Characterisation of Porosity

Porous Polymeric Implant

Materials

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AlllOfc, EMd15?3

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U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Dental and Medicai Materials

Polymer Science and Standards Division

Washington, DC 20234

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February 1 983

I Annua* Report for period April thru September 1982

Prepared for: Office of Medical Devices

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Matronal Center for Devices and Radiological Health

:ri and Ding Administration

er Spring, MD 20910

NBSIR 83-2645 (FDA)

CHARACTERIZATION OF POROSITY IN

POROUS POLYMERIC IMPLANT

MATERIALS

R. E. Dehl

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Dental and Medical Materials

Polymer Science and Standards Division

Washington, DC 20234

February 1983

Annual Report for period April thru September 1982

Prepared for: Office of Medical Devices

National Center for Devices and Radiological Health

Food and Drug Administration

Silver Spring, MD 20910

U.S. DEPARTMENT OF COMMERCE, Malcolm Baidrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

NATIONAL BUREAU

OF STANDARDS

LIBRARY MAR 11 1983

t LA
•Horr;. •
TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS 1

ABSTRACT 2

I. INTRODUCTION 3

II. POROSITY MEASUREMENTS BY QUANTITATIVE MICROSCOPY 4

A. Pore Volume Methods 5

B. Pore Size Methods . 6

1. General Considerations

2. Mean Intercept Length

C. Statistical Analysis and Prediction 10

D. Optical Analysis of Porous Polyethylene 11

1. Sample Preparation

2. Photomicrography

3. Results

III. PORE SIZE DISTRIBUTION BY MERCURY POROSIMETRY 15

A. Instrumental Sensitivity 18

B. Random Error Analysis 18

C. Volume Weighted Size Distribution ... 19

IV. PORE SIZE BY BET METHOD 23

V. COMPARISON OF POROSITY MEASUREMENT METHODS 28

A. Pore Volume 28

B. Pore Size 29

C. Summary Table 31

1 . Mercury Porosimetry

2. Optical Image Analysis

3. BET Method

VI. MECHANICAL PROPERTIES OF POROUS IMPLANT MATERIALS 32

A. Experimental 33

B. Results 33

C. Implications for Mercury Porosimetry 37

VII. SURFACE AREA BY MERCURY POROSIMETRY 38

A. Theory 38

B. Results . 40

C. Comparison of Pore Size by Two Surface

Area-Pore Volume Methods 42

VIII. SUMMARY 44

REFERENCES 47
FIGURES

Page

Fig. 1. Photomicrographs of polished cross-sections of filled

porous polyethylene, (a) resin undyed and (b) resin

dyed 13

Fig. 2a. Volume-weighted pore size histogram for one sample

of PTFE-C composite . Pressure increment is 0.5 psia 21

Fig. 2b. Normalized plot of Fig. 2a 22

Fig. 3a Volume-weighted pore size histogram for same sample of PTFE-C composite as Fig. 2a. Pressure increment

is 1.0 psia 24

Fig. 3b. Normalized plot of Fig. 3a 25

Fig. 4. Volume-weighted pore size histogram for one sample

of porous polyethylene. Pressure increment is 1.0 psia. ... 26

Fig. 5. Compressive stress-strain curves for 2 samples of porous

polyethylene 34

Fig. 6. Compressive stress-strain curves for 4 samples of PTFE-C

composite. Two samples aligned parallel ( || ) and 2

perpendicular (J_) to applied stress 36

Fig. 7. Relationship of solid-liquid contact angle to the work

of forming a meniscus 39

Fig. 8. Linear plot of V vs. P obtained by mercury porosimetry

for porous polyethylene. Surface area proportional to

integrated shaded area 41
ACKNOWLEDGMENTS

The author is indebted to a number of members of the Dental and Medical

Materials Group for their assistance in this work; to Dr. S. Venz, a guest

worker from the Free University of Berlin, for her assistance in performing

the compressive stress-strain measurements; to Mr. J. E. McKinney for

his suggestions about the resin and polishing methods used in preparing

samples for optical microscopy, to Dr. R. L. Bowen for suggesting the dye

used to color the resin, and to Dr. W.-L. Wu for the use of the microscope

and camera in the optical analysis work.

The author is also grateful to Professor E. E. Underwood of the Georgia

Institute of Technology, a well-known authority in quantitative microscopy,

for his valuable suggestions about the optical analysis of filled porous

polyethylene.

1
ABSTRACT

In this report, we describe (1) the continued exploration of

methods for characterizing the porosity of two commercial implant

materials, a porous polyethylene and a composite of polytetrafluoroethylene and carbon, and (2) the compressive stress-strain behavior of

these materials. A major emphasis was placed upon optical image analysis

of porous polyethylene. The pore volume fraction (0.47) obtained from analysis of 20 photomicrographs agreed well with the fraction previously

found by two other methods. The mean intercept length, determined from

the same photomicrographs , was about 75 urn, a value considerably higher

than the average "interconnecting" pore diameter determined by mercury

porosimetry (30 ym). Replotting our mercury porosimetry data, we found

that the volume-weighted pore size distribution curve resembled a lognormal distribution, skewed to the right of the "most probable" pore

radius. The surface area determined from mercury porosimetry data was

o somewhat larger (0.125 m /g) for the porous polyethylene than that

determined by the BET method (0.082 m^g) , while the reverse was true for

the composite material (0.19 vs 0.45 m /g). Compressive stress-strain

measurements on the laminated composite demonstrated that the initial

compression modulus is approximately six times greater when the stress

is applied parallel rather than perpendicular to the laminar planes.

2
I. INTRODUCTION

The rationale for this project and the approaches to be used in

characterizing the porosity of porous polymeric implant materials have

been discussed in previous Annual Reports to the Bureau of Medical

Devices (FDA) *. During the current half-year reporting period (Apr. 1,

1982 - September 30, 1982), we were guided by a work plan which was

drafted by mutual agreement between staff members of the Bureau of

Medical Devices and the National Bureau of Standards. It was agreed at

the time the work plan was drafted that the 7 items in the plan likely

would require a greater effort than could reasonably be expected, given

the available resources, in half a year. We therefore were faced with a

choice about how to apportion the available time. We could either make

a thorough investigation of 2 or 3 items in the plan, or attempt to make

some progress on most or all of the tasks. The latter approach was

chosen, because we thought it important to pass the exploratory phase of

this work as soon as possible. In this way, we could lay the foundation

for future investigations, with enough knowledge about each of the

porosity characterization methods to have a rational basis for selecting

the most appropriate one(s) for any given problem that we might encounter.

In retrospect, we believe that this was a wise choice. We believe that

we now have the expertise to perform each of the tasks specified in our

work plan and that future acquisition and interpretation of data will be

limited largely by time and resources.

In accordance with the priorities assigned to the items in our work

plan, we have placed more emphasis on optical image analysis than on

some other methods which were investigated last year. This emphasis has

culminated in some very encouraging experimental results, as discussed

3
in Section I ID . In addition, progress was made in corroborating our

surface area measurements of last year according to the BET method, sonamed for the initials of its inventors ; in establishing another

method for measuring surface area; in measuring the limits of mechanical

stress which should be applied to the porous materials; and in understanding how to plot mercury porosimetry data in order to extract the

maximum information from such data.

The two porous implant materials which are discussed in this report

3

(D) 4* are Plastipore and Proplast . The former is a porous polyethylene

(PPE), and the latter is a composite of polytetrafluoroethylene (PTFE)

and carbon (C)

.

