A Method Of Calculating The Concentration Of PEG For Freeze-Drying Waterlogged Wood
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A Method Of Calculating The Concentration Of PEG For Freeze-Drying Waterlogged Wood
It has been shown that freeze-drying after pretreatment with a PEG solution is a satisfactory way of treating waterlogged wood. Under certain circumstances it is possible to prevent shrinkage with this method. Recently, the approach has been refined and two molecular weight grades of PEG are now employed. A liquid grade, such as PEG 200, is used to control the cell wall shrinkage and waxy solid PEG 3350 is added to give some structural strength to the weak wood. An important aspect of this approach is the desire to use the minimum amount of PEG in the most effective way, and to adjust the treatment to suit the wood.
Ideally, treatments should be adjusted to suit each wood object. Wood density, anatomical characteristics, environmental effects, state of degradation, etc., are all factors that distinguish wooden artifacts one from another, and it is these that should determine the grade of PEG and the conditions of treatment. To adopt this approach it is necessary to carry out analysis to determine:
(1) the wood species and
(2) the actual density of the wood.
In addition it is important to know:
Simple procedures for obtaining this information have been developed, and these data are entered into a computer program called "PEGcon" which calculates appropriate PEG concentrations. This program also calculates weights and volumes for making up PEG treatment solutions. In addition it will calculate PEG concentrations according to certain other treatment regimes.
The procedure derives from experimental observations made over a number of years and in order to explain its use, it is worth reviewing the background. The anti-shrink effect of PEG 400
In 1981, while investigating the freeze-drying method developed by Ambrose (1), Grattan (2) showed that for a number of samples of undeteriorated waterlogged wood, the shrinkage depended on the concentration of PEG 400 in the impregnation bath. Wood exposed to higher concentrations had less shrinkage. The volume of PEG required was between 1.2 and 2.0 times the second-order space at the fibre saturation point. This behaviour was explained in terms of the replacement of water in the cell walls by PEG. The conclusion drawn was that if all the second-order space was replaced with a substance with chemical properties similar to water and which would not evaporate in the vacuum chamber of a freeze-drier, then there would be no reason for the cell wall to shrink as the wood dried.
In a second series of experiments (3), the effect of deterioration was investigated and again it was found that as the level of PEG was increased so shrinkage (as expressed by anti-shrink efficiency) was reduced. It was noted that more deteriorated wood required more PEG per unit weight of dry cell matter to be stabilized. (The volume of PEG required was more than 1.8 times that which would fill the second-order space for more deteriorated wood.) The reason for this was thought to be that the cell walls of deteriorated wood are more porous than undeteriorated wood and thus require relatively more PEG to bulk them.
In calculating how much PEG is required to bulk a given sample of wood it is, however, not enough simply to calculate the second-order space and assume that if exactly that amount of PEG is impregnated into the wood all will find its way to the desired location. There are a number of other factors to consider which influence the final PEG distribution.
For example, consider a sample of wood soaking in an aqueous PEG solution of x%. Let us assume that there is perfect penetration of the solution through all lumens and also through the microcapillaries in the cell wall. Thus in the impregnation phase of a treatment, the solution concentration together with the space available within the wood determine the amount of PEG that can enter. In the drying phase no additional PEG can enter. The PEG in the wood may, however, redistribute. If cell walls are to remain fully swollen after freeze-drying, it is probable that PEG must replace about 90% of the waterlogging water. Simple impregnation thus cannot provide enough PEG in cell walls to prevent shrinkage. At some stage of the drying more PEG must enter cell walls. For more to enter (and there is evidence that it does as discussed below) PEG must migrate into the cell wall from the lumens to replace evaporating ater as freeze- drying takes place. Certain factors may facilitate this, one of which is discussed in the following.
