Large-scale preparation of ordered titania nanorods with enhanced photocatalytic activity

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1 Introduction
so far that allow for reduction/rewriting of phones in a word depending on word context. Ignoring the word neighbours and still allowing for all sorts of phonetic reduction would result in a long list of confusion pairs of very frequent words. Consider of example word sequences like \KIND OF" and \SORT OF" which are often reduced to \KINDA" and \SORTA". If, in order to capture this reduction of \OF", we would introduce the pronunciation variant \OF(A)" transcribed with the unstressed vowel AX, the confusability in the dictionary would increase signi cantly. Segmentation: In Switchboard utterance boundaries are not well de ned. It turned out that a lot of utterances were split incorrectly into utterances such that words at the beginning or end of an utterance were either only partially existent or not there at all. The idea of this paper is to automatically retranscribe the training corpus using a speaking mode dependent pronunciation model which also takes crossword dependencies into account by merging words into multiword units. Training based on utterance transcription graphs which allow for a large number of alternative pronunciations and for a more exible alignment and utterance segmentation yields a signi cant improvement in terms of word error rate of our Switchboard/CallHome recognizer.

Generalized cross-validation for large scale problems

GENERALIZED CROSS-VALIDATION FOR LARGE SCALE PROBLEMS, REVISED VERSION
GENE H. GOLUB AND URS VON MATT
Abstract. Although generalized cross-validation is a popular tool for calculating a regularization
parameter it has been rarely applied to large scale problems until recently. A major di culty lies in the evaluation of the cross-validation function which requires the calculation of the trace of an inverse matrix. In the last few years stochastic trace estimators have been proposed to alleviate this problem. In this paper numerical approximation techniques are used to further reduce the computational complexity. The new approach employs Gauss quadrature to compute lower and upper bounds on the cross-validation function. It only requires the operator form of the system matrix, i.e., a subroutine to evaluate matrix-vector products. Thus the factorization of large matrices can be avoided. The new approach has been implemented in MATLAB. Numerical experiments con rm the remarkable accuracy of the stochastic trace estimator. Regularization parameters are computed for ill-posed problems with 100, 1000, and 10000 unknowns.

