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    J. Photochem Phot obiol . A: Chem, 79 (1994)

    189-195

    Photochemistry of semiconductor

    I. Optical properties of ZnS sols

    189

    particles

    Ling Zang, Chun-Yan Liu and Xin-Min Rent

    Insti tef Phot ogmphic Chemi sby, Academi a Si nicu, Be g 100101 (Peoples Republi c of

    China)

    (Received October 15, 1993; accepted

    November 30, 1993)

    Abstract

    A ZnS sol stabilized by polyphosphate was prepared. The particle size is smaller than 3 nm. During the aging

    and illuminating processes, the change in particle size was followed by the absorption and fluorescence measurement.

    The mean size of ZnS particles in the solution has a limited value which did not decrease further owing to the

    large surface tension. A more reasonable description of the optical processes in ZnS sols has been given. This

    explains well the disappearance of discernibility of the exciton peak, as well as the band shift of

    fluorescence

    which was caused by the surface modification. The effects of such parameters as aging, temperature, illumination

    and surface condition on the fluorescence intensity of ZnS sols were studied. The luminescence efficiency could

    be increased by a factor of 5 under the most favorable conditions.

    1 Introduction

    In recent years, numerous investigations have

    been conducted on the photophysical and pho-

    tochemical properties of semiconductor sols [l-5],

    such as TiOz, CdS or ZnO, while only a few studies

    have been done on the ZnS sol. This may be due

    to its high electrical resistance and large band gap

    which prevents electrochemical and photochemical

    studies on it.

    The luminescence of ZnS has been extensively

    studied because ZnS crystals have a high emission

    efficiency [6, 71. Since the first report on the

    luminescence of colloidal ZnS was made by Becker

    and Bard [8], a few significant studies have been

    done by some workers [g-11]. The luminescence

    properties can serve as a probe of not only the

    interfacial electron-hole process but also the size

    change in colloidal particles. Such a change was

    observed by Henglein and coworkers in their earlier

    work [9, lo], in which a continuous decrease in

    size was found for ZnS colloids under illumination.

    It is in contrast with the results obtained in our

    and some other workers experiments [ll, 121. A

    more reasonable explanation of the size change

    of ZnS colloids under various experimental con-

    ditions (such as aging and illumination) was pro-

    posed in this study.

    Author to whom correspondence should be addressed.

    lOlO-6030/94/ 07.00 Q 1994 Elsevier Sequoia. All rights reserved

    SSDI 1010-6030(93)03760-E

    A generally accepted view of the absorption

    process in semiconductor colloids is that the initial

    step involves the excitation of an electron into the

    conduction band or the exciton level (slightly below

    the conduction band) of the semiconductor by

    ultraband gap radiation. If so, the absorption

    spectra of semiconductor sols should be such that

    the exciton peak falls slightly below the absorption

    edge. However, the absorption edge often lies far

    above the exciton peak. A more plausible de-

    scription of the absorption process is indispensable

    although a description of such process, with specific

    reference to that in CdS, using a quantum-me-

    chanical model has been developed by Chestnoy

    et al. [13]. In this study, we tried to give a more

    reasonable depiction of the optical processes in

    ZnS sols, which has not, to our knowledge, been

    reported in previous work.

    2. Experimental details

    2 1 Materials

    Zn(NO,),, Na,S, NaOH and polyphosphate (PP)

    were of analytical grades. They were all used

    without further purification. Doubly distilled water

    was used in all experiments.

    2.2. Preparat ion of ZnS sols

    The ZnS sol was prepared by a simple rapid

    injection technique: 0.8 ml of 0.1 M Na,S solution

    was added ragidly under vigorous stirring to 199.2

    ml of 4

    X 10-

    M Zn(NO& aqueous solution with

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    190

    L. Zmg et al. I Photochemistry of semiconductor particles I

    2 10m4 M PP, the concentration of which is given

    by referring to the formula Na,P,O10 (formula

    weight, 367.86). ZnS sols were aged in the re-

    frigerator at about 10 C. The absorption and

    fluorescence measurement were followed during

    aging.

    2.3. Ilumination

    Two kinds of ZnS sol (fresh and aged for 3

    days) were used in the illumination experiments.

    The illumination was carried out with a 500 W

    high pressure Hg lamp (distance, about 15 cm;

    without a fllter), and the solution was saturated

    with air during the process. Absorption and fluor-

    escence spectra were measured at given time in-

    tervals during the illumination experiments.

