Phase Transition - an overview | ScienceDirect Topics

A phase transition is a qualitative change in the state of a system under a continuous change in an external parameter (Li, 2002).

3.2 Differential Scanning Calorimetry (DSC)

Phase transitions are accompanied by a change in enthalpy, ΔH, and thus by a change in entropy, ΔS (ΔS = ΔH/Ttransition under equilibrium conditions, ΔG = 0). The magnitude of the entropy change is related to the amount of order that is lost or gained during the transition. In a DSC experiment, the enthalpy changes corresponding to the different phase transitions of a sample are measured by determining the power supplied to (or absorbed by) the sample. The phase transition temperatures can be accurately determined by this method. Phase transitions can be of first or second order. A first-order phase transition is characterized by a discontinuous jump in the first derivative of the Gibbs free energy (G) in function of the temperature (T), ∂G(T)/∂T. The enthalpy H, entropy S, and volume V can all be defined by appropriate first derivatives of the Gibbs free energy (e.g., ΔS = − Δ(∂G/∂T)) and consequently all these variables change discontinuously at a first-order transition. In a so-called thermogram, in which the heat flow is plotted as a function of time (t) or temperature (T), first-order phase transitions can be visually distinguished by sharp peaks and large enthalpy changes (i.e., large peak areas). Typical first-order phase transitions are the melting and clearing process of a LC, but also some mesophase-to-mesophase transitions can be of first order. A second-order phase transition is characterized by a continuous first derivative of the Gibbs free energy, but a discontinuous second derivative. In this case, the heat capacity Cp will exhibit a discontinuous jump, and results in a step in the baseline of the thermogram. The SmA–SmC transition (with a continuous change of the tilt angle) is a typical example of a second-order transition.

DSC is a widely used technique in the investigation of phase transitions of LCs. There are two types of DSC modules on the market: the heat-flux DSC and the power-compensation DSC. The principle of heat-flux DSC is illustrated in Fig. 17. Heat-flux DSC makes use of one furnace to heat both the sample crucible and an empty reference crucible, which corrects for the heat capacity of the crucible material. Symmetrical heating is achieved by constructing the furnace from a metal with a high thermal conductivity, such as silver. The temperature is measured at the heat-flux plate, which generates a very controlled heat flow from the furnace surface wall to the sample and reference, and between the two crucibles. When a sample S and a reference R are uniformly heated in a furnace and when an exothermic effect takes place in the sample, the temperature of the sample TS will be higher than that of the reference, TR. In the case of an endothermic effect the temperature of the sample will be lower than that of the reference. The temperature difference ΔT = TS − TR is recorded against the temperature TR. Because the sample and reference are placed on the heat-flux plate, ΔT is proportional to the heat-flux difference between the sample and reference. When the sample mass is known and the temperature lag is measured very accurately, the energy of the transition (the enthalpy change) can be calculated. In addition, precise transition temperatures are obtained. However, calibration with a standard compound (e.g., indium, Tm = 156.6 °C) remains necessary. In a power-compensating DSC, the sample and reference are placed in two different furnaces. The temperature difference between the sample and the reference is kept at zero (ΔT = TS − TR = 0) by independent heaters in the sample and reference furnaces (Fig. 18). The small crucibles or sample pans for DSC measurements are usually made of aluminum (Tm = 660 °C), and sealed with a lid. A hole can be pierced into the lid to allow possible decomposition products to escape from the crucible, instead of building up an internal pressure, and/or to create a specific atmosphere around the sample (e.g., a helium atmosphere). A few milligrams of sample are needed (e.g., 2 mg if a good resolution of phase transition peaks is required, 5 mg if a good sensitivity is required). Typical heating rates for the investigation of liquid-crystalline samples are 2–10 °C min− 1. Heating normally occurs under an inert atmosphere, preferentially helium (because of the good thermal conductivity of this gas).

Sign in to download full-size image Figure 17. Heat-flux DSC cell. S = sample, R = reference.

