Light Scattering Investigations Near The Critical Point In Some Solvophobic Systems And The Design And Analysis Of A Microkelvin Thermostat For Critical Phenomena Studies
Unni, P K Madhavan
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This thesis reports light-scattering experiments and visual investigations close to the critical point, in the solvophobic systems, 3-methylpyridine (3MP) + heavy water (D2O) + sodium bromide (NaBr) and methyl ethyl ketone (MEK) + water (W) + secondary butyl alcohol (sBA). The system 3MP + D2O + NaBr was chosen in order to throw more light on the reported crossover from mean-field to Ising-type of critical behaviour shown by this system and to investigate the existence of a mean-field tricritical point in it at an NaBr weight fraction of X = 0.1700, two issues that have been the subject of an intense scientific debate in recent years. The system MEK + W + sBA is the result of our search for a system, other than, the well known 3-methylpyridine (3MP) + water (W) + heavy water (HW) + potassium iodide (KI), in which a quadruple critical point (QCP) can potentially be realized. In addition to this the thesis provides exhaustive details regarding the design, fabrication, and characterization, of a microkelvin thermostat in which a temperature stability of the order of a few microkelvin is achievable despite its relatively simple thermal design. The thesis is organized into 6 Chapters. Chapter 1 provides an introduction to the field of critical phenomena in liquid mixtures. The critical phenomena observed in various systems such as simple fluids, ionic fluids, polymer blends and polymer solutions, and micellar and microemulsion systems, are discussed in brief. Particular attention has been paid to the investigations by various researchers, into, the crossover from Ising to mean-field critical behaviour in electrolyte and polymer solutions, and in amphiphilic systems. Recent theoretical attempts at modeling ionic criticality have also been cited and summarized. A brief discussion on the various types of special critical points and multicritical points that are observed in multicomponent liquid mixtures and other condensed matter systems has been provided. The appealing possiblity of the presence of multicritical points in ionic fluids leading to crossover behaviour is also discussed. The chapter ends with a statement on the goals of this thesis. Chapter 2 describes the instrumentation and other aspects of the experimental techniques used for the light-scattering studies reported in this thesis. Details about the thermal instrumentation such as the water bath and the silicone-oil bath used for the visual investigation experiments and the metal thermostat used for the light-scattering experiments have been provided. The important design considerations relating to the achievement of a high degree of temperature stability (Formula) have been elucidated clearly. The modifications made to the design of the light-scattering thermostat, that enables achievement of a temperature stability of ± 2.5 mK at temperatures 19 ≤ T ≤ 24°C has been discussed. A section has been devoted to the description of the calibration of the temperature sensors we used in our experiments. The light-scattering instrumentation has been discussed in depth. The difficulties associated with the light-scattering techniques when it is used as a tool to study critical phenomena have been detailed. This is followed by a description of the method we used in correcting our light-scattering data for double-scattering effects. A description of the sample cells used for visual investigations and light-scattering experiments along with the sample filling and cleaning procedures followed by us has been described. Chapter 3 deals with the first of the three important problems discussed in this thesis. The chapter is aimed at investigating the crossover behaviour of the solvo-phobic system 3-methylpyridine (3MP)+ water (H2O) + sodium bromide (NaBr), by means of light-scattering studies on the strongly motivated and non-trivial system of 3-methylpyridine (3MP) + heavywater (D2O) + sodium bromide (NaBr). The replacement of H2O by D2O in 3MP + D2O + NaBr, is expected to accentuate the crossover behaviour reportedly displayed by 3MP + H2O + NaBr, and thereby, provide conclusive evidence regarding the existence or otherwise of a crossover between the Ising- and the mean-field-types of critical