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Opthalmic glass particularly photochromic glass
Journal of Non-Crystalline Solids 47, 1 (1982) 69-86 North-llolland Publishing Company
OPTIIALMIC GLASS
PARTICULARLY
69
PHOTOCHROMIC
GLASS
R. J. A r a u j o Research
and D e v e l o p m e n t L a b o r a t o r i e s C o r n i n g Glass Works Corning, N e w York 14831
P h o t o l y s i s of c e r t a i n g l a s s e s c o n t a i n i n g minute silver h a l i d e d r o p l e t s leads to v i s i b l e absorption° The t e m p e r a t u r e d e p e n d e n c e of the i n d u c e d a b s o r p t i o n is s t r o n g l y c o r r e l a t e d w i t h the rate at w h i c h the glass r e v e r t s to its c l e a r state upon the c e s s a t i o n of r a d i a t i o n . The factors w h i c h i n f l u e n c e the c o m p r o m i s e s in fade rates and t e m p e r a t u r e d e p e n d e n c e will be discussed. I. S U N G L A S S
SPECIFICATIONS
A p p r o x i m a t e l y o n e - h u n d r e d m i l l i o n pairs of s u n g l a s s e s are sold in the U n i t e d States every year. ~ Not o n l y is the use of s u n g l a s s e s a w i d e s p r e a d p r a c t i c e , it is a v e r y old p r a c t i c e . Tuberville, a B r i t i s h o p h t h a l m o l o g i s t , p r e s c r i b e d silk v e i l s for p o s t - o p e r a t i v e p a t i e n t s c o m p l a i n i n g of p h o t o p h o b i a in the f i f t e e n t h century. ~ The c u r r e n t p o p u l a r i t y of s u n g l a s s e s is p r o b a b l y due l a r g e l y to a s u b j e c t i v e f e e l i n g of c o m f o r t on the part of the w e a r e r but, in addition, there are c i r c u m s t a n c e s u n d e r w h i c h s u n g l a s s e s improve vision. ~ I m p r o v e d v i s i o n i n c l u d e s i m p r o v e d c o n t r a s t d i s c r i m i n a t i o n , i m p r o v e d r e s o l u t i o n and c e r t a i n l y s h o r t e r a d a p t a t i o n times. In the range from 300 c a n d e l a s / m e t e r 2 (very g o o d r o o m light) to 3000 c a n d e l a s / m e t e r 2 (moderate o u t d o o r lighting) for the a v e r a g e p e r s o n the sense of c o n t r a s t stays the same and s u n g l a s s e s are not h e l p f u l and, not s u r p r i s i n g l y , are not n o r m a l l y worn. In the range from 3000 to 30,000 c a n d e l a s / m e t e r 2, c o n t r a s t d i s c r i m i n a t i o n dec l i n e s w i t h i n c r e a s i n g i n t e n s i t y . ~ The r e a s o n for this may be related to the f i n d i n g that g r e a t e r noise is g e n e r a t e d in the retinal c i r c u i t r y at h i g h - l i g h t levels, s In the same range of light intensities, r e s o l u t i o n d e c r e a s e s w i t h i n c r e a s e d i l l u m i n a t i o n . This is p r o b a b l y r e l a t e d to the f l u o r e s c e n c e (530 nm peak) of the human lens w h i c h acts as a noise source. 4 The i m p o r t a n c e of this e f f e c t in y o u n g p e o p l e is c o n t r o v e r s i a l but in o l d e r p e o p l e (>50 years) inc r e a s e d f l u o r e s c e n s e and d r a m a t i c a l l y i n c r e a s e d i n t r a o c u l a r light s c a t t e r i n g m a g n i f y the e f f e c t v e r y s i g n i f i c a n t l y . The s h o r t e n i n g of a d a p t a t i o n times is a b e n e f i t of s u n g l a s s e s that is b e y o n d c o n t r o v e r s y . A w h o l e day at the b e a c h w i t h o u t s u n g l a s s e s will r e d u c e the eye s e n s i t i v i t y at d u s k by a l m o s t fifty percent. ~ This e f f e c t can be c u m u l a t i v e . S t u d i e s on l i f e g u a r d s who spent two w e e k s at the b e a c h w i t h o u t s u n g l a s s e s found that they did not r e g a i n their n o r m a l d a r k - a d a p t e d s e n s i t i v i t y in a full day.
0022-3093/82/0000 0000/$02.75 © 1982 North-Holland
R. Arau/o / Photochromic Glass
70
Table
I
Condition
Light Level
Effect of Increasing
300 candelas/m 2
Very good room light
1
3000 candelas/m 2
Moderate
outdoor
J
3000 candelas/m 2
Moderate light
outdoor
30,000
Bright outdoor light
candelas/m 2
Table
i) Diminishing contrast discrimination 2) Diminishing resolution 3) Increasing adaptation time
II
RecoF~ended for long time in very bright surroundings
10-20%
Recommended
20-30%
Range of sunglasses
>50%
NONE
Circumstance
Transmittance
1%
light
Intensity
Doubtful
for normal
benefit
sunlight
protection
sold in greatest
other
than cosmetic
numbers
R. Arau/o / Photochromic Glass
71
To r e n d e r b e n e f i t s in c o m f o r t and i m p r o v e d vision, s u n g l a s s e s should have t r a n s m i t t a n c e s b e t w e e n ten and t w e n t y percent. 3 R e s e a r c h e r s u n a n i m o u s l y a g r e e that g l a s s e s h a v i n g t r a n s m i t t a n c e s g r e a t e r than fifty p e r c e n t are g o o d for p r o t e c t i n g the eye from d u s t p a r t i c l e s . 8 P e o p l e s p e n d i n g s e v e r a l hours u n d e r v e r y bright, o u t d o o r c o n d i t i o n s p r o b a b l y s h o u l d w e a r g l a s s e s h a v i n g one p e r c e n t t r a n s m i t t a n c e . 9 It s h o u l d be e m p h a s i z e d that the p u p i l l a r y m e c h a n i s m does not o p e r a t e as an a u t o m a t i c sunglass. The pupil goes from m a x i m u m d i l a t i o n to s l i g h t l y less than 3 mm in d i a m e t e r o v e r an i l l u m i n a t i o n range from i0 -~ lumens (dark night) to 10 lumens (poorly l i g h t e d room). From I0 lumens to 10,000 lumens (very b r i g h t day) the pupil s h r i n k s to about 2 mm, less than a factor of two d i f f e r e n c e in area. It s h o u l d be p o i n t e d out that the a v e r a g e p e r s o n will e x p e r i e n c e no d i f f i c u l t y s e e i n g t h r o u g h g l a s s e s h a v i n g one p e r c e n t t r a n s m i t t a n c e even at light levels as low as 300 c a n d e l a s / m e t e r 2. Such dark glasse: are not popular, however, p r o b a b l y for c o s m e t i c reasons. W i t h such dark g l a s s e s the eyes of the w e a r e r can be o b s c u r e d to an o b s e r v e r and the o b s e r v e r w i l l see r e f l e c t i o n s . W e a r e r s a p p e a r to be more s e n s i t i v e to the n e g a t i v e c o m m e n t s of o b s e r v e r s than to the d e l e t e r i o u s a c t i o n of i n t e n s e sunlight. F u r t h e r m o r e , g l a s s e s t r a n s m i t t i n g less than five p e r c e n t have been d i s c o u r a g e d by some c o m m i t t e e s on s t a n d a r d s and even b a n n e d by some governments. The r e a s o n s for this are not clear. S u n g l a s s e s h a v i n g a t r a n s m i t t a n c e in the range b e t w e e n t w e n t y p e r c e n t and t h i r t y p e r c e n t c o m p r i s e a v e r y large f r a c t i o n of all the sung l a s s e s sold and to the A m e r i c a n c o n s u m e r t h e y a p p a r e n t l y r e p r e s e n t an a c c e p t a b l e c o m p r o m i s e b e t w e e n f u n c t i o n and c o s m e t i c s . Sunglasses w h i c h t r a n s m i t m o r e than fifty p e r c e n t of the i n c i d e n t light p r o b a b l y are used o n l y for c o s m e t i c effect. The i n t u i t i v e b e l i e f that s u n g l a s s w e a r e r s w o u l d p r e f e r not to look t h r o u g h d a r k g l a s s e s i n d o o r s a p p a r e n t l y p r o v i d e d m o t i v a t i o n for the d e v e l o p m e n t of p h o t o c h r o m i c glasses, i.e., g l a s s e s w h i c h d a r k e n in s u n l i g h t and a u t o m a t i c a l l y r e v e r t to the c l e a r state in the a b s e n c e of sunlight. F r o m the f o r e g o i n g d i s c u s s i o n , it is o b v i o u s that a s t e a d y - s t a t e t r a n s m i t t a n c e of 20% (in sunlight) is a r e a s o n a b l e target for a p h o t o c h r o m i c s u n g l a s s but there is little i n f o r m a t i o n w h i c h is u s e f u l in the s e l e c t i o n of a t a r g e t for f a d i n g rate e x c e p t p e r h a p s an i n t u i t i v e f e e l i n g that f a s t e r is better. W h e n it was r e c o g n i z e d that the s t e a d y - s t a t e t r a n s m i t t a n c e of the glass u n d e r a given level of i r r a d i a t i o n was a f u n c t i o n of t e m p e r a t u r e and that this t e m p e r a ture d e p e n d e n c e was c o r r e l a t e d w i t h the f a d i n g rate, s e t t i n g t a r g e t s became even more difficult. The f o l l o w i n g s e c t i o n is a brief d i s c u s s i o n of the p h y s i c s of p h o t o c h r o m i c glass to s u p p l y a b a s i s for u n d e r s t a n d i n g the i n t e r d e p e n d e n c e of the v a r i o u s p e r f o r m a n c e c h a r a c t e r i s t i c s w h i c h w i l l be d i s c u s s e d in the t h i r d section. The final s e c t i o n is c o m p r i s e d of a v e r y brief r e v i e w of the p e r f o r m a n c e c h a r a c t e r i s t i c s of one of the g l a s s e s a v a i l a b l e c o m m e r c i a l l y and an a t t e m p t to p r e d i c t how the c h a r a c t e r istics of p h o t o c h r o m i c g l a s s e s may e v o l v e in the future.
