.
Thermoset polymers are materials that become rigid on heating usually by chemical reactions leading to a rigid cross-linked network. This contrasts with thermoplastic materials.
This is a type of liquid crystal that is formed by heating a material from a solid phase or cooling a liquid. This thermal treatment to induce the change contrasts with that in lyotropic liquid crystals.
This is a solvent for a polymer in which the macromolecule has the same interactions with a solvent molecule as with monomers of polymer molecules. The dimensions of polymers will vary in the same way as in the amorphous solid state or in a melt, e.g. the radius of gyration, Rg ~ N0.5 where N is the degree of polymerisation. This contrast with a good solvent in which interactions of solvent with the polymer are energetically favoured and the polymers expand.
A formal mathematical definition of the theta condition is a point at which the second virial coefficient for the polymer in solution is zero. The theta condition will generally exist at only a single temperature (or not at all) for a given solvent. The temperature is known as the theta temperature (θ-temperature).
This is a specific temperature at which a specified combination of polymer and solvent for a theta solution. This contrasts with a good solvent in which interactions of polymer and solvent are energetically favoured.
A principal that explains how properties of a polymer measured at low frequency correspond to those at high temperatures and those measured at high frequencies correspond to low temperatures. For example brittle behaviour is observed either at low temperatures or in a high frequency (high-speed) mechanical test. A mathematical statement of this principal is found in the Williams Landel Ferry (WLF) equation.
A transmission electron microscope uses the scattering of electrons from a thin film of sample to form an image. This can be used to form images of colloidal particles as well as other structures with a resolution that could identify individual atoms. Measurements are normally performed in high vacuum. Some samples may need to be protected from damage by coating with a conducting film of metal or carbon.
Tribology is the study of friction and wear of materials and the means to lubricate contacts.
In the field of surfactants it is common to encounter hydrocarbon chains that are known by old, or 'trivial', names rather than by systematic naming conventions. These names are often much shorter and can be quite precise. Some of these names for acids (or the corresponding alkyl groups) are set out in the table below. The equivalence of the names sodium dodecyl sulfate and sodium lauryl sulfate for the surfactant SDS is easily identified.
| Trivial Name | Systematic Name | Chemical Formula |
|---|---|---|
| Caproic | Hexanoic | C5H11COOH |
| Caprylic | Octanoic | C7H15COOH |
| Capric | Decanoic | C9H19COOH |
| Lauric | Dodecanoic | C11H23COOH |
| Myristic | Tetradecanoic | C13H27COOH |
| Palmitic | Hexadecanoic | C15H31COOH |
| Stearic | Octadecanoic | C17H35COOH |
| Oleic | cis-9-Octadecenoic | cis-C8H17CH=CHC7H14COOH |
| Elaidic | trans-9-Octadecenoic | trans-C8H17CH=CHC7H14COOH |
| Arachidic | Eicosanoic | C19H39COOH |
| Behenic | Docosanoic | C21H43COOH |
The names of these acids (or their initial letter) are frequently used in describing phospholipids. Examples are DMPC (dimyristoylglycerophosphocholine) and DPPC (dipalmitoylglycerophosphocholine).
The restraints on the motion of entangled polymers in melts and concentrated solutions are such that a long molecule only has freedom to move along its length. It cannot disentangle from the original constraints except by moving completely along its original path. The idea that the entanglements define a virtual 'tube' of constraints was proposed by Edwards and co-workers. This model has become the basis of modern theories of motion of polymers such as reptation.
This is the name given to scattering of light by dispersions of particles. In particular as the scattering depends on the wavelength, λ, of the light distinctive colours are seen in the scattered light. To a first simple approximation the scattered intensity of light is proportional to 1/λ4. The blue colour of the sky can be attributed to strong scattering of this part of the optical spectrum from molecules in the atmosphere. Light scattering is often used to determine the size and molecular mass of colloids and polymers. Such measurements usually involve studies of the variation of the scattered intensity with angle.
A quantity that is sometimes used to describe the molecular mass distribution of polymers is:
U = MW/MN - 1
This is mostly found in the German literature where U stands Uneinheitlichkeit.
These forces arise from the interaction of fluctuating electric dipoles in materials. There is generally an attractive potential between molecules that varies as 1/r6 where r is the separation. The integration of these interactions over all parts of a particle can give rise to longer-range attractions with an exponent much smaller than 6. These forces are commonly the dominant attractive interaction between colloidal particles or between particles and other large objects. When the separation is large the dipoles will not fluctuate in phase and the potential is reduced. This retarded potential between molecules will vary as 1/r7.
An assembly of surfactant molecules that contains solvent, usually water, both inside and outside. The 'wall' may consist of a single bilayer or be formed of multiple layers (multilamellar). Phospholipids are examples of typical vesicle forming surfactants.
A vinyl polymer is made with 'vinyl' monomers that have the form CH2=CHX where X is a substituent group and = stands for a carbon-carbon double bond. These can form addition polymers with the general formula -(CH2CHX)-n. A common vinyl monomer is vinyl chloride (CH2=CHCl) which is used to make poly vinyl chloride (PVC). This plastic is sometimes known colloquially as 'vinyl' but strictly the term can include a wide range of different polymers.
A 'virtual tube' defines the constraints on a polymer imposed by entanglements. This can be used to explain the motion (reptation) of polymers in melts and concentrated solutions. See also Tube Model.