Sign in to download full-size image Figure 18. Power-compensation DSC cell. S = sample, R = reference.

In a thermogram, the heat flow (∂Q/∂t, in mW) is plotted as a function of time (t) or temperature (T). The enthalpy change ΔH associated with a certain transition corresponds to the integral of the DSC curve with respect to time (peak area). According to the commonly used definition in LC research, the heat flow It has a positive value for endothermic transitions (in which heat is absorbed by the sample), and a negative value for exothermic transitions (in which heat is released by the sample). Enthalpy changes between successive liquid-crystalline phases or between a liquid-crystalline phase and the isotropic liquid are typically quite small, around 0.5–10 kJ mol− 1. Mesophase-to-mesophase transitions are sometimes not even detectable by DSC. The enthalpy change between a crystalline phase and a liquid-crystalline phase is usually quite large, in the range 10–80 kJ mol− 1. However, the ΔH values strongly depend on the types of solid and liquid-crystalline phases. Large enthalpy changes correspond to large changes of molecular organization in the sample. The change in entropy can be determined by dividing the enthalpy change ΔH by the transition temperature, Ttransition (expressed in Kelvin): ΔS = ΔH/Ttransition. DSC is strictly complementary to optical microscopy. Sometimes a phase transition is accompanied by only a very small textural change, which might be overlooked by the observer. On the other hand, not all textural changes result from phase changes. Enthalpy and entropy values can give an indication of the type of mesophase. An example of DSC trace is given in Section 4 (Figure 30).

2.03.4.2.3 MORB

Phase transitions in basaltic compositions, such as illustrated in Figure 10(c) for a MORB composition, are quite different from those expected in pyrolite and harzburgite compositions. Basaltic compositions are shown to crystallize to Mj + small amounts of stishovite (St) in the mantle transition region (Irifune and Ringwood, 1987, 1993; Hirose et al., 1999; Ono et al., 2001), which progressively transform to an assemblage of Ca-Pv + Mg-Pv + St + Al-rich phase (hexagonal or CF/CT structures) over a wide pressure range of ∼ 3 GPa (from ∼ 24 to ∼ 27 GPa). Although the garnetite facies of MORB, composed mainly of Mj, is substantially denser than pyrolite, a density crossover is expected to occur in a limited depth range (660 to ∼ 720 km) of the uppermost lower mantle due to this smeared-out nature of the garnetite-to-Pv transition in MORB.

Once Ca-Pv and Mg-Pv are formed in basaltic compositions, it is shown that they become denser than pyrolite or peridotite throughout almost the entire region of the lower mantle (Irifune and Ringwood, 1993; Hirose et al., 1999, 2005; Ono et al., 2001, 2005d). As St is highly incompressible (Figure 9), the density of the perovskite facies of basaltic compositions may approach that of the pyrolitic composition with increasing pressure. However, the transition of St to CaCl2 (CC) and α-PbO2 (AP) structures should keep this lithology denser than pyrolite throughout the lower mantle, as shown in Figure 11. In fact, most recent experimental studies using LHDAC (Ono et al., 2005d; Hirose et al., 2005) conclude that densities of basaltic compositions are higher than those in the representative model mantle compositions throughout the lower mantle by about 0.02–0.08 g cm−3, depending on the adopted pressure scale for gold.

2.03.4.2.3 Mid-ocean ridge basalt

Phase transitions in basaltic compositions, such as illustrated in Figure 10(c) for a MORB composition, are quite different from those expected in pyrolite and harzburgite compositions. Basaltic compositions are shown to crystallize to Mj + small amounts of St in the mantle transition region (Hirose et al., 1999; Irifune and Ringwood, 1987, 1993; Ono et al., 2001), and then progressively transform to an assemblage of Ca-Pv + Mg-Pv + St + Al-rich phase (NAL phase, which is replaced by the CF phase at pressures greater than ~ 50 GPa according to Ricolleau et al., 2010) over a wide pressure range of ~ 3 GPa (from ~ 24 to ~ 27 GPa). Although the garnetite facies of MORB, composed mainly of Mj, are substantially denser than pyrolite, a density crossover is expected to occur in a limited depth range (660 to ~ 720 km) of the uppermost lower mantle due to this smeared-out nature of the garnetite to Pv transition in MORB.