Large-scale machine learning with stochastic gradient descent

Large-Scale Machine Learningwith Stochastic Gradient DescentL´e on BottouNEC Labs America,Princeton NJ08542,USAleon@Abstract.During the last decade,the data sizes have grown faster than the speed of processors.In this context,the capabilities of statistical machine learning meth-ods is limited by the computing time rather than the sample size.A more pre-cise analysis uncovers qualitatively diﬀerent tradeoﬀs for the case of small-scale and large-scale learning problems.The large-scale case involves the computational complexity of the underlying optimization algorithm in non-trivial ways.Unlikely optimization algorithms such as stochastic gradient descent show amazing perfor-mance for large-scale problems.In particular,second order stochastic gradient and averaged stochastic gradient are asymptotically eﬃcient after a single pass on the training set.Keywords:Stochastic gradient descent,Online learning,Eﬃciency1IntroductionThe computational complexity of learning algorithm becomes the critical limiting factor when one envisions very large datasets.This contribution ad-vocates stochastic gradient algorithms for large scale machine learning prob-lems.Theﬁrst section describes the stochastic gradient algorithm.The sec-ond section presents an analysis that explains why stochastic gradient algo-rithms are attractive when the data is abundant.The third section discusses the asymptotical eﬃciency of estimates obtained after a single pass over the training set.The last section presents empirical evidence.2Learning with gradient descentLet usﬁrst consider a simple supervised learning setup.Each example z is a pair(x,y)composed of an arbitrary input x and a scalar output y.We consider a loss function (ˆy,y)that measures the cost of predictingˆy when the actual answer is y,and we choose a family F of functions f w(x)parametrized by a weight vector w.We seek the function f∈F that minimizes the loss Q(z,w)= (f w(x),y)averaged on the examples.Although we would like to average over the unknown distribution dP(z)that embodies the Laws of2L´e on BottouNature,we must often settle for computing the average on a sample z1...z n.E(f)=(f(x),y)dP(z)E n(f)=1nni=1(f(x i),y i)(1)The empirical risk E n(f)measures the training set performance.The expected risk E(f)measures the generalization performance,that is,the expected performance on future examples.The statistical learning theory(Vapnik and Chervonenkis,1971)justiﬁes minimizing the empirical risk instead of the expected risk when the chosen family F is suﬃciently restrictive.2.1Gradient descentIt has often been proposed(e.g.,Rumelhart et al.,1986)to minimize the empirical risk E n(f w)using gradient descent(GD).Each iteration updates the weights w on the basis of the gradient of E n(f w),w t+1=w t−γ1nni=1∇w Q(z i,w t),(2)whereγis an adequately chosen gain.Under suﬃcient regularity assumptions, when the initial estimate w0is close enough to the optimum,and when the gainγis suﬃciently small,this algorithm achieves linear convergence(Dennis and Schnabel,1983),that is,−logρ∼t,whereρrepresents the residual error.Much better optimization algorithms can be designed by replacing the scalar gainγby a positive deﬁnite matrixΓt that approaches the inverse of the Hessian of the cost at the optimum:w t+1=w t−Γt 1nni=1∇w Q(z i,w t).(3)This second order gradient descent(2GD)is a variant of the well known Newton algorithm.Under suﬃciently optimistic regularity assumptions,and provided that w0is suﬃciently close to the optimum,second order gradient descent achieves quadratic convergence.When the cost is quadratic and the scaling matrixΓis exact,the algorithm reaches the optimum after a single iteration.Otherwise,assuming suﬃcient smoothness,we have−log logρ∼t.2.2Stochastic gradient descentThe stochastic gradient descent(SGD)algorithm is a drastic simpliﬁcation. Instead of computing the gradient of E n(f w)exactly,each iteration estimates this gradient on the basis of a single randomly picked example z t:w t+1=w t−γt∇w Q(z t,w t).(4)Large-Scale Machine Learning 3The stochastic process {w t ,t =1,...}depends on the examples randomly picked at each iteration.It is hoped that (4)behaves like its expectation (2)despite the noise introduced by this simpliﬁed procedure.Since the stochastic algorithm does not need to remember which examples were visited during the previous iterations,it can process examples on the ﬂy in a deployed system.In such a situation,the stochastic gradient descent directly optimizes the expected risk,since the examples are randomly drawn from the ground truth distribution.The convergence of stochastic gradient descent has been studied exten-sively in the stochastic approximation literature.Convergence results usuallyrequire decreasing gains satisfying the conditions t γ2t <∞and t γt =∞.The Robbins-Siegmund theorem (Robbins and Siegmund,1971)provides the means to establish almost sure convergence under mild conditions (Bottou,1998),including cases where the loss function is not everywhere diﬀerentiable.The convergence speed of stochastic gradient descent is in fact limited by the noisy approximation of the true gradient.When the gains decrease too slowly,the variance of the parameter estimate w t decreases equally slowly.When the gains decrease too quickly,the expectation of the parameter es-timate w t takes a very long time to approach the optimum.Under suﬃ-cient regularity conditions (e.g.Murata,1998),the best convergence speed is achieved using gains γt ∼t −1.The expectation of the residual error then decreases with similar speed,that is,E ρ∼t −1.The second order stochastic gradient descent (2SGD)multiplies the gradi-ents by a positive deﬁnite matrix Γt approaching the inverse of the Hessian :w t +1=w t −γt Γt ∇w Q (z t ,w t ).(5)Unfortunately,this modiﬁcation does not reduce the stochastic noise and therefore does not signiﬁcantly improve the variance of w t .Although con-stants are improved,the expectation of the residual error still decreases like t −1,that is,E ρ∼t −1,(e.g.Bordes et al.,2009,appendix).2.3Stochastic gradient examplesTable 1illustrates stochastic gradient descent algorithms for a number of classic machine learning schemes.The stochastic gradient descent for the Perceptron,for the Adaline,and for k -Means match the algorithms proposed in the original papers.The SVM and the Lasso were ﬁrst described with traditional optimization techniques.Both Q svm and Q lasso include a regular-ization term controlled by the hyperparameter λ.The K-means algorithm converges to a local minimum because Q kmeans is nonconvex.On the other hand,the proposed update rule uses second order gains that ensure a fast convergence.The proposed Lasso algorithm represents each weight as the diﬀerence of two positive variables.Applying the stochastic gradient rule to these variables and enforcing their positivity leads to sparser solutions.4L´e on BottouTable 1.Stochastic gradient algorithms for various learning systems.Loss Stochastic gradient algorithmAdaline (Widrow and Hoﬀ,1960)Q adaline =12 y −w Φ(x ) 2Φ(x )∈R d ,y =±1w ←w +γt y t −w Φ(x t ) Φ(x t )Perceptron (Rosenblatt,1957)Q perceptron =max {0,−y w Φ(x )}Φ(x )∈R d ,y =±1w ←w +γt y t Φ(x t )if y t w Φ(x t )≤00otherwise K-Means (MacQueen,1967)Q kmeans =min k 1(z −w k )2z ∈R d ,w 1...w k ∈R dn 1...n k ∈N ,initially 0k ∗=arg min k (z t −w k )2n k ∗←n k ∗+1w k ∗←w k ∗+1n k∗(z t −w k ∗)SVM (Cortes and Vapnik,1995)Q svm =λw 2+max {0,1−y w Φ(x )}Φ(x )∈R d ,y =±1,λ>0w ←w −γt λw if y t w Φ(x t )>1,λw −y t Φ(x t )sso (Tibshirani,1996)Q lasso =λ|w |1+12 y −w Φ(x ) 2w =(u 1−v 1,...,u d −v d )Φ(x )∈R d ,y ∈R ,λ>0u i ← u i −γt λ−(y t −w Φ(x t ))Φi (x t ) +v i ← v i −γt λ+(y t −w t Φ(x t ))Φi (x t ) +with notation [x ]+=max {0,x }.3Learning with large training setsLet f ∗=arg min f E (f )be the best possible prediction function.Since we seek the prediction function from a parametrized family of functions F ,let f ∗F =arg min f ∈F E (f )be the best function in this family.Since we optimize the empirical risk instead of the expected risk,let f n =arg min f ∈F E n (f )be the empirical optimum.Since this optimization can be costly,let us stop the algorithm when it reaches an solution ˜f n that minimizes the objective function with a predeﬁned accuracy E n (˜f n )<E n (f n )+ρ.3.1The tradeoﬀs of large scale learningThe excess error E =E E (˜f n)−E (f ∗) can be decomposed in three terms (Bottou and Bousquet,2008):E =E E (f ∗F )−E (f ∗) +E E (f n )−E (f ∗F ) +E E (˜f n )−E (f n ) .(6)•The approximation error E app =E E (f ∗F )−E (f ∗) measures how closelyfunctions in F can approximate the optimal solution f ∗.The approxima-tion error can be reduced by choosing a larger family of functions.•The estimation error E est =E E (f n )−E (f ∗F ) measures the eﬀect of minimizing the empirical risk E n (f )instead of the expected risk E (f ).Large-Scale Machine Learning 5The estimation error can be reduced by choosing a smaller family of functions or by increasing the size of the training set.•The optimization error E opt =E (˜f n )−E (f n )measures the impact of the approximate optimization on the expected risk.The optimization error can be reduced by running the optimizer longer.The additional computing time depends of course on the family of function and on the size of the training set.Given constraints on the maximal computation time T max and the maximal training set size n max ,this decomposition outlines a tradeoﬀinvolving the size of the family of functions F ,the optimization accuracy ρ,and the number of examples n eﬀectively processed by the optimization algorithm.min F ,ρ,nE =E app +E est +E opt subject to n ≤n max T (F ,ρ,n )≤T max (7)Two cases should be distinguished:•Small-scale learning problems are ﬁrst constrained by the maximal num-ber of examples.Since the computing time is not an issue,we can reduce the optimization error E opt to insigniﬁcant levels by choosing ρarbitrarily small,and we can minimize the estimation error by chosing n =n max .We then recover the approximation-estimation tradeoﬀthat has been widely studied in statistics and in learning theory.