R. Arau/o / Photochromic Glass
72
II. P H Y S I C A L
MODEL
P h o t o c h r o m i c g l a s s e s can be v i e w e d as a c o l l e c t i o n of small (~100k) s i l v e r h a l i d e d r o p l e t s d o p e d w i t h c u p r o u s ions and s u s p e n d e d in an inert glass matrix. E x c i t a t i o n by UV g e n e r a t e s e l e c t r o n - h o l e pairs. The e l e c t r o n s are t r a p p e d and lead to the f o r m a t i o n of tiny anisotropic silver specks in a m a n n e r a n a l o g o u s to image f u n c t i o n in photo g r a p h i c films. C u p r o u s ions trap the holes and are t h e r e b y converte6 to c u p r i c ions. il See F i g u r e i. For r e a s o n s that w i l l be m a d e cleal
0
xE
x2
Schematic representation of silver speck and copper ions in a silver halide eryst allite. X 1 represents m a x i m u m distance at which hole trapping is possible. X 2 r e p r ~ n t ~ distance within which tunnelling is probable. The silver speck is the origin of the coordinate system.
FIGURE SCHEmaTIC
i
R E P R E S E N T A T I O N OF S I L V E R SPECK AND C O P P E R IONS IN A S I L V E R H A L I D E D R O P L E T
the p r o b a b i l i t y of hole t r a p p i n g by c u p r o u s ions d e c r e a s e s r a p i d l y w i t h d i s t a n c e from the s i l v e r speck w h i c h is g e n e r a t e d . B l e a c h i n g o] f a d i n g is a f f e c t e d by an e l e c t r o n t u n n e l i n g from the silver speck to a n e a r b y c u p r i c ion. D i f f u s i o n m a i n t a i n s a s u p p l y of c u p r i c ions in a r e g i o n close e n o u g h to the s i l v e r speck to a l l o w t u n n e l i n g . 12 D i f f u s i o n is, of course, a t e m p e r a t u r e - d e p e n d e n t process. The popul a t i o n of e l e c t r o n s h a v i n g the e n e r g y r e q u i r e d to tunnel to the cupr~ ions (see F i g u r e 2) obeys the Fermi Dirac d i s t r i b u t i o n and so the t u n n e l i n g rate is a l s o t e m p e r a t u r e d e p e n d e n t . The c o m p l e x i t y of the s y s t e m is i n c r e a s e d f u r t h e r by the fact that the Fermi Level, itself~ moves d u r i n g the d a r k e n i n g and f a d i n g process. As F i g u r e 3 indicate~ the l o c a l i z e d states a s s o c i a t e d w i t h c u p r o u s ions lie b e l o w the Fermi Level and, t h e r e f o r e , t e n d to raise it, w h i l e states a s s o c i a t e d w i t h c u p r i c ions lie above the Fermi Level and, t h e r e f o r e , tend to depres~ it. 13 This v a r i a t i o n in the Fermi Level i n f l u e n c e s the t u n n e l i n g rate and, t h e r e f o r e , the fading rate b e c a u s e it c h a n g e s the e n e r g y r e q u i r e d for t u n n e l i n g by an electron. F u r t h e r m o r e , it has the add i t i o n a l i n f l u e n c e of c h a n g i n g the rate of hole t r a p p i n g (without w h i c h d a r k e n i n g c a n n o t occur). This e f f e c t p e r h a p s r e q u i r e s f u r t h e r
R. Arau/o / Photochromic Glass
73
'//////k /////////////////// CONDUCTION BAND ELECTRON ENERGY LEVEL REQUIRED FOR TUNNELLING
Cu * ENERGY LEVEL FERMI LEVEL
VALENCE BAND
FIGURE ENERGY
DIAGRAM
//
///
FOR
I //
2
THE
/ / / / /
///////////
Ag-AgCl
/ //
INTERFACE
/ / / / /
// ///
////
/ /'/,
/ /
/ / /,," / Eo
- - E 2
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Ef
Ev
FIGURE STATES
OF
CUPROUS
3 AND
CUPRIC
IONS
R. Arau]o / Photochromic Glass
74
clarification. If the hole is not t r a p p e d it w i l l q u i c k l y r e c o m b i n e w i t h the t r a p p e d e l e c t r o n and d a r k e n i n g does not occur. W h e n a hole is t r a p p e d by a c u p r o u s ion, the r e s u l t i n g i n c r e a s e in p o s i t i v e charg, causes a l a t t i c e r e l a x a t i o n w h i c h r a i s e s the e n e r g y level a s s o c i a t e d w i t h the c o p p e r f r o m a value of El to a value of E2 (both shown in F i g u r e 3). This e f f e c t is v e r y important, for w i t h o u t it the hole w o u l d t u n n e l from one c o p p e r site to a n o t h e r until it r e c o m b i n e d w i t h the e l e c t r o n a g a i n p r e v e n t i n g d a r k e n i n g . L a t t i c e r e l a x a t i o n is a slow process, however, and w o u l d not o c c u r b e f o r e the h o l e - e l e c t r o n r e c o m b i n a t i o n o c c u r r e d if it w e r e not for the final e f f e c t to be d e s c r i b e d in this p r e s e n t a t i o n . A p o s i t i v e c h a r g e p l a c e d near the silver speck induces in the speck a n e g a t i v e image (analogous to an i n d u c e d dipole) w h i c h raises the e n e r g y of the site. W h e n the e n e r g y of the u n r e l a x e d c o p p e r site is above the Fermi Level b e c a u s e of this image p o t e n t i a l , the m o b i l i t y of the hole b e c o m e s low e n o u g h to a l l o w l a t t i c e r e l a x a t i o n to occur. Thus, the p r o b a b i l i t y of hole t r a p p i n g is h i g h o n l y for c o p p e r ions quite near the s i l v e r speck. As the Fermi Level is d e p r e s s e d for any reason, it i n t e r s e c t s the image p o t e n t i a l at larger d i s t a n c e s from the silver. Thus, the total h o l e - t r a p p i n g rate is i n c r e a s e d and, c o n s e q u e n t l y , so is the d a r k e n i n g rate. See F i g u r e s 4 and 5.
Ag
Ag CI
Ec
....................... E~ {RELAXED COPPER LEVELS)
(UNRELAXED COPPER LEVELS) Ef
~G(×))O--+
FIGURE EFFECT
OF IMAGE
G(x)=O
-
-
4
POTENTIAL
ON D O N O R
LEVELS
R. Arau/o /Photochromic Glass
75
I0
o=10 lq= L
A0-10 A,q~ 9
A0=5 A.q: I
T=O° C
I
55
60
65
7O
x (~,)
FIGURE DISTANCE
DEPENDENCE
5 OF HOLE T R A P P I N G
R a i s i n g the Fermi Level is the m o s t e f f e c t i v e way to i n c r e a s e the fading rate of a p h o t o c h r o m i c glass. Of course, r a i s i n g the fade rate has an i n d i r e c t e f f e c t on d i m i n i s h i n g the d e g r e e of d a r k e n i n g . M o r e o v e r , in this s y s t e m the d a r k e n i n g rate, itself, is d i m i n i s h e d by r a i s i n g the F e r m i Level. A n y t h i n g that raises the Fermi Level i n c l u d i n g r a i s i n g the t e m p e r a t u r e , not o n l y i n c r e a s e s the fade rate but it d e c r e a s e s the d a r k e n i n g rate and has a d o u b l e i n f l u e n c e on d i m i n i s h i n g the s t e a d y - s t a t e d a r k e n i n g . It c a n n o t be e m p h a s i z e d too s t r o n g l y that the fading rate and the t e m p e r a t u r e d e p e n d e n c e of the s t e a d y - s t a t e d a r k e n i n g are u n u s u a l l y s t r o n g l y c o u p l e d in this system. III.