behaviour in this system. The chapter begins with a detailed literature survey on the topic of the crossover behaviour shown by the system 3MP + H2O + NaBr. We also provide a survey of the effect of the iso-topic H→D substitution on the critical behaviour of binary and quasibinary systems. Through an argument based on small-angle neutron scattering (SANS) studies and the Kirkwood-Buff integrals (KBIs), a strong and cogent motivation is established, which proves that, if the reported crossover behaviour in 3MP + H2O + NaBr is assumed to be correct, then the system 3MP + D2O + NaBr should display not just the same crossover behaviour as shown by the undeuterated system 3MP + H2O + NaBr, but, in addition, also a more pronounced dependence of the crossover temperature on the concentration of NaBr in the mixture than that seen in 3MP + H2O + NaBr. This approach to understand the crossover behaviour of 3MP + H2O + NaBr, has not been used by any of the previous investigators. The coexistence curve data for the system 3MP + D2O + NaBr are obtained at six different values of the NaBr weight fractions viz. X = 0, 0.0250, 0.0800, 0.1200, 0.1500, and 0.1800. The closed-loop immiscibility loop obtained for X = 0, agrees well with the reported phase diagram for 3MP + D2O in the literature. A comparison between the lower-critical lines obtained for the deuterated and the undeuterated system has been provided. Within error bars, no perceptible dip was observed in the critical line at X = 0.1700 in the case of the system 3MP + D2O + NaBr. Hence, our study does not indicate the presence of a mean-field tricritical point that has been reported at X = 0.1700 in the system 3MP + H2O + NaBr. A large section of Chapter 3 is devoted to the results and discussions of our extensive light-scattering experiments on the system 3MP + D2O + NaBr. The experiments were performed on 13 different samples of 3MP + D2O + NaBr with NaBr weight fractions in the range of 0 ≤ X ≤ 0.1900. The choice of the X values were guided by the NaBr concentrations at which earlier investigators have done light-scattering experiments on the system 3MP + H2O + NaBr. Detailed light-scattering experiments reveal that the system 3MP + D2O + NaBr shows a simple Ising-type critical behaviour with γ ' 1.24 and ν ' 0.63 over the entire NaBr concentration range 0 ≤ X ≤ 0.1900. The crossover behaviour is predominantly nonmonotonic, and the crossover is completed well outside the critical domain. An analysis in terms of the effective susceptibility exponent (γeff) showed that the crossover behaviour is nonmonotonic for 0 ≤ X ≤ 0.1793 and tends to become monotonic for X > 0.1793. The correlation length amplitude, ξo, has a value of (Formula) for 0.0250 < X ≤ 0.1900, whereas for (Formula). Since isotopic H—> D substitution is not expected to change the critical behaviour of the system, our results shows that the system 3MP + H2O + NaBr should exhibit universal Ising-type critical behaviour that is typical for aqueous solutions. Our search for a new system in which a quadruple critical point (QCP) could possibly be realized forms the subject matter of the Chapter 4 of the thesis. The system methyl ethyl ketone (MEK) + water (W) + secondary butyl alcohol (sBA) is identified as a very promising candidate-system for this purpose. The chapter begins with a brief survey of the various types of multicritical points and special critical points realizable in multicomponent liquid mixtures. The importance of investigating special critical points such as the QCP is motivated. A detailed coexistence surface for MEK + W + sBA was developed by generating the coexistence curves corresponding to five different, but onstant, values of MEK weight fractions XM = 0.0500, 0.1000, 0.1750, 0.2300, and 0.3000, respectively. The complete isobaric coexistence surface (at 1 atm) for the system MEK + W + sBA was visualized in the form of a prismatic phase diagram. The surface is found to display a tunnel-like appearance in the MEK weight fraction range of 0.0500 ≤ XM ≤ 0.1750, with the tunnel being the narrowest at the point (XM,XW,XSBA) = (0.1750, 0.5801, 0.2449), where, xw and XSBA are, respectively, the weight fractions of water and sBA in the mixture. An analysis of the order parameter data showed that MEK + W + sBA shows near Ising-type of critical behaviour near their upper critical solution temperatures, TU's. It was seen that the critical temperature Tc shows