•Large-scale learning problems are ﬁrst constrained by the maximal com-puting time.Approximate optimization can achieve better expected risk because more training examples can be processed during the allowed time.The speciﬁcs depend on the computational properties of the chosen op-timization algorithm.3.2Asymptotic analysisSolving (7)in the asymptotic regime amounts to ensuring that the terms of the decomposition (6)decrease at similar rates.Since the asymptotic conver-gence rate of the excess error (6)is the convergence rate of its slowest term,the computational eﬀort required to make a term decrease faster would be wasted.For simplicity,we assume in this section that the Vapnik-Chervonenkis dimensions of the families of functions F are bounded by a common constant.We also assume that the optimization algorithms satisfy all the assumptions required to achieve the convergence rates discussed in section 2.Similar anal-yses can be carried out for speciﬁc algorithms under weaker assumptions (e.g.Shalev-Shwartz and Srebro,2008).A simple application of the uniform convergence results of (Vapnik and Chervonenkis,1971)gives then the upper bound E =E app +E est +E opt =E app +O log n n+ρ .6L´e on BottouTable 2.Asymptotic equivalents for various optimization algorithms:gradient descent(GD,eq.2),second order gradient descent(2GD,eq.3),stochastic gradient descent(SGD,eq.4),and second order stochastic gradient descent(2SGD,eq.5). Although they are the worst optimization algorithms,SGD and2SGD achieve the fastest convergence speed on the expected risk.They diﬀer only by constant factors not shown in this table,such as condition numbers and weight vector dimension.GD2GD SGD2SGD Time per iteration:n n11Iterations to accuracyρ:log1ρlog log1ρ1ρ1ρTime to accuracyρ:n log1ρn log log1ρ1ρ1ρTime to excess error E:1E1/αlog21E1E1/αlog1Elog log1E1E1EUnfortunately the convergence rate of this bound is too pessimistic.Faster convergence occurs when the loss function has strong convexity properties (Lee et al.,2006)or when the data distribution satisﬁes certain assumptions (Tsybakov,2004).The equivalenceE=E app+E est+E opt∼E app+log nnα+ρ,for someα∈1,1,(8)provides a more realistic view of the asymptotic behavior of the excess er-ror(e.g.Massart,2000,Bousquet,2002).Since the three component of the excess error should decrease at the same rate,the solution of the tradeoﬀproblem(7)must then obey the multiple asymptotic equivalencesE∼E app∼E est∼E opt∼log nnα∼ρ.(9)Table2summarizes the asymptotic behavior of the four gradient algo-rithm described in section2.Theﬁrst three rows list the computational cost of each iteration,the number of iterations required to reach an optimization accuracyρ,and the corresponding computational cost.The last row provides a more interesting measure for large scale machine learning purposes.Assum-ing we operate at the optimum of the approximation-estimation-optimization tradeoﬀ(7),this line indicates the computational cost necessary to reach a predeﬁned value of the excess error,and therefore of the expected risk.This is computed by applying the equivalences(9)to eliminate n andρfrom the third row results.Although the stochastic gradient algorithms,SGD and2SGD,are clearly the worst optimization algorithms(third row),they need less time than the other algorithms to reach a predeﬁned expected risk(fourth row).Therefore, in the large scale setup,that is,when the limiting factor is the computing time rather than the number of examples,the stochastic learning algorithms performs asymptotically better!Large-Scale Machine Learning 74Eﬃcient learningLet us add an additional example z t to a training set z 1...z t −1.Since the new empirical risk E t (f )remains close to E t −1(f ),the empirical minimum w ∗t +1=arg min w E t (f w )remains close to w ∗t =arg min w E t −1(f w ).With suﬃcient regularity assumptions,a ﬁrst order calculation gives the resultw ∗t +1=w ∗t −t −1Ψt ∇w Q (z t ,w ∗t )+O t −2 ,(10)where Ψt is the inverse of the Hessian of E t (f w )in w ∗t .The similarity be-tween this expression and the second order stochastic gradient descent rule(5)has deep consequences.Let w t be the sequence of weights obtained by performing a single second order stochastic gradient pass on the randomly shuﬄed training set.With adequate regularity and convexity assumptions,we can prove (e.g.Bottou and LeCun,2004)lim t →∞t E (f w t )−E (f ∗F ) =lim t →∞t E (f w ∗t )−E (f ∗F ) =I >0.(11)Therefore,a single pass of second order stochastic gradient provides a pre-diction function f w t that approaches the optimum f ∗Fas eﬃciently as the empirical optimum f w ∗t .In particular,when the loss function is the log like-lihood,the empirical optimum is the asymptotically eﬃcient maximum like-lihood estimate,and the second order stochastic gradient estimate is also asymptotically eﬃcient.Unfortunately,second order stochastic gradient descent is computation-ally costly because each iteration (5)performs a computation that involves the large dense matrix Γt .Two approaches can work around this problem.•Computationally eﬃcient approximations of the inverse Hessian trade asymptotic optimality for computation speed.For instance,the SGDQN algorithm (Bordes et al.,2009)achieves interesting speeds using a diag-onal approximation.•The averaged stochastic gradient descent (ASGD)algorithm (Polyak and Juditsky,1992)performs the normal stochastic gradient update (4)and recursively computes the average ¯w t =1tt i =1w t :w t +1=w t −γt ∇w Q (z t ,w t ),¯w t +1=t t +1¯w t +1t +1w t +1.(12)When the gains γt decrease slower than t −1,the ¯w t converges with the optimal asymptotic speed (11).Reaching this asymptotic regime can take a very long time in practice.A smart selection of the gains γt helps achieving the promised performance (Xu,2010).8L´e on BottouAlgorithm Time Test ErrorHinge loss SVM,λ=10−4.SVMLight 23,642s. 6.02%SVMPerf 66s. 6.03%SGD 1.4s. 6.02%Log loss SVM,λ=10−5.TRON (-e0.01)30s. 5.68%TRON (-e0.001)44s. 5.70%SGD 2.3s. 5.66%Optimization accuracy (trainingCost−optimalTrainingCost)Fig.1.Results achieved with a linear SVM on the RCV1task.The lower half of the plot shows the time required by SGD and TRON to reach a predeﬁned accuracy ρon the log loss task.The upper half shows that the expected risk stops improving long before the superlinear TRON algorithm overcomes SGD.0.300.320.340.360.380.400 1 2 34 5E x p e c t e d r i s k Number of epochs SGD SGDQN ASGD 21.022.023.024.025.026.027.0 0 1 2 3 4 5T e s t E r r o r (%)Number of epochsSGD SGDQN ASGD paraison of the test set performance of SGD,SGDQN,and ASGD for a linear squared hinge SVM trained on the ALPHA task of the 2008Pascal Large Scale Learning Challenge.ASGD nearly reaches the optimal expected risk after a single pass.44004500460047004800490050005100520053005400epochs epochsparison of the test set performance of SGD,SGDQN,and ASGD on a CRF trained on the CONLL Chunking task.On this task,SGDQN appears more attractive because ASGD does not reach its asymptotic performance.Large-Scale Machine Learning9 5ExperimentsThis section brieﬂy reports experimental results illustrating the actual per-formance of stochastic gradient algorithms on a variety of linear systems. We use gainsγt=γ0(1+λγ0t)−1for SGD and,following(Xu,2010),γt=γ0(1+λγ0t)−0.75for ASGD.The initial gainsγ0were set manually by observing the performance of each algorithm running on a subset of the training examples.Figure1reports results achieved using SGD for a linear SVM trained for the recognition of the CCAT category in the RCV1dataset(Lewis et al.,2004)using both the hinge loss(Q svm in table1),and the log loss, (Q logsvm=λw2+log(1+exp(−y w Φ(x)))).The training set contains781,265 documents represented by47,152relatively sparse TF/IDF features.SGD runs considerably faster than either the standard SVM solvers SVMLight and SVMPerf(Joachims,2006)or the superlinear optimization algorithm TRON(Lin et al.,2007).Figure2reports results achieved using SGD,SGDQN,and ASGD for a linear SVM trained on the ALPHA task of the2008Pascal Large Scale Learning Challenge(see Bordes et al.,2009)using the squared hinge loss (Q sqsvm=λw2+max{0,1−y w Φ(x)}2).The training set contains100,000 patterns represented by500centered and normalized variables.Performances measured on a separate testing set are plotted against the number of passes over the training set.ASGD achieves near optimal results after one pass.Figure3reports results achieved using SGD,SGDQN,and ASGD for a CRF(Laﬀerty et al.,2001)trained on the CONLL2000Chunking task (Tjong Kim Sang and Buchholz,2000).The training set contains8936sen-tences for a1.68×106dimensional parameter space.Performances measured on a separate testing set are plotted against the number of passes over the training set.SGDQN appears more attractive because ASGD does not reach its asymptotic performance.All three algorithms reach the best test set per-formance in a couple minutes.The standard CRF L-BFGS optimizer takes 72minutes to compute an equivalent solution.ReferencesBORDES.A.,BOTTOU,L.,and GALLINARI,P.(2009):SGD-QN:Careful Quasi-Newton Stochastic Gradient Descent.Journal of Machine Learning Research, 10:1737-1754.With Erratum(to appear).BOTTOU,L.and BOUSQUET,O.(2008):The Tradeoﬀs of Large Scale Learning, In Advances in Neural Information Processing Systems,vol.20,161-168. BOTTOU,L.and LECUN,Y.(2004):On-line Learning for Very Large Datasets.Applied Stochastic Models in Business and Industry,21(2):137-151 BOUSQUET,O.(2002):Concentration Inequalities and Empirical Processes The-ory Applied to the Analysis of Learning Algorithms.Th`e se de doctorat,Ecole Polytechnique,Palaiseau,France.10L´e on BottouCORTES, C.and VAPNIK,V.N.(1995):Support Vector Networks,Machine Learning,20:273-297.DENNIS,J.E.,Jr.,and SCHNABEL,R.B.(1983):Numerical Methods For Un-constrained Optimization and Nonlinear Equations.Prentice-Hall JOACHIMS,T.(2006):Training Linear SVMs in Linear Time.In Proceedings of the12th ACM SIGKDD,ACM Press.LAFFERTY,J.D.,MCCALLUM,A.,and PEREIRA,F.(2001):Conditional Ran-dom Fields:Probabilistic Models for Segmenting and Labeling Sequence Data.In Proceedings of ICML2001,282-289,Morgan Kaufman.LEE,W.S.,BARTLETT,P.L.,and WILLIAMSON,R.C.(1998):The Importance of Convexity in Learning with Squared Loss.IEEE Transactions on Informa-tion Theory,44(5):1974-1980.LEWIS,D.D.,YANG,Y.,ROSE,T.G.,and LI,F.(2004):RCV1:A New Bench-mark Collection for Text Categorization Research.Journal of Machine Learn-ing Research,5:361-397.LIN,C.J.,WENG,R.C.,and KEERTHI,S.S.(2007):Trust region Newton methods for large-scale logistic regression.In Proceedings of ICML2007,561-568,ACM Press.MACQUEEN,J.(1967):Some Methods for Classiﬁcation and Analysis of Multi-variate Observations.In Fifth Berkeley Symposium on Mathematics,Statistics, and Probabilities,vol.1,281-297,University of California Press. MASSART,P.(2000):Some applications of concentration inequalities to Statistics, Annales de la Facult´e des Sciences de Toulouse,series6,9,(2):245-303. MURATA,N.(1998):A Statistical Study of On-line Learning.In Online Learning and Neural Networks,Cambridge University Press.POLYAK,B.T.and JUDITSKY,A.B.(1992):Acceleration of stochastic approx-imation by averaging.SIAM J.Control and Optimization,30(4):838-855. ROSENBLATT,F.(1957):The Perceptron:A perceiving and recognizing automa-ton.Technical Report85-460-1,Project PARA,Cornell Aeronautical Lab. RUMELHART,D.E.,HINTON,G.E.,and WILLIAMS,R.J.(1986):Learning internal representations by error propagation.In Parallel distributed processing: Explorations in the microstructure of cognition,vol.I,318-362,Bradford Books. SHALEV-SHWARTZ,S.and SREBRO,N.(2008):SVM optimization:inverse de-pendence on training set size.In Proceedings of the ICML2008,928-935,ACM. TIBSHIRANI,R.(1996):Regression shrinkage and selection via the Lasso.Journal of the Royal Statistical Society,Series B,58(1):267-288.TJONG KIM SANG E. F.,and BUCHHOLZ,S.(2000):Introduction to the CoNLL-2000Shared Task:Chunking.In Proceedings of CoNLL-2000,127-132. TSYBAKOV,A.B.(2004):Optimal aggregation of classiﬁers in statistical learning, Annals of Statististics,32(1).VAPNIK,V.N.and CHERVONENKIS,A.YA.(1971):On the Uniform Con-vergence of Relative Frequencies of Events to Their Probabilities.Theory of Probability and its Applications,16(2):264-280.WIDROW, B.and HOFF,M. E.(1960):Adaptive switching circuits.IRE WESCON Conv.Record,Part4.,96-104.XU,W.(2010):Towards Optimal One Pass Large Scale Learning with Averaged Stochastic Gradient Descent.Journal of Machine Learning Research(to ap-pear).。