PECULIAR
EFFECTS
OBSERVED
IN P H O T O C H R O M I C
GLASSES
Since the p o s i t i o n of the Fermi Level is i n f l u e n c e d by the ratio of c u p r o u s to c u p r i c ions, one can e x p e c t that c h a n g i n g the c o p p e r content of a p h o t o c h r o m i c glas's will have s i g n i f i c a n t c o n s e q u e n c e s . S p e c i f i c a l l y , F i g u r e 6 shows the s u r p r i s i n g p r e d i c t i o n that w h e n g l a s s e s are d a r k e n e d at low t e m p e r a t u r e s , a glass c o n t a i n i n g a high level of c o p p e r d a r k e n s m o r e than a s i m i l a r glass c o n t a i n i n g less c o p p e r but w h e n the g l a s s e s are d a r k e n e d at high t e m p e r a t u r e , the o p p o s i t e b e h a v i o r is o b s e r v e d . F i g u r e 7 shows the e x p e r i m e n t a l v e r i f i c a t i o n of this effect. The price in h i g h e r t e m p e r a t u r e dep e n d e n c e one pays for i n c r e a s i n g the fade rate by i n c r e a s i n g the c o p p e r is, thus, d r a m a t i c a l l y i l l u s t r a t e d .
76
R. Araujo / Photochromic Glass
Aeq
5 .....
-20
x\\
0
i
20 40 T (°C)
FIGURE THEORETICAL
60
80
6
COPPER
CROSSOVER
20
16 Cu = . 12
12 E o
4
-80
I
I
I
-60
-40
-20
TEMP,
FIGURE EXPERIMENTAL
I 0
I 20
°C
7
COPPER
CROSSOVER
40
R. Araujo / Photochromic Glass
77
The i n t e r p l a y of the m a n y e f f e c t s i n v o l v e d c a u s e an i n d i v i d u a l glass to r e s p o n d in s t r a n g e ways to c h a n g e s in t e m p e r a t u r e and intensity. F i g u r e 8 shows the p r e d i c t e d d e p e n d e n c e of the s t e a d y - s t a t e a b s o r p tion (Aeq) on the i n t e n s i t y of UV at c o n s t a n t t e m p e r a t u r e . Note the s y s t e m does not e x h i b i t the a s s y m p t o t i c b e h a v i o r that one i g n o r a n t of
I t
I
/ /
2
3 4 5 6 7 kdI ~ (15000)
8
9
Aeq VS
I
I0
E, : Ef ( [ c ~ ] / [c,~])
FIGURE THEORETICAL the m o v i n g Fermi Level shows Aeq as a f u n c t i o n b e c a u s e o b s e r v a t i o n at m a k e o b s e r v a t i o n s as a decreases exponentially d e p e n d e n c e is v e r i f i e d
8
i n t u i t i v e l y w o u l d have expected. Figure 9 of d i s t a n c e from the i r r a d i a t e d s u r f a c e a range of d i s t a n c e s is a c o n v e n i e n t way to f u n c t i o n of intensity, since the i n t e n s i t y w i t h d e p t h into the glass. The p r e d i c t e d completely.
The solid line in F i g u r e i0 shows the p r e d i c t e d d e p e n d e n c e of Aeq on t e m p e r a t u r e at c o n s t a n t UV intensity. The e x p e r i m e n t a l p o i n t s fail to v e r i f y the p r e d i c t e d s i g m o i d a l curve b e c a u s e at such low t e m p e r atures, the d a r k e n i n g rate b e c o m e s so slow that true s t e a d y state c a n n o t be a c h i e v e d in a v a i l a b l e times. To test this p r e d i c t i o n further, a v e r y slow f a d i n g glass w i t h a p r e d i c t e d m a x i m u m in A e q at h i g h e r t e m p e r a t u r e s is required. F i g u r e ii shows that the p r e d i c t e d e f f e c t is o b s e r v e d in an e x p e r i m e n t a l glass, GBH.
R. Araujo / Photochromic Glass
78
E o <
I/I 05
L
_
A
L
_
I 2 Z 4 DISTANCE FROM FRONT EDGE
_l 5 (ram)
J
._
FIGURE 9 EXP Ae~~ VS I
,o F
- 5Ci~
0
25--
,5~o ~
.o'o~o
o~
~o
~o
TEMP °C
ca]tu]at~.d A,. xel~n, T.
The eitel~,s
are
.,xpelinlt,nta] ])llhlts foI" Blass A~X.
FIGURE i0 THEORETICAL AND EXPERIMENTAL Aeq VS T FOR GLASS ABN
R. Araujo /Photochromic Glass
79
r £;~;', °C EquiliLril.n al~.pti,m
hi exp~'r'imenlal ula~- GL{H t - a ~rl{t.~nl ,d l , . U . ' l a r t ~ r ,
FIGURE
ii
EXP Aeq VS T F O R GLASS
GBH
The fade rate, as well as Aeq , r e s p o n d s in s t r a n g e ways to c h a n g e s in t e m p e r a t u r e and i n t e n s i t y . F i g u r e 12 shows the p r e d i c t e d i n i t i a l fade rate vis d a r k e n i n g i n t e n s i t y of a glass d a r k e n e d to s t e a d y state, The data in F i g u r e 13 shows that the fade rate does, indeed, c h a n g e w i t h the i n t e n s i t y of the d a r k e n i n g source. A l t h o u g h the c a l c u l a t i o n of fade rate from a glass d a r k e n e d o n l y for finite times is p r o h i b i t i v e l y tedious, c o n s i d e r a t i o n of the m o d e l s u g g e s t s that the initial fade rate of g l a s s e s d a r k e n e d at high i n t e n s i t y s h o u l d show a m a x i m u m at i n t e r m e d i a t e d a r k e n i n g times. F i g u r e 14 shows that in a glass sold c o m m e r c i a l l y u n d e r the t r a d e m a r k " P h o t o s u n R'' the e f f e c t is quite d r a m a t i c and s i m i l a r to that shown in the t h e o r e t i c a l curve in F i g u r e ii. F i g u r e 15 shows a p e c u l i a r e f f e c t that can be o b s e r v e d if fade rates are m e a s u r e d at c e r t a i n p a r t i c u l a r t e m p e r a t u r e s . The initial fade rate is faster at the lower t e m p e r a t u r e but at l o n g e r times, the a v e r a g e fade rate is h i g h e r at the h i g h e r t e m p e r a t u r e . F i g u r e 16 shows the e f f e c t for two e x p e r i m e n t a l glasses. In use as a sunglass, the g l a s s w i l l o f t e n be d a r k e n e d at one temp e r a t u r e and faded w h i l e the t e m p e r a t u r e is c h a n g i n g . Such a situation o c c u r s w h e n a user steps from the cold o u t d o o r s into a h e a t e d building. F i g u r e 17 shows the p r e d i c t e d b e h a v i o r of a glass under such c o n d i t i o n s . F i g u r e 18 v e r i f i e s the p r e d i c t i o n . In m o s t glasses, This, of course, not be d i s c u s s e d
long w a v e l e n g t h i r r a d i a t i o n c a u s e s o p t i c a l b l e a c h i n g f u r t h e r c o m p l i c a t e s all the above e f f e c t s but will here.
The c o m p l e x i t y of the e f f e c t s i n v o l v e d in this s y s t e m m a k e s the c h a r a c t e r i z a t i o n of glass p e r f o r m a n c e very d i f f i c u l t . Disagreements
R. Arau/o / Photochromic Glass
80
AEQ 30 47q I
I
790 •
1445 ]
"
iooo
_
]_ 3000
I
o
q
2000
1
....
4000
14 93
J
5000
Iuv(ARBITRARY UNITS)
PREDICTED
FADE
FIGURE
12
RATE
FROM
Aeq
VS
I,
Aeq
,o< IMAX/ IO
i L__
I
__
L. . . . .
20
io
]
___
FROM
Aeq
50
•
40
.._
TiME { m i n u t e s }
FIGURE EXPERIMENTAL
FADE
13
RATE
VS
I
"
50
R. Arau/o / Photochromic Glass
81
FADERATEVSABSORPTIONFORPHOTOSUN
I oF
/
"O ¥
./,,-
o+
./"
i ~./e
I__ 5
IO
FIGURE EXPERIMENTAL
INITIAL
2C
14 FADE
1
FIGURE
15
A(cm~)
RATE
.