    2.4. Apparatus

    Absorption spectra were recorded on a Hew-

    lett-Packard diode array 8451A spectrophotometer

    and the fluorescence spectra were recorded on a

    Perkin-Elmer IS-05 fluorometer equipped with a

    computer for data acquisition, storage and ma-

    nipulation. Fluorescence quantum yields were de-

    termined by comparison with rhodamine B in

    ethanol, which is known to fluoresce with a quan-

    tum yield of 0.69 [14].

    3.

    Results

    3.1. Effect of aging on the optical propetiies

    The absorption spectra of ZnS sols aged for

    different lengths of time are shown in Fig. 1. The

    particle size of these sols cannot be larger than

    3 nm since the absorption edge (about 315 nm)

    is lower than 335 nm, which corresponds to the

    size range of 2-3 nm [9]. Some changes in the

    absorption spectra of ZnSsol occurred upon aging.

    Wovelength d

    Wavelength

    hml

    Pi.

    1. Absorption spectra of ZnS sol at various aging times

    (ZnS (diatomic) concentration, 4x lo- M, stabilizer, 2~10~

    M PP). The sol was used in all the subsequent experiments.

    Fig. 2. Fluorescence spectra of ZnS sol at various aging times.

    The inset shows the dependence of fluorescence intensity cm the

    aging time.

    The absorbance reduced by about 10 in 9 days

    (Fig. 1). This was believed to be a result of the

    slow air oxidation

    ZnS+202- Zn2++S0,2-

    (1)

    The Zn+ ions in the sol thus were in excess. The

    exciton peak became pronounced and shifted

    slightly to a longer wavelength, whereas hardly

    any shift in the absorption edge was found.

    Figure 2 shows the fluorescence spectra of ZnS

    sols aged for different lengths of time. The quantum

    efficiency for the fresh sol is about 1.7 and

    reaches a highest level of about 5.5 for the sol

    aged for 6 days. This efficiency is much higher

    than that reported in the work of Dunstan et al.

    [ll], in which the ZnS sols luminesced with a

    quantum yield of 2X10-. In addition to the

    increase in intensity with increasing aging time,

    the maximum fluorescence shifted slightly to a

    longer wavelength within the first 3 days. This

    implies that the particle size increases slightly. No

    band gap emission was observed for the ZnS ~01s.

    3.2. Ef fect of il lumination on the optical

    properties

    The ZnS sol is very sensitive to illumination

    with a photon energy higher than its band gap.

    The absorption spectrum changed drastically with

    illumination time, as shown in Fig. 3. First, the

    shoulder (the exciton peak) at about 282 nm

    became slightly pronounced. On increasing the

    illumination time, it became increasingly vague

    and almost disappeared after about 60 min. In

    the meantime, the absorption edge shifted to a

    longer wavelength. This was quite different from

    the results obtained by Henglein and Gutierrez

    [9], in which the onset of light absorption shifted

    continuously to a shorter wavelength and the ex-

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    L . Zang et al. / Photochemdy of semiconductor panicles I

    191

    Wavelength nm)

    Fig. 3. Absorption spectra of the ZnS sol aged for 3 days at

    various times of illumination in the presence of air. The fresh

    sol showed a simlar behavior

    .V

    fresh

    ol

    40 60

    I

    6

    z

    :

    60

    c

    2

    .g 40

    5

    20

    0

    330 400

    450 500

    loo

    3-day-aped

    ol

    1

    8 60

    Fig. 4. Fluorescence spectra of the two ZnS sols at various times

    f

    ihninatiDn in the presence Of air. The flUOreXence hItenSit&

    were manipulated to be at the same kvel for the

    observation

    Of band shift.

    citon peak became more and more pronounced

    during the whole illumination process. The ab-

    sorbance of ZnS sol decreases very quickly upon

    illumination, as can be seen in Fig. 3.

    The fluorescence spectra of ZnS sols illuminated

    for different times are shown in Fig. 4. It can be

    seen that the fluorescence spectra of the two sols

    escence maximum of the fresh sol shifted contin-

    uously to a longer wavelength in the whole illu-

    mination period. In fact, the shift in the initial

    period is a consequence of the decrease in fluor-

    escence at a shorter wavelength. The width of the

    fluorescence band became narrower and narrower

    at the same time. For the sol aged for 3 days,

    the fluorescence maximum shifted to a shorter

    wavelength in the first 4 min and then shifted to

    a longer wavelength as in the case of the fresh

    sol.

