Sıvı kristal karışımlarda polarizasyonun ve duygunluğun üçlü kritik nokta yakınındaki davranışının incelenmesi

Abstract

SmektikA-Ferroelektrik-SmektikC faz geçişi gösteren belli konsantrasyonlardaki sıvı kristal karışımı bu çalışmada üçlü kritik nokta civarında Landau ortalama alan teorisi ile incelenmiştir. SmA-SmC*geçişinde düzen parametreleri olarak tanımlanan polarizasyon (P) ve yönelim açısı (9)'nın P6, P282. Pe+P292 çifttenim terimlerini içeren Landau serbest enerjisinden harekette sistemi karekterize eden fiziksel niceliklerin kritik davranışı incelenmiştir. Uygulanan elektrik alanına (E ) göre polarizasyonun ve yönelim açısının değişimi, ferroelektrik C7 sıvı kristalinin Sm A-SmC* faz geçişi bölgesinde literatürde verilen deneysel veriler kullanılarak incelenmiştir. 10.O.4 sıvı kristalinin farklı konsantrasyonlarında C7+10.O.4 sıvı kristal bileşiği için polarizasyon değerleri elde edilmiş ve literatürdeki deneysel değerlerle karşılaştırılmıştır. Yukarıda verilen analizler sonucu polarizasyonun farklı konsantrasyonlarda kritik davranışını betimleyen p kritik üs değerleri üçlü kritik nokta yakınında C7+10.O.4 sıvı kristal bileşiği için elde edilmiştir. Polarizasyonun elektrik alana göre değişimi ile tanımlı duygunluğun kritik üssü y ve kritik izoterm 8 değerleri C7 sıvı kristali için elde edilmiştir. Bulunan p değerleri ortalama alan teorisinin öngördüğü değerlerle uyum içindedir. Bulunan 8 değeri ise ortalama alan değerinden farklıdır. Bu çalışmada elde edilen sonuçlar 07 sıvı kristalinin SmA-SmC* ve C7+10.O.4 sıvı kristal bileşiğinin SmA-SmC faz geçişinin, Landau ortalama alan teorisi çerçevesi içinde betimlenebileceğim göstermektedir.