VS
Ama x
0
~
15
PREDICTED CROSSOVER IN FADING AT TWO TEMPERATURES
I
o w
,,~
--50°C ~. 200C
0.5-
i
1
I
I
i
r
2
5
TIME, MIN
t 4
I 5
R. Arau/o / Photochromic Glass
82
10C
8C
_~ 6O ~E
~
40
/
23°C
X
16a 20
80oc/" OFF
I
5
I
I0
I
I
15 20 TIME (MIN)
1
25
I
i
3O
5
1.0~ FIGURE
16
EXPERIMENTAL CROSSOVER IN FADING AT TWO TEMPERATURES 0.9
O~
• o.7
I I
F 2
TIME, MIN
(b) 16b
(b) erossing in fading curves tot gb.ss ABX.
I 3
R. Arau/o /Photochromic Glass
I0 r
83
~1~ _ _ . _ _ ~
b~
3) 2~ '|~-
I
l
I
]___~__L
I
2
3
4
J_
5
6
7
_J 8
TIME (MINUTES)
PREDICTED
CROSSOVER
FOR
FIGURE
17
FADING
AT
!•[ i
i
i
VARIABLE
i
i
1
L
1
9~2A-~I
FIGURE EXPERIMENTAL
18 CROSSOVER
TEMPERATURES
,
R. Araujo /Photochromic Glass
84
b e t w e e n m e a s u r e m e n t s on the same glass is no i n d i c a t i o n of error or dishonesty. The c h a r a c t e r i z a t i o n of p e r f o r m a n c e is m e a n i n g f u l o n l y for the exact c o n d i t i o n s under w h i c h the c h a r a c t e r i z a t i o n was done. A m e a s u r e m e n t of the fade rate, for example, is i n f l u e n c e d by the i n t e n s i t y of the d a r k e n i n g light source, by the length of time d a r k e n i n g , by the t e m p e r a t u r e at w h i c h the glass was darkened, by the t e m p e r a t u r e at w h i c h the glass is faded and by the i n t e n s i t y of v i s u a l light i n c i d e n t on the glass d u r i n g d a r k e n i n g and fading. IV. P H O T O C H R O M I C
PRODUCT
PERFOR}LAi~CE S P E C I F I C A T I O N S
S e t t i n g p e r f o r m a n c e t r a g e t s for p r o d u c t s m a d e from such a c o m p l i c a t e d glass is o b v i o u s l y not a t r i v i a l job. Communicating performance s t a n d a r d s to a p o t e n t i a l c u s t o m e r is e x t r e m e l y d i f f i c u l t . The a p p r o a c h t a k e n by the C o r n i n g Glass W o r k s will be d i s c u s s e d simply b e c a u s e it serves as an e x a m p l e and the o n l y e x a m p l e w i t h w h i c h the p r e s e n t a u t h o r is t o t a l l y familiar. The t e m p e r a t u r e of g l a s s e s w o r n on the face in hot w e a t h e r has been found to e x c e e d a m b i e n t t e m p e r a t u r e s by as m u c h as five c e n t i g r a d e degrees. S u n g l a s s e s w o r n in the summer or in v e r y w a r m c o u n t r i e s can be e x p e c t e d to r e a c h t e m p e r a t u r e s of 40°C quite c o m m o n l y . Hence, the s t e a d y - s t a t e t r a n s m i t t a n c e at 40°C is a v e r y i m p o r t a n t c h a r a c teristic. Since some c o u n t r i e s ban g l a s s e s w h i c h t r a n s m i t less than some s p e c i f i e d lower limit, it is i m p o r t a n t to a s c e r t a i n the d a r k e s t level the glass w i l l a c h i e v e u n d e r any n o r m a l l y a c h i e v a b l e c o n d i t i o n s of t e m p e r a t u r e and i n t e n s i t y . Since fading is m o s t o f t e n done indoors, m e a s u r e m e n t of the fading rate at 20 to 22°C is a r e a s o n a b l e characterization. M o r e o v e r , since the s l o w e s t fade rates that can p o s s i b l y be o b s e r v e d at 20°C are those m e a s u r e d in g l a s s e s h a v i n g been d a r k e n e d for v e r y long times at high t e m p e r a t u r e s , those are the ones that the C o m i n g Glass W o r k s has c h o s e n to p u b l i s h in the l i t e r a t u r e w h i c h d e s c r i b e s their p r o d u c t s .
90 80
BOROSILICATE . GLASS B ~//
~
--. . . . "IS.,1__
!
FIGURE
70
/!
60
/
C O M P A R I S O N OF CANDIDATE GLASSES
50 4C-3O
I°lo
EXTRA
i
19
I
lO
I
20
TEMPERATURE 20oC THICKNESS 2MM
I
I
I0 20 TIME (MIN)
I
50
~
I 60
R. Arau]~ / Photochromic Glass
85
Figure 19 shows the p e r f o r m a n c e c h a r a c t e r i s t i c s of two g l a s s e s w h i c h were c a n d i d a t e s for use in the p r o d u c t i n t r o d u c e d in 1979 u n d e r the r e g i s t e r e d t r a d e m a r k " P h o t o g r a y Extra R Lenses". The d e c i s i o n was m a d e to m a r k e t the s l o w e r glass b e c a u s e of the lower t r a n s m i t t a n c e at 40°C. A l t h o u g h the r e a s o n s for this c h o i c e are f a i r l y c o m p e l l i n g , as we have a l r e a d y seen, they are, n o n e t h e l e s s , b a s e d on s u b j e c t i v e c r i t e r i a and o t h e r m a n u f a c t u r e r s w o u l d p e r h a p s have c h o s e n differently. V. THE F U T U R E Any c o m m e n t about the future is, at best, a guess. In p a r t i c u l a r , my c o m m e n t s about the future e v o l u t i o n of p h o t o c h r o m i c g l a s s e s represents o n l y my own p e r s o n a l o p i n i o n s on w h a t is d e s i r a b l e and w h a t is possible. U n l e s s g l a s s e s can be m a d e w h i c h fade c o m p l e t e l y in a small n u m b e r of seconds, i m p r o v i n g the fade rate of the g l a s s e s is of l i m i t e d value. I m p r o v i n g the t e m p e r a t u r e d e p e n d e n c e so that g l a s s e s d a r k e n to less than t w e n t y p e r c e n t t r a n s m i t t a n c e at all t e m p e r a t u r e s will be a benefit to eye c o m f o r t and p e r h a p s to i m p r o v e d vision. On the o t h e r h a n d the b e n e f i t may not be p e r c e i v e d by e v e r y o n e as b e i n g w o r t h the problems a s s o c i a t e d w i t h a d d i n g a n o t h e r glass into the d i s t r i b u t i o n system. F u r t h e r m o r e , a l t h o u g h the p a r a m e t e r s in the model are u n d e r stood w e l l e n o u g h so that a glass can, in p r i n c i p l e , be d e s i g n e d w i t h i m p r o v e d t e m p e r a t u r e d e p e n d e n c e and u n c o m p r o m i s e d f a d i n g rates, the s p e c i f i c c h e m i c a l a p p r o a c h to a d j u s t i n g those p a r a m e t e r s is o n l y imperfectly appreciated. C o n s e q u e n t l y , there is no c e r t a i n t y that such a glass can be m a d e in a m a n n e r that is c o m m e r c i a l l y p r o f i t a b l e . My own p e r s o n a l w i s h is for a g l a s s that d a r k e n s to one p e r c e n t transm i t t a n c e at all t e m p e r a t u r e s if f a d i n g b a c k to t w e n t y p e r c e n t can be a c h i e v e d in five m i n u t e s indoors. I s u s p e c t that c o n s i d e r a t i o n s of c o s m e t i c f a c t o r s and g o v e r n m e n t a l r e g u l a t i o n s p r e c l u d e the w i d e spread, e n t h u s i a s t i c r e c e p t i o n of such a product. Furthermore, a c a r e f u l c o n s i d e r a t i o n of the m o d e l c a u s e s me to have some d o u b t s that such a glass can be m a d e in the silver h a l i d e system. N e w p r o d u c t s m a y well r e p r e s e n t slight c h a n g e s in j u d g m e n t of the r e l a t i v e i m p o r t a n c e of the v a r i o u s c h a r a c t e r i s t i c s of p h o t o c h r o m i c glasses, but as far as d r a m a t i c i m p r o v e m e n t s in the p e r f o r m a n c e of silver h a l i d e p h o t o c h r o m i c g l a s s e s go - O s c a r H a m m e r s t e i n a n t i c i p a t e d my f e e l i n g w h e n he said "they've gone about as far as they can go".
REFERENCES i. Cool
Ray,
Inc.,
2. Snyder,
C.
3. Miller,
D.,
4. Miller,
D.,
5. Barlow,
H. B.,
Fact
(1965), (1974), Beth
Book,
Arch.
(1958),
6. Hect, S., Hendley, Am. J. O p t h a l m o l . ,
9068,
Opthalmol.,
Survey
Israel
No.
Cool
Ray,
private
J. P h y s i o l . ,
C. D., Ross, 3_~i, 1573.
S.,
1972.