    It was also found that the intensity of fluor-

    escence of the two sols underwent different changes

    during the illumination process (Fig. 5). Consid-

    ering the great change in absorbance during the

    illumination, the specific intensity (the ratio of the

    fluorescence intensity to the absorbance at 282

    nm) was used to compare the fluorescence in-

    tensities of sols in different illumination times.

    With the exception of the slight decrease in the

    first 4 min, the fluorescence intensity of the sol

    aged for 3 days increases steadily with illumination.

    However, for the fresh sol, the fluorescence in-

    tensity increased sharply in the first 20 min of

    illumination and then decreased quickly with fur-

    ther illumination.

    3.3.

    Ef fect of temperatur e on f luorescence

    It is known that the fluorescence intensity de-

    pends strongly upon temperature [lo, 151. In the

    Arrhenius plot (Fig. 6), In l / I is plotted vs. the

    reciprocal temperature as is usually done for fluor-

    escence processes with competing thermal deac-

    tivation, where

    I

    is the fluorescence intensity. With

    increasing temperature for 0 C to about 50 C,

    -B-fresh sol

    --+--3-doy-oqsd sol

    01

    I

    I I

    0

    20

    40 60

    J

    Illumination time, t min.1

    Fig. 5. Fluorescence intensity of the two ZnS sols as a function

    changed differently upon illumination. The fluor-

    of the illumination time (from the data in Fig. 4).

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    L. Zang et al. / Photochemir ny of semiconductor

    parricks

    I.6

    1.2

    z

    C

    5

    e 0.0

    D

    w

    .

    5

    0.4

    0

    -4-day-aged sol

    --+--14-day-aged sol

    I/T (I lO+K-

    Fig. 6. Plot of In(W) VS. the reciprocal temperature for the hvo

    zas sols.

    the fluorescence intensity decreased to about 25

    of its value at 0 C. The fluorescence intensity of

    the two ZnS sols changed similarly with temper-

    ature. In other words, the degree of dependence

    does not change with the surface condition, which

    may be quite different for various aging times.

    The activation energy for the competing process

    can be calculated from the slope of line in Fig.

    6, to be about 19 kJ mol-l.

    3.4. Efi ct of surface condit i on on fl uorescence

    In our experiments, various ions, such as Cu+,

    Ag+,Cd2+,Zn2+, m+,.S-,OH-,I- andSCN-,

    were used to modify the surface of ZnS colloids.

    Some of the ions were found to be very effective

    in changing the optical properties of the ZnS ~01s;

    this will be described in the next paper of this

    series. Figure 7 showed the change in the fluor-

    escence spectrum of the ZnS sol aged for 9 days

    with the addition of OH- and Zn+ ions. The

    fluorescence intensity increased on addition of

    OH- ions up to 5 X 10e4 M, and no increase was

    found on further addition (inset in Fig. 7). The

    fluorescence spectra became wider owing to the

    addition of OH- ions. The intensity increased

    were markedly at longer wavelengths than at

    shorter wavelengths. If 2.5X 10e8 M Zn2+ was

    added to the ZnS sol with a prior addition of

    5~10~~ M OH-, the fluorescence intensity de-

    creased and the shape of the spectra did not

    change. The same effect was also shown in spectrum

    d in Fig. 7 which was obtained by adding 2

    X

    low4

    M Zn2+ to the ZnS sol aged for 9 days without

    any prior addition. The fluorescence intensity de-

    420 460

    Wavelength Lnml

    Fig. 7. Fluorescence spectra of the ZnS sol aged for 9 days upon

    addition of OH- and Zn2+ ions: curve a, no addition; curve b,

    addition of 5 X lo- M OH-; curve c, addition of 2.5

    X

    10ms M

    Zn2* to sample for curve b; curve d, addition of 2x10- M

    zn2+.

    creased about 60 . A clear red shift of fluorescence

    maximum was observed, as shown in Fig. 7.

    4. Discussion

    4.1. Sire of ZnS colloids

    It is well known that the colloids are thermo-

    dynamically unstable with respect to the bulk phase.

    The surface tension favors a small surface area.