高低转速下频闪式转速表的校准

高低转連下频闪式转連表的枝准席勇辉(昆明船舶设备研究试验中心，昆明650051)摘要：随着仪器技术的发展，现有计量技术规范中提供的转速表计量方法有一定局限性，特别是在大量程和高精度频闪式转速表的校准方面。

通过对频闪法测转速基本原理的分析，该文阐述了一种能够适应大量程和高精度频闪式转速表的校准方法。

该方法通过设置合理的频闪像数量和停留序数，实现对大量程频闪式转速表的校准，满足测量准确度要求，同时分别从低转速和高转速范围2种情况对校准方法以及主要不确定度分量作了分析论述，并结合具体实例对示值误差的测量不确定度进行了计算。

关键词：频闪式转速表;低转速；高转速;读数误差；校准中图分类号:TM930.8 文献标识码：A文章编号#1000 -0682(2020)03 -0079 -04T h e c a lib ra tio n o f th e stro b o sco p ic ta c h o m e te r fo r h ij^h a n d lo w speedXI Yonghui(K u n m in g S h ip B o rn e E q u ip m e n t R e se a rc h a n d T est C e n tr e,K u n m in g650051, C h in a)Abstract&With the development 〇[the instrument technology,the tachometer measurement methodprovided in the e xisting measurement technical specification has some limitations，especially in the calibration of tlie large- range and high- precision strobo- type tachometer.Based on the basic principle of the stroboscopic tachometer，a calibration method for the stroboscopic tachometer withlarge range and high precision is described.This method can calibrate the large range stroboscopic tachometer witli satisfactory accuracy，by setting the reasonable number of stroboscopic images and stokes.The calibration method and m ain uncertainty component of the measurement were discussed in the aspectsof low- speed and high- speed ranges，and the uncertainty introduced by human reading error ed for a practical example.Keywords&stroboscopic tachometer+lowspeed+high speed+reading error+calibration〇引言频闪式转速表是基于频闪效应原理测量旋转物体转速的仪器，又称频闪仪[1]。

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USP 干燥失重法中英文对照

<731>LOSS ON DRYINGThe procedure set forth in this chapter determines the amount of volatile matter of any kind that is driven off under the conditions specified.For substances appearing to contain water as the only volatile constituent, the procedure given in the chapter,Water Determination921,is appropriate,and is specified in the individual monograph.Mix and accurately weigh the substance to be tested,and,unless otherwise directed in the individual monograph,conduct the determination on1to 2g.If the test specimen is in the form of large crystals,reduce the particle size to about2mm by quickly crushing.Tare a glass-stoppered, shallow weighing bottle that has been dried for30minutes under the same conditions to be employed in the determination.Put the test specimen in the bottle,replace the cover,and accurately weigh the bottle and the contents.By gentle,sidewise shaking,distribute the test specimen as evenly as practicable to a depth of about5mm generally,and not more than10mm in the case of bulky materials.Place the loaded bottle in the drying chamber,removing the stopper and leaving it also in the chamber. Dry the test specimen at the temperature and for the time specified in the monograph.[NOTE—The temperature specified in the monograph is to be regarded as being within the range of±2of the stated figure.]Upon opening the chamber,close the bottle promptly,and allow it to come to room temperature in a desiccator before weighing.If the substance melts at a lower temperature than that specified for the determination of Loss on drying,maintain the bottle with its contents for1to2hours at a temperature5to10below the melting temperature, then dry at the specified temperature.Where the specimen under test is Capsules,use a portion of the mixed contents of not fewer than4capsules.Where the specimen under test is Tablets,use powder from not fewer than 4tablets ground to a fine powder.Where the individual monograph directs that loss on drying be determined by thermogravimetric analysis,a sensitive electrobalance is to be used.Where drying in vacuum over a desiccant is directed in the individual monograph,a vacuum desiccator or a vacuum drying pistol,or other suitable vacuum drying apparatus,is to be used.Where drying in a desiccator is specified,exercise particular care to ensure that the desiccant is kept fully effective by frequent replacement.Where drying in a capillary-stoppered bottle*in vacuum is directed in the individual monograph,use a bottle or tube fitted with a stopper having a225±25µm diameter capillary,and maintain the heating chamber at a pressure of5mm or less of mercury.At the end of the heating period, admit dry air to the heating chamber,remove the bottle,and with the capillary stopper still in place allow it to cool in a desiccator before weighing.本章中给出的方法阐述了在特定的条件下物质中的挥发性成分的测定。

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Large-scale Monitoring and Provisioning Systems