Once Ca-Pv and Mg-Pv are formed in basaltic compositions, it is shown that they become denser than pyrolite or peridotite throughout almost the entire region of the lower mantle (Hirose et al., 1999, 2005; Irifune and Ringwood, 1993; Ono et al., 2001, 2005d). As St is highly incompressable (Figure 9), the density of the perovskite facies of basaltic compositions may approach that of the pyrolitic composition with increasing pressure. However, the transition of St to CaCl2 (CC) and α-PbO2 (AP) structures should keep this lithology denser than pyrolite throughout the lower mantle, as shown in Figure 11. In fact, most recent experimental studies using LHDAC (Hirose et al., 2005; Ono et al., 2005d; Ricolleau et al., 2010) conclude that densities of basaltic compositions are higher than those in the representative model mantle compositions throughout the lower mantle by about 0.02–0.08 g cm− 3, depending on the adopted pressure scale for gold.

2.18.2.6 Shock Melting

Phase transitions may be identified in experiments employing shock waves by the measurement of discontinuities; in sound velocities, temperature, and pressure–volume Hugoniot curves. Discontinuities in the P−V Hugoniot, originating from melting, are generally too small to be reliable, except for very accurate data. Because of the loss of shear strength in the liquid, measurements of the sound velocity has proved to be the most useful method for detecting the pressure and density at melting. Since temperature measurements have not proven feasible for opaque materials, such as Fe (Yoo et al., 1993), they need to be calculated. These calculations (Boness and Brown, 1990; Brown and McQueen, 1986) depend on estimates of the specific heat and Grüneisen parameter, which for iron lead to uncertainties of order ±500 K. Each of the diagnostic methods suffer from the possibility that the short nanosecond timescales of the shock transit may cause overshoot of the equilibrium melt pressure resulting in an overestimate of the melting temperatures.

Brown and McQueen (1986) have reported two discontinuities in the sound velocity from measurements along the iron Hugoniot, one at 200 GPa (∼4000 K) and a second at 243 GPa (∼5500 K). The first was identified as the onset of a solid–solid transition, and the second as the onset of shock melting. Recently, however, Nguyen and Holmes (2004) have reported sound velocity measurements, which show only a single transition, interpreted as melting, with an onset at 225 GPa (5100 ± 500 K), a pressure lying between the two transitions of BM. These data are plotted in Figure 8.

Sign in to download full-size image Figure 8. Sound velocities along the iron Hugoniot (Brown and McQueen, 1986; Nguyen and Holmes, 2004). BM (lower dashed line) have reported two discontinuities, one near 200 GPa (∼4000 K) and a second at 243 GPa (∼5500 K). The first was identified as the onset of solid–solid transition, and the second as the onset of shock melting. NH (upper dashed line) have reported only a single transition, interpreted as melting, with an onset at 225 GPa (5100 ± 500 K).

Except for the region between about 200 GPa and 240 GPa, the shock melting data of Brown and McQueen and Nguyen and Holmes are in good agreement. A consistent picture can be drawn in which the solid melts at 200 GPa to a viscous melt, and the normal, less viscous liquid exists above 225–243 GPa. The corresponding calculated temperature at 200 GPa is 4350 ± 500 K (Boness and Brown, 1990), compared to 3850 ± 200 K on Boehler’s melting curve. Thus, the two data sets would agree within their experimental uncertainties. We suggest that a plausible explanation for the offset is due to an overshoot and superheating in the shock experiment.