The effect of the eutectic pointAt the temperature commonly used in freeze-drying (ca. -20"C), PEG-water solutions remain partially unfrozen and are thus not completely solid. In the region of -20°C, frozen PEG solutions consist of ice intimately mixed with a viscous solution of 55% PEG in water (the pseudo eutectic mixture) (4). As such a solution freeze-dries, it becomes progressively enriched in PEG. The behaviour is described by the simple two- component phase diagram for water-PEG (4) in that the melting point decreases as the solution becomes more concentrated in PEG until the pseudo eutectic mixture, at 55% PEG, is reached. Here, the freezing point is below -25°C and it is indefinite. As drying continues beyond this point, solid PEG separates until, when all moisture is gone, only PEG remains. All this activity appears to take place within a rather narrow zone with solid PEG on one side in the outer region of the wood and frozen PEG/water mixture on the other. This zone is referred to as the freeze- drying front (5). As wood freeze-dries, the front slowly penetrates the frozen block of wood. It is possible that PEG (or the 55% solution) is quite mobile; the viscosity of the solution is surprisingly low at ca. 100 centistokes (4). Since drying is rather slow, the front must progress quite slowly and it may thus allow time for the migration of PEG into the cell wall to replace water which has sublimed. Capillary action rather than diffusive exchange may be responsible.
Direct confirmation of PEG in the cell walls of dried wood
The presence of low molecular weight PEG in the cell walls has been confirmed in two ways. Young and Wainwright (6), and later Young and Sims (7), observed PEG directly with a cobalt thiocyanate staining procedure. Low molecular weight PEGs (200, 400, and 600) were observed in the cell wall of some species although higher molecular weights (1000, 1450, 3350) were not. The most effective "penetrant" was PEG 200. There were also major differences between species. North American white oak (Quercus alba) and cedars (Thuja occidentalis and Thuja plicata) were found to be very difficult to penetrate, even when deteriorated. No penetration of the libriform fibres in oak (25% of the total wood volume) was ever observed. PEG penetration of the cell wall (as well as the lack of it) was also shown indirectly in a study of the response of PEG 400 and PEG 3350 treated waterlogged wood to varying RH (relative humidity) (8). The dimensions of wood samples treated with PEG 400 were immune to RH change while those treated with PEG 3350 responded little differently from untreated wood.
The mixed PEG method
These observations led to the idea of treating wood with a mixture composed of a good "penetrant" such as PEG 200 (or PEG 400) to control the shrinkage of cell walls and waxy solid PEG 3350 to remain in the lumens in an attempt to counteract the collapse of weak deteriorated wood. From studies of the microscopic condition of waterlogged wood, such as that by Barbour (9), it was known that deterioration reduces the strength of wood by destroying the secondary cell wall. Wood in this condition is soft and the cells are unable to withstand the capillary tension forces of drying (as demonstrated very effectively by Barbour). Freeze-drying largely removes those forces, but since the amount of wood substance that remains can be quite minimal something must be added to consolidate the cells.
Mention should also be made of Hoffmann's studies (10) of the shrinkage of oak treated with 50% solutions of PEG. Although the method was not intended as a pretreatment for freeze- drying, Hoffmann clearly showed that PEG 200 gave least shrinkage for undeteriorated wood, whereas for deteriorated wood, PEG 3350 was most effective. Intermediate grades were never as effective for either state. These observations accorded well with those of Young and Sims mentioned above.
In Grattan and Cook's study on the treatment of wood with two grades of PEG (3), various recipes were tried and mixtures such as 15% PEG 400 and 15% PEG 3350 were experimented with. Strengthening agents including a number of water soluble resins other than PEG 3350 were also tested. Only PEG 3350 gave adequate performance. The mixed PEG methods were quite successful, but there were certain problems that required that the method be refined. The technique did not take account of the variations between species or condition. It was thus somewhat open to chance whether wood given a standard recipe would receive a completely successful treatment. The problems caused by unsuitable PEG concentrations may be summarized as follows:
Not enough PEG 400 ... cell wall shrinkage resulting in cracking and warping, treated wood not dimensionally stable to RH change.