4 II. POROSITY MEASUREMENTS BY QUANTITATIVE MICROSCOPY

5-9

Several books have been written about the inference of 3-dimensional

structures from the examination of 2-dimensional planar cross-sections of

particulate or multiphase materials. The methods have been applied

extensively to metal alloys, ceramics, biological tissues, and powdered

materials, as well as to porous polymers. A science of "stereology" has

developed to treat the various types of information which can be derived

from 2-dimensional analysis of solid materials, with a standardized

system of nomenclature developed by the International Society for Stereology.

In the following discussion, we will define the few symbols needed to

describe our measurements for pore size and pore volume, as measured on

planar cross-sections of the material.

^Certain commercial materials and laboratories are identified in this report in

order to specify experimental procedures adequately. In no case does such

identification imply recommendation or endorsement by the National Bureau of

Standards, nor does it imply that the identified materials or laboratories

are necessarily the best available.

4
A. Pore Volume

The symbols needed for these discussions are V s A, L and P, which

stand for volume, area, length, and points, respectively. A fraction,

such as the volume fraction of voids in a solid material, is represented

by the symbol V , which stands for volume (of voids)/total volume. The

equations which allow us to infer 3-dimensional information about void

volume from planar cross-sections of the material are very simple, quite

general, and independent of any weakening assumptions about shape, size,

or spatial distribution of pores in the solid. In all cases, they represent

a statistical average of a large number of measurements. In the fractional

notation, they are (e.g. Ref. 5, Chap. 3):

V V

= A

A

= L L

= P

P ^

The volume fraction of voids (Vy) which we want to know, is the same as

the area fraction in 2 dimensions (A^) and the one-dimensional intercept

length fraction of total length (L^), for random lines drawn on the 2-

dimensional surface. The fraction P

p is derived by placing a transparent

grid of crossed lines on the photomicrograph. Each line intersection

is called a "point" and the number of these points falling within the

regions of interest, divided by the total number of intersections, is

Pp. For ambiguous points which may or may not lie in the region of

interest, one assigns the value 1/2, because on the average, over a large

number of counts, such points will lie in this region 50 percent of the

time. From these equations, we see that there are 3 different ways to

measure void volume on a planar cross-section. The point-count (P

p

) method

is generally found to be the easiest to perform by manual methods. Of

course, one such point count is not a good measure of Vy, and if the

sample is anisotropic, one cross-section may not be an adequate sampling.

5
A method for estimating the sample size necessary to achieve a given

level of accuracy is given in Section IIC.

B. Pore Size

1. General Considerations

As we have stated previously, the "size" of irregularly shaped

objects such as the pores in implant materials is not a well defined

physical property. The only pore shape which can be treated rigorously

by stereological methods is the sphere. We will discuss this case in

some detail, because it illustrates the method by which, in principle at

least, any pore "size" may be deduced by 2-dimensional stereological

analysis.

We imagine a solid material having spherical holes randomly distributed throughout. For simplicity, we assume that all the holes have the

same diameter D, although it is also possible to deduce the distribution

of spherical pore diameters, if more than one is present, by stereological methods. If we slice through the porous solid, we will see

circles on the surface of the cross-sections which result from random

sectioning of the spheres, and the diameters of these circles will range

from 0 to D. Obviously, the average diameter of these circles will be

less than D, whereas the average diameter of the spherical holes, which

we want to know, is exactly D. If we examine a very large number of

cross-sections, we will occasionally see a circle which has a diameter

very close to D, so that one way to estimate D would be to look at a

great many cross-sections and find the largest circle. However, this

method is relatively inefficient, and one could never be sure that the

next section would not reveal a D larger than any found previously. A

more efficient way to converge on the desired answer with fewer cross6
sections is to use all of the data, i.e., all of the measured diameters

obtained in each cross-section. A straightforward geometrical analysis^

shows that the average diameter obtained in this way (cT) is related to

the spherical diameter D by the relationship

d = tt/4 D. (2)

Instead of measuring the diameters of all the circles, one may measure

the average chord length 1, obtained by drawing lines at random across

the cross-sections. The average chord length will be less than d",

because only chords which happen to pass through the center of the

circles will be equal to d. In fact, it is easily shown that T is

related to d" by the relationship

T = tt/ 4 d. (3)

From Eqs 2 and 3, we find that

D = (4/tt)

2 T = 1.62 T (4)

In other words, we can deduce the diameter of the spherical pores in the

solid by measuring the average intersected chord lengths in one dimension.

Although derived for spherical pores, Eqs. 2, 3 and 4 apply equally

well to irregularly shaped pores, if we remember that we are not measuring

a true "diameter" when the shapes are irregular. In such cases, the D

which one finds by measuring cross-section "diameters" or chord lengths

is a parameter which may be thought of as an equivalent pore diameter,

or the diameter which one would determine if the pores were spherical in

shape.

The methods described above for measuring pore diameters and chord

lengths might appear to be prohibitively time-consuming and tedious,

requiring the use of rulers and calipers to measure the lengths, and a

computer to store and process the data. We must seek ways of measuring

7
these "size" parameters which can be more easily performed. Two principles

are a guide to finding a more suitable method:

(1) Since we are limited to manual, rather than instrumental,

methods of analysis, we seek methods which are as simple and rapid as

possible, in order to produce a statistically significant amount of

useful data in a reasonable time.

(2) The methods should also be as objective as possible, requiring

a minimum of operator judgment in making the measurements. In this way,

one hopes to select methods by which different researchers will obtain

essentially the same results for the same materials.

In theory, a third criterion should be added to these 2, namely

that the method should measure aspects of pore shape as well as size,

since these are undoubtedly related to the tissue ingrowth process.

Unfortunately, we do not know how this process is affected by pore

shape, so that we really do not know what "shape factors" to measure.

Even if we did know this, the measurements of shape (pore contours,

tangent diameters, etc.) would require the use of at least semi-automatic

instrumentation for measuring such quantities and storing the data.

Manual methods would be prohibitively time-consuming.

Fortunately, there is at least one objective and relatively easy

way to measure pore "size" manually by optical image analysis. It

yields the so-called "mean intercept length", L.

2. Mean Intercept Length

The mean intercept length is defined as the average length of all

possible chords intersecting the pores, for all possible lines drawn

through the sample. Fortunately, it is not necessary to use rulers or

calipers in order to make this measurement. The task is reduced to a

8
simple counting procedure on sample cross-sections by one of the basic

stereological relations^,

L=Pp/N

L

, (5)

where P

p is the point count fraction of the desired phase, described

above, and is the number of chord lengths for that phase per unit

test length. This equation is readily constructed if we remember (Eq.

1) that P

p =L^. The average intercept length is just the total intercept

length for a given test line, divided by the number of intercepts in

that line, N^. The method is illustrated below:

Here, we have placed a 3 x 5 line transparent test grid on a photomicrograph

of a planar cross-section of a 2-phase solid. If we are interested in

measuring L for the shaded phase, we first measure P

p

. There are 3 out

of 15 intersections which lie in the shaded phase regions, so that P

p =

3/15 = 0.2. The number of intercept chords N for the horizontal lines

is 5 1/2, where the fractional count comes from the intercept in the

upper right corner which only traverses part of that cut-off area. Over

a large number of counts, these partial chords will average to half the

actual chord lengths which one would measure if the entire area were

visible. In the same way, we find that N for the 5 vertical lines is

also 5 1/2. Thus, for all the lines is 11 divided by the total test

length L. We have calibrated the test grid by photographing a ruled

9
graticule, by which we found that 1 cm of test line in the photograph

equals 20 pm of sample length. The total length of test lines, horizontal

and vertical, is 50 cm, or 1000 urn of sample length. Therefore, N L

=

11/1000 yin, and L = P

p /N

L = 18 urn.