In order to superheat a bulk solid, there must be a barrier to the nucleation of the melt. Appreciable bulk superheating of solids with shock waves has been observed in alkali halides (Boness and Brown, 1993; Swenson et al., 1985) and fused quartz (Lyzenga et al., 1983) and discussed by Luo (Luo and Ahrens, 2003) for metals. In the case of alkali halides and fused quartz, the overshoot is due to a need for a structural reorganization from the solid to liquid on a nanosecond timescale. A possible mechanism for an overshoot in iron is the presence of ISRO clusters in the melt providing a viscosity sufficiently high as to delay melting by about 10% in pressure, from 200 to 225 GPa. Brown (2001) has reported that an examination of a definitive set of Los Alamos Hugoniot data (Brown et al., 2000) for iron, in the pressure range to 442 GPa, shows a small density-change discontinuity of about −0.7% at 200 GPa. Brown infers that this supports the conclusion that a phase of iron other than h.c.p. may be stable above 200 GPa.

F Phase transitions and phase equilibria

A phase transition is a change in state from one phase to another. The defining characteristic of a phase transition is the abrupt change in one or more physical properties with an infinitesimal change in temperature. Dry ice subliming to CO2 (g), ice melting to water, water boiling to steam, orthorhombic sulfur transforming to monoclinic sulfur, calcite transforming to aragonite, and graphite transforming to diamond are all examples of phase transitions. Each of these phase transitions can be represented by a reaction. For example, Eq. (7-3) represents the transition of orthorhombic to monoclinic sulfur at 368.54 K at one bar total pressure. Likewise, Eq. (7-4) represents monoclinic sulfur melting to liquid sulfur at 388.36 K at one bar total pressure.

Water boils to steam at 100°C at one atmosphere pressure. (We use a pressure of one atmosphere because the normal boiling point is defined as the temperature at which a liquid boils to vapor with one atmosphere pressure.) However, if we are at high altitudes, water boils at a lower temperature because atmospheric pressure is lower.

In general, the temperature at which a phase transition occurs depends on the total pressure. We could rephrase this to say that the pressure at which a phase transition occurs depends on the temperature. The two statements are equivalent. The set of P-T points at which a phase transition occurs can thus be represented by a curve on a plot of temperature versus pressure. Figure 7-1 shows an example for water boiling to steam, or more scientifically, for the vaporization curve of liquid water. The curve in Figure 7-1 extends from 0°C (where air-saturated liquid water and ice stably coexist at one atmosphere pressure) to 373.946°C (647.096 K, the critical point of water where liquid water and steam merge into one phase). The shape of the vaporization curve of liquid water is characteristic of all vaporization curves: convex toward the temperature axis. Figure 7-2 shows the curve for dry ice (solid CO2) subliming to CO2 (g). A comparison of Figures 7-1 and 7-2 shows that the vaporization curve for water and the sublimation curve for CO2 have the same characteristic shape. The vaporization curve for a liquid (e.g., water) and the sublimation curve for a solid (e.g., solid CO2) are the same as the vapor pressure curves for the liquid and solid.

Sign in to download full-size image FIGURE 7-1. The vaporization curve for liquid water from 0°C to 374°C.

Sign in to download full-size image FIGURE 7-2. The sublimation curve for solid CO2 (dry ice) from 140 K to 200 K.

Equations (7-1) to (7-4) are also examples of phase equilibria in which the different phases stably coexist with one another. Thus, orthorhombic and monoclinic sulfur stably coexist at one bar pressure if we maintain the temperature at 368.54 K. Equilibrium between two or more phases is independent of the amount, size, and shape of the phases, except for very small droplets or particles, for which the surface energy becomes important. For example, at 273 K the vapor pressure of water droplets with radii of 0.1, 0.01, and 0.001 μm are 1.012, 1.128, and 3.326 times higher, respectively, than that over pure water (Dufour and Defay, 1963). These effects are important for the thermodynamics of clouds in planetary atmospheres.