Too much PEG 400 ... in the freeze-drying phase it may bring the wood needlessly close to the eutectic point making the wood difficult to freeze, slow to dry, and giving a poor result. Treated wood may be excessively heavy, hygroscopic (surface weeping in humid conditions), soft, and easily damaged with an unattractively "wet" appearance and dirt retention problems. If humidity sensitive components are present - such as metals in a composite artifact - this is of particular concern because of the greater risk of corrosion. The impregnation would also be needlessly lengthy and PEG would be wasted.
Not enough PEG 3350 ... cell collapse during drying and insufficiently strengthened wood.
Too much PEG 3350 ... in the freeze-drying phase it may bring the wood needlessly close to the eutectic point making the wood difficult to freeze, slow to dry, and giving a poor result. Treated wood may be excessively heavy. The impregnation would also be needlessly lengthy and PEG would be wasted.
For these reasons it seemed important to be able to get the PEG concentrations exactly right. In order to do this, it is important to match treatment conditions to the wood undergoing impregnation. The quantitative assessment of deterioration thus became an important consideration.
In conservation, two main approaches have been taken in the characterization of wood deterioration. They both, however, have limitations. One approach is to study alterations in the micro-morphology to find out how deterioration has affected the wood at the cellular level. Important though this is, it is not always easy to generalize from this type of information, and neither is it always clear what the implications are for treatment. The second approach is to analyse the wood chemically and examine changes in the chemical constitution. Studies along these lines have been carried out a number of times (11). Chemical analysis requires 20 g of wood, is time consuming, and/or expensive. It also may not be possible to remove this quantity of material from an artifact for ethical reasons. Consequently, it is impossible to analyse every artifact to be treated.
Nature seems to have provided us with a way round this difficulty. In waterlogged wood, it is the holocellulose (i.e. alpha cellulose plus the hemicellulose) rather than the lignin that deteriorates first. For many wood species and for all burial conditions, this pattern of deterioration is noted. Graphs of holocellulose versus maximum moisture content show that a value of maximum moisture for a given species allows one to estimate the amount of residual holocellulose. Grattan and Mathias have argued from this observation that for calculating PEG concentrations, it was unnecessary to conduct chemical analyses and it was sufficient to evaluate Umax, the maximum moisture content (12). Umax is a function of deterioration, i.e. of loss of holocellulose, because it depends upon the void space in wood. As holocellulose deteriorates and is lost, so the void space within the cell wall, and hence Umax, increases. One difficulty of this approach is that the significance of Umax is dependent on the density of the wood. A high Umax might mean that a wood of low density (i.e. balsa or cedar) is undeteriorated whereas for a dense species such as oak or mahogany such a value would reflect large scale deterioration.
Grattan and Mathias (12) suggested, therefore, that if species is known, then it is worthwhile to evaluate the probable loss of woody material caused by deterioration. For this, the density of the wood in the deteriorated condition is compared with that of a normal sample of new wood. The difference between these densities is assumed to represent the holocellulose that has been lost. This value, i.e. the loss, is denoted by "Lws" and is expressed as a percentage of the original normal density.
Derivation Of PEG Concentration Equations
PEG concentrations are calculated on the basis that the PEG in the wood at the completion of the soaking period will remain within the wood during freeze-drying. Thus the space within the wood accessible to PEG solution and the amount of cell wall present are important considerations in determining the PEG concentrations to be used.
N.B. The following derivations are based on 1 cc of wood.
PEG 200 concentrationAt the FSP (Fibre Saturation Point), the water held in wood (Mf) exactly fills the second-order space, and the lumens remain empty. Mf therefore defines the second-order space or the cell wall void volume of residual undeteriorated cell wall. The volume of PEG 200 to be added should, as a first approximation, be enough to fill this space exactly, thus the PEG volume in the wood is given by Mf.