This method is relatively efficient, because the same overlay grid

can be used to measure P p and N

L> Unfortunately, we must make a large

number of such measurements in order to obtain a good statistical average.

The estimation of sample size is described in the following section.

C. Statistical Analysis and Prediction

It is important to be able to estimate the number of measurements

needed to achieve the desired degree of accuracy in our stereological

analysis. The equation which defines this required number (N) of measure5

ments is quite general . It may be written in the form

M r SD ( 1 00 ) s ( x ) -| 2 t r \ N

=

^ (%acc.fm(xT] ' (6)

where x is the measured quantity (e.g., P p

for our volume fraction

measurement), m(x) and s(x) are the sample mean and standard deviation,

respectively, SD is the number of standard deviations desired, and the

percent accuracy [% acc.) is defined as the half width of the chosen

confidence interval divided by the mean. It may be assumed that

u(x) = m(x) and a(x) = s(x), where y and a represent the population

(or true) mean and standard deviation, and m and s are for one large

sample taken from the population. (A sample of at least 30 is recommended

to give a reasonable estimate of y and a). Having determined m and s,

we can use Eq. 6 to estimate N.

Because N varies inversely with the square of the percent accuracy,

it may be necessary to compromise this latter quantity somewhat in order

to keep the number of measurements within reason. Of course, one can

10
arbitrarily decide on a reasonable N and accept the percent accuracy

and/or the confidence interval required to satisfy Eq. 6.

D. Optical Analysis of Porous Polyethylene

Porous polyethylene was selected as the first material to be examined

by stereological techniques, rather than the PTFE-C composite. The

latter has a more complex morphology than PPE, due in part to the fact

that there are 3 phases present, and it was decided that our experimental

procedures should be developed and tested on the less complex material.

1. Sample Preparation

Two criteria must be met in preparing a sample for analysis by

optical microscopy. First, the surface of the specimen must be flat and

smooth, so that each sample area can be brought entirely into the focal

plane of the microscope. Second, there must be sufficient light or

color contrast between the different phases so that they can be clearly

differentiated. The first criterion was easily achieved for the PPE,

but the second proved to be somewhat more difficult.

It was not possible to polish unfilled PPE to give a smooth surface,

due to the softness and elasticity of the material. Rather, it was

necessary first to fill the pores with a matrix material which became

hard enough to provide the necessary sample rigidity for grinding and

polishing. For this purpose, we used a clear polyester resin^ which

hardens upon addition of a small amount of peroxide initiator. The curing

rate of this resin-peroxide mixture was sufficiently slow to permit the PPE

to imbibe the liquid to a depth of about 1 mm before the penetration stopped.

After the resin was sufficiently hard (about 1-2 days), the filled samples

11
were polished with graded carborundum papers (minimum roughness 600

grit), followed by polishing with 0.05 ym alumina powder.

2. Photomicrography

A typical photomicrograph of polished, filled PPE using overhead

(direct) illumination is shown in Fig. 1(a). The pictures were taken

with a Polaroid ©camera attached to the microscope, using type 52

medium contrast positive film. Careful examination of this photograph

reveals that there is probably more than one phase present; however, the

contrast is not sufficient to permit quantitative measurements to be

made. After a number of unsuccessful attempts, we discovered a dye,

Sudan B Black, which was soluble in the liquid resin, did not inhibit

the curing process excessively, and yet provided enough light contrast

to outline the phase boundaries. A typical photomicrograph of the PPE

filled with the dyed resin is shown in Fig. 2b.

The photographs are inferior in quality to the direct visual image

as seen through the stereo eyepieces. Ideally, therefore, one should

perform the stereological analysis directly on the visual image rather

than on photographs. However, direct visual methods also have some

drawbacks, particularly if one wishes to make a large number of measurements. They require intense operator attention, leading to rapid fatigue,

because one cannot use a pointer as on a photograph to keep track of the

linear traverses. Any distraction necessitates a recount. There is

also an obvious advantage in having a hardcopy record of the images for

future reference. For these reasons, we chose to use the photograhic

method of image analysis.

The stereological measurements were performed using a 6 x 4 line

test grid overlay scribed on transparent film. The choice of grid

12
!*igure 1. Photomicrographs of polished cross-sections of filled porous

polyethylene; (a) resin undyed, (b) resin dyed. One

polyethylene "blister 1 ' marked X.

-L J
spacing is not a critical matter, but as a rule it is well to avoid

spacings which are very large or small as compared with the size of the

regions of interest in the photomicrograph. If the grid spacing is too

small, time and effort are wasted in counting many adjacent points lying

in the same phase region. If the spacing is too wide, one discards a

great deal of available information in the photograph. Similarly, the

microscope magnification was chosen to give photographic images which

allowed us to distinguish the phases easily but were not so enlarged as

to contain very few phase regions.

At first sight. Fig. 1(b) may not appear to offer enough phase

contrast to differentiate the 2 types of phase regions. The visual

image, however, allowed us to make this distinction and provided the

clues necessary to permit quantitative analysis. A careful examination

of the photograph reveals that one phase seems to consist of slightly

raised areas or "blisters", elevated above the other phase. Apparently,

during the grinding and polishing of the sample, one of the phases

lagged slightly behind the other as the wear proceeded. The question of

which phase was which, while not obvious from the photographs, was

resolved by close examination of the visual image. The lower (nonraised) phase was seen to contain many small bubbles, as one would

expect in a cured resin but not in the polyethylene. We therefore

assumed that the lower areas represent the filled pores, and it was this

phase that was measured stereologically.

3. Results

Two sets of 10 photomicrographs each were taken on randomly selected

areas of one sample of filled, polished PPE. The 2 sets were taken

14
under somewhat different conditions. For the first set, a 10X microscope objective was used in combination with a 1 OX camera projection

lens. The exposure times were rather long (90 s), and we took the other

set of photographs using a 20X objective and 4X projection lens which

shortened the exposure to 11 s. The photographic magnification was

adjusted in each case by raising or lowering the camera bellows. The

magnification was measured by photographing a ruled graticule graduated

in 10 ym increments. In this way, the two sets of photographs were

found to have magnification ratios of 5.7 and 6.9 ym (sample)/mm (photograph).

The results obtained for the pore volume fraction (P

p

) and mean

intercept length (L) for the 2 sets of photomicrographs are given in

Table 1. Despite the wide range of values obtained within each set of

photographs for both P

p and U, the 2 sets are in very close agreement

with respect to all 4 properties reported in Table 1. All of the photographs were used; none was discarded because it appeared less clear or

less "typical" than the others. This procedure was intended to minimize

possible bias in the measurements due to subjective selection of the

data.

Even a casual inspection of the various photographs revealed that

there was indeed quite a wide variation in pore volume fraction and

intercept lengths for the different sampled areas. In other words, the

surface was not at all homogeneous on the dimensional scale of the areas

sampled in these photographs. Many more measurements should be made on

these and other samples of filled PPE in order to establish confidence

in the measured values of P

p and U.