2.14.4.5 Ferroelastic Phase Transition and Flip of Twinning State

Ferroelastic phase transitions are important processes for materials such as perovskite. Stress induces transformation from one twin state to another, a process that can consume energy and introduce a transformational strain, which may lower the elastic moduli. Figure 16 illustrates diffraction patterns taken as a function of time during a single stress cycle. The pattern illustrates the (020), (112), (200) triplet of the perovskite pattern for NaMgF3. Stress drives the structure between these three orientations through a twinning process. The change in lattice spacing as indicated by the position of the diffraction peak emphasizes the strain induced by the twinning process.

Sign in to download full-size image Figure 16. Several diffraction patterns, as a function of time, centered on the (020), (112), (200) triplet during a single stress cycle. The peak position, reflecting the lattice spacing, moves back and forth between the spacing for each of the three peaks.

2.2 Quantum Critical Theory

A QPT is a second order phase transition that occurs at zero temperature, as a function of pressure, magnetic field or any tuning parameter g other than temperature. A standard way of obtaining such a transition is by suppressing the critical temperature of an ordered state—such as a ferromagnet or antiferromagnet—to zero temperature by, for example, pressure. When the pressure exceeds the critical pressure, a quantum disordered regime appears.

Exactly at the critical value of the tuning parameter g = gc, the system develops many unconventional properties. The relevance of QPTs is that for nonzero temperatures close to the critical value gc the system is still dominated by quantum critical excitations. Thus can arise unconventional specific heat, resistivity, magnetic susceptibility, and so on. This “quantum critical regime,” as shown in the typical phase diagram of Fig. 2, is thought to be the key toward understanding many abnormal properties of materials.

Sign in to download full-size image Fig. 2. The typical phase diagram of a quantum phase transition. The horizontal axis represents a tuning parameter g, which can be pressure, magnetic field, or particle density; the vertical axis represents temperature. The high g regime to the right represents the “quantum disordered” phase: a paramagnet or just a regular Fermi liquid. At low g there is an ordered phase, for example, a (anti) ferromagnet. The quantum critical point resides exactly at T = 0 where the system goes from the ordered to the disordered phase. At this critical value of g = gc, the nonzero temperature regime is denoted as “quantum critical.” In this part of the phase diagram, many properties such as the specific heat or the resistivity are unconventional due to the vicinity of the quantum critical point. Such unconventional behavior is usually referred to as “non-Fermi liquid” behavior.

In this section, we first provide the traditional theory of how such a quantum critical regime appears. As for all phase transitions, the key lies in the concept of scaling functions and the corresponding exponents close to the transition. In fact, there is an intricate link between QPTs and thermal phase transitions, which becomes clear by considering the example of the Ising model.

Critical exponents for any given model can be computed using the methods of statistical physics. The starting point is to define the microscopic Hamiltonian H relevant for the system under study. For the Ising model, a model of interacting spins that can describe (anti)ferromagnetic phase transitions, the Hamiltonian is

(5)$\begin{array}{c}H=-J\sum _{〈ij〉}{S}_i^z{S}_j^z,\end{array}$

where $S_i^z$ is the z-component of a classical spin at a lattice site i. For J > 0, this model has a ferromagnetic ground state and we therefore expect that below some temperature the system develops spontaneous magnetization.

The Ising model is classical, so that the partition function $Z={\sum }_n{e}^{-\beta E_n}$, where the sum runs over all possible spin states with energy En. Any macroscopic quantities that we are interested in, such as magnetization or specific heat, can be derived from the free energy $F=-k_{B}TlogZ$. In some cases, the partition function and, hence, the free energy can be computed exactly, in most cases, however, we need to resort to an approximation scheme.

The most successful theory is Landau mean field theory: here we assume that spins interact only with the average field of all other spins, given by m(x). A free energy functional can then be written as a function of the magnetization m(x) and temperature T. In general, for a d-dimensional system, we have

(6)$\begin{array}{c}F(m,T)=\int d^{d}x\left(c{(\nabla m(x\left)\right)}^2+a_2\left(T\right)m{\left(x\right)}^2+a_{4}m{\left(x\right)}^4+\cdots \right)\end{array}$

where a2, a4, and c are some parameters. For a CPT, Landau showed, we must have a2 ∼ t with t the reduced temperature, a4 and c are positive definite. The magnetization can be found by minimizing $F(m,T)$ with respect to the order parameter m(x).