Mf = 100 * Wwat / Wwood %
Wwat = weight of water held in the wood (g) at the FSP for undeteriorated wood
Wwood = oven-dry weight of wood (g)
Wwat = Mf * Wwood / 100 g
Since the density of water approximates to unity, the weight of the water Wwat approximately equals Vwat, the volume of the water in the wood at the FSP. Furthermore, Vwat (FSP) equals Vsos, the second-order space at the FSP.
Vsos = Vwat = Wwat = Mf * Wwood / 100 cc
As mentioned above, the volume of PEG 200 (Vp200) required (i.e. not the volume of PEG impregnation solution, but the volume of undiluted PEG), should exactly fill the second-order space.
Vp200 = Vsos = Mf * Wwood / 100 cc equation 1
The actual density (i.e. that of the deteriorated state) of the wood is given by Rg, the oven-dry weight of wood divided by Vwood the volume occupied by the wood in the fully waterlogged condition: Rg = Wwood / Vwood g/cc but since the volume of wood is unity, Rg can be substituted for Wwood in equation 1:
Vp200 = Mf * Rg / 100 cc equation 2
The density of cell wall material (i.e. cellulose, hemicellulose, and lignin) has been found to be a rather invariant quantity at about 1.5 g/cc for many species (13). Even when there is substantial degradation (i.e. losses of cell wall substance), the density of that which remains has been found to be close to this value (9). This allows the calculation of interior volume, Vint (i.e. that of lumens plus the second-order space), to be calculated.
In unit volume (1 cc) of wood the volume occupied by cell wall substance (Vwall) is:
Vwall = Rg / 1.5 g/cc
The volume not occupied by cell wall substance, the interior volume Vint (which we assume will be entirely filled with PEG solution), is thus:
Vint = (1.5 - Rg) / 1.5 cc
The concentration of PEG 200 solution (c 200) necessary to introduce exactly the desired volume of PEG 200 into the cell wall is:
c 200 = Vp200 / Vint cc PEG 200 / cc solution
= Mf * Rg * 1.5 / (100(1.5 - Rg)) cc PEG 200 / cc solution
The density of PEG 200 = 1.127 g/cc (4), therefore the PEG concentration (c 200) expressed as weight percent is:
c 200 = 1.127 * Mf * Rg * 1.5 / (1.5 - Rg) % PEG w/v equation 3A
or as a volume percent:
c 200 = Mf * Rg * 1.5 / (1.5 - Rg) % PEG v/v equation 3B
Equations 3A and 3B may be used to calculate PEG 200 strength for undeteriorated and deteriorated wood.
(If, for the reasons discussed elsewhere in this paper, it is considered that there should be a ratio of PEG 200 to Mf, i.e. a PEG coefficient greater than unity, then this ratio is multiplied by the concentrations shown in equations 3A and 3B to give the increased impregnation concentration.)
PEG 3350 concentration
The next step is to calculate the PEG 3350 requirement for deteriorated wood. As a working hypothesis it was decided that the volume of PEG 3350 necessary in the wood should equal the volume of wood missing through deterioration. Obviously, it is not expected that the PEG will exactly replace the missing volume, however, it is thought that more solid PEG will be deposited on the surfaces of the larger cavities within the wood. Since lumen volume increases with deterioration as the cell wall is destroyed, a deteriorated cell should receive more PEG 3350 on the cell walls than an undeteriorated cell. (For a tubular cell the ratio of the surface area to the volume approximates to 2/r, where r is the cell radius. Thus, as r increases, the volume increases relative to the surface area, thus larger cells contain more PEG solution per unit surface area than smaller ones.)
The percent loss in wood substance, Lws (i.e. oven-dry weight of wood missing through deterioration), is estimated by the difference between the normal density of the species and the actual density:
Lws (w/v) = 100 (Rgn - Rg) / Rgn %weight/volume
Expressed in terms of volume per unit volume of wood, and using the assumption that cell wall substance weighs approximately 1.5 g/cc, the volume missing through deterioration is:
Vlws = (Rgn - Rg) / 1.5 cc
Vlws therefore gives the volume of PEG 3350 required to replace missing cell wall substance per unit volume of wood.