15
Table 1: Optical Microscopic Measurements of Porosity in Porous Polyethylene

Volume Fraction of Pores (P

p

)

10 Photographs Mean Std. Deviation High Low

Set 1 0.48 0.09 0.58 0.37

Set 2 0.46 0.07 0.54 0.33

Mean Intercept Length (urn)

10 Photographs Mean Std. Deviation High Low

Set 1 74 18 99 44

Set 2 76 15 97 48

III. PORE SIZE DISTRIBUTION BY MERCURY POROSIMETRY

2

In our last Annual Report , we have discussed the use of mercury

intrusion porosimetry to measure both the pore volume and the pore size

distribution in the porous implant materials. Briefly, the technique

consists of forcing mercury into an evacuated sample of the material with

applied pressure and measuring the volume of intruding mercury as a function

of pressure. There is an inverse relation between the pressure and pore

"diameter". The latter is strictly defined only for circular cylindrical

pores, for which the equation relating diameter (D) to pressure (P) was

found by Washburn^ to be

PD = -4yCOS0,

where y and e are, respectively, the surface tension of mercury and its

contact angle on the material of interest. When the pores are of irregular

shape, as in the porous implant materials, the quantity D may just be considered a parameter related to the average size of the interconnecting

pores in the matrix.

16
Mercury porosimetry appears to be the only technique by which a

distribution of pore "diameters" can easily be obtained, and for this

reason it is important to consider how best to plot the data in order to

extract the maximum amount of useful information from it. As a first

approximation, the distribution can simply be plotted as a bar graph of

void volume fraction vs pore size range. This procedure was illustrated

in Ref. 2, page 17. For some purposes, this type of plot may be sufficiently detailed to contain all the desired information. However, it is

possible to make a more detailed plot, as discussed in the following

sections

.

The question of the distribution of pore "sizes" depends in part

upon the kind of information desired. There are at least two ways to

describe a distribution of pore sizes:

(1) Distribution of pore volumes or volume-weighted pore size

distribution. In this case, a given range of pore "diameters" is plotted

vs. the volume fraction having this pore size range.

(2) Distribution of pore "diameters "

. In this case, a given range

of pore diameters is plotted vs. the number fraction of pores having

these diameters.

While either of the above could be a useful way of characterizing

the pore size distribution, (1) is the only one that can be obtained

directly from mercury intrusion data. It might be argued that the

volume-weighted distribution is the more meaningful of the two in terms

of tissue ingrowth. For example, if one is interested in the pore size

range 50-100 ym for tissue ingrowth, it would seem to be more useful to

know that 30% of the total pore volume has this "diameter" range than

simply to know that a certain fraction of all the pores lie within this

17
range of diameters. For the anchoring of these materials by tissue

ingrowth, it is surely not only the diameter of the pores but also the

volume of pores to be filled with tissue that is important.

A. Instrumental Sensitivity

There is a problem in obtaining a very well defined plot of pore

size vs. pore volume from mercury porosimetry data, due to the fact that

the sensitivity of a porosimeter as a pore size measuring device varies

over any given pressure range, and it is especially poor in the size

range corresponding to large pores. For example, the range of aP from

0-1 psia corresponds to a pore "radius" range from 116 ym-°°, whereas

same aP in the range 4-5 psia corresponds to 23-29 \im pores, and the

range 14-15 psia corresponds to a radius range of only 7.7 - 8.0 ym.

Clearly, the sensitivity of a mercury porosimeter as a pore-size measuring

device increases rapidly with increasing pressure . It is, in fact, not

possible to obtain detailed information about pore sizes below about 1.5

psia (80 urn pore radius and up) because P and V cannot be read with

sufficient precision.

B. Random Error Analysis

It is useful to begin the discussion of pore size distribution by

estimating the random errors in the mercury intrusion experiment, and it

is emphasized that this analysis pertains only to random errors. Systematic

errors of unknown magnitude are also present, and they have been discussed

o in our last Annual Report . The volume of intruded mercury (V) can be

estimated on the dilatometer stem to about ±0.001 cm 3 (±1 uL). This

range of aV corresponds to a aP of about ±0.05 psia near the low end of

our P-V plot. Because the slope of the P-V curve varies considerably

over its course, the aP corresponding to a given AV also varies. In

18
addition, there is an estimated uncertainty of about ±0.02 psia in

reading the pressure gauge. There is also a small uncertainty due to

the tendency of both the mercury column and the pressure gauge to "stick"

slightly. All together, these effects appear to add up to random error

limits of about ±0.1 psia for any P corresponding to a given V.

C. Volume-Weighted Pore Size Distributions

In order to construct a volume-weighted pore size distribution plot

from mercury porosimetry data, we start with a volume vs pressure plot

of the data obtained in a single mercury intrusion experiment. Examples

of these s-shaped curves were given in our last Annual Report (Ref. 2,

pp 15, 18, 19). Reading directly from these plots, we make a table of aV

corresponding to each AP increment, from P = 0 to the maximum applied

pressure. Our choice of AP is guided in part by the above random error

analysis, which indicates that we are not justified in choosing AP < 0.2

psi, due to uncertainties in the measurement. Of course, AP may have

any value larger than 0.2 psi, and it does not need to be constant over

the entire curve. We could then make a histogram plot of AV vs P, using

our chosen interval width(s) for AP. However, what we really want to

know is the void volume fraction a V/Vy, where Vy is the total volume,

which corresponds to each pore radius interval Ar.

From the Washburn equation, we know that r varies inversely with P,

so that a plot which is linear with respect to r will not be linear with

respect to P. It is impractical to try to plot AV/Vy vs a constant Ar,

even though this is the desired histogram, because of the problem of

4 varying sensitivity discussed above. A Ar which corresponds to a

measurable AV near the low pressure end of the P-V curve would be much

too large near the high pressure end, where it would correspond to a 19
large fraction of the total pore volume and obscure much of the desired

details of the histogram. However, this difficulty is easily overcome,

either by using a variable Ar or a constant or variable aP. A constant

aP usually seems to cause an appropriate variation of Ar automatically,

because of the inverse relationship. In Fig. 2a we have plotted a

histogram of aV/V-j. (%) vs. r, using a constant aP = 0.5 psi, for one

sample of the composite material. This histogram has increasing radius

interval widths, reading from left to right, which is a graphical

demonstration of the decreasing accuracy of mercury porosimetry data as

P decreases (or r increases). Note that the step widths are so small at

the left end of the plot that one cannot read off Ar directly from the plot.

Clearly, Fig. 2a would be more useful if the radius interval widths

were constant across the plot. In this way we could, for example,

easily compare the fraction of pores falling within any 10 urn radius

interval. It is not possible to plot the void fraction directly vs a

constant Ar, for the reason discussed above. However, we can obtain

such a plot from Fig. 2a, if we divide the void fraction corresponding

to each step of the histogram by its radius interval width. If this

width is greater than 1 ym, this procedure has the effect of lowering

the step height, while the height is increased if Ar is less than 1 ym.