MOBILITY AND COMPLETENESS IN PUBLISH/SUBSCRIBE TOPOLOGIESSasu Tarkoma and Jaakko KangasharjuHelsinki Institute for Information TechnologyP.O.Box9800,FIN-02015HUT,Finlandemail:{sasu.tarkoma,jaakko.kangasharju}@hiit.ﬁABSTRACTThe event paradigm and publish/subscribe systems allow clients to asynchronously receive information that matches their interests.The requirements of mobile computing present new challenges pertaining to event delivery that need to be solved.In this paper,we formally examine sev-eral state transfer protocols for different pub/sub topolo-gies.The new results of this paper are the cost functions for both subscriber and publisher mobility,and investigation and formulation of completeness of subscriptions and ad-vertisements.The results show that rendezvous points are good for pub/sub mobility,handovers in incomplete topolo-gies are more costly than in complete,and the brokers in-volved with mobility have no way of detecting complete-ness based on local information alone.KEY WORDSMobile Computing,Content Distribution Networking, Large-scale Monitoring and Provisioning Systems1IntroductionTwo important middleware services are event monitoring and event notiﬁcation.Environment monitoring and notiﬁ-cation are usually provided by the event or notiﬁcation ser-vice,which allows software components to communicate asynchronously[1].In this paper,we focus on content-based routing in which event brokers forward notiﬁcations based on a routing conﬁguration established by advertise-ment and subscription messages.Most research on event systems has focused on event dissemination in theﬁxed-network,where clients are usually stationary and have re-liable,low-latency,and high bandwidth communication links.Recently,mobility and wireless communication have become an active topic in many research projects working with event systems,such as Siena[2]and Rebeca[3].In subscription semantics subscription messages are propagated throughout the pub/sub network and notiﬁca-tions are sent on the reverse path of subscriptions.Ad-vertisement semantics extends this model byﬂooding ad-vertisements throughout the network and propagating sub-scriptions on the reverse path of advertisement messages. Content-based routing and advertisement semantics was in-vestigated in the Siena project,and most current event sys-tems use advertisements,for example Hermes[8]and Re-beca,because they improve scalability.Techniques such as covering relations-based optimization andﬁlter merging are used to reduce the size of routing tables at servers.Aﬁl-ter F1is said to cover anotherﬁlter F2when F1matches all the notiﬁcations matched by F2.Filter merging is a tech-nique for combining twoﬁlters to aﬁlter that is equivalent to the disjunction of the inputﬁlters.In content-based rout-ing servers typically propagate either non-coveredﬁlters or mergedﬁlters to minimize the size of routing tables.In advertisement-based pub/sub networks a succesful activation of a subscription may require that an advertise-ment isﬁrst propagated through the network,and then a connecting subscription is propagated on the reverse path to the source.These mechanisms become challenging when the topology needs to be reconﬁgured with the introduction of mobile components.In this paper,we follow the general notiﬁcation data model:a notiﬁcation is a set of3-tuples <name,type,value>.Aﬁlter is a set of constraints on notiﬁcations.We assume that the pub/system follows the weakly valid routing conﬁguration[4],which means that all up-dates will eventuallyﬁnish and notiﬁcations will match all subscriptions that are terminated.In this paper,we call such update procedures that have ended succesfully com-plete in the topology,and use completeness to characterize the properties of pub/sub mobility.Deﬁnition1An advertisement A is complete in a pub/sub system P S iff there does not exist a broker s with an over-lapping subscription that has not processed A.Similarly,a subscription S is complete in P S iff there does not exist a broker s such that s has an an advertisement that overlaps with S and S is not active on s.In this model false negatives that occur during topol-ogy reconﬁguration caused by stationary components are tolerated.A false negative is a notiﬁcation that is pub-lished,but not delivered to a client with an active subscrip-tion that matches the event.Based on this notion,we deﬁne a mobility-safe pub/sub system as follows:Deﬁnition2A pub/sub system is mobility-safe if starting from an initial conﬁguration C0at time T0and ending in a ﬁnal conﬁguration C e at time T e handovers will not cause any false negatives.We also relax Deﬁnition2by not considering server failures or by assuming that faults may be masked.Falsepositives may be removed by using event identiﬁers so they are not considered.In distributed pub/sub systems it is ev-ident that after issuing a subscription it may take several hops before the subscription is activated for all publish-ers.During this time several notiﬁcations may be missed. In our mobility-aware weakly valid routing conﬁguration false negatives that occur during topology reconﬁguration caused by subscriptions and advertisements from station-ary components are tolerated.In our subsequent examina-tion we do not count these notiﬁcations as false negatives. Mobile clients change the scenario,because theﬂow end-points are mobile and brokers transfer end-points using a handover process.False negatives that occur during mo-bility are not tolerated.In subsequent examination,terms complete and incomplete refer to the completeness and in-completeness of the subscriptions and advertisements in-volved in mobility.In this paper,we formally examine a state transfer protocol for acyclic pub/sub networks based on advertise-ment semantics.The new results of this paper are: 1. establishing the communication cost of pub/sub mobility, paring three pub/sub mobility mechanisms and topologies:generic mobility support,acyclic graphs,and rendezvous-based topologies.Due to brevity,we do not present mobility-safety proofs for the mobility protocols for complete topologies.It is evident that once the topology is complete it is possible to construct an efﬁcient mobil-ity protocol.This motivates this investigation of different pub/sub topologies.The main motivation for a pub/sub mo-bility protocol is the avoidance of triangle routing through a designated home broker,which may be inefﬁcient.Experi-mental results show that home broker based approaches do not perform well[5,6].Mobility protocols are also needed for load balancing subscribers and advertisers between bro-kers.The rest of the paper is organized as follows.Sec-tion2presents a generic pub/sub mobility protocol,in Sec-tion3we examine subscriber and publisher mobility in networks based on acyclic graphs.Section4examines rendezvous-based pub/sub.Finally,Section5presents the conclusions.2Generic Mobility SupportThe Siena event system was extended with generic mobility support,which uses existing pub/sub primitives: publish and subscribe[2].The beneﬁt of a generic protocol is that it may work on top of various pub/sub systems and requires no changes to the system API.On the other hand, the performance of the mobility support decreases,because mobility speciﬁc optimizations are difﬁcult to realize when the underlying topology is hidden by the APIs.Indeed,in this section we show that a general API-based pub/sub mo-bility support may have a very high cost in terms of mes-sage exchanges.The use of advertisement semantics was not discussed for the Siena mobility support service so we extend the generic model to cover also advertisements.The mobility protocol proceeds in four distinct phases:ﬁrst,the target subscribes all events,then the target and source synchronize by sending ping and pong events in order to ensure that the subscriptions have taken effect, the source unsubscribes,andﬁnally the events are relocated and merged.In addition,there may be further costs trig-gered by changes in the subscription tables of the interme-diate routers.Let N denote the number of brokers in the network and n the number of brokers between the source and target of mobility.The cost structure for this procedure is presented in Table1as the number of brokers that will be updated during each phase.For advertisement semantics we assume that the publication of a ping message includes also the advertisement.The unsubscription cost depends also on other active subscriptions on the servers and is a worst-case estimate.For subscription semantics the basic problem with the ping-based synchronization protocol is that the ping mes-sage is guaranteed not to be subscribed by any other bro-ker on the network and hence the ping subscription mes-sage will be introduced at every broker on the network.If uniqueness is not guaranteed simultaneous mobility by dif-ferent clients becomes impossible.If the client relocates faster than the ping message is propagated it has to wait un-til the target receives the ping subscription.This requires that the pub/sub API allows to query subscription status of the broker.The Siena support service does not require API support,because the ping/pong messages are continuously resent[2],but this kind of behaviour further burdens the network.The ping is published by the target along with the pong subscription and they will reach the source,which replies with the pong event.It is clear that when the pong reaches the target the subscription is established between the source and target.Advertisement semantics presents several problems for mobility,because the ping and pong messages need to be advertised before they may be subscribed.The source advertises pong and subscribes ping,whereas the target ad-vertises ping and subscribes pong.This is problematic be-cause the advertisement from source needsﬁrst to reach the target before target’s subscription starts to propagate on the reverse path.We envisage that this kind of oscilla-tion may be avoided by using virtual advertisements for the ping/pong messages so that they are propagated using sub-scription semantics.Another solution is to bundle the ad-vertisement and notiﬁcation into one,which we have pro-posed previously[5].The pub/sub API needs to support either solution.Publisher mobility for subscription semantics does not require any changes,but it is supported directly by the pub/sub system.Publisher mobility for advertisement se-mantics follows the ping/pong model and has a similar cost structure.Table1.Cost structure for generic mobilityPhase Sub semantics Adv semantics Source:Subsc.Ping(id)N-Target:Subsc.Filter0≤x≤N0≤x≤N Target:Subsc.Pong(id)N-Target:Pub.Ping(id)n NSource:Pub.Pong(id)n NSource:Unsub.Ping(id)N nTarget:Unsub.Pong(id)N nTarget:Unadv.Ping(id)-NSource:Unadv.Pong(id)-N3Acyclic Graphs with Advertisements3.1OverviewAn outline of the protocol we describe was presented in[3,7]with mobility restricted between border brokers.A mobility protocol for a hierarchical routing topology with more assumptions was examined in[6].Formally,the net-work of application-level event brokers is an undirected acyclic graph G=(E,V),where E is the set of edges and V is the set of vertices of the graph.We are interested inﬁnding the theoretical cost for the handover protocol in terms of message exchanges.Some systems allow mobility only between border-brokers,the leaves of the routing tree, which limits mobility.We allow clients to roam between any two brokers.In subsequent examination we assume that the servers use reliable communication mechanism,G is connected, and messages are delivered in order.We assume that clients know the subscriptions and the address of the origin server (for direct communication).Some handover protocols use pub/sub routing toﬁnd the origin server;however,this ap-proach may require the use ofﬂooding toﬁnd the origin server,for example in scenarios where the relocated sub-scriptions are not advertised.We also assume that buffered events are delivered out-side the event routing framework,since they have already been routed and it is not efﬁcient to reroute them.Also,by transferring the notiﬁcations in one compressed message the overhead may be reduced considerably.In some ex-isting systems buffered events are delivered using the event routing system.While this approach adheres to the pub/sub communication,it has been shown that this cost dominates the pub/sub signalling cost[6]in mobility scenarios.We consider the number of exchanged messages,because up-date processing and propagation causes the most stress for the pub/sub system.3.2Mobile SubscribersFigure1presents an overview of the subscription handover both for complete and incomplete topologies.Prior to the handover a set of brokers have advertised the events that are being relocated.Handover is performed between two brokers in the network:a,b∈V.The handover starts when b receives a message,typically from the client,that a set of subscriptions S should be relocated from a to b. Now,b may optimize the operation if S has been already subscribed by b.In this case b simply starts to buffer no-tiﬁcations for S and retrieves the notiﬁcations buffered at a for the client.If the optimization cannot be applied,b issues a subscription message,which is propagated by the event system.The subscription message must include those parts that are not covered by existing subscriptions.Complete SubscriptionTopologyIncomplete SubscriptionTopologyComplete AdvertisementTopologyIncomplete Advertisement Topology Figure1.Subscription handover with a complete and in-complete topology.Colored nodes represent the inactive path.up-date b2.a’s3.M anda maycase the procedure is similar,but the subscription update message may be sent to several directions as depicted in the1.phase of theﬁgure.In2.subscriptions from a and b meet and the meeting point,M,notiﬁes a in3.It is clear that all subscriptions contained in S must be covered at M.We view a path as consisting of the edges on the path, since that makes it more convenient to handle split paths. An edge between a and b is called active with respect to S if S has been sent on that edge.A path is active if all of its edges are active.An inactive path is one that is not active, i.e.contains at least one inactive edge.We know that a and b are connected since G is con-nected.Also the path between a and b is unique,since G is acyclic.If the covering optimization is not applicable we know that S is not active on all edges on the path from a to b.Let S a be the set of active edges on the path,and S i theset of inactive edges on the path.Proposition1states that active and inactive paths meet at node M.The topology update cost is the cost of updating S i.Proposition1There