Now the volume that is accessible to PEG 3350 solution is the lumen volume only. The second- order space is not included, since Young and Sims' work (discussed above) indicates that PEG 3350 cannot penetrate it.
Lumen volume is calculated as follows
Second-order space per unit volume of wood is given by equation 1.
Vsos = Mf * Rg / 100 cc
Lumen volume, Vlum, is given by:
Vlum = Vint - Vsos
The concentration of PEG 3350 that must be achieved in the wood is thus:
c3350 = (Rgn - Rg) / (1.5 (Vint - Vsos)) cc/cc
= (Rgn - Rg) / (1.5 * (1.5 - Rg) / 1.5 - Mf * Rg / 100)) cc/cc
= (Rgn - Rg) / (1.5 - Rg * (1 + 1.5 Mf / 100)) cc/cc Equation 4A
Expressed as weight percent the ideal concentration for PEG 3350 is:
c3350 = 100 * 1.072 * (Rgn - Rg)/(1.5 - Rg(1 + 1.5Mf / 100)) %w/v Equation 4B
Equations 3 and 4 can be used to determine the most suitable concentration of PEGs for freeze- drying waterlogged wood. To make them into practically useful tools, more information is required.
Normal density (Rgn)
There are extensive literature sources of normal density values. For this work, all major North American compilations were considered. Summitt and Sliker's data were most comprehensive and were thus adopted (14).
We recognize that the concept of "normal" density is rather artificial because of the large variations within a given tree - not only between different types of tissue (root, branch, compression wood, juvenile wood, etc.) but also within the trunk depending on age, etc. In addition, there can be major variations from tree to tree depending on the environment of growth. In practice, the consequences of the uncertainty surrounding the original density of an object are not serious. The value of Rgn determines the amount of PEG 3350, and has no effect on the PEG 200 concentration. As mentioned above, the intention is simply to replace estimated losses of wood substance with an equal volume of PEG 3350 as a first approximation. An error in Rgn does not therefore have very serious consequences. Another effect is that an artifact may be found to have Rg greater than Rgn simply because its original density was much higher than normal. The effect of this not serious. In these circumstances, the value of PEG 3350 given by the computer program is zero, which is probably a sensible suggestion because the high Rg value almost certainly means that the wood is undeteriorated. It may be wise to carry out an ash content of the wood in such circumstances to eliminate the possibility of extensive mineralization being a cause of the high Rg value.
Actual density (Rg)
This is determined most easily by two weighings. The weight of a sample of waterlogged wood in air (Wair) is the oven-dry weight of wood (Wwood) plus the weight of waterlogging water (Wwat).
Weight in air:
Wair = Wwood + Wwat g
If a sample is weighed, fully submerged, in water the weight (Wsub), assuming absence of air bubbles, is given by Archimedes principle as the oven-dry weight of wood minus the weight of an equal volume of water (Weqvol).
Weight submerged in water:
Wsub = Wwood - Weqvol g
Since, as explained above, the cell wall can be assumed to have a density of 1.5
Weqvol = Wwood / 1.5 g
thus the submerged weight can be related to the oven-dry weight of wood:
Wsub = Wwood - Wwood / 1.5 = Wwood / 3
Therefore the oven-dry weight of wood is given by:
Wwood = 3 * Wsub
and the weight of water contained in the wood is:
Wwat = Wair - 3.Wsub
The actual density (Rg) is given by the oven-dry weight divided by the volume in the fully waterlogged condition, which from the above is given by:
Rg = 3 * Wsub (Wwat + 3 * Wsub / 1.5) = 3 * Wsub (Wair - Wsub)
Information to calculate Rg is thus easily obtained by weighing the wood samples submerged and in air. Wsub can be measured by suspending the samples from the hook below a top loading balance. To remove any trapped air, samples are held fully submerged under vacuum before weighing. A freeze-drying chamber is a very useful means of doing this. Evacuation and weighing are repeated until constant weight is obtained.