7_~3, 897.
of O p t h a l m o l o g y ,
Hospital,
U. S. A.,
141,
19,
38.
communication. 337.
and R i c h m o n d ,
P. N.,
(1948),
R. Arau/o / Photochromic Glass
86
7. Peckham, 624. 8. Evans,
R. H. and Harley,
P. Y.,
R. D.,
(1950), Arch. Ophthalmol.,
(1978), Pharmacy Times,
4_44,
June, pg. 44.
9. Wolbarsht, M. L., Departments of Ophthalmology and Biomedical Engineering, Duke University, private communication. 10. Moon, P., (1961), The Scientific Basis of Illuminating Engineering, p. 401, Dover Publications, New York. ii. Araujo,
R. J.,
(1980), Contemp. Phys.,
21, 77.
12. Araujo, R. J., Borrelli, N. F., and Nolan, Mag., 42, 279.
D. A.,
(1979), Phil.
13. Araujo, R. J., Borrelli, N. F., and Nolan, D. A., Mag., 44, 453.
(1981), Phil.
OPTIIALMIC GLASS
PARTICULARLY
69
PHOTOCHROMIC
GLASS
R. J. A r a u j o Research
and D e v e l o p m e n t L a b o r a t o r i e s C o r n i n g Glass Works Corning, N e w York 14831
P h o t o l y s i s of c e r t a i n g l a s s e s c o n t a i n i n g minute silver h a l i d e d r o p l e t s leads to v i s i b l e absorption° The t e m p e r a t u r e d e p e n d e n c e of the i n d u c e d a b s o r p t i o n is s t r o n g l y c o r r e l a t e d w i t h the rate at w h i c h the glass r e v e r t s to its c l e a r state upon the c e s s a t i o n of r a d i a t i o n . The factors w h i c h i n f l u e n c e the c o m p r o m i s e s in fade rates and t e m p e r a t u r e d e p e n d e n c e will be discussed. I. S U N G L A S S
SPECIFICATIONS
A p p r o x i m a t e l y o n e - h u n d r e d m i l l i o n pairs of s u n g l a s s e s are sold in the U n i t e d States every year. ~ Not o n l y is the use of s u n g l a s s e s a w i d e s p r e a d p r a c t i c e , it is a v e r y old p r a c t i c e . Tuberville, a B r i t i s h o p h t h a l m o l o g i s t , p r e s c r i b e d silk v e i l s for p o s t - o p e r a t i v e p a t i e n t s c o m p l a i n i n g of p h o t o p h o b i a in the f i f t e e n t h century. ~ The c u r r e n t p o p u l a r i t y of s u n g l a s s e s is p r o b a b l y due l a r g e l y to a s u b j e c t i v e f e e l i n g of c o m f o r t on the part of the w e a r e r but, in addition, there are c i r c u m s t a n c e s u n d e r w h i c h s u n g l a s s e s improve vision. ~ I m p r o v e d v i s i o n i n c l u d e s i m p r o v e d c o n t r a s t d i s c r i m i n a t i o n , i m p r o v e d r e s o l u t i o n and c e r t a i n l y s h o r t e r a d a p t a t i o n times. In the range from 300 c a n d e l a s / m e t e r 2 (very g o o d r o o m light) to 3000 c a n d e l a s / m e t e r 2 (moderate o u t d o o r lighting) for the a v e r a g e p e r s o n the sense of c o n t r a s t stays the same and s u n g l a s s e s are not h e l p f u l and, not s u r p r i s i n g l y , are not n o r m a l l y worn. In the range from 3000 to 30,000 c a n d e l a s / m e t e r 2, c o n t r a s t d i s c r i m i n a t i o n dec l i n e s w i t h i n c r e a s i n g i n t e n s i t y . ~ The r e a s o n for this may be related to the f i n d i n g that g r e a t e r noise is g e n e r a t e d in the retinal c i r c u i t r y at h i g h - l i g h t levels, s In the same range of light intensities, r e s o l u t i o n d e c r e a s e s w i t h i n c r e a s e d i l l u m i n a t i o n . This is p r o b a b l y r e l a t e d to the f l u o r e s c e n c e (530 nm peak) of the human lens w h i c h acts as a noise source. 4 The i m p o r t a n c e of this e f f e c t in y o u n g p e o p l e is c o n t r o v e r s i a l but in o l d e r p e o p l e (>50 years) inc r e a s e d f l u o r e s c e n s e and d r a m a t i c a l l y i n c r e a s e d i n t r a o c u l a r light s c a t t e r i n g m a g n i f y the e f f e c t v e r y s i g n i f i c a n t l y . The s h o r t e n i n g of a d a p t a t i o n times is a b e n e f i t of s u n g l a s s e s that is b e y o n d c o n t r o v e r s y . A w h o l e day at the b e a c h w i t h o u t s u n g l a s s e s will r e d u c e the eye s e n s i t i v i t y at d u s k by a l m o s t fifty percent. ~ This e f f e c t can be c u m u l a t i v e . S t u d i e s on l i f e g u a r d s who spent two w e e k s at the b e a c h w i t h o u t s u n g l a s s e s found that they did not r e g a i n their n o r m a l d a r k - a d a p t e d s e n s i t i v i t y in a full day.
0022-3093/82/0000 0000/$02.75 © 1982 North-Holland
R. Arau/o / Photochromic Glass
70
Table
I
Condition
Light Level
Effect of Increasing
300 candelas/m 2
Very good room light
1
3000 candelas/m 2
Moderate
outdoor
J
3000 candelas/m 2
Moderate light
outdoor
30,000
Bright outdoor light
candelas/m 2
Table
i) Diminishing contrast discrimination 2) Diminishing resolution 3) Increasing adaptation time
II
RecoF~ended for long time in very bright surroundings
10-20%
Recommended
20-30%
Range of sunglasses
>50%
NONE
Circumstance
Transmittance
1%
light
Intensity
Doubtful
for normal
benefit
sunlight
protection
sold in greatest
other
than cosmetic
numbers
R. Arau/o / Photochromic Glass
71
To r e n d e r b e n e f i t s in c o m f o r t and i m p r o v e d vision, s u n g l a s s e s should have t r a n s m i t t a n c e s b e t w e e n ten and t w e n t y percent. 3 R e s e a r c h e r s u n a n i m o u s l y a g r e e that g l a s s e s h a v i n g t r a n s m i t t a n c e s g r e a t e r than fifty p e r c e n t are g o o d for p r o t e c t i n g the eye from d u s t p a r t i c l e s . 8 P e o p l e s p e n d i n g s e v e r a l hours u n d e r v e r y bright, o u t d o o r c o n d i t i o n s p r o b a b l y s h o u l d w e a r g l a s s e s h a v i n g one p e r c e n t t r a n s m i t t a n c e . 9 It s h o u l d be e m p h a s i z e d that the p u p i l l a r y m e c h a n i s m does not o p e r a t e as an a u t o m a t i c sunglass. The pupil goes from m a x i m u m d i l a t i o n to s l i g h t l y less than 3 mm in d i a m e t e r o v e r an i l l u m i n a t i o n range from i0 -~ lumens (dark night) to 10 lumens (poorly l i g h t e d room). From I0 lumens to 10,000 lumens (very b r i g h t day) the pupil s h r i n k s to about 2 mm, less than a factor of two d i f f e r e n c e in area. It s h o u l d be p o i n t e d out that the a v e r a g e p e r s o n will e x p e r i e n c e no d i f f i c u l t y s e e i n g t h r o u g h g l a s s e s h a v i n g one p e r c e n t t r a n s m i t t a n c e even at light levels as low as 300 c a n d e l a s / m e t e r 2. Such dark glasse: are not popular, however, p r o b a b l y for c o s m e t i c reasons. W i t h such dark g l a s s e s the eyes of the w e a r e r can be o b s c u r e d to an o b s e r v e r and the o b s e r v e r w i l l see r e f l e c t i o n s . W e a r e r s a p p e a r to be more s e n s i t i v e to the n e g a t i v e c o m m e n t s of o b s e r v e r s than to the d e l e t e r i o u s a c t i o n of i n t e n s e sunlight. F u r t h e r m o r e , g l a s s e s t r a n s m i t t i n g less than five p e r c e n t have been d i s c o u r a g e d by some c o m m i t t e e s on s t a n d a r d s and even b a n n e d by some governments. The r e a s o n s for this are not clear. S u n g l a s s e s h a v i n g a t r a n s m i t t a n c e in the range b e t w e e n t w e n t y p e r c e n t and t h i r t y p e r c e n t c o m p r i s e a v e r y large f r a c t i o n of all the sung l a s s e s sold and to the A m e r i c a n c o n s u m e r t h e y a p p a r e n t l y r e p r e s e n t an a c c e p t a b l e c o m p r o m i s e b e t w e e n f u n c t i o n and c o s m e t i c s . Sunglasses w h i c h t r a n s m i t m o r e than fifty p e r c e n t of the i n c i d e n t light p r o b a b l y are used o n l y for c o s m e t i c effect. The i n t u i t i v e b e l i e f that s u n g l a s s w e a r e r s w o u l d p r e f e r not to look t h r o u g h d a r k g l a s s e s i n d o o r s a p p a r e n t l y p r o v i d e d m o t i v a t i o n for the d e v e l o p m e n t of p h o t o c h r o m i c glasses, i.e., g l a s s e s w h i c h d a r k e n in s u n l i g h t and a u t o m a t i c a l l y r e v e r t to the c l e a r state in the a b s e n c e of sunlight. F r o m the f o r e g o i n g d i s c u s s i o n , it is o b v i o u s that a s t e a d y - s t a t e t r a n s m i t t a n c e of 20% (in sunlight) is a r e a s o n a b l e target for a p h o t o c h r o m i c s u n g l a s s but there is little i n f o r m a t i o n w h i c h is u s e f u l in the s e l e c t i o n of a t a r g e t for f a d i n g rate e x c e p t p e r h a p s an i n t u i t i v e f e e l i n g that f a s t e r is better. W h e n it was r e c o g n i z e d that the s t e a d y - s t a t e t r a n s m i t t a n c e of the glass u n d e r a given level of i r r a d i a t i o n was a f u n c t i o n of t e m p e r a t u r e and that this t e m p e r a ture d e p e n d e n c e was c o r r e l a t e d w i t h the f a d i n g rate, s e t t i n g t a r g e t s became even more difficult. The f o l l o w i n g s e c t i o n is a brief d i s c u s s i o n of the p h y s i c s of p h o t o c h r o m i c glass to s u p p l y a b a s i s for u n d e r s t a n d i n g the i n t e r d e p e n d e n c e of the v a r i o u s p e r f o r m a n c e c h a r a c t e r i s t i c s w h i c h w i l l be d i s c u s s e d in the t h i r d section. The final s e c t i o n is c o m p r i s e d of a v e r y brief r e v i e w of the p e r f o r m a n c e c h a r a c t e r i s t i c s of one of the g l a s s e s a v a i l a b l e c o m m e r c i a l l y and an a t t e m p t to p r e d i c t how the c h a r a c t e r istics of p h o t o c h r o m i c g l a s s e s may e v o l v e in the future.
