CECRl has a Micromeritics mercury penetration porosimeter for

characterisation of porous electrodes. For quick evaluation of the

experimental data on porous electrodes, computer programme has

been written and tested for reported results. Good agreement an

pore size diibutian, surface area, and particle size distribution

has been observed. The used numerical results and computer

results are briefe

Birlasekaran, S.

Kalidoss, R.

IR@CECRI

Bulletin of Electrochemistry 1 (2) Mar-Apr t 985 pp. 195-20 1 COM~UTER PROGRAM FOR MERCURY PENETRATION POROSIMETER-DATA AN ALY SlS S BRLASEKARAN AND R KALJDOSS Central Electrochemical Research Institute, Karaikudi-623 006 ABSTRACT CECRl has a Micromeritics mercury penetration porosimeter for characterisation of porous electrodes. For quick evaluation of the experimental data on porous electrodes, computer programme has been written and tested for reported results. Good agreement an pore size d i ibu t ian ,  surface area, and particle size distribution has been observed. The used numerical results and computer results are briefed. INTRODUCTION A porous medium is a solid that contains a large number of pore spaces distributed throughout the volume. To characerise the electrodes for electrochemical reaction, poresize distribution study. [ I  ] is made using the physical method, namely, mercury intrusion. With a mercury penetration poroslmeter, one can determine size and quantity of void spaces and pores in porous materials. In addition. one can cak la te  specific surface area and obtain a rneagure of part~cle size distribution in the case of powders. The analysis of the data is laborlous and the company advises one to follow the calculation sheet to ovo~d errors. Computer programme has been developed both in Basic and Fortran IV to simplify the entire procedure. TEST PROCEDURE The Instruction manual 121 gives the brief description of the experimental procedure. The volume of mercury entering an evacuated porous sample at low pressure is measured and recorded. The pressure is Increased and the incremental volume of mercury entering the sample is again recorded. The procedure 1s continued untd the incremental volume is of no further interest. Thus increasing the pressure on a material having a given pore size and/or void space results in a unique'pressure-volume curve as shown in Fig. 1. r Fig. 1 : Pressure vs volume of pores Curve 1 represents a catalyst where the volume of pores exceed the volume of void spaces. The pores tend to be predominantly I about 0.005 micron in radius while the volume average void space is of the order of 1 micron in radius. The pores and voids thus differ greatly in we .  The curve designated No.2 was obtained for a powder with relatively coarse grains. Accordingly the curve consists of two distinct parts. The volume of mercury penetrating the sample at pressures less than 50 psia (344740 N/m2) went into void spaces among the individual particles, while the volume above' 50 psia penetrated pares within the powder grains. Curve 3 is for a mmeral having unique structuml characteristics. It has pores, for example, predominantly of about 0.04 micron radius. It appears from the figure 1 further that it has a few pores of about 0.01 micron radius. This has been tested in our analysis. THEORY (2) Following the theoret~cal model taken in the ~nstruction manual [2], the following equations are taken for the computation of results. I (a) Pore radius The pore radius in which mercury will penetrate at an applied P can be determined from -2 0 cos ( 8 )  r = P (1 where, a - is the surface tension of mercury 8 a - is the contact angle P - applied pressure in psia r - pore radius in microns (b) Pore size distribution The pore size distribution of porous electrodes is one of the " fundamental parameters determining the extent to which the available surface of electrocatalyst is  effective in electrochemical reactions. It is determined by P2 dV D (r) = x - 2 a cos (8) dP Birloseftoron ond Kolrdos - Comprjter progrom for mercury peretrotion porosimeter-doto onolysis where D(r) is the pore-size distribution function, dV is the vo!ume of pores having radii between r and (r+dr) and dP is the corresponding change in pressure. D(r) is estimated at each pressure from figure 1 data. Plotting D(r) against s gives the pore-size distribution. If the D(r) vs r curve displays N maxima, each maximum at r(i)ti = 1,2, ... N)  is assigned, to a large number of pores with the radius r( i )  It is said that the porous structure consists largely of N types of pores. (c) Specific surface area It is determined using the equation (3) j P  dV S = -  a cos (8) where S is specific surface area over the range of integration. (d) Particle size distribution The relationship between particle radius, r and applied pressure P, is (3)  r = 68.77 X P' (4) P where P' is the so-called breakthrough pressure. It is defined as that pressure required to force mercury through a uniform bed of uniform size particles. Its magnitude depends' on the porosity of the bed and the contact angle between the particle and mercury. ANALYSIS From recorded presswe data, it can be seen that the pressure readings ronge from 1 psia to  50000 psia. In any instrument, it is not possible to have pressure control with 1 psia sensitivity. As some of the peaks may lie in the column in which readings are not taken, interpolation