    This means that the colloidal particles have a

    natural tendency to aggregate. The smaller the

    particles, the more dramatic is the increase in the

    specific surface area, and hence the stronger is

    the tendency to particle aggregation. Such tendency

    was found in the initial aging period of ZnS sols

    (Fig. 2). The smaller particles in the fresh sol

    tend to dissolve and the larger particles grow

    through Ostwald ripening.

    Considering the size dependence of the tendency

    to particle aggregation, the average size of ZnS

    particles under the condition of our experiments

    should have a limited value, which does not de-

    crease further even under photodegradation. The

    results shown in Fig. 4 can be regarded as an

    indication of the change in particle size in view

    of the size quantization effect, which has been

    reported elsewhere [lo, 16, 171. The blue shift

    and red shift of the fluorescence maximum suggest

    a decrease and an increase respectively in particle

    size. This is similar to the results obtained by

    Dunstan et al. [ll] and Rossetti et al. [12], but

    quite contrary to the results obtained by Henglein

    and Gutierrez [9], in which a continuous decrease

    in particle size of the ZnS sol was found during

    illumination. The contraditory results may be

    caused by the different stabilizers used in the

    experiments.

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    L. Zang t a. I Photochemishy of semi conduct0ra r t i c l e s

    193

    4.2. Absorption process in ZnS sols

    In our studies, the exciton peak (absorption

    involved between the valence band and the exciton

    level) of ZnS sols is not so pronounced as that

    obtained in methanol by Rossetti et

    nl.

    [12]. Even

    in their results, the ZnS sol prepared in aqueous

    solution shows a much less pronounced exciton

    peak compared with that prepared in methanol

    solution. A similar phenomenon was also observed

    for CdS sols prepared in water and propanol-2

    solution [18]. Obviously, the solvent is the most

    effective factor that affects the characteristics of

    the exciton peak. In the work of Rossetti er al.,

    this solvent effect was referred to as a prevention

    of the colloid particles from aggregation, which

    was believed to be the origin of the difference

    between the exciton peaks. The ZnS sol obtained

    in our experiments, which was stabilized by PP,

    was very stable and no obvious aggregation can

    be found after a long aging time (e.g. 14 days).

    This can be seen from the fact that the onset of

    the absorption spectra did not shift significantly

    to a longer wavelength, while the exciton peak

    became a little more pronounced upon aging. This

    is also in contrast with the results of Rossetti et

    al.

    [12].

    The disappearance of the discernibility of the

    exciton peak can be attributed to either a broad-

    ening or a decrease in this peak. This may be due

    to trapping of the excitons by an impurity center

    at the surface. This may happen as follows: the

    impurity center first traps an electron (or hole)

    and, once this has happened, the impurity center

    (now charged) can attract a hole (or electron)

    through the coulombic force. The level of such a

    trapped exciton is lower than that of an untrapped

    exciton by the interaction energy of the exciton

    with the impurity center. Thus the exciton peak

    is broadened to a longer wavelength where the

    absorption associated with the trapped exciton

    level occurs. The intensity of the original exciton

    peak weakens owing to the decrease in the number

    of untrapped excitons. Roth Zn and S2- ions

    on the surface can trap photogenerated excitons

    in ZnS colloids. The increase in the discernibility

    of the exciton peak during aging (in the process

    the Zn* ions were in excess) indicates that S2-

    (hole trap) is more efficient than Zn*+ (electron

    trap) in trapping excitons. This is understandable

    considering the different electrode

    potentials of

    the

    two onpairs,E(S-S), -0.51 V;E(Zn+-Zn),

    -0.76 V.

    The trapping of excitons is affected

    by the

    dielectric properties of the environment of the

    ZnS particle, which in turn is determined to a

    great extent by the properties of the solvent. A

    solvent with a higher polarity is always favorable

    for the creation of a gradient of electrostatic

    potential around the ZnS particle and hence is

    conducive to the movement of photogenerated

    charge carriers (hole and electron) from the in-

    terior to the surface. Tbe difference in the polarities

    of the solvents used in the experiments of Rossetti

    et al. [12] and in our experiments can therefore

    be reasonably regarded as an origin of the dif-

    ference in the discemibilities of the exciton peaks.