Factors that can lead to an incorrect assessment of the deterioration are the presence of mineral substances within the wood or that the original density of the wood diverged significantly from the normal value. This is discussed below in the section under determination of normal density.
Fibre saturation point
There is little information in the literature on fibre saturation points for specific species of wood. Furthermore, Voffeiter (15) pointed out that although it is popularly believed that the moisture content at the fibre saturation point is the same for all wood species, this is not in fact so. He found that the moisture content at the fibre saturation point decreases with increasing wood density until it reaches 16% at a wood density of 1.51 g/cc (the density of the cell wall substance). Vorreiter showed that a plot of log Mf is very approximately proportional to the log of the wood density Rg. There have been a number of investigations of the dependence of fibre saturation point upon density since Vorreiter's work, and it has been noted that Vorreiter's method underestimated the fibre saturation point of denser wood because of the presence of extractives. Waterlogged wood tends to have small amounts of extractives, thus the data of Feist and Tarkow (16), obtained by the PEG exclusion method with extractive free wood, probably give a better indication of the true Mf for denser wood (17). Feist and Tarkow's data were plotted in the same logarithmic form as Vorreiter's, and the following linear relationship was obtained (and is included in the computer program):
Mf (Feist/Tarkow) = 10^(1.454 - 0.384 * log10 Rgn)
Kollmann and Cöté also reviewed fibre saturation point for various categories of wood (18), and their information is also included in the computer program for comparison. At present, we recommend the Feist/Tarkow data as being probably the most useful.
The Computer Program - PEGcon
PEGcon employs the equations derived above and also lists all the published data on the density of North American species. For very deteriorated wood it suggests that the treatment solution should be composed almost completely of PEG 3350 with very little PEG 200, whilst for sound wood it suggests the reverse.
To run the program it is only necessary to know the species of the wood and the actual density (or maximum moisture content or the weights submerged and in air as described above).
Using the program
The concentrations given by the program should be interpreted with discretion. It is still necessary, for example, to examine wooden artifacts with the pin test, to explore the very soft areas, and to find out about the environment of the wood. Careful consideration should be given to the possible presence of minerals. In some instances it may be important to conduct other more extensive analyses.
It must be remembered that the concentration of PEG 3350 is not critical and that it can be adjusted when necessary. In this context it is important to note that the density of wood in the undeteriorated state is extremely variable and may differ markedly from the "normal" value. As a result, actual density is sometimes greater than normal density, even when the wood seems to be partially deteriorated. If such values are entered into the program it gives a warning and yields a value of zero for the concentration of PEG 3350.
If the total PEG concentration is within 10% of the eutectic point at 55% PEG the mixture may not freeze, thus such solutions should be avoided. The program warns the user if the solutions are in this region, and it is suggested that the PEG 3350 component be adjusted to avoid this region.
Making up and changing the solutions
Part two of the program gives a method of making up the rather complex solutions necessary for this approach.
To explain certain problems and how the computer program overcomes the difficulties a hypothetical example is given in the following:
Imagine that the concentrations given by the first part of the program are 7.5% PEG 200 and 18% PEG 3350. With normal procedure, we would carry out such an impregnation in at least three steps:
In step one, the wood is placed in 7.5% (v/v) PEG 200. (N.B. normally the low molecular weight impregnation phase is accomplished in one step.)
In step two, the PEG 200 concentration is kept constant and 9% (w/v) PEG 3350 added (i.e. the solution is 7.5% (v/v) in PEG 200 and 9% (w/v) in PEG 3350).
In a third and final bath, the wood is exposed to 7.5% (v/v) PEG 200 and 18% (w/v) PEG 3350.