From just these very general considerations, we can compute critical exponents. For example, minimizing the free energy with respect to a homogeneous m gives us the order parameter exponent β = 1/2. The second derivative $C_V=\frac{{\partial }^{2}F}{\partial T^2}$ yields the specific heat exponent α = 0. Explicitly writing out the correlation functions for an inhomogeneous order parameter m(x) yields ν = 1/2 and η = 0. Finally, an external magnetic field can be included by adding $-h\int d^{d}xm\left(x\right)$ to the free energy, which yields δ = 3 and γ = 1. (See chapter 4 from Yeomans, 1992 for more details.)

Mean field theory ignores fluctuations, but with increasing dimensionality of the system these fluctuations become less and less relevant. In fact, the mean field exponents become exact in $d>\frac{2-\alpha }{\nu }$ dimensions. This is called the upper critical dimension, so that, for example, the Ising model in d > 4 dimensions is determined by mean field exponents.

We are now in a position to continue toward quantum systems, where the phase transition does not occur as a function of temperature but at zero temperature due to a change in model parameters. Because in a quantum system the Hamiltonian is an operator the partition function is now given by,

(7)$\begin{array}{c}Z=\text{Tr}exp\left(-\beta Ĥ\right).\end{array}$

The Ising model can be extended to a quantum model, known as the transverse field Ising model. The properties of this model are described in detail by Sachdev (2011). It is the prime example of a magnetic system exhibiting a QPT. The Hamiltonian is

(8)$\begin{array}{c}{H}_{TFIM}=-Jg\sum _i{S}_i^x-J\sum _{〈ij〉}{S}_i^z{S}_j^z\end{array}$

where J > 0 is the magnetic exchange coupling between spins, and g is the magnitude of a transversal magnetic field. Now g acts as the tuning parameter that can induce a phase transition between a ferromagnetic phase and a paramagnetic phase. For g≪1 (ferro)magnetic order prevails with two possible ground states,

(9)$\begin{array}{c}|{\psi }_0〉=\prod _i|\uparrow {〉}_i,\text{or}\prod _i|\downarrow {〉}_i.\end{array}$

Oppositely, for a large transverse field g≫1, the ground state is an uncorrelated ($〈S_i^z{S}_j^z〉={\delta }_{ij}$) paramagnet

|ψ0〉=∏i|→〉i=∏i(|↑〉i+|↓〉i)/2.

The paramagnet and the ferromagnet are distinctively different. Therefore, under increase of the transverse field g there will be a QPT from the ferro- to the paramagnet at g = gc.

Suzuki (1976) discovered that the free energy of the d-dimensional quantum Ising model is equivalent to the (d + 1)-dimensional classical Ising model. Explicitly, the quantum partition function can be rewritten as a Feynman path integral where the inverse temperature β = 1/kBT acts an extra dimension called imaginary time τ ∈ [0, β). At zero temperature, the free energy for the d-dimensional quantum Ising model becomes

(10)$\begin{array}{c}F(m,g)=\int d^{d}xd\tau \left\{c{\left({\partial }_{\mu }m\right(x,\tau \left)\right)}^2+a_2\left(g\right)m{(x,\tau )}^2+a_{4}m{(x,\tau )}^4+\cdots \right),\end{array}$

so that the tuning parameter is now g as opposed to T for the classical phase transition.

The parameter a2 ∼ (g − gc) changes sign when the transverse field is increased. At the transition, not only spatial correlation length diverges, but also the imaginary time correlations ξτ. They are related by the dynamical critical exponent z,

(11)$\begin{array}{c}{\xi }_{\tau }\sim {\xi }^z.\end{array}$

It is easy to see that for the Ising model, the dynamical critical exponent is z = 1, since x and τ are treated on the same footing.