    In addition to the absorption processes asso-

    ciated with band gap and exciton excitation, the

    absorption processes involving impurities (acceptor

    and donor) in semiconductor colloids may also

    occur. This is shown in Fig. 8, where a and b

    represent the processes in which an electron is

    excited from the valence band to a donor or from

    an acceptor to the conduction band, and c illus-

    trates an absorption process involving transition

    from an acceptor to a donor. Such processes lead

    to absorption with a photon energy lower than

    the band gap if the donor or acceptor exists in

    a relatively deep site.

    For small particles, the number of molecules

    on the surface is comparable with that in the

    interior. Even a minute amount of impurities ad-

    sorbed on the surface lattice can cause a striking

    increase in the concentration of defects in one

    particle. Zn2+ or S*- ions strongly adsorbed at

    the surface lattice can be regarded as the deep

    traps contributing to absorption lower than the

    band gap.

    It can be seen from the above discussion that

    the absorption edge of the semiconductor sol is

    not equivalent exactly to the band gap but is lower

    than the latter in energy. In fact, the exciton peak

    (if it is sufficiently pronounced) is more precise

    than the absorption edge as an indicator for the

    change in particle size.

    CB

    A

    VE

    Fig. 8. Various absorption processes invoting impurities (see

    text for details): CB, conduction band; VB, valence band; A,

    acceptor; D, donor.

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    194

    L. Zang et al. I Photochemirhy of semiconductor particles I

    4.3. Fluorescence

    4.3.1. I ntensity

    It is commonly accepted that the S2- vacancy

    (in the surface layer) is the fluorescence center

    for the sols of CdS [I 213 or ZnS [lo] in the

    cubic zinc-blende structure. That is to say, the

    S2- ion can quench the fluorescence more effi-

    ciently than the cations Cd+ or ZP. Removal

    of S2- ions on the surface is always favorable to

    the enhancement of fluorescence. The removal

    can be achieved either by illumination (photo-

    oxidation) or by aging (air oxidation). Owing to

    oxidation the Zn ions on the surface were in

    excess. A sufficiently high concentration of ZrP

    ions can also effectively quench the fluorescence.

    This is because the high concentration of Zn+

    favors the electron-trapping reaction

    Zn2+ +2e---, Zn

    (2)

    which hardly occurs in the condition of a low

    concentration of Zn+ ions.

    Of particular interest is .the sharp decrease in

    the fluorescence intensity of the ZnS sol. This can

    be attributed to the high concentration of defects

    generated in the colloidal particles. The size dis-

    tribution of the fresh ZnS particles is not narrow.

    Under illumination, larger particles in a poor crystal

    structure were formed through Ostwald ripening,

    which proceeded much faster under illumination

    than under aging [X3]. In contrast, few of these

    poor crystalline particles can be formed in the

    ZnS sol aged for 3 days owing to its narrow size

    distribution.

    As reported by the previous workers [19, 221,

    the fluorescence intensity also depends to some

    extent on the pH of the solution. The OH- ion

    is effective for blocking the defect on the surface

    of colloid. Such a defect is believed to be the

    center for the radiationless recombination of the

    photogenerated charge carriers. The increase in

    the fluorescence intensity caused by OH- has not

    been clearly explained to date, although Henglein

    et al. [17] postulated a possible explanation for

    the CdS ~01s: he removal of SH- groups and the

    accumulation of Cd* on the surface in the form

    of S2-. . .Cd2*.. .OH- seem to destroy the sites

    where radiationless recombination of the charge

    carriers occurs. This is hard to accept because the

    excess Cd+ ions in the case of a high pH should

    precipitate to form Cd(OH)2 and they could not

    be in the postulated form. The binding of OH-

    with the excess cations Cd2 or Zn2+ at the surface

    lattice seems to be the main reason for the fluor-

    escence enhancement because the binding can

    weaken the ability of the cation+ for trapping the

    photogenerated electron (eqn. (2)). This was ver-

    ified by the results shown in Fig. 7. The addition

    of OH- to the ZnS sol aged for 9 days (with

    excess Zn2 + ions) resulted in an enhancement in

    fluorescence. The subsequent addition of Zn2+ (in

    the form of Zn(OH),, n 22) [24], however, de-

    creased the intensity. This led us to conclude that

    the excess Zn(OH), which covered the surface

    acted as new centers for the radiationless recom-

    bination of the photogenerated charge carriers.