Fig. 2b, the result of treating Fig. 2a by the above procedure, is

a histogram with a constant radius interval width of 1 ym. For example,

the plot shows that approximately 1% of the pores have a radius of

25 ± 0.5 ym. The approximate void fraction of pores having radii between

50 and 100 ym could be found either by (a) integrating the area under

that portion of the histogram and dividing by the total area of the

20
oo

04

O <4- I O

LU

Lu CL

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h* at o

a. +> 4J

to

<4- CO o -C CL U <u

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CO CT CO

<uC -M c t/S O -a -r- c co

to o c o Cl O <4- to

0) s S- 03

03 S_ (U t- O S- cn U IT3 o4-> -t-s -O

CO c <u

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rs* CJ

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CD QJ *F-* to S. CO o 3 a. a cf> CO CO a> -a a» . >

CD SO ir*

4-> a.

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JZ CO CO CD •r— ai

*r- * s_ <D <U -£= 3s +J CLO i •r- 03 4J

<D CO S- s O CHi 3 CL r— S CD 03 o O -C e > U 4-> CO

03 CM

<D

S-3

cn

•r— LU

(%) ©ainjoA pioA

21
oo

CM

i = JV

(%) siunjoA PfOA

22

r(pm)

Figure

2b.

Normalized

plot

of

Fig.

2a,

formed

by

dividing

each

void

fraction

step

in

2aby

its

radius

interval

width.

The

vertical

lines

in

the

histogram

are

omitted

for

clarity.
histogram, or (b) adding together the void fractions, as read on the yaxis, corresponding to each 1 ym interval between 50 and 100 ym.

While the data are not sufficiently precise, particularly near the

ends of the curve, to reveal the exact shape of this normalized plot, it

has the general appearance of a log-normal distribution, a type which is

often found for particles, metal grains, and other systems in which

there is a definite lower limit to the size (in this case r = 0) but no

definite upper limit. The curve is definitely skewed to the right of

the "most probable" r represented by the peak of the curve. The distribution function is not symmetric about its maximum value as it would be,

for example, for a normal (Gaussian) curve.

Figs. 3a and 3b are replots of Figs. 2a and 2b, formed by increasing

the AP interval to 1 psi. Fig. 4 is an unnormalized histogram for one

sample of the porous polyethylene, using aP = 1 psi. As compared with

the corresponding plot for the composite material (Fig. 3a), it illustrates

the much narrower pore size range of PPE.

IV. PORE SIZE BY BET METHOD

2

In our last Annual Report , we have described a method for measuring

the average pore size based upon a simple geometrical relationship,

D = kV/S,

where D is the pore "diameter", V is the specific pore volume, S is the

specific surface area, which we measured by the BET method, and k is a

"shape factor" which varies with the assumed geometry of the pores. For

spherical pores, k=6, and we used this factor to compare the pore sizes

of the 2 implant materials. As compared with mercury porosimetry values

for the average pore "diameter", based upon cylindrical pore shapes, the

BET method yielded a pore diameter which was about twice the mercury

intrusion value for PPE, and about half the mercury value for the composite.

23
(%)euin|OA P!OA

24

r

(pm)

Figure

3a.

Volume-weighted

pore

size

histogram

for

same

sample

of

PTFE-C

composite

as

Fig.

2a.

Pressure

increment

is

1.0

psi

.

Vertical

lines

are

omitted.
014

a

~t

—

•

100

06

r

. o

00

70 )

;iurt)j 09

50

" 40

1

30

1 J

CM

. O

i i i O

to co cm t- o

wit/ j = jtj

% P!°A

25

Figure

3b.

Normalized

plot

of

Fig.

3a.
(%) euin|OA pjOA

26

r(pm)

Figure

4.

Volume-weighted

pore

size

histogram

for

one

sample

of

porous

polyethylene.

Pressure

increment

is

1.0

psi

.

Vertical

lines

are

omitted.
The reason for these discrepancies was not readily apparent, but since

we had analyzed only one sample of each material by the BET method, it

was clearly necessary to confirm these results with more BET data.

During the current reporting period, we have analyzed 3 more samples

of the composite and 2 more of the PPE by the BET method at a commercial

12

laboratory .

The results of all 7 analyses to date are presented in Table 2.

Table 2. BET Surface Area Measurements for Two Porous Implant Materials

2 2

Sample Wgt. (g) Surface Area (m ) Specific Surface Area (m /g )

PPE

0.5091 0.0425 0.083

0.2818 0.0235 0.083

0.2680 0.0213 0.080

PTFE-C Composite

(block) 0.6869 0.271 0.39

0.4931 0.221 0.45

0.5156 0.258 0.50

(sheet) 0.0730 0.0368 0.50

These sample sizes are not large enough to be subjected to statistical analysis. However, the consistency of these data indicates that

our initially reported values, the first listed for each material in

Table 2, were approximately correct. For the composite, the initial

value of S may have been somewhat low, according to Table 2, but if we

use a higher value we calculate an even lower value for D, which was

already much lower than the mercury porosimetry value. It is apparent

27
even from these few BET measurements that the discrepancy between pore

diameters as determined by the mercury intrusion and BET methods cannot

be explained by faulty BET data.

V. COMPARISON OF POROSITY MEASUREMENT METHODS

While the amount of data which we have obtained to date is insufficient to permit statistically well founded comparisons of the accuracy

and precision of the various methods of porosity measurement, certain

tentative conclusions can be drawn on the basis of our current data.

These are discussed in the following sections.

A. Pore Volume

2

On page 9 of our last Annual Report , we reported the pore volume

fraction in PPE as obtained by the "apparent density" and mercury intrusion

methods. The 2 methods yielded void volume fractions of 0.44 - 0.45 and

0.44, respectively. Our preliminary measurements by the optical microscopic technique, as reported above yielded 0.48 and 0.46 for the 2 sets

of photographs, with standard deviations of 0.09 and 0.07. From these

data, we conclude that there is little if any significant difference

between the 3 different methods in their estimation of the pore volume.

Indeed, if we assume that essentially all of the pores are interconnected,

with no included voids, the 3 methods should give the same answer, and

our results seem to confirm this expectation.

These preliminary results are quite encouraging. If, for example,

the PPE samples were in some way distorted during preparation for optical

microscopy, one might expect that the measured volume fraction would be

affected. The good agreement which we find among the 3 methods reinforces

our confidence in each one.

28
The BET method does not measure pore volume and therefore cannot be

compared with the other methods.

B. Pore Size

We first recall that "size" is not a well defined physical property

of an object until we arbitrarily give it meaning in terms of some

measurable quantity. In the mercury intrusion method, "size" was defined

as the diameter of an assumed cylindrical pore shape pertaining to

interconnecting pores in the matrix. In the optical microscopy work, we

have arbitrarily defined "size" as the mean intercept length. Other

arbitrary definitions such as the mean or maximum tangent diameter could

have been chosen equally well, but we have selected a measurement which

appeared to be relatively simple as well as having a low probability of

introducing operator bias.

2

As we have reported for PPE , the mercury intrusion method indicates

that most (^80%) of the interconnecting pore "diameters" lie in the

range 20-40 ym. Our optically measured mean intercept length, reported

above, is about 75 ym or about twice the mercury intrusion "diameter".

If we correct this U for the "sectioning" effect discussed in Section

I IB above, the number is increased by the factor (4/tt) 2 to about 120 ym,

which is much greater than the "diameter" found by mercury intrusion.

Certainly, the interconnecting pores measured by mercury intrusion are

expected to be smaller than the "true" average pore size, although one

might be somewhat surprised at the magnitude of the difference reported

above. It must be remembered that our choice of the parameter to be

measured by optical image analysis was arbitrary. A different choice

might well have led to quite different conclusions than we have found by

our chosen method.