R. Arau/o / Photochromic Glass
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II. P H Y S I C A L
MODEL
P h o t o c h r o m i c g l a s s e s can be v i e w e d as a c o l l e c t i o n of small (~100k) s i l v e r h a l i d e d r o p l e t s d o p e d w i t h c u p r o u s ions and s u s p e n d e d in an inert glass matrix. E x c i t a t i o n by UV g e n e r a t e s e l e c t r o n - h o l e pairs. The e l e c t r o n s are t r a p p e d and lead to the f o r m a t i o n of tiny anisotropic silver specks in a m a n n e r a n a l o g o u s to image f u n c t i o n in photo g r a p h i c films. C u p r o u s ions trap the holes and are t h e r e b y converte6 to c u p r i c ions. il See F i g u r e i. For r e a s o n s that w i l l be m a d e cleal
0
xE
x2
Schematic representation of silver speck and copper ions in a silver halide eryst allite. X 1 represents m a x i m u m distance at which hole trapping is possible. X 2 r e p r ~ n t ~ distance within which tunnelling is probable. The silver speck is the origin of the coordinate system.
FIGURE SCHEmaTIC
i
R E P R E S E N T A T I O N OF S I L V E R SPECK AND C O P P E R IONS IN A S I L V E R H A L I D E D R O P L E T
the p r o b a b i l i t y of hole t r a p p i n g by c u p r o u s ions d e c r e a s e s r a p i d l y w i t h d i s t a n c e from the s i l v e r speck w h i c h is g e n e r a t e d . B l e a c h i n g o] f a d i n g is a f f e c t e d by an e l e c t r o n t u n n e l i n g from the silver speck to a n e a r b y c u p r i c ion. D i f f u s i o n m a i n t a i n s a s u p p l y of c u p r i c ions in a r e g i o n close e n o u g h to the s i l v e r speck to a l l o w t u n n e l i n g . 12 D i f f u s i o n is, of course, a t e m p e r a t u r e - d e p e n d e n t process. The popul a t i o n of e l e c t r o n s h a v i n g the e n e r g y r e q u i r e d to tunnel to the cupr~ ions (see F i g u r e 2) obeys the Fermi Dirac d i s t r i b u t i o n and so the t u n n e l i n g rate is a l s o t e m p e r a t u r e d e p e n d e n t . The c o m p l e x i t y of the s y s t e m is i n c r e a s e d f u r t h e r by the fact that the Fermi Level, itself~ moves d u r i n g the d a r k e n i n g and f a d i n g process. As F i g u r e 3 indicate~ the l o c a l i z e d states a s s o c i a t e d w i t h c u p r o u s ions lie b e l o w the Fermi Level and, t h e r e f o r e , t e n d to raise it, w h i l e states a s s o c i a t e d w i t h c u p r i c ions lie above the Fermi Level and, t h e r e f o r e , tend to depres~ it. 13 This v a r i a t i o n in the Fermi Level i n f l u e n c e s the t u n n e l i n g rate and, t h e r e f o r e , the fading rate b e c a u s e it c h a n g e s the e n e r g y r e q u i r e d for t u n n e l i n g by an electron. F u r t h e r m o r e , it has the add i t i o n a l i n f l u e n c e of c h a n g i n g the rate of hole t r a p p i n g (without w h i c h d a r k e n i n g c a n n o t occur). This e f f e c t p e r h a p s r e q u i r e s f u r t h e r
R. Arau/o / Photochromic Glass
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'//////k /////////////////// CONDUCTION BAND ELECTRON ENERGY LEVEL REQUIRED FOR TUNNELLING
Cu * ENERGY LEVEL FERMI LEVEL
VALENCE BAND
FIGURE ENERGY
DIAGRAM
//
///
FOR
I //
2
THE
/ / / / /
///////////
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.
.
.
.
.
.
.
.
.
.
.
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.
.
.
.
.
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Ev
FIGURE STATES
OF
CUPROUS
3 AND
CUPRIC
IONS
R. Arau]o / Photochromic Glass
74
clarification. If the hole is not t r a p p e d it w i l l q u i c k l y r e c o m b i n e w i t h the t r a p p e d e l e c t r o n and d a r k e n i n g does not occur. W h e n a hole is t r a p p e d by a c u p r o u s ion, the r e s u l t i n g i n c r e a s e in p o s i t i v e charg, causes a l a t t i c e r e l a x a t i o n w h i c h r a i s e s the e n e r g y level a s s o c i a t e d w i t h the c o p p e r f r o m a value of El to a value of E2 (both shown in F i g u r e 3). This e f f e c t is v e r y important, for w i t h o u t it the hole w o u l d t u n n e l from one c o p p e r site to a n o t h e r until it r e c o m b i n e d w i t h the e l e c t r o n a g a i n p r e v e n t i n g d a r k e n i n g . L a t t i c e r e l a x a t i o n is a slow process, however, and w o u l d not o c c u r b e f o r e the h o l e - e l e c t r o n r e c o m b i n a t i o n o c c u r r e d if it w e r e not for the final e f f e c t to be d e s c r i b e d in this p r e s e n t a t i o n . A p o s i t i v e c h a r g e p l a c e d near the silver speck induces in the speck a n e g a t i v e image (analogous to an i n d u c e d dipole) w h i c h raises the e n e r g y of the site. W h e n the e n e r g y of the u n r e l a x e d c o p p e r site is above the Fermi Level b e c a u s e of this image p o t e n t i a l , the m o b i l i t y of the hole b e c o m e s low e n o u g h to a l l o w l a t t i c e r e l a x a t i o n to occur. Thus, the p r o b a b i l i t y of hole t r a p p i n g is h i g h o n l y for c o p p e r ions quite near the s i l v e r speck. As the Fermi Level is d e p r e s s e d for any reason, it i n t e r s e c t s the image p o t e n t i a l at larger d i s t a n c e s from the silver. Thus, the total h o l e - t r a p p i n g rate is i n c r e a s e d and, c o n s e q u e n t l y , so is the d a r k e n i n g rate. See F i g u r e s 4 and 5.