    Temperature has another significant effect on

    the intensity of fluorescence. The photogenerated

    charge carriers decay in two competitive ways,

    namely radiation and radiationless recombination.

    radiationles

    ZnSh ZnS (e--h*)

    rJ

    heat + ZnS

    photodecomposition products

    \

    (Zn+ S, SOJz-etc.)

    radiation

    hv + ZnS

    The radiationless process is temperature depen-

    dent with an exp(

    -E/RT)

    law, where

    E

    is the

    activation energy. The higher the temperature, the

    faster is the radiationless process, and hence the

    lower is the fluorescence intensity. The dependence

    of the radiationless process on temperature was

    little affected by the surface condition (Fig. 6).

    Thii implies that the radiationless recombination

    of the charge carriers possibly happens in the inner

    part of ZnS colloids.

    4.3.2.

    Wavelength

    In addition to the size change, the shift in the

    fluorescence maximum can also be caused by sur-

    face modification with adsorbed ions. The adsorbed

    ions often act as shallow traps of photogenerated

    charge carriers in the luminescence process. As

    a result, the fluorescence maximum shifts to a

    longer wavelength. The excess OH- ions (possibly

    ppose that the binding form of M(OH)2, the standard

    potential of the reaction M(OH),+2e- =M+20H-(aq) can be

    obtained as

    &(M(OH),OH-, M)==E(ti+-M)+ g In rz,

    where M represents the element Cd or Zn and K,_ is the solubility

    product of &OH) Using the standard potent& and solubili6

    oroducts EKd2-Cd~ = - 0.40 V, EfZn2+-ZnI= -0.76 V.

    jC,(Cd(OH)& 2.5 X lo-l4

    and Kz(kn(Ok)z)= 1.2~ lo-l7 froi

    ref. 23, one can ohtain the standard potential EO(M(OH)+H-,

    M) as follows: E(OH--Cd(OH)2, Cd)= -0.80 V,

    E(OH--ZII(OH)~, Zn)= -1.26 V. So the negative potential

    makes it hard for Cd(OH)2 and Zn(OH), to trap the photo-

    generated electrons.

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    L. Zang et al. I Photochemi ptry

    of

    emi conductor parti cles I

    195

    in the form of Zn(OH),, n B 2) at the surface of

    It should be emphasized here that the optical

    ZnS particles can be regarded as shallow traps

    process in semiconductor sols is very complicated

    which caused a red shift in the fluorescence spectra and cannot be thoroughly discussed in this article.

    (Fig. 7).

    Some further studies are necessary in this regard.

    The absence of band gap emission (Fig. 2)

    indicates that electrons in the conduction band

    or exciton level cannot recombine directly with

    holes in the valence band. As postulated by Weller

    [25], at least one of the charge carriers is trapped

    in the luminescence process. In this paper, the

    trapped charge carrier is further described in the

    form of trapped exciton as described above. Prior

    to luminescence, the trapped exciton relaxes

    through interaction with other charge carriers or

    defects in the surface layer where the trapping is

    believed to take place. This relaxation causes a

    decrease in energy of the trapped exciton which

    now luminesces with a longer wavelength. One

    can see that the decrease in energy of the trapped

    exciton depends upon the concentration of defects

    in the surface layer of the particle. For zinc sulfide,

    it is hard to obtain colloidal particles with a perfect

    crystal structure by&situ generation. Some defects

    always exist in the generated particles (especially

    in the surface layers) owing to the peculiar prop-

    erties of the Zn+ ion in alkaline solutions [24].

    During the rapid precipitation, such ions as

    Zn(OH),- and Zn(OH)42- can be formed as

    interstitials in the particle. On the contrary, band

    Acknowledgments

    Thanks are due to the National Natural Science

    Foundation of China and Eastman Kodak Com-

    pany for their financial support for this work.

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    5. Conclusions

    For a stable semiconductor sol, a limiting low

    value of the particle size exists because the large

    surface tension of small particles favors aggre-

    gation. The decrease in absorbance of ZnS sols

    under illumination is caused by the reduction in

    the number of particles and not by the decrease

    in particle size.

    Owing to the small size of the colloidal particles

    and thus the large surface-to-bulk ratio, the nature

    of the surface is responsible for the physi-

    cal-chemical properties of the particle. Therefore

    surface effects should be taken into account when

    studying optical processes in semiconductor ~01s.

    As the particle size decreases, not only quantization

    effects but also surface effects become significant.

    The changes in optical properties are caused si-

    multaneously by the two kinds of effect instead

    of by just one of them.

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