All other critical exponents can be derived from the critical exponents of the (d + 1)-dimensional classical Ising model. We have m ∼ (g−gc)β for the order parameter, and similar expressions for the susceptibility exponents and the correlation length exponents. All of those are listed in Table 1. Note that there is not an analogue of the specific heat exponent at zero temperature.

In conclusion, we note that both classical and quantum field theories are described by a free energy functional that depends on the order parameter. The quantum transverse field Ising model in d dimensions is equivalent to the classical Ising model in (d + 1) dimensions. This allows us to find the critical exponents associated by the QPT in the quantum Ising model from the classical exponents. In Section 2.4.1, we will discuss Li(HoY)F4, a rare earth material that displays characteristics of a quantum Ising phase transition.

The Transition Phase

During the transition phase, known also as the ‘pause phase,’ the seed-water content, respiration rate, and apparent morphology remain almost unchanged. Nevertheless, a variety of metabolic processes are activated, and differences in the activity levels of these processes and in their order of occurrence have been observed among seeds of different species and among seeds that have reached different hydration levels. Therefore, any adverse environmental conditions that lead to redrying of the seeds, e.g., by subjecting them to water stress, or reduce the seed–soil contact area, and thus influence their hydration levels, may impair, retard, or even inhibit germination. If no damage had resulted, no secondary dormancy been induced, and no inhibitory processes been blocked, the germination of these seeds upon rewetting would be enhanced because of the high concentration of unused metabolites accumulated prior to drying. The duration of the transition phase influences the initiation time and the extent of radicle growth. Seeds have been observed to reach the transition phase and to remain in it for long periods that may extends for days, weeks, or more before germination. Toward the end of the transition phase, the embryonic cells of the radicle start to divide.

8.15.4.4.2 Thermal methods

The volume phase transition of a temperature-sensitive polymer is correlated with the dissociation of the bound water molecules from the hydrophobic groups of the polymer chains. For NIPAAm-based polymers the dissociation enthalpy is large enough to be detected by methods of thermal analysis (Figure 28). The measurement of this enthalpy by DSC of a solution or of a swollen network gives us the possibility to determine the temperature of volume phase transition.322,337 Often this temperature is defined as the intersection of the baseline and the leading edge of the enthalpy curves (exotherms of gel swelling, cooling; endotherms of gel shrinking, heating). The experiments show a slight difference between the temperature of transition in solution and in gel (T(gel) > T(solution)), but no effect of polymer concentration in the swollen gel. The enthalpy of volume phase transition in BIS cross-linked PNIPAAm is measured to (3.3 … 5.2) kJ mol−1.322

Sign in to download full-size image Figure 28. DSC thermograms of (a) PNIPAAm solutions and (b) PNIPAAm gels. The term ‘first run’ indicates a virgin sample. After DSC scanning of a first-run sample, the DSC pan was rapidly cooled to ambient temperature and aged for a given time t. Successive DSC scanning was then conducted. Reprinted with permission from Shibayama, M.; Suetoh, Y.; Nomura, S. Macromolecules 1996, 29, 6966–6968.337 Copyright 1996 American Chemical Society.

9.05.3.5.3 Protein purification

The phase transition of elastin-mimetic materials may be utilized for purification recombinant proteins as fusions to the elastin sequence.124 This method has the advantage that the purification can be performed through the relatively benign method of inverse temperature cycling (Figure 12), which can afford high purity fusions without the need for complex and potentially expensive chromatographic purification techniques. Numerous proteins have been purified using this technique, although the sequence and length of the elastin fusion may need to be optimized for a specific fusion partner.125 A recent improvement in the process involves the use of a self-cleaving intein sequence between the protein of interest and the elastin purification tag.126 After induction of the protein-splicing event, the target protein is released in an effectively traceless cleavage process and can be purified from the elastin tag through inverse temperature cycling. The elastin fusion proteins have been employed as reagents in several applications, including controlled release, surface modification, and environmental remediation.

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