1 Lecture 12 The cooperative relaxation of water at the pore surface of silica glasses

2 Complex systems? Complex systems involve the appearance of a new ("mesoscopic") length scale, intermediate between molecular and macroscopic. Complex liquids (microemulsions, emulsions, organic particulate systems ) Glass forming liquids and polymers. Porous materials (sol-gel glasses, porous glasses, porous silicon, etc.) Biological systems ( protein solutions, membranes and cell suspensions)

3 Initial sodium borosilicate glass of the following composition (% by weight): 62.6% SiO 2, 30.4% B 2 O 3, 7%Na 2 O heat treatment at C for 100h heat treatment at C for 165h immersion in deionised water 0.5N HCL drying at C rinsing in deionized water additional treatment in 0.5N KOH drying at C rinsing in deionized water Porous borosilicate glass samples

4 additional treatment in 0.5M KOH drying rinsing in deionized water drying bithermal heat treatment treatment at C and at C thermal treatment at C immersion in deionised water 3M HCL rinsing in deionized water Commercial alkali borosilicate glass DV1 of the following composition (mol.%): 7% Na 2 O, 23% B 2 O 3, 70% SiO 2

5 Structure parameters and water content

 Sample C Sample C  Sample C after heating Sample C after heating Dielectric response of the porous glass materials

7 3-D PLOTS OF THE DIELECTRIC LOSSES FOR THE POROUS GLASS MATERIALS Sample C Sample II

8 Low frequency behaviour ~20 Hz High frequency behaviour ~ 100 kHz   C   C

9 1 2  * (  ) = B *  n-1,   >> 1  * (  ) = -i  0 /  0  1) Jonscher Conductivity  * (  ) =  / [1 + ( i   )  ]  +   2) Havriliak-Negami The fitting model

10 A - 50 kJ/mol B - 42 kJ/mol C - 67 kJ/mol D - 19 kJ/mol Ice - 60 kJ/mol I - 64 kJ/mol II - 36 kJ/mol III - 61 kJ/mol Ice - 60 kJ/mol 1 st Process

11 Samples Humidity h, % II 0.63 A 1.2 B 1.4 D 1.6 C 3.2 III 3.39 I 3.6 Dependence of the Cole-Cole parameter  from ln(  )

12 Temperature dependence of the dielectric strength

13 Parallel and anti-parallel orientation B(T) anti-parallel Temperature Orientation of the relaxing dipole units parallel non- correlated system

14 2 Second Process

15 L -defect V * is the defect effective volume V f is the mean free volume for one defect N is the number of defects in the volume of system V, where Si O Si O O Si Orientation Defect Orientation DefectD-defect

16  H a is the activation energy of the reorientation  H d is the activation energy of the defect formation  o is the reorientation (libration) time of the restricted water molecule in the hydrated cluster  is the maximum possible defect concentration The fitting results for the second process

17  ( t /  ) ~ e  t / , D f = 3, where D f is a fractal dimension Percolation: Percolation: Transfer of electric excitation through the developed system of open pores Dielectric relaxation in percolation

18 The Fractal Dimension of Percolation Pass

19 w w : size distribution function , , A , , A: empirical parameters   : porosity of two phase solid-pore system V p : volume of the whole empty space V : whole volume of the sample , , : upper and lower limits of self- similarity D D : regular fractal dimension of the system  = /   : scale parameter   [ ,1] Porous medium in terms of regular and random fractals

20 Porosity Determination (A.Puzenko,et al., Phys. Rev. (B), 60, 14348, 1999)