To adjust concentration accurately without waste while maintaining constant volume is not easy, thus Part two of the program does the necessary calculations. The program assumes that an initial solution of PEG 200 of a known volume has already been prepared, and that it is required that PEG 3350 is to be added. You are requested to specify the concentration of PEG 3350 required and the program responds by telling you to pour out some PEG 200 solution and to add a weight of PEG 3350 (in kilograms) and a volume of PEG 200 (in litres) in order to keep the concentration of PEG 200 constant. It then asks you if you want to make further increases in PEG 3350 concentration. The PEG 3350 concentration can be adjusted in as many increments as required. Note that it asks for the total PEG 3350 concentration rather than the incremental value.
Are The Concentrations Suggested Correct?
As mentioned above, there is evidence that suggests that it is necessary to add more PEG 200 than the amount required to fill the second-order space. There may be several reasons for this. A higher concentration of PEG may be required in the lumen to drive the PEG into the cell wall. Cell wall impregnation is uneven and in order to limit shrinkage it may be necessary to cause some cells to swell to compensate for those that are not impregnated and shrink. Grattan and Cook found that PEG had to be added to 1.2 to 2 times the moisture content at the fibre saturation point for relatively undeteriorated wood and above 1.8 times for deteriorated wood (3). This factor which takes into account such practical experience has been named by us "the PEG coefficient" and is easy to factor into the calculations as mentioned above. The program requests a value for this at the end.
At present, we err on the side of caution and suggest that unless you have data that suggest otherwise, it is best to use a PEG coefficient of 1. ASE will still be about 85 +/- 10%, but the danger of hygroscopic wood etc. will be avoided.
It is interesting to compare the optimum PEG values found by Hoffmann with these data. Optimum PEG is the minimum amount of PEG necessary to produce minimal shrinkage, and is given in units of percentage on the oven-dry weight of cell wall substance. Hoffmann (10) noted that PEGopt was proportional to the maximum moisture content and an empirical equation of the following form was observed
PEGopt = A * Umax + B
where Umax is the maximum moisture content and A and B are constant terms.
On rearrangement of equations 3 and 4 for total PEG concentration, an equation of exactly the same form as Hoffmann's can be derived. (N.B. this is possible because Umax is a function of Rg.) Hoffmann's experimentally observed relationship can thus be given a theoretical interpretation:
PEG200 + PEG3350 = Rgn * 0.667 * Umax + Mf + 44.44 * Rgn - 100
Using Hoffmann's values for A and B (10) it is possible to calculate values of Rgn and Mf. For old European white oak treated with PEG 200, Hoffmann's data yield Rgn = 0.75 and Mf = 52, treated with PEG 3000 they yield Rgn = 0.6 and Mf = 56. These calculated values of Rgn are rather close to the normal value for white oak which is about 0.6 g/cc. Interestingly, the calculated values of Mf are approximately double that of normal oak. Hoffmann's data tell us, therefore, that to achieve minimal shrinkage and fill the cell wall with PEG we must use an amount of PEG that is 52/28 to 56/28 times the Mf (i.e. the PEG coefficient is 1.85 for PEG 200 and 2.0 for PEG 3000). Hoffmann's data not only lend support to the method of calculating PEG strength but also agree quantitatively with Grattan and Cook's earlier data.
We would like to offer this program to our colleagues for testing. Please try it. We hope that it is found to be useful. If someone would like to add European, Asian, or other species to the density list we would be happy to cooperate. Furthermore, if someone wishes to use this program with other ratios of PEG to wood, with other impregnation materials such as sucrose, or to treat materials other than wood we would be happy to provide assistance. Copies of the program which runs on DOS (for IBM compatible computers) may be obtained from either of the authors by supplying us with a floppy disc (3.5" - 8.9 cm or 5.25" - 13.3 cm). We think it can be useful for all workers in this field and we welcome assistance in developing it further.
The authors would like to thank Parks Canada and the Canadian Conservation Institute for support of this work.
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The work of Young and Sims (7), and also of Hoffmann (10), clearly shows that the impregnant that penetrates the cell wall most effectively is PEG 200. We therefore recommend its use over PEG 400 in freeze-drying. In the following argument, PEG 400 can replace PEG 200 - it makes no difference to any of the argument.