exists a node M on the path from a to b such that the path from a to M consists of exactly the edges in S a(and then S i is the path from b to M).Given that there are simultaneous unadvertisements Proposition1is not necessarily valid.Consider a scenario in which during the handover of a subscriber the subscribed advertisement is removed from the system.In this case,M may not exist or may disappear during the handover.The propagation of the update message from b will reach nei-ther a nor M.The protocol must be able to cope with this and signal to a that the update is complete.Simultaneous advertisements do not cause such a problem.It also fol-lows for complete topologies that if an update is required it is sent by b to exactly one output interface.If this were not the case there would be a publisher on an interface not con-nected with the subscriptions from a,which would violate the assumption that the topology is complete.When S reaches M the subscription has taken effect. After this a may unsubscribe S if necessary.M can do that for a,but since the a’s state may have changed after the update was sent by b,M contacts a.The problem with covering and merging is that M does not know the exact interface from which a is reachable.Therefore M needs to forward the completion message to all interfaces that have covering subscriptions.In essence,this is content-based ﬂooding.Now,this phase may be optimized in complete topologies by allowing M to directly contact a,which is feasible since the topology has already been updated for the path from a to b.After this a may unsubscribe if necessary.3.2.1Communication CostAssuming completeness,the total cost for the mobility in terms of exchanged messages for the subgraph deﬁned by the path from a to b is|S i|messages for the path,one mes-sage from M to a,the cost of transferring the buffered events,and then the cost of unsubscription C unsub.The worst case size of S i is n−1,where n is the number of brokers in the routing topology.Therefore for the com-plete topology the update cost for subscriptions is at most n+C unsub.If S is already covered at b then the cost is 1+C unsub.3.2.2Handovers on Incomplete TopologyIt may also be the case that the set of subscriptions,S,is still being propagated and the subscription path is not to-tally active at the time of the handover.This happens when the handover happens while the system propagates and pro-cesses subscription messages or update messages.This kind of behaviour may occur because the handover is trig-gered by out-of-band mechanisms,for example by terminal mobility.If mobility is activated by sending a message us-ing the pub/sub system this problem may be avoided.Protocols that forward the update message to inter-faces that have overlapping advertisements work in this scenario.Clearly,a does not know when the topology is complete.Node b may detect the local incompleteness of the subgraph deﬁned by the path from a to b;however,b cannot detect the completeness of the subgraph based on lo-cal information.For example,consider the scenario where there is one broker between a and b that has not yet pro-cessed the subscription from a and S is covered at b.Now, since S is covered at b,b will ask a to send the session even-though the subscriptions may not be complete on the path at the time.This incompleteness of the path means that the handover is not necessarily mobility-safe.This may be solved by synchronizing a and b using a message passed through the path.The update message is needed even when S is covered at b and requires at least|S a∪S i|messages. The problem is that b does not know where a is located so the update isﬂooded on the reverse-path of covering sub-scriptions.Incompleteness may also causeﬂooding when S is not covered at b and the protocol needs to cope with the existence of multiple meeting points M.3.3Mobile PublishersRelated work has typically considered only the protocol for relocating subscriptions.Since it is probable that subscrip-tions are relocated more often this is reasonable.The prob-lem with mobile publishers is that advertisements are prop-agated throughout the routing network.This means that the removal of an advertisement may have a high cost.We follow a similar approach as with mobile subscribers.The protocol proceeds in four phases:1.b sends an update mes-sage towards a and overlapping subscriptions are sent to-wards b,2.Existing advertisements and subscriptions meet the advertisement sent by b and a is notiﬁed by M that the topology has been updated.3.a sends an update message to b to ensure completeness.Finally,4.a unadvertises if necessary.If we assume that the advertisement topology is com-plete weﬁnd that the set A of advertisements to be relo-cated from a to b is already advertised to b.The advertise-ment may be more general due to covering and merging. The problem is that the advertisements point to a,which needs to be changed.We have the two paths,the active path A a,and the inactive path A i and M at their inter-section.If there are no publishers that advertise covering advertisements on the path A a∪A i it follows that A a=∅.When b receives A,it does not need to propagate A to those interfaces where A has already been forwarded. Those parts of the routing network are already updated.If all interfaces advertise A at b then the handover is com-plete.If all interfaces do not advertise A at b,they need to be updated.If there are more than one interface that does not advertise a set of advertisements that covers A then the topology is incomplete.(The one is the interface that re-ceived the advertisement).By deﬁnition each router adver-tises a received advertisement to all other interfaces.Now,b sends the update message to all interfaces that do not cover A and advertises A from b.This means that subscriptions on are hop-by-hop connected with b.Here we have the inactive path S i towards a,which is the path from b to subscribers that are not yet connected.In order to avoid false negatives a and b must wait that the subscrip-tions are connected.In order to avoid false negatives,a sends a ping message to b to indicate when the subscrip-tions on the path have been updated.For complete topolo-gies the ping message can be sent from M,if completeness cannot be assumed it is sent by a.In some cases,subscribers are already connected af-ter theﬁrst advertisement update sent by b.Since b does not know if there are other subscriptions that overlap with A later in the path,the whole path from b to a needs to be checked.It is important that the protocol is ended properly in order to ensure that published events are properly dis-seminated to subscribers,and that the next handover may be started from a complete conﬁguration.If the advertisements are not successfully terminated in G the publisher handover protocol ensures that upon completion of the handover the subgraph deﬁned by the path from a to b is complete for both advertisements and subscriptions.In this case,it may be necessary to useﬂood-ing toﬁnd M and a.3.3.1Communication CostThe total cost for the mobility in terms of exchanged mes-sages for the subgraph deﬁned by the path from a to b is|A i|messages for the advertisement update.The sub-scription update requires at least|S i|for the ping mes-sage.One message is needed to notify a that the sub-scriptions are complete.This happens after b receives the ping message.Finally,we have the cost of unadvertisement C unadv.Assuming completeness this gives the total cost of 1+|A i|+|S i|+C unadv.The worst case size for both A i and S i is n−1,where n is the number of brokers in the routing topology.Therefore the handover cost for relocat-ing advertisements from a to b is at most2n−1+C unadv. If A is already covered at b then the cost is1+C unadv.4Rendezvous-Point ModelsHermes is peer-to-peer event system based on an overlay called Pan that supports a variant of the advertisement se-mantics.Systems such as Hermes[8]leverage the fea-tures of the underlying overlay system for message rout-ing,scalability,and improved fault-tolerance.Hermes sup-ports the basic pub/sub operations introduced previously. Each eventﬂow is rooted at a designated server,the Ren-dezvous Point(RP),and messages are propagated toward that node.The RP manages the event type and Hermes supports chaining RPs into type hierarchies.In general,the RP of an event type is obtained by hashing the event type to theﬂat addressing space of the overlay.Most current overlays are based onﬂat addressing spaces.This means that rendezvous points are uniformly distributed over the addressing space[8].Figure2illustrates RP-based notiﬁcation: 1.Pub-lisher advertises an event type with aﬁlter,2.Advertise-ment is forwarded to the RP,3.Subscriber subscribes an event of the same type with aﬁlter,4.The subscription message is not covered at any intermediate broker and for-warded to the RP,5.Another subscriber subscribes,6. Subscription is forwarded to the RP.After step6.in the type/attribute-based routing supported by Hermes,the RP sends the subscriptions on the reverse path of advertise-ments.Any events conforming to the advertisement from the publisher are sent on the reverse path of subscriptions.The model is the advertisement semantics model with three key differences.First,all subs/advs are sent to-wards the RP.Thus routing topology is constrained by the RP.Second,advertisements are introduced only on the path from the advertiser to RP.Third,subscriptions are introduced on the path from the subscriber to RP and on any nodes with overlapping advertisements.These differ-ences are interesting,because advertisement becomes a lo-cal property of a branch of the multicast tree rooted at RP. This may modelled using virtual advertisements:a RP has virtual advertisements for all events of the event type man-aged by the RP and hence subscriptions are sent towards it.In the following examination we assume that the over-lay topology is static—a dynamic topology requires more complex investigation.Figure2.Example of the Hermes model4.1IncompletenessThe RP may be used to guarantee completeness of adver-tisements and subscriptions by requiring an acknowledge-ment from the RP.We propose to solve the problems posed by incomplete topologies using two mechanisms:•RP completeness checking both at the origin and des-tination of mobility.•Preventing content-basedﬂooding using the overlay-address,which allows to determine in which direc-tion a node is located.This property may also be used to prevent the content-basedﬂooding at M when forwarding the mobility update messages within the event topology.The problems of incompleteness with the regular sub/adv semantics can be avoided with the RP model by ensuring that each subscription and advertisement is com-plete to RP.This incurs additional cost,but the number of acknowledgement messages may be minimized by push-ing the acknowledgement generation away from the RP to nodes that have covering subscriptions that are complete to RP.The two central problems that are solved are:false neg-atives due to incompleteness of the path and a ping between source and destination is not needed,and by using the over-lay address to locate the source content-basedﬂooding does not need to be used.4.2Communication CostThe RP completeness simpliﬁes subscriber and producer mobility protocols and the communication costs.Within one branch the update message from b to a eventually meets the subscription from a to RP.Between branches the cost is the distance from b to the RP.Hence,the worst-case cost for topology update if RP completeness is assumed is given by RP max,where RP max is the maximum number of nodes between any node and a RP.One message is needed to no-tify a and one is needed to transfer buffered events.The case when a relocated subscription is covered is handled as before.Producer mobility is also simpler than before and for a new branch it is sufﬁcient to synchronize b with the RP or RPs in question.Although RPs are good for mobility,the cost of a han-dover grows with the number of RP updates for cyclic over-lay routing.Rendezvous points models with acyclic over-lay routing have the simplifying features mentioned above and the upper bound cost cannot be greater than for the general acyclic graphs.5ConclusionsIn this paper,we examined the cost of pub/sub mobility using three mobility mechanisms and topologies:generic mobility support,acyclic graphs,and rendezvous-based topologies.We also discussed the impact of completeness and incompleteness of the pub/sub topology on the cost of mobility.The generic mechanism has a high cost for mobil-ity.The other two mobility mechanisms have considerably smaller cost.If an acyclic graph-based routing topology is incom-plete content-basedﬂooding may or must be used to com-plete the handover succesfully.This means that the op-timizations discussed for complete topologies may not be applied for incomplete topologies.Since it is not possible to detect completeness and many systems are inherently in-complete,the optimizations that avoid content-basedﬂood-ing may not be applied in practise.Mobility-safety cannot be guaranteed if protocols engineered with the complete-ness assumption are used for incomplete topologies.Rendezvous point-based topologies were identiﬁed to be good for pub/sub mobility support,because they may be extended to guarantee the completeness of subscriptions and advertisements.In addition,the RP models with adver-tisements do not require theﬂooding of the whole network with advertisement messages.References[1]P.Eugster,P.Felber,R.Guerraoui,andA.Kermarrec,The many faces of pub-lish/subscribe,ACM Computing Surveys,(2):114–131,2003.[2]M.Caporuscio, A.Carzaniga,and A.L.Wolf,An experience in evaluating pub-lish/subscribe services in a wireles network,In Third International Workshop on Softwareand Performance,Rome,Italy,July2002. [3] A.Zeidler and L.Fiege,Mobility supportwith Rebeca,In Proceedings of the ICDCSWorkshop on Mobile Computing Middleware,2003.[4]G.M¨u hl,Large-scale content-based pub-lish/subscribe systems,Ph.D.thesis,Univer-sity of Darmstadt,2002.[5]S.Tarkoma,J.Kangasharju,andK.Raatikainen,Client mobility inrendezvous-notify,In Intl.Workshop on Dis-tributed Event-Based Systems(DEBS’03),2003.[6]I.Burcea,H-A.Jacobsen, E.de Lara,V.Muthusamy,and M.Petrovic,Disconnectedoperation in publish/subscribe middleware,In IEEE International Conference on MobileData Management,2004.[7]G.M¨u hl,A.Ulbrich,K.Herrmann,and T.Weis,Disseminating information to mobileclients using publish/subscribe,IEEE Inter-net Computing,pages46–53,May2004. [8]P.Pietzuch,Hermes:A Scalable Event-BasedMiddleware,Ph.D.thesis,Computer Labo-ratory,Queens’College,University of Cam-bridge,February2004.。