29
The usefulness of any analytical technique depends in large part

upon its ability to yield reliable data in a reasonable time and with a

minimum of operator effort or judgment. In these respects, mercury

porosimetry appears to have a clear advantage over image analysis methods,

particularly if one is restricted to manual analysis. It requires no

sample preparation and, if the instrument is working properly, yields a

great deal of information about the pore size distribution with a single

pressure-volume plot. Optical image analysis requires a much greater

amount of operator time to give a statistically meaningful estimate of

either pore size or pore volume. Furthermore, there is apparently no

simple or rapid way to determine the pore size distribution by optical

methods, whereas the mercury intrusion method provides at least semiquantitative information about the distribution very quickly.

The BET method of measuring pore "size", discussed above and in our

2

last Annual Report , is a hybrid method involving a surface area measurement, a pore volume measurement, and an assumed pore geometry in order

to determine the average pore "diameter". The assumed pore shape can

have a considerable effect on the calculated pore "diameter", and, as we

have discussed before, one has no reason to choose any particular pore

geometry over another for irregularly shaped pores. Our experience does

indicate that both surface area and pore volume can be estimated fairly

precisely with very few measurements. In this respect, the BET method

appears to have an advantage over image analysis methods. Like the

latter, however, the BET method gives no information about the pore size

distribution.

30
C. Summary Table

1. Mercury Porosimetry

Advantages

- relatively little operator time required for each measurement

- no sample preparation required

- no operator judgment required

- gives pore size distribution rather than just an average value

- gives much information in a single P-V plot

- capable of measuring smaller pores than is possible by optical

techniques at high Hg pressure, though advantage not needed for

pores in implant materials

Disadvantages

- gives interconnecting rather than "true" pore diameters

- requires assumed pore shape to interpret the data

- only 2 or 3 PV plots obtainable per day, due to long vacuum

pump-down time

- sensitivity poor for large pores

2. Optical Image Analysis

Advantages

- little operator judgment required

- gives "true" pore size, rather than interconnecting pore size

- sensitivity equally good for large and small pores, but minimum

measurable size limited by chosen magnification

Disadvantages

- sample preparation can be difficult and time consuming

- sample preparation may alter the porosity

31
- may be difficult to obtain good phase contrast

- difficult to obtain information about distribution of pore sizes

- many measurements needed to obtain statistically meaningful

results

3. BET Method

Advantages

- both surface area and pore volume can be estimated well with few

measurements

- more rapid than optical image analysis

- no sample preparation required

- gives "true" pore size rather than interconnecting pore size

Disadvantages

- requires assumed pore shape to calculate pore "diameter"

- does not give pore size distribution

- surface area measurement may be subject to unknown systematic

errors

VI. MECHANICAL PROPERTIES OF POROUS IMPLANT MATERIALS

One item in our work plan for the current year requested a range of

pressures which can safely be applied to PPE and the PTFE-C composite

without distorting the materials. This information is important not

only in determining whether the materials would be expected to deform

significantly during a mercury intrusion experiment, but also in suggesting

the degree of care which should be exercised by clinical workers in

handling the materials prior to and during implantation. In order to

answer these questions, we have performed compressive stress-strain

measurements on the porous implant materials using our Instron universal

testing machine.

32
A. Experimental

Small, rectangular specimens of PPE and PTFE-C composite were cut

from blocks of these materials with a fresh scalpel. For the composite,

samples were cut in 2 ways, with the laminar planes parallel or perpendicular to the area of applied stress. Sample dimensions were measured

with precision calipers. The crosshead speed of the instrument was 0.02

in/min (0.05 cm/min), and the maximum resolution of the stress measurement was 10 g per division of chart paper, with a 1 Kg full scale stress

B. Results

Figure 5 shows the stress (a) vs. strain (e) plots obtained for 2

samples of PPE. The curves are parallel, except for their initial

compression moduli (act/Ae), which differ by about a factor of 2, up to

4% strain. The bottom curve is somewhat suspect due to its rather

O £

abrupt change in slope at about lOkg/cm (1.01 x 10 Pa). It is probabl

that the initial compression modulus was higher than our assumed value

for this curve, due to the fact that the initial area of applied stress

was smaller than our measured area, so that our calculated stress was

too low. Using only hand tools, it was not always possible to cut the

top and bottom stress areas exactly parallel, as they should be for

proper sample alignment. In such a case, the two opposing stress areas

were soon forced into parallel alignment by the descending crosshead of

the instrument, so that the curves in Figure 5 are parallel for e

greater than about 0.05.

As expected, the strain resulting from 1 atmosphere stress (1

kg/cm^, 1.01 x 10^ Pa) was very small (<1%) for PPE. To induce a 1%

2 strain in this material, a pressure of about 10 kg/cm was required

according to the top curve in Figure 5. We also observe that this

33
0.1 0.2 0.3

£(AULo)

Figure 5. Compressive stress-strain curves for 2 samples of

porous polyethylene.

34
material had an approximately constant compression modulus (i.e., it was _ 2 - elastically compressed) up to a pressure of 25-30 kg/cm , corresponding

2

to about 5% strain. Above 30 kg/cm , the material became slightly more

compressible and retained this smaller modulus up to the highest applied

2

pressure, 66 kg/cm .

Figure 6 shows stress-strain plots for 4 samples of the PTFE-C

composite. As noted on the figure, 2 of the samples were stressed

parallel to the laminar planes and 2 were stressed perpendicular to the

laminae. The plots clearly illustrate the mechanical anisotropy of this

material. The compression modulus was much higher for parallel stress,

because the laminar planes stiffen the material with respect to compression

in this direction. Elastic compression occurred up to about 5-7% strain,

after which the modulus began to decrease, passed through 0, and became

negative at about 10% strain. These phenomena resulted from the bending

of the sample as the pressure was increased, so that the applied force

was no longer exactly parallel to the laminar planes. The material thus

became more easily compressed as the bending continued. The difference

between the 2 curves for parallel compression is greater than the difference

for the 2 perpendicular compression curves due to the fact that sample

alignment with respect to the crosshead was more critical in the parallel

direction, and we did not have a very precise method for adjusting this

alignment. Following this reasoning, we assume that the curve displaying

the higher initial compression modulus represented the better alignment,

because the modulus should be greatest when the laminar planes are

exactly parallel to the applied stress.

When the sample was compressed perpendicular to the laminar planes.

35
36

£(AULo)

Fig.

6.

Compressive

stress-strain

curves

for 4

samples

of

PTFE-C

composite.

Two

samples

aligned

parallel

(

||)

and 2

perpendicular

(_[_)

to

applied

stress
its initial modulus was only about 1/6 that in the parallel direction.

However, unlike parallel compression, the modulus increased monotonically

2

with increasing stress, above about 2.5 kg/cm . A pressure of 1 atmoso phere (1 kg/cm ), the maximum applied during a mercury intrusion experiment,

induced about 8-9% strain. This compression was not entirely elastic, as

we learned by increasing the stress to 1 atmosphere, releasing the

stress, and recycling to 1 atmosphere. If this compression were entirely

elastic, the stress-strain curve would be reproducible and independent

of the number of previous compression cycles. However, each time we

repeated this compression cycle, the modulus increased (by diminishing

amounts), indicating increasing inelastic deformation of the material.