This describes the properties of some liquids to show both viscous and elastic response to an applied stress and is commonly observed in melts of polymers, concentrated polymer solutions and concentrated colloidal dispersions.
The viscosity, η is the ratio of shear stress, σ to shear strain rate γ. and describes the resistance to flow of a liquid.
η = σ / γ.
The viscosity of dilute polymer solutions is often used as a means to determine the molecular mass of a polymer. In this case the change in viscosity with concentration is used to determine the intrinsic viscosity that is then interpreted using tabulated, empirical values specific to each polymer and solvent in the Mark-Houwink equation.
This definition refers strictly to the dynamic viscosity, a related quantity differing only by a factor of the density is known as the kinematic viscosity.
This is a means of cross-linking polymers to form a network based on sulphur bonds. It is used to make elastomers and was developed originally to process natural rubber.
The Weber number, We, is used to characterise the flow of one fluid in another and is defined as:
We = (ρ v2 l )/ γ
where ρ is the density of the fluid, v is the velocity, l is a characteristic length such as the diameter of a drop and γ is the surface tension. It provides a measure of the relative importance of inertial forces and interfacial tension. It is useful to estimate, for example, the formation or break-up of drops and bubbles in a flow.
The distribution of polymer sizes in most synthetic materials (polydispersity of molecular mass) implies that different averages will give different values. The weight average is defined as the sum of niMi2 divided by the sum of niMi where ni is the number of molecules in the distribution with mass Mi. The weight average molecular mass is the quantity measured in an elastic light scattering experiment. The weight average molecular mass will always be bigger than the number average molecular mass for polydisperse materials.
MW = Σ niMi2 / Σ niMi
A liquid is said to wet a solid or another liquid if it spreads over the interface to provide a contact angle of zero.
This is a means to measure surface tension of a liquid. A rectangular plate is dipped in to the surface and the force due to the contact line of liquid and solid is measured with a sensitive balance that supports the plate. The force, F, is given by:
F = 2 γ x cos θ
where x is the length of the plate, γ is the surface tension and θ is the contact angle of the liquid on the plate. Normally the material of the plate is chosen so that the contact angle is zero and cos θ is 1. Typical materials are filter paper, glass or a metal such as platinum/iridium alloy. The thickness of the plate is assumed to be negligible and so the length of the contact line is 2x. There may be additional corrections to the measured force for buoyancy of the plate (or displacement of the liquid).
The characteristic times of polymers such as the reptation time described above vary with temperature. Often the effects of time and temperature can be related by a time/temperature superposition principle of the form:
ln (t/t0) = - a ( T - Tg) / { b + (T - Tg) }
where t0 is a characteristic relaxation time at some temperature Tg and t is the relaxation time at a temperature T above the temperature Tg. There are two constants that have similar values for many polymers: a has the value of about 17 and b is approximately 52 K. The quantity Tg is the glass transition temperature and does vary widely between different polymers.
Some micelles of surfactants will grow as elongated structures. When long enough these resemble solutions of flexible polymers more than rods. While these materials can be entangled and may display properties such as reptation there is an extra degree of freedom in that the micelles are dynamic structures and may break and reform.
The yield stress is a finite stress at which a material starts to flow or yield.
Young's equation relates the contact angle, θ of a liquid on a solid and interfacial tensions of the material:
γSV = γSL + γLV cos θ
where γSV is the solid-vapour interfacial tension, γSL is the solid-liquid interfacial tension and γLV is the liquid-vapour interfacial tension.
The Young's modulus, E, is the elastic constant of a material that describes the relationship between elongational stress, σe and elongational strain, γ.
E = σe / γ.
The distribution of polymer sizes in most synthetic materials (polydispersity of molecular mass) implies that different averages will give different values. The Z-average is defined as the sum of niMi3 divided by the sum of niMi 2 where ni is the number of molecules in the distribution with mass Mi. This quantity can be compared with other averages of the molecular mass such as the weight average and the number average.
MZ = Σ niMi3 / Σ niMi2
The viscosity of many fluids varies with shear rate due to the structural changes in the sample that occur as it is deformed. It is often convenient to determine the viscosity extrapolated to zero shear rate to provide a consistent, uniform comparison with other systems. This is the zero shear viscosity.
The zeta (ζ) potential of a colloidal particle is the interaction potential observed by hydrodynamic measurements such as electrophoresis. The force on an electric charge in an electric field is balanced by the viscous drag such that the particle moves at a constant velocity. The potential measured in this way can differ from those seen in static measurements or titration of charge as it will depend on details of viscous drag (the hydrodynamic radius) and the screening of charge by ions in the solution.
A Zimm plot displays scattering data (static light scattering, small-angle neutron scattering or small-angle X-ray scattering) for polymers. Intensity, I(Q), is plotted as:
c / I(Q) vs. Q2
or
c / I(Q) vs. Q2 + const. x c
where c is the concentration and Q is the scattering vector given by:
Q = (4π/λ) sin(θ/2)
where λ is the wavelength and θ is the scattering angle.
The data should lie on a straight line for QRg less than 1 and the gradient divided by the intercept is Rg2/3. Rg is the radius of gyration. The intercept is inversely proportional to the molecular mass if an extrapolation of the data to zero concentration is made. This can be compared with a Guinier plot that is frequently used for solid particles (colloids).
This is a surfactant molecule that contains two different groups, one that may gain and the other that may lose a charge, such as an acid and a base. The two groups can dissociate and provide an ionic head group with no net charge.
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Last Updated 27 December 2022