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Large-Scale Preparation of Ordered Titania Nanorods with Enhanced Photocatalytic ActivityJin-Ming Wu*and Tian-Wei ZhangDepartment of Materials Science&Engineering,Zhejiang University,Hangzhou310027,ChinaYue-Wu ZengAnalytical&Measurement Center of Zhejiang University,Xixi Campus,Hangzhou310028,ChinaSatoshi Hayakawa,†Kanji Tsuru,†,‡and Akiyoshi Osaka†,‡Faculty of Engineering and Research Center for Biomedical Engineering,Okayama University,Tsushima,Okayama-shi,700-8530,JapanReceived January5,2005.In Final Form:May8,2005A titania layer with ordered nanostructures is expected to be of high photocatalytic activity due mainly to its high specific surface area.In the present work,large-area films with ordered titania nanorods were deposited on titanium substrates through a solution approach.The nanorods,with the phase composition of a mixture of anatase and rutile,grew on top of a condensed anatase interlayer along mainly the rutile [001]-axis.The photocatalytic activity was evaluated by decomposing rhodamineB in water and compared with the general sol-gel derived titania films and a commercial DP-25titania coating.It is found that the as-deposited titania nanorods exhibited extremely high initial photocatalytic activity but declined to a poor value after the consumption of beneficial oxidative peroxo complexes coordinated to Ti(IV).A subsequent thermal treatment eliminated such complexes but at the same time improved the crystallinity of the titania nanorods.The photocatalytic activity of the thermally treated titania nanorods was stable and significantly higher than that of the sol-gel derived film and commercial DP-25coating.IntroductionEver since the discovery of the photocatalytic splitting of water on titania electrodes by Fujishima and Honda in 1972,1numerous papers have appeared on titania as a photocatalyst to degrade trace organics in water.2-11The photodegradation process involves ultraviolet(UV)light to excite an electron from the valence band of titania to its conduction band,leaving a hole to oxidize organics in water directly or indirectly.This approach wins an advantage over traditional wastewater treatment tech-niques due to its characteristics of economical,nontoxic, nonselectivity,and high chemical stability.2,3Unfortu-nately,the industrial application is limited to date due mainly to the scarcity of a low-cost technique to prepare titania with satisfactory photocatalytic activity(PA), although numerous efforts have been made either to explore novel preparation methods3,5or to improve the PA through surface modifications such as metal elements embedding,6-8nonmetal elements doping,9,10and surface sensitizing,11etc.Titania films with ordered nanostructures have aroused great interest due to their potential uses in sensors, catalysts,and some device applications.12-18However, most of the approaches involve either templates or annoying reagents and processes.Low-cost preparation of large-area films with ordered nanostructures still remains a challenge,and reports on the PA of such films are very scarce.Wu et al.have focused on the low-temperature deposition of crystalline titania films through direct oxidizing Ti with hydrogen peroxide,an oxidant*Corresponding author.Phone:+86-571-87953115.Fax:+86-571-87952358.E-mail:msewjm@.†Faculty of Engineering,Okayama University.‡Research Center for Biomedical Engineering,Okayama Unviersity.(1)Fujishima,A.;Honda,K.Nature1972,37,238.(2)Linsebigler,A.L.;Lu,G.Q.;Yates,J.T.,Jr.Chem.Rev.1995, 95,735.(3)Hoffmann,M.R.;Martin,S.T.;Choi,W.Y.;Bahnemannt,D.W. Chem.Rev.1995,95,69.(4)Matsumoto,Y.;Ishikawa,Y.;Nishida,M.;Ii,S.J.Phys.Chem. B2000,104,4204.(5)Peiro´,A.M.;Peral,J.;Domingo,C.;Dome`nech,X.;Ayllo´n,J.A. Chem.Mater.2001,13,2567.(6)Sakthivel,S.;Shankar,M.V.;Palanichamy,M.;Arabindoo,B.; Bahnemann,D.W.;Murugesan,V.Water Res.2004,38,3001.(7)Zhang,Y.H.;Ebbinghaus,S.G.;Weidenkaff,A.;Kurz,T.;Nidda,H.A.K.;Klar,P.J.;Gu¨ngerich,M.;Reller,A.Chem.Mater.2003,15, 4028.(8)Subramanian,V.;Wolf,E.E.;Kamat,P.V.J.Am.Chem.Soc. 2004,126,4943.(9)Asahi,R.;Morikawa,T.;Ohwaki,T.;Aoki,K.;Taga,Y.Science 2001,293,269.(10)Khan,S.U.M.;Al-Shahry,M.;Ingler W.B.,Jr.Science2002, 297,2243.(11)Nazeeruddin,M.K.;Pe´chy,P.;Renouard,T.;Zakeeruddin,S. M.;Baker,R.H.;Comte,P.;Liska,P.;Cevey,L.;Costa,E.;Shklover, V.;Spiccia,L.;Deacon,G.B.;Bignozzi,C.A.;Gra¨tzel,M.J.Am.Chem. Soc.2001,123,1613.(12)Varghese,O.K.;Gong,D.;Paulose,M.;Ong,K.G.;Dickey,E.C.;Grimes,C.A.Adv.Mater.2003,15,624.(13)Tian,Z.R.;Voigt,J.A.;Liu,J.;Mckenzie,B.;Xu,H.F.J.Am. Chem.Soc.2003,125,12384.(14)Miao,Z.;Xu,D.S.;Ouyang,J.H.;Guo,G.L.;Zhao,X.S.;Tang, Y.Q.Nano.Lett.2002,2,717.(15)Bullen,H.A.;Garrett,S.J.Nano.Lett.2002,2,739.(16)Weng,C.C.;Hsu,K.F.;Wei,K.H.Chem.Mater.2004,16,4080.(17)Liu,Y.X.;Tsuru,K.;Satoshi,H.;Osaka,A.J.Ceram.Soc.Jpn. 2004,112,567.(18)Hosono,E.;Fujihara,S.;Kakiuchi,K.;Imai,H.J.Am.Chem. Soc.2004,126,7790.6995Langmuir2005,21,6995-700210.1021/la0500272CCC:$30.25©2005American Chemical SocietyPublished on Web06/16/2005bringing no contaminants to the reaction.19,20With care-fully controlled reaction parameters,large-area films consisting of ordered titania nanorods have been syn-thesized through such a template-free simple approach.21This paper focuses on their ability to photodegrade trace organics in water.To our knowledge,this is the first report on the PA of large-area titania films with ordered nanostructures.Special attention has been paid to the advantages of such ordered films to be used as photo-catalysts.Experimental SectionSample Preparations.Cold-rolled Ti sheets (99.5%in purity,Institute of Iron &Steel,Baoshan,Shanghai,China)with sizes of 5×5×0.01cm 3were pickled at 60°C in a solution consisting of 55mass %HF,65-68mass %HNO 3,and deionized water (DW),with a ratio of 1:3:6in volume.After being ultrasonically cleaned in DW,each piece of the Ti sheet was soaked in 50mL of 30mass %H 2O 2solution and maintained at 80°C in an oven for 3days.Then,the Ti sheet was taken out and rinsed gently with DW and dried in air.Such obtained samples were identified as HO,or termed as the H 2O 2-oxidized Ti in the text.Thermal treatment of HO was conducted in an air-oven maintained at 450°C for 1h,with a heating rate of 10K/min followed by furnace cooling to a temperature below 200°C.The thermal-treated sample was designated as HO_HT.A layer of anatase was further coated on the HO surface through a sol -gel dip-coating method,with a withdrawal speed of 5cm/s.The same thermal treatment used to treat the H 2O 2-oxidized Ti was followed to induce the crystallization.Such a prepared sample was designated as HO_SG.The sol was prepared following mainly Yu et al.22In short,17.0mL of titanium(IV)butoxide and 4.8mL of diethanolamine were dissolved in 67.3mL of ethanol.After stirring vigorously for 2h at ambient temperature,a solution of 0.9mL of water and 10mL of ethanol was added slowly and the solution was further stirred for 2h.For comparison,the sample SG was prepared by alternatively dip-coating the pickled Ti sheet and heating the film at 450°C for 1h for a total of 14cycles to give an identical film weight to the sample HO_HT.Particles of a commercial DP-25(Degussa,Germany)TiO 2(an average particle size of 30nm and BET surface area of 50m 2/g)were deposited on the pickled Ti sheet by repetitively dipping them in the DP-25ethanolic suspension of 25g/L and drying in air at 105°C to give an identical film weight.Such a prepared sample was designated as DP.A summary of the above-mentioned samples can be found in Table 1.Sample Characterizations.The thin-film X-ray diffraction (TF-XRD)measurements were conducted on a Rigaku D/max 2550PC diffractometer with Cu K R radiation,operated at 40KV,300mA (λ)0.154056nm).Other testing conditions are as follows:DS/SS,1°;RS,0.3mm;scanning rate,10°/min;step size,0.02°;the incidence of the X-ray beam,3°.The plane in which the detector moves is perpendicular to the specimen surface.The common XRD patterns were recorded using a Rigaku D/max-3B diffractometer with Cu K R radiation,operated at 40kV,36mA (λ)0.154056nm).Surface morphology was observed using a field emission scanning electron microscopy (FE-SEM,Sirion,FEI,USA).The samples were coated with a thin golden layer to improve the electrical conductivity before the SEM examination.The powders detached from the sample of HO through ultrasonic vibrations were subjected to the high-resolution transmission electron microscopy (HR-TEM)exami-nation,which was conducted employing a JEM-2010microscope (JEOL,Japan)working at 200kV.The differential thermal analysis (DTA)and thermogravimetric analysis (TG)were conducted using Rigaku TAS 300.In the DTA and TG measure-ments,the powder collected from the solution was annealed in air from room temperature to 950°C with a heating rate of 5K/min.The interfacial strength of the film was qualitatively evaluated by soaking the film in a beaker containing water and submitting to ultrasonic vibrations 5(KQ3200B,120W,Kunshan Ultrasonic Instrument Co.,Ltd.,China).Photocatalytic Activity Tests.The PA was measured using rhodamine B (RhB)aqueous solution as a probe,in a Pyrex reactor with a water jacket.A 100mL aliquot of the RhB solution with an initial concentration of 0.01mM in the presence of the titania films (5×5cm 2)was illuminated with a 450W high-pressure mercury lamp 6cm high over the solution.The average intensity of UV irradiance reaching the samples was measured to be ca.1700µW/cm 2,using a UV irradiance meter (Model:UV-A,Beijing Normal University,China;measured for the wavelength range of 320-400nm with a peak wavelength of 365nm).The solution was stirred continuously and exposed to air during the photo-catalytic reaction.During the illumination,the temperature rise of the solution was found to be less than 3K,thanks to the cooling water.The change in the RhB concentration was(19)Wu,J.M.;Satoshi,H.;Tsuru,K.;Osaka,A.J.Am.Ceram.Soc.2004,87,1635.(20)Wu,J.M.;Satoshi,H.;Tsuru,K.;Osaka,A.Cryst.Growth Des.2002,2,147.(21)Wu,J.M.J.Cryst.Growth 2004,269,347.(22)Yu,J.G.;Yu,J.C.;Cheng,B.;Zhao,X.J.J.Sol -Gel Sci.Technol.2002,24,39.Table 1.Film Weight,Surface Morphology,RhB Adsorption Ability,and Photocatalytic Activity of the Titania FilmsObtained through Various Coating Techniques sample ID coating techniques film weight a (mg/cm 2)surface morphology RhB adsorption b (×10-9mol/cm 2)photocatalytic activity k c (×10-2min -1)HO chemical oxidation with 30mass %H 2O 2solution at 80°C for 72h1.17(0.06ordered nanorods 7.92initiate,1.74(0.04;stable,0.31(0.03HO_HTchemical oxidation with 30mass %H 2O 2solution at 80°C for 72h,followed by heating in air at 450°C for 1h1.00(0.03ordered nanorods4.441.17(0.19HO_SG chemical oxidation with 30mass %H 2O 2solution at 80°C for 72h,followed by dip-coating and heating for 1cycle1.15(0.01smooth films with cracks on top of the ordered nanorods 0.050.84(0.06SG dip-coating and heating for 14cycles1.03(0.02smooth films with cracks0.960.25(0.002DPdip-coating and drying from DP-25ethanolic suspension0.98(0.050.550.62(0.02aAverage (standard deviations obtained from four samples.b Determined by soaking in the 100mL of 0.01mM RhB solution under stirring for 8h in the dark.c Average (standard deviations obtained from six runs of the photocatalytic tests;the 1-5and 10-12runs of the photocatalytic test were used to give the initiate and stable value for HO,respectively.6996Langmuir,Vol.21,No.15,2005Wu et al.monitored with a 752UV -Vis spectrophotometer at a wavelength of 555nm,using a quartz cuvette of 1cm of optical path length.Parallel experiments have been carried out to secure the reproducibility.The ability of the titania films to adsorb RhB molecules was assessed by the decrease in the concentration of the 0.01mM RhB solution for up to 8h stirring in the dark,in the presence of the films.ResultsPreparation of Ordered Titania Nanorods.Mac-roscale homogeneous films were deposited on both sides of the titanium substrate through soaking the Ti sheet into the 30mass %H 2O 2solution at 80°C for 3days.The film thickness was estimated from the weight change to be ca.3.2µm,assuming that condensed titania layers deposited homogeneously on both sides of the Ti substrate.No remarkable difference was found in morphologies of the film before and after a subsequent thermal treatment at 450°C for 1h.Figure 1shows a cross-sectional view of the film.A dual structure,that is,well-aligned nanorods on the top of a condensed inner layer,can be clearly seen.The inner layer with a thickness of ca.2µm was aggregates of anatase nanoparticles with sizes of 10-30nm,whereas the top layer,ca.1µm in thickness,was ordered nanorods aggregates of tiny ones.As will be disclosed later by the TEM examination,the tiny nanorods were 20-30nm in diameter and 150nm in length.The total film thickness measured by the SEM examination agreed well with the one estimated from the weight change.Figure 2shows the TF-XRD patterns of the sample HO before and after ultrasonic vibration for 5min in water.The titania film as a whole was identified to be a mix-ture of anatase and rutile (Figure 2a).For the rutile phase,the 50%intensity (101)peak was abnormally stronger than the 100%intensity (110)peak (reference JCPDS card No.21-1276),suggesting the oriented growth of the rutile against the substrate.After the sub-sequent ultrasonic vibration,the top nanorods layer was removed thoroughly and only the anatase phase was detected.It is also noted that,compared to the JCPDScard No.44-1294,the Ti substrate exhibited a texture along the (002)plane.For normally grown titania films with a mixture of anatase and rutile,the mass fraction of rutile,W R ,can be estimated using the followed formula,19where I A and I R designate the X-ray integrated intensities of the (101)diffraction of anatase and the (110)diffraction of rutile,respectively.For a rough estimation,in Figure 2a,if we take the X-ray intensity of the abnormally strong (101)plane for I R ,the value of W R is calculated to be ca.32.5%.When one notes that the nanorods layer consisted of only one-third of the whole film in thickness (Figure 1),the estimated W R seems to be reasonable.Figure 3b and Figure 3c show the Raman spectra of the sample HO before and after ultrasonic vibration for 5min in water,respectively.The peaks located at 400,515,and 639cm -1can be ascribed to anatase;23,24those located at 250,448,and 616cm -1correspond to rutile.23,24Thus,it(23)Kasuga,T.;Hiramatsu,M.;Hoson,A.;Sekino,T.;Niihara,K.Adv.Mater.1999,11,1307.