C. Implications for Mercury Porosimetry

It is important to decide whether the small strain induced in the

composite material at 1 atmosphere pressure should be considered a

deterrent to the use of mercury porosimetry in studying this material.

While any amount of compression is undesirable, we recall that 1 atmosphere was the highest pressure applied during the mercury intrusion

experiment, and it corresponds to a pore size smaller than that generally thought to be optimum for tissue ingrowth. Less than 0.5 atmosphere pressure is required to measure pores larger than about 30 urn in

diameter, and our stress-strain plots indicate that this stress induces

only about 5% strain in the material. For pores 80 ym in diameter, only

0.2 atmosphere pressure is required, and this corresponds to a strain of

only about 2%. Thus, the strain induced in this material is small over

the pressure range corresponding to pores large enough for tissue ingrowth.

Furthermore, as the mercury begins to enter the pores at low pressure,

one might expect the compression modulus to increase somewhat, due to

37
the stiffening effect of the intruding liquid, so that our stress-strain

measurements in air may overestimate the actual strains induced during

mercury intrusion.

Taken all together, these observations indicate that the pressures

necessary to measure the pores of interest in the PTFE-C composite by

mercury porosimetry are not likely to introduce more than very small errors

due to bulk compression of the material.

VII. SURFACE AREA BY MERCURY POROSIMETRY

A. Theory

In addition to the well known BET method for measuring the surface

area of porous materials, which we have discussed above, there are other

methods available as well for measuring this quantity. One which is

particularly pertinent to our current work involves the use of mercury

1

3

porosimetry data . It rests upon the same assumptions that were used

to determine pore "diameters" from mercury intrusion data. As in the

latter, the usual assumption is that the pores are cylindrical in shape,

because the calculation can be done exactly for this pore geometry.

Work is required to force mercury into a cylindrical pore. The

amount of work is proportional to the surface tension of mercury (y) and

to the increase in surface area of mercury which is created when it is

forced into the pores. This work (W) is as given by the equation

W = 2Trrly cose (7)

where r and 1 are the radius and length of the pore and e is the contact

angle of mercury on the surface of interest. The factor cos 9 represents

a reduction in the work required; it is of course maximum for e = 0°

or 180°, corresponding to a hemispherical meniscus. Figure 7 illustrates

the way a liquid behaves in a capillary when e<90° (a), 0>9O° (b).

38
and 0 = 90° (c). Mercury, which is "non-wetting" on most surfaces,

corresponds to case (b). Case (c) would result if the liquid did not

form a meniscus. Physically this situation means that the energy of the

liquid-solid interaction is identical to the interaction of the liquid

with itself, so that no additional energy is gained or lost when the

liquid contacts the solid surface.

Figure 7. Relationship of Solid-Liquid Contact Angle to the Work of

Forming a Meniscus.

The work of forcing mercury into a cylindrical pore can also be

related to the pressure (P) and volume increment (a V) of the intruding

mercury according to the equation

W = PaV = Pirr2

1. (8)

Equating (7) and (8), we obtain the familiar Washburn equation,

2-rrr 1 y | cose | = P-rrr2

! , (9)

or Pr = 2y | cose | . (10)

(Cos e must be taken as a positive quantity because all other terms are

positive). From Eqs. 8 and 9 we can also form the equality

39
PaV = 2ttt 1 y | cose | . (11)

Since 2iTrl is the surface area (S) of a cylindrical pore, Eq. 11 may

be written

PaV = Sy I cose I . (12)

This may also be written as a differential equation,

PdV = dSy | cose | ,

or dS = PdV/ y

| cose |

.

Integrating, we find

V

S = l/y| cose | / PdV (13)

o Equation 13 provides the basis for using mercury porosimetry data to

obtain the surface area of a porous material. Instead of plotting the

mercury volume V vs. log P, as is customary in the usual plot used to

obtain pore size information, we make a linear plot of V vs. P. A

typical such plot is shown in Fig. 8 , with the shaded area to be integrated.

We used a mechanical planimeter to perform these integrations.

When S is divided by the sample weight, one obtains the specific

surface area which, in combination with the specific void volume of the

material, may be used to estimate the average pore size in the test

sample. This is the same procedure as our BET method, except for the

different method of determining S.

B. Results

In Table 3, we summarize the results of 4 specific surface area

determinations by the method outlined above, together with the BET

results reported in Section IV.

40
37

(Z<H x euio) auinjOA

HI

Figure

0

.

Linear

plot

of

V

vs.

P

obtained

by

nlercury

porosimetry

for

porous

polyethylene.

Surface

area

proportional

to

integrated

shaded

area.
Table 3. Specific Surface Area (m /g)

BET

PPE 0.082

(av. of 3)

PTFE-C 0.45

(block) (av. of 3)

PTFE-C 0.50

(sheet) (1 only)

Determined by Two Different Methods

Mercury Intrusion

0.125

0.192

0.171

0.173

While these results must be considered tentative, due to the small

number of samples, certain trends are evident even from these few data.

The mercury intrusion method yields a specific surface area which is

probably somewhat larger than the BET value for PPE, while the results

for the PTFE-C composite are reversed, with the BET value probably at

least twice the mercury intrusion value.

C. Comparison of Pore Size by Two Surface-Pore Volume Methods

In our last Annual Report , on page 25, we discussed the pore

"diameters" determined for both implant materials by the BET method

using the formula D = 6V/S, which assumes spherical pores, to calculate

the diameters. For PPE and the PTFE-C composite, the average "diameters"

determined in this way were found to be 61 ym and 25 ym, respectively.

If we correct the diameter of the composite's pores by using our current

average BET surface area for 3 samples of the material, the calculated

diameter decreases slightly from 25 to 22 ym. As compared with the

average pore size determined by the direct mercury porosimetry method,

using the Washburn equation, the BET method gave a larger value for PPE,

by about a factor of two, while the value for the composite was only

about half that obtained by the mercury intrusion method.

42
If we use the same factor 6V/S to determine the pore diameter, with

S measured by the mercury intrusion method, the average diameter for PPE

is found to be 40 urn, while the diameter for the composite is 52 ym.

These values are to be compared with our reported values of 30 ym for

PPE and 50 ym for the composite, as determined directly from analysis of

the mercury intrusion P-V plot, using the Washburn equation.

It is not surprising that the two mercury intrusion methods, i.e.,

the direct method using the Washburn equation and the indirect method

using the mercury intrusion surface area, agree so well in their determination of average pore diameter. Both use the same pressure-volume

data, and both are constrained to the measurement of "interconnecting"

pores in the matrix. This so-called "ink bottle" effect discussed in

our last Annual Report causes the Washburn equation to underestimate the

average pore diameter. It also overestimates the average pressure

required to force mercury into the pores, because pressure and pore

diameter are inversely related according to the Washburn equation.

Therefore, when we measure surface area by integrating the pressurevolume plot, since the pressures are higher than the "true" pressures

would be if the pores were indeed cylindrical in shape, we obtain a

surface area which is larger than the true value. Since the pore diameter

according to this method is proportional to V/S, and since S is overestimated, the diameter which we obtain is underestimated. In other

words, both the direct and indirect methods of measuring pore diameter

by mercury intrusion lead to an underestimation of pore diameter for the

same reason.