Ag
Ag CI
Ec
....................... E~ {RELAXED COPPER LEVELS)
(UNRELAXED COPPER LEVELS) Ef
~G(×))O--+
FIGURE EFFECT
OF IMAGE
G(x)=O
-
-
4
POTENTIAL
ON D O N O R
LEVELS
R. Arau/o /Photochromic Glass
75
I0
o=10 lq= L
A0-10 A,q~ 9
A0=5 A.q: I
T=O° C
I
55
60
65
7O
x (~,)
FIGURE DISTANCE
DEPENDENCE
5 OF HOLE T R A P P I N G
R a i s i n g the Fermi Level is the m o s t e f f e c t i v e way to i n c r e a s e the fading rate of a p h o t o c h r o m i c glass. Of course, r a i s i n g the fade rate has an i n d i r e c t e f f e c t on d i m i n i s h i n g the d e g r e e of d a r k e n i n g . M o r e o v e r , in this s y s t e m the d a r k e n i n g rate, itself, is d i m i n i s h e d by r a i s i n g the F e r m i Level. A n y t h i n g that raises the Fermi Level i n c l u d i n g r a i s i n g the t e m p e r a t u r e , not o n l y i n c r e a s e s the fade rate but it d e c r e a s e s the d a r k e n i n g rate and has a d o u b l e i n f l u e n c e on d i m i n i s h i n g the s t e a d y - s t a t e d a r k e n i n g . It c a n n o t be e m p h a s i z e d too s t r o n g l y that the fading rate and the t e m p e r a t u r e d e p e n d e n c e of the s t e a d y - s t a t e d a r k e n i n g are u n u s u a l l y s t r o n g l y c o u p l e d in this system. III.
PECULIAR
EFFECTS
OBSERVED
IN P H O T O C H R O M I C
GLASSES
Since the p o s i t i o n of the Fermi Level is i n f l u e n c e d by the ratio of c u p r o u s to c u p r i c ions, one can e x p e c t that c h a n g i n g the c o p p e r content of a p h o t o c h r o m i c glas's will have s i g n i f i c a n t c o n s e q u e n c e s . S p e c i f i c a l l y , F i g u r e 6 shows the s u r p r i s i n g p r e d i c t i o n that w h e n g l a s s e s are d a r k e n e d at low t e m p e r a t u r e s , a glass c o n t a i n i n g a high level of c o p p e r d a r k e n s m o r e than a s i m i l a r glass c o n t a i n i n g less c o p p e r but w h e n the g l a s s e s are d a r k e n e d at high t e m p e r a t u r e , the o p p o s i t e b e h a v i o r is o b s e r v e d . F i g u r e 7 shows the e x p e r i m e n t a l v e r i f i c a t i o n of this effect. The price in h i g h e r t e m p e r a t u r e dep e n d e n c e one pays for i n c r e a s i n g the fade rate by i n c r e a s i n g the c o p p e r is, thus, d r a m a t i c a l l y i l l u s t r a t e d .
76
R. Araujo / Photochromic Glass
Aeq
5 .....
-20
x\\
0
i
20 40 T (°C)
FIGURE THEORETICAL
60
80
6
COPPER
CROSSOVER
20
16 Cu = . 12
12 E o
4
-80
I
I
I
-60
-40
-20
TEMP,
FIGURE EXPERIMENTAL
I 0
I 20
°C
7
COPPER
CROSSOVER
40
R. Araujo / Photochromic Glass
77
The i n t e r p l a y of the m a n y e f f e c t s i n v o l v e d c a u s e an i n d i v i d u a l glass to r e s p o n d in s t r a n g e ways to c h a n g e s in t e m p e r a t u r e and intensity. F i g u r e 8 shows the p r e d i c t e d d e p e n d e n c e of the s t e a d y - s t a t e a b s o r p tion (Aeq) on the i n t e n s i t y of UV at c o n s t a n t t e m p e r a t u r e . Note the s y s t e m does not e x h i b i t the a s s y m p t o t i c b e h a v i o r that one i g n o r a n t of
I t
I
/ /
2
3 4 5 6 7 kdI ~ (15000)
8
9
Aeq VS
I
I0
E, : Ef ( [ c ~ ] / [c,~])
FIGURE THEORETICAL the m o v i n g Fermi Level shows Aeq as a f u n c t i o n b e c a u s e o b s e r v a t i o n at m a k e o b s e r v a t i o n s as a decreases exponentially d e p e n d e n c e is v e r i f i e d
8
i n t u i t i v e l y w o u l d have expected. Figure 9 of d i s t a n c e from the i r r a d i a t e d s u r f a c e a range of d i s t a n c e s is a c o n v e n i e n t way to f u n c t i o n of intensity, since the i n t e n s i t y w i t h d e p t h into the glass. The p r e d i c t e d completely.
The solid line in F i g u r e i0 shows the p r e d i c t e d d e p e n d e n c e of Aeq on t e m p e r a t u r e at c o n s t a n t UV intensity. The e x p e r i m e n t a l p o i n t s fail to v e r i f y the p r e d i c t e d s i g m o i d a l curve b e c a u s e at such low t e m p e r atures, the d a r k e n i n g rate b e c o m e s so slow that true s t e a d y state c a n n o t be a c h i e v e d in a v a i l a b l e times. To test this p r e d i c t i o n further, a v e r y slow f a d i n g glass w i t h a p r e d i c t e d m a x i m u m in A e q at h i g h e r t e m p e r a t u r e s is required. F i g u r e ii shows that the p r e d i c t e d e f f e c t is o b s e r v e d in an e x p e r i m e n t a l glass, GBH.
R. Araujo / Photochromic Glass
78
E o <
I/I 05
L
_
A
L
_
I 2 Z 4 DISTANCE FROM FRONT EDGE
_l 5 (ram)
J
._
FIGURE 9 EXP Ae~~ VS I
,o F
- 5Ci~
0
25--
,5~o ~
.o'o~o
o~
~o
~o
TEMP °C
ca]tu]at~.d A,. xel~n, T.
The eitel~,s
are
.,xpelinlt,nta] ])llhlts foI" Blass A~X.
FIGURE i0 THEORETICAL AND EXPERIMENTAL Aeq VS T FOR GLASS ABN
R. Araujo /Photochromic Glass
79
r £;~;', °C EquiliLril.n al~.pti,m
hi exp~'r'imenlal ula~- GL{H t - a ~rl{t.~nl ,d l , . U . ' l a r t ~ r ,
FIGURE
ii
EXP Aeq VS T F O R GLASS
GBH
The fade rate, as well as Aeq , r e s p o n d s in s t r a n g e ways to c h a n g e s in t e m p e r a t u r e and i n t e n s i t y . F i g u r e 12 shows the p r e d i c t e d i n i t i a l fade rate vis d a r k e n i n g i n t e n s i t y of a glass d a r k e n e d to s t e a d y state, The data in F i g u r e 13 shows that the fade rate does, indeed, c h a n g e w i t h the i n t e n s i t y of the d a r k e n i n g source. A l t h o u g h the c a l c u l a t i o n of fade rate from a glass d a r k e n e d o n l y for finite times is p r o h i b i t i v e l y tedious, c o n s i d e r a t i o n of the m o d e l s u g g e s t s that the initial fade rate of g l a s s e s d a r k e n e d at high i n t e n s i t y s h o u l d show a m a x i m u m at i n t e r m e d i a t e d a r k e n i n g times. F i g u r e 14 shows that in a glass sold c o m m e r c i a l l y u n d e r the t r a d e m a r k " P h o t o s u n R'' the e f f e c t is quite d r a m a t i c and s i m i l a r to that shown in the t h e o r e t i c a l curve in F i g u r e ii. F i g u r e 15 shows a p e c u l i a r e f f e c t that can be o b s e r v e d if fade rates are m e a s u r e d at c e r t a i n p a r t i c u l a r t e m p e r a t u r e s . The initial fade rate is faster at the lower t e m p e r a t u r e but at l o n g e r times, the a v e r a g e fade rate is h i g h e r at the h i g h e r t e m p e r a t u r e . F i g u r e 16 shows the e f f e c t for two e x p e r i m e n t a l glasses. In use as a sunglass, the g l a s s w i l l o f t e n be d a r k e n e d at one temp e r a t u r e and faded w h i l e the t e m p e r a t u r e is c h a n g i n g . Such a situation o c c u r s w h e n a user steps from the cold o u t d o o r s into a h e a t e d building. F i g u r e 17 shows the p r e d i c t e d b e h a v i o r of a glass under such c o n d i t i o n s . F i g u r e 18 v e r i f i e s the p r e d i c t i o n . In m o s t glasses, This, of course, not be d i s c u s s e d
long w a v e l e n g t h i r r a d i a t i o n c a u s e s o p t i c a l b l e a c h i n g f u r t h e r c o m p l i c a t e s all the above e f f e c t s but will here.
The c o m p l e x i t y of the e f f e c t s i n v o l v e d in this s y s t e m m a k e s the c h a r a c t e r i z a t i o n of glass p e r f o r m a n c e very d i f f i c u l t . Disagreements
R. Arau/o / Photochromic Glass
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AEQ 30 47q I
I
790 •
1445 ]
"
iooo
_
]_ 3000
I
o
q
2000
1
....
4000
14 93
J
5000
Iuv(ARBITRARY UNITS)
PREDICTED
FADE
FIGURE
12
RATE
FROM
Aeq
VS
I,
Aeq
,o< IMAX/ IO
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I
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L. . . . .