A binary liquid-crystal system possessing a tricritical point in its Smectic A-Smectic C* (SmA-SmC*) phase boundary is studied. The electronic tilt susceptibility and the spontaneous polarization behavior are analyzed near the tricritical point. The investigations of those tricritical systems are of interest with respect to the origin of the first order SmA-SmC behavior. SmecticA (SmA) and SmectikC (SmC) liquid-crystal phases are orientationally ordered fluids. Director (average direction of the long molecular axes) is either parallel (SmA ) or tilted by an angle 8 (SmC) with respect to the density wave vector. If these phases are composed of chiral molecules, the reduced symmetry of the material leads to a coupling between the tilt angle and the electrical polarization. This results in the ferroelectric spontaneous polarization in the Sm C phase and quasi piezoelectric behavior in the Sm A phase which becomes tilted in an external electric field. Binary systems consisting of a first order SmA-SmC compound and second order SmA-SmC compound exhibit a (TCP). Our binary system consists of the compound 4-(3-methyl-2-choroprntanoyloxy)-4- heptyloxybiphenyl ( abbreviated C7), which shows a first order SmA-SmC phase transition and the compound 4-butyl-oxsyphenyl-4-ducyloxybenzoate (abbreviated as 10. 0.4) which shows a second order SmA-SmC transition. In the presence of a dc electric field applied parallel to the smectic layers Sm A and Sm C phase show a tilt angle with the same homogenous tilt direction. SmA-SmC transition of the C7 compound in an external electric field can be described by a simple Landau model using a free energy expended in powers of the tilt angle and the polarization ( where tilt angle is primary order parameter, polarization is the second order parameter ) and the coupling between tilt angle and the polarization, Here we use in the Landau free energy with the three different coupling between the tilt angle and the polarization namely, P0, p2e2 and PS+P^2- Also by adding a small amount of a second liquid crystal compound to the initial sample, the first order SmA- SmC transition tends to become a second order. We then use this form of the Landau free energy to analyze the experimental data from the literature [2-4]. Landau free energy equations are obtained for each coupling in order to compare couplings. Using this vii electric field equation, polarization is found as a function of concentration of 10.O.4 mixture C7+10.O.4. from this analyses we determine the critical behavior of polarization at various concentration and the tilt susceptibility. For P8 coupling, Landau free energy is written as; g=g o+Ia(T-T0)e2+-&84+-ce6+- !- P2-CPQ-EP ° 2 V 0) 4 6 2%060 From this equation electric field equation is found. E = -±-{[a(T-T0)-C2los0]e + bQ3+ce5} By using E versus 0 experimental data, coefficients are calculated by curve fitting method. Also using this electric field equation, polarization equation is calculated as a function concentration by JO f _Y h=Mıof) c = e0(ioo-*) This polarization curve is compared with experimental polarization data. For P 8 coupling, this two curves are similar of each other. Polarization power coefficient 0 that is in the tricritical region is also found using polarization equation and temperature data. For the mixture far from the tricritical value of ^depends on the closeness to the transition temperature (0«O.3 for below transition 0«O.7 near the transition. 58 The electronic tilt susceptibility % is described by - ( 8 denotes the field dE induced tilt, E denotes the electric field) in the near tricritical point for the mixture (0 - %10). The linear behavior can be described by a simple power law of the form X"|j-Tc or for TTc, The tilt susceptibility % versus T curves exhibit a maximum which increases as the critical point is approached. The best least square fit according equation of taking into account all experimental data given in (ref. 4) is obtained for y «1 The course of the critical isotherm is expected to follow a power law as V1U E-Ec«(P-Pc)8 It is found that experimental data didn't fit well to this equation, when it is determined, it is found as 2.5 for all region of data. This P6 coupling results compare with P2©2 coupling. For P2Q2 coupling, Landau free energy is written as; g = go +~a(T-T0)82 +-bB4 +-C06 +- - P2 -DP2Q2 +-eP4 - ° 2 V °' 4 6 2Xoe0 4 EP From this equation electric field equation is found. 1 V °' Wo e \2D 4D2XozJ By using E versus 8 experimental data, coefficients are calculated by curve fitting method. Also using this electric field equation, polarization equation is calculated as a function concentration by, -.10.5 -xN " "t % ( 10 5 ) C=C0(100-*) This polarization curve is compared with experimental polarization data. This two curves are similar of each other like P0 coupling but p202 coupling gives more close curve according to the P8 coupling curve. Polarization power coefficient p that is in the tricritical region is also found using polarization equation and temperature data. For the mixture far from the tricritical value of ^depends on the closeness to the transition temperature (p«0.3 for below transition p«0.6 near the transition. o0 The electronic tilt susceptibility % is described by - ( 0 denotes the 5E field induced tilt, E denotes the electric field) in the near tricritical point for the mixture (0 - %10). The linear behavior can be described by a simple power low of the form XJ|«:(T-T»)r öE To determine y, the critical point must be approached on a certain path in the P-T plane for T>Tc or for TTc, The tilt susceptibility % versus T curves exhibit a maximum which increases as the critical point is IX approached. The best least square fit according equation of taking into account all experimental data given in (ref. 4) is obtained for y »1 The course of the critical isotherm is expected to follow a power law as E-Ec«(P-Pc)8 It is found that this equation didn't fit well to experimental data in all region For P8+P292 coupling, Landau free energy is written as; g = g +Ia(T -T0)92 +-bQ4 +-cQ6 +- L_ p2 _CPQ -KP2B2 - EP So 2 V °r 4 6 2%080 From this equation electric field equation is found as a(T-Te0)+^(b-4DKYoB20f}Q + (b-4DK2Xy0y+cd5 \6ac By using E versus 0 experimental data, coefficients are calculated by curve fitting method. Also using these electric field equation, polarization equation is calculated as a function concentration by b=b0(-°'5~X) C = C0(lOO-x) v 10.5 J °v ; P = Ke0%o{-^(b-4DK2xlsljj This polarization curve is compared with experimental polarization data. For PO+P2©2 coupling, this two curves are similar of each other. Polarization power coefficient J3 that is in the tricritical region is also found using polarization equation and temperature data. For the mixture far from the tricritical value of pdepends on the closeness to the transition temperature (0«O.18 for below transition 0«O.25 near the transition. The electronic tilt susceptibility % is described by - ( 6 denotes the BE field induced tilt, E denotes the electric field) in the near tricritical point for the mixture (0 - %10). The linear behavior can be described by a simple power law of the form X~!^(T-T*)Y To determine y, the critical point must be approached on a certain path in the P-T plane for T>Tc or for TTc, The tilt susceptibility % versus T curves exhibit a maximum which increases as the critical point is approached. The best least square fit according equation of taking into account all experimental data given in (ref. 4) is obtained for y «1 The course of the critical isotherm is expected to follow a power law as E-Ec*(P-Pc)5 It is found 8*2. From our analysis we get the critical isotherm between 2 - 2.5 for all data region that does not agree with the mean field value of 8*3. All calculations given above made with first method. That means polarization equations is calculated by using electric field equal to 0 (E=0). For second method polarization equation calculated by E*o. In these method for P282 coupling, free energy equation g = g0+ -«(T - To)02 + -bQ4 + -cQ6 + -t-P2 - DP2B2 - EP 2 V 0} 4 6 2Xos0 Using this equation electric field equation is calculated as E = 1,Xo*V \2DJ 4t-tc0)+ 2D AD 2\ e J + bQ2+cQ4 But this it is found that this electric field equation didn't not comply with experimental data. Calculation same with above is made for P0+P282 and P02 coupling, but results obtained by the second method are not meaningful. Our analyses show that the Landau model considered here is adequate to describe the observed behavior of C7 and C7+10.O.4 liquid crystals near their phase transitions.