(24)Parker,J.C.;Siegel,R.W.J.Mater.Res.1990,5,1246.Figure 1.Vertical cross-sectional view of the H 2O 2-oxidized and thermal-treated Ti:(a)an overall view showing the dual structure;(b)a high-magnification image showing the condensed inner layer consisting of spherical nanoparticles with sizes of 10-30nm in diameter;(c)a high-magnification image showing the top layer consisting of well-aligned nanorods;(d)a detached nanorods cluster on top of the nanorods layer,showing the growth of the nanorods from the condensed inner layer.Figure 2.Thin-film XRD patterns of the H 2O 2-oxidized Ti (a)before and (b)after ultrasonic vibration.Note the different phase composition of the two layers and the abnormally strong peaks of the rutile (101)and (002).A,anatase;R,rutile;Ti,titanium substrate.W R )1/(1+0.8I A /I R )Large-Scale Preparation Ordered Titania Nanorods Langmuir,Vol.21,No.15,20056997is further confirmed that the inner layer after ultrasonic cleaning consisted mainly of anatase and the film as a whole was a mixture of anatase and rutile.Significantly stronger peaks can be discerned after heating the nanorods layer in air at 450°C for 1h (Figure 3d).The increasing Raman peak intensity is ascribed to the greater concen-trations of the crystalline titania phase;25therefore,the subsequent calcination improved significantly the crys-tallinity of the low-temperature derived titania film.The ascription of the weak broad band near 680cm -1in Figure 3c is not clear at the present time.One notes that it also appeared in the spectrum collected from rutile powder by Kasuga et al.23However,it is not clear why the band disappeared after heating the film in air at 450°C for 1h.Without subsequent thermal treatment,both polycrys-talline nanorods consisted of anatase and rutile and nearly single-crystal rutile nanorods were observed under the HR-TEM examination.The nanorods were 20-30nm in diameter and 150nm in length.Figure 4and Figure 5show the two typical titania nanorods,respectively.Two distinct regions with parallel fringes can be identified in Figure 4.The distances between the adjacent fringes of the two regions were determined to be 0.325and 0.352nm,respectively,which can be ascribed to the interplanerdistance of rutile (110)and anatase (101).Therefore,the nanorod was a polycrystalline consisting of anatase and rutile.This agrees well with the electron diffraction (ED)pattern collected from the whole rod (an inset of Figure 4),which shows diffraction spots corresponding to both anatase and rutile.In Figure 5,nearly all the lattice fringes paralleling the nanorod wall can be ascribed to the rutile (110).The corresponding ED pattern (an inset of Figure 5)suggests the nanorod as nearly a rutile single crystal,but not a pure one since another set of spots,which were not identified here due to the scarcity of more clear spots,seems to superpose over the rutile one.However,with the help of the corresponding ED pattern,one can conclude that the nanorod grew predominately along the rutile [001]-axis.It is noted that the growth of the present rutile nanorods was similar to that of the sub-micrometer-scale rectangular rutile rods prepared by Hosono et al.18Also noted in Figure 4and Figure 5are regions showing no lattice fringes.The selected area electron diffraction revealed only halo rings in these regions.Thus,it is clear that the low-temperature deposited titania nanorods were not thoroughly crystallized.There is still the possibility for further improving the crystallinity through a subse-quent thermal treatment,as can be discerned from the Raman spectra in Figure 3.Figure 6illustrates the TG-DTA curves of the TiO 2powder collected from the resultant solution of the reaction between the Ti sheet and 30mass %H 2O 2solution at 80°C for 3days.The TG curve shows a gradual weight loss for temperatures up to 400°C,with a complete weight loss of ∼11%.This weight loss is due to the removal of water and the peroxo complexes incorporated into the Ti(IV).One endothermic and two exothermic peaks on(25)Lottici,P.P.;Bersani,D.;Braghini,M.;Montenero,A.J.Mater.Sci.1993,28,177.Figure 3.Raman spectra of (a)the as-pickled Ti,(b)the H 2O 2-oxidized Ti followed by the ultrasonic cleaning,(c)the H 2O 2-oxidized Ti,and (d)the H 2O 2-oxidized Ti followed by heating in air at 450°C for 1h.Note the difference in the y -scales.Figure 4.HR-TEM of a typical titania nanorod.Inserted are a low-magnification image and the electron diffraction pattern of the nanorod.Figure 5.HR-TEM of a nearly single-crystalline rutile nanorod.Inserted is the electron diffraction pattern of the nanorod.6998Langmuir,Vol.21,No.15,2005Wu et al.the DTA curve can be observed.The broad endothermic peak around 92°C can be ascribed to the evaporation of physically absorbed water.The broad exothermic peak located at the temperature range of 310and 365°C resulted from the removal of the peroxo complexes,and also,probably the crystallization of the small portion of amorphous titania.The much sharper exothermic peak located at 727°C corresponds to the transformation of anatase to rutile.A complete conversion of anatase to rutile in coarse-grained TiO 2powders takes place at 750°C in air.24The decreased anatase-to-rutile transformation temperature is attributed to the decreasing grain size.24Figure 7shows the XRD patterns of the titania-coated Ti samples used for the photocatalytic tests (Table 1).Their corresponding surface morphologies can be found in Figure 8.The surface of HO consisted of well-aligned nanorods,with a phase composition of mixed anatase and paring the XRD patterns in Figure 7a,b and the SEM images in Figure 8a,b and Figure 8c,d,it is clear that no remarkable difference in both the phase composi-tion and the morphology can be discerned after heating the film at 450°C for 1h in air.However,the subsequent thermal treatment induced a weight loss of ∼14%in the titania film (Table 1),which was comparable to the value obtained from the TG measurement of the powders (Figure 6).The well-aligned titania nanorods layer was covered with a cracked titania gel with a thickness of about 0.4µm after a subsequent dip-coating cycle (Figure 8e,f).Dip-coating for 14cycles on the Ti substrate obtained a cracked gel with a thickness of about 2.8µm (Figure 8g,h).The gel was identified to be pure anatase from the XRD pattern (Figure 7d).The total amounts of RhB adsorbed per cm 2on the titania films after 8h of stirring in the dark have been listed in Table 1.Very few RhB molecules were adsorbed on the samples of HO_SG,SG,and DP even after 8h.The adsorption of RhB on the samples of HO and HO_HT was evident;hence their time evolutions were traced and shown in Figure 9.The adsorption follows the first-order kinetics,and the rate constants for HO and HO_HT were calculated to be 9.8×10-4/min and 5.1×10-4/min,respectively.The as-deposited titania nanorods adsorbed the most RhB molecules.After the subsequent thermal treatment,less RhB molecules were adsorbed on the surface.However,compared with the sol -gel derived film and the DP-25coating,the nanorod films,either heated or not,possessed much higher adsorbility for the RhB molecules.The BET surface area of the powders scratched from the surface of the samples HO has been determined by the N 2adsorption method to be 304m 2/g,much higher than that of the DP powder of 50m 2/g.Although the BET surface area of the sol -gel derived titania is not determined in the present experiment,it is safe to say that the present nanorod films possess very high specific surface areas and hence high RhB adsorption ability,which contributes to the photo-degradation of RhB in water.Photocatalytic Tests.Figure 10shows the photo-degradation curves of the 0.01mM RhB for various runs,in the presence of the sample HO.For the first five runs,almost all the RhB molecules were absent after 3h of the illumination.Unfortunately,the PA decayed significantly for the following 6-9runs and reached a stable value for the 10-12runs.The other samples of HO_HT,HO_SG,SG,and DP (see Table 1for the sample ID)exhibited photocatalytic activities with good reproducibility,and their photodegradation curves obtained from an average of six runs are given in Figure 11a.Figure 11b shows the relationship between ln(c 0/c )and the irradiation time t .Since all the curves can be fitted roughly to a straight line,the photocatalytic degradation reaction can be assumed to follow a pseudo-first-order expression,26where c/c 0is the normalized RhB concentration and k is the apparent reaction rate in term of min -1.Table 1lists the corresponding pseudo-first-order reaction rate con-stants (k ).It is clear that their photocatalytic activities follow the order of HO_HT >HO_SG >DP >SG.Although HO exhibited the highest PA at the initial five runs,its stable rate constant declined to a value comparable to that of SG.The significant RhB adsorption ability of the samples HO and HO_HT may lead to overestimated rate constants,as the RhB adsorbed on the side opposite to the illumina-tion was not actually photodegraded.For a conservative estimate,the rate of the purely photocatalytic process can be obtained by subtracting the mere dark adsorption rate,which gave the rate constants of HO and HO_HT to be on average 1.64×10-2/min (initiate value)and 1.12×10-2/min,respectively.This does not alter the order of the photoactivity of the studied samples.DiscussionDeposition of the Ordered Nanorods.Our prior works have focused on the low-temperature preparation of well-crystallized titania through direct oxidation of Ti(26)Wu,J.M.;Zhang,T.W.J.Photochem.Photobiol.,A 2004,162,171.Figure 6.TG-DTA curves of the powders obtained by the reaction between the Ti plate and the 30mass %H 2O 2solution at 80°C for 72h.Figure 7.XRD patterns of the titania-coated Ti samples used for the photocatalytic tests.See Table 1for the sample ID.A,anatase;R,rutile;Ti,titanium substrate.ln(c 0c))kt Large-Scale Preparation Ordered Titania Nanorods Langmuir,Vol.21,No.15,20056999with hydrogen peroxide solutions.19-21The crystalline titania is supposed to come into being through crystal-lization of the previously formed amorphous titania on the Ti substrates.The low-temperature crystallization may proceed in situ or,more likely,occurs through a dissolution precipitation mechanism.19-21The formation of titania nanorods can be ascribed to a relatively lower precipitation or deposition rate.21In the present experiment,it is interesting to find out that a dual structure,condensed inner layer(anatase) and nanorods top layer(anatase and rutile),was achievedFigure8.FE-SEM images of some titania-coated Ti samples used for the photocatalytic tests:(a and b)HO;(c and d)HO_HT;(e and f)HO_SG;(g and h)SG.Figure9.Dark adsorption curves of RhB in the presence of HO and HO_HT.Inset shows that the adsorption follows first-order kinetics.Figure10.Photodegradation of the0.01mM RhB in the presence of HO for various runs.7000Langmuir,Vol.21,No.15,2005Wu etal.after soaking the Ti sheet into the hydrogen peroxide solution at 80°C for 3days.The formation of this dual structure can be well-described when one assumes that the precipitation of the crystalline titania occurs mainly after the thorough dissolution of the amorphous one.In this case,the concentration of Ti(IV)ions is relatively high at the early precipitation stage.According to the thermodynamic equilibrium diagram given by Yamabi and Imai,27at a given pH value,the solution with higher Ti(IV)concentration tends to precipitate titania in the form of anatase.Thus,a nearly pure anatase inner layer was deposited first on the titanium substrates,and then a mixture of anatase and rutile was obtained with the decreasing Ti(IV)concentration.The dual structure is also expected when considering dynamics:a lower precipita-tion rate can be anticipated from the solution with decreasing Ti(IV)concentration,which favors the forma-tion of rutile with a much larger length/width ratio and hence resulted in a top layer of well-aligned titania nanorods.21Hosono et al.argued that the addition of NaCl is the key to achieve the rutile rods in their reactions utilizing hydrolysis of TiCl 3,which lowers the degrees of supersaturation and at the same time suppresses the growth of titania in the [110]direction through adsorption of Cl -ions onto the rutile (110)plane.18However,the present reaction requires no such external inhibitor.It seems that the growth of titania along the rutile [001]-axis is naturally favored in dynamics or thermodynamics in the case in which a low degree of supersaturation is maintained.Photocatalytic Activity of the Ordered Nanorods.It is reported that,in the absence of any photocatalysts,illumination of the RhB solution under visible light leadsto no changes.28Under the illumination of the high-pressure mercury lamp,which emits both UV and visible light,and in the presence of the titania,the photodecom-position of the RhB will proceed in both photocatalytic pathway and photosensitization pathway,both of which are dependent on the photocatalytic activity of the titania.28,29Therefore,the photodegradation of RhB in water reflects the PA of the titania films.The subsequent thermal treatment did not alter sig-nificantly the surface morphology (Figure 8)and the phase composition (Figure 7)of the titania film;therefore,in addition to the contributions of the ordered nanostructure,which will be discussed later,the relatively high initial PA before thermal treatment can also be ascribed to the oxidative peroxo complexes coordinated to Ti(IV).30It is very likely for the present reaction system of Ti -H 2O 2to result in a Ti peroxy gel,which may be viewed as a stable or semistable intermediate in the oxidation and decom-position process.Tengvall et al.have identified such a gel to be 30These complexes are highly oxidative,30which contrib-uted positively to the photodegradation of organics through either oxidizing the RhB directly or trapping photoge-nerated holes to form highly oxidative radicals and then to oxidize the RhB indirectly.The high RhB adsorption ability of the sample HO also contributed to its excellent initial PA.After stirring in the dark for 8h,the most RhB molecules were adsorbed on the surface of the sample HO (Table 1).The average points of zero charge (PZC)of both anatase and rutile were recommended to be pH 5.9by Kosmulski;31hence the titania nanorods were negatively charged in the RhB solution with a neutral pH value of 7.0.The titania with abundant peroxo complexes was even more negatively charged,30which adsorbed much readily the RhB +in the solution and hence accelerated the photodegradation process.The fact that the RhB adsorption ability reduced after a subsequent heating,which eliminated the peroxo complexes,well-supports such an assumption.Unfortu-nately,with the consumption of these beneficial complexes,the PA of the low-temperature prepared crystalline titania nanorods decayed abruptly.The TG-DTA curves shown in Figure 6suggest that heating the low-temperature prepared nanorod layer at 450°C eliminated thoroughly the peroxo complexes;however,the crystallinity of the titania nanorods was improved greatly,as can be discerned from the Raman spectra shown in Figure 3.Because defects in the titania usually serve as the recombination centers of the pho-togenerated electron -hole pairs,it is not strange that the PA of the nanorods layer after thermal treatment was significantly improved compared with the stable value of the as-deposited one,in the case in which the subsequent thermal treatment did not induce remarkable change in both the morphology and the phase composition.More importantly,the ordered titania nanorods adhered very strongly to the substrate after the subsequent thermal treatment:it sustained 10min of ultrasonic vibrations(27)Yamabi,S.;Imai,H.Chem.Mater.2002,14,609.(28)Wu,T.X.;Liu,G.M.;Zhao,J.C.;Hidaka H.;Serpone,N.J.Phys.Chem.B 1998,102,5845.(29)Ma,Y.;Yao,J.N.Chemosphere 1999,38,2407.(30)Tengvall,P.;Elwing,H.;Lundstrom,I.J.Colloid Interface Sci .1989,130,405.(31)Kosmulski,M.Adv.Colloid Interface Sci.2002,99,255.Figure 11.(a)Photodegradation of the 0.01mM RhB in the presence of HO_HT,HO_SG,SG,and DP,obtained from an average of six runs,the error bar reflects the root-mean-square deviations of the values from each run;(b)replot of a in the ln(c 0/c )-t coordinates,suggesting that the photodegradation of RhB follows roughly the pseudo-first-order reaction.Ti 4+(OH -)2O 22--Ti 4+(OH -)2O 2--Ti 4+(OH)x -TiO 2‚n H 2OLarge-Scale Preparation Ordered Titania Nanorods Langmuir,Vol.21,No.15,20057001。