a low drift with time (Formula)/day and that the tunnel-like portion in the phase diagram of MEK + W + sBA was very symmetric. These two features make (MEK + W + sBA) a considerably more promising system than (3MP + W + HW + KI )for the realization of the QCP. It may be recalled that 3MP + W + HW + KI is the only system in which QCP studies have been reported so far in literature. The light-scattering investigations in MEK + W + sBA near the lower critical solution temperatures TL are described next. We corrected our light-scattering data for both turbidity as well as double-scattering effects. Our experiments revealed that (MEK + W + sBA) shows near three-dimensional-Ising type of critical behaviour at the lower critical solution temperatures, with the susceptibility exponent (γ) in the range of 1.217 ≤ γ ≤ 1.246. The correlation length amplitudes (ξo) and the critical exponent (ν) of the correlation length (ξ) were in the ranges of 3.536 ≤ ξo ≤ 4.611 A and 0.619 ≤ ν ≤ 0.633, respectively. An analysis in terms of the effective susceptibility exponent (γeff) results in the interesting result, namely that, the critical behaviour of (MEK + W + sBA ) is of the Ising-type for MEK concentrations in the ranges of 0.1000 ≤ XM ≤ 0.1250 and XM ≥ 0.3000; but, for the intermediate range of 0.1750 < XM < 0.3000, the system shows a tendency towards mean-field type of critical behaviour. This behaviour is interesting because both the constituent binary systems of the ternary system (MEK + W + sBA), namely, (MEK + W) and (W + sBA) show Ising-type of critical behaviour. Chapter 5 discusses another crucial objective of this thesis, namely, the fabrication and characterization of a microkelvin thermostat, which has been built for the purpose of performing light-scattering studies exceptionally close to the critical temperature. At the outset, the need for a temperature stability of the order of a few microkelvin for performing reliable critical point phenomena experiments very close to the critical point, is justified and demonstrated. This is followed by an in-depth account of the thermal design of the thermostat and the electronic circuitry used in the temperature controller. The variations in the ambient temperature and the stability of the bridge excitation source are identified and demonstrated to be crucial factors that affect the long-term temperature stability of the thermostat. A simple compensation scheme to nullify the effects of ambient temprature variations on the controller performance is suggested. It is demonstrated that the thermostat gives a temperature stability of (Formula) and ±60−90 µK for 7 − 14 h over a broad range of 25 − 103 °C. A detailed profile of thermal gradients within the sample recess is provided. It is shown that the parameter ∆Teff [i.e., the difference between the maximum (minimum if ∆Teff has a negative value) temperature within the sample recess and the temperature just outside the sample recess] is a more relevant parameter than ∆T (i.e., the temperature difference between the inner and the outer stages) in understanding the behaviour of multistage thermostats. The most important result that emerges from our study is that the thermal gradients and the transient response of the controller, can both be tuned by varying ∆Teff (or by varying ∆T). The best horizontal and vertical thermal gradient performance observed within our thermostat were 250 and 100 µK/mm, respectively, which are observed for a ∆Teff = 4.46 mK. The transient response of the controller is almost invariant for ∆Teff > 0 but it shows a dramatic decrease of almost 50% when ∆Teff < 0. It is seen that, the limit ∆Teff →>• 0, provides the best operating conditions of the thermostat from the standpoints of temperature stability, transient response and gradient performance. An error analysis relevant to the circuitry used by us is provided at the end of the chapter, which clearly indicates the efficacy of the compensations scheme proposed by us to nullify the effects of ambient temperature variations. Chapter 6 summarizes the important results obtained in this thesis. It also presents a range of open problems that need to be explored further in order to fully understand the results that are reported in this thesis, especially, regarding the type of crossover behaviour seen in the systems 3MP + D2O + NaBr and MEK + W + sBA.
- Physics (PHY) 
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