Unfortunately, none of the above discussion reveals the reason why

our BET surface area for the PTFE-C composite is larger than the area

43
determined by mercury porosimetry. Exactly the opposite would be expected

if the BET method is considered to yield the "true" surface area. It is

possible that the presence of finely divided carbon in the material

could be responsible for this inconsistency, although it is difficult to

predict exactly how this would affect the measurements. Certainly,

finely divided particles can add a great deal to the surface area of a

material but little to the volume, because the surface/volume ratio is

inversely proportional to the radius of the particles. Perhaps mercury

intrusion could change this surface area by pressing the fine particles

against the larger PTFE particles, or perhaps the carbon tends to "float"

ahead of the intruding mercury, since it is probably not bonded to PTFE.

At present, however, we must conclude that the apparent inconsistency in

surface area determinations between BET and mercury intrusion methods

for the composite material is not well understood.

VIII. SUMMARY

The major accomplishments during the current reporting period may

be summarized as follows:

(1) Quantitative Optical Microscopy

For porous polyethylene, we have developed a method for preparing

samples for the stereological analysis which provided both the mechanical rigidity needed for grinding and polishing the material and the

phase contrast necessary for performing quantitative measurements on

photomicrographs of the material. The volume fraction of voids in the

material was measured by the point count method, and the size of pores

was measured by the mean intercept method, where the mean intercept

length

L = P

p /N

L

.

44
We have reported a method for determining the number of measurements needed to obtain any desired degree of accuracy, given an initial

estimation of the population mean and standard deviation.

According to the above, we have made preliminary measurements of

the pore volume fraction and mean intercept length for filled PPE. The

pore volume fraction (Pp) was found to be about 0.46 - 0.48, while U was

found to be about 75 vim.

(2) Mercury Porosimetry

We have made plots of the volume-weighted pore size distribution

from mercury porosimetry data, using interval lengths of r estimated by

a random error analysis of the mercury intrusion experiment. These

plots clearly show that the sensitivity of a mercury porosimeter as pore

size measuring device increases rapidly with increasing pressure, and it

is especially poor when the pore radius exceeds about 80 urn. When these

plots were normalized to a constant radius interval length, they assumed

the general appearance of a log-normal distribution, with the curve

skewed to the right of the "most probable" radius.

(3) BET Pore Size Method

A total of 3 BET surface area measurements have been made for PPE,

and 4 measurements for the composite material. The results indicate

that our single values for each material reported in our last Annual

Report were approximately correct. There remains the question of why

the average pore size predicted by the BET-pore volume method is less

than that found by mercury porosimetry for the composite material.

Exactly the opposite is predicted from the fact that mercury porosimetry

senses "interconnecting" rather than "true" pore diameters.

45
(4) Mechanical Properties

Compressive stress-strain measurements have been performed on both

of the porous implant materials, using our Instron® machine. For

o PPE, the stress necessary to introduce 1% strain was about 10 kg/cm (10

atmospheres), indicating that one may safely perform mercury intrusion

experiments up to 1 atmosphere pressure with negligible deformation of

the material. The PTFE-C composite in block form was quite anisotropic

mechanically. When the stress was applied parallel to the laminar

planes, the initial compression modulus was about 6 times that found for

compression in the perpendicular direction. One atmosphere pressure

induced about 8-9% strain in the latter direction.

(5) Surface Area by Mercury Porosimetry

In addition to the BET method, surface area may be measured independently by integration of pressure-volume plots obtained from mercury

intrusion data. We have found that this method leads to a surface area

for the PPE which is somewhat greater than that obtained by the BET

method; the opposite is true for the composite, with the mercury intrusion

value less than half that found by the BET method. The reasons for

these discrepancies were not readily apparent.

A summary of the advantages and disadvantages of mercury porosimetry,

optical image analysis, and the BET method is given in Section VC.

46
REFERENCES

1. Dehl , R. E., Grant, W. H., and Cassel , J. M., "Evaluation of Methods

of Characterizing the Porosity of Porous Polymeric Implant Materials:

A Review of the Current Status of Porosity Measurements", NBSIR 81-

81-2212 (available from National Technical Information Service).

Annual Report prepared for the Bureau of Medical Devices, Food and

Drug Administration, Silver Spring, MD (February 1981).

2. Dehl , R. E., Grant, W. H., and Cassel, J. M., "Characterization of

Porosity in Porous Polymeric Implant Materials", NBSIR 31-2459

(Available from National Technical Information Service ). Annual

Report Prepared for the Bureau of Medical Devices, Food and Drug

Administration, Silver Spring, MD (February 1982).

3. Registered trademark of the Richards Manufacturing Company.

4. Registered trademark of Vitek, Inc.

5. DeHoff, R. I. and Rhines, F. N., "Quantitative Microscopy", McGrawHill, New York, 1968.

6. Underwood, E. E., "Quantitative Stereology" , Addison-Wesley , Reading,

MA, 1970.

7. Beddow, J. K. and Meloy, T., "Testing and Characterization of

Powders and Fine Particles", Heyden, Philadelphia, PA, 1980.

8. Allen, T, "Particle Size Measurement", 3rd Ed., Chapman and Hall,

New York, 1981

.

9. Kaye, B. H., "Direct Characterization of Fine Particles", John

Wiley and Sons, New York, 1981.

TM

10. Castolite Resin, trademark of Buehler, Ltd.

11. Washburn, E. W.; Proc. Nat. Acad. Sci . _,1 , 115 (1921).

12. Quantachrome Corporation, Syosset, NY.

13. Lowell, S., "Introduction to Powder Surface Area", John Wiley

and Sons, New York, 1979.

47

NBS-114A (rev. 2 -ao) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

4. TITLE AND SUBTITLE

PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3.

NBSIR 83-2645

Characterization of Porosity in Porous Polymeric Implant Materials

Publication Date

February 1983

5. AUTHOR(S)

Ronald E. Dehl

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

8 . Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Bureau of Medical Devices

Food and Drug Administration

Silver Spring, MD 20910

10.

SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

In this report, we describe (1) the continued exploration of methods for characterizing the porosity of two commercial implant materials, a porous polyethylene and a composite of polytetrafluoroethylene and carbon, and (2) the compressive stress-strain

oehavior of these materials. A major emphasis was placed upon optical image analysis

of porous polyethylene. The pore volume fraction obtained from analysis of 20 photomicrcgraphs (0.47) agreed well with the fraction previously found by two other methods.

The mean intercept length, determined from the same photomicrographs, was about 75 ym,

a value considerably higher than the average "interconnecting" pore diameter determined

Dy mercury porosimetry (30 ym). Replotting our mercury porosimetry data, we found

that the volume-weighted pore size distribution curve resembled a log-normal distriDution, skewed to the right of the "most probable" pore radius. The surface area

determined from mercury porosimetry data was somewhat larger (0. 125

?iTr/g) for the

Dorous polyethylene than that determined by the BET method 10.082 m/tj), while the reverse was true for the composite material (0.19 vs 0.45 nr /g). Compressive stressstrain measurements on the laminated composite demonstrated that the initial compression modulus is approximately six times greater when the stress is applied parallel

rather than perpendicular to the laminar planes.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

3 o re size; pore volume; porous implants; porous polyethylene; PTFE-carbon composite;

stereology; stress-strain plots; surface area.

13.

AVAILABILITY

XX] Unlimited

| | For Official Distribution. Do Not Release to NTIS

1 | Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

XXI Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

51

15. Price

$;q . q q- USCOMM-DC 6043-P80
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