20
io
]
___
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50
•
40
.._
TiME { m i n u t e s }
FIGURE EXPERIMENTAL
FADE
13
RATE
VS
I
"
50
R. Arau/o / Photochromic Glass
81
FADERATEVSABSORPTIONFORPHOTOSUN
I oF
/
"O ¥
./,,-
o+
./"
i ~./e
I__ 5
IO
FIGURE EXPERIMENTAL
INITIAL
2C
14 FADE
1
FIGURE
15
A(cm~)
RATE
.
VS
Ama x
0
~
15
PREDICTED CROSSOVER IN FADING AT TWO TEMPERATURES
I
o w
,,~
--50°C ~. 200C
0.5-
i
1
I
I
i
r
2
5
TIME, MIN
t 4
I 5
R. Arau/o / Photochromic Glass
82
10C
8C
_~ 6O ~E
~
40
/
23°C
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R. Araujo /Photochromic Glass
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b e t w e e n m e a s u r e m e n t s on the same glass is no i n d i c a t i o n of error or dishonesty. The c h a r a c t e r i z a t i o n of p e r f o r m a n c e is m e a n i n g f u l o n l y for the exact c o n d i t i o n s under w h i c h the c h a r a c t e r i z a t i o n was done. A m e a s u r e m e n t of the fade rate, for example, is i n f l u e n c e d by the i n t e n s i t y of the d a r k e n i n g light source, by the length of time d a r k e n i n g , by the t e m p e r a t u r e at w h i c h the glass was darkened, by the t e m p e r a t u r e at w h i c h the glass is faded and by the i n t e n s i t y of v i s u a l light i n c i d e n t on the glass d u r i n g d a r k e n i n g and fading. IV. P H O T O C H R O M I C
PRODUCT
PERFOR}LAi~CE S P E C I F I C A T I O N S
S e t t i n g p e r f o r m a n c e t r a g e t s for p r o d u c t s m a d e from such a c o m p l i c a t e d glass is o b v i o u s l y not a t r i v i a l job. Communicating performance s t a n d a r d s to a p o t e n t i a l c u s t o m e r is e x t r e m e l y d i f f i c u l t . The a p p r o a c h t a k e n by the C o r n i n g Glass W o r k s will be d i s c u s s e d simply b e c a u s e it serves as an e x a m p l e and the o n l y e x a m p l e w i t h w h i c h the p r e s e n t a u t h o r is t o t a l l y familiar. The t e m p e r a t u r e of g l a s s e s w o r n on the face in hot w e a t h e r has been found to e x c e e d a m b i e n t t e m p e r a t u r e s by as m u c h as five c e n t i g r a d e degrees. S u n g l a s s e s w o r n in the summer or in v e r y w a r m c o u n t r i e s can be e x p e c t e d to r e a c h t e m p e r a t u r e s of 40°C quite c o m m o n l y . Hence, the s t e a d y - s t a t e t r a n s m i t t a n c e at 40°C is a v e r y i m p o r t a n t c h a r a c teristic. Since some c o u n t r i e s ban g l a s s e s w h i c h t r a n s m i t less than some s p e c i f i e d lower limit, it is i m p o r t a n t to a s c e r t a i n the d a r k e s t level the glass w i l l a c h i e v e u n d e r any n o r m a l l y a c h i e v a b l e c o n d i t i o n s of t e m p e r a t u r e and i n t e n s i t y . Since fading is m o s t o f t e n done indoors, m e a s u r e m e n t of the fading rate at 20 to 22°C is a r e a s o n a b l e characterization. M o r e o v e r , since the s l o w e s t fade rates that can p o s s i b l y be o b s e r v e d at 20°C are those m e a s u r e d in g l a s s e s h a v i n g been d a r k e n e d for v e r y long times at high t e m p e r a t u r e s , those are the ones that the C o m i n g Glass W o r k s has c h o s e n to p u b l i s h in the l i t e r a t u r e w h i c h d e s c r i b e s their p r o d u c t s .
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R. Arau]~ / Photochromic Glass
85
Figure 19 shows the p e r f o r m a n c e c h a r a c t e r i s t i c s of two g l a s s e s w h i c h were c a n d i d a t e s for use in the p r o d u c t i n t r o d u c e d in 1979 u n d e r the r e g i s t e r e d t r a d e m a r k " P h o t o g r a y Extra R Lenses". The d e c i s i o n was m a d e to m a r k e t the s l o w e r glass b e c a u s e of the lower t r a n s m i t t a n c e at 40°C. A l t h o u g h the r e a s o n s for this c h o i c e are f a i r l y c o m p e l l i n g , as we have a l r e a d y seen, they are, n o n e t h e l e s s , b a s e d on s u b j e c t i v e c r i t e r i a and o t h e r m a n u f a c t u r e r s w o u l d p e r h a p s have c h o s e n differently. V. THE F U T U R E Any c o m m e n t about the future is, at best, a guess. In p a r t i c u l a r , my c o m m e n t s about the future e v o l u t i o n of p h o t o c h r o m i c g l a s s e s represents o n l y my own p e r s o n a l o p i n i o n s on w h a t is d e s i r a b l e and w h a t is possible. U n l e s s g l a s s e s can be m a d e w h i c h fade c o m p l e t e l y in a small n u m b e r of seconds, i m p r o v i n g the fade rate of the g l a s s e s is of l i m i t e d value. I m p r o v i n g the t e m p e r a t u r e d e p e n d e n c e so that g l a s s e s d a r k e n to less than t w e n t y p e r c e n t t r a n s m i t t a n c e at all t e m p e r a t u r e s will be a benefit to eye c o m f o r t and p e r h a p s to i m p r o v e d vision. On the o t h e r h a n d the b e n e f i t may not be p e r c e i v e d by e v e r y o n e as b e i n g w o r t h the problems a s s o c i a t e d w i t h a d d i n g a n o t h e r glass into the d i s t r i b u t i o n system. F u r t h e r m o r e , a l t h o u g h the p a r a m e t e r s in the model are u n d e r stood w e l l e n o u g h so that a glass can, in p r i n c i p l e , be d e s i g n e d w i t h i m p r o v e d t e m p e r a t u r e d e p e n d e n c e and u n c o m p r o m i s e d f a d i n g rates, the s p e c i f i c c h e m i c a l a p p r o a c h to a d j u s t i n g those p a r a m e t e r s is o n l y imperfectly appreciated. C o n s e q u e n t l y , there is no c e r t a i n t y that such a glass can be m a d e in a m a n n e r that is c o m m e r c i a l l y p r o f i t a b l e . My own p e r s o n a l w i s h is for a g l a s s that d a r k e n s to one p e r c e n t transm i t t a n c e at all t e m p e r a t u r e s if f a d i n g b a c k to t w e n t y p e r c e n t can be a c h i e v e d in five m i n u t e s indoors. I s u s p e c t that c o n s i d e r a t i o n s of c o s m e t i c f a c t o r s and g o v e r n m e n t a l r e g u l a t i o n s p r e c l u d e the w i d e spread, e n t h u s i a s t i c r e c e p t i o n of such a product. Furthermore, a c a r e f u l c o n s i d e r a t i o n of the m o d e l c a u s e s me to have some d o u b t s that such a glass can be m a d e in the silver h a l i d e system. N e w p r o d u c t s m a y well r e p r e s e n t slight c h a n g e s in j u d g m e n t of the r e l a t i v e i m p o r t a n c e of the v a r i o u s c h a r a c t e r i s t i c s of p h o t o c h r o m i c glasses, but as far as d r a m a t i c i m p r o v e m e n t s in the p e r f o r m a n c e of silver h a l i d e p h o t o c h r o m i c g l a s s e s go - O s c a r H a m m e r s t e i n a n t i c i p a t e d my f e e l i n g w h e n he said "they've gone about as far as they can go".
REFERENCES i. Cool
Ray,
Inc.,
2. Snyder,
C.
3. Miller,
D.,
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U. S. A.,
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communication. 337.
and R i c h m o n d ,
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86
7. Peckham, 624. 8. Evans,
R. H. and Harley,
P. Y.,
R. D.,
(1950), Arch. Ophthalmol.,
(1978), Pharmacy Times,
4_44,
June, pg. 44.
9. Wolbarsht, M. L., Departments of Ophthalmology and Biomedical Engineering, Duke University, private communication. 10. Moon, P., (1961), The Scientific Basis of Illuminating Engineering, p. 401, Dover Publications, New York. ii. Araujo,
R. J.,
(1980), Contemp. Phys.,
21, 77.
12. Araujo, R. J., Borrelli, N. F., and Nolan, Mag., 42, 279.
D. A.,
(1979), Phil.
13. Araujo, R. J., Borrelli, N. F., and Nolan, D. A., Mag., 44, 453.
(1981), Phil.