Phase transitions from the isotropic liquid to liquid crystalline mesophases studied by linear and nonlinear static dielectric permittivity Aleksandra Drozd-Rzoska and Sylwester J. Rzoska Institute of Physics, Silesian University, ulica Uniwersytecka 4, 40-007 Katowice, Poland Krzysztof Czupryn ˜ ski Military Technical Academy, ulica S. Kaliskiego, 01-489 Warsaw, Poland ~Received 2 September 1999! Results of studies of static dielectric permittivity ~«! and nonlinear dielectric effect ~NDE! in the isotropic phase of 4-n-48-isothiocyanatobiphenyl ( n BT) homologous series from n 52 to n 510 exhibiting the isotropic- smectic E ( I -SmE ) transition, are presented. They are compared with results of similar studies in 4-cyano-4- n-alkylbiphenyls ( n CB) from n 54 to n 512. In this homologous series isotropic-nematic ( I - N ) and isotropic- smectic-A ( I –Sm- A ) transitions take place. Despite significant differences between N, Sm-A , and Sm- E phases the same pretransitional behavior of « and NDE in the isotropic phase, described by critical exponents g 51 and a 50.5, was found. It has been shown that when the length of the alkyl chain of a compound increases the discontinuity of the transition drops in n BT and rises in n CB. The influence of pressure on the discontinuity is also discussed. PACS number~s!: 64.70.Md, 64.30.1t, 77.22.Ch INTRODUCTION Despite several decades of studies there is still a limited knowledge concerning properties of phase transitions from the isotropic liquid to liquid crystalline mesophases @1–9#. Liquid crystalline phases are an intermediate state of matter between the liquid and the solid crystal and hence the weakly discontinuous character of this transition is not surprising. The phenomenological, mean field Landau–de Gennes ~LdG! model made a quantitative estimation of this discon- tinuity possible @1–3#. It enabled the parameterization of strong pretransitional anomalies of susceptibility related properties as the Kerr effect ~KE!, the Cotton-Mouton effect ~CME! and the intensity of the scattered light ( I L ) on ap- proaching the isotropic-nematic ( I - N ) transition @1–22#: E KE 21 , E CME 21 , E I L 21 } T 2T * , T .T C 5T * 1D T , ~1! where E KE , E CME , E I L are experimental measures of KE, CME, and I L respectively. T * denotes the extrapolated, tem- perature of hypothetical continuous phase transition, T C is the clearing temperature. The obtained values of discontinuity of the I - N transition range from 0.7–2 K @1–3,9–22# whereas mean-field based models point to a much stronger discontinuity with D T 57.6– 26 K @3,9,23–25#. The mean-field approximation @6# does not predict pretransitional anomalies of a specific heat and density which are weak but detectable in experiments @6,26–28#. Only recently, an essential breakthrough in this long-standing puzzle due to the introduction of the fluidlike critical description was possible. Assuming that the nematic clearing point lies on a branch of a hypothetical coexistence curve and applying the fluidlike scaling equation of state Mukherjee et al. obtained D T 51–3K @9,29–31#. Significant insight into properties of the complex structure of the isotropic liquid phase strongly penetrated by nematic fluctuations was possible due to recent studies of 5CB and MBBA by the transient grating Kerr effect @32–34#, isother- mal nonlinear dielectric effect studies in 7CB-benzene solu- tion @35#, and the NDE and dielectric permittivity fluidlike analysis in several nematogenic and smectogenic ( n CB) @36–42#. For the latter it was shown that for the ‘‘static’’ measurement frequency @37,39# « ~ T ! 5« * 1b ~ T 2T * ! 1B ~ T 2T * ! 1 2a , ~2! E NDE 5 A NDE T T 2T * 5 2 « 0 3 a ~ D« 0 ! 2 ~ T 2T * ! g } ^ D M 2 & v x , ~3! where E NDE is the measure of NDE, A NDE T , b, B are ampli- tudes, a is the constant amplitude of the second rank term in the LdG expansion of the free energy, D« 0 is the molecular anisotropy of dielectric permittivity in the zero frequency limit, ^ D M 2 & v is the mean of the square of the order param- eter fluctuations, x } ( T 2T * ) 21 denotes the susceptibility, a is the critical exponent of the specific heat: in this case a ’0.5 was found. Relations ~2! and ~3! are valid for the ‘‘static’’ conditions: f t !1 and f t m !1 where f is the NDE measurement frequency, t is the relaxation time of pretran- sitional processes and t m is the molecular relaxation time of rodlike molecules. These equations are similar to those applied in the isotro- pic phase of critical solutions @37,39,43#. The reciprocal of E NDE 1 ( T ) was found to be linear up to T x ’T C 138 K, with no distortions in the immediate vicinity of T C @39#. The value of T x agrees with the temperature at which prenematic fluctua- tions cease to exist @32–34#. Concerning dielectric permittiv- ity equation ~2! was found to be valid even 100 K from T C @39#. It is worth noticing that in KE, CME, or I L studies, experimental data describing relation ~1! are valid in the range 5–10 K from T C only, with small distortions in its immediate vicinity @1–20#. Furthermore additional, empirical PHYSICAL REVIEW E MAY 2000 VOLUME 61, NUMBER 5 PRE 61 1063-651X/2000/61~5!/5355~6!/$15.00 5355 ©2000 The American Physical Society