technique is used to predict pore size distribution. To interpolate in the unequal intervals of pressure readings, we have Newton's general interpolation formula and Lagrange's interpolation formula. Mathematics of the formula can be seen in reference 14). LAGRANGE The interpolating polynomial passing through unevenly spaced (n + 1 ) points is given by n P n (X) = Y = x  yi X Li (X) ,i =O where Li (X) = n n'(X - Xr 1 r = O  (r # i) (r + i) NEWTON Using divided differences, the values are derlved Y = yo + (X - Xo) 6(Xo, XI) + (X - Xo) (X - Xi) 6(X0, Xi ,  X2) + ......... + (X -- Xo) (X - Xi) ..... (X - Xn) 6(X, Xo, XI, ... Xn) where 6(Xo, X i )  = (yo - yi)/(Xo - X h )  and so on. Lagrange's interpolation formula offered the best fitting. Each interval between two consecutive recorded readings is divided 196 - Bulletin o f  Electrochemistry 1 (2) Mar-Apr 1985 into three and polynominal upto 3rd degree was used. Program listing 1 briefs the written program. (The entire set of programs in basic and Fortran IV are available at  CECRl computer centre). The pressure variable is divided initially and boundary values are evaluated. Later interpolation is done by taking the nearest y value on either side. Using the formulae 1-4, the various required parameters are evaluated. The results are transferred to MAKEGRAF routine available with the cornputel; RESULTS As has'been done in the manual, curve 1 in Fig. 1 is used for pore size distribution, curve 2 is used for particle size calculation and curve 3 is used for surface area calculation. In Fig. 2 the plots of pore size distribution by the two techniques are shown. Fig. 2 : Pore distribution (pore radius vs distributian functioi~) B -- Curve (Ref. I) A -- First ordercurve -- Second ordercurve -- Third ordercurve In the manual, the peak is found to  occur at  a radlus of 0.004 microns as can be seen in curve 1 in Fig. 2. With third order polynomial, the peak is at 0.00343 micron. Wlth second order polynomial, it is at  0.0038 micron and with first order it is at  0.0031 micron. The pores tend to be predominantly about 0.0038 micron. By Interfacing with the Graphics utility, we can get the analysed data immediately in the graphical form either on video display unlt or in the printed sheet. 1 In Fig. 3 for curve 2 pore size dlstributlon IS shown. It is found that ~t contains voids of 21.818 micron and.pores of 0.021 8/0.09 and 0.21 micron. In Fig. 4 for curve 3 it is found to have pores of 0.04/0.017/0.0075 and 0.001 87 micron. Brrlosekoran and Kalrdas - Computer program for mercury peretratron porosrmeterdota anolysrs Fig. 3 : Pore distribution (pore rodius vs distributron function) (Arrow mork indicates pore rodius rn microns) -- First order-curve -- Second order-curve A -- Third order-curve Fig. 4 : Pore distribution (pore rodius vs distribution function) (Arrow mork indicates pore radius in microns) A , --  First order-curve -- Second order-curve -- Third order-curve - For surface area calculation the result with Computer analysis on curve 3 is 30.8 X 103m2/kg. Manual's graphical integration result is 29.4 x 103m2/kg, and low temperature gas adsorption test resub is 31.2 X 103m2/kg. In computer analysis, change in degree of polynomial caused a variation of 2%. For particle size distribution study curve 2 in Fig. 1 has been taken. The results are shown in Table I. Very good agreement with other methods can be noticed. Table I : Particle size calculation from mercury penetration data - - - - - - - - Pressure Volume frac- % less than Partrcle radius tion greater (volume basis) MP S~ev- S ~ I -  P M C M C M C Ing menta- tion - - - - M - Readings reported In the manual 121 C - Result from our computer analys~s MP - Mercury penetrat~on (Part~cle radius expressed In micron) After testing the developed software some of our laboratory experimental readings are tested for pore size distribution. Fig. 5 1 i o  too 1000 ABSOLUTE PRESSURE (PSU) Fig. 5 : Pore size distribution function vs absolute pressure; oxygen electrode No. 623A dual porosity type (Arrow mark indicates pore radius in microns) Bulletin of Electrochemistry 1 (2) Mar-Apr 1985 - 197 Birlasekaran and Kalidas - Computer program for mercury peretration porosimeter-data analysis Fig. 6 : VDU - Photograph of Fig. 5. shows the pore-size distribution of the oxygen gas diffusion electrode of dual porous type evaluated in a short time. It can be seen that the electrode contains predommantly pores of sues 0.539, 0.254 and 0.073 microns. ACKNOWLEDGEMENTS : The encouragement received from Shri H N Venkoba Roo, Head of the Electrochemical Instrumentation and Equipment Design Division and Dr V K Venkatesan, Head of in carrying out such type of analysis is greatly acknowledged. We thank Mr Pattabiraman and Mr R Chandrasekaran for referring the problem to us. REFERENCES H A Liebhafsky and E J Cairns, Fuel Cells and Fuel Batteries,A Guide to Their Research and Development, John Wiley 8 Sons, N.Y. (1 968) pp. 356-360. . Micrornentics (USA) lnstructron Manual on Mercury Penetration Porosimeter Mode1 900/9 10 Series. R P Mayer and R A Stowe, J Colloid Sci 20 (1 965) 893. J B Scarborough, Numerical Methods of Analysis,'Oxford and IBH Publishing Co., Calcutta (1971) Chap 111. FOR PROGRAM LISTING REFER T O  THE FOLL~WING THREE PAGES. 198 - Bulletin of Electrochem~stry 1 (2